ucla mse104 chapter 1

Chapter 1 - 1

MSE 104 Introduction to

Materials Science amp Engineering Course Objective Introduce fundamental concepts in Materials

Science and Engineering

You will learn about bull material structure

bull how structure dictates properties

bull how processing can change structure

This course will help you to

bull use materials properly

bull realize new design opportunities with materials

bull select the appropriate materials for engineering

applications

Chapter 1 - 2

Chapter 1 - Introduction bull What is materials science materials engineering

Chapter 1 - 3

ex hardness vs structure of steel bull Properties depend on structure

Data obtained from Figs 1030(a)

and 1032 with 4 wt C composition

and from Fig 1114 and associated

discussion Callister amp Rethwisch 8e

Micrographs adapted from (a) Fig

1019 (b) Fig 930(c) Fig 1033

and (d) Fig 1021 Callister amp

Rethwisch 8e

ex structure vs cooling rate of steel bull Processing can change structure

Structure Processing amp Properties

Hard

ness (

BH

N)

Cooling Rate (ordmCs)

100

2 00

3 00

4 00

5 00

6 00

001 01 1 10 100 1000

(d)

30 mm (c)

4 mm

(b)

30 mm

(a)

30 mm

Chapter 1 - 4

Classes of Engineered Materials bull Metals

ndash High thermal amp electrical conductivity

ndash Opaque reflective strong ductile

bull Polymersplastics Covalent bonding sharing of ersquos

ndash Thermal amp electrical insulators

ndash Optically translucent or transparent

ndash Soft ductile low strength low density

bull Ceramics ionic bonding (refractory) ndash compounds of metallic

amp non-metallic elements (oxides carbides nitrides sulfides)

ndash Non-conducting (insulators)

ndash Brittle glassy inelastic

bull Semiconductors covalent Mixed (ionic) ndash elements (silicon

germanium) or compounds of metallic amp non-metallic elements (arsenides phosphides nitrides)

ndash Engineered Conduction

ndash Brittle inelastic

Chapter 1 - 5

1 Pick Application Determine required Properties

Processing changes structure and overall shape

ex casting sintering vapor deposition doping

forming joining annealing

Properties mechanical electrical thermal optical

corrosive

Material structure composition

2 Properties Identify candidate Material(s)

3 Material Identify required Processing

The Materials Selection Process

Chapter 1 - 6

ELECTRICAL

bull Electrical Resistivity of Copper

bull Adding ldquoimpurityrdquo atoms to Cu (Cu-Ni alloy) increases resistivity

bull Deforming Cu increases resistivity

Adapted from Fig 188 Callister amp

Rethwisch 8e (Fig 188 adapted

from JO Linde Ann Physik 5 219

(1932) and CA Wert and RM

Thomson Physics of Solids 2nd

edition McGraw-Hill Company New

York 1970)

T (ordmC) -200 -100 0

1

2

3

4

5

6

Resis

tivity

r

(10

-8 O

hm

-m)

0

Chapter 1 - 7

THERMAL bull Space Shuttle Tiles -- Silica fiber insulation

offers low heat conduction

bull Thermal Conductivity

of Copper -- It decreases when

you add zinc

Adapted from

Fig 194W Callister

6e (Courtesy of

Lockheed Aerospace

Ceramics Systems

Sunnyvale CA)

(Note W denotes fig

is on CD-ROM)

Adapted from Fig 194 Callister amp Rethwisch

8e (Fig 194 is adapted from Metals Handbook

Properties and Selection Nonferrous alloys and

Pure Metals Vol 2 9th ed H Baker

(Managing Editor) American Society for Metals

1979 p 315)

Composition (wt Zinc) T

herm

al C

ond

uctivity

(Wm

-K)

400

300

200

100

0 0 10 20 30 40

100 mm

Adapted from chapter-

opening photograph

Chapter 17 Callister amp

Rethwisch 3e (Courtesy

of Lockheed

Missiles and Space

Company Inc)

Chapter 1 - 8

bull Transmittance -- Aluminum oxide may be transparent translucent or

opaque depending on the material structure

Adapted from Fig 12

Callister amp Rethwisch 8e

(Specimen preparation

PA Lessing photo by S

Tanner)

single crystal

polycrystal

low porosity

polycrystal

high porosity

OPTICAL

Chapter 1 - 9

bull Use the right material for the job

bull Understand the relation among properties

structure processing and performance

bull Recognize new design opportunities offered

by materials selection

Course Goals

SUMMARY

Chapter 1 - 10

ISSUES TO ADDRESS

bull What promotes bonding

bull What types of bonds are there

bull What properties are inferred from bonding

Chapter 2 Atomic Structure amp

Interatomic Bonding

Chapter 1 - 11

Atomic Structure

bull Atom ndash electrons ndash 911 x 10-31 kg protons neutrons

bull Atomic number = of protons in nucleus of atom = of electrons of neutral species

bull A [=] atomic mass unit = amu = 112 mass of 12C Atomic wt = wt of 6022 x 1023 molecules or atoms

1 amuatom = 1gmol

C 12011 H 1008 etc

167 x 10-27 kg

Chapter 1 - 12

Atomic Structure

bull Valence electrons determine all of the

following properties

1) Chemical

2) Electrical

3) Thermal

4) Optical

Chapter 1 - 13

Electronic Structure

bull

Quantum Designation

n = principal (energy level-shell) K L M N O (1 2 3 etc)

l = subsidiary (orbitals) s p d f (0 1 2 3hellip n -1)

ml = magnetic 1 3 5 7 (-l to +l)

ms = spin frac12 -frac12

Chapter 1 - 14

Electron Energy States

1s

2s 2p

K-shell n = 1

L-shell n = 2

3s 3p M-shell n = 3

3d

4s

4p 4d

Energy

N-shell n = 4

bull Have discrete energy states

bull Tend to occupy lowest available energy state

eg Potassium (K) ndash 1s22s22p63s23p64s1

Electrons

Adapted from Fig 24


Chapter 1 - 15

bull Why Valence (outer) shell usually not filled completely

bull Most elements Electron configuration not stable

Survey of Elements

Electron configuration

(stable)

1s 2 2s 2 2p 6 3s 2 3p 6 (stable)

1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 4s 2 4p 6 (stable)

Atomic

18

36

Element

1s 1 1 Hydrogen

1s 2 2 Helium

1s 2 2s 1 3 Lithium

1s 2 2s 2 4 Beryllium

1s 2 2s 2 2p 1 5 Boron

1s 2 2s 2 2p 2 6 Carbon

1s 2 2s 2 2p 6 (stable) 10 Neon 1s 2 2s 2 2p 6 3s 1 11 Sodium

1s 2 2s 2 2p 6 3s 2 12 Magnesium

1s 2 2s 2 2p 6 3s 2 3p 1 13 Aluminum

Argon

Krypton

Adapted from Table 22


Chapter 1 - 16

Electron Configurations

bull Valence electrons ndash those in unfilled shells

bull Filled shells more stable

bull Valence electrons are most available for bonding and tend to control the chemical properties

ndash example C (atomic number = 6)

1s2 2s2 2p2

valence electrons

Chapter 1 - 17

The Periodic Table bull Columns Similar Valence Structure

Adapted from

Fig 26

Callister amp

Rethwisch 8e

Electropositive elements

Readily give up electrons

to become + ions

Electronegative elements

Readily acquire electrons

to become - ions

giv

e u

p 1

e-

giv

e u

p 2

e-

giv

e u

p 3

e- inert

gases

accept 1e

-

accept 2e

-

O

Se

Te

Po At

I

Br

He

Ne

Ar

Kr

Xe

Rn

F

Cl S

Li Be

H

Na Mg

Ba Cs

Ra Fr

Ca K Sc

Sr Rb Y

Chapter 1 - 18

bull Ranges from 07 to 40

Smaller electronegativity Larger electronegativity

bull Large values tendency to acquire electrons

Adapted from Fig 27 Callister amp Rethwisch 8e (Fig 27 is adapted from Linus Pauling The Nature of the

Chemical Bond 3rd edition Copyright 1939 and 1940 3rd edition Copyright 1960 by Cornell University

Electronegativity

Also increases from bottom to top

Chapter 1 - 19

Ionic Bond Metal + Non-metal

donates accepts

electrons electrons

Dissimilar electronegativities

ex MgO Mg 1s2 2s2 2p6 3s2 O 1s2 2s2 2p4

[Ne] 3s2

Mg2+ 1s2 2s2 2p6 O2- 1s2 2s2 2p6

[Ne] [Ne]

Chapter 1 - 20

bull Occurs between + and - ions

bull Requires electron transfer

bull Large difference in electronegativity required

bull Example NaCl

Ionic Bonding

Na (metal) unstable

Cl (nonmetal) unstable

electron

+ - Coulombic Attraction

Na (cation) stable

Cl (anion) stable

Chapter 1 - 21

Ionic Bonding

bull Attractive forces Depends on bonding

bull Repulsive forces Interactions between e- cloud

bull At FA + FR = 0 equilibrium

exists at atomic spacing r0

bull Potential energy E = int F dr

Chapter 1 - 22

Ionic Bonding

bull Energy ndash minimum energy most stable

ndash Energy balance of attractive and repulsive

terms

Attractive energy EA

Net energy EN

Repulsive energy ER

Interatomic separation r

r A

n r B

EN = EA + ER = + -

Adapted from Fig 28(b)


Chapter 1 - 23

bull Predominant bonding in ceramics



Examples Ionic Bonding

Give up electrons Acquire electrons

NaCl

MgO

CaF 2 CsCl

Chapter 1 - 24

Examples Ionic Bonding (NaCl)

bull Coulombic attractive forces due

to +ve and ndashve charged ions

bull Ionic bonding is non-directional

bull Magnitude of the bond equal in

all directions

Adapted from Fig 29


Chapter 1 - 25

C has 4 valence e-

needs 4 more

H has 1 valence e-

needs 1 more

Electronegativities

are comparable

Adapted from Fig 210 Callister amp Rethwisch 8e

Covalent Bonding bull Similar electronegativity share electrons

bull Bonds determined by valence ndash s amp p orbitals

dominate bonding

bull Example CH4 shared electrons from carbon atom

shared electrons from hydrogen atoms

H

H

H

H

C

CH4

Chapter 1 - 26

Mixed Bonding

bull Ionic-Covalent Mixed Bonding

ionic character =

where XA amp XB are the electronegativities and XA gt XB

bull Depends on relative positions of constituent atoms in periodic table

) 100 ( x

1-e-

(XA-XB )2

4

ionic 734 (100) x e1 characterionic 4

)2153(

2

-

--

Ex MgO XMg = 12 XO = 35

Chapter 1 - 27

Metallic Bonding

bull Valence e- are not bound to any particular atom

bull Delocalized as electron cloud

bull Excellent conductors of heat and electricity

Adapted from Fig 211


Chapter 1 - 28

Arises from coulombic interaction between dipoles

bull Permanent dipoles-molecule induced

bull Fluctuating dipoles

-general case

-ex liquid HCl

-ex polymer





Secondary (van der Waals)

Bonding

asymmetric electron clouds

+ - + - secondary bonding

H H H H

H2 H2

secondary bonding

ex liquid H2

H Cl H Cl secondary

bonding

secondary bonding

+ - + -

secondary bonding

Chapter 1 - 29

Type

Ionic

Covalent

Metallic

Secondary

Bond Energy

Large

Variable

large-Diamond

small-Bismuth

Variable

large-Tungsten

small-Mercury

Smallest

Comments

Nondirectional (ceramics)

Directional

(semiconductors ceramics

polymer chains)

Nondirectional (metals)

Directional

inter-chain (polymer)

inter-molecular

Summary Bonding

Chapter 1 - 30

bull Bond Length r

bull Bond Energy Eo

bull Melting Temperature Tm

Tm is larger if Eo is larger

Properties From Bonding Tm

r o r

Energy

r

larger Tm

smaller Tm

Eo =

ldquobond energyrdquo

Energy

r o r

unstretched length

Chapter 1 - 31

bull Modulus of elasticity (Youngrsquos modulus) E

bull Slope of stress-strain curve

depends on bond strength

E is larger if E0 is larger

Properties From Bonding E

= E F

A0

D L

L0

Hookes Law

s = E e

s

Linear- elastic

E

e

F

F simple tension test

Chapter 1 - 32

Ceramics

(Ionic amp covalent bonding)

Large bond energy large Tm

large E

small a

Metals

(Metallic bonding)

Variable bond energy moderate Tm

moderate E

moderate a

Summary

Polymers (Covalent amp Secondary)

Directional Properties Secondary bonding dominates

small Tm

small E

large a

Chapter 1 - 33

bullHow do atoms arrange themselves to form solids

bull Fundamental concepts and language

bull Unit cells

bull Crystal structures

1048766 Face-centered cubic

1048766 Body-centered cubic

1048766 Hexagonal close-packed

bull Close packed crystal structures

bull Density computations

bull Types of solids

Single crystal

Polycrystalline

Amorphous

How do atoms assemble into solid structures

Chapter 3 The Structure of Crystalline

Solids

Chapter 1 - 34

Core Problems Ex 33

ANNOUNCEMENTS

Reading 31-37 317

38-315

Chapter 1 - 35

SUMMARY

bull Atoms may assemble into crystalline or

amorphous structures

bull We can predict the density of a material provided we

know the atomic weight atomic radius and crystal

geometry (eg FCC BCC HCP)

bull Common metallic crystal structures are FCC BCC and

HCP Coordination number and atomic packing factor

are the same for both FCC and HCP crystal structures

bull Crystallographic points directions and planes are

specified in terms of indexing schemes

Crystallographic directions and planes are related

to atomic linear densities and planar densities

Chapter 1 - 36

bull Some materials can have more than one crystal

structure This is referred to as polymorphism (or

allotropy)

SUMMARY

bull Materials can be single crystals or polycrystalline

Material properties generally vary with single crystal

orientation (ie they are anisotropic) but are generally

non-directional (ie they are isotropic) in polycrystals

with randomly oriented grains

bull X-ray diffraction is used for crystal structure and

interplanar spacing determinations

Chapter 1 - 37

bull Non dense random packing

bull Dense ordered packing

Dense ordered packed structures tend to have

lower energies

Energy and Packing

Energy

r

typical neighbor bond length

typical neighbor bond energy

Energy

r



Chapter 1 - 38

bull atoms pack in periodic 3D arrays Crystalline materials

-metals

-many ceramics

-some polymers

bull atoms have no periodic packing

Noncrystalline materials

-complex structures

-rapid cooling

crystalline SiO2

noncrystalline SiO2 Amorphous = Noncrystalline Adapted from Fig 323(b)

CampR8e

Adapted from Fig 323(a)

CampR8e

Materials and Packing

Si Oxygen

bull typical of

bull occurs for

Chapter 1 - 39

bull Tend to be densely packed (billiard balls)

bull Reasons for dense packing

- Typically only one element is present so all atomic

radii are the same

- Metallic bonding is not directional

- Nearest neighbor distances tend to be small in

order to lower bond energy

- Electron cloud shields cores from each other

bull Have the simplest crystal structures

We will examine four such structures

Metallic Crystal Structures

Chapter 1 - 40

bull Rare due to low packing density (only Po has this structure)

bull Close-packed directions are cube edges

bull Coordination = 6

( nearest neighbors)

Simple Cubic Structure (SC)

Chapter 1 - 41

bull APF for a simple cubic structure = 052

APF =

a 3

4

3 p (05a) 3 1

atoms

unit cell atom

volume

unit cell

volume

Atomic Packing Factor (APF)

APF = Volume of atoms in unit cell

Volume of unit cell

assume hard spheres

Adapted from Fig 324 CampR8e

close-packed directions

a

R=05a

contains 8 x 18 = 1 atomunit cell

Chapter 1 - 42



bull Atoms touch each other along cube diagonals --Note All atoms are identical the center atom is shaded

differently only for ease of viewing

Body Centered Cubic Structure (BCC)

ex Cr W Fe (a) Tantalum Molybdenum

2 atomsunit cell 1 center + 8 corners x 18

Chapter 1 - 43

Atomic Packing Factor BCC

a

APF =

4

3 p ( 3 a4 ) 3 2

atoms

unit cell atom

volume

a 3

unit cell

volume

length = 4R =

Close-packed directions

3 a

bull APF for a body-centered cubic structure = 068

a R Adapted from

Fig 32(a) CampR8e

a 2

a 3

Chapter 1 - 44



bull Atoms touch each other along face diagonals --Note All atoms are identical the face-centered atoms are shaded


Face Centered Cubic Structure (FCC)

ex Al Cu Au Pb Ni Pt Ag

4 atomsunit cell 6 face x 12 + 8 corners x 18 Click once on image to start animation

(Courtesy PM Anderson)

Chapter 1 - 45

bull APF for a face-centered cubic structure = 074

Atomic Packing Factor FCC

maximum achievable APF

APF =

4

3 p ( 2 a4 ) 3 4

atoms

unit cell atom

volume

a 3

unit cell

volume


length = 4R = 2 a

Unit cell contains 6 x 12 + 8 x 18 = 4 atomsunit cell

a

2 a

Adapted from

Fig 31(a)

CampR8e

Chapter 1 - 46

A sites

B B

B

B B

B B

C sites

C C

C A

B

B sites

bull ABCABC Stacking Sequence

bull 2D Projection

bull FCC Unit Cell

FCC Stacking Sequence

B B

B

B B

B B

B sites C C

C A

C C

C A

A B

C

Chapter 1 - 47


bull ABAB Stacking Sequence

bull APF = 074

bull 3D Projection bull 2D Projection


CampR8e

Hexagonal Close-Packed Structure

(HCP)

6 atomsunit cell

ex Cd Mg Ti Zn

bull ca = 1633

c

a

A sites

B sites

A sites Bottom layer

Middle layer

Top layer

Chapter 1 - 48

Theoretical Density r

where n = number of atomsunit cell

A = atomic weight

VC = Volume of unit cell = a3 for cubic

NA = Avogadrorsquos number

= 6022 x 1023 atomsmol

Density = r =

VC NA

n A r =

Cell Unit of Volume Total

Cell Unit in Atoms of Mass

Chapter 1 - 49

bull Ex Cr (BCC)

A = 5200 gmol

R = 0125 nm

n = 2 atomsunit cell

rtheoretical

a = 4R 3 = 02887 nm

ractual

a R

r = a3

5200 2

atoms

unit cell mol

g

unit cell

volume atoms

mol

6022 x 1023


= 718 gcm3

= 719 gcm3

Adapted from

Fig 32(a) CampR8e

Chapter 1 - 50

Densities of Material Classes

r metals gt r ceramics gt r polymers

Why

Data from Table B1 Callister amp Rethwisch 8e

r (g

cm

)

3

Graphite Ceramics Semicond

Metals Alloys

Composites fibers

Polymers

1

2

2 0

30 B ased on data in Table B1 Callister

GFRE CFRE amp AFRE are Glass Carbon amp Aramid Fiber-Reinforced Epoxy composites (values based on 60 volume fraction of aligned fibers

in an epoxy matrix) 10

3

4

5

03

04

05

Magnesium

Aluminum

Steels

Titanium

CuNi

Tin Zinc

Silver Mo

Tantalum Gold W Platinum

G raphite

Silicon

Glass - soda Concrete

Si nitride Diamond Al oxide

Zirconia

H DPE PS PP LDPE

PC

PTFE

PET PVC Silicone

Wood

AFRE

CFRE

GFRE

Glass fibers

Carbon fibers

A ramid fibers

Metals have bull close-packing

(metallic bonding)

bull often large atomic masses

Ceramics have bull less dense packing

bull often lighter elements

Polymers have bull low packing density

(often amorphous)

bull lighter elements (CHO)

Composites have bull intermediate values

In general

Chapter 1 - 51

Chapter 1 - 52

Chapter 1 - 53

Chapter 1 - 54

Fig 34 CampR8e

Crystal Systems

7 crystal systems

14 crystal lattices

Unit cell smallest repetitive volume which

contains the complete lattice pattern of a crystal

a b and c are the lattice constants

Chapter 1 - 55

Chapter 1 - 56

Point Coordinates

Point coordinates for unit cell center are

a2 b2 c2 frac12 frac12 frac12

Point coordinates for unit cell corner are 111

Translation integer multiple of lattice constants identical position in another unit cell

z

x

y a b

c

000

111

y

z

2c

b

b

Chapter 1 - 57

Crystallographic Directions

1 Vector repositioned (if necessary) to pass

through origin

2 Read off projections in terms of

unit cell dimensions a b and c

3 Adjust to smallest integer values

4 Enclose in square brackets no commas

[uvw]

ex 1 0 frac12 =gt 2 0 1 =gt [ 201 ]

-1 1 1

families of directions ltuvwgt

z

x

Algorithm

where overbar represents a

negative index

[ 111 ] =gt

y

Chapter 1 - 58

ex linear density of Al in [110]

direction

a = 0405 nm

Linear Density

bull Linear Density of Atoms LD =

a

[110]

Unit length of direction vector

Number of atoms

atoms

length

1 35 nm

a 2

2 LD -

Adapted from

Fig 31(a)

CampR8e

Chapter 1 -

BCC vs simple cubic

59

Chapter 1 -

BCC vs Simple C

bull Unit cell should reflect the symmetry of

the overall structure

bull If we look at smallest possible unit cell we

miss the symmetry of the structure

60

Chapter 1 -

On to HCP

bull Same answer ndash sort ofhellip

bull What is the best unit cell for HCP structure

bull Smaller one is all we need but it doesnrsquot show

the symmetry When we speak of the hcp unit

cell we refer to the hexagonal one 61

c

Chapter 1 -

Reading

bull 3-10 ndash 3-15

bull 4-1 ndash 4-7

bull 5-1 ndash 5-5

62

Chapter 1 - 63

HCP Crystallographic Directions


through origin

2 Read off projections in terms of unit

cell dimensions a1 a2 a3 or c



[uvtw]

[ 1120 ] ex frac12 frac12 -1 0 =gt


CampR8e

dashed red lines indicate

projections onto a1 and a2 axes a1

a2

a3

-a3

2

a 2

2

a 1

- a3

a1

a2

z

Algorithm

In text example problems 38 and 39

Chapter 1 - 64

HCP Crystallographic Directions bull Hexagonal Crystals

ndash 4 parameter Miller-Bravais lattice coordinates

are related to the direction indices (ie uvw)

as follows

w w

t

v

u

) v u ( + -

) u v 2 ( 3

1 -

) v u 2 ( 3

1 -

] uvtw [ ] w v u [

Fig 38(a) CampR8e

- a3

a1

a2

z

Chapter 1 - 65

Crystallographic Planes


CampR8e

Chapter 1 - 66


bull Miller Indices Reciprocals of the (three) axial intercepts for a plane cleared of fractions amp common multiples All parallel planes have same Miller indices

bull Algorithm 1 Read off intercepts of plane with axes in terms of a b c 2 Take reciprocals of intercepts 3 Reduce to smallest integer values 4 Enclose in parentheses no commas ie (hkl)

Chapter 1 - 67

Crystallographic Planes z

x

y a b

c

4 Miller Indices (110)

example a b c z

x

y a b

c


1 Intercepts 1 1

2 Reciprocals 11 11 1

1 1 0 3 Reduction 1 1 0

1 Intercepts 12

2 Reciprocals 1frac12 1 1

2 0 0 3 Reduction 2 0 0

example a b c

Chapter 1 - 68


z

x

y a b

c


example 1 Intercepts 12 1 34

a b c

2 Reciprocals 1frac12 11 1frac34

2 1 43

3 Reduction 6 3 4

(001) (010)

Family of Planes hkl

(100) (010) (001) Ex 100 = (100)

Chapter 1 - 69

Crystallographic Planes (HCP)

bull In hexagonal unit cells the same idea is

used

example a1 a2 a3 c

4 Miller-Bravais Indices (1011)

1 Intercepts 1 -1 1 2 Reciprocals 1 1

1 0

-1

-1

1

1

3 Reduction 1 0 -1 1

a2

a3

a1

z


CampR8e

Chapter 1 - 70


bull We want to examine the atomic packing

of crystallographic planes

bull Iron foil can be used as a catalyst The

atomic packing of the exposed planes is

important

a) Draw (100) and (111) crystallographic planes

for Fe

b) Calculate the planar density for each of these

planes

Chapter 1 - 71

Planar Density of (100) Iron

Solution At T lt 912ordmC iron has the BCC structure

(100)

Radius of iron R = 01241 nm

R 3

3 4 a

Adapted from Fig 32(c) CampR8e

2D repeat unit

= Planar Density = a 2

1

atoms

2D repeat unit

= nm2

atoms 121

m2

atoms = 12 x 1019

1

2

R 3

3 4 area

2D repeat unit

Chapter 1 - 72

bull Some engineering applications require single crystals

bull Properties of crystalline materials

often related to crystal structure


-- Ex Quartz fractures more easily

along some crystal planes than

others

-- diamond single

crystals for abrasives

-- turbine blades

Fig 833(c) CampR8e (Fig

833(c) courtesy of Pratt

and Whitney) (Courtesy Martin Deakins

GE Superabrasives

Worthington OH Used with

permission)

Crystals as Building Blocks

Chapter 1 - 73

Polycrystals

Chapter 1 - 74

bull Single Crystals

-Properties vary with

direction anisotropic

-Example the modulus

of elasticity (E) in BCC iron

Data from Table 33

CampR8e (Source of data

is RW Hertzberg

Deformation and

Fracture Mechanics of

Engineering Materials

3rd ed John Wiley and

Sons 1989)

bull Polycrystals

-Properties maymay not

vary with direction

-If grains are randomly

oriented isotropic

(Epoly iron = 210 GPa)

-If grains are textured

anisotropic

200 mm Adapted from Fig

414(b) CampR8e

(Fig 414(b) is courtesy

of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now

the National Institute of

Standards and

Technology

Gaithersburg MD])

Single vs Polycrystals E (diagonal) = 273 GPa

E (edge) = 125 GPa

Chapter 1 - 75

bull Most engineering materials are polycrystals

bull Each grain is a single crystal

bull If grains are randomly oriented

overall component properties are not directional

bull Grain sizes typically range from 1 nm to 2 cm

(ie from a few to millions of atomic layers)

A6 alloy ldquo the heat effected zonersquos (weld area) molecular structure is

reformed and A6 regains its original strengthrdquo

Nb-Hf-W plate with an

electron beam weld Adapted from Fig K color

inset pages of Callister 5e

(Fig K is courtesy of Paul E

Danielson Teledyne Wah

Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism

bull Two or more distinct crystal structures for the

same material (allotropypolymorphism)

titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY

bull Atoms may assemble into crystalline or amorphous structures

bull We can predict the density of a material provided we know the

atomic weight atomic radius and crystal geometry (eg FCC BCC

HCP)




bull Crystallographic points directions and planes are specified in

terms of indexing schemes

Crystallographic directions and planes are related to atomic linear

densities and planar densities

Chapter 1 - 78



allotropy)

SUMMARY






bull X-ray diffraction (not discussed here) is used for crystal

structure and interplanar spacing determinations

Chapter 1 - 2

Chapter 1 - Introduction bull What is materials science materials engineering

Chapter 1 - 3







1019 (b) Fig 930(c) Fig 1033


Rethwisch 8e



Hard

ness (

BH

N)


100

2 00

3 00

4 00

5 00

6 00

001 01 1 10 100 1000

(d)

30 mm (c)

4 mm

(b)

30 mm

(a)

30 mm

Chapter 1 - 4
















Chapter 1 - 5






corrosive





Chapter 1 - 6

ELECTRICAL










York 1970)

T (ordmC) -200 -100 0

1

2

3

4

5

6

Resis

tivity

r

(10

-8 O

hm

-m)

0

Chapter 1 - 7





you add zinc

Adapted from

Fig 194W Callister

6e (Courtesy of

Lockheed Aerospace

Ceramics Systems

Sunnyvale CA)

(Note W denotes fig

is on CD-ROM)






1979 p 315)


herm

al C

ond

uctivity

(Wm

-K)

400

300

200

100

0 0 10 20 30 40

100 mm


opening photograph



of Lockheed

Missiles and Space

Company Inc)

Chapter 1 - 8



Adapted from Fig 12




Tanner)

single crystal

polycrystal

low porosity

polycrystal

high porosity

OPTICAL

Chapter 1 - 9






Course Goals

SUMMARY

Chapter 1 - 10

ISSUES TO ADDRESS





Interatomic Bonding

Chapter 1 - 11

Atomic Structure




1 amuatom = 1gmol

C 12011 H 1008 etc

167 x 10-27 kg

Chapter 1 - 12

Atomic Structure



1) Chemical

2) Electrical

3) Thermal

4) Optical

Chapter 1 - 13


bull

Quantum Designation





Chapter 1 - 14


1s

2s 2p

K-shell n = 1

L-shell n = 2

3s 3p M-shell n = 3

3d

4s

4p 4d

Energy

N-shell n = 4




Electrons

Adapted from Fig 24


Chapter 1 - 15



Survey of Elements


(stable)

1s 2 2s 2 2p 6 3s 2 3p 6 (stable)

1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 4s 2 4p 6 (stable)

Atomic

18

36

Element

1s 1 1 Hydrogen

1s 2 2 Helium

1s 2 2s 1 3 Lithium


1s 2 2s 2 2p 1 5 Boron

1s 2 2s 2 2p 2 6 Carbon



1s 2 2s 2 2p 6 3s 2 3p 1 13 Aluminum

Argon

Krypton



Chapter 1 - 16






1s2 2s2 2p2

valence electrons

Chapter 1 - 17


Adapted from

Fig 26

Callister amp

Rethwisch 8e



to become + ions



to become - ions

giv

e u

p 1

e-

giv

e u

p 2

e-

giv

e u

p 3

e- inert

gases

accept 1e

-

accept 2e

-

O

Se

Te

Po At

I

Br

He

Ne

Ar

Kr

Xe

Rn

F

Cl S

Li Be

H

Na Mg

Ba Cs

Ra Fr

Ca K Sc

Sr Rb Y

Chapter 1 - 18






Electronegativity


Chapter 1 - 19


donates accepts

electrons electrons



[Ne] 3s2

Mg2+ 1s2 2s2 2p6 O2- 1s2 2s2 2p6

[Ne] [Ne]

Chapter 1 - 20




bull Example NaCl

Ionic Bonding

Na (metal) unstable


electron


Na (cation) stable

Cl (anion) stable

Chapter 1 - 21

Ionic Bonding






Chapter 1 - 22

Ionic Bonding



terms


Net energy EN

Repulsive energy ER


r A

n r B

EN = EA + ER = + -



Chapter 1 - 23






NaCl

MgO

CaF 2 CsCl

Chapter 1 - 24






all directions

Adapted from Fig 29


Chapter 1 - 25

C has 4 valence e-

needs 4 more

H has 1 valence e-

needs 1 more

Electronegativities

are comparable




dominate bonding



H

H

H

H

C

CH4

Chapter 1 - 26

Mixed Bonding


ionic character =



) 100 ( x

1-e-

(XA-XB )2

4


)2153(

2

-

--


Chapter 1 - 27

Metallic Bonding






Chapter 1 - 28




-general case

-ex liquid HCl

-ex polymer






Bonding



H H H H

H2 H2

secondary bonding

ex liquid H2

H Cl H Cl secondary

bonding

secondary bonding

+ - + -

secondary bonding

Chapter 1 - 29

Type

Ionic

Covalent

Metallic

Secondary

Bond Energy

Large

Variable

large-Diamond

small-Bismuth

Variable

large-Tungsten

small-Mercury

Smallest

Comments


Directional


polymer chains)


Directional


inter-molecular

Summary Bonding

Chapter 1 - 30

bull Bond Length r

bull Bond Energy Eo




r o r

Energy

r

larger Tm

smaller Tm

Eo =


Energy

r o r

unstretched length

Chapter 1 - 31






= E F

A0

D L

L0

Hookes Law

s = E e

s

Linear- elastic

E

e

F


Chapter 1 - 32

Ceramics



large E

small a

Metals

(Metallic bonding)


moderate E

moderate a

Summary



small Tm

small E

large a

Chapter 1 - 33



bull Unit cells








Single crystal

Polycrystalline

Amorphous



Solids

Chapter 1 - 34

Core Problems Ex 33

ANNOUNCEMENTS

Reading 31-37 317

38-315

Chapter 1 - 35

SUMMARY













Chapter 1 - 36



allotropy)

SUMMARY








Chapter 1 - 37




lower energies

Energy and Packing

Energy

r



Energy

r



Chapter 1 - 38


-metals

-many ceramics

-some polymers



-complex structures

-rapid cooling

crystalline SiO2


CampR8e


CampR8e


Si Oxygen

bull typical of

bull occurs for

Chapter 1 - 39




radii are the same








Chapter 1 - 40






Chapter 1 - 41


APF =

a 3

4

3 p (05a) 3 1

atoms

unit cell atom

volume

unit cell

volume



Volume of unit cell

assume hard spheres



a

R=05a


Chapter 1 - 42








Chapter 1 - 43


a

APF =

4

3 p ( 3 a4 ) 3 2

atoms

unit cell atom

volume

a 3

unit cell

volume

length = 4R =


3 a


a R Adapted from

Fig 32(a) CampR8e

a 2

a 3

Chapter 1 - 44









Chapter 1 - 45




APF =

4

3 p ( 2 a4 ) 3 4

atoms

unit cell atom

volume

a 3

unit cell

volume


length = 4R = 2 a


a

2 a

Adapted from

Fig 31(a)

CampR8e

Chapter 1 - 46

A sites

B B

B

B B

B B

C sites

C C

C A

B

B sites


bull 2D Projection

bull FCC Unit Cell


B B

B

B B

B B

B sites C C

C A

C C

C A

A B

C

Chapter 1 - 47



bull APF = 074



CampR8e


(HCP)

6 atomsunit cell

ex Cd Mg Ti Zn

bull ca = 1633

c

a

A sites

B sites


Middle layer

Top layer

Chapter 1 - 48



A = atomic weight




Density = r =

VC NA

n A r =



Chapter 1 - 49

bull Ex Cr (BCC)

A = 5200 gmol

R = 0125 nm


rtheoretical

a = 4R 3 = 02887 nm

ractual

a R

r = a3

5200 2

atoms

unit cell mol

g

unit cell

volume atoms

mol

6022 x 1023


= 718 gcm3

= 719 gcm3

Adapted from

Fig 32(a) CampR8e

Chapter 1 - 50



Why


r (g

cm

)

3


Metals Alloys

Composites fibers

Polymers

1

2

2 0




3

4

5

03

04

05

Magnesium

Aluminum

Steels

Titanium

CuNi

Tin Zinc

Silver Mo


G raphite

Silicon



Zirconia

H DPE PS PP LDPE

PC

PTFE

PET PVC Silicone

Wood

AFRE

CFRE

GFRE

Glass fibers

Carbon fibers

A ramid fibers


(metallic bonding)





(often amorphous)



In general

Chapter 1 - 51

Chapter 1 - 52

Chapter 1 - 53

Chapter 1 - 54

Fig 34 CampR8e

Crystal Systems

7 crystal systems

14 crystal lattices




Chapter 1 - 55

Chapter 1 - 56

Point Coordinates





z

x

y a b

c

000

111

y

z

2c

b

b

Chapter 1 - 57



through origin





[uvw]

ex 1 0 frac12 =gt 2 0 1 =gt [ 201 ]

-1 1 1


z

x

Algorithm


negative index

[ 111 ] =gt

y

Chapter 1 - 58


direction

a = 0405 nm

Linear Density


a

[110]


Number of atoms

atoms

length

1 35 nm

a 2

2 LD -

Adapted from

Fig 31(a)

CampR8e

Chapter 1 -

BCC vs simple cubic

59

Chapter 1 -

BCC vs Simple C





60

Chapter 1 -

On to HCP






c

Chapter 1 -

Reading


bull 4-1 ndash 4-7

bull 5-1 ndash 5-5

62

Chapter 1 - 63



through origin





[uvtw]

[ 1120 ] ex frac12 frac12 -1 0 =gt


CampR8e



a2

a3

-a3

2

a 2

2

a 1

- a3

a1

a2

z

Algorithm


Chapter 1 - 64




as follows

w w

t

v

u

) v u ( + -

) u v 2 ( 3

1 -

) v u 2 ( 3

1 -

] uvtw [ ] w v u [

Fig 38(a) CampR8e

- a3

a1

a2

z

Chapter 1 - 65



CampR8e

Chapter 1 - 66




Chapter 1 - 67


x

y a b

c


example a b c z

x

y a b

c


1 Intercepts 1 1


1 1 0 3 Reduction 1 1 0

1 Intercepts 12


2 0 0 3 Reduction 2 0 0

example a b c

Chapter 1 - 68


z

x

y a b

c



a b c


2 1 43

3 Reduction 6 3 4

(001) (010)


(100) (010) (001) Ex 100 = (100)

Chapter 1 - 69



used

example a1 a2 a3 c



1 0

-1

-1

1

1


a2

a3

a1

z


CampR8e

Chapter 1 - 70






important


for Fe


planes

Chapter 1 - 71



(100)


R 3

3 4 a


2D repeat unit


1

atoms

2D repeat unit

= nm2

atoms 121

m2

atoms = 12 x 1019

1

2

R 3

3 4 area

2D repeat unit

Chapter 1 - 72







others

-- diamond single


-- turbine blades




GE Superabrasives


permission)


Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 3







1019 (b) Fig 930(c) Fig 1033


Rethwisch 8e



Hard

ness (

BH

N)


100

2 00

3 00

4 00

5 00

6 00

001 01 1 10 100 1000

(d)

30 mm (c)

4 mm

(b)

30 mm

(a)

30 mm

Chapter 1 - 4
















Chapter 1 - 5






corrosive





Chapter 1 - 6

ELECTRICAL










York 1970)

T (ordmC) -200 -100 0

1

2

3

4

5

6

Resis

tivity

r

(10

-8 O

hm

-m)

0

Chapter 1 - 7





you add zinc

Adapted from

Fig 194W Callister

6e (Courtesy of

Lockheed Aerospace

Ceramics Systems

Sunnyvale CA)

(Note W denotes fig

is on CD-ROM)






1979 p 315)


herm

al C

ond

uctivity

(Wm

-K)

400

300

200

100

0 0 10 20 30 40

100 mm


opening photograph



of Lockheed

Missiles and Space

Company Inc)

Chapter 1 - 8



Adapted from Fig 12




Tanner)

single crystal

polycrystal

low porosity

polycrystal

high porosity

OPTICAL

Chapter 1 - 9






Course Goals

SUMMARY

Chapter 1 - 10

ISSUES TO ADDRESS





Interatomic Bonding

Chapter 1 - 11

Atomic Structure




1 amuatom = 1gmol

C 12011 H 1008 etc

167 x 10-27 kg

Chapter 1 - 12

Atomic Structure



1) Chemical

2) Electrical

3) Thermal

4) Optical

Chapter 1 - 13


bull

Quantum Designation





Chapter 1 - 14


1s

2s 2p

K-shell n = 1

L-shell n = 2

3s 3p M-shell n = 3

3d

4s

4p 4d

Energy

N-shell n = 4




Electrons

Adapted from Fig 24


Chapter 1 - 15



Survey of Elements


(stable)

1s 2 2s 2 2p 6 3s 2 3p 6 (stable)

1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 4s 2 4p 6 (stable)

Atomic

18

36

Element

1s 1 1 Hydrogen

1s 2 2 Helium

1s 2 2s 1 3 Lithium


1s 2 2s 2 2p 1 5 Boron

1s 2 2s 2 2p 2 6 Carbon



1s 2 2s 2 2p 6 3s 2 3p 1 13 Aluminum

Argon

Krypton



Chapter 1 - 16






1s2 2s2 2p2

valence electrons

Chapter 1 - 17


Adapted from

Fig 26

Callister amp

Rethwisch 8e



to become + ions



to become - ions

giv

e u

p 1

e-

giv

e u

p 2

e-

giv

e u

p 3

e- inert

gases

accept 1e

-

accept 2e

-

O

Se

Te

Po At

I

Br

He

Ne

Ar

Kr

Xe

Rn

F

Cl S

Li Be

H

Na Mg

Ba Cs

Ra Fr

Ca K Sc

Sr Rb Y

Chapter 1 - 18






Electronegativity


Chapter 1 - 19


donates accepts

electrons electrons



[Ne] 3s2

Mg2+ 1s2 2s2 2p6 O2- 1s2 2s2 2p6

[Ne] [Ne]

Chapter 1 - 20




bull Example NaCl

Ionic Bonding

Na (metal) unstable


electron


Na (cation) stable

Cl (anion) stable

Chapter 1 - 21

Ionic Bonding






Chapter 1 - 22

Ionic Bonding



terms


Net energy EN

Repulsive energy ER


r A

n r B

EN = EA + ER = + -



Chapter 1 - 23






NaCl

MgO

CaF 2 CsCl

Chapter 1 - 24






all directions

Adapted from Fig 29


Chapter 1 - 25

C has 4 valence e-

needs 4 more

H has 1 valence e-

needs 1 more

Electronegativities

are comparable




dominate bonding



H

H

H

H

C

CH4

Chapter 1 - 26

Mixed Bonding


ionic character =



) 100 ( x

1-e-

(XA-XB )2

4


)2153(

2

-

--


Chapter 1 - 27

Metallic Bonding






Chapter 1 - 28




-general case

-ex liquid HCl

-ex polymer






Bonding



H H H H

H2 H2

secondary bonding

ex liquid H2

H Cl H Cl secondary

bonding

secondary bonding

+ - + -

secondary bonding

Chapter 1 - 29

Type

Ionic

Covalent

Metallic

Secondary

Bond Energy

Large

Variable

large-Diamond

small-Bismuth

Variable

large-Tungsten

small-Mercury

Smallest

Comments


Directional


polymer chains)


Directional


inter-molecular

Summary Bonding

Chapter 1 - 30

bull Bond Length r

bull Bond Energy Eo




r o r

Energy

r

larger Tm

smaller Tm

Eo =


Energy

r o r

unstretched length

Chapter 1 - 31






= E F

A0

D L

L0

Hookes Law

s = E e

s

Linear- elastic

E

e

F


Chapter 1 - 32

Ceramics



large E

small a

Metals

(Metallic bonding)


moderate E

moderate a

Summary



small Tm

small E

large a

Chapter 1 - 33



bull Unit cells








Single crystal

Polycrystalline

Amorphous



Solids

Chapter 1 - 34

Core Problems Ex 33

ANNOUNCEMENTS

Reading 31-37 317

38-315

Chapter 1 - 35

SUMMARY













Chapter 1 - 36



allotropy)

SUMMARY








Chapter 1 - 37




lower energies

Energy and Packing

Energy

r



Energy

r



Chapter 1 - 38


-metals

-many ceramics

-some polymers



-complex structures

-rapid cooling

crystalline SiO2


CampR8e


CampR8e


Si Oxygen

bull typical of

bull occurs for

Chapter 1 - 39




radii are the same








Chapter 1 - 40






Chapter 1 - 41


APF =

a 3

4

3 p (05a) 3 1

atoms

unit cell atom

volume

unit cell

volume



Volume of unit cell

assume hard spheres



a

R=05a


Chapter 1 - 42








Chapter 1 - 43


a

APF =

4

3 p ( 3 a4 ) 3 2

atoms

unit cell atom

volume

a 3

unit cell

volume

length = 4R =


3 a


a R Adapted from

Fig 32(a) CampR8e

a 2

a 3

Chapter 1 - 44









Chapter 1 - 45




APF =

4

3 p ( 2 a4 ) 3 4

atoms

unit cell atom

volume

a 3

unit cell

volume


length = 4R = 2 a


a

2 a

Adapted from

Fig 31(a)

CampR8e

Chapter 1 - 46

A sites

B B

B

B B

B B

C sites

C C

C A

B

B sites


bull 2D Projection

bull FCC Unit Cell


B B

B

B B

B B

B sites C C

C A

C C

C A

A B

C

Chapter 1 - 47



bull APF = 074



CampR8e


(HCP)

6 atomsunit cell

ex Cd Mg Ti Zn

bull ca = 1633

c

a

A sites

B sites


Middle layer

Top layer

Chapter 1 - 48



A = atomic weight




Density = r =

VC NA

n A r =



Chapter 1 - 49

bull Ex Cr (BCC)

A = 5200 gmol

R = 0125 nm


rtheoretical

a = 4R 3 = 02887 nm

ractual

a R

r = a3

5200 2

atoms

unit cell mol

g

unit cell

volume atoms

mol

6022 x 1023


= 718 gcm3

= 719 gcm3

Adapted from

Fig 32(a) CampR8e

Chapter 1 - 50



Why


r (g

cm

)

3


Metals Alloys

Composites fibers

Polymers

1

2

2 0




3

4

5

03

04

05

Magnesium

Aluminum

Steels

Titanium

CuNi

Tin Zinc

Silver Mo


G raphite

Silicon



Zirconia

H DPE PS PP LDPE

PC

PTFE

PET PVC Silicone

Wood

AFRE

CFRE

GFRE

Glass fibers

Carbon fibers

A ramid fibers


(metallic bonding)





(often amorphous)



In general

Chapter 1 - 51

Chapter 1 - 52

Chapter 1 - 53

Chapter 1 - 54

Fig 34 CampR8e

Crystal Systems

7 crystal systems

14 crystal lattices




Chapter 1 - 55

Chapter 1 - 56

Point Coordinates





z

x

y a b

c

000

111

y

z

2c

b

b

Chapter 1 - 57



through origin





[uvw]

ex 1 0 frac12 =gt 2 0 1 =gt [ 201 ]

-1 1 1


z

x

Algorithm


negative index

[ 111 ] =gt

y

Chapter 1 - 58


direction

a = 0405 nm

Linear Density


a

[110]


Number of atoms

atoms

length

1 35 nm

a 2

2 LD -

Adapted from

Fig 31(a)

CampR8e

Chapter 1 -

BCC vs simple cubic

59

Chapter 1 -

BCC vs Simple C





60

Chapter 1 -

On to HCP






c

Chapter 1 -

Reading


bull 4-1 ndash 4-7

bull 5-1 ndash 5-5

62

Chapter 1 - 63



through origin





[uvtw]

[ 1120 ] ex frac12 frac12 -1 0 =gt


CampR8e



a2

a3

-a3

2

a 2

2

a 1

- a3

a1

a2

z

Algorithm


Chapter 1 - 64




as follows

w w

t

v

u

) v u ( + -

) u v 2 ( 3

1 -

) v u 2 ( 3

1 -

] uvtw [ ] w v u [

Fig 38(a) CampR8e

- a3

a1

a2

z

Chapter 1 - 65



CampR8e

Chapter 1 - 66




Chapter 1 - 67


x

y a b

c


example a b c z

x

y a b

c


1 Intercepts 1 1


1 1 0 3 Reduction 1 1 0

1 Intercepts 12


2 0 0 3 Reduction 2 0 0

example a b c

Chapter 1 - 68


z

x

y a b

c



a b c


2 1 43

3 Reduction 6 3 4

(001) (010)


(100) (010) (001) Ex 100 = (100)

Chapter 1 - 69



used

example a1 a2 a3 c



1 0

-1

-1

1

1


a2

a3

a1

z


CampR8e

Chapter 1 - 70






important


for Fe


planes

Chapter 1 - 71



(100)


R 3

3 4 a


2D repeat unit


1

atoms

2D repeat unit

= nm2

atoms 121

m2

atoms = 12 x 1019

1

2

R 3

3 4 area

2D repeat unit

Chapter 1 - 72







others

-- diamond single


-- turbine blades




GE Superabrasives


permission)


Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 4
















Chapter 1 - 5






corrosive





Chapter 1 - 6

ELECTRICAL










York 1970)

T (ordmC) -200 -100 0

1

2

3

4

5

6

Resis

tivity

r

(10

-8 O

hm

-m)

0

Chapter 1 - 7





you add zinc

Adapted from

Fig 194W Callister

6e (Courtesy of

Lockheed Aerospace

Ceramics Systems

Sunnyvale CA)

(Note W denotes fig

is on CD-ROM)






1979 p 315)


herm

al C

ond

uctivity

(Wm

-K)

400

300

200

100

0 0 10 20 30 40

100 mm


opening photograph



of Lockheed

Missiles and Space

Company Inc)

Chapter 1 - 8



Adapted from Fig 12




Tanner)

single crystal

polycrystal

low porosity

polycrystal

high porosity

OPTICAL

Chapter 1 - 9






Course Goals

SUMMARY

Chapter 1 - 10

ISSUES TO ADDRESS





Interatomic Bonding

Chapter 1 - 11

Atomic Structure




1 amuatom = 1gmol

C 12011 H 1008 etc

167 x 10-27 kg

Chapter 1 - 12

Atomic Structure



1) Chemical

2) Electrical

3) Thermal

4) Optical

Chapter 1 - 13


bull

Quantum Designation





Chapter 1 - 14


1s

2s 2p

K-shell n = 1

L-shell n = 2

3s 3p M-shell n = 3

3d

4s

4p 4d

Energy

N-shell n = 4




Electrons

Adapted from Fig 24


Chapter 1 - 15



Survey of Elements


(stable)

1s 2 2s 2 2p 6 3s 2 3p 6 (stable)

1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 4s 2 4p 6 (stable)

Atomic

18

36

Element

1s 1 1 Hydrogen

1s 2 2 Helium

1s 2 2s 1 3 Lithium


1s 2 2s 2 2p 1 5 Boron

1s 2 2s 2 2p 2 6 Carbon



1s 2 2s 2 2p 6 3s 2 3p 1 13 Aluminum

Argon

Krypton



Chapter 1 - 16






1s2 2s2 2p2

valence electrons

Chapter 1 - 17


Adapted from

Fig 26

Callister amp

Rethwisch 8e



to become + ions



to become - ions

giv

e u

p 1

e-

giv

e u

p 2

e-

giv

e u

p 3

e- inert

gases

accept 1e

-

accept 2e

-

O

Se

Te

Po At

I

Br

He

Ne

Ar

Kr

Xe

Rn

F

Cl S

Li Be

H

Na Mg

Ba Cs

Ra Fr

Ca K Sc

Sr Rb Y

Chapter 1 - 18






Electronegativity


Chapter 1 - 19


donates accepts

electrons electrons



[Ne] 3s2

Mg2+ 1s2 2s2 2p6 O2- 1s2 2s2 2p6

[Ne] [Ne]

Chapter 1 - 20




bull Example NaCl

Ionic Bonding

Na (metal) unstable


electron


Na (cation) stable

Cl (anion) stable

Chapter 1 - 21

Ionic Bonding






Chapter 1 - 22

Ionic Bonding



terms


Net energy EN

Repulsive energy ER


r A

n r B

EN = EA + ER = + -



Chapter 1 - 23






NaCl

MgO

CaF 2 CsCl

Chapter 1 - 24






all directions

Adapted from Fig 29


Chapter 1 - 25

C has 4 valence e-

needs 4 more

H has 1 valence e-

needs 1 more

Electronegativities

are comparable




dominate bonding



H

H

H

H

C

CH4

Chapter 1 - 26

Mixed Bonding


ionic character =



) 100 ( x

1-e-

(XA-XB )2

4


)2153(

2

-

--


Chapter 1 - 27

Metallic Bonding






Chapter 1 - 28




-general case

-ex liquid HCl

-ex polymer






Bonding



H H H H

H2 H2

secondary bonding

ex liquid H2

H Cl H Cl secondary

bonding

secondary bonding

+ - + -

secondary bonding

Chapter 1 - 29

Type

Ionic

Covalent

Metallic

Secondary

Bond Energy

Large

Variable

large-Diamond

small-Bismuth

Variable

large-Tungsten

small-Mercury

Smallest

Comments


Directional


polymer chains)


Directional


inter-molecular

Summary Bonding

Chapter 1 - 30

bull Bond Length r

bull Bond Energy Eo




r o r

Energy

r

larger Tm

smaller Tm

Eo =


Energy

r o r

unstretched length

Chapter 1 - 31






= E F

A0

D L

L0

Hookes Law

s = E e

s

Linear- elastic

E

e

F


Chapter 1 - 32

Ceramics



large E

small a

Metals

(Metallic bonding)


moderate E

moderate a

Summary



small Tm

small E

large a

Chapter 1 - 33



bull Unit cells








Single crystal

Polycrystalline

Amorphous



Solids

Chapter 1 - 34

Core Problems Ex 33

ANNOUNCEMENTS

Reading 31-37 317

38-315

Chapter 1 - 35

SUMMARY













Chapter 1 - 36



allotropy)

SUMMARY








Chapter 1 - 37




lower energies

Energy and Packing

Energy

r



Energy

r



Chapter 1 - 38


-metals

-many ceramics

-some polymers



-complex structures

-rapid cooling

crystalline SiO2


CampR8e


CampR8e


Si Oxygen

bull typical of

bull occurs for

Chapter 1 - 39




radii are the same








Chapter 1 - 40






Chapter 1 - 41


APF =

a 3

4

3 p (05a) 3 1

atoms

unit cell atom

volume

unit cell

volume



Volume of unit cell

assume hard spheres



a

R=05a


Chapter 1 - 42








Chapter 1 - 43


a

APF =

4

3 p ( 3 a4 ) 3 2

atoms

unit cell atom

volume

a 3

unit cell

volume

length = 4R =


3 a


a R Adapted from

Fig 32(a) CampR8e

a 2

a 3

Chapter 1 - 44









Chapter 1 - 45




APF =

4

3 p ( 2 a4 ) 3 4

atoms

unit cell atom

volume

a 3

unit cell

volume


length = 4R = 2 a


a

2 a

Adapted from

Fig 31(a)

CampR8e

Chapter 1 - 46

A sites

B B

B

B B

B B

C sites

C C

C A

B

B sites


bull 2D Projection

bull FCC Unit Cell


B B

B

B B

B B

B sites C C

C A

C C

C A

A B

C

Chapter 1 - 47



bull APF = 074



CampR8e


(HCP)

6 atomsunit cell

ex Cd Mg Ti Zn

bull ca = 1633

c

a

A sites

B sites


Middle layer

Top layer

Chapter 1 - 48



A = atomic weight




Density = r =

VC NA

n A r =



Chapter 1 - 49

bull Ex Cr (BCC)

A = 5200 gmol

R = 0125 nm


rtheoretical

a = 4R 3 = 02887 nm

ractual

a R

r = a3

5200 2

atoms

unit cell mol

g

unit cell

volume atoms

mol

6022 x 1023


= 718 gcm3

= 719 gcm3

Adapted from

Fig 32(a) CampR8e

Chapter 1 - 50



Why


r (g

cm

)

3


Metals Alloys

Composites fibers

Polymers

1

2

2 0




3

4

5

03

04

05

Magnesium

Aluminum

Steels

Titanium

CuNi

Tin Zinc

Silver Mo


G raphite

Silicon



Zirconia

H DPE PS PP LDPE

PC

PTFE

PET PVC Silicone

Wood

AFRE

CFRE

GFRE

Glass fibers

Carbon fibers

A ramid fibers


(metallic bonding)





(often amorphous)



In general

Chapter 1 - 51

Chapter 1 - 52

Chapter 1 - 53

Chapter 1 - 54

Fig 34 CampR8e

Crystal Systems

7 crystal systems

14 crystal lattices




Chapter 1 - 55

Chapter 1 - 56

Point Coordinates





z

x

y a b

c

000

111

y

z

2c

b

b

Chapter 1 - 57



through origin





[uvw]

ex 1 0 frac12 =gt 2 0 1 =gt [ 201 ]

-1 1 1


z

x

Algorithm


negative index

[ 111 ] =gt

y

Chapter 1 - 58


direction

a = 0405 nm

Linear Density


a

[110]


Number of atoms

atoms

length

1 35 nm

a 2

2 LD -

Adapted from

Fig 31(a)

CampR8e

Chapter 1 -

BCC vs simple cubic

59

Chapter 1 -

BCC vs Simple C





60

Chapter 1 -

On to HCP






c

Chapter 1 -

Reading


bull 4-1 ndash 4-7

bull 5-1 ndash 5-5

62

Chapter 1 - 63



through origin





[uvtw]

[ 1120 ] ex frac12 frac12 -1 0 =gt


CampR8e



a2

a3

-a3

2

a 2

2

a 1

- a3

a1

a2

z

Algorithm


Chapter 1 - 64




as follows

w w

t

v

u

) v u ( + -

) u v 2 ( 3

1 -

) v u 2 ( 3

1 -

] uvtw [ ] w v u [

Fig 38(a) CampR8e

- a3

a1

a2

z

Chapter 1 - 65



CampR8e

Chapter 1 - 66




Chapter 1 - 67


x

y a b

c


example a b c z

x

y a b

c


1 Intercepts 1 1


1 1 0 3 Reduction 1 1 0

1 Intercepts 12


2 0 0 3 Reduction 2 0 0

example a b c

Chapter 1 - 68


z

x

y a b

c



a b c


2 1 43

3 Reduction 6 3 4

(001) (010)


(100) (010) (001) Ex 100 = (100)

Chapter 1 - 69



used

example a1 a2 a3 c



1 0

-1

-1

1

1


a2

a3

a1

z


CampR8e

Chapter 1 - 70






important


for Fe


planes

Chapter 1 - 71



(100)


R 3

3 4 a


2D repeat unit


1

atoms

2D repeat unit

= nm2

atoms 121

m2

atoms = 12 x 1019

1

2

R 3

3 4 area

2D repeat unit

Chapter 1 - 72







others

-- diamond single


-- turbine blades




GE Superabrasives


permission)


Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 5






corrosive





Chapter 1 - 6

ELECTRICAL










York 1970)

T (ordmC) -200 -100 0

1

2

3

4

5

6

Resis

tivity

r

(10

-8 O

hm

-m)

0

Chapter 1 - 7





you add zinc

Adapted from

Fig 194W Callister

6e (Courtesy of

Lockheed Aerospace

Ceramics Systems

Sunnyvale CA)

(Note W denotes fig

is on CD-ROM)






1979 p 315)


herm

al C

ond

uctivity

(Wm

-K)

400

300

200

100

0 0 10 20 30 40

100 mm


opening photograph



of Lockheed

Missiles and Space

Company Inc)

Chapter 1 - 8



Adapted from Fig 12




Tanner)

single crystal

polycrystal

low porosity

polycrystal

high porosity

OPTICAL

Chapter 1 - 9






Course Goals

SUMMARY

Chapter 1 - 10

ISSUES TO ADDRESS





Interatomic Bonding

Chapter 1 - 11

Atomic Structure




1 amuatom = 1gmol

C 12011 H 1008 etc

167 x 10-27 kg

Chapter 1 - 12

Atomic Structure



1) Chemical

2) Electrical

3) Thermal

4) Optical

Chapter 1 - 13


bull

Quantum Designation





Chapter 1 - 14


1s

2s 2p

K-shell n = 1

L-shell n = 2

3s 3p M-shell n = 3

3d

4s

4p 4d

Energy

N-shell n = 4




Electrons

Adapted from Fig 24


Chapter 1 - 15



Survey of Elements


(stable)

1s 2 2s 2 2p 6 3s 2 3p 6 (stable)

1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 4s 2 4p 6 (stable)

Atomic

18

36

Element

1s 1 1 Hydrogen

1s 2 2 Helium

1s 2 2s 1 3 Lithium


1s 2 2s 2 2p 1 5 Boron

1s 2 2s 2 2p 2 6 Carbon



1s 2 2s 2 2p 6 3s 2 3p 1 13 Aluminum

Argon

Krypton



Chapter 1 - 16






1s2 2s2 2p2

valence electrons

Chapter 1 - 17


Adapted from

Fig 26

Callister amp

Rethwisch 8e



to become + ions



to become - ions

giv

e u

p 1

e-

giv

e u

p 2

e-

giv

e u

p 3

e- inert

gases

accept 1e

-

accept 2e

-

O

Se

Te

Po At

I

Br

He

Ne

Ar

Kr

Xe

Rn

F

Cl S

Li Be

H

Na Mg

Ba Cs

Ra Fr

Ca K Sc

Sr Rb Y

Chapter 1 - 18






Electronegativity


Chapter 1 - 19


donates accepts

electrons electrons



[Ne] 3s2

Mg2+ 1s2 2s2 2p6 O2- 1s2 2s2 2p6

[Ne] [Ne]

Chapter 1 - 20




bull Example NaCl

Ionic Bonding

Na (metal) unstable


electron


Na (cation) stable

Cl (anion) stable

Chapter 1 - 21

Ionic Bonding






Chapter 1 - 22

Ionic Bonding



terms


Net energy EN

Repulsive energy ER


r A

n r B

EN = EA + ER = + -



Chapter 1 - 23






NaCl

MgO

CaF 2 CsCl

Chapter 1 - 24






all directions

Adapted from Fig 29


Chapter 1 - 25

C has 4 valence e-

needs 4 more

H has 1 valence e-

needs 1 more

Electronegativities

are comparable




dominate bonding



H

H

H

H

C

CH4

Chapter 1 - 26

Mixed Bonding


ionic character =



) 100 ( x

1-e-

(XA-XB )2

4


)2153(

2

-

--


Chapter 1 - 27

Metallic Bonding






Chapter 1 - 28




-general case

-ex liquid HCl

-ex polymer






Bonding



H H H H

H2 H2

secondary bonding

ex liquid H2

H Cl H Cl secondary

bonding

secondary bonding

+ - + -

secondary bonding

Chapter 1 - 29

Type

Ionic

Covalent

Metallic

Secondary

Bond Energy

Large

Variable

large-Diamond

small-Bismuth

Variable

large-Tungsten

small-Mercury

Smallest

Comments


Directional


polymer chains)


Directional


inter-molecular

Summary Bonding

Chapter 1 - 30

bull Bond Length r

bull Bond Energy Eo




r o r

Energy

r

larger Tm

smaller Tm

Eo =


Energy

r o r

unstretched length

Chapter 1 - 31






= E F

A0

D L

L0

Hookes Law

s = E e

s

Linear- elastic

E

e

F


Chapter 1 - 32

Ceramics



large E

small a

Metals

(Metallic bonding)


moderate E

moderate a

Summary



small Tm

small E

large a

Chapter 1 - 33



bull Unit cells








Single crystal

Polycrystalline

Amorphous



Solids

Chapter 1 - 34

Core Problems Ex 33

ANNOUNCEMENTS

Reading 31-37 317

38-315

Chapter 1 - 35

SUMMARY













Chapter 1 - 36



allotropy)

SUMMARY








Chapter 1 - 37




lower energies

Energy and Packing

Energy

r



Energy

r



Chapter 1 - 38


-metals

-many ceramics

-some polymers



-complex structures

-rapid cooling

crystalline SiO2


CampR8e


CampR8e


Si Oxygen

bull typical of

bull occurs for

Chapter 1 - 39




radii are the same








Chapter 1 - 40






Chapter 1 - 41


APF =

a 3

4

3 p (05a) 3 1

atoms

unit cell atom

volume

unit cell

volume



Volume of unit cell

assume hard spheres



a

R=05a


Chapter 1 - 42








Chapter 1 - 43


a

APF =

4

3 p ( 3 a4 ) 3 2

atoms

unit cell atom

volume

a 3

unit cell

volume

length = 4R =


3 a


a R Adapted from

Fig 32(a) CampR8e

a 2

a 3

Chapter 1 - 44









Chapter 1 - 45




APF =

4

3 p ( 2 a4 ) 3 4

atoms

unit cell atom

volume

a 3

unit cell

volume


length = 4R = 2 a


a

2 a

Adapted from

Fig 31(a)

CampR8e

Chapter 1 - 46

A sites

B B

B

B B

B B

C sites

C C

C A

B

B sites


bull 2D Projection

bull FCC Unit Cell


B B

B

B B

B B

B sites C C

C A

C C

C A

A B

C

Chapter 1 - 47



bull APF = 074



CampR8e


(HCP)

6 atomsunit cell

ex Cd Mg Ti Zn

bull ca = 1633

c

a

A sites

B sites


Middle layer

Top layer

Chapter 1 - 48



A = atomic weight




Density = r =

VC NA

n A r =



Chapter 1 - 49

bull Ex Cr (BCC)

A = 5200 gmol

R = 0125 nm


rtheoretical

a = 4R 3 = 02887 nm

ractual

a R

r = a3

5200 2

atoms

unit cell mol

g

unit cell

volume atoms

mol

6022 x 1023


= 718 gcm3

= 719 gcm3

Adapted from

Fig 32(a) CampR8e

Chapter 1 - 50



Why


r (g

cm

)

3


Metals Alloys

Composites fibers

Polymers

1

2

2 0




3

4

5

03

04

05

Magnesium

Aluminum

Steels

Titanium

CuNi

Tin Zinc

Silver Mo


G raphite

Silicon



Zirconia

H DPE PS PP LDPE

PC

PTFE

PET PVC Silicone

Wood

AFRE

CFRE

GFRE

Glass fibers

Carbon fibers

A ramid fibers


(metallic bonding)





(often amorphous)



In general

Chapter 1 - 51

Chapter 1 - 52

Chapter 1 - 53

Chapter 1 - 54

Fig 34 CampR8e

Crystal Systems

7 crystal systems

14 crystal lattices




Chapter 1 - 55

Chapter 1 - 56

Point Coordinates





z

x

y a b

c

000

111

y

z

2c

b

b

Chapter 1 - 57



through origin





[uvw]

ex 1 0 frac12 =gt 2 0 1 =gt [ 201 ]

-1 1 1


z

x

Algorithm


negative index

[ 111 ] =gt

y

Chapter 1 - 58


direction

a = 0405 nm

Linear Density


a

[110]


Number of atoms

atoms

length

1 35 nm

a 2

2 LD -

Adapted from

Fig 31(a)

CampR8e

Chapter 1 -

BCC vs simple cubic

59

Chapter 1 -

BCC vs Simple C





60

Chapter 1 -

On to HCP






c

Chapter 1 -

Reading


bull 4-1 ndash 4-7

bull 5-1 ndash 5-5

62

Chapter 1 - 63



through origin





[uvtw]

[ 1120 ] ex frac12 frac12 -1 0 =gt


CampR8e



a2

a3

-a3

2

a 2

2

a 1

- a3

a1

a2

z

Algorithm


Chapter 1 - 64




as follows

w w

t

v

u

) v u ( + -

) u v 2 ( 3

1 -

) v u 2 ( 3

1 -

] uvtw [ ] w v u [

Fig 38(a) CampR8e

- a3

a1

a2

z

Chapter 1 - 65



CampR8e

Chapter 1 - 66




Chapter 1 - 67


x

y a b

c


example a b c z

x

y a b

c


1 Intercepts 1 1


1 1 0 3 Reduction 1 1 0

1 Intercepts 12


2 0 0 3 Reduction 2 0 0

example a b c

Chapter 1 - 68


z

x

y a b

c



a b c


2 1 43

3 Reduction 6 3 4

(001) (010)


(100) (010) (001) Ex 100 = (100)

Chapter 1 - 69



used

example a1 a2 a3 c



1 0

-1

-1

1

1


a2

a3

a1

z


CampR8e

Chapter 1 - 70






important


for Fe


planes

Chapter 1 - 71



(100)


R 3

3 4 a


2D repeat unit


1

atoms

2D repeat unit

= nm2

atoms 121

m2

atoms = 12 x 1019

1

2

R 3

3 4 area

2D repeat unit

Chapter 1 - 72







others

-- diamond single


-- turbine blades




GE Superabrasives


permission)


Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 6

ELECTRICAL










York 1970)

T (ordmC) -200 -100 0

1

2

3

4

5

6

Resis

tivity

r

(10

-8 O

hm

-m)

0

Chapter 1 - 7





you add zinc

Adapted from

Fig 194W Callister

6e (Courtesy of

Lockheed Aerospace

Ceramics Systems

Sunnyvale CA)

(Note W denotes fig

is on CD-ROM)






1979 p 315)


herm

al C

ond

uctivity

(Wm

-K)

400

300

200

100

0 0 10 20 30 40

100 mm


opening photograph



of Lockheed

Missiles and Space

Company Inc)

Chapter 1 - 8



Adapted from Fig 12




Tanner)

single crystal

polycrystal

low porosity

polycrystal

high porosity

OPTICAL

Chapter 1 - 9






Course Goals

SUMMARY

Chapter 1 - 10

ISSUES TO ADDRESS





Interatomic Bonding

Chapter 1 - 11

Atomic Structure




1 amuatom = 1gmol

C 12011 H 1008 etc

167 x 10-27 kg

Chapter 1 - 12

Atomic Structure



1) Chemical

2) Electrical

3) Thermal

4) Optical

Chapter 1 - 13


bull

Quantum Designation





Chapter 1 - 14


1s

2s 2p

K-shell n = 1

L-shell n = 2

3s 3p M-shell n = 3

3d

4s

4p 4d

Energy

N-shell n = 4




Electrons

Adapted from Fig 24


Chapter 1 - 15



Survey of Elements


(stable)

1s 2 2s 2 2p 6 3s 2 3p 6 (stable)

1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 4s 2 4p 6 (stable)

Atomic

18

36

Element

1s 1 1 Hydrogen

1s 2 2 Helium

1s 2 2s 1 3 Lithium


1s 2 2s 2 2p 1 5 Boron

1s 2 2s 2 2p 2 6 Carbon



1s 2 2s 2 2p 6 3s 2 3p 1 13 Aluminum

Argon

Krypton



Chapter 1 - 16






1s2 2s2 2p2

valence electrons

Chapter 1 - 17


Adapted from

Fig 26

Callister amp

Rethwisch 8e



to become + ions



to become - ions

giv

e u

p 1

e-

giv

e u

p 2

e-

giv

e u

p 3

e- inert

gases

accept 1e

-

accept 2e

-

O

Se

Te

Po At

I

Br

He

Ne

Ar

Kr

Xe

Rn

F

Cl S

Li Be

H

Na Mg

Ba Cs

Ra Fr

Ca K Sc

Sr Rb Y

Chapter 1 - 18






Electronegativity


Chapter 1 - 19


donates accepts

electrons electrons



[Ne] 3s2

Mg2+ 1s2 2s2 2p6 O2- 1s2 2s2 2p6

[Ne] [Ne]

Chapter 1 - 20




bull Example NaCl

Ionic Bonding

Na (metal) unstable


electron


Na (cation) stable

Cl (anion) stable

Chapter 1 - 21

Ionic Bonding






Chapter 1 - 22

Ionic Bonding



terms


Net energy EN

Repulsive energy ER


r A

n r B

EN = EA + ER = + -



Chapter 1 - 23






NaCl

MgO

CaF 2 CsCl

Chapter 1 - 24






all directions

Adapted from Fig 29


Chapter 1 - 25

C has 4 valence e-

needs 4 more

H has 1 valence e-

needs 1 more

Electronegativities

are comparable




dominate bonding



H

H

H

H

C

CH4

Chapter 1 - 26

Mixed Bonding


ionic character =



) 100 ( x

1-e-

(XA-XB )2

4


)2153(

2

-

--


Chapter 1 - 27

Metallic Bonding






Chapter 1 - 28




-general case

-ex liquid HCl

-ex polymer






Bonding



H H H H

H2 H2

secondary bonding

ex liquid H2

H Cl H Cl secondary

bonding

secondary bonding

+ - + -

secondary bonding

Chapter 1 - 29

Type

Ionic

Covalent

Metallic

Secondary

Bond Energy

Large

Variable

large-Diamond

small-Bismuth

Variable

large-Tungsten

small-Mercury

Smallest

Comments


Directional


polymer chains)


Directional


inter-molecular

Summary Bonding

Chapter 1 - 30

bull Bond Length r

bull Bond Energy Eo




r o r

Energy

r

larger Tm

smaller Tm

Eo =


Energy

r o r

unstretched length

Chapter 1 - 31






= E F

A0

D L

L0

Hookes Law

s = E e

s

Linear- elastic

E

e

F


Chapter 1 - 32

Ceramics



large E

small a

Metals

(Metallic bonding)


moderate E

moderate a

Summary



small Tm

small E

large a

Chapter 1 - 33



bull Unit cells








Single crystal

Polycrystalline

Amorphous



Solids

Chapter 1 - 34

Core Problems Ex 33

ANNOUNCEMENTS

Reading 31-37 317

38-315

Chapter 1 - 35

SUMMARY













Chapter 1 - 36



allotropy)

SUMMARY








Chapter 1 - 37




lower energies

Energy and Packing

Energy

r



Energy

r



Chapter 1 - 38


-metals

-many ceramics

-some polymers



-complex structures

-rapid cooling

crystalline SiO2


CampR8e


CampR8e


Si Oxygen

bull typical of

bull occurs for

Chapter 1 - 39




radii are the same








Chapter 1 - 40






Chapter 1 - 41


APF =

a 3

4

3 p (05a) 3 1

atoms

unit cell atom

volume

unit cell

volume



Volume of unit cell

assume hard spheres



a

R=05a


Chapter 1 - 42








Chapter 1 - 43


a

APF =

4

3 p ( 3 a4 ) 3 2

atoms

unit cell atom

volume

a 3

unit cell

volume

length = 4R =


3 a


a R Adapted from

Fig 32(a) CampR8e

a 2

a 3

Chapter 1 - 44









Chapter 1 - 45




APF =

4

3 p ( 2 a4 ) 3 4

atoms

unit cell atom

volume

a 3

unit cell

volume


length = 4R = 2 a


a

2 a

Adapted from

Fig 31(a)

CampR8e

Chapter 1 - 46

A sites

B B

B

B B

B B

C sites

C C

C A

B

B sites


bull 2D Projection

bull FCC Unit Cell


B B

B

B B

B B

B sites C C

C A

C C

C A

A B

C

Chapter 1 - 47



bull APF = 074



CampR8e


(HCP)

6 atomsunit cell

ex Cd Mg Ti Zn

bull ca = 1633

c

a

A sites

B sites


Middle layer

Top layer

Chapter 1 - 48



A = atomic weight




Density = r =

VC NA

n A r =



Chapter 1 - 49

bull Ex Cr (BCC)

A = 5200 gmol

R = 0125 nm


rtheoretical

a = 4R 3 = 02887 nm

ractual

a R

r = a3

5200 2

atoms

unit cell mol

g

unit cell

volume atoms

mol

6022 x 1023


= 718 gcm3

= 719 gcm3

Adapted from

Fig 32(a) CampR8e

Chapter 1 - 50



Why


r (g

cm

)

3


Metals Alloys

Composites fibers

Polymers

1

2

2 0




3

4

5

03

04

05

Magnesium

Aluminum

Steels

Titanium

CuNi

Tin Zinc

Silver Mo


G raphite

Silicon



Zirconia

H DPE PS PP LDPE

PC

PTFE

PET PVC Silicone

Wood

AFRE

CFRE

GFRE

Glass fibers

Carbon fibers

A ramid fibers


(metallic bonding)





(often amorphous)



In general

Chapter 1 - 51

Chapter 1 - 52

Chapter 1 - 53

Chapter 1 - 54

Fig 34 CampR8e

Crystal Systems

7 crystal systems

14 crystal lattices




Chapter 1 - 55

Chapter 1 - 56

Point Coordinates





z

x

y a b

c

000

111

y

z

2c

b

b

Chapter 1 - 57



through origin





[uvw]

ex 1 0 frac12 =gt 2 0 1 =gt [ 201 ]

-1 1 1


z

x

Algorithm


negative index

[ 111 ] =gt

y

Chapter 1 - 58


direction

a = 0405 nm

Linear Density


a

[110]


Number of atoms

atoms

length

1 35 nm

a 2

2 LD -

Adapted from

Fig 31(a)

CampR8e

Chapter 1 -

BCC vs simple cubic

59

Chapter 1 -

BCC vs Simple C





60

Chapter 1 -

On to HCP






c

Chapter 1 -

Reading


bull 4-1 ndash 4-7

bull 5-1 ndash 5-5

62

Chapter 1 - 63



through origin





[uvtw]

[ 1120 ] ex frac12 frac12 -1 0 =gt


CampR8e



a2

a3

-a3

2

a 2

2

a 1

- a3

a1

a2

z

Algorithm


Chapter 1 - 64




as follows

w w

t

v

u

) v u ( + -

) u v 2 ( 3

1 -

) v u 2 ( 3

1 -

] uvtw [ ] w v u [

Fig 38(a) CampR8e

- a3

a1

a2

z

Chapter 1 - 65



CampR8e

Chapter 1 - 66




Chapter 1 - 67


x

y a b

c


example a b c z

x

y a b

c


1 Intercepts 1 1


1 1 0 3 Reduction 1 1 0

1 Intercepts 12


2 0 0 3 Reduction 2 0 0

example a b c

Chapter 1 - 68


z

x

y a b

c



a b c


2 1 43

3 Reduction 6 3 4

(001) (010)


(100) (010) (001) Ex 100 = (100)

Chapter 1 - 69



used

example a1 a2 a3 c



1 0

-1

-1

1

1


a2

a3

a1

z


CampR8e

Chapter 1 - 70






important


for Fe


planes

Chapter 1 - 71



(100)


R 3

3 4 a


2D repeat unit


1

atoms

2D repeat unit

= nm2

atoms 121

m2

atoms = 12 x 1019

1

2

R 3

3 4 area

2D repeat unit

Chapter 1 - 72







others

-- diamond single


-- turbine blades




GE Superabrasives


permission)


Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 7





you add zinc

Adapted from

Fig 194W Callister

6e (Courtesy of

Lockheed Aerospace

Ceramics Systems

Sunnyvale CA)

(Note W denotes fig

is on CD-ROM)






1979 p 315)


herm

al C

ond

uctivity

(Wm

-K)

400

300

200

100

0 0 10 20 30 40

100 mm


opening photograph



of Lockheed

Missiles and Space

Company Inc)

Chapter 1 - 8



Adapted from Fig 12




Tanner)

single crystal

polycrystal

low porosity

polycrystal

high porosity

OPTICAL

Chapter 1 - 9






Course Goals

SUMMARY

Chapter 1 - 10

ISSUES TO ADDRESS





Interatomic Bonding

Chapter 1 - 11

Atomic Structure




1 amuatom = 1gmol

C 12011 H 1008 etc

167 x 10-27 kg

Chapter 1 - 12

Atomic Structure



1) Chemical

2) Electrical

3) Thermal

4) Optical

Chapter 1 - 13


bull

Quantum Designation





Chapter 1 - 14


1s

2s 2p

K-shell n = 1

L-shell n = 2

3s 3p M-shell n = 3

3d

4s

4p 4d

Energy

N-shell n = 4




Electrons

Adapted from Fig 24


Chapter 1 - 15



Survey of Elements


(stable)

1s 2 2s 2 2p 6 3s 2 3p 6 (stable)

1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 4s 2 4p 6 (stable)

Atomic

18

36

Element

1s 1 1 Hydrogen

1s 2 2 Helium

1s 2 2s 1 3 Lithium


1s 2 2s 2 2p 1 5 Boron

1s 2 2s 2 2p 2 6 Carbon



1s 2 2s 2 2p 6 3s 2 3p 1 13 Aluminum

Argon

Krypton



Chapter 1 - 16






1s2 2s2 2p2

valence electrons

Chapter 1 - 17


Adapted from

Fig 26

Callister amp

Rethwisch 8e



to become + ions



to become - ions

giv

e u

p 1

e-

giv

e u

p 2

e-

giv

e u

p 3

e- inert

gases

accept 1e

-

accept 2e

-

O

Se

Te

Po At

I

Br

He

Ne

Ar

Kr

Xe

Rn

F

Cl S

Li Be

H

Na Mg

Ba Cs

Ra Fr

Ca K Sc

Sr Rb Y

Chapter 1 - 18






Electronegativity


Chapter 1 - 19


donates accepts

electrons electrons



[Ne] 3s2

Mg2+ 1s2 2s2 2p6 O2- 1s2 2s2 2p6

[Ne] [Ne]

Chapter 1 - 20




bull Example NaCl

Ionic Bonding

Na (metal) unstable


electron


Na (cation) stable

Cl (anion) stable

Chapter 1 - 21

Ionic Bonding






Chapter 1 - 22

Ionic Bonding



terms


Net energy EN

Repulsive energy ER


r A

n r B

EN = EA + ER = + -



Chapter 1 - 23






NaCl

MgO

CaF 2 CsCl

Chapter 1 - 24






all directions

Adapted from Fig 29


Chapter 1 - 25

C has 4 valence e-

needs 4 more

H has 1 valence e-

needs 1 more

Electronegativities

are comparable




dominate bonding



H

H

H

H

C

CH4

Chapter 1 - 26

Mixed Bonding


ionic character =



) 100 ( x

1-e-

(XA-XB )2

4


)2153(

2

-

--


Chapter 1 - 27

Metallic Bonding






Chapter 1 - 28




-general case

-ex liquid HCl

-ex polymer






Bonding



H H H H

H2 H2

secondary bonding

ex liquid H2

H Cl H Cl secondary

bonding

secondary bonding

+ - + -

secondary bonding

Chapter 1 - 29

Type

Ionic

Covalent

Metallic

Secondary

Bond Energy

Large

Variable

large-Diamond

small-Bismuth

Variable

large-Tungsten

small-Mercury

Smallest

Comments


Directional


polymer chains)


Directional


inter-molecular

Summary Bonding

Chapter 1 - 30

bull Bond Length r

bull Bond Energy Eo




r o r

Energy

r

larger Tm

smaller Tm

Eo =


Energy

r o r

unstretched length

Chapter 1 - 31






= E F

A0

D L

L0

Hookes Law

s = E e

s

Linear- elastic

E

e

F


Chapter 1 - 32

Ceramics



large E

small a

Metals

(Metallic bonding)


moderate E

moderate a

Summary



small Tm

small E

large a

Chapter 1 - 33



bull Unit cells








Single crystal

Polycrystalline

Amorphous



Solids

Chapter 1 - 34

Core Problems Ex 33

ANNOUNCEMENTS

Reading 31-37 317

38-315

Chapter 1 - 35

SUMMARY













Chapter 1 - 36



allotropy)

SUMMARY








Chapter 1 - 37




lower energies

Energy and Packing

Energy

r



Energy

r



Chapter 1 - 38


-metals

-many ceramics

-some polymers



-complex structures

-rapid cooling

crystalline SiO2


CampR8e


CampR8e


Si Oxygen

bull typical of

bull occurs for

Chapter 1 - 39




radii are the same








Chapter 1 - 40






Chapter 1 - 41


APF =

a 3

4

3 p (05a) 3 1

atoms

unit cell atom

volume

unit cell

volume



Volume of unit cell

assume hard spheres



a

R=05a


Chapter 1 - 42








Chapter 1 - 43


a

APF =

4

3 p ( 3 a4 ) 3 2

atoms

unit cell atom

volume

a 3

unit cell

volume

length = 4R =


3 a


a R Adapted from

Fig 32(a) CampR8e

a 2

a 3

Chapter 1 - 44









Chapter 1 - 45




APF =

4

3 p ( 2 a4 ) 3 4

atoms

unit cell atom

volume

a 3

unit cell

volume


length = 4R = 2 a


a

2 a

Adapted from

Fig 31(a)

CampR8e

Chapter 1 - 46

A sites

B B

B

B B

B B

C sites

C C

C A

B

B sites


bull 2D Projection

bull FCC Unit Cell


B B

B

B B

B B

B sites C C

C A

C C

C A

A B

C

Chapter 1 - 47



bull APF = 074



CampR8e


(HCP)

6 atomsunit cell

ex Cd Mg Ti Zn

bull ca = 1633

c

a

A sites

B sites


Middle layer

Top layer

Chapter 1 - 48



A = atomic weight




Density = r =

VC NA

n A r =



Chapter 1 - 49

bull Ex Cr (BCC)

A = 5200 gmol

R = 0125 nm


rtheoretical

a = 4R 3 = 02887 nm

ractual

a R

r = a3

5200 2

atoms

unit cell mol

g

unit cell

volume atoms

mol

6022 x 1023


= 718 gcm3

= 719 gcm3

Adapted from

Fig 32(a) CampR8e

Chapter 1 - 50



Why


r (g

cm

)

3


Metals Alloys

Composites fibers

Polymers

1

2

2 0




3

4

5

03

04

05

Magnesium

Aluminum

Steels

Titanium

CuNi

Tin Zinc

Silver Mo


G raphite

Silicon



Zirconia

H DPE PS PP LDPE

PC

PTFE

PET PVC Silicone

Wood

AFRE

CFRE

GFRE

Glass fibers

Carbon fibers

A ramid fibers


(metallic bonding)





(often amorphous)



In general

Chapter 1 - 51

Chapter 1 - 52

Chapter 1 - 53

Chapter 1 - 54

Fig 34 CampR8e

Crystal Systems

7 crystal systems

14 crystal lattices




Chapter 1 - 55

Chapter 1 - 56

Point Coordinates





z

x

y a b

c

000

111

y

z

2c

b

b

Chapter 1 - 57



through origin





[uvw]

ex 1 0 frac12 =gt 2 0 1 =gt [ 201 ]

-1 1 1


z

x

Algorithm


negative index

[ 111 ] =gt

y

Chapter 1 - 58


direction

a = 0405 nm

Linear Density


a

[110]


Number of atoms

atoms

length

1 35 nm

a 2

2 LD -

Adapted from

Fig 31(a)

CampR8e

Chapter 1 -

BCC vs simple cubic

59

Chapter 1 -

BCC vs Simple C





60

Chapter 1 -

On to HCP






c

Chapter 1 -

Reading


bull 4-1 ndash 4-7

bull 5-1 ndash 5-5

62

Chapter 1 - 63



through origin





[uvtw]

[ 1120 ] ex frac12 frac12 -1 0 =gt


CampR8e



a2

a3

-a3

2

a 2

2

a 1

- a3

a1

a2

z

Algorithm


Chapter 1 - 64




as follows

w w

t

v

u

) v u ( + -

) u v 2 ( 3

1 -

) v u 2 ( 3

1 -

] uvtw [ ] w v u [

Fig 38(a) CampR8e

- a3

a1

a2

z

Chapter 1 - 65



CampR8e

Chapter 1 - 66




Chapter 1 - 67


x

y a b

c


example a b c z

x

y a b

c


1 Intercepts 1 1


1 1 0 3 Reduction 1 1 0

1 Intercepts 12


2 0 0 3 Reduction 2 0 0

example a b c

Chapter 1 - 68


z

x

y a b

c



a b c


2 1 43

3 Reduction 6 3 4

(001) (010)


(100) (010) (001) Ex 100 = (100)

Chapter 1 - 69



used

example a1 a2 a3 c



1 0

-1

-1

1

1


a2

a3

a1

z


CampR8e

Chapter 1 - 70






important


for Fe


planes

Chapter 1 - 71



(100)


R 3

3 4 a


2D repeat unit


1

atoms

2D repeat unit

= nm2

atoms 121

m2

atoms = 12 x 1019

1

2

R 3

3 4 area

2D repeat unit

Chapter 1 - 72







others

-- diamond single


-- turbine blades




GE Superabrasives


permission)


Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 8



Adapted from Fig 12




Tanner)

single crystal

polycrystal

low porosity

polycrystal

high porosity

OPTICAL

Chapter 1 - 9






Course Goals

SUMMARY

Chapter 1 - 10

ISSUES TO ADDRESS





Interatomic Bonding

Chapter 1 - 11

Atomic Structure




1 amuatom = 1gmol

C 12011 H 1008 etc

167 x 10-27 kg

Chapter 1 - 12

Atomic Structure



1) Chemical

2) Electrical

3) Thermal

4) Optical

Chapter 1 - 13


bull

Quantum Designation





Chapter 1 - 14


1s

2s 2p

K-shell n = 1

L-shell n = 2

3s 3p M-shell n = 3

3d

4s

4p 4d

Energy

N-shell n = 4




Electrons

Adapted from Fig 24


Chapter 1 - 15



Survey of Elements


(stable)

1s 2 2s 2 2p 6 3s 2 3p 6 (stable)

1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 4s 2 4p 6 (stable)

Atomic

18

36

Element

1s 1 1 Hydrogen

1s 2 2 Helium

1s 2 2s 1 3 Lithium


1s 2 2s 2 2p 1 5 Boron

1s 2 2s 2 2p 2 6 Carbon



1s 2 2s 2 2p 6 3s 2 3p 1 13 Aluminum

Argon

Krypton



Chapter 1 - 16






1s2 2s2 2p2

valence electrons

Chapter 1 - 17


Adapted from

Fig 26

Callister amp

Rethwisch 8e



to become + ions



to become - ions

giv

e u

p 1

e-

giv

e u

p 2

e-

giv

e u

p 3

e- inert

gases

accept 1e

-

accept 2e

-

O

Se

Te

Po At

I

Br

He

Ne

Ar

Kr

Xe

Rn

F

Cl S

Li Be

H

Na Mg

Ba Cs

Ra Fr

Ca K Sc

Sr Rb Y

Chapter 1 - 18






Electronegativity


Chapter 1 - 19


donates accepts

electrons electrons



[Ne] 3s2

Mg2+ 1s2 2s2 2p6 O2- 1s2 2s2 2p6

[Ne] [Ne]

Chapter 1 - 20




bull Example NaCl

Ionic Bonding

Na (metal) unstable


electron


Na (cation) stable

Cl (anion) stable

Chapter 1 - 21

Ionic Bonding






Chapter 1 - 22

Ionic Bonding



terms


Net energy EN

Repulsive energy ER


r A

n r B

EN = EA + ER = + -



Chapter 1 - 23






NaCl

MgO

CaF 2 CsCl

Chapter 1 - 24






all directions

Adapted from Fig 29


Chapter 1 - 25

C has 4 valence e-

needs 4 more

H has 1 valence e-

needs 1 more

Electronegativities

are comparable




dominate bonding



H

H

H

H

C

CH4

Chapter 1 - 26

Mixed Bonding


ionic character =



) 100 ( x

1-e-

(XA-XB )2

4


)2153(

2

-

--


Chapter 1 - 27

Metallic Bonding






Chapter 1 - 28




-general case

-ex liquid HCl

-ex polymer






Bonding



H H H H

H2 H2

secondary bonding

ex liquid H2

H Cl H Cl secondary

bonding

secondary bonding

+ - + -

secondary bonding

Chapter 1 - 29

Type

Ionic

Covalent

Metallic

Secondary

Bond Energy

Large

Variable

large-Diamond

small-Bismuth

Variable

large-Tungsten

small-Mercury

Smallest

Comments


Directional


polymer chains)


Directional


inter-molecular

Summary Bonding

Chapter 1 - 30

bull Bond Length r

bull Bond Energy Eo




r o r

Energy

r

larger Tm

smaller Tm

Eo =


Energy

r o r

unstretched length

Chapter 1 - 31






= E F

A0

D L

L0

Hookes Law

s = E e

s

Linear- elastic

E

e

F


Chapter 1 - 32

Ceramics



large E

small a

Metals

(Metallic bonding)


moderate E

moderate a

Summary



small Tm

small E

large a

Chapter 1 - 33



bull Unit cells








Single crystal

Polycrystalline

Amorphous



Solids

Chapter 1 - 34

Core Problems Ex 33

ANNOUNCEMENTS

Reading 31-37 317

38-315

Chapter 1 - 35

SUMMARY













Chapter 1 - 36



allotropy)

SUMMARY








Chapter 1 - 37




lower energies

Energy and Packing

Energy

r



Energy

r



Chapter 1 - 38


-metals

-many ceramics

-some polymers



-complex structures

-rapid cooling

crystalline SiO2


CampR8e


CampR8e


Si Oxygen

bull typical of

bull occurs for

Chapter 1 - 39




radii are the same








Chapter 1 - 40






Chapter 1 - 41


APF =

a 3

4

3 p (05a) 3 1

atoms

unit cell atom

volume

unit cell

volume



Volume of unit cell

assume hard spheres



a

R=05a


Chapter 1 - 42








Chapter 1 - 43


a

APF =

4

3 p ( 3 a4 ) 3 2

atoms

unit cell atom

volume

a 3

unit cell

volume

length = 4R =


3 a


a R Adapted from

Fig 32(a) CampR8e

a 2

a 3

Chapter 1 - 44









Chapter 1 - 45




APF =

4

3 p ( 2 a4 ) 3 4

atoms

unit cell atom

volume

a 3

unit cell

volume


length = 4R = 2 a


a

2 a

Adapted from

Fig 31(a)

CampR8e

Chapter 1 - 46

A sites

B B

B

B B

B B

C sites

C C

C A

B

B sites


bull 2D Projection

bull FCC Unit Cell


B B

B

B B

B B

B sites C C

C A

C C

C A

A B

C

Chapter 1 - 47



bull APF = 074



CampR8e


(HCP)

6 atomsunit cell

ex Cd Mg Ti Zn

bull ca = 1633

c

a

A sites

B sites


Middle layer

Top layer

Chapter 1 - 48



A = atomic weight




Density = r =

VC NA

n A r =



Chapter 1 - 49

bull Ex Cr (BCC)

A = 5200 gmol

R = 0125 nm


rtheoretical

a = 4R 3 = 02887 nm

ractual

a R

r = a3

5200 2

atoms

unit cell mol

g

unit cell

volume atoms

mol

6022 x 1023


= 718 gcm3

= 719 gcm3

Adapted from

Fig 32(a) CampR8e

Chapter 1 - 50



Why


r (g

cm

)

3


Metals Alloys

Composites fibers

Polymers

1

2

2 0




3

4

5

03

04

05

Magnesium

Aluminum

Steels

Titanium

CuNi

Tin Zinc

Silver Mo


G raphite

Silicon



Zirconia

H DPE PS PP LDPE

PC

PTFE

PET PVC Silicone

Wood

AFRE

CFRE

GFRE

Glass fibers

Carbon fibers

A ramid fibers


(metallic bonding)





(often amorphous)



In general

Chapter 1 - 51

Chapter 1 - 52

Chapter 1 - 53

Chapter 1 - 54

Fig 34 CampR8e

Crystal Systems

7 crystal systems

14 crystal lattices




Chapter 1 - 55

Chapter 1 - 56

Point Coordinates





z

x

y a b

c

000

111

y

z

2c

b

b

Chapter 1 - 57



through origin





[uvw]

ex 1 0 frac12 =gt 2 0 1 =gt [ 201 ]

-1 1 1


z

x

Algorithm


negative index

[ 111 ] =gt

y

Chapter 1 - 58


direction

a = 0405 nm

Linear Density


a

[110]


Number of atoms

atoms

length

1 35 nm

a 2

2 LD -

Adapted from

Fig 31(a)

CampR8e

Chapter 1 -

BCC vs simple cubic

59

Chapter 1 -

BCC vs Simple C





60

Chapter 1 -

On to HCP






c

Chapter 1 -

Reading


bull 4-1 ndash 4-7

bull 5-1 ndash 5-5

62

Chapter 1 - 63



through origin





[uvtw]

[ 1120 ] ex frac12 frac12 -1 0 =gt


CampR8e



a2

a3

-a3

2

a 2

2

a 1

- a3

a1

a2

z

Algorithm


Chapter 1 - 64




as follows

w w

t

v

u

) v u ( + -

) u v 2 ( 3

1 -

) v u 2 ( 3

1 -

] uvtw [ ] w v u [

Fig 38(a) CampR8e

- a3

a1

a2

z

Chapter 1 - 65



CampR8e

Chapter 1 - 66




Chapter 1 - 67


x

y a b

c


example a b c z

x

y a b

c


1 Intercepts 1 1


1 1 0 3 Reduction 1 1 0

1 Intercepts 12


2 0 0 3 Reduction 2 0 0

example a b c

Chapter 1 - 68


z

x

y a b

c



a b c


2 1 43

3 Reduction 6 3 4

(001) (010)


(100) (010) (001) Ex 100 = (100)

Chapter 1 - 69



used

example a1 a2 a3 c



1 0

-1

-1

1

1


a2

a3

a1

z


CampR8e

Chapter 1 - 70






important


for Fe


planes

Chapter 1 - 71



(100)


R 3

3 4 a


2D repeat unit


1

atoms

2D repeat unit

= nm2

atoms 121

m2

atoms = 12 x 1019

1

2

R 3

3 4 area

2D repeat unit

Chapter 1 - 72







others

-- diamond single


-- turbine blades




GE Superabrasives


permission)


Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 9






Course Goals

SUMMARY

Chapter 1 - 10

ISSUES TO ADDRESS





Interatomic Bonding

Chapter 1 - 11

Atomic Structure




1 amuatom = 1gmol

C 12011 H 1008 etc

167 x 10-27 kg

Chapter 1 - 12

Atomic Structure



1) Chemical

2) Electrical

3) Thermal

4) Optical

Chapter 1 - 13


bull

Quantum Designation





Chapter 1 - 14


1s

2s 2p

K-shell n = 1

L-shell n = 2

3s 3p M-shell n = 3

3d

4s

4p 4d

Energy

N-shell n = 4




Electrons

Adapted from Fig 24


Chapter 1 - 15



Survey of Elements


(stable)

1s 2 2s 2 2p 6 3s 2 3p 6 (stable)

1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 4s 2 4p 6 (stable)

Atomic

18

36

Element

1s 1 1 Hydrogen

1s 2 2 Helium

1s 2 2s 1 3 Lithium


1s 2 2s 2 2p 1 5 Boron

1s 2 2s 2 2p 2 6 Carbon



1s 2 2s 2 2p 6 3s 2 3p 1 13 Aluminum

Argon

Krypton



Chapter 1 - 16






1s2 2s2 2p2

valence electrons

Chapter 1 - 17


Adapted from

Fig 26

Callister amp

Rethwisch 8e



to become + ions



to become - ions

giv

e u

p 1

e-

giv

e u

p 2

e-

giv

e u

p 3

e- inert

gases

accept 1e

-

accept 2e

-

O

Se

Te

Po At

I

Br

He

Ne

Ar

Kr

Xe

Rn

F

Cl S

Li Be

H

Na Mg

Ba Cs

Ra Fr

Ca K Sc

Sr Rb Y

Chapter 1 - 18






Electronegativity


Chapter 1 - 19


donates accepts

electrons electrons



[Ne] 3s2

Mg2+ 1s2 2s2 2p6 O2- 1s2 2s2 2p6

[Ne] [Ne]

Chapter 1 - 20




bull Example NaCl

Ionic Bonding

Na (metal) unstable


electron


Na (cation) stable

Cl (anion) stable

Chapter 1 - 21

Ionic Bonding






Chapter 1 - 22

Ionic Bonding



terms


Net energy EN

Repulsive energy ER


r A

n r B

EN = EA + ER = + -



Chapter 1 - 23






NaCl

MgO

CaF 2 CsCl

Chapter 1 - 24






all directions

Adapted from Fig 29


Chapter 1 - 25

C has 4 valence e-

needs 4 more

H has 1 valence e-

needs 1 more

Electronegativities

are comparable




dominate bonding



H

H

H

H

C

CH4

Chapter 1 - 26

Mixed Bonding


ionic character =



) 100 ( x

1-e-

(XA-XB )2

4


)2153(

2

-

--


Chapter 1 - 27

Metallic Bonding






Chapter 1 - 28




-general case

-ex liquid HCl

-ex polymer






Bonding



H H H H

H2 H2

secondary bonding

ex liquid H2

H Cl H Cl secondary

bonding

secondary bonding

+ - + -

secondary bonding

Chapter 1 - 29

Type

Ionic

Covalent

Metallic

Secondary

Bond Energy

Large

Variable

large-Diamond

small-Bismuth

Variable

large-Tungsten

small-Mercury

Smallest

Comments


Directional


polymer chains)


Directional


inter-molecular

Summary Bonding

Chapter 1 - 30

bull Bond Length r

bull Bond Energy Eo




r o r

Energy

r

larger Tm

smaller Tm

Eo =


Energy

r o r

unstretched length

Chapter 1 - 31






= E F

A0

D L

L0

Hookes Law

s = E e

s

Linear- elastic

E

e

F


Chapter 1 - 32

Ceramics



large E

small a

Metals

(Metallic bonding)


moderate E

moderate a

Summary



small Tm

small E

large a

Chapter 1 - 33



bull Unit cells








Single crystal

Polycrystalline

Amorphous



Solids

Chapter 1 - 34

Core Problems Ex 33

ANNOUNCEMENTS

Reading 31-37 317

38-315

Chapter 1 - 35

SUMMARY













Chapter 1 - 36



allotropy)

SUMMARY








Chapter 1 - 37




lower energies

Energy and Packing

Energy

r



Energy

r



Chapter 1 - 38


-metals

-many ceramics

-some polymers



-complex structures

-rapid cooling

crystalline SiO2


CampR8e


CampR8e


Si Oxygen

bull typical of

bull occurs for

Chapter 1 - 39




radii are the same








Chapter 1 - 40






Chapter 1 - 41


APF =

a 3

4

3 p (05a) 3 1

atoms

unit cell atom

volume

unit cell

volume



Volume of unit cell

assume hard spheres



a

R=05a


Chapter 1 - 42








Chapter 1 - 43


a

APF =

4

3 p ( 3 a4 ) 3 2

atoms

unit cell atom

volume

a 3

unit cell

volume

length = 4R =


3 a


a R Adapted from

Fig 32(a) CampR8e

a 2

a 3

Chapter 1 - 44









Chapter 1 - 45




APF =

4

3 p ( 2 a4 ) 3 4

atoms

unit cell atom

volume

a 3

unit cell

volume


length = 4R = 2 a


a

2 a

Adapted from

Fig 31(a)

CampR8e

Chapter 1 - 46

A sites

B B

B

B B

B B

C sites

C C

C A

B

B sites


bull 2D Projection

bull FCC Unit Cell


B B

B

B B

B B

B sites C C

C A

C C

C A

A B

C

Chapter 1 - 47



bull APF = 074



CampR8e


(HCP)

6 atomsunit cell

ex Cd Mg Ti Zn

bull ca = 1633

c

a

A sites

B sites


Middle layer

Top layer

Chapter 1 - 48



A = atomic weight




Density = r =

VC NA

n A r =



Chapter 1 - 49

bull Ex Cr (BCC)

A = 5200 gmol

R = 0125 nm


rtheoretical

a = 4R 3 = 02887 nm

ractual

a R

r = a3

5200 2

atoms

unit cell mol

g

unit cell

volume atoms

mol

6022 x 1023


= 718 gcm3

= 719 gcm3

Adapted from

Fig 32(a) CampR8e

Chapter 1 - 50



Why


r (g

cm

)

3


Metals Alloys

Composites fibers

Polymers

1

2

2 0




3

4

5

03

04

05

Magnesium

Aluminum

Steels

Titanium

CuNi

Tin Zinc

Silver Mo


G raphite

Silicon



Zirconia

H DPE PS PP LDPE

PC

PTFE

PET PVC Silicone

Wood

AFRE

CFRE

GFRE

Glass fibers

Carbon fibers

A ramid fibers


(metallic bonding)





(often amorphous)



In general

Chapter 1 - 51

Chapter 1 - 52

Chapter 1 - 53

Chapter 1 - 54

Fig 34 CampR8e

Crystal Systems

7 crystal systems

14 crystal lattices




Chapter 1 - 55

Chapter 1 - 56

Point Coordinates





z

x

y a b

c

000

111

y

z

2c

b

b

Chapter 1 - 57



through origin





[uvw]

ex 1 0 frac12 =gt 2 0 1 =gt [ 201 ]

-1 1 1


z

x

Algorithm


negative index

[ 111 ] =gt

y

Chapter 1 - 58


direction

a = 0405 nm

Linear Density


a

[110]


Number of atoms

atoms

length

1 35 nm

a 2

2 LD -

Adapted from

Fig 31(a)

CampR8e

Chapter 1 -

BCC vs simple cubic

59

Chapter 1 -

BCC vs Simple C





60

Chapter 1 -

On to HCP






c

Chapter 1 -

Reading


bull 4-1 ndash 4-7

bull 5-1 ndash 5-5

62

Chapter 1 - 63



through origin





[uvtw]

[ 1120 ] ex frac12 frac12 -1 0 =gt


CampR8e



a2

a3

-a3

2

a 2

2

a 1

- a3

a1

a2

z

Algorithm


Chapter 1 - 64




as follows

w w

t

v

u

) v u ( + -

) u v 2 ( 3

1 -

) v u 2 ( 3

1 -

] uvtw [ ] w v u [

Fig 38(a) CampR8e

- a3

a1

a2

z

Chapter 1 - 65



CampR8e

Chapter 1 - 66




Chapter 1 - 67


x

y a b

c


example a b c z

x

y a b

c


1 Intercepts 1 1


1 1 0 3 Reduction 1 1 0

1 Intercepts 12


2 0 0 3 Reduction 2 0 0

example a b c

Chapter 1 - 68


z

x

y a b

c



a b c


2 1 43

3 Reduction 6 3 4

(001) (010)


(100) (010) (001) Ex 100 = (100)

Chapter 1 - 69



used

example a1 a2 a3 c



1 0

-1

-1

1

1


a2

a3

a1

z


CampR8e

Chapter 1 - 70






important


for Fe


planes

Chapter 1 - 71



(100)


R 3

3 4 a


2D repeat unit


1

atoms

2D repeat unit

= nm2

atoms 121

m2

atoms = 12 x 1019

1

2

R 3

3 4 area

2D repeat unit

Chapter 1 - 72







others

-- diamond single


-- turbine blades




GE Superabrasives


permission)


Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 10

ISSUES TO ADDRESS





Interatomic Bonding

Chapter 1 - 11

Atomic Structure




1 amuatom = 1gmol

C 12011 H 1008 etc

167 x 10-27 kg

Chapter 1 - 12

Atomic Structure



1) Chemical

2) Electrical

3) Thermal

4) Optical

Chapter 1 - 13


bull

Quantum Designation





Chapter 1 - 14


1s

2s 2p

K-shell n = 1

L-shell n = 2

3s 3p M-shell n = 3

3d

4s

4p 4d

Energy

N-shell n = 4




Electrons

Adapted from Fig 24


Chapter 1 - 15



Survey of Elements


(stable)

1s 2 2s 2 2p 6 3s 2 3p 6 (stable)

1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 4s 2 4p 6 (stable)

Atomic

18

36

Element

1s 1 1 Hydrogen

1s 2 2 Helium

1s 2 2s 1 3 Lithium


1s 2 2s 2 2p 1 5 Boron

1s 2 2s 2 2p 2 6 Carbon



1s 2 2s 2 2p 6 3s 2 3p 1 13 Aluminum

Argon

Krypton



Chapter 1 - 16






1s2 2s2 2p2

valence electrons

Chapter 1 - 17


Adapted from

Fig 26

Callister amp

Rethwisch 8e



to become + ions



to become - ions

giv

e u

p 1

e-

giv

e u

p 2

e-

giv

e u

p 3

e- inert

gases

accept 1e

-

accept 2e

-

O

Se

Te

Po At

I

Br

He

Ne

Ar

Kr

Xe

Rn

F

Cl S

Li Be

H

Na Mg

Ba Cs

Ra Fr

Ca K Sc

Sr Rb Y

Chapter 1 - 18






Electronegativity


Chapter 1 - 19


donates accepts

electrons electrons



[Ne] 3s2

Mg2+ 1s2 2s2 2p6 O2- 1s2 2s2 2p6

[Ne] [Ne]

Chapter 1 - 20




bull Example NaCl

Ionic Bonding

Na (metal) unstable


electron


Na (cation) stable

Cl (anion) stable

Chapter 1 - 21

Ionic Bonding






Chapter 1 - 22

Ionic Bonding



terms


Net energy EN

Repulsive energy ER


r A

n r B

EN = EA + ER = + -



Chapter 1 - 23






NaCl

MgO

CaF 2 CsCl

Chapter 1 - 24






all directions

Adapted from Fig 29


Chapter 1 - 25

C has 4 valence e-

needs 4 more

H has 1 valence e-

needs 1 more

Electronegativities

are comparable




dominate bonding



H

H

H

H

C

CH4

Chapter 1 - 26

Mixed Bonding


ionic character =



) 100 ( x

1-e-

(XA-XB )2

4


)2153(

2

-

--


Chapter 1 - 27

Metallic Bonding






Chapter 1 - 28




-general case

-ex liquid HCl

-ex polymer






Bonding



H H H H

H2 H2

secondary bonding

ex liquid H2

H Cl H Cl secondary

bonding

secondary bonding

+ - + -

secondary bonding

Chapter 1 - 29

Type

Ionic

Covalent

Metallic

Secondary

Bond Energy

Large

Variable

large-Diamond

small-Bismuth

Variable

large-Tungsten

small-Mercury

Smallest

Comments


Directional


polymer chains)


Directional


inter-molecular

Summary Bonding

Chapter 1 - 30

bull Bond Length r

bull Bond Energy Eo




r o r

Energy

r

larger Tm

smaller Tm

Eo =


Energy

r o r

unstretched length

Chapter 1 - 31






= E F

A0

D L

L0

Hookes Law

s = E e

s

Linear- elastic

E

e

F


Chapter 1 - 32

Ceramics



large E

small a

Metals

(Metallic bonding)


moderate E

moderate a

Summary



small Tm

small E

large a

Chapter 1 - 33



bull Unit cells








Single crystal

Polycrystalline

Amorphous



Solids

Chapter 1 - 34

Core Problems Ex 33

ANNOUNCEMENTS

Reading 31-37 317

38-315

Chapter 1 - 35

SUMMARY













Chapter 1 - 36



allotropy)

SUMMARY








Chapter 1 - 37




lower energies

Energy and Packing

Energy

r



Energy

r



Chapter 1 - 38


-metals

-many ceramics

-some polymers



-complex structures

-rapid cooling

crystalline SiO2


CampR8e


CampR8e


Si Oxygen

bull typical of

bull occurs for

Chapter 1 - 39




radii are the same








Chapter 1 - 40






Chapter 1 - 41


APF =

a 3

4

3 p (05a) 3 1

atoms

unit cell atom

volume

unit cell

volume



Volume of unit cell

assume hard spheres



a

R=05a


Chapter 1 - 42








Chapter 1 - 43


a

APF =

4

3 p ( 3 a4 ) 3 2

atoms

unit cell atom

volume

a 3

unit cell

volume

length = 4R =


3 a


a R Adapted from

Fig 32(a) CampR8e

a 2

a 3

Chapter 1 - 44









Chapter 1 - 45




APF =

4

3 p ( 2 a4 ) 3 4

atoms

unit cell atom

volume

a 3

unit cell

volume


length = 4R = 2 a


a

2 a

Adapted from

Fig 31(a)

CampR8e

Chapter 1 - 46

A sites

B B

B

B B

B B

C sites

C C

C A

B

B sites


bull 2D Projection

bull FCC Unit Cell


B B

B

B B

B B

B sites C C

C A

C C

C A

A B

C

Chapter 1 - 47



bull APF = 074



CampR8e


(HCP)

6 atomsunit cell

ex Cd Mg Ti Zn

bull ca = 1633

c

a

A sites

B sites


Middle layer

Top layer

Chapter 1 - 48



A = atomic weight




Density = r =

VC NA

n A r =



Chapter 1 - 49

bull Ex Cr (BCC)

A = 5200 gmol

R = 0125 nm


rtheoretical

a = 4R 3 = 02887 nm

ractual

a R

r = a3

5200 2

atoms

unit cell mol

g

unit cell

volume atoms

mol

6022 x 1023


= 718 gcm3

= 719 gcm3

Adapted from

Fig 32(a) CampR8e

Chapter 1 - 50



Why


r (g

cm

)

3


Metals Alloys

Composites fibers

Polymers

1

2

2 0




3

4

5

03

04

05

Magnesium

Aluminum

Steels

Titanium

CuNi

Tin Zinc

Silver Mo


G raphite

Silicon



Zirconia

H DPE PS PP LDPE

PC

PTFE

PET PVC Silicone

Wood

AFRE

CFRE

GFRE

Glass fibers

Carbon fibers

A ramid fibers


(metallic bonding)





(often amorphous)



In general

Chapter 1 - 51

Chapter 1 - 52

Chapter 1 - 53

Chapter 1 - 54

Fig 34 CampR8e

Crystal Systems

7 crystal systems

14 crystal lattices




Chapter 1 - 55

Chapter 1 - 56

Point Coordinates





z

x

y a b

c

000

111

y

z

2c

b

b

Chapter 1 - 57



through origin





[uvw]

ex 1 0 frac12 =gt 2 0 1 =gt [ 201 ]

-1 1 1


z

x

Algorithm


negative index

[ 111 ] =gt

y

Chapter 1 - 58


direction

a = 0405 nm

Linear Density


a

[110]


Number of atoms

atoms

length

1 35 nm

a 2

2 LD -

Adapted from

Fig 31(a)

CampR8e

Chapter 1 -

BCC vs simple cubic

59

Chapter 1 -

BCC vs Simple C





60

Chapter 1 -

On to HCP






c

Chapter 1 -

Reading


bull 4-1 ndash 4-7

bull 5-1 ndash 5-5

62

Chapter 1 - 63



through origin





[uvtw]

[ 1120 ] ex frac12 frac12 -1 0 =gt


CampR8e



a2

a3

-a3

2

a 2

2

a 1

- a3

a1

a2

z

Algorithm


Chapter 1 - 64




as follows

w w

t

v

u

) v u ( + -

) u v 2 ( 3

1 -

) v u 2 ( 3

1 -

] uvtw [ ] w v u [

Fig 38(a) CampR8e

- a3

a1

a2

z

Chapter 1 - 65



CampR8e

Chapter 1 - 66




Chapter 1 - 67


x

y a b

c


example a b c z

x

y a b

c


1 Intercepts 1 1


1 1 0 3 Reduction 1 1 0

1 Intercepts 12


2 0 0 3 Reduction 2 0 0

example a b c

Chapter 1 - 68


z

x

y a b

c



a b c


2 1 43

3 Reduction 6 3 4

(001) (010)


(100) (010) (001) Ex 100 = (100)

Chapter 1 - 69



used

example a1 a2 a3 c



1 0

-1

-1

1

1


a2

a3

a1

z


CampR8e

Chapter 1 - 70






important


for Fe


planes

Chapter 1 - 71



(100)


R 3

3 4 a


2D repeat unit


1

atoms

2D repeat unit

= nm2

atoms 121

m2

atoms = 12 x 1019

1

2

R 3

3 4 area

2D repeat unit

Chapter 1 - 72







others

-- diamond single


-- turbine blades




GE Superabrasives


permission)


Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 11

Atomic Structure




1 amuatom = 1gmol

C 12011 H 1008 etc

167 x 10-27 kg

Chapter 1 - 12

Atomic Structure



1) Chemical

2) Electrical

3) Thermal

4) Optical

Chapter 1 - 13


bull

Quantum Designation





Chapter 1 - 14


1s

2s 2p

K-shell n = 1

L-shell n = 2

3s 3p M-shell n = 3

3d

4s

4p 4d

Energy

N-shell n = 4




Electrons

Adapted from Fig 24


Chapter 1 - 15



Survey of Elements


(stable)

1s 2 2s 2 2p 6 3s 2 3p 6 (stable)

1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 4s 2 4p 6 (stable)

Atomic

18

36

Element

1s 1 1 Hydrogen

1s 2 2 Helium

1s 2 2s 1 3 Lithium


1s 2 2s 2 2p 1 5 Boron

1s 2 2s 2 2p 2 6 Carbon



1s 2 2s 2 2p 6 3s 2 3p 1 13 Aluminum

Argon

Krypton



Chapter 1 - 16






1s2 2s2 2p2

valence electrons

Chapter 1 - 17


Adapted from

Fig 26

Callister amp

Rethwisch 8e



to become + ions



to become - ions

giv

e u

p 1

e-

giv

e u

p 2

e-

giv

e u

p 3

e- inert

gases

accept 1e

-

accept 2e

-

O

Se

Te

Po At

I

Br

He

Ne

Ar

Kr

Xe

Rn

F

Cl S

Li Be

H

Na Mg

Ba Cs

Ra Fr

Ca K Sc

Sr Rb Y

Chapter 1 - 18






Electronegativity


Chapter 1 - 19


donates accepts

electrons electrons



[Ne] 3s2

Mg2+ 1s2 2s2 2p6 O2- 1s2 2s2 2p6

[Ne] [Ne]

Chapter 1 - 20




bull Example NaCl

Ionic Bonding

Na (metal) unstable


electron


Na (cation) stable

Cl (anion) stable

Chapter 1 - 21

Ionic Bonding






Chapter 1 - 22

Ionic Bonding



terms


Net energy EN

Repulsive energy ER


r A

n r B

EN = EA + ER = + -



Chapter 1 - 23






NaCl

MgO

CaF 2 CsCl

Chapter 1 - 24






all directions

Adapted from Fig 29


Chapter 1 - 25

C has 4 valence e-

needs 4 more

H has 1 valence e-

needs 1 more

Electronegativities

are comparable




dominate bonding



H

H

H

H

C

CH4

Chapter 1 - 26

Mixed Bonding


ionic character =



) 100 ( x

1-e-

(XA-XB )2

4


)2153(

2

-

--


Chapter 1 - 27

Metallic Bonding






Chapter 1 - 28




-general case

-ex liquid HCl

-ex polymer






Bonding



H H H H

H2 H2

secondary bonding

ex liquid H2

H Cl H Cl secondary

bonding

secondary bonding

+ - + -

secondary bonding

Chapter 1 - 29

Type

Ionic

Covalent

Metallic

Secondary

Bond Energy

Large

Variable

large-Diamond

small-Bismuth

Variable

large-Tungsten

small-Mercury

Smallest

Comments


Directional


polymer chains)


Directional


inter-molecular

Summary Bonding

Chapter 1 - 30

bull Bond Length r

bull Bond Energy Eo




r o r

Energy

r

larger Tm

smaller Tm

Eo =


Energy

r o r

unstretched length

Chapter 1 - 31






= E F

A0

D L

L0

Hookes Law

s = E e

s

Linear- elastic

E

e

F


Chapter 1 - 32

Ceramics



large E

small a

Metals

(Metallic bonding)


moderate E

moderate a

Summary



small Tm

small E

large a

Chapter 1 - 33



bull Unit cells








Single crystal

Polycrystalline

Amorphous



Solids

Chapter 1 - 34

Core Problems Ex 33

ANNOUNCEMENTS

Reading 31-37 317

38-315

Chapter 1 - 35

SUMMARY













Chapter 1 - 36



allotropy)

SUMMARY








Chapter 1 - 37




lower energies

Energy and Packing

Energy

r



Energy

r



Chapter 1 - 38


-metals

-many ceramics

-some polymers



-complex structures

-rapid cooling

crystalline SiO2


CampR8e


CampR8e


Si Oxygen

bull typical of

bull occurs for

Chapter 1 - 39




radii are the same








Chapter 1 - 40






Chapter 1 - 41


APF =

a 3

4

3 p (05a) 3 1

atoms

unit cell atom

volume

unit cell

volume



Volume of unit cell

assume hard spheres



a

R=05a


Chapter 1 - 42








Chapter 1 - 43


a

APF =

4

3 p ( 3 a4 ) 3 2

atoms

unit cell atom

volume

a 3

unit cell

volume

length = 4R =


3 a


a R Adapted from

Fig 32(a) CampR8e

a 2

a 3

Chapter 1 - 44









Chapter 1 - 45




APF =

4

3 p ( 2 a4 ) 3 4

atoms

unit cell atom

volume

a 3

unit cell

volume


length = 4R = 2 a


a

2 a

Adapted from

Fig 31(a)

CampR8e

Chapter 1 - 46

A sites

B B

B

B B

B B

C sites

C C

C A

B

B sites


bull 2D Projection

bull FCC Unit Cell


B B

B

B B

B B

B sites C C

C A

C C

C A

A B

C

Chapter 1 - 47



bull APF = 074



CampR8e


(HCP)

6 atomsunit cell

ex Cd Mg Ti Zn

bull ca = 1633

c

a

A sites

B sites


Middle layer

Top layer

Chapter 1 - 48



A = atomic weight




Density = r =

VC NA

n A r =



Chapter 1 - 49

bull Ex Cr (BCC)

A = 5200 gmol

R = 0125 nm


rtheoretical

a = 4R 3 = 02887 nm

ractual

a R

r = a3

5200 2

atoms

unit cell mol

g

unit cell

volume atoms

mol

6022 x 1023


= 718 gcm3

= 719 gcm3

Adapted from

Fig 32(a) CampR8e

Chapter 1 - 50



Why


r (g

cm

)

3


Metals Alloys

Composites fibers

Polymers

1

2

2 0




3

4

5

03

04

05

Magnesium

Aluminum

Steels

Titanium

CuNi

Tin Zinc

Silver Mo


G raphite

Silicon



Zirconia

H DPE PS PP LDPE

PC

PTFE

PET PVC Silicone

Wood

AFRE

CFRE

GFRE

Glass fibers

Carbon fibers

A ramid fibers


(metallic bonding)





(often amorphous)



In general

Chapter 1 - 51

Chapter 1 - 52

Chapter 1 - 53

Chapter 1 - 54

Fig 34 CampR8e

Crystal Systems

7 crystal systems

14 crystal lattices




Chapter 1 - 55

Chapter 1 - 56

Point Coordinates





z

x

y a b

c

000

111

y

z

2c

b

b

Chapter 1 - 57



through origin





[uvw]

ex 1 0 frac12 =gt 2 0 1 =gt [ 201 ]

-1 1 1


z

x

Algorithm


negative index

[ 111 ] =gt

y

Chapter 1 - 58


direction

a = 0405 nm

Linear Density


a

[110]


Number of atoms

atoms

length

1 35 nm

a 2

2 LD -

Adapted from

Fig 31(a)

CampR8e

Chapter 1 -

BCC vs simple cubic

59

Chapter 1 -

BCC vs Simple C





60

Chapter 1 -

On to HCP






c

Chapter 1 -

Reading


bull 4-1 ndash 4-7

bull 5-1 ndash 5-5

62

Chapter 1 - 63



through origin





[uvtw]

[ 1120 ] ex frac12 frac12 -1 0 =gt


CampR8e



a2

a3

-a3

2

a 2

2

a 1

- a3

a1

a2

z

Algorithm


Chapter 1 - 64




as follows

w w

t

v

u

) v u ( + -

) u v 2 ( 3

1 -

) v u 2 ( 3

1 -

] uvtw [ ] w v u [

Fig 38(a) CampR8e

- a3

a1

a2

z

Chapter 1 - 65



CampR8e

Chapter 1 - 66




Chapter 1 - 67


x

y a b

c


example a b c z

x

y a b

c


1 Intercepts 1 1


1 1 0 3 Reduction 1 1 0

1 Intercepts 12


2 0 0 3 Reduction 2 0 0

example a b c

Chapter 1 - 68


z

x

y a b

c



a b c


2 1 43

3 Reduction 6 3 4

(001) (010)


(100) (010) (001) Ex 100 = (100)

Chapter 1 - 69



used

example a1 a2 a3 c



1 0

-1

-1

1

1


a2

a3

a1

z


CampR8e

Chapter 1 - 70






important


for Fe


planes

Chapter 1 - 71



(100)


R 3

3 4 a


2D repeat unit


1

atoms

2D repeat unit

= nm2

atoms 121

m2

atoms = 12 x 1019

1

2

R 3

3 4 area

2D repeat unit

Chapter 1 - 72







others

-- diamond single


-- turbine blades




GE Superabrasives


permission)


Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 12

Atomic Structure



1) Chemical

2) Electrical

3) Thermal

4) Optical

Chapter 1 - 13


bull

Quantum Designation





Chapter 1 - 14


1s

2s 2p

K-shell n = 1

L-shell n = 2

3s 3p M-shell n = 3

3d

4s

4p 4d

Energy

N-shell n = 4




Electrons

Adapted from Fig 24


Chapter 1 - 15



Survey of Elements


(stable)

1s 2 2s 2 2p 6 3s 2 3p 6 (stable)

1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 4s 2 4p 6 (stable)

Atomic

18

36

Element

1s 1 1 Hydrogen

1s 2 2 Helium

1s 2 2s 1 3 Lithium


1s 2 2s 2 2p 1 5 Boron

1s 2 2s 2 2p 2 6 Carbon



1s 2 2s 2 2p 6 3s 2 3p 1 13 Aluminum

Argon

Krypton



Chapter 1 - 16






1s2 2s2 2p2

valence electrons

Chapter 1 - 17


Adapted from

Fig 26

Callister amp

Rethwisch 8e



to become + ions



to become - ions

giv

e u

p 1

e-

giv

e u

p 2

e-

giv

e u

p 3

e- inert

gases

accept 1e

-

accept 2e

-

O

Se

Te

Po At

I

Br

He

Ne

Ar

Kr

Xe

Rn

F

Cl S

Li Be

H

Na Mg

Ba Cs

Ra Fr

Ca K Sc

Sr Rb Y

Chapter 1 - 18






Electronegativity


Chapter 1 - 19


donates accepts

electrons electrons



[Ne] 3s2

Mg2+ 1s2 2s2 2p6 O2- 1s2 2s2 2p6

[Ne] [Ne]

Chapter 1 - 20




bull Example NaCl

Ionic Bonding

Na (metal) unstable


electron


Na (cation) stable

Cl (anion) stable

Chapter 1 - 21

Ionic Bonding






Chapter 1 - 22

Ionic Bonding



terms


Net energy EN

Repulsive energy ER


r A

n r B

EN = EA + ER = + -



Chapter 1 - 23






NaCl

MgO

CaF 2 CsCl

Chapter 1 - 24






all directions

Adapted from Fig 29


Chapter 1 - 25

C has 4 valence e-

needs 4 more

H has 1 valence e-

needs 1 more

Electronegativities

are comparable




dominate bonding



H

H

H

H

C

CH4

Chapter 1 - 26

Mixed Bonding


ionic character =



) 100 ( x

1-e-

(XA-XB )2

4


)2153(

2

-

--


Chapter 1 - 27

Metallic Bonding






Chapter 1 - 28




-general case

-ex liquid HCl

-ex polymer






Bonding



H H H H

H2 H2

secondary bonding

ex liquid H2

H Cl H Cl secondary

bonding

secondary bonding

+ - + -

secondary bonding

Chapter 1 - 29

Type

Ionic

Covalent

Metallic

Secondary

Bond Energy

Large

Variable

large-Diamond

small-Bismuth

Variable

large-Tungsten

small-Mercury

Smallest

Comments


Directional


polymer chains)


Directional


inter-molecular

Summary Bonding

Chapter 1 - 30

bull Bond Length r

bull Bond Energy Eo




r o r

Energy

r

larger Tm

smaller Tm

Eo =


Energy

r o r

unstretched length

Chapter 1 - 31






= E F

A0

D L

L0

Hookes Law

s = E e

s

Linear- elastic

E

e

F


Chapter 1 - 32

Ceramics



large E

small a

Metals

(Metallic bonding)


moderate E

moderate a

Summary



small Tm

small E

large a

Chapter 1 - 33



bull Unit cells








Single crystal

Polycrystalline

Amorphous



Solids

Chapter 1 - 34

Core Problems Ex 33

ANNOUNCEMENTS

Reading 31-37 317

38-315

Chapter 1 - 35

SUMMARY













Chapter 1 - 36



allotropy)

SUMMARY








Chapter 1 - 37




lower energies

Energy and Packing

Energy

r



Energy

r



Chapter 1 - 38


-metals

-many ceramics

-some polymers



-complex structures

-rapid cooling

crystalline SiO2


CampR8e


CampR8e


Si Oxygen

bull typical of

bull occurs for

Chapter 1 - 39




radii are the same








Chapter 1 - 40






Chapter 1 - 41


APF =

a 3

4

3 p (05a) 3 1

atoms

unit cell atom

volume

unit cell

volume



Volume of unit cell

assume hard spheres



a

R=05a


Chapter 1 - 42








Chapter 1 - 43


a

APF =

4

3 p ( 3 a4 ) 3 2

atoms

unit cell atom

volume

a 3

unit cell

volume

length = 4R =


3 a


a R Adapted from

Fig 32(a) CampR8e

a 2

a 3

Chapter 1 - 44









Chapter 1 - 45




APF =

4

3 p ( 2 a4 ) 3 4

atoms

unit cell atom

volume

a 3

unit cell

volume


length = 4R = 2 a


a

2 a

Adapted from

Fig 31(a)

CampR8e

Chapter 1 - 46

A sites

B B

B

B B

B B

C sites

C C

C A

B

B sites


bull 2D Projection

bull FCC Unit Cell


B B

B

B B

B B

B sites C C

C A

C C

C A

A B

C

Chapter 1 - 47



bull APF = 074



CampR8e


(HCP)

6 atomsunit cell

ex Cd Mg Ti Zn

bull ca = 1633

c

a

A sites

B sites


Middle layer

Top layer

Chapter 1 - 48



A = atomic weight




Density = r =

VC NA

n A r =



Chapter 1 - 49

bull Ex Cr (BCC)

A = 5200 gmol

R = 0125 nm


rtheoretical

a = 4R 3 = 02887 nm

ractual

a R

r = a3

5200 2

atoms

unit cell mol

g

unit cell

volume atoms

mol

6022 x 1023


= 718 gcm3

= 719 gcm3

Adapted from

Fig 32(a) CampR8e

Chapter 1 - 50



Why


r (g

cm

)

3


Metals Alloys

Composites fibers

Polymers

1

2

2 0




3

4

5

03

04

05

Magnesium

Aluminum

Steels

Titanium

CuNi

Tin Zinc

Silver Mo


G raphite

Silicon



Zirconia

H DPE PS PP LDPE

PC

PTFE

PET PVC Silicone

Wood

AFRE

CFRE

GFRE

Glass fibers

Carbon fibers

A ramid fibers


(metallic bonding)





(often amorphous)



In general

Chapter 1 - 51

Chapter 1 - 52

Chapter 1 - 53

Chapter 1 - 54

Fig 34 CampR8e

Crystal Systems

7 crystal systems

14 crystal lattices




Chapter 1 - 55

Chapter 1 - 56

Point Coordinates





z

x

y a b

c

000

111

y

z

2c

b

b

Chapter 1 - 57



through origin





[uvw]

ex 1 0 frac12 =gt 2 0 1 =gt [ 201 ]

-1 1 1


z

x

Algorithm


negative index

[ 111 ] =gt

y

Chapter 1 - 58


direction

a = 0405 nm

Linear Density


a

[110]


Number of atoms

atoms

length

1 35 nm

a 2

2 LD -

Adapted from

Fig 31(a)

CampR8e

Chapter 1 -

BCC vs simple cubic

59

Chapter 1 -

BCC vs Simple C





60

Chapter 1 -

On to HCP






c

Chapter 1 -

Reading


bull 4-1 ndash 4-7

bull 5-1 ndash 5-5

62

Chapter 1 - 63



through origin





[uvtw]

[ 1120 ] ex frac12 frac12 -1 0 =gt


CampR8e



a2

a3

-a3

2

a 2

2

a 1

- a3

a1

a2

z

Algorithm


Chapter 1 - 64




as follows

w w

t

v

u

) v u ( + -

) u v 2 ( 3

1 -

) v u 2 ( 3

1 -

] uvtw [ ] w v u [

Fig 38(a) CampR8e

- a3

a1

a2

z

Chapter 1 - 65



CampR8e

Chapter 1 - 66




Chapter 1 - 67


x

y a b

c


example a b c z

x

y a b

c


1 Intercepts 1 1


1 1 0 3 Reduction 1 1 0

1 Intercepts 12


2 0 0 3 Reduction 2 0 0

example a b c

Chapter 1 - 68


z

x

y a b

c



a b c


2 1 43

3 Reduction 6 3 4

(001) (010)


(100) (010) (001) Ex 100 = (100)

Chapter 1 - 69



used

example a1 a2 a3 c



1 0

-1

-1

1

1


a2

a3

a1

z


CampR8e

Chapter 1 - 70






important


for Fe


planes

Chapter 1 - 71



(100)


R 3

3 4 a


2D repeat unit


1

atoms

2D repeat unit

= nm2

atoms 121

m2

atoms = 12 x 1019

1

2

R 3

3 4 area

2D repeat unit

Chapter 1 - 72







others

-- diamond single


-- turbine blades




GE Superabrasives


permission)


Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 13


bull

Quantum Designation





Chapter 1 - 14


1s

2s 2p

K-shell n = 1

L-shell n = 2

3s 3p M-shell n = 3

3d

4s

4p 4d

Energy

N-shell n = 4




Electrons

Adapted from Fig 24


Chapter 1 - 15



Survey of Elements


(stable)

1s 2 2s 2 2p 6 3s 2 3p 6 (stable)

1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 4s 2 4p 6 (stable)

Atomic

18

36

Element

1s 1 1 Hydrogen

1s 2 2 Helium

1s 2 2s 1 3 Lithium


1s 2 2s 2 2p 1 5 Boron

1s 2 2s 2 2p 2 6 Carbon



1s 2 2s 2 2p 6 3s 2 3p 1 13 Aluminum

Argon

Krypton



Chapter 1 - 16






1s2 2s2 2p2

valence electrons

Chapter 1 - 17


Adapted from

Fig 26

Callister amp

Rethwisch 8e



to become + ions



to become - ions

giv

e u

p 1

e-

giv

e u

p 2

e-

giv

e u

p 3

e- inert

gases

accept 1e

-

accept 2e

-

O

Se

Te

Po At

I

Br

He

Ne

Ar

Kr

Xe

Rn

F

Cl S

Li Be

H

Na Mg

Ba Cs

Ra Fr

Ca K Sc

Sr Rb Y

Chapter 1 - 18






Electronegativity


Chapter 1 - 19


donates accepts

electrons electrons



[Ne] 3s2

Mg2+ 1s2 2s2 2p6 O2- 1s2 2s2 2p6

[Ne] [Ne]

Chapter 1 - 20




bull Example NaCl

Ionic Bonding

Na (metal) unstable


electron


Na (cation) stable

Cl (anion) stable

Chapter 1 - 21

Ionic Bonding






Chapter 1 - 22

Ionic Bonding



terms


Net energy EN

Repulsive energy ER


r A

n r B

EN = EA + ER = + -



Chapter 1 - 23






NaCl

MgO

CaF 2 CsCl

Chapter 1 - 24






all directions

Adapted from Fig 29


Chapter 1 - 25

C has 4 valence e-

needs 4 more

H has 1 valence e-

needs 1 more

Electronegativities

are comparable




dominate bonding



H

H

H

H

C

CH4

Chapter 1 - 26

Mixed Bonding


ionic character =



) 100 ( x

1-e-

(XA-XB )2

4


)2153(

2

-

--


Chapter 1 - 27

Metallic Bonding






Chapter 1 - 28




-general case

-ex liquid HCl

-ex polymer






Bonding



H H H H

H2 H2

secondary bonding

ex liquid H2

H Cl H Cl secondary

bonding

secondary bonding

+ - + -

secondary bonding

Chapter 1 - 29

Type

Ionic

Covalent

Metallic

Secondary

Bond Energy

Large

Variable

large-Diamond

small-Bismuth

Variable

large-Tungsten

small-Mercury

Smallest

Comments


Directional


polymer chains)


Directional


inter-molecular

Summary Bonding

Chapter 1 - 30

bull Bond Length r

bull Bond Energy Eo




r o r

Energy

r

larger Tm

smaller Tm

Eo =


Energy

r o r

unstretched length

Chapter 1 - 31






= E F

A0

D L

L0

Hookes Law

s = E e

s

Linear- elastic

E

e

F


Chapter 1 - 32

Ceramics



large E

small a

Metals

(Metallic bonding)


moderate E

moderate a

Summary



small Tm

small E

large a

Chapter 1 - 33



bull Unit cells








Single crystal

Polycrystalline

Amorphous



Solids

Chapter 1 - 34

Core Problems Ex 33

ANNOUNCEMENTS

Reading 31-37 317

38-315

Chapter 1 - 35

SUMMARY













Chapter 1 - 36



allotropy)

SUMMARY








Chapter 1 - 37




lower energies

Energy and Packing

Energy

r



Energy

r



Chapter 1 - 38


-metals

-many ceramics

-some polymers



-complex structures

-rapid cooling

crystalline SiO2


CampR8e


CampR8e


Si Oxygen

bull typical of

bull occurs for

Chapter 1 - 39




radii are the same








Chapter 1 - 40






Chapter 1 - 41


APF =

a 3

4

3 p (05a) 3 1

atoms

unit cell atom

volume

unit cell

volume



Volume of unit cell

assume hard spheres



a

R=05a


Chapter 1 - 42








Chapter 1 - 43


a

APF =

4

3 p ( 3 a4 ) 3 2

atoms

unit cell atom

volume

a 3

unit cell

volume

length = 4R =


3 a


a R Adapted from

Fig 32(a) CampR8e

a 2

a 3

Chapter 1 - 44









Chapter 1 - 45




APF =

4

3 p ( 2 a4 ) 3 4

atoms

unit cell atom

volume

a 3

unit cell

volume


length = 4R = 2 a


a

2 a

Adapted from

Fig 31(a)

CampR8e

Chapter 1 - 46

A sites

B B

B

B B

B B

C sites

C C

C A

B

B sites


bull 2D Projection

bull FCC Unit Cell


B B

B

B B

B B

B sites C C

C A

C C

C A

A B

C

Chapter 1 - 47



bull APF = 074



CampR8e


(HCP)

6 atomsunit cell

ex Cd Mg Ti Zn

bull ca = 1633

c

a

A sites

B sites


Middle layer

Top layer

Chapter 1 - 48



A = atomic weight




Density = r =

VC NA

n A r =



Chapter 1 - 49

bull Ex Cr (BCC)

A = 5200 gmol

R = 0125 nm


rtheoretical

a = 4R 3 = 02887 nm

ractual

a R

r = a3

5200 2

atoms

unit cell mol

g

unit cell

volume atoms

mol

6022 x 1023


= 718 gcm3

= 719 gcm3

Adapted from

Fig 32(a) CampR8e

Chapter 1 - 50



Why


r (g

cm

)

3


Metals Alloys

Composites fibers

Polymers

1

2

2 0




3

4

5

03

04

05

Magnesium

Aluminum

Steels

Titanium

CuNi

Tin Zinc

Silver Mo


G raphite

Silicon



Zirconia

H DPE PS PP LDPE

PC

PTFE

PET PVC Silicone

Wood

AFRE

CFRE

GFRE

Glass fibers

Carbon fibers

A ramid fibers


(metallic bonding)





(often amorphous)



In general

Chapter 1 - 51

Chapter 1 - 52

Chapter 1 - 53

Chapter 1 - 54

Fig 34 CampR8e

Crystal Systems

7 crystal systems

14 crystal lattices




Chapter 1 - 55

Chapter 1 - 56

Point Coordinates





z

x

y a b

c

000

111

y

z

2c

b

b

Chapter 1 - 57



through origin





[uvw]

ex 1 0 frac12 =gt 2 0 1 =gt [ 201 ]

-1 1 1


z

x

Algorithm


negative index

[ 111 ] =gt

y

Chapter 1 - 58


direction

a = 0405 nm

Linear Density


a

[110]


Number of atoms

atoms

length

1 35 nm

a 2

2 LD -

Adapted from

Fig 31(a)

CampR8e

Chapter 1 -

BCC vs simple cubic

59

Chapter 1 -

BCC vs Simple C





60

Chapter 1 -

On to HCP






c

Chapter 1 -

Reading


bull 4-1 ndash 4-7

bull 5-1 ndash 5-5

62

Chapter 1 - 63



through origin





[uvtw]

[ 1120 ] ex frac12 frac12 -1 0 =gt


CampR8e



a2

a3

-a3

2

a 2

2

a 1

- a3

a1

a2

z

Algorithm


Chapter 1 - 64




as follows

w w

t

v

u

) v u ( + -

) u v 2 ( 3

1 -

) v u 2 ( 3

1 -

] uvtw [ ] w v u [

Fig 38(a) CampR8e

- a3

a1

a2

z

Chapter 1 - 65



CampR8e

Chapter 1 - 66




Chapter 1 - 67


x

y a b

c


example a b c z

x

y a b

c


1 Intercepts 1 1


1 1 0 3 Reduction 1 1 0

1 Intercepts 12


2 0 0 3 Reduction 2 0 0

example a b c

Chapter 1 - 68


z

x

y a b

c



a b c


2 1 43

3 Reduction 6 3 4

(001) (010)


(100) (010) (001) Ex 100 = (100)

Chapter 1 - 69



used

example a1 a2 a3 c



1 0

-1

-1

1

1


a2

a3

a1

z


CampR8e

Chapter 1 - 70






important


for Fe


planes

Chapter 1 - 71



(100)


R 3

3 4 a


2D repeat unit


1

atoms

2D repeat unit

= nm2

atoms 121

m2

atoms = 12 x 1019

1

2

R 3

3 4 area

2D repeat unit

Chapter 1 - 72







others

-- diamond single


-- turbine blades




GE Superabrasives


permission)


Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 14


1s

2s 2p

K-shell n = 1

L-shell n = 2

3s 3p M-shell n = 3

3d

4s

4p 4d

Energy

N-shell n = 4




Electrons

Adapted from Fig 24


Chapter 1 - 15



Survey of Elements


(stable)

1s 2 2s 2 2p 6 3s 2 3p 6 (stable)

1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 4s 2 4p 6 (stable)

Atomic

18

36

Element

1s 1 1 Hydrogen

1s 2 2 Helium

1s 2 2s 1 3 Lithium


1s 2 2s 2 2p 1 5 Boron

1s 2 2s 2 2p 2 6 Carbon



1s 2 2s 2 2p 6 3s 2 3p 1 13 Aluminum

Argon

Krypton



Chapter 1 - 16






1s2 2s2 2p2

valence electrons

Chapter 1 - 17


Adapted from

Fig 26

Callister amp

Rethwisch 8e



to become + ions



to become - ions

giv

e u

p 1

e-

giv

e u

p 2

e-

giv

e u

p 3

e- inert

gases

accept 1e

-

accept 2e

-

O

Se

Te

Po At

I

Br

He

Ne

Ar

Kr

Xe

Rn

F

Cl S

Li Be

H

Na Mg

Ba Cs

Ra Fr

Ca K Sc

Sr Rb Y

Chapter 1 - 18






Electronegativity


Chapter 1 - 19


donates accepts

electrons electrons



[Ne] 3s2

Mg2+ 1s2 2s2 2p6 O2- 1s2 2s2 2p6

[Ne] [Ne]

Chapter 1 - 20




bull Example NaCl

Ionic Bonding

Na (metal) unstable


electron


Na (cation) stable

Cl (anion) stable

Chapter 1 - 21

Ionic Bonding






Chapter 1 - 22

Ionic Bonding



terms


Net energy EN

Repulsive energy ER


r A

n r B

EN = EA + ER = + -



Chapter 1 - 23






NaCl

MgO

CaF 2 CsCl

Chapter 1 - 24






all directions

Adapted from Fig 29


Chapter 1 - 25

C has 4 valence e-

needs 4 more

H has 1 valence e-

needs 1 more

Electronegativities

are comparable




dominate bonding



H

H

H

H

C

CH4

Chapter 1 - 26

Mixed Bonding


ionic character =



) 100 ( x

1-e-

(XA-XB )2

4


)2153(

2

-

--


Chapter 1 - 27

Metallic Bonding






Chapter 1 - 28




-general case

-ex liquid HCl

-ex polymer






Bonding



H H H H

H2 H2

secondary bonding

ex liquid H2

H Cl H Cl secondary

bonding

secondary bonding

+ - + -

secondary bonding

Chapter 1 - 29

Type

Ionic

Covalent

Metallic

Secondary

Bond Energy

Large

Variable

large-Diamond

small-Bismuth

Variable

large-Tungsten

small-Mercury

Smallest

Comments


Directional


polymer chains)


Directional


inter-molecular

Summary Bonding

Chapter 1 - 30

bull Bond Length r

bull Bond Energy Eo




r o r

Energy

r

larger Tm

smaller Tm

Eo =


Energy

r o r

unstretched length

Chapter 1 - 31






= E F

A0

D L

L0

Hookes Law

s = E e

s

Linear- elastic

E

e

F


Chapter 1 - 32

Ceramics



large E

small a

Metals

(Metallic bonding)


moderate E

moderate a

Summary



small Tm

small E

large a

Chapter 1 - 33



bull Unit cells








Single crystal

Polycrystalline

Amorphous



Solids

Chapter 1 - 34

Core Problems Ex 33

ANNOUNCEMENTS

Reading 31-37 317

38-315

Chapter 1 - 35

SUMMARY













Chapter 1 - 36



allotropy)

SUMMARY








Chapter 1 - 37




lower energies

Energy and Packing

Energy

r



Energy

r



Chapter 1 - 38


-metals

-many ceramics

-some polymers



-complex structures

-rapid cooling

crystalline SiO2


CampR8e


CampR8e


Si Oxygen

bull typical of

bull occurs for

Chapter 1 - 39




radii are the same








Chapter 1 - 40






Chapter 1 - 41


APF =

a 3

4

3 p (05a) 3 1

atoms

unit cell atom

volume

unit cell

volume



Volume of unit cell

assume hard spheres



a

R=05a


Chapter 1 - 42








Chapter 1 - 43


a

APF =

4

3 p ( 3 a4 ) 3 2

atoms

unit cell atom

volume

a 3

unit cell

volume

length = 4R =


3 a


a R Adapted from

Fig 32(a) CampR8e

a 2

a 3

Chapter 1 - 44









Chapter 1 - 45




APF =

4

3 p ( 2 a4 ) 3 4

atoms

unit cell atom

volume

a 3

unit cell

volume


length = 4R = 2 a


a

2 a

Adapted from

Fig 31(a)

CampR8e

Chapter 1 - 46

A sites

B B

B

B B

B B

C sites

C C

C A

B

B sites


bull 2D Projection

bull FCC Unit Cell


B B

B

B B

B B

B sites C C

C A

C C

C A

A B

C

Chapter 1 - 47



bull APF = 074



CampR8e


(HCP)

6 atomsunit cell

ex Cd Mg Ti Zn

bull ca = 1633

c

a

A sites

B sites


Middle layer

Top layer

Chapter 1 - 48



A = atomic weight




Density = r =

VC NA

n A r =



Chapter 1 - 49

bull Ex Cr (BCC)

A = 5200 gmol

R = 0125 nm


rtheoretical

a = 4R 3 = 02887 nm

ractual

a R

r = a3

5200 2

atoms

unit cell mol

g

unit cell

volume atoms

mol

6022 x 1023


= 718 gcm3

= 719 gcm3

Adapted from

Fig 32(a) CampR8e

Chapter 1 - 50



Why


r (g

cm

)

3


Metals Alloys

Composites fibers

Polymers

1

2

2 0




3

4

5

03

04

05

Magnesium

Aluminum

Steels

Titanium

CuNi

Tin Zinc

Silver Mo


G raphite

Silicon



Zirconia

H DPE PS PP LDPE

PC

PTFE

PET PVC Silicone

Wood

AFRE

CFRE

GFRE

Glass fibers

Carbon fibers

A ramid fibers


(metallic bonding)





(often amorphous)



In general

Chapter 1 - 51

Chapter 1 - 52

Chapter 1 - 53

Chapter 1 - 54

Fig 34 CampR8e

Crystal Systems

7 crystal systems

14 crystal lattices




Chapter 1 - 55

Chapter 1 - 56

Point Coordinates





z

x

y a b

c

000

111

y

z

2c

b

b

Chapter 1 - 57



through origin





[uvw]

ex 1 0 frac12 =gt 2 0 1 =gt [ 201 ]

-1 1 1


z

x

Algorithm


negative index

[ 111 ] =gt

y

Chapter 1 - 58


direction

a = 0405 nm

Linear Density


a

[110]


Number of atoms

atoms

length

1 35 nm

a 2

2 LD -

Adapted from

Fig 31(a)

CampR8e

Chapter 1 -

BCC vs simple cubic

59

Chapter 1 -

BCC vs Simple C





60

Chapter 1 -

On to HCP






c

Chapter 1 -

Reading


bull 4-1 ndash 4-7

bull 5-1 ndash 5-5

62

Chapter 1 - 63



through origin





[uvtw]

[ 1120 ] ex frac12 frac12 -1 0 =gt


CampR8e



a2

a3

-a3

2

a 2

2

a 1

- a3

a1

a2

z

Algorithm


Chapter 1 - 64




as follows

w w

t

v

u

) v u ( + -

) u v 2 ( 3

1 -

) v u 2 ( 3

1 -

] uvtw [ ] w v u [

Fig 38(a) CampR8e

- a3

a1

a2

z

Chapter 1 - 65



CampR8e

Chapter 1 - 66




Chapter 1 - 67


x

y a b

c


example a b c z

x

y a b

c


1 Intercepts 1 1


1 1 0 3 Reduction 1 1 0

1 Intercepts 12


2 0 0 3 Reduction 2 0 0

example a b c

Chapter 1 - 68


z

x

y a b

c



a b c


2 1 43

3 Reduction 6 3 4

(001) (010)


(100) (010) (001) Ex 100 = (100)

Chapter 1 - 69



used

example a1 a2 a3 c



1 0

-1

-1

1

1


a2

a3

a1

z


CampR8e

Chapter 1 - 70






important


for Fe


planes

Chapter 1 - 71



(100)


R 3

3 4 a


2D repeat unit


1

atoms

2D repeat unit

= nm2

atoms 121

m2

atoms = 12 x 1019

1

2

R 3

3 4 area

2D repeat unit

Chapter 1 - 72







others

-- diamond single


-- turbine blades




GE Superabrasives


permission)


Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 15



Survey of Elements


(stable)

1s 2 2s 2 2p 6 3s 2 3p 6 (stable)

1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 4s 2 4p 6 (stable)

Atomic

18

36

Element

1s 1 1 Hydrogen

1s 2 2 Helium

1s 2 2s 1 3 Lithium


1s 2 2s 2 2p 1 5 Boron

1s 2 2s 2 2p 2 6 Carbon



1s 2 2s 2 2p 6 3s 2 3p 1 13 Aluminum

Argon

Krypton



Chapter 1 - 16






1s2 2s2 2p2

valence electrons

Chapter 1 - 17


Adapted from

Fig 26

Callister amp

Rethwisch 8e



to become + ions



to become - ions

giv

e u

p 1

e-

giv

e u

p 2

e-

giv

e u

p 3

e- inert

gases

accept 1e

-

accept 2e

-

O

Se

Te

Po At

I

Br

He

Ne

Ar

Kr

Xe

Rn

F

Cl S

Li Be

H

Na Mg

Ba Cs

Ra Fr

Ca K Sc

Sr Rb Y

Chapter 1 - 18






Electronegativity


Chapter 1 - 19


donates accepts

electrons electrons



[Ne] 3s2

Mg2+ 1s2 2s2 2p6 O2- 1s2 2s2 2p6

[Ne] [Ne]

Chapter 1 - 20




bull Example NaCl

Ionic Bonding

Na (metal) unstable


electron


Na (cation) stable

Cl (anion) stable

Chapter 1 - 21

Ionic Bonding






Chapter 1 - 22

Ionic Bonding



terms


Net energy EN

Repulsive energy ER


r A

n r B

EN = EA + ER = + -



Chapter 1 - 23






NaCl

MgO

CaF 2 CsCl

Chapter 1 - 24






all directions

Adapted from Fig 29


Chapter 1 - 25

C has 4 valence e-

needs 4 more

H has 1 valence e-

needs 1 more

Electronegativities

are comparable




dominate bonding



H

H

H

H

C

CH4

Chapter 1 - 26

Mixed Bonding


ionic character =



) 100 ( x

1-e-

(XA-XB )2

4


)2153(

2

-

--


Chapter 1 - 27

Metallic Bonding






Chapter 1 - 28




-general case

-ex liquid HCl

-ex polymer






Bonding



H H H H

H2 H2

secondary bonding

ex liquid H2

H Cl H Cl secondary

bonding

secondary bonding

+ - + -

secondary bonding

Chapter 1 - 29

Type

Ionic

Covalent

Metallic

Secondary

Bond Energy

Large

Variable

large-Diamond

small-Bismuth

Variable

large-Tungsten

small-Mercury

Smallest

Comments


Directional


polymer chains)


Directional


inter-molecular

Summary Bonding

Chapter 1 - 30

bull Bond Length r

bull Bond Energy Eo




r o r

Energy

r

larger Tm

smaller Tm

Eo =


Energy

r o r

unstretched length

Chapter 1 - 31






= E F

A0

D L

L0

Hookes Law

s = E e

s

Linear- elastic

E

e

F


Chapter 1 - 32

Ceramics



large E

small a

Metals

(Metallic bonding)


moderate E

moderate a

Summary



small Tm

small E

large a

Chapter 1 - 33



bull Unit cells








Single crystal

Polycrystalline

Amorphous



Solids

Chapter 1 - 34

Core Problems Ex 33

ANNOUNCEMENTS

Reading 31-37 317

38-315

Chapter 1 - 35

SUMMARY













Chapter 1 - 36



allotropy)

SUMMARY








Chapter 1 - 37




lower energies

Energy and Packing

Energy

r



Energy

r



Chapter 1 - 38


-metals

-many ceramics

-some polymers



-complex structures

-rapid cooling

crystalline SiO2


CampR8e


CampR8e


Si Oxygen

bull typical of

bull occurs for

Chapter 1 - 39




radii are the same








Chapter 1 - 40






Chapter 1 - 41


APF =

a 3

4

3 p (05a) 3 1

atoms

unit cell atom

volume

unit cell

volume



Volume of unit cell

assume hard spheres



a

R=05a


Chapter 1 - 42








Chapter 1 - 43


a

APF =

4

3 p ( 3 a4 ) 3 2

atoms

unit cell atom

volume

a 3

unit cell

volume

length = 4R =


3 a


a R Adapted from

Fig 32(a) CampR8e

a 2

a 3

Chapter 1 - 44









Chapter 1 - 45




APF =

4

3 p ( 2 a4 ) 3 4

atoms

unit cell atom

volume

a 3

unit cell

volume


length = 4R = 2 a


a

2 a

Adapted from

Fig 31(a)

CampR8e

Chapter 1 - 46

A sites

B B

B

B B

B B

C sites

C C

C A

B

B sites


bull 2D Projection

bull FCC Unit Cell


B B

B

B B

B B

B sites C C

C A

C C

C A

A B

C

Chapter 1 - 47



bull APF = 074



CampR8e


(HCP)

6 atomsunit cell

ex Cd Mg Ti Zn

bull ca = 1633

c

a

A sites

B sites


Middle layer

Top layer

Chapter 1 - 48



A = atomic weight




Density = r =

VC NA

n A r =



Chapter 1 - 49

bull Ex Cr (BCC)

A = 5200 gmol

R = 0125 nm


rtheoretical

a = 4R 3 = 02887 nm

ractual

a R

r = a3

5200 2

atoms

unit cell mol

g

unit cell

volume atoms

mol

6022 x 1023


= 718 gcm3

= 719 gcm3

Adapted from

Fig 32(a) CampR8e

Chapter 1 - 50



Why


r (g

cm

)

3


Metals Alloys

Composites fibers

Polymers

1

2

2 0




3

4

5

03

04

05

Magnesium

Aluminum

Steels

Titanium

CuNi

Tin Zinc

Silver Mo


G raphite

Silicon



Zirconia

H DPE PS PP LDPE

PC

PTFE

PET PVC Silicone

Wood

AFRE

CFRE

GFRE

Glass fibers

Carbon fibers

A ramid fibers


(metallic bonding)





(often amorphous)



In general

Chapter 1 - 51

Chapter 1 - 52

Chapter 1 - 53

Chapter 1 - 54

Fig 34 CampR8e

Crystal Systems

7 crystal systems

14 crystal lattices




Chapter 1 - 55

Chapter 1 - 56

Point Coordinates





z

x

y a b

c

000

111

y

z

2c

b

b

Chapter 1 - 57



through origin





[uvw]

ex 1 0 frac12 =gt 2 0 1 =gt [ 201 ]

-1 1 1


z

x

Algorithm


negative index

[ 111 ] =gt

y

Chapter 1 - 58


direction

a = 0405 nm

Linear Density


a

[110]


Number of atoms

atoms

length

1 35 nm

a 2

2 LD -

Adapted from

Fig 31(a)

CampR8e

Chapter 1 -

BCC vs simple cubic

59

Chapter 1 -

BCC vs Simple C





60

Chapter 1 -

On to HCP






c

Chapter 1 -

Reading


bull 4-1 ndash 4-7

bull 5-1 ndash 5-5

62

Chapter 1 - 63



through origin





[uvtw]

[ 1120 ] ex frac12 frac12 -1 0 =gt


CampR8e



a2

a3

-a3

2

a 2

2

a 1

- a3

a1

a2

z

Algorithm


Chapter 1 - 64




as follows

w w

t

v

u

) v u ( + -

) u v 2 ( 3

1 -

) v u 2 ( 3

1 -

] uvtw [ ] w v u [

Fig 38(a) CampR8e

- a3

a1

a2

z

Chapter 1 - 65



CampR8e

Chapter 1 - 66




Chapter 1 - 67


x

y a b

c


example a b c z

x

y a b

c


1 Intercepts 1 1


1 1 0 3 Reduction 1 1 0

1 Intercepts 12


2 0 0 3 Reduction 2 0 0

example a b c

Chapter 1 - 68


z

x

y a b

c



a b c


2 1 43

3 Reduction 6 3 4

(001) (010)


(100) (010) (001) Ex 100 = (100)

Chapter 1 - 69



used

example a1 a2 a3 c



1 0

-1

-1

1

1


a2

a3

a1

z


CampR8e

Chapter 1 - 70






important


for Fe


planes

Chapter 1 - 71



(100)


R 3

3 4 a


2D repeat unit


1

atoms

2D repeat unit

= nm2

atoms 121

m2

atoms = 12 x 1019

1

2

R 3

3 4 area

2D repeat unit

Chapter 1 - 72







others

-- diamond single


-- turbine blades




GE Superabrasives


permission)


Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 16






1s2 2s2 2p2

valence electrons

Chapter 1 - 17


Adapted from

Fig 26

Callister amp

Rethwisch 8e



to become + ions



to become - ions

giv

e u

p 1

e-

giv

e u

p 2

e-

giv

e u

p 3

e- inert

gases

accept 1e

-

accept 2e

-

O

Se

Te

Po At

I

Br

He

Ne

Ar

Kr

Xe

Rn

F

Cl S

Li Be

H

Na Mg

Ba Cs

Ra Fr

Ca K Sc

Sr Rb Y

Chapter 1 - 18






Electronegativity


Chapter 1 - 19


donates accepts

electrons electrons



[Ne] 3s2

Mg2+ 1s2 2s2 2p6 O2- 1s2 2s2 2p6

[Ne] [Ne]

Chapter 1 - 20




bull Example NaCl

Ionic Bonding

Na (metal) unstable


electron


Na (cation) stable

Cl (anion) stable

Chapter 1 - 21

Ionic Bonding






Chapter 1 - 22

Ionic Bonding



terms


Net energy EN

Repulsive energy ER


r A

n r B

EN = EA + ER = + -



Chapter 1 - 23






NaCl

MgO

CaF 2 CsCl

Chapter 1 - 24






all directions

Adapted from Fig 29


Chapter 1 - 25

C has 4 valence e-

needs 4 more

H has 1 valence e-

needs 1 more

Electronegativities

are comparable




dominate bonding



H

H

H

H

C

CH4

Chapter 1 - 26

Mixed Bonding


ionic character =



) 100 ( x

1-e-

(XA-XB )2

4


)2153(

2

-

--


Chapter 1 - 27

Metallic Bonding






Chapter 1 - 28




-general case

-ex liquid HCl

-ex polymer






Bonding



H H H H

H2 H2

secondary bonding

ex liquid H2

H Cl H Cl secondary

bonding

secondary bonding

+ - + -

secondary bonding

Chapter 1 - 29

Type

Ionic

Covalent

Metallic

Secondary

Bond Energy

Large

Variable

large-Diamond

small-Bismuth

Variable

large-Tungsten

small-Mercury

Smallest

Comments


Directional


polymer chains)


Directional


inter-molecular

Summary Bonding

Chapter 1 - 30

bull Bond Length r

bull Bond Energy Eo




r o r

Energy

r

larger Tm

smaller Tm

Eo =


Energy

r o r

unstretched length

Chapter 1 - 31






= E F

A0

D L

L0

Hookes Law

s = E e

s

Linear- elastic

E

e

F


Chapter 1 - 32

Ceramics



large E

small a

Metals

(Metallic bonding)


moderate E

moderate a

Summary



small Tm

small E

large a

Chapter 1 - 33



bull Unit cells








Single crystal

Polycrystalline

Amorphous



Solids

Chapter 1 - 34

Core Problems Ex 33

ANNOUNCEMENTS

Reading 31-37 317

38-315

Chapter 1 - 35

SUMMARY













Chapter 1 - 36



allotropy)

SUMMARY








Chapter 1 - 37




lower energies

Energy and Packing

Energy

r



Energy

r



Chapter 1 - 38


-metals

-many ceramics

-some polymers



-complex structures

-rapid cooling

crystalline SiO2


CampR8e


CampR8e


Si Oxygen

bull typical of

bull occurs for

Chapter 1 - 39




radii are the same








Chapter 1 - 40






Chapter 1 - 41


APF =

a 3

4

3 p (05a) 3 1

atoms

unit cell atom

volume

unit cell

volume



Volume of unit cell

assume hard spheres



a

R=05a


Chapter 1 - 42








Chapter 1 - 43


a

APF =

4

3 p ( 3 a4 ) 3 2

atoms

unit cell atom

volume

a 3

unit cell

volume

length = 4R =


3 a


a R Adapted from

Fig 32(a) CampR8e

a 2

a 3

Chapter 1 - 44









Chapter 1 - 45




APF =

4

3 p ( 2 a4 ) 3 4

atoms

unit cell atom

volume

a 3

unit cell

volume


length = 4R = 2 a


a

2 a

Adapted from

Fig 31(a)

CampR8e

Chapter 1 - 46

A sites

B B

B

B B

B B

C sites

C C

C A

B

B sites


bull 2D Projection

bull FCC Unit Cell


B B

B

B B

B B

B sites C C

C A

C C

C A

A B

C

Chapter 1 - 47



bull APF = 074



CampR8e


(HCP)

6 atomsunit cell

ex Cd Mg Ti Zn

bull ca = 1633

c

a

A sites

B sites


Middle layer

Top layer

Chapter 1 - 48



A = atomic weight




Density = r =

VC NA

n A r =



Chapter 1 - 49

bull Ex Cr (BCC)

A = 5200 gmol

R = 0125 nm


rtheoretical

a = 4R 3 = 02887 nm

ractual

a R

r = a3

5200 2

atoms

unit cell mol

g

unit cell

volume atoms

mol

6022 x 1023


= 718 gcm3

= 719 gcm3

Adapted from

Fig 32(a) CampR8e

Chapter 1 - 50



Why


r (g

cm

)

3


Metals Alloys

Composites fibers

Polymers

1

2

2 0




3

4

5

03

04

05

Magnesium

Aluminum

Steels

Titanium

CuNi

Tin Zinc

Silver Mo


G raphite

Silicon



Zirconia

H DPE PS PP LDPE

PC

PTFE

PET PVC Silicone

Wood

AFRE

CFRE

GFRE

Glass fibers

Carbon fibers

A ramid fibers


(metallic bonding)





(often amorphous)



In general

Chapter 1 - 51

Chapter 1 - 52

Chapter 1 - 53

Chapter 1 - 54

Fig 34 CampR8e

Crystal Systems

7 crystal systems

14 crystal lattices




Chapter 1 - 55

Chapter 1 - 56

Point Coordinates





z

x

y a b

c

000

111

y

z

2c

b

b

Chapter 1 - 57



through origin





[uvw]

ex 1 0 frac12 =gt 2 0 1 =gt [ 201 ]

-1 1 1


z

x

Algorithm


negative index

[ 111 ] =gt

y

Chapter 1 - 58


direction

a = 0405 nm

Linear Density


a

[110]


Number of atoms

atoms

length

1 35 nm

a 2

2 LD -

Adapted from

Fig 31(a)

CampR8e

Chapter 1 -

BCC vs simple cubic

59

Chapter 1 -

BCC vs Simple C





60

Chapter 1 -

On to HCP






c

Chapter 1 -

Reading


bull 4-1 ndash 4-7

bull 5-1 ndash 5-5

62

Chapter 1 - 63



through origin





[uvtw]

[ 1120 ] ex frac12 frac12 -1 0 =gt


CampR8e



a2

a3

-a3

2

a 2

2

a 1

- a3

a1

a2

z

Algorithm


Chapter 1 - 64




as follows

w w

t

v

u

) v u ( + -

) u v 2 ( 3

1 -

) v u 2 ( 3

1 -

] uvtw [ ] w v u [

Fig 38(a) CampR8e

- a3

a1

a2

z

Chapter 1 - 65



CampR8e

Chapter 1 - 66




Chapter 1 - 67


x

y a b

c


example a b c z

x

y a b

c


1 Intercepts 1 1


1 1 0 3 Reduction 1 1 0

1 Intercepts 12


2 0 0 3 Reduction 2 0 0

example a b c

Chapter 1 - 68


z

x

y a b

c



a b c


2 1 43

3 Reduction 6 3 4

(001) (010)


(100) (010) (001) Ex 100 = (100)

Chapter 1 - 69



used

example a1 a2 a3 c



1 0

-1

-1

1

1


a2

a3

a1

z


CampR8e

Chapter 1 - 70






important


for Fe


planes

Chapter 1 - 71



(100)


R 3

3 4 a


2D repeat unit


1

atoms

2D repeat unit

= nm2

atoms 121

m2

atoms = 12 x 1019

1

2

R 3

3 4 area

2D repeat unit

Chapter 1 - 72







others

-- diamond single


-- turbine blades




GE Superabrasives


permission)


Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 17


Adapted from

Fig 26

Callister amp

Rethwisch 8e



to become + ions



to become - ions

giv

e u

p 1

e-

giv

e u

p 2

e-

giv

e u

p 3

e- inert

gases

accept 1e

-

accept 2e

-

O

Se

Te

Po At

I

Br

He

Ne

Ar

Kr

Xe

Rn

F

Cl S

Li Be

H

Na Mg

Ba Cs

Ra Fr

Ca K Sc

Sr Rb Y

Chapter 1 - 18






Electronegativity


Chapter 1 - 19


donates accepts

electrons electrons



[Ne] 3s2

Mg2+ 1s2 2s2 2p6 O2- 1s2 2s2 2p6

[Ne] [Ne]

Chapter 1 - 20




bull Example NaCl

Ionic Bonding

Na (metal) unstable


electron


Na (cation) stable

Cl (anion) stable

Chapter 1 - 21

Ionic Bonding






Chapter 1 - 22

Ionic Bonding



terms


Net energy EN

Repulsive energy ER


r A

n r B

EN = EA + ER = + -



Chapter 1 - 23






NaCl

MgO

CaF 2 CsCl

Chapter 1 - 24






all directions

Adapted from Fig 29


Chapter 1 - 25

C has 4 valence e-

needs 4 more

H has 1 valence e-

needs 1 more

Electronegativities

are comparable




dominate bonding



H

H

H

H

C

CH4

Chapter 1 - 26

Mixed Bonding


ionic character =



) 100 ( x

1-e-

(XA-XB )2

4


)2153(

2

-

--


Chapter 1 - 27

Metallic Bonding






Chapter 1 - 28




-general case

-ex liquid HCl

-ex polymer






Bonding



H H H H

H2 H2

secondary bonding

ex liquid H2

H Cl H Cl secondary

bonding

secondary bonding

+ - + -

secondary bonding

Chapter 1 - 29

Type

Ionic

Covalent

Metallic

Secondary

Bond Energy

Large

Variable

large-Diamond

small-Bismuth

Variable

large-Tungsten

small-Mercury

Smallest

Comments


Directional


polymer chains)


Directional


inter-molecular

Summary Bonding

Chapter 1 - 30

bull Bond Length r

bull Bond Energy Eo




r o r

Energy

r

larger Tm

smaller Tm

Eo =


Energy

r o r

unstretched length

Chapter 1 - 31






= E F

A0

D L

L0

Hookes Law

s = E e

s

Linear- elastic

E

e

F


Chapter 1 - 32

Ceramics



large E

small a

Metals

(Metallic bonding)


moderate E

moderate a

Summary



small Tm

small E

large a

Chapter 1 - 33



bull Unit cells








Single crystal

Polycrystalline

Amorphous



Solids

Chapter 1 - 34

Core Problems Ex 33

ANNOUNCEMENTS

Reading 31-37 317

38-315

Chapter 1 - 35

SUMMARY













Chapter 1 - 36



allotropy)

SUMMARY








Chapter 1 - 37




lower energies

Energy and Packing

Energy

r



Energy

r



Chapter 1 - 38


-metals

-many ceramics

-some polymers



-complex structures

-rapid cooling

crystalline SiO2


CampR8e


CampR8e


Si Oxygen

bull typical of

bull occurs for

Chapter 1 - 39




radii are the same








Chapter 1 - 40






Chapter 1 - 41


APF =

a 3

4

3 p (05a) 3 1

atoms

unit cell atom

volume

unit cell

volume



Volume of unit cell

assume hard spheres



a

R=05a


Chapter 1 - 42








Chapter 1 - 43


a

APF =

4

3 p ( 3 a4 ) 3 2

atoms

unit cell atom

volume

a 3

unit cell

volume

length = 4R =


3 a


a R Adapted from

Fig 32(a) CampR8e

a 2

a 3

Chapter 1 - 44









Chapter 1 - 45




APF =

4

3 p ( 2 a4 ) 3 4

atoms

unit cell atom

volume

a 3

unit cell

volume


length = 4R = 2 a


a

2 a

Adapted from

Fig 31(a)

CampR8e

Chapter 1 - 46

A sites

B B

B

B B

B B

C sites

C C

C A

B

B sites


bull 2D Projection

bull FCC Unit Cell


B B

B

B B

B B

B sites C C

C A

C C

C A

A B

C

Chapter 1 - 47



bull APF = 074



CampR8e


(HCP)

6 atomsunit cell

ex Cd Mg Ti Zn

bull ca = 1633

c

a

A sites

B sites


Middle layer

Top layer

Chapter 1 - 48



A = atomic weight




Density = r =

VC NA

n A r =



Chapter 1 - 49

bull Ex Cr (BCC)

A = 5200 gmol

R = 0125 nm


rtheoretical

a = 4R 3 = 02887 nm

ractual

a R

r = a3

5200 2

atoms

unit cell mol

g

unit cell

volume atoms

mol

6022 x 1023


= 718 gcm3

= 719 gcm3

Adapted from

Fig 32(a) CampR8e

Chapter 1 - 50



Why


r (g

cm

)

3


Metals Alloys

Composites fibers

Polymers

1

2

2 0




3

4

5

03

04

05

Magnesium

Aluminum

Steels

Titanium

CuNi

Tin Zinc

Silver Mo


G raphite

Silicon



Zirconia

H DPE PS PP LDPE

PC

PTFE

PET PVC Silicone

Wood

AFRE

CFRE

GFRE

Glass fibers

Carbon fibers

A ramid fibers


(metallic bonding)





(often amorphous)



In general

Chapter 1 - 51

Chapter 1 - 52

Chapter 1 - 53

Chapter 1 - 54

Fig 34 CampR8e

Crystal Systems

7 crystal systems

14 crystal lattices




Chapter 1 - 55

Chapter 1 - 56

Point Coordinates





z

x

y a b

c

000

111

y

z

2c

b

b

Chapter 1 - 57



through origin





[uvw]

ex 1 0 frac12 =gt 2 0 1 =gt [ 201 ]

-1 1 1


z

x

Algorithm


negative index

[ 111 ] =gt

y

Chapter 1 - 58


direction

a = 0405 nm

Linear Density


a

[110]


Number of atoms

atoms

length

1 35 nm

a 2

2 LD -

Adapted from

Fig 31(a)

CampR8e

Chapter 1 -

BCC vs simple cubic

59

Chapter 1 -

BCC vs Simple C





60

Chapter 1 -

On to HCP






c

Chapter 1 -

Reading


bull 4-1 ndash 4-7

bull 5-1 ndash 5-5

62

Chapter 1 - 63



through origin





[uvtw]

[ 1120 ] ex frac12 frac12 -1 0 =gt


CampR8e



a2

a3

-a3

2

a 2

2

a 1

- a3

a1

a2

z

Algorithm


Chapter 1 - 64




as follows

w w

t

v

u

) v u ( + -

) u v 2 ( 3

1 -

) v u 2 ( 3

1 -

] uvtw [ ] w v u [

Fig 38(a) CampR8e

- a3

a1

a2

z

Chapter 1 - 65



CampR8e

Chapter 1 - 66




Chapter 1 - 67


x

y a b

c


example a b c z

x

y a b

c


1 Intercepts 1 1


1 1 0 3 Reduction 1 1 0

1 Intercepts 12


2 0 0 3 Reduction 2 0 0

example a b c

Chapter 1 - 68


z

x

y a b

c



a b c


2 1 43

3 Reduction 6 3 4

(001) (010)


(100) (010) (001) Ex 100 = (100)

Chapter 1 - 69



used

example a1 a2 a3 c



1 0

-1

-1

1

1


a2

a3

a1

z


CampR8e

Chapter 1 - 70






important


for Fe


planes

Chapter 1 - 71



(100)


R 3

3 4 a


2D repeat unit


1

atoms

2D repeat unit

= nm2

atoms 121

m2

atoms = 12 x 1019

1

2

R 3

3 4 area

2D repeat unit

Chapter 1 - 72







others

-- diamond single


-- turbine blades




GE Superabrasives


permission)


Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 18






Electronegativity


Chapter 1 - 19


donates accepts

electrons electrons



[Ne] 3s2

Mg2+ 1s2 2s2 2p6 O2- 1s2 2s2 2p6

[Ne] [Ne]

Chapter 1 - 20




bull Example NaCl

Ionic Bonding

Na (metal) unstable


electron


Na (cation) stable

Cl (anion) stable

Chapter 1 - 21

Ionic Bonding






Chapter 1 - 22

Ionic Bonding



terms


Net energy EN

Repulsive energy ER


r A

n r B

EN = EA + ER = + -



Chapter 1 - 23






NaCl

MgO

CaF 2 CsCl

Chapter 1 - 24






all directions

Adapted from Fig 29


Chapter 1 - 25

C has 4 valence e-

needs 4 more

H has 1 valence e-

needs 1 more

Electronegativities

are comparable




dominate bonding



H

H

H

H

C

CH4

Chapter 1 - 26

Mixed Bonding


ionic character =



) 100 ( x

1-e-

(XA-XB )2

4


)2153(

2

-

--


Chapter 1 - 27

Metallic Bonding






Chapter 1 - 28




-general case

-ex liquid HCl

-ex polymer






Bonding



H H H H

H2 H2

secondary bonding

ex liquid H2

H Cl H Cl secondary

bonding

secondary bonding

+ - + -

secondary bonding

Chapter 1 - 29

Type

Ionic

Covalent

Metallic

Secondary

Bond Energy

Large

Variable

large-Diamond

small-Bismuth

Variable

large-Tungsten

small-Mercury

Smallest

Comments


Directional


polymer chains)


Directional


inter-molecular

Summary Bonding

Chapter 1 - 30

bull Bond Length r

bull Bond Energy Eo




r o r

Energy

r

larger Tm

smaller Tm

Eo =


Energy

r o r

unstretched length

Chapter 1 - 31






= E F

A0

D L

L0

Hookes Law

s = E e

s

Linear- elastic

E

e

F


Chapter 1 - 32

Ceramics



large E

small a

Metals

(Metallic bonding)


moderate E

moderate a

Summary



small Tm

small E

large a

Chapter 1 - 33



bull Unit cells








Single crystal

Polycrystalline

Amorphous



Solids

Chapter 1 - 34

Core Problems Ex 33

ANNOUNCEMENTS

Reading 31-37 317

38-315

Chapter 1 - 35

SUMMARY













Chapter 1 - 36



allotropy)

SUMMARY








Chapter 1 - 37




lower energies

Energy and Packing

Energy

r



Energy

r



Chapter 1 - 38


-metals

-many ceramics

-some polymers



-complex structures

-rapid cooling

crystalline SiO2


CampR8e


CampR8e


Si Oxygen

bull typical of

bull occurs for

Chapter 1 - 39




radii are the same








Chapter 1 - 40






Chapter 1 - 41


APF =

a 3

4

3 p (05a) 3 1

atoms

unit cell atom

volume

unit cell

volume



Volume of unit cell

assume hard spheres



a

R=05a


Chapter 1 - 42








Chapter 1 - 43


a

APF =

4

3 p ( 3 a4 ) 3 2

atoms

unit cell atom

volume

a 3

unit cell

volume

length = 4R =


3 a


a R Adapted from

Fig 32(a) CampR8e

a 2

a 3

Chapter 1 - 44









Chapter 1 - 45




APF =

4

3 p ( 2 a4 ) 3 4

atoms

unit cell atom

volume

a 3

unit cell

volume


length = 4R = 2 a


a

2 a

Adapted from

Fig 31(a)

CampR8e

Chapter 1 - 46

A sites

B B

B

B B

B B

C sites

C C

C A

B

B sites


bull 2D Projection

bull FCC Unit Cell


B B

B

B B

B B

B sites C C

C A

C C

C A

A B

C

Chapter 1 - 47



bull APF = 074



CampR8e


(HCP)

6 atomsunit cell

ex Cd Mg Ti Zn

bull ca = 1633

c

a

A sites

B sites


Middle layer

Top layer

Chapter 1 - 48



A = atomic weight




Density = r =

VC NA

n A r =



Chapter 1 - 49

bull Ex Cr (BCC)

A = 5200 gmol

R = 0125 nm


rtheoretical

a = 4R 3 = 02887 nm

ractual

a R

r = a3

5200 2

atoms

unit cell mol

g

unit cell

volume atoms

mol

6022 x 1023


= 718 gcm3

= 719 gcm3

Adapted from

Fig 32(a) CampR8e

Chapter 1 - 50



Why


r (g

cm

)

3


Metals Alloys

Composites fibers

Polymers

1

2

2 0




3

4

5

03

04

05

Magnesium

Aluminum

Steels

Titanium

CuNi

Tin Zinc

Silver Mo


G raphite

Silicon



Zirconia

H DPE PS PP LDPE

PC

PTFE

PET PVC Silicone

Wood

AFRE

CFRE

GFRE

Glass fibers

Carbon fibers

A ramid fibers


(metallic bonding)





(often amorphous)



In general

Chapter 1 - 51

Chapter 1 - 52

Chapter 1 - 53

Chapter 1 - 54

Fig 34 CampR8e

Crystal Systems

7 crystal systems

14 crystal lattices




Chapter 1 - 55

Chapter 1 - 56

Point Coordinates





z

x

y a b

c

000

111

y

z

2c

b

b

Chapter 1 - 57



through origin





[uvw]

ex 1 0 frac12 =gt 2 0 1 =gt [ 201 ]

-1 1 1


z

x

Algorithm


negative index

[ 111 ] =gt

y

Chapter 1 - 58


direction

a = 0405 nm

Linear Density


a

[110]


Number of atoms

atoms

length

1 35 nm

a 2

2 LD -

Adapted from

Fig 31(a)

CampR8e

Chapter 1 -

BCC vs simple cubic

59

Chapter 1 -

BCC vs Simple C





60

Chapter 1 -

On to HCP






c

Chapter 1 -

Reading


bull 4-1 ndash 4-7

bull 5-1 ndash 5-5

62

Chapter 1 - 63



through origin





[uvtw]

[ 1120 ] ex frac12 frac12 -1 0 =gt


CampR8e



a2

a3

-a3

2

a 2

2

a 1

- a3

a1

a2

z

Algorithm


Chapter 1 - 64




as follows

w w

t

v

u

) v u ( + -

) u v 2 ( 3

1 -

) v u 2 ( 3

1 -

] uvtw [ ] w v u [

Fig 38(a) CampR8e

- a3

a1

a2

z

Chapter 1 - 65



CampR8e

Chapter 1 - 66




Chapter 1 - 67


x

y a b

c


example a b c z

x

y a b

c


1 Intercepts 1 1


1 1 0 3 Reduction 1 1 0

1 Intercepts 12


2 0 0 3 Reduction 2 0 0

example a b c

Chapter 1 - 68


z

x

y a b

c



a b c


2 1 43

3 Reduction 6 3 4

(001) (010)


(100) (010) (001) Ex 100 = (100)

Chapter 1 - 69



used

example a1 a2 a3 c



1 0

-1

-1

1

1


a2

a3

a1

z


CampR8e

Chapter 1 - 70






important


for Fe


planes

Chapter 1 - 71



(100)


R 3

3 4 a


2D repeat unit


1

atoms

2D repeat unit

= nm2

atoms 121

m2

atoms = 12 x 1019

1

2

R 3

3 4 area

2D repeat unit

Chapter 1 - 72







others

-- diamond single


-- turbine blades




GE Superabrasives


permission)


Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 19


donates accepts

electrons electrons



[Ne] 3s2

Mg2+ 1s2 2s2 2p6 O2- 1s2 2s2 2p6

[Ne] [Ne]

Chapter 1 - 20




bull Example NaCl

Ionic Bonding

Na (metal) unstable


electron


Na (cation) stable

Cl (anion) stable

Chapter 1 - 21

Ionic Bonding






Chapter 1 - 22

Ionic Bonding



terms


Net energy EN

Repulsive energy ER


r A

n r B

EN = EA + ER = + -



Chapter 1 - 23






NaCl

MgO

CaF 2 CsCl

Chapter 1 - 24






all directions

Adapted from Fig 29


Chapter 1 - 25

C has 4 valence e-

needs 4 more

H has 1 valence e-

needs 1 more

Electronegativities

are comparable




dominate bonding



H

H

H

H

C

CH4

Chapter 1 - 26

Mixed Bonding


ionic character =



) 100 ( x

1-e-

(XA-XB )2

4


)2153(

2

-

--


Chapter 1 - 27

Metallic Bonding






Chapter 1 - 28




-general case

-ex liquid HCl

-ex polymer






Bonding



H H H H

H2 H2

secondary bonding

ex liquid H2

H Cl H Cl secondary

bonding

secondary bonding

+ - + -

secondary bonding

Chapter 1 - 29

Type

Ionic

Covalent

Metallic

Secondary

Bond Energy

Large

Variable

large-Diamond

small-Bismuth

Variable

large-Tungsten

small-Mercury

Smallest

Comments


Directional


polymer chains)


Directional


inter-molecular

Summary Bonding

Chapter 1 - 30

bull Bond Length r

bull Bond Energy Eo




r o r

Energy

r

larger Tm

smaller Tm

Eo =


Energy

r o r

unstretched length

Chapter 1 - 31






= E F

A0

D L

L0

Hookes Law

s = E e

s

Linear- elastic

E

e

F


Chapter 1 - 32

Ceramics



large E

small a

Metals

(Metallic bonding)


moderate E

moderate a

Summary



small Tm

small E

large a

Chapter 1 - 33



bull Unit cells








Single crystal

Polycrystalline

Amorphous



Solids

Chapter 1 - 34

Core Problems Ex 33

ANNOUNCEMENTS

Reading 31-37 317

38-315

Chapter 1 - 35

SUMMARY













Chapter 1 - 36



allotropy)

SUMMARY








Chapter 1 - 37




lower energies

Energy and Packing

Energy

r



Energy

r



Chapter 1 - 38


-metals

-many ceramics

-some polymers



-complex structures

-rapid cooling

crystalline SiO2


CampR8e


CampR8e


Si Oxygen

bull typical of

bull occurs for

Chapter 1 - 39




radii are the same








Chapter 1 - 40






Chapter 1 - 41


APF =

a 3

4

3 p (05a) 3 1

atoms

unit cell atom

volume

unit cell

volume



Volume of unit cell

assume hard spheres



a

R=05a


Chapter 1 - 42








Chapter 1 - 43


a

APF =

4

3 p ( 3 a4 ) 3 2

atoms

unit cell atom

volume

a 3

unit cell

volume

length = 4R =


3 a


a R Adapted from

Fig 32(a) CampR8e

a 2

a 3

Chapter 1 - 44









Chapter 1 - 45




APF =

4

3 p ( 2 a4 ) 3 4

atoms

unit cell atom

volume

a 3

unit cell

volume


length = 4R = 2 a


a

2 a

Adapted from

Fig 31(a)

CampR8e

Chapter 1 - 46

A sites

B B

B

B B

B B

C sites

C C

C A

B

B sites


bull 2D Projection

bull FCC Unit Cell


B B

B

B B

B B

B sites C C

C A

C C

C A

A B

C

Chapter 1 - 47



bull APF = 074



CampR8e


(HCP)

6 atomsunit cell

ex Cd Mg Ti Zn

bull ca = 1633

c

a

A sites

B sites


Middle layer

Top layer

Chapter 1 - 48



A = atomic weight




Density = r =

VC NA

n A r =



Chapter 1 - 49

bull Ex Cr (BCC)

A = 5200 gmol

R = 0125 nm


rtheoretical

a = 4R 3 = 02887 nm

ractual

a R

r = a3

5200 2

atoms

unit cell mol

g

unit cell

volume atoms

mol

6022 x 1023


= 718 gcm3

= 719 gcm3

Adapted from

Fig 32(a) CampR8e

Chapter 1 - 50



Why


r (g

cm

)

3


Metals Alloys

Composites fibers

Polymers

1

2

2 0




3

4

5

03

04

05

Magnesium

Aluminum

Steels

Titanium

CuNi

Tin Zinc

Silver Mo


G raphite

Silicon



Zirconia

H DPE PS PP LDPE

PC

PTFE

PET PVC Silicone

Wood

AFRE

CFRE

GFRE

Glass fibers

Carbon fibers

A ramid fibers


(metallic bonding)





(often amorphous)



In general

Chapter 1 - 51

Chapter 1 - 52

Chapter 1 - 53

Chapter 1 - 54

Fig 34 CampR8e

Crystal Systems

7 crystal systems

14 crystal lattices




Chapter 1 - 55

Chapter 1 - 56

Point Coordinates





z

x

y a b

c

000

111

y

z

2c

b

b

Chapter 1 - 57



through origin





[uvw]

ex 1 0 frac12 =gt 2 0 1 =gt [ 201 ]

-1 1 1


z

x

Algorithm


negative index

[ 111 ] =gt

y

Chapter 1 - 58


direction

a = 0405 nm

Linear Density


a

[110]


Number of atoms

atoms

length

1 35 nm

a 2

2 LD -

Adapted from

Fig 31(a)

CampR8e

Chapter 1 -

BCC vs simple cubic

59

Chapter 1 -

BCC vs Simple C





60

Chapter 1 -

On to HCP






c

Chapter 1 -

Reading


bull 4-1 ndash 4-7

bull 5-1 ndash 5-5

62

Chapter 1 - 63



through origin





[uvtw]

[ 1120 ] ex frac12 frac12 -1 0 =gt


CampR8e



a2

a3

-a3

2

a 2

2

a 1

- a3

a1

a2

z

Algorithm


Chapter 1 - 64




as follows

w w

t

v

u

) v u ( + -

) u v 2 ( 3

1 -

) v u 2 ( 3

1 -

] uvtw [ ] w v u [

Fig 38(a) CampR8e

- a3

a1

a2

z

Chapter 1 - 65



CampR8e

Chapter 1 - 66




Chapter 1 - 67


x

y a b

c


example a b c z

x

y a b

c


1 Intercepts 1 1


1 1 0 3 Reduction 1 1 0

1 Intercepts 12


2 0 0 3 Reduction 2 0 0

example a b c

Chapter 1 - 68


z

x

y a b

c



a b c


2 1 43

3 Reduction 6 3 4

(001) (010)


(100) (010) (001) Ex 100 = (100)

Chapter 1 - 69



used

example a1 a2 a3 c



1 0

-1

-1

1

1


a2

a3

a1

z


CampR8e

Chapter 1 - 70






important


for Fe


planes

Chapter 1 - 71



(100)


R 3

3 4 a


2D repeat unit


1

atoms

2D repeat unit

= nm2

atoms 121

m2

atoms = 12 x 1019

1

2

R 3

3 4 area

2D repeat unit

Chapter 1 - 72







others

-- diamond single


-- turbine blades




GE Superabrasives


permission)


Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 20




bull Example NaCl

Ionic Bonding

Na (metal) unstable


electron


Na (cation) stable

Cl (anion) stable

Chapter 1 - 21

Ionic Bonding






Chapter 1 - 22

Ionic Bonding



terms


Net energy EN

Repulsive energy ER


r A

n r B

EN = EA + ER = + -



Chapter 1 - 23






NaCl

MgO

CaF 2 CsCl

Chapter 1 - 24






all directions

Adapted from Fig 29


Chapter 1 - 25

C has 4 valence e-

needs 4 more

H has 1 valence e-

needs 1 more

Electronegativities

are comparable




dominate bonding



H

H

H

H

C

CH4

Chapter 1 - 26

Mixed Bonding


ionic character =



) 100 ( x

1-e-

(XA-XB )2

4


)2153(

2

-

--


Chapter 1 - 27

Metallic Bonding






Chapter 1 - 28




-general case

-ex liquid HCl

-ex polymer






Bonding



H H H H

H2 H2

secondary bonding

ex liquid H2

H Cl H Cl secondary

bonding

secondary bonding

+ - + -

secondary bonding

Chapter 1 - 29

Type

Ionic

Covalent

Metallic

Secondary

Bond Energy

Large

Variable

large-Diamond

small-Bismuth

Variable

large-Tungsten

small-Mercury

Smallest

Comments


Directional


polymer chains)


Directional


inter-molecular

Summary Bonding

Chapter 1 - 30

bull Bond Length r

bull Bond Energy Eo




r o r

Energy

r

larger Tm

smaller Tm

Eo =


Energy

r o r

unstretched length

Chapter 1 - 31






= E F

A0

D L

L0

Hookes Law

s = E e

s

Linear- elastic

E

e

F


Chapter 1 - 32

Ceramics



large E

small a

Metals

(Metallic bonding)


moderate E

moderate a

Summary



small Tm

small E

large a

Chapter 1 - 33



bull Unit cells








Single crystal

Polycrystalline

Amorphous



Solids

Chapter 1 - 34

Core Problems Ex 33

ANNOUNCEMENTS

Reading 31-37 317

38-315

Chapter 1 - 35

SUMMARY













Chapter 1 - 36



allotropy)

SUMMARY








Chapter 1 - 37




lower energies

Energy and Packing

Energy

r



Energy

r



Chapter 1 - 38


-metals

-many ceramics

-some polymers



-complex structures

-rapid cooling

crystalline SiO2


CampR8e


CampR8e


Si Oxygen

bull typical of

bull occurs for

Chapter 1 - 39




radii are the same








Chapter 1 - 40






Chapter 1 - 41


APF =

a 3

4

3 p (05a) 3 1

atoms

unit cell atom

volume

unit cell

volume



Volume of unit cell

assume hard spheres



a

R=05a


Chapter 1 - 42








Chapter 1 - 43


a

APF =

4

3 p ( 3 a4 ) 3 2

atoms

unit cell atom

volume

a 3

unit cell

volume

length = 4R =


3 a


a R Adapted from

Fig 32(a) CampR8e

a 2

a 3

Chapter 1 - 44









Chapter 1 - 45




APF =

4

3 p ( 2 a4 ) 3 4

atoms

unit cell atom

volume

a 3

unit cell

volume


length = 4R = 2 a


a

2 a

Adapted from

Fig 31(a)

CampR8e

Chapter 1 - 46

A sites

B B

B

B B

B B

C sites

C C

C A

B

B sites


bull 2D Projection

bull FCC Unit Cell


B B

B

B B

B B

B sites C C

C A

C C

C A

A B

C

Chapter 1 - 47



bull APF = 074



CampR8e


(HCP)

6 atomsunit cell

ex Cd Mg Ti Zn

bull ca = 1633

c

a

A sites

B sites


Middle layer

Top layer

Chapter 1 - 48



A = atomic weight




Density = r =

VC NA

n A r =



Chapter 1 - 49

bull Ex Cr (BCC)

A = 5200 gmol

R = 0125 nm


rtheoretical

a = 4R 3 = 02887 nm

ractual

a R

r = a3

5200 2

atoms

unit cell mol

g

unit cell

volume atoms

mol

6022 x 1023


= 718 gcm3

= 719 gcm3

Adapted from

Fig 32(a) CampR8e

Chapter 1 - 50



Why


r (g

cm

)

3


Metals Alloys

Composites fibers

Polymers

1

2

2 0




3

4

5

03

04

05

Magnesium

Aluminum

Steels

Titanium

CuNi

Tin Zinc

Silver Mo


G raphite

Silicon



Zirconia

H DPE PS PP LDPE

PC

PTFE

PET PVC Silicone

Wood

AFRE

CFRE

GFRE

Glass fibers

Carbon fibers

A ramid fibers


(metallic bonding)





(often amorphous)



In general

Chapter 1 - 51

Chapter 1 - 52

Chapter 1 - 53

Chapter 1 - 54

Fig 34 CampR8e

Crystal Systems

7 crystal systems

14 crystal lattices




Chapter 1 - 55

Chapter 1 - 56

Point Coordinates





z

x

y a b

c

000

111

y

z

2c

b

b

Chapter 1 - 57



through origin





[uvw]

ex 1 0 frac12 =gt 2 0 1 =gt [ 201 ]

-1 1 1


z

x

Algorithm


negative index

[ 111 ] =gt

y

Chapter 1 - 58


direction

a = 0405 nm

Linear Density


a

[110]


Number of atoms

atoms

length

1 35 nm

a 2

2 LD -

Adapted from

Fig 31(a)

CampR8e

Chapter 1 -

BCC vs simple cubic

59

Chapter 1 -

BCC vs Simple C





60

Chapter 1 -

On to HCP






c

Chapter 1 -

Reading


bull 4-1 ndash 4-7

bull 5-1 ndash 5-5

62

Chapter 1 - 63



through origin





[uvtw]

[ 1120 ] ex frac12 frac12 -1 0 =gt


CampR8e



a2

a3

-a3

2

a 2

2

a 1

- a3

a1

a2

z

Algorithm


Chapter 1 - 64




as follows

w w

t

v

u

) v u ( + -

) u v 2 ( 3

1 -

) v u 2 ( 3

1 -

] uvtw [ ] w v u [

Fig 38(a) CampR8e

- a3

a1

a2

z

Chapter 1 - 65



CampR8e

Chapter 1 - 66




Chapter 1 - 67


x

y a b

c


example a b c z

x

y a b

c


1 Intercepts 1 1


1 1 0 3 Reduction 1 1 0

1 Intercepts 12


2 0 0 3 Reduction 2 0 0

example a b c

Chapter 1 - 68


z

x

y a b

c



a b c


2 1 43

3 Reduction 6 3 4

(001) (010)


(100) (010) (001) Ex 100 = (100)

Chapter 1 - 69



used

example a1 a2 a3 c



1 0

-1

-1

1

1


a2

a3

a1

z


CampR8e

Chapter 1 - 70






important


for Fe


planes

Chapter 1 - 71



(100)


R 3

3 4 a


2D repeat unit


1

atoms

2D repeat unit

= nm2

atoms 121

m2

atoms = 12 x 1019

1

2

R 3

3 4 area

2D repeat unit

Chapter 1 - 72







others

-- diamond single


-- turbine blades




GE Superabrasives


permission)


Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 21

Ionic Bonding






Chapter 1 - 22

Ionic Bonding



terms


Net energy EN

Repulsive energy ER


r A

n r B

EN = EA + ER = + -



Chapter 1 - 23






NaCl

MgO

CaF 2 CsCl

Chapter 1 - 24






all directions

Adapted from Fig 29


Chapter 1 - 25

C has 4 valence e-

needs 4 more

H has 1 valence e-

needs 1 more

Electronegativities

are comparable




dominate bonding



H

H

H

H

C

CH4

Chapter 1 - 26

Mixed Bonding


ionic character =



) 100 ( x

1-e-

(XA-XB )2

4


)2153(

2

-

--


Chapter 1 - 27

Metallic Bonding






Chapter 1 - 28




-general case

-ex liquid HCl

-ex polymer






Bonding



H H H H

H2 H2

secondary bonding

ex liquid H2

H Cl H Cl secondary

bonding

secondary bonding

+ - + -

secondary bonding

Chapter 1 - 29

Type

Ionic

Covalent

Metallic

Secondary

Bond Energy

Large

Variable

large-Diamond

small-Bismuth

Variable

large-Tungsten

small-Mercury

Smallest

Comments


Directional


polymer chains)


Directional


inter-molecular

Summary Bonding

Chapter 1 - 30

bull Bond Length r

bull Bond Energy Eo




r o r

Energy

r

larger Tm

smaller Tm

Eo =


Energy

r o r

unstretched length

Chapter 1 - 31






= E F

A0

D L

L0

Hookes Law

s = E e

s

Linear- elastic

E

e

F


Chapter 1 - 32

Ceramics



large E

small a

Metals

(Metallic bonding)


moderate E

moderate a

Summary



small Tm

small E

large a

Chapter 1 - 33



bull Unit cells








Single crystal

Polycrystalline

Amorphous



Solids

Chapter 1 - 34

Core Problems Ex 33

ANNOUNCEMENTS

Reading 31-37 317

38-315

Chapter 1 - 35

SUMMARY













Chapter 1 - 36



allotropy)

SUMMARY








Chapter 1 - 37




lower energies

Energy and Packing

Energy

r



Energy

r



Chapter 1 - 38


-metals

-many ceramics

-some polymers



-complex structures

-rapid cooling

crystalline SiO2


CampR8e


CampR8e


Si Oxygen

bull typical of

bull occurs for

Chapter 1 - 39




radii are the same








Chapter 1 - 40






Chapter 1 - 41


APF =

a 3

4

3 p (05a) 3 1

atoms

unit cell atom

volume

unit cell

volume



Volume of unit cell

assume hard spheres



a

R=05a


Chapter 1 - 42








Chapter 1 - 43


a

APF =

4

3 p ( 3 a4 ) 3 2

atoms

unit cell atom

volume

a 3

unit cell

volume

length = 4R =


3 a


a R Adapted from

Fig 32(a) CampR8e

a 2

a 3

Chapter 1 - 44









Chapter 1 - 45




APF =

4

3 p ( 2 a4 ) 3 4

atoms

unit cell atom

volume

a 3

unit cell

volume


length = 4R = 2 a


a

2 a

Adapted from

Fig 31(a)

CampR8e

Chapter 1 - 46

A sites

B B

B

B B

B B

C sites

C C

C A

B

B sites


bull 2D Projection

bull FCC Unit Cell


B B

B

B B

B B

B sites C C

C A

C C

C A

A B

C

Chapter 1 - 47



bull APF = 074



CampR8e


(HCP)

6 atomsunit cell

ex Cd Mg Ti Zn

bull ca = 1633

c

a

A sites

B sites


Middle layer

Top layer

Chapter 1 - 48



A = atomic weight




Density = r =

VC NA

n A r =



Chapter 1 - 49

bull Ex Cr (BCC)

A = 5200 gmol

R = 0125 nm


rtheoretical

a = 4R 3 = 02887 nm

ractual

a R

r = a3

5200 2

atoms

unit cell mol

g

unit cell

volume atoms

mol

6022 x 1023


= 718 gcm3

= 719 gcm3

Adapted from

Fig 32(a) CampR8e

Chapter 1 - 50



Why


r (g

cm

)

3


Metals Alloys

Composites fibers

Polymers

1

2

2 0




3

4

5

03

04

05

Magnesium

Aluminum

Steels

Titanium

CuNi

Tin Zinc

Silver Mo


G raphite

Silicon



Zirconia

H DPE PS PP LDPE

PC

PTFE

PET PVC Silicone

Wood

AFRE

CFRE

GFRE

Glass fibers

Carbon fibers

A ramid fibers


(metallic bonding)





(often amorphous)



In general

Chapter 1 - 51

Chapter 1 - 52

Chapter 1 - 53

Chapter 1 - 54

Fig 34 CampR8e

Crystal Systems

7 crystal systems

14 crystal lattices




Chapter 1 - 55

Chapter 1 - 56

Point Coordinates





z

x

y a b

c

000

111

y

z

2c

b

b

Chapter 1 - 57



through origin





[uvw]

ex 1 0 frac12 =gt 2 0 1 =gt [ 201 ]

-1 1 1


z

x

Algorithm


negative index

[ 111 ] =gt

y

Chapter 1 - 58


direction

a = 0405 nm

Linear Density


a

[110]


Number of atoms

atoms

length

1 35 nm

a 2

2 LD -

Adapted from

Fig 31(a)

CampR8e

Chapter 1 -

BCC vs simple cubic

59

Chapter 1 -

BCC vs Simple C





60

Chapter 1 -

On to HCP






c

Chapter 1 -

Reading


bull 4-1 ndash 4-7

bull 5-1 ndash 5-5

62

Chapter 1 - 63



through origin





[uvtw]

[ 1120 ] ex frac12 frac12 -1 0 =gt


CampR8e



a2

a3

-a3

2

a 2

2

a 1

- a3

a1

a2

z

Algorithm


Chapter 1 - 64




as follows

w w

t

v

u

) v u ( + -

) u v 2 ( 3

1 -

) v u 2 ( 3

1 -

] uvtw [ ] w v u [

Fig 38(a) CampR8e

- a3

a1

a2

z

Chapter 1 - 65



CampR8e

Chapter 1 - 66




Chapter 1 - 67


x

y a b

c


example a b c z

x

y a b

c


1 Intercepts 1 1


1 1 0 3 Reduction 1 1 0

1 Intercepts 12


2 0 0 3 Reduction 2 0 0

example a b c

Chapter 1 - 68


z

x

y a b

c



a b c


2 1 43

3 Reduction 6 3 4

(001) (010)


(100) (010) (001) Ex 100 = (100)

Chapter 1 - 69



used

example a1 a2 a3 c



1 0

-1

-1

1

1


a2

a3

a1

z


CampR8e

Chapter 1 - 70






important


for Fe


planes

Chapter 1 - 71



(100)


R 3

3 4 a


2D repeat unit


1

atoms

2D repeat unit

= nm2

atoms 121

m2

atoms = 12 x 1019

1

2

R 3

3 4 area

2D repeat unit

Chapter 1 - 72







others

-- diamond single


-- turbine blades




GE Superabrasives


permission)


Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 22

Ionic Bonding



terms


Net energy EN

Repulsive energy ER


r A

n r B

EN = EA + ER = + -



Chapter 1 - 23






NaCl

MgO

CaF 2 CsCl

Chapter 1 - 24






all directions

Adapted from Fig 29


Chapter 1 - 25

C has 4 valence e-

needs 4 more

H has 1 valence e-

needs 1 more

Electronegativities

are comparable




dominate bonding



H

H

H

H

C

CH4

Chapter 1 - 26

Mixed Bonding


ionic character =



) 100 ( x

1-e-

(XA-XB )2

4


)2153(

2

-

--


Chapter 1 - 27

Metallic Bonding






Chapter 1 - 28




-general case

-ex liquid HCl

-ex polymer






Bonding



H H H H

H2 H2

secondary bonding

ex liquid H2

H Cl H Cl secondary

bonding

secondary bonding

+ - + -

secondary bonding

Chapter 1 - 29

Type

Ionic

Covalent

Metallic

Secondary

Bond Energy

Large

Variable

large-Diamond

small-Bismuth

Variable

large-Tungsten

small-Mercury

Smallest

Comments


Directional


polymer chains)


Directional


inter-molecular

Summary Bonding

Chapter 1 - 30

bull Bond Length r

bull Bond Energy Eo




r o r

Energy

r

larger Tm

smaller Tm

Eo =


Energy

r o r

unstretched length

Chapter 1 - 31






= E F

A0

D L

L0

Hookes Law

s = E e

s

Linear- elastic

E

e

F


Chapter 1 - 32

Ceramics



large E

small a

Metals

(Metallic bonding)


moderate E

moderate a

Summary



small Tm

small E

large a

Chapter 1 - 33



bull Unit cells








Single crystal

Polycrystalline

Amorphous



Solids

Chapter 1 - 34

Core Problems Ex 33

ANNOUNCEMENTS

Reading 31-37 317

38-315

Chapter 1 - 35

SUMMARY













Chapter 1 - 36



allotropy)

SUMMARY








Chapter 1 - 37




lower energies

Energy and Packing

Energy

r



Energy

r



Chapter 1 - 38


-metals

-many ceramics

-some polymers



-complex structures

-rapid cooling

crystalline SiO2


CampR8e


CampR8e


Si Oxygen

bull typical of

bull occurs for

Chapter 1 - 39




radii are the same








Chapter 1 - 40






Chapter 1 - 41


APF =

a 3

4

3 p (05a) 3 1

atoms

unit cell atom

volume

unit cell

volume



Volume of unit cell

assume hard spheres



a

R=05a


Chapter 1 - 42








Chapter 1 - 43


a

APF =

4

3 p ( 3 a4 ) 3 2

atoms

unit cell atom

volume

a 3

unit cell

volume

length = 4R =


3 a


a R Adapted from

Fig 32(a) CampR8e

a 2

a 3

Chapter 1 - 44









Chapter 1 - 45




APF =

4

3 p ( 2 a4 ) 3 4

atoms

unit cell atom

volume

a 3

unit cell

volume


length = 4R = 2 a


a

2 a

Adapted from

Fig 31(a)

CampR8e

Chapter 1 - 46

A sites

B B

B

B B

B B

C sites

C C

C A

B

B sites


bull 2D Projection

bull FCC Unit Cell


B B

B

B B

B B

B sites C C

C A

C C

C A

A B

C

Chapter 1 - 47



bull APF = 074



CampR8e


(HCP)

6 atomsunit cell

ex Cd Mg Ti Zn

bull ca = 1633

c

a

A sites

B sites


Middle layer

Top layer

Chapter 1 - 48



A = atomic weight




Density = r =

VC NA

n A r =



Chapter 1 - 49

bull Ex Cr (BCC)

A = 5200 gmol

R = 0125 nm


rtheoretical

a = 4R 3 = 02887 nm

ractual

a R

r = a3

5200 2

atoms

unit cell mol

g

unit cell

volume atoms

mol

6022 x 1023


= 718 gcm3

= 719 gcm3

Adapted from

Fig 32(a) CampR8e

Chapter 1 - 50



Why


r (g

cm

)

3


Metals Alloys

Composites fibers

Polymers

1

2

2 0




3

4

5

03

04

05

Magnesium

Aluminum

Steels

Titanium

CuNi

Tin Zinc

Silver Mo


G raphite

Silicon



Zirconia

H DPE PS PP LDPE

PC

PTFE

PET PVC Silicone

Wood

AFRE

CFRE

GFRE

Glass fibers

Carbon fibers

A ramid fibers


(metallic bonding)





(often amorphous)



In general

Chapter 1 - 51

Chapter 1 - 52

Chapter 1 - 53

Chapter 1 - 54

Fig 34 CampR8e

Crystal Systems

7 crystal systems

14 crystal lattices




Chapter 1 - 55

Chapter 1 - 56

Point Coordinates





z

x

y a b

c

000

111

y

z

2c

b

b

Chapter 1 - 57



through origin





[uvw]

ex 1 0 frac12 =gt 2 0 1 =gt [ 201 ]

-1 1 1


z

x

Algorithm


negative index

[ 111 ] =gt

y

Chapter 1 - 58


direction

a = 0405 nm

Linear Density


a

[110]


Number of atoms

atoms

length

1 35 nm

a 2

2 LD -

Adapted from

Fig 31(a)

CampR8e

Chapter 1 -

BCC vs simple cubic

59

Chapter 1 -

BCC vs Simple C





60

Chapter 1 -

On to HCP






c

Chapter 1 -

Reading


bull 4-1 ndash 4-7

bull 5-1 ndash 5-5

62

Chapter 1 - 63



through origin





[uvtw]

[ 1120 ] ex frac12 frac12 -1 0 =gt


CampR8e



a2

a3

-a3

2

a 2

2

a 1

- a3

a1

a2

z

Algorithm


Chapter 1 - 64




as follows

w w

t

v

u

) v u ( + -

) u v 2 ( 3

1 -

) v u 2 ( 3

1 -

] uvtw [ ] w v u [

Fig 38(a) CampR8e

- a3

a1

a2

z

Chapter 1 - 65



CampR8e

Chapter 1 - 66




Chapter 1 - 67


x

y a b

c


example a b c z

x

y a b

c


1 Intercepts 1 1


1 1 0 3 Reduction 1 1 0

1 Intercepts 12


2 0 0 3 Reduction 2 0 0

example a b c

Chapter 1 - 68


z

x

y a b

c



a b c


2 1 43

3 Reduction 6 3 4

(001) (010)


(100) (010) (001) Ex 100 = (100)

Chapter 1 - 69



used

example a1 a2 a3 c



1 0

-1

-1

1

1


a2

a3

a1

z


CampR8e

Chapter 1 - 70






important


for Fe


planes

Chapter 1 - 71



(100)


R 3

3 4 a


2D repeat unit


1

atoms

2D repeat unit

= nm2

atoms 121

m2

atoms = 12 x 1019

1

2

R 3

3 4 area

2D repeat unit

Chapter 1 - 72







others

-- diamond single


-- turbine blades




GE Superabrasives


permission)


Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 23






NaCl

MgO

CaF 2 CsCl

Chapter 1 - 24






all directions

Adapted from Fig 29


Chapter 1 - 25

C has 4 valence e-

needs 4 more

H has 1 valence e-

needs 1 more

Electronegativities

are comparable




dominate bonding



H

H

H

H

C

CH4

Chapter 1 - 26

Mixed Bonding


ionic character =



) 100 ( x

1-e-

(XA-XB )2

4


)2153(

2

-

--


Chapter 1 - 27

Metallic Bonding






Chapter 1 - 28




-general case

-ex liquid HCl

-ex polymer






Bonding



H H H H

H2 H2

secondary bonding

ex liquid H2

H Cl H Cl secondary

bonding

secondary bonding

+ - + -

secondary bonding

Chapter 1 - 29

Type

Ionic

Covalent

Metallic

Secondary

Bond Energy

Large

Variable

large-Diamond

small-Bismuth

Variable

large-Tungsten

small-Mercury

Smallest

Comments


Directional


polymer chains)


Directional


inter-molecular

Summary Bonding

Chapter 1 - 30

bull Bond Length r

bull Bond Energy Eo




r o r

Energy

r

larger Tm

smaller Tm

Eo =


Energy

r o r

unstretched length

Chapter 1 - 31






= E F

A0

D L

L0

Hookes Law

s = E e

s

Linear- elastic

E

e

F


Chapter 1 - 32

Ceramics



large E

small a

Metals

(Metallic bonding)


moderate E

moderate a

Summary



small Tm

small E

large a

Chapter 1 - 33



bull Unit cells








Single crystal

Polycrystalline

Amorphous



Solids

Chapter 1 - 34

Core Problems Ex 33

ANNOUNCEMENTS

Reading 31-37 317

38-315

Chapter 1 - 35

SUMMARY













Chapter 1 - 36



allotropy)

SUMMARY








Chapter 1 - 37




lower energies

Energy and Packing

Energy

r



Energy

r



Chapter 1 - 38


-metals

-many ceramics

-some polymers



-complex structures

-rapid cooling

crystalline SiO2


CampR8e


CampR8e


Si Oxygen

bull typical of

bull occurs for

Chapter 1 - 39




radii are the same








Chapter 1 - 40






Chapter 1 - 41


APF =

a 3

4

3 p (05a) 3 1

atoms

unit cell atom

volume

unit cell

volume



Volume of unit cell

assume hard spheres



a

R=05a


Chapter 1 - 42








Chapter 1 - 43


a

APF =

4

3 p ( 3 a4 ) 3 2

atoms

unit cell atom

volume

a 3

unit cell

volume

length = 4R =


3 a


a R Adapted from

Fig 32(a) CampR8e

a 2

a 3

Chapter 1 - 44









Chapter 1 - 45




APF =

4

3 p ( 2 a4 ) 3 4

atoms

unit cell atom

volume

a 3

unit cell

volume


length = 4R = 2 a


a

2 a

Adapted from

Fig 31(a)

CampR8e

Chapter 1 - 46

A sites

B B

B

B B

B B

C sites

C C

C A

B

B sites


bull 2D Projection

bull FCC Unit Cell


B B

B

B B

B B

B sites C C

C A

C C

C A

A B

C

Chapter 1 - 47



bull APF = 074



CampR8e


(HCP)

6 atomsunit cell

ex Cd Mg Ti Zn

bull ca = 1633

c

a

A sites

B sites


Middle layer

Top layer

Chapter 1 - 48



A = atomic weight




Density = r =

VC NA

n A r =



Chapter 1 - 49

bull Ex Cr (BCC)

A = 5200 gmol

R = 0125 nm


rtheoretical

a = 4R 3 = 02887 nm

ractual

a R

r = a3

5200 2

atoms

unit cell mol

g

unit cell

volume atoms

mol

6022 x 1023


= 718 gcm3

= 719 gcm3

Adapted from

Fig 32(a) CampR8e

Chapter 1 - 50



Why


r (g

cm

)

3


Metals Alloys

Composites fibers

Polymers

1

2

2 0




3

4

5

03

04

05

Magnesium

Aluminum

Steels

Titanium

CuNi

Tin Zinc

Silver Mo


G raphite

Silicon



Zirconia

H DPE PS PP LDPE

PC

PTFE

PET PVC Silicone

Wood

AFRE

CFRE

GFRE

Glass fibers

Carbon fibers

A ramid fibers


(metallic bonding)





(often amorphous)



In general

Chapter 1 - 51

Chapter 1 - 52

Chapter 1 - 53

Chapter 1 - 54

Fig 34 CampR8e

Crystal Systems

7 crystal systems

14 crystal lattices




Chapter 1 - 55

Chapter 1 - 56

Point Coordinates





z

x

y a b

c

000

111

y

z

2c

b

b

Chapter 1 - 57



through origin





[uvw]

ex 1 0 frac12 =gt 2 0 1 =gt [ 201 ]

-1 1 1


z

x

Algorithm


negative index

[ 111 ] =gt

y

Chapter 1 - 58


direction

a = 0405 nm

Linear Density


a

[110]


Number of atoms

atoms

length

1 35 nm

a 2

2 LD -

Adapted from

Fig 31(a)

CampR8e

Chapter 1 -

BCC vs simple cubic

59

Chapter 1 -

BCC vs Simple C





60

Chapter 1 -

On to HCP






c

Chapter 1 -

Reading


bull 4-1 ndash 4-7

bull 5-1 ndash 5-5

62

Chapter 1 - 63



through origin





[uvtw]

[ 1120 ] ex frac12 frac12 -1 0 =gt


CampR8e



a2

a3

-a3

2

a 2

2

a 1

- a3

a1

a2

z

Algorithm


Chapter 1 - 64




as follows

w w

t

v

u

) v u ( + -

) u v 2 ( 3

1 -

) v u 2 ( 3

1 -

] uvtw [ ] w v u [

Fig 38(a) CampR8e

- a3

a1

a2

z

Chapter 1 - 65



CampR8e

Chapter 1 - 66




Chapter 1 - 67


x

y a b

c


example a b c z

x

y a b

c


1 Intercepts 1 1


1 1 0 3 Reduction 1 1 0

1 Intercepts 12


2 0 0 3 Reduction 2 0 0

example a b c

Chapter 1 - 68


z

x

y a b

c



a b c


2 1 43

3 Reduction 6 3 4

(001) (010)


(100) (010) (001) Ex 100 = (100)

Chapter 1 - 69



used

example a1 a2 a3 c



1 0

-1

-1

1

1


a2

a3

a1

z


CampR8e

Chapter 1 - 70






important


for Fe


planes

Chapter 1 - 71



(100)


R 3

3 4 a


2D repeat unit


1

atoms

2D repeat unit

= nm2

atoms 121

m2

atoms = 12 x 1019

1

2

R 3

3 4 area

2D repeat unit

Chapter 1 - 72







others

-- diamond single


-- turbine blades




GE Superabrasives


permission)


Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 24






all directions

Adapted from Fig 29


Chapter 1 - 25

C has 4 valence e-

needs 4 more

H has 1 valence e-

needs 1 more

Electronegativities

are comparable




dominate bonding



H

H

H

H

C

CH4

Chapter 1 - 26

Mixed Bonding


ionic character =



) 100 ( x

1-e-

(XA-XB )2

4


)2153(

2

-

--


Chapter 1 - 27

Metallic Bonding






Chapter 1 - 28




-general case

-ex liquid HCl

-ex polymer






Bonding



H H H H

H2 H2

secondary bonding

ex liquid H2

H Cl H Cl secondary

bonding

secondary bonding

+ - + -

secondary bonding

Chapter 1 - 29

Type

Ionic

Covalent

Metallic

Secondary

Bond Energy

Large

Variable

large-Diamond

small-Bismuth

Variable

large-Tungsten

small-Mercury

Smallest

Comments


Directional


polymer chains)


Directional


inter-molecular

Summary Bonding

Chapter 1 - 30

bull Bond Length r

bull Bond Energy Eo




r o r

Energy

r

larger Tm

smaller Tm

Eo =


Energy

r o r

unstretched length

Chapter 1 - 31






= E F

A0

D L

L0

Hookes Law

s = E e

s

Linear- elastic

E

e

F


Chapter 1 - 32

Ceramics



large E

small a

Metals

(Metallic bonding)


moderate E

moderate a

Summary



small Tm

small E

large a

Chapter 1 - 33



bull Unit cells








Single crystal

Polycrystalline

Amorphous



Solids

Chapter 1 - 34

Core Problems Ex 33

ANNOUNCEMENTS

Reading 31-37 317

38-315

Chapter 1 - 35

SUMMARY













Chapter 1 - 36



allotropy)

SUMMARY








Chapter 1 - 37




lower energies

Energy and Packing

Energy

r



Energy

r



Chapter 1 - 38


-metals

-many ceramics

-some polymers



-complex structures

-rapid cooling

crystalline SiO2


CampR8e


CampR8e


Si Oxygen

bull typical of

bull occurs for

Chapter 1 - 39




radii are the same








Chapter 1 - 40






Chapter 1 - 41


APF =

a 3

4

3 p (05a) 3 1

atoms

unit cell atom

volume

unit cell

volume



Volume of unit cell

assume hard spheres



a

R=05a


Chapter 1 - 42








Chapter 1 - 43


a

APF =

4

3 p ( 3 a4 ) 3 2

atoms

unit cell atom

volume

a 3

unit cell

volume

length = 4R =


3 a


a R Adapted from

Fig 32(a) CampR8e

a 2

a 3

Chapter 1 - 44









Chapter 1 - 45




APF =

4

3 p ( 2 a4 ) 3 4

atoms

unit cell atom

volume

a 3

unit cell

volume


length = 4R = 2 a


a

2 a

Adapted from

Fig 31(a)

CampR8e

Chapter 1 - 46

A sites

B B

B

B B

B B

C sites

C C

C A

B

B sites


bull 2D Projection

bull FCC Unit Cell


B B

B

B B

B B

B sites C C

C A

C C

C A

A B

C

Chapter 1 - 47



bull APF = 074



CampR8e


(HCP)

6 atomsunit cell

ex Cd Mg Ti Zn

bull ca = 1633

c

a

A sites

B sites


Middle layer

Top layer

Chapter 1 - 48



A = atomic weight




Density = r =

VC NA

n A r =



Chapter 1 - 49

bull Ex Cr (BCC)

A = 5200 gmol

R = 0125 nm


rtheoretical

a = 4R 3 = 02887 nm

ractual

a R

r = a3

5200 2

atoms

unit cell mol

g

unit cell

volume atoms

mol

6022 x 1023


= 718 gcm3

= 719 gcm3

Adapted from

Fig 32(a) CampR8e

Chapter 1 - 50



Why


r (g

cm

)

3


Metals Alloys

Composites fibers

Polymers

1

2

2 0




3

4

5

03

04

05

Magnesium

Aluminum

Steels

Titanium

CuNi

Tin Zinc

Silver Mo


G raphite

Silicon



Zirconia

H DPE PS PP LDPE

PC

PTFE

PET PVC Silicone

Wood

AFRE

CFRE

GFRE

Glass fibers

Carbon fibers

A ramid fibers


(metallic bonding)





(often amorphous)



In general

Chapter 1 - 51

Chapter 1 - 52

Chapter 1 - 53

Chapter 1 - 54

Fig 34 CampR8e

Crystal Systems

7 crystal systems

14 crystal lattices




Chapter 1 - 55

Chapter 1 - 56

Point Coordinates





z

x

y a b

c

000

111

y

z

2c

b

b

Chapter 1 - 57



through origin





[uvw]

ex 1 0 frac12 =gt 2 0 1 =gt [ 201 ]

-1 1 1


z

x

Algorithm


negative index

[ 111 ] =gt

y

Chapter 1 - 58


direction

a = 0405 nm

Linear Density


a

[110]


Number of atoms

atoms

length

1 35 nm

a 2

2 LD -

Adapted from

Fig 31(a)

CampR8e

Chapter 1 -

BCC vs simple cubic

59

Chapter 1 -

BCC vs Simple C





60

Chapter 1 -

On to HCP






c

Chapter 1 -

Reading


bull 4-1 ndash 4-7

bull 5-1 ndash 5-5

62

Chapter 1 - 63



through origin





[uvtw]

[ 1120 ] ex frac12 frac12 -1 0 =gt


CampR8e



a2

a3

-a3

2

a 2

2

a 1

- a3

a1

a2

z

Algorithm


Chapter 1 - 64




as follows

w w

t

v

u

) v u ( + -

) u v 2 ( 3

1 -

) v u 2 ( 3

1 -

] uvtw [ ] w v u [

Fig 38(a) CampR8e

- a3

a1

a2

z

Chapter 1 - 65



CampR8e

Chapter 1 - 66




Chapter 1 - 67


x

y a b

c


example a b c z

x

y a b

c


1 Intercepts 1 1


1 1 0 3 Reduction 1 1 0

1 Intercepts 12


2 0 0 3 Reduction 2 0 0

example a b c

Chapter 1 - 68


z

x

y a b

c



a b c


2 1 43

3 Reduction 6 3 4

(001) (010)


(100) (010) (001) Ex 100 = (100)

Chapter 1 - 69



used

example a1 a2 a3 c



1 0

-1

-1

1

1


a2

a3

a1

z


CampR8e

Chapter 1 - 70






important


for Fe


planes

Chapter 1 - 71



(100)


R 3

3 4 a


2D repeat unit


1

atoms

2D repeat unit

= nm2

atoms 121

m2

atoms = 12 x 1019

1

2

R 3

3 4 area

2D repeat unit

Chapter 1 - 72







others

-- diamond single


-- turbine blades




GE Superabrasives


permission)


Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 25

C has 4 valence e-

needs 4 more

H has 1 valence e-

needs 1 more

Electronegativities

are comparable




dominate bonding



H

H

H

H

C

CH4

Chapter 1 - 26

Mixed Bonding


ionic character =



) 100 ( x

1-e-

(XA-XB )2

4


)2153(

2

-

--


Chapter 1 - 27

Metallic Bonding






Chapter 1 - 28




-general case

-ex liquid HCl

-ex polymer






Bonding



H H H H

H2 H2

secondary bonding

ex liquid H2

H Cl H Cl secondary

bonding

secondary bonding

+ - + -

secondary bonding

Chapter 1 - 29

Type

Ionic

Covalent

Metallic

Secondary

Bond Energy

Large

Variable

large-Diamond

small-Bismuth

Variable

large-Tungsten

small-Mercury

Smallest

Comments


Directional


polymer chains)


Directional


inter-molecular

Summary Bonding

Chapter 1 - 30

bull Bond Length r

bull Bond Energy Eo




r o r

Energy

r

larger Tm

smaller Tm

Eo =


Energy

r o r

unstretched length

Chapter 1 - 31






= E F

A0

D L

L0

Hookes Law

s = E e

s

Linear- elastic

E

e

F


Chapter 1 - 32

Ceramics



large E

small a

Metals

(Metallic bonding)


moderate E

moderate a

Summary



small Tm

small E

large a

Chapter 1 - 33



bull Unit cells








Single crystal

Polycrystalline

Amorphous



Solids

Chapter 1 - 34

Core Problems Ex 33

ANNOUNCEMENTS

Reading 31-37 317

38-315

Chapter 1 - 35

SUMMARY













Chapter 1 - 36



allotropy)

SUMMARY








Chapter 1 - 37




lower energies

Energy and Packing

Energy

r



Energy

r



Chapter 1 - 38


-metals

-many ceramics

-some polymers



-complex structures

-rapid cooling

crystalline SiO2


CampR8e


CampR8e


Si Oxygen

bull typical of

bull occurs for

Chapter 1 - 39




radii are the same








Chapter 1 - 40






Chapter 1 - 41


APF =

a 3

4

3 p (05a) 3 1

atoms

unit cell atom

volume

unit cell

volume



Volume of unit cell

assume hard spheres



a

R=05a


Chapter 1 - 42








Chapter 1 - 43


a

APF =

4

3 p ( 3 a4 ) 3 2

atoms

unit cell atom

volume

a 3

unit cell

volume

length = 4R =


3 a


a R Adapted from

Fig 32(a) CampR8e

a 2

a 3

Chapter 1 - 44









Chapter 1 - 45




APF =

4

3 p ( 2 a4 ) 3 4

atoms

unit cell atom

volume

a 3

unit cell

volume


length = 4R = 2 a


a

2 a

Adapted from

Fig 31(a)

CampR8e

Chapter 1 - 46

A sites

B B

B

B B

B B

C sites

C C

C A

B

B sites


bull 2D Projection

bull FCC Unit Cell


B B

B

B B

B B

B sites C C

C A

C C

C A

A B

C

Chapter 1 - 47



bull APF = 074



CampR8e


(HCP)

6 atomsunit cell

ex Cd Mg Ti Zn

bull ca = 1633

c

a

A sites

B sites


Middle layer

Top layer

Chapter 1 - 48



A = atomic weight




Density = r =

VC NA

n A r =



Chapter 1 - 49

bull Ex Cr (BCC)

A = 5200 gmol

R = 0125 nm


rtheoretical

a = 4R 3 = 02887 nm

ractual

a R

r = a3

5200 2

atoms

unit cell mol

g

unit cell

volume atoms

mol

6022 x 1023


= 718 gcm3

= 719 gcm3

Adapted from

Fig 32(a) CampR8e

Chapter 1 - 50



Why


r (g

cm

)

3


Metals Alloys

Composites fibers

Polymers

1

2

2 0




3

4

5

03

04

05

Magnesium

Aluminum

Steels

Titanium

CuNi

Tin Zinc

Silver Mo


G raphite

Silicon



Zirconia

H DPE PS PP LDPE

PC

PTFE

PET PVC Silicone

Wood

AFRE

CFRE

GFRE

Glass fibers

Carbon fibers

A ramid fibers


(metallic bonding)





(often amorphous)



In general

Chapter 1 - 51

Chapter 1 - 52

Chapter 1 - 53

Chapter 1 - 54

Fig 34 CampR8e

Crystal Systems

7 crystal systems

14 crystal lattices




Chapter 1 - 55

Chapter 1 - 56

Point Coordinates





z

x

y a b

c

000

111

y

z

2c

b

b

Chapter 1 - 57



through origin





[uvw]

ex 1 0 frac12 =gt 2 0 1 =gt [ 201 ]

-1 1 1


z

x

Algorithm


negative index

[ 111 ] =gt

y

Chapter 1 - 58


direction

a = 0405 nm

Linear Density


a

[110]


Number of atoms

atoms

length

1 35 nm

a 2

2 LD -

Adapted from

Fig 31(a)

CampR8e

Chapter 1 -

BCC vs simple cubic

59

Chapter 1 -

BCC vs Simple C





60

Chapter 1 -

On to HCP






c

Chapter 1 -

Reading


bull 4-1 ndash 4-7

bull 5-1 ndash 5-5

62

Chapter 1 - 63



through origin





[uvtw]

[ 1120 ] ex frac12 frac12 -1 0 =gt


CampR8e



a2

a3

-a3

2

a 2

2

a 1

- a3

a1

a2

z

Algorithm


Chapter 1 - 64




as follows

w w

t

v

u

) v u ( + -

) u v 2 ( 3

1 -

) v u 2 ( 3

1 -

] uvtw [ ] w v u [

Fig 38(a) CampR8e

- a3

a1

a2

z

Chapter 1 - 65



CampR8e

Chapter 1 - 66




Chapter 1 - 67


x

y a b

c


example a b c z

x

y a b

c


1 Intercepts 1 1


1 1 0 3 Reduction 1 1 0

1 Intercepts 12


2 0 0 3 Reduction 2 0 0

example a b c

Chapter 1 - 68


z

x

y a b

c



a b c


2 1 43

3 Reduction 6 3 4

(001) (010)


(100) (010) (001) Ex 100 = (100)

Chapter 1 - 69



used

example a1 a2 a3 c



1 0

-1

-1

1

1


a2

a3

a1

z


CampR8e

Chapter 1 - 70






important


for Fe


planes

Chapter 1 - 71



(100)


R 3

3 4 a


2D repeat unit


1

atoms

2D repeat unit

= nm2

atoms 121

m2

atoms = 12 x 1019

1

2

R 3

3 4 area

2D repeat unit

Chapter 1 - 72







others

-- diamond single


-- turbine blades




GE Superabrasives


permission)


Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 26

Mixed Bonding


ionic character =



) 100 ( x

1-e-

(XA-XB )2

4


)2153(

2

-

--


Chapter 1 - 27

Metallic Bonding






Chapter 1 - 28




-general case

-ex liquid HCl

-ex polymer






Bonding



H H H H

H2 H2

secondary bonding

ex liquid H2

H Cl H Cl secondary

bonding

secondary bonding

+ - + -

secondary bonding

Chapter 1 - 29

Type

Ionic

Covalent

Metallic

Secondary

Bond Energy

Large

Variable

large-Diamond

small-Bismuth

Variable

large-Tungsten

small-Mercury

Smallest

Comments


Directional


polymer chains)


Directional


inter-molecular

Summary Bonding

Chapter 1 - 30

bull Bond Length r

bull Bond Energy Eo




r o r

Energy

r

larger Tm

smaller Tm

Eo =


Energy

r o r

unstretched length

Chapter 1 - 31






= E F

A0

D L

L0

Hookes Law

s = E e

s

Linear- elastic

E

e

F


Chapter 1 - 32

Ceramics



large E

small a

Metals

(Metallic bonding)


moderate E

moderate a

Summary



small Tm

small E

large a

Chapter 1 - 33



bull Unit cells








Single crystal

Polycrystalline

Amorphous



Solids

Chapter 1 - 34

Core Problems Ex 33

ANNOUNCEMENTS

Reading 31-37 317

38-315

Chapter 1 - 35

SUMMARY













Chapter 1 - 36



allotropy)

SUMMARY








Chapter 1 - 37




lower energies

Energy and Packing

Energy

r



Energy

r



Chapter 1 - 38


-metals

-many ceramics

-some polymers



-complex structures

-rapid cooling

crystalline SiO2


CampR8e


CampR8e


Si Oxygen

bull typical of

bull occurs for

Chapter 1 - 39




radii are the same








Chapter 1 - 40






Chapter 1 - 41


APF =

a 3

4

3 p (05a) 3 1

atoms

unit cell atom

volume

unit cell

volume



Volume of unit cell

assume hard spheres



a

R=05a


Chapter 1 - 42








Chapter 1 - 43


a

APF =

4

3 p ( 3 a4 ) 3 2

atoms

unit cell atom

volume

a 3

unit cell

volume

length = 4R =


3 a


a R Adapted from

Fig 32(a) CampR8e

a 2

a 3

Chapter 1 - 44









Chapter 1 - 45




APF =

4

3 p ( 2 a4 ) 3 4

atoms

unit cell atom

volume

a 3

unit cell

volume


length = 4R = 2 a


a

2 a

Adapted from

Fig 31(a)

CampR8e

Chapter 1 - 46

A sites

B B

B

B B

B B

C sites

C C

C A

B

B sites


bull 2D Projection

bull FCC Unit Cell


B B

B

B B

B B

B sites C C

C A

C C

C A

A B

C

Chapter 1 - 47



bull APF = 074



CampR8e


(HCP)

6 atomsunit cell

ex Cd Mg Ti Zn

bull ca = 1633

c

a

A sites

B sites


Middle layer

Top layer

Chapter 1 - 48



A = atomic weight




Density = r =

VC NA

n A r =



Chapter 1 - 49

bull Ex Cr (BCC)

A = 5200 gmol

R = 0125 nm


rtheoretical

a = 4R 3 = 02887 nm

ractual

a R

r = a3

5200 2

atoms

unit cell mol

g

unit cell

volume atoms

mol

6022 x 1023


= 718 gcm3

= 719 gcm3

Adapted from

Fig 32(a) CampR8e

Chapter 1 - 50



Why


r (g

cm

)

3


Metals Alloys

Composites fibers

Polymers

1

2

2 0




3

4

5

03

04

05

Magnesium

Aluminum

Steels

Titanium

CuNi

Tin Zinc

Silver Mo


G raphite

Silicon



Zirconia

H DPE PS PP LDPE

PC

PTFE

PET PVC Silicone

Wood

AFRE

CFRE

GFRE

Glass fibers

Carbon fibers

A ramid fibers


(metallic bonding)





(often amorphous)



In general

Chapter 1 - 51

Chapter 1 - 52

Chapter 1 - 53

Chapter 1 - 54

Fig 34 CampR8e

Crystal Systems

7 crystal systems

14 crystal lattices




Chapter 1 - 55

Chapter 1 - 56

Point Coordinates





z

x

y a b

c

000

111

y

z

2c

b

b

Chapter 1 - 57



through origin





[uvw]

ex 1 0 frac12 =gt 2 0 1 =gt [ 201 ]

-1 1 1


z

x

Algorithm


negative index

[ 111 ] =gt

y

Chapter 1 - 58


direction

a = 0405 nm

Linear Density


a

[110]


Number of atoms

atoms

length

1 35 nm

a 2

2 LD -

Adapted from

Fig 31(a)

CampR8e

Chapter 1 -

BCC vs simple cubic

59

Chapter 1 -

BCC vs Simple C





60

Chapter 1 -

On to HCP






c

Chapter 1 -

Reading


bull 4-1 ndash 4-7

bull 5-1 ndash 5-5

62

Chapter 1 - 63



through origin





[uvtw]

[ 1120 ] ex frac12 frac12 -1 0 =gt


CampR8e



a2

a3

-a3

2

a 2

2

a 1

- a3

a1

a2

z

Algorithm


Chapter 1 - 64




as follows

w w

t

v

u

) v u ( + -

) u v 2 ( 3

1 -

) v u 2 ( 3

1 -

] uvtw [ ] w v u [

Fig 38(a) CampR8e

- a3

a1

a2

z

Chapter 1 - 65



CampR8e

Chapter 1 - 66




Chapter 1 - 67


x

y a b

c


example a b c z

x

y a b

c


1 Intercepts 1 1


1 1 0 3 Reduction 1 1 0

1 Intercepts 12


2 0 0 3 Reduction 2 0 0

example a b c

Chapter 1 - 68


z

x

y a b

c



a b c


2 1 43

3 Reduction 6 3 4

(001) (010)


(100) (010) (001) Ex 100 = (100)

Chapter 1 - 69



used

example a1 a2 a3 c



1 0

-1

-1

1

1


a2

a3

a1

z


CampR8e

Chapter 1 - 70






important


for Fe


planes

Chapter 1 - 71



(100)


R 3

3 4 a


2D repeat unit


1

atoms

2D repeat unit

= nm2

atoms 121

m2

atoms = 12 x 1019

1

2

R 3

3 4 area

2D repeat unit

Chapter 1 - 72







others

-- diamond single


-- turbine blades




GE Superabrasives


permission)


Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 27

Metallic Bonding






Chapter 1 - 28




-general case

-ex liquid HCl

-ex polymer






Bonding



H H H H

H2 H2

secondary bonding

ex liquid H2

H Cl H Cl secondary

bonding

secondary bonding

+ - + -

secondary bonding

Chapter 1 - 29

Type

Ionic

Covalent

Metallic

Secondary

Bond Energy

Large

Variable

large-Diamond

small-Bismuth

Variable

large-Tungsten

small-Mercury

Smallest

Comments


Directional


polymer chains)


Directional


inter-molecular

Summary Bonding

Chapter 1 - 30

bull Bond Length r

bull Bond Energy Eo




r o r

Energy

r

larger Tm

smaller Tm

Eo =


Energy

r o r

unstretched length

Chapter 1 - 31






= E F

A0

D L

L0

Hookes Law

s = E e

s

Linear- elastic

E

e

F


Chapter 1 - 32

Ceramics



large E

small a

Metals

(Metallic bonding)


moderate E

moderate a

Summary



small Tm

small E

large a

Chapter 1 - 33



bull Unit cells








Single crystal

Polycrystalline

Amorphous



Solids

Chapter 1 - 34

Core Problems Ex 33

ANNOUNCEMENTS

Reading 31-37 317

38-315

Chapter 1 - 35

SUMMARY













Chapter 1 - 36



allotropy)

SUMMARY








Chapter 1 - 37




lower energies

Energy and Packing

Energy

r



Energy

r



Chapter 1 - 38


-metals

-many ceramics

-some polymers



-complex structures

-rapid cooling

crystalline SiO2


CampR8e


CampR8e


Si Oxygen

bull typical of

bull occurs for

Chapter 1 - 39




radii are the same








Chapter 1 - 40






Chapter 1 - 41


APF =

a 3

4

3 p (05a) 3 1

atoms

unit cell atom

volume

unit cell

volume



Volume of unit cell

assume hard spheres



a

R=05a


Chapter 1 - 42








Chapter 1 - 43


a

APF =

4

3 p ( 3 a4 ) 3 2

atoms

unit cell atom

volume

a 3

unit cell

volume

length = 4R =


3 a


a R Adapted from

Fig 32(a) CampR8e

a 2

a 3

Chapter 1 - 44









Chapter 1 - 45




APF =

4

3 p ( 2 a4 ) 3 4

atoms

unit cell atom

volume

a 3

unit cell

volume


length = 4R = 2 a


a

2 a

Adapted from

Fig 31(a)

CampR8e

Chapter 1 - 46

A sites

B B

B

B B

B B

C sites

C C

C A

B

B sites


bull 2D Projection

bull FCC Unit Cell


B B

B

B B

B B

B sites C C

C A

C C

C A

A B

C

Chapter 1 - 47



bull APF = 074



CampR8e


(HCP)

6 atomsunit cell

ex Cd Mg Ti Zn

bull ca = 1633

c

a

A sites

B sites


Middle layer

Top layer

Chapter 1 - 48



A = atomic weight




Density = r =

VC NA

n A r =



Chapter 1 - 49

bull Ex Cr (BCC)

A = 5200 gmol

R = 0125 nm


rtheoretical

a = 4R 3 = 02887 nm

ractual

a R

r = a3

5200 2

atoms

unit cell mol

g

unit cell

volume atoms

mol

6022 x 1023


= 718 gcm3

= 719 gcm3

Adapted from

Fig 32(a) CampR8e

Chapter 1 - 50



Why


r (g

cm

)

3


Metals Alloys

Composites fibers

Polymers

1

2

2 0




3

4

5

03

04

05

Magnesium

Aluminum

Steels

Titanium

CuNi

Tin Zinc

Silver Mo


G raphite

Silicon



Zirconia

H DPE PS PP LDPE

PC

PTFE

PET PVC Silicone

Wood

AFRE

CFRE

GFRE

Glass fibers

Carbon fibers

A ramid fibers


(metallic bonding)





(often amorphous)



In general

Chapter 1 - 51

Chapter 1 - 52

Chapter 1 - 53

Chapter 1 - 54

Fig 34 CampR8e

Crystal Systems

7 crystal systems

14 crystal lattices




Chapter 1 - 55

Chapter 1 - 56

Point Coordinates





z

x

y a b

c

000

111

y

z

2c

b

b

Chapter 1 - 57



through origin





[uvw]

ex 1 0 frac12 =gt 2 0 1 =gt [ 201 ]

-1 1 1


z

x

Algorithm


negative index

[ 111 ] =gt

y

Chapter 1 - 58


direction

a = 0405 nm

Linear Density


a

[110]


Number of atoms

atoms

length

1 35 nm

a 2

2 LD -

Adapted from

Fig 31(a)

CampR8e

Chapter 1 -

BCC vs simple cubic

59

Chapter 1 -

BCC vs Simple C





60

Chapter 1 -

On to HCP






c

Chapter 1 -

Reading


bull 4-1 ndash 4-7

bull 5-1 ndash 5-5

62

Chapter 1 - 63



through origin





[uvtw]

[ 1120 ] ex frac12 frac12 -1 0 =gt


CampR8e



a2

a3

-a3

2

a 2

2

a 1

- a3

a1

a2

z

Algorithm


Chapter 1 - 64




as follows

w w

t

v

u

) v u ( + -

) u v 2 ( 3

1 -

) v u 2 ( 3

1 -

] uvtw [ ] w v u [

Fig 38(a) CampR8e

- a3

a1

a2

z

Chapter 1 - 65



CampR8e

Chapter 1 - 66




Chapter 1 - 67


x

y a b

c


example a b c z

x

y a b

c


1 Intercepts 1 1


1 1 0 3 Reduction 1 1 0

1 Intercepts 12


2 0 0 3 Reduction 2 0 0

example a b c

Chapter 1 - 68


z

x

y a b

c



a b c


2 1 43

3 Reduction 6 3 4

(001) (010)


(100) (010) (001) Ex 100 = (100)

Chapter 1 - 69



used

example a1 a2 a3 c



1 0

-1

-1

1

1


a2

a3

a1

z


CampR8e

Chapter 1 - 70






important


for Fe


planes

Chapter 1 - 71



(100)


R 3

3 4 a


2D repeat unit


1

atoms

2D repeat unit

= nm2

atoms 121

m2

atoms = 12 x 1019

1

2

R 3

3 4 area

2D repeat unit

Chapter 1 - 72







others

-- diamond single


-- turbine blades




GE Superabrasives


permission)


Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 28




-general case

-ex liquid HCl

-ex polymer






Bonding



H H H H

H2 H2

secondary bonding

ex liquid H2

H Cl H Cl secondary

bonding

secondary bonding

+ - + -

secondary bonding

Chapter 1 - 29

Type

Ionic

Covalent

Metallic

Secondary

Bond Energy

Large

Variable

large-Diamond

small-Bismuth

Variable

large-Tungsten

small-Mercury

Smallest

Comments


Directional


polymer chains)


Directional


inter-molecular

Summary Bonding

Chapter 1 - 30

bull Bond Length r

bull Bond Energy Eo




r o r

Energy

r

larger Tm

smaller Tm

Eo =


Energy

r o r

unstretched length

Chapter 1 - 31






= E F

A0

D L

L0

Hookes Law

s = E e

s

Linear- elastic

E

e

F


Chapter 1 - 32

Ceramics



large E

small a

Metals

(Metallic bonding)


moderate E

moderate a

Summary



small Tm

small E

large a

Chapter 1 - 33



bull Unit cells








Single crystal

Polycrystalline

Amorphous



Solids

Chapter 1 - 34

Core Problems Ex 33

ANNOUNCEMENTS

Reading 31-37 317

38-315

Chapter 1 - 35

SUMMARY













Chapter 1 - 36



allotropy)

SUMMARY








Chapter 1 - 37




lower energies

Energy and Packing

Energy

r



Energy

r



Chapter 1 - 38


-metals

-many ceramics

-some polymers



-complex structures

-rapid cooling

crystalline SiO2


CampR8e


CampR8e


Si Oxygen

bull typical of

bull occurs for

Chapter 1 - 39




radii are the same








Chapter 1 - 40






Chapter 1 - 41


APF =

a 3

4

3 p (05a) 3 1

atoms

unit cell atom

volume

unit cell

volume



Volume of unit cell

assume hard spheres



a

R=05a


Chapter 1 - 42








Chapter 1 - 43


a

APF =

4

3 p ( 3 a4 ) 3 2

atoms

unit cell atom

volume

a 3

unit cell

volume

length = 4R =


3 a


a R Adapted from

Fig 32(a) CampR8e

a 2

a 3

Chapter 1 - 44









Chapter 1 - 45




APF =

4

3 p ( 2 a4 ) 3 4

atoms

unit cell atom

volume

a 3

unit cell

volume


length = 4R = 2 a


a

2 a

Adapted from

Fig 31(a)

CampR8e

Chapter 1 - 46

A sites

B B

B

B B

B B

C sites

C C

C A

B

B sites


bull 2D Projection

bull FCC Unit Cell


B B

B

B B

B B

B sites C C

C A

C C

C A

A B

C

Chapter 1 - 47



bull APF = 074



CampR8e


(HCP)

6 atomsunit cell

ex Cd Mg Ti Zn

bull ca = 1633

c

a

A sites

B sites


Middle layer

Top layer

Chapter 1 - 48



A = atomic weight




Density = r =

VC NA

n A r =



Chapter 1 - 49

bull Ex Cr (BCC)

A = 5200 gmol

R = 0125 nm


rtheoretical

a = 4R 3 = 02887 nm

ractual

a R

r = a3

5200 2

atoms

unit cell mol

g

unit cell

volume atoms

mol

6022 x 1023


= 718 gcm3

= 719 gcm3

Adapted from

Fig 32(a) CampR8e

Chapter 1 - 50



Why


r (g

cm

)

3


Metals Alloys

Composites fibers

Polymers

1

2

2 0




3

4

5

03

04

05

Magnesium

Aluminum

Steels

Titanium

CuNi

Tin Zinc

Silver Mo


G raphite

Silicon



Zirconia

H DPE PS PP LDPE

PC

PTFE

PET PVC Silicone

Wood

AFRE

CFRE

GFRE

Glass fibers

Carbon fibers

A ramid fibers


(metallic bonding)





(often amorphous)



In general

Chapter 1 - 51

Chapter 1 - 52

Chapter 1 - 53

Chapter 1 - 54

Fig 34 CampR8e

Crystal Systems

7 crystal systems

14 crystal lattices




Chapter 1 - 55

Chapter 1 - 56

Point Coordinates





z

x

y a b

c

000

111

y

z

2c

b

b

Chapter 1 - 57



through origin





[uvw]

ex 1 0 frac12 =gt 2 0 1 =gt [ 201 ]

-1 1 1


z

x

Algorithm


negative index

[ 111 ] =gt

y

Chapter 1 - 58


direction

a = 0405 nm

Linear Density


a

[110]


Number of atoms

atoms

length

1 35 nm

a 2

2 LD -

Adapted from

Fig 31(a)

CampR8e

Chapter 1 -

BCC vs simple cubic

59

Chapter 1 -

BCC vs Simple C





60

Chapter 1 -

On to HCP






c

Chapter 1 -

Reading


bull 4-1 ndash 4-7

bull 5-1 ndash 5-5

62

Chapter 1 - 63



through origin





[uvtw]

[ 1120 ] ex frac12 frac12 -1 0 =gt


CampR8e



a2

a3

-a3

2

a 2

2

a 1

- a3

a1

a2

z

Algorithm


Chapter 1 - 64




as follows

w w

t

v

u

) v u ( + -

) u v 2 ( 3

1 -

) v u 2 ( 3

1 -

] uvtw [ ] w v u [

Fig 38(a) CampR8e

- a3

a1

a2

z

Chapter 1 - 65



CampR8e

Chapter 1 - 66




Chapter 1 - 67


x

y a b

c


example a b c z

x

y a b

c


1 Intercepts 1 1


1 1 0 3 Reduction 1 1 0

1 Intercepts 12


2 0 0 3 Reduction 2 0 0

example a b c

Chapter 1 - 68


z

x

y a b

c



a b c


2 1 43

3 Reduction 6 3 4

(001) (010)


(100) (010) (001) Ex 100 = (100)

Chapter 1 - 69



used

example a1 a2 a3 c



1 0

-1

-1

1

1


a2

a3

a1

z


CampR8e

Chapter 1 - 70






important


for Fe


planes

Chapter 1 - 71



(100)


R 3

3 4 a


2D repeat unit


1

atoms

2D repeat unit

= nm2

atoms 121

m2

atoms = 12 x 1019

1

2

R 3

3 4 area

2D repeat unit

Chapter 1 - 72







others

-- diamond single


-- turbine blades




GE Superabrasives


permission)


Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 29

Type

Ionic

Covalent

Metallic

Secondary

Bond Energy

Large

Variable

large-Diamond

small-Bismuth

Variable

large-Tungsten

small-Mercury

Smallest

Comments


Directional


polymer chains)


Directional


inter-molecular

Summary Bonding

Chapter 1 - 30

bull Bond Length r

bull Bond Energy Eo




r o r

Energy

r

larger Tm

smaller Tm

Eo =


Energy

r o r

unstretched length

Chapter 1 - 31






= E F

A0

D L

L0

Hookes Law

s = E e

s

Linear- elastic

E

e

F


Chapter 1 - 32

Ceramics



large E

small a

Metals

(Metallic bonding)


moderate E

moderate a

Summary



small Tm

small E

large a

Chapter 1 - 33



bull Unit cells








Single crystal

Polycrystalline

Amorphous



Solids

Chapter 1 - 34

Core Problems Ex 33

ANNOUNCEMENTS

Reading 31-37 317

38-315

Chapter 1 - 35

SUMMARY













Chapter 1 - 36



allotropy)

SUMMARY








Chapter 1 - 37




lower energies

Energy and Packing

Energy

r



Energy

r



Chapter 1 - 38


-metals

-many ceramics

-some polymers



-complex structures

-rapid cooling

crystalline SiO2


CampR8e


CampR8e


Si Oxygen

bull typical of

bull occurs for

Chapter 1 - 39




radii are the same








Chapter 1 - 40






Chapter 1 - 41


APF =

a 3

4

3 p (05a) 3 1

atoms

unit cell atom

volume

unit cell

volume



Volume of unit cell

assume hard spheres



a

R=05a


Chapter 1 - 42








Chapter 1 - 43


a

APF =

4

3 p ( 3 a4 ) 3 2

atoms

unit cell atom

volume

a 3

unit cell

volume

length = 4R =


3 a


a R Adapted from

Fig 32(a) CampR8e

a 2

a 3

Chapter 1 - 44









Chapter 1 - 45




APF =

4

3 p ( 2 a4 ) 3 4

atoms

unit cell atom

volume

a 3

unit cell

volume


length = 4R = 2 a


a

2 a

Adapted from

Fig 31(a)

CampR8e

Chapter 1 - 46

A sites

B B

B

B B

B B

C sites

C C

C A

B

B sites


bull 2D Projection

bull FCC Unit Cell


B B

B

B B

B B

B sites C C

C A

C C

C A

A B

C

Chapter 1 - 47



bull APF = 074



CampR8e


(HCP)

6 atomsunit cell

ex Cd Mg Ti Zn

bull ca = 1633

c

a

A sites

B sites


Middle layer

Top layer

Chapter 1 - 48



A = atomic weight




Density = r =

VC NA

n A r =



Chapter 1 - 49

bull Ex Cr (BCC)

A = 5200 gmol

R = 0125 nm


rtheoretical

a = 4R 3 = 02887 nm

ractual

a R

r = a3

5200 2

atoms

unit cell mol

g

unit cell

volume atoms

mol

6022 x 1023


= 718 gcm3

= 719 gcm3

Adapted from

Fig 32(a) CampR8e

Chapter 1 - 50



Why


r (g

cm

)

3


Metals Alloys

Composites fibers

Polymers

1

2

2 0




3

4

5

03

04

05

Magnesium

Aluminum

Steels

Titanium

CuNi

Tin Zinc

Silver Mo


G raphite

Silicon



Zirconia

H DPE PS PP LDPE

PC

PTFE

PET PVC Silicone

Wood

AFRE

CFRE

GFRE

Glass fibers

Carbon fibers

A ramid fibers


(metallic bonding)





(often amorphous)



In general

Chapter 1 - 51

Chapter 1 - 52

Chapter 1 - 53

Chapter 1 - 54

Fig 34 CampR8e

Crystal Systems

7 crystal systems

14 crystal lattices




Chapter 1 - 55

Chapter 1 - 56

Point Coordinates





z

x

y a b

c

000

111

y

z

2c

b

b

Chapter 1 - 57



through origin





[uvw]

ex 1 0 frac12 =gt 2 0 1 =gt [ 201 ]

-1 1 1


z

x

Algorithm


negative index

[ 111 ] =gt

y

Chapter 1 - 58


direction

a = 0405 nm

Linear Density


a

[110]


Number of atoms

atoms

length

1 35 nm

a 2

2 LD -

Adapted from

Fig 31(a)

CampR8e

Chapter 1 -

BCC vs simple cubic

59

Chapter 1 -

BCC vs Simple C





60

Chapter 1 -

On to HCP






c

Chapter 1 -

Reading


bull 4-1 ndash 4-7

bull 5-1 ndash 5-5

62

Chapter 1 - 63



through origin





[uvtw]

[ 1120 ] ex frac12 frac12 -1 0 =gt


CampR8e



a2

a3

-a3

2

a 2

2

a 1

- a3

a1

a2

z

Algorithm


Chapter 1 - 64




as follows

w w

t

v

u

) v u ( + -

) u v 2 ( 3

1 -

) v u 2 ( 3

1 -

] uvtw [ ] w v u [

Fig 38(a) CampR8e

- a3

a1

a2

z

Chapter 1 - 65



CampR8e

Chapter 1 - 66




Chapter 1 - 67


x

y a b

c


example a b c z

x

y a b

c


1 Intercepts 1 1


1 1 0 3 Reduction 1 1 0

1 Intercepts 12


2 0 0 3 Reduction 2 0 0

example a b c

Chapter 1 - 68


z

x

y a b

c



a b c


2 1 43

3 Reduction 6 3 4

(001) (010)


(100) (010) (001) Ex 100 = (100)

Chapter 1 - 69



used

example a1 a2 a3 c



1 0

-1

-1

1

1


a2

a3

a1

z


CampR8e

Chapter 1 - 70






important


for Fe


planes

Chapter 1 - 71



(100)


R 3

3 4 a


2D repeat unit


1

atoms

2D repeat unit

= nm2

atoms 121

m2

atoms = 12 x 1019

1

2

R 3

3 4 area

2D repeat unit

Chapter 1 - 72







others

-- diamond single


-- turbine blades




GE Superabrasives


permission)


Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 30

bull Bond Length r

bull Bond Energy Eo




r o r

Energy

r

larger Tm

smaller Tm

Eo =


Energy

r o r

unstretched length

Chapter 1 - 31






= E F

A0

D L

L0

Hookes Law

s = E e

s

Linear- elastic

E

e

F


Chapter 1 - 32

Ceramics



large E

small a

Metals

(Metallic bonding)


moderate E

moderate a

Summary



small Tm

small E

large a

Chapter 1 - 33



bull Unit cells








Single crystal

Polycrystalline

Amorphous



Solids

Chapter 1 - 34

Core Problems Ex 33

ANNOUNCEMENTS

Reading 31-37 317

38-315

Chapter 1 - 35

SUMMARY













Chapter 1 - 36



allotropy)

SUMMARY








Chapter 1 - 37




lower energies

Energy and Packing

Energy

r



Energy

r



Chapter 1 - 38


-metals

-many ceramics

-some polymers



-complex structures

-rapid cooling

crystalline SiO2


CampR8e


CampR8e


Si Oxygen

bull typical of

bull occurs for

Chapter 1 - 39




radii are the same








Chapter 1 - 40






Chapter 1 - 41


APF =

a 3

4

3 p (05a) 3 1

atoms

unit cell atom

volume

unit cell

volume



Volume of unit cell

assume hard spheres



a

R=05a


Chapter 1 - 42








Chapter 1 - 43


a

APF =

4

3 p ( 3 a4 ) 3 2

atoms

unit cell atom

volume

a 3

unit cell

volume

length = 4R =


3 a


a R Adapted from

Fig 32(a) CampR8e

a 2

a 3

Chapter 1 - 44









Chapter 1 - 45




APF =

4

3 p ( 2 a4 ) 3 4

atoms

unit cell atom

volume

a 3

unit cell

volume


length = 4R = 2 a


a

2 a

Adapted from

Fig 31(a)

CampR8e

Chapter 1 - 46

A sites

B B

B

B B

B B

C sites

C C

C A

B

B sites


bull 2D Projection

bull FCC Unit Cell


B B

B

B B

B B

B sites C C

C A

C C

C A

A B

C

Chapter 1 - 47



bull APF = 074



CampR8e


(HCP)

6 atomsunit cell

ex Cd Mg Ti Zn

bull ca = 1633

c

a

A sites

B sites


Middle layer

Top layer

Chapter 1 - 48



A = atomic weight




Density = r =

VC NA

n A r =



Chapter 1 - 49

bull Ex Cr (BCC)

A = 5200 gmol

R = 0125 nm


rtheoretical

a = 4R 3 = 02887 nm

ractual

a R

r = a3

5200 2

atoms

unit cell mol

g

unit cell

volume atoms

mol

6022 x 1023


= 718 gcm3

= 719 gcm3

Adapted from

Fig 32(a) CampR8e

Chapter 1 - 50



Why


r (g

cm

)

3


Metals Alloys

Composites fibers

Polymers

1

2

2 0




3

4

5

03

04

05

Magnesium

Aluminum

Steels

Titanium

CuNi

Tin Zinc

Silver Mo


G raphite

Silicon



Zirconia

H DPE PS PP LDPE

PC

PTFE

PET PVC Silicone

Wood

AFRE

CFRE

GFRE

Glass fibers

Carbon fibers

A ramid fibers


(metallic bonding)





(often amorphous)



In general

Chapter 1 - 51

Chapter 1 - 52

Chapter 1 - 53

Chapter 1 - 54

Fig 34 CampR8e

Crystal Systems

7 crystal systems

14 crystal lattices




Chapter 1 - 55

Chapter 1 - 56

Point Coordinates





z

x

y a b

c

000

111

y

z

2c

b

b

Chapter 1 - 57



through origin





[uvw]

ex 1 0 frac12 =gt 2 0 1 =gt [ 201 ]

-1 1 1


z

x

Algorithm


negative index

[ 111 ] =gt

y

Chapter 1 - 58


direction

a = 0405 nm

Linear Density


a

[110]


Number of atoms

atoms

length

1 35 nm

a 2

2 LD -

Adapted from

Fig 31(a)

CampR8e

Chapter 1 -

BCC vs simple cubic

59

Chapter 1 -

BCC vs Simple C





60

Chapter 1 -

On to HCP






c

Chapter 1 -

Reading


bull 4-1 ndash 4-7

bull 5-1 ndash 5-5

62

Chapter 1 - 63



through origin





[uvtw]

[ 1120 ] ex frac12 frac12 -1 0 =gt


CampR8e



a2

a3

-a3

2

a 2

2

a 1

- a3

a1

a2

z

Algorithm


Chapter 1 - 64




as follows

w w

t

v

u

) v u ( + -

) u v 2 ( 3

1 -

) v u 2 ( 3

1 -

] uvtw [ ] w v u [

Fig 38(a) CampR8e

- a3

a1

a2

z

Chapter 1 - 65



CampR8e

Chapter 1 - 66




Chapter 1 - 67


x

y a b

c


example a b c z

x

y a b

c


1 Intercepts 1 1


1 1 0 3 Reduction 1 1 0

1 Intercepts 12


2 0 0 3 Reduction 2 0 0

example a b c

Chapter 1 - 68


z

x

y a b

c



a b c


2 1 43

3 Reduction 6 3 4

(001) (010)


(100) (010) (001) Ex 100 = (100)

Chapter 1 - 69



used

example a1 a2 a3 c



1 0

-1

-1

1

1


a2

a3

a1

z


CampR8e

Chapter 1 - 70






important


for Fe


planes

Chapter 1 - 71



(100)


R 3

3 4 a


2D repeat unit


1

atoms

2D repeat unit

= nm2

atoms 121

m2

atoms = 12 x 1019

1

2

R 3

3 4 area

2D repeat unit

Chapter 1 - 72







others

-- diamond single


-- turbine blades




GE Superabrasives


permission)


Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 31






= E F

A0

D L

L0

Hookes Law

s = E e

s

Linear- elastic

E

e

F


Chapter 1 - 32

Ceramics



large E

small a

Metals

(Metallic bonding)


moderate E

moderate a

Summary



small Tm

small E

large a

Chapter 1 - 33



bull Unit cells








Single crystal

Polycrystalline

Amorphous



Solids

Chapter 1 - 34

Core Problems Ex 33

ANNOUNCEMENTS

Reading 31-37 317

38-315

Chapter 1 - 35

SUMMARY













Chapter 1 - 36



allotropy)

SUMMARY








Chapter 1 - 37




lower energies

Energy and Packing

Energy

r



Energy

r



Chapter 1 - 38


-metals

-many ceramics

-some polymers



-complex structures

-rapid cooling

crystalline SiO2


CampR8e


CampR8e


Si Oxygen

bull typical of

bull occurs for

Chapter 1 - 39




radii are the same








Chapter 1 - 40






Chapter 1 - 41


APF =

a 3

4

3 p (05a) 3 1

atoms

unit cell atom

volume

unit cell

volume



Volume of unit cell

assume hard spheres



a

R=05a


Chapter 1 - 42








Chapter 1 - 43


a

APF =

4

3 p ( 3 a4 ) 3 2

atoms

unit cell atom

volume

a 3

unit cell

volume

length = 4R =


3 a


a R Adapted from

Fig 32(a) CampR8e

a 2

a 3

Chapter 1 - 44









Chapter 1 - 45




APF =

4

3 p ( 2 a4 ) 3 4

atoms

unit cell atom

volume

a 3

unit cell

volume


length = 4R = 2 a


a

2 a

Adapted from

Fig 31(a)

CampR8e

Chapter 1 - 46

A sites

B B

B

B B

B B

C sites

C C

C A

B

B sites


bull 2D Projection

bull FCC Unit Cell


B B

B

B B

B B

B sites C C

C A

C C

C A

A B

C

Chapter 1 - 47



bull APF = 074



CampR8e


(HCP)

6 atomsunit cell

ex Cd Mg Ti Zn

bull ca = 1633

c

a

A sites

B sites


Middle layer

Top layer

Chapter 1 - 48



A = atomic weight




Density = r =

VC NA

n A r =



Chapter 1 - 49

bull Ex Cr (BCC)

A = 5200 gmol

R = 0125 nm


rtheoretical

a = 4R 3 = 02887 nm

ractual

a R

r = a3

5200 2

atoms

unit cell mol

g

unit cell

volume atoms

mol

6022 x 1023


= 718 gcm3

= 719 gcm3

Adapted from

Fig 32(a) CampR8e

Chapter 1 - 50



Why


r (g

cm

)

3


Metals Alloys

Composites fibers

Polymers

1

2

2 0




3

4

5

03

04

05

Magnesium

Aluminum

Steels

Titanium

CuNi

Tin Zinc

Silver Mo


G raphite

Silicon



Zirconia

H DPE PS PP LDPE

PC

PTFE

PET PVC Silicone

Wood

AFRE

CFRE

GFRE

Glass fibers

Carbon fibers

A ramid fibers


(metallic bonding)





(often amorphous)



In general

Chapter 1 - 51

Chapter 1 - 52

Chapter 1 - 53

Chapter 1 - 54

Fig 34 CampR8e

Crystal Systems

7 crystal systems

14 crystal lattices




Chapter 1 - 55

Chapter 1 - 56

Point Coordinates





z

x

y a b

c

000

111

y

z

2c

b

b

Chapter 1 - 57



through origin





[uvw]

ex 1 0 frac12 =gt 2 0 1 =gt [ 201 ]

-1 1 1


z

x

Algorithm


negative index

[ 111 ] =gt

y

Chapter 1 - 58


direction

a = 0405 nm

Linear Density


a

[110]


Number of atoms

atoms

length

1 35 nm

a 2

2 LD -

Adapted from

Fig 31(a)

CampR8e

Chapter 1 -

BCC vs simple cubic

59

Chapter 1 -

BCC vs Simple C





60

Chapter 1 -

On to HCP






c

Chapter 1 -

Reading


bull 4-1 ndash 4-7

bull 5-1 ndash 5-5

62

Chapter 1 - 63



through origin





[uvtw]

[ 1120 ] ex frac12 frac12 -1 0 =gt


CampR8e



a2

a3

-a3

2

a 2

2

a 1

- a3

a1

a2

z

Algorithm


Chapter 1 - 64




as follows

w w

t

v

u

) v u ( + -

) u v 2 ( 3

1 -

) v u 2 ( 3

1 -

] uvtw [ ] w v u [

Fig 38(a) CampR8e

- a3

a1

a2

z

Chapter 1 - 65



CampR8e

Chapter 1 - 66




Chapter 1 - 67


x

y a b

c


example a b c z

x

y a b

c


1 Intercepts 1 1


1 1 0 3 Reduction 1 1 0

1 Intercepts 12


2 0 0 3 Reduction 2 0 0

example a b c

Chapter 1 - 68


z

x

y a b

c



a b c


2 1 43

3 Reduction 6 3 4

(001) (010)


(100) (010) (001) Ex 100 = (100)

Chapter 1 - 69



used

example a1 a2 a3 c



1 0

-1

-1

1

1


a2

a3

a1

z


CampR8e

Chapter 1 - 70






important


for Fe


planes

Chapter 1 - 71



(100)


R 3

3 4 a


2D repeat unit


1

atoms

2D repeat unit

= nm2

atoms 121

m2

atoms = 12 x 1019

1

2

R 3

3 4 area

2D repeat unit

Chapter 1 - 72







others

-- diamond single


-- turbine blades




GE Superabrasives


permission)


Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 32

Ceramics



large E

small a

Metals

(Metallic bonding)


moderate E

moderate a

Summary



small Tm

small E

large a

Chapter 1 - 33



bull Unit cells








Single crystal

Polycrystalline

Amorphous



Solids

Chapter 1 - 34

Core Problems Ex 33

ANNOUNCEMENTS

Reading 31-37 317

38-315

Chapter 1 - 35

SUMMARY













Chapter 1 - 36



allotropy)

SUMMARY








Chapter 1 - 37




lower energies

Energy and Packing

Energy

r



Energy

r



Chapter 1 - 38


-metals

-many ceramics

-some polymers



-complex structures

-rapid cooling

crystalline SiO2


CampR8e


CampR8e


Si Oxygen

bull typical of

bull occurs for

Chapter 1 - 39




radii are the same








Chapter 1 - 40






Chapter 1 - 41


APF =

a 3

4

3 p (05a) 3 1

atoms

unit cell atom

volume

unit cell

volume



Volume of unit cell

assume hard spheres



a

R=05a


Chapter 1 - 42








Chapter 1 - 43


a

APF =

4

3 p ( 3 a4 ) 3 2

atoms

unit cell atom

volume

a 3

unit cell

volume

length = 4R =


3 a


a R Adapted from

Fig 32(a) CampR8e

a 2

a 3

Chapter 1 - 44









Chapter 1 - 45




APF =

4

3 p ( 2 a4 ) 3 4

atoms

unit cell atom

volume

a 3

unit cell

volume


length = 4R = 2 a


a

2 a

Adapted from

Fig 31(a)

CampR8e

Chapter 1 - 46

A sites

B B

B

B B

B B

C sites

C C

C A

B

B sites


bull 2D Projection

bull FCC Unit Cell


B B

B

B B

B B

B sites C C

C A

C C

C A

A B

C

Chapter 1 - 47



bull APF = 074



CampR8e


(HCP)

6 atomsunit cell

ex Cd Mg Ti Zn

bull ca = 1633

c

a

A sites

B sites


Middle layer

Top layer

Chapter 1 - 48



A = atomic weight




Density = r =

VC NA

n A r =



Chapter 1 - 49

bull Ex Cr (BCC)

A = 5200 gmol

R = 0125 nm


rtheoretical

a = 4R 3 = 02887 nm

ractual

a R

r = a3

5200 2

atoms

unit cell mol

g

unit cell

volume atoms

mol

6022 x 1023


= 718 gcm3

= 719 gcm3

Adapted from

Fig 32(a) CampR8e

Chapter 1 - 50



Why


r (g

cm

)

3


Metals Alloys

Composites fibers

Polymers

1

2

2 0




3

4

5

03

04

05

Magnesium

Aluminum

Steels

Titanium

CuNi

Tin Zinc

Silver Mo


G raphite

Silicon



Zirconia

H DPE PS PP LDPE

PC

PTFE

PET PVC Silicone

Wood

AFRE

CFRE

GFRE

Glass fibers

Carbon fibers

A ramid fibers


(metallic bonding)





(often amorphous)



In general

Chapter 1 - 51

Chapter 1 - 52

Chapter 1 - 53

Chapter 1 - 54

Fig 34 CampR8e

Crystal Systems

7 crystal systems

14 crystal lattices




Chapter 1 - 55

Chapter 1 - 56

Point Coordinates





z

x

y a b

c

000

111

y

z

2c

b

b

Chapter 1 - 57



through origin





[uvw]

ex 1 0 frac12 =gt 2 0 1 =gt [ 201 ]

-1 1 1


z

x

Algorithm


negative index

[ 111 ] =gt

y

Chapter 1 - 58


direction

a = 0405 nm

Linear Density


a

[110]


Number of atoms

atoms

length

1 35 nm

a 2

2 LD -

Adapted from

Fig 31(a)

CampR8e

Chapter 1 -

BCC vs simple cubic

59

Chapter 1 -

BCC vs Simple C





60

Chapter 1 -

On to HCP






c

Chapter 1 -

Reading


bull 4-1 ndash 4-7

bull 5-1 ndash 5-5

62

Chapter 1 - 63



through origin





[uvtw]

[ 1120 ] ex frac12 frac12 -1 0 =gt


CampR8e



a2

a3

-a3

2

a 2

2

a 1

- a3

a1

a2

z

Algorithm


Chapter 1 - 64




as follows

w w

t

v

u

) v u ( + -

) u v 2 ( 3

1 -

) v u 2 ( 3

1 -

] uvtw [ ] w v u [

Fig 38(a) CampR8e

- a3

a1

a2

z

Chapter 1 - 65



CampR8e

Chapter 1 - 66




Chapter 1 - 67


x

y a b

c


example a b c z

x

y a b

c


1 Intercepts 1 1


1 1 0 3 Reduction 1 1 0

1 Intercepts 12


2 0 0 3 Reduction 2 0 0

example a b c

Chapter 1 - 68


z

x

y a b

c



a b c


2 1 43

3 Reduction 6 3 4

(001) (010)


(100) (010) (001) Ex 100 = (100)

Chapter 1 - 69



used

example a1 a2 a3 c



1 0

-1

-1

1

1


a2

a3

a1

z


CampR8e

Chapter 1 - 70






important


for Fe


planes

Chapter 1 - 71



(100)


R 3

3 4 a


2D repeat unit


1

atoms

2D repeat unit

= nm2

atoms 121

m2

atoms = 12 x 1019

1

2

R 3

3 4 area

2D repeat unit

Chapter 1 - 72







others

-- diamond single


-- turbine blades




GE Superabrasives


permission)


Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 33



bull Unit cells








Single crystal

Polycrystalline

Amorphous



Solids

Chapter 1 - 34

Core Problems Ex 33

ANNOUNCEMENTS

Reading 31-37 317

38-315

Chapter 1 - 35

SUMMARY













Chapter 1 - 36



allotropy)

SUMMARY








Chapter 1 - 37




lower energies

Energy and Packing

Energy

r



Energy

r



Chapter 1 - 38


-metals

-many ceramics

-some polymers



-complex structures

-rapid cooling

crystalline SiO2


CampR8e


CampR8e


Si Oxygen

bull typical of

bull occurs for

Chapter 1 - 39




radii are the same








Chapter 1 - 40






Chapter 1 - 41


APF =

a 3

4

3 p (05a) 3 1

atoms

unit cell atom

volume

unit cell

volume



Volume of unit cell

assume hard spheres



a

R=05a


Chapter 1 - 42








Chapter 1 - 43


a

APF =

4

3 p ( 3 a4 ) 3 2

atoms

unit cell atom

volume

a 3

unit cell

volume

length = 4R =


3 a


a R Adapted from

Fig 32(a) CampR8e

a 2

a 3

Chapter 1 - 44









Chapter 1 - 45




APF =

4

3 p ( 2 a4 ) 3 4

atoms

unit cell atom

volume

a 3

unit cell

volume


length = 4R = 2 a


a

2 a

Adapted from

Fig 31(a)

CampR8e

Chapter 1 - 46

A sites

B B

B

B B

B B

C sites

C C

C A

B

B sites


bull 2D Projection

bull FCC Unit Cell


B B

B

B B

B B

B sites C C

C A

C C

C A

A B

C

Chapter 1 - 47



bull APF = 074



CampR8e


(HCP)

6 atomsunit cell

ex Cd Mg Ti Zn

bull ca = 1633

c

a

A sites

B sites


Middle layer

Top layer

Chapter 1 - 48



A = atomic weight




Density = r =

VC NA

n A r =



Chapter 1 - 49

bull Ex Cr (BCC)

A = 5200 gmol

R = 0125 nm


rtheoretical

a = 4R 3 = 02887 nm

ractual

a R

r = a3

5200 2

atoms

unit cell mol

g

unit cell

volume atoms

mol

6022 x 1023


= 718 gcm3

= 719 gcm3

Adapted from

Fig 32(a) CampR8e

Chapter 1 - 50



Why


r (g

cm

)

3


Metals Alloys

Composites fibers

Polymers

1

2

2 0




3

4

5

03

04

05

Magnesium

Aluminum

Steels

Titanium

CuNi

Tin Zinc

Silver Mo


G raphite

Silicon



Zirconia

H DPE PS PP LDPE

PC

PTFE

PET PVC Silicone

Wood

AFRE

CFRE

GFRE

Glass fibers

Carbon fibers

A ramid fibers


(metallic bonding)





(often amorphous)



In general

Chapter 1 - 51

Chapter 1 - 52

Chapter 1 - 53

Chapter 1 - 54

Fig 34 CampR8e

Crystal Systems

7 crystal systems

14 crystal lattices




Chapter 1 - 55

Chapter 1 - 56

Point Coordinates





z

x

y a b

c

000

111

y

z

2c

b

b

Chapter 1 - 57



through origin





[uvw]

ex 1 0 frac12 =gt 2 0 1 =gt [ 201 ]

-1 1 1


z

x

Algorithm


negative index

[ 111 ] =gt

y

Chapter 1 - 58


direction

a = 0405 nm

Linear Density


a

[110]


Number of atoms

atoms

length

1 35 nm

a 2

2 LD -

Adapted from

Fig 31(a)

CampR8e

Chapter 1 -

BCC vs simple cubic

59

Chapter 1 -

BCC vs Simple C





60

Chapter 1 -

On to HCP






c

Chapter 1 -

Reading


bull 4-1 ndash 4-7

bull 5-1 ndash 5-5

62

Chapter 1 - 63



through origin





[uvtw]

[ 1120 ] ex frac12 frac12 -1 0 =gt


CampR8e



a2

a3

-a3

2

a 2

2

a 1

- a3

a1

a2

z

Algorithm


Chapter 1 - 64




as follows

w w

t

v

u

) v u ( + -

) u v 2 ( 3

1 -

) v u 2 ( 3

1 -

] uvtw [ ] w v u [

Fig 38(a) CampR8e

- a3

a1

a2

z

Chapter 1 - 65



CampR8e

Chapter 1 - 66




Chapter 1 - 67


x

y a b

c


example a b c z

x

y a b

c


1 Intercepts 1 1


1 1 0 3 Reduction 1 1 0

1 Intercepts 12


2 0 0 3 Reduction 2 0 0

example a b c

Chapter 1 - 68


z

x

y a b

c



a b c


2 1 43

3 Reduction 6 3 4

(001) (010)


(100) (010) (001) Ex 100 = (100)

Chapter 1 - 69



used

example a1 a2 a3 c



1 0

-1

-1

1

1


a2

a3

a1

z


CampR8e

Chapter 1 - 70






important


for Fe


planes

Chapter 1 - 71



(100)


R 3

3 4 a


2D repeat unit


1

atoms

2D repeat unit

= nm2

atoms 121

m2

atoms = 12 x 1019

1

2

R 3

3 4 area

2D repeat unit

Chapter 1 - 72







others

-- diamond single


-- turbine blades




GE Superabrasives


permission)


Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 34

Core Problems Ex 33

ANNOUNCEMENTS

Reading 31-37 317

38-315

Chapter 1 - 35

SUMMARY













Chapter 1 - 36



allotropy)

SUMMARY








Chapter 1 - 37




lower energies

Energy and Packing

Energy

r



Energy

r



Chapter 1 - 38


-metals

-many ceramics

-some polymers



-complex structures

-rapid cooling

crystalline SiO2


CampR8e


CampR8e


Si Oxygen

bull typical of

bull occurs for

Chapter 1 - 39




radii are the same








Chapter 1 - 40






Chapter 1 - 41


APF =

a 3

4

3 p (05a) 3 1

atoms

unit cell atom

volume

unit cell

volume



Volume of unit cell

assume hard spheres



a

R=05a


Chapter 1 - 42








Chapter 1 - 43


a

APF =

4

3 p ( 3 a4 ) 3 2

atoms

unit cell atom

volume

a 3

unit cell

volume

length = 4R =


3 a


a R Adapted from

Fig 32(a) CampR8e

a 2

a 3

Chapter 1 - 44









Chapter 1 - 45




APF =

4

3 p ( 2 a4 ) 3 4

atoms

unit cell atom

volume

a 3

unit cell

volume


length = 4R = 2 a


a

2 a

Adapted from

Fig 31(a)

CampR8e

Chapter 1 - 46

A sites

B B

B

B B

B B

C sites

C C

C A

B

B sites


bull 2D Projection

bull FCC Unit Cell


B B

B

B B

B B

B sites C C

C A

C C

C A

A B

C

Chapter 1 - 47



bull APF = 074



CampR8e


(HCP)

6 atomsunit cell

ex Cd Mg Ti Zn

bull ca = 1633

c

a

A sites

B sites


Middle layer

Top layer

Chapter 1 - 48



A = atomic weight




Density = r =

VC NA

n A r =



Chapter 1 - 49

bull Ex Cr (BCC)

A = 5200 gmol

R = 0125 nm


rtheoretical

a = 4R 3 = 02887 nm

ractual

a R

r = a3

5200 2

atoms

unit cell mol

g

unit cell

volume atoms

mol

6022 x 1023


= 718 gcm3

= 719 gcm3

Adapted from

Fig 32(a) CampR8e

Chapter 1 - 50



Why


r (g

cm

)

3


Metals Alloys

Composites fibers

Polymers

1

2

2 0




3

4

5

03

04

05

Magnesium

Aluminum

Steels

Titanium

CuNi

Tin Zinc

Silver Mo


G raphite

Silicon



Zirconia

H DPE PS PP LDPE

PC

PTFE

PET PVC Silicone

Wood

AFRE

CFRE

GFRE

Glass fibers

Carbon fibers

A ramid fibers


(metallic bonding)





(often amorphous)



In general

Chapter 1 - 51

Chapter 1 - 52

Chapter 1 - 53

Chapter 1 - 54

Fig 34 CampR8e

Crystal Systems

7 crystal systems

14 crystal lattices




Chapter 1 - 55

Chapter 1 - 56

Point Coordinates





z

x

y a b

c

000

111

y

z

2c

b

b

Chapter 1 - 57



through origin





[uvw]

ex 1 0 frac12 =gt 2 0 1 =gt [ 201 ]

-1 1 1


z

x

Algorithm


negative index

[ 111 ] =gt

y

Chapter 1 - 58


direction

a = 0405 nm

Linear Density


a

[110]


Number of atoms

atoms

length

1 35 nm

a 2

2 LD -

Adapted from

Fig 31(a)

CampR8e

Chapter 1 -

BCC vs simple cubic

59

Chapter 1 -

BCC vs Simple C





60

Chapter 1 -

On to HCP






c

Chapter 1 -

Reading


bull 4-1 ndash 4-7

bull 5-1 ndash 5-5

62

Chapter 1 - 63



through origin





[uvtw]

[ 1120 ] ex frac12 frac12 -1 0 =gt


CampR8e



a2

a3

-a3

2

a 2

2

a 1

- a3

a1

a2

z

Algorithm


Chapter 1 - 64




as follows

w w

t

v

u

) v u ( + -

) u v 2 ( 3

1 -

) v u 2 ( 3

1 -

] uvtw [ ] w v u [

Fig 38(a) CampR8e

- a3

a1

a2

z

Chapter 1 - 65



CampR8e

Chapter 1 - 66




Chapter 1 - 67


x

y a b

c


example a b c z

x

y a b

c


1 Intercepts 1 1


1 1 0 3 Reduction 1 1 0

1 Intercepts 12


2 0 0 3 Reduction 2 0 0

example a b c

Chapter 1 - 68


z

x

y a b

c



a b c


2 1 43

3 Reduction 6 3 4

(001) (010)


(100) (010) (001) Ex 100 = (100)

Chapter 1 - 69



used

example a1 a2 a3 c



1 0

-1

-1

1

1


a2

a3

a1

z


CampR8e

Chapter 1 - 70






important


for Fe


planes

Chapter 1 - 71



(100)


R 3

3 4 a


2D repeat unit


1

atoms

2D repeat unit

= nm2

atoms 121

m2

atoms = 12 x 1019

1

2

R 3

3 4 area

2D repeat unit

Chapter 1 - 72







others

-- diamond single


-- turbine blades




GE Superabrasives


permission)


Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 35

SUMMARY













Chapter 1 - 36



allotropy)

SUMMARY








Chapter 1 - 37




lower energies

Energy and Packing

Energy

r



Energy

r



Chapter 1 - 38


-metals

-many ceramics

-some polymers



-complex structures

-rapid cooling

crystalline SiO2


CampR8e


CampR8e


Si Oxygen

bull typical of

bull occurs for

Chapter 1 - 39




radii are the same








Chapter 1 - 40






Chapter 1 - 41


APF =

a 3

4

3 p (05a) 3 1

atoms

unit cell atom

volume

unit cell

volume



Volume of unit cell

assume hard spheres



a

R=05a


Chapter 1 - 42








Chapter 1 - 43


a

APF =

4

3 p ( 3 a4 ) 3 2

atoms

unit cell atom

volume

a 3

unit cell

volume

length = 4R =


3 a


a R Adapted from

Fig 32(a) CampR8e

a 2

a 3

Chapter 1 - 44









Chapter 1 - 45




APF =

4

3 p ( 2 a4 ) 3 4

atoms

unit cell atom

volume

a 3

unit cell

volume


length = 4R = 2 a


a

2 a

Adapted from

Fig 31(a)

CampR8e

Chapter 1 - 46

A sites

B B

B

B B

B B

C sites

C C

C A

B

B sites


bull 2D Projection

bull FCC Unit Cell


B B

B

B B

B B

B sites C C

C A

C C

C A

A B

C

Chapter 1 - 47



bull APF = 074



CampR8e


(HCP)

6 atomsunit cell

ex Cd Mg Ti Zn

bull ca = 1633

c

a

A sites

B sites


Middle layer

Top layer

Chapter 1 - 48



A = atomic weight




Density = r =

VC NA

n A r =



Chapter 1 - 49

bull Ex Cr (BCC)

A = 5200 gmol

R = 0125 nm


rtheoretical

a = 4R 3 = 02887 nm

ractual

a R

r = a3

5200 2

atoms

unit cell mol

g

unit cell

volume atoms

mol

6022 x 1023


= 718 gcm3

= 719 gcm3

Adapted from

Fig 32(a) CampR8e

Chapter 1 - 50



Why


r (g

cm

)

3


Metals Alloys

Composites fibers

Polymers

1

2

2 0




3

4

5

03

04

05

Magnesium

Aluminum

Steels

Titanium

CuNi

Tin Zinc

Silver Mo


G raphite

Silicon



Zirconia

H DPE PS PP LDPE

PC

PTFE

PET PVC Silicone

Wood

AFRE

CFRE

GFRE

Glass fibers

Carbon fibers

A ramid fibers


(metallic bonding)





(often amorphous)



In general

Chapter 1 - 51

Chapter 1 - 52

Chapter 1 - 53

Chapter 1 - 54

Fig 34 CampR8e

Crystal Systems

7 crystal systems

14 crystal lattices




Chapter 1 - 55

Chapter 1 - 56

Point Coordinates





z

x

y a b

c

000

111

y

z

2c

b

b

Chapter 1 - 57



through origin





[uvw]

ex 1 0 frac12 =gt 2 0 1 =gt [ 201 ]

-1 1 1


z

x

Algorithm


negative index

[ 111 ] =gt

y

Chapter 1 - 58


direction

a = 0405 nm

Linear Density


a

[110]


Number of atoms

atoms

length

1 35 nm

a 2

2 LD -

Adapted from

Fig 31(a)

CampR8e

Chapter 1 -

BCC vs simple cubic

59

Chapter 1 -

BCC vs Simple C





60

Chapter 1 -

On to HCP






c

Chapter 1 -

Reading


bull 4-1 ndash 4-7

bull 5-1 ndash 5-5

62

Chapter 1 - 63



through origin





[uvtw]

[ 1120 ] ex frac12 frac12 -1 0 =gt


CampR8e



a2

a3

-a3

2

a 2

2

a 1

- a3

a1

a2

z

Algorithm


Chapter 1 - 64




as follows

w w

t

v

u

) v u ( + -

) u v 2 ( 3

1 -

) v u 2 ( 3

1 -

] uvtw [ ] w v u [

Fig 38(a) CampR8e

- a3

a1

a2

z

Chapter 1 - 65



CampR8e

Chapter 1 - 66




Chapter 1 - 67


x

y a b

c


example a b c z

x

y a b

c


1 Intercepts 1 1


1 1 0 3 Reduction 1 1 0

1 Intercepts 12


2 0 0 3 Reduction 2 0 0

example a b c

Chapter 1 - 68


z

x

y a b

c



a b c


2 1 43

3 Reduction 6 3 4

(001) (010)


(100) (010) (001) Ex 100 = (100)

Chapter 1 - 69



used

example a1 a2 a3 c



1 0

-1

-1

1

1


a2

a3

a1

z


CampR8e

Chapter 1 - 70






important


for Fe


planes

Chapter 1 - 71



(100)


R 3

3 4 a


2D repeat unit


1

atoms

2D repeat unit

= nm2

atoms 121

m2

atoms = 12 x 1019

1

2

R 3

3 4 area

2D repeat unit

Chapter 1 - 72







others

-- diamond single


-- turbine blades




GE Superabrasives


permission)


Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 36



allotropy)

SUMMARY








Chapter 1 - 37




lower energies

Energy and Packing

Energy

r



Energy

r



Chapter 1 - 38


-metals

-many ceramics

-some polymers



-complex structures

-rapid cooling

crystalline SiO2


CampR8e


CampR8e


Si Oxygen

bull typical of

bull occurs for

Chapter 1 - 39




radii are the same








Chapter 1 - 40






Chapter 1 - 41


APF =

a 3

4

3 p (05a) 3 1

atoms

unit cell atom

volume

unit cell

volume



Volume of unit cell

assume hard spheres



a

R=05a


Chapter 1 - 42








Chapter 1 - 43


a

APF =

4

3 p ( 3 a4 ) 3 2

atoms

unit cell atom

volume

a 3

unit cell

volume

length = 4R =


3 a


a R Adapted from

Fig 32(a) CampR8e

a 2

a 3

Chapter 1 - 44









Chapter 1 - 45




APF =

4

3 p ( 2 a4 ) 3 4

atoms

unit cell atom

volume

a 3

unit cell

volume


length = 4R = 2 a


a

2 a

Adapted from

Fig 31(a)

CampR8e

Chapter 1 - 46

A sites

B B

B

B B

B B

C sites

C C

C A

B

B sites


bull 2D Projection

bull FCC Unit Cell


B B

B

B B

B B

B sites C C

C A

C C

C A

A B

C

Chapter 1 - 47



bull APF = 074



CampR8e


(HCP)

6 atomsunit cell

ex Cd Mg Ti Zn

bull ca = 1633

c

a

A sites

B sites


Middle layer

Top layer

Chapter 1 - 48



A = atomic weight




Density = r =

VC NA

n A r =



Chapter 1 - 49

bull Ex Cr (BCC)

A = 5200 gmol

R = 0125 nm


rtheoretical

a = 4R 3 = 02887 nm

ractual

a R

r = a3

5200 2

atoms

unit cell mol

g

unit cell

volume atoms

mol

6022 x 1023


= 718 gcm3

= 719 gcm3

Adapted from

Fig 32(a) CampR8e

Chapter 1 - 50



Why


r (g

cm

)

3


Metals Alloys

Composites fibers

Polymers

1

2

2 0




3

4

5

03

04

05

Magnesium

Aluminum

Steels

Titanium

CuNi

Tin Zinc

Silver Mo


G raphite

Silicon



Zirconia

H DPE PS PP LDPE

PC

PTFE

PET PVC Silicone

Wood

AFRE

CFRE

GFRE

Glass fibers

Carbon fibers

A ramid fibers


(metallic bonding)





(often amorphous)



In general

Chapter 1 - 51

Chapter 1 - 52

Chapter 1 - 53

Chapter 1 - 54

Fig 34 CampR8e

Crystal Systems

7 crystal systems

14 crystal lattices




Chapter 1 - 55

Chapter 1 - 56

Point Coordinates





z

x

y a b

c

000

111

y

z

2c

b

b

Chapter 1 - 57



through origin





[uvw]

ex 1 0 frac12 =gt 2 0 1 =gt [ 201 ]

-1 1 1


z

x

Algorithm


negative index

[ 111 ] =gt

y

Chapter 1 - 58


direction

a = 0405 nm

Linear Density


a

[110]


Number of atoms

atoms

length

1 35 nm

a 2

2 LD -

Adapted from

Fig 31(a)

CampR8e

Chapter 1 -

BCC vs simple cubic

59

Chapter 1 -

BCC vs Simple C





60

Chapter 1 -

On to HCP






c

Chapter 1 -

Reading


bull 4-1 ndash 4-7

bull 5-1 ndash 5-5

62

Chapter 1 - 63



through origin





[uvtw]

[ 1120 ] ex frac12 frac12 -1 0 =gt


CampR8e



a2

a3

-a3

2

a 2

2

a 1

- a3

a1

a2

z

Algorithm


Chapter 1 - 64




as follows

w w

t

v

u

) v u ( + -

) u v 2 ( 3

1 -

) v u 2 ( 3

1 -

] uvtw [ ] w v u [

Fig 38(a) CampR8e

- a3

a1

a2

z

Chapter 1 - 65



CampR8e

Chapter 1 - 66




Chapter 1 - 67


x

y a b

c


example a b c z

x

y a b

c


1 Intercepts 1 1


1 1 0 3 Reduction 1 1 0

1 Intercepts 12


2 0 0 3 Reduction 2 0 0

example a b c

Chapter 1 - 68


z

x

y a b

c



a b c


2 1 43

3 Reduction 6 3 4

(001) (010)


(100) (010) (001) Ex 100 = (100)

Chapter 1 - 69



used

example a1 a2 a3 c



1 0

-1

-1

1

1


a2

a3

a1

z


CampR8e

Chapter 1 - 70






important


for Fe


planes

Chapter 1 - 71



(100)


R 3

3 4 a


2D repeat unit


1

atoms

2D repeat unit

= nm2

atoms 121

m2

atoms = 12 x 1019

1

2

R 3

3 4 area

2D repeat unit

Chapter 1 - 72







others

-- diamond single


-- turbine blades




GE Superabrasives


permission)


Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 37




lower energies

Energy and Packing

Energy

r



Energy

r



Chapter 1 - 38


-metals

-many ceramics

-some polymers



-complex structures

-rapid cooling

crystalline SiO2


CampR8e


CampR8e


Si Oxygen

bull typical of

bull occurs for

Chapter 1 - 39




radii are the same








Chapter 1 - 40






Chapter 1 - 41


APF =

a 3

4

3 p (05a) 3 1

atoms

unit cell atom

volume

unit cell

volume



Volume of unit cell

assume hard spheres



a

R=05a


Chapter 1 - 42








Chapter 1 - 43


a

APF =

4

3 p ( 3 a4 ) 3 2

atoms

unit cell atom

volume

a 3

unit cell

volume

length = 4R =


3 a


a R Adapted from

Fig 32(a) CampR8e

a 2

a 3

Chapter 1 - 44









Chapter 1 - 45




APF =

4

3 p ( 2 a4 ) 3 4

atoms

unit cell atom

volume

a 3

unit cell

volume


length = 4R = 2 a


a

2 a

Adapted from

Fig 31(a)

CampR8e

Chapter 1 - 46

A sites

B B

B

B B

B B

C sites

C C

C A

B

B sites


bull 2D Projection

bull FCC Unit Cell


B B

B

B B

B B

B sites C C

C A

C C

C A

A B

C

Chapter 1 - 47



bull APF = 074



CampR8e


(HCP)

6 atomsunit cell

ex Cd Mg Ti Zn

bull ca = 1633

c

a

A sites

B sites


Middle layer

Top layer

Chapter 1 - 48



A = atomic weight




Density = r =

VC NA

n A r =



Chapter 1 - 49

bull Ex Cr (BCC)

A = 5200 gmol

R = 0125 nm


rtheoretical

a = 4R 3 = 02887 nm

ractual

a R

r = a3

5200 2

atoms

unit cell mol

g

unit cell

volume atoms

mol

6022 x 1023


= 718 gcm3

= 719 gcm3

Adapted from

Fig 32(a) CampR8e

Chapter 1 - 50



Why


r (g

cm

)

3


Metals Alloys

Composites fibers

Polymers

1

2

2 0




3

4

5

03

04

05

Magnesium

Aluminum

Steels

Titanium

CuNi

Tin Zinc

Silver Mo


G raphite

Silicon



Zirconia

H DPE PS PP LDPE

PC

PTFE

PET PVC Silicone

Wood

AFRE

CFRE

GFRE

Glass fibers

Carbon fibers

A ramid fibers


(metallic bonding)





(often amorphous)



In general

Chapter 1 - 51

Chapter 1 - 52

Chapter 1 - 53

Chapter 1 - 54

Fig 34 CampR8e

Crystal Systems

7 crystal systems

14 crystal lattices




Chapter 1 - 55

Chapter 1 - 56

Point Coordinates





z

x

y a b

c

000

111

y

z

2c

b

b

Chapter 1 - 57



through origin





[uvw]

ex 1 0 frac12 =gt 2 0 1 =gt [ 201 ]

-1 1 1


z

x

Algorithm


negative index

[ 111 ] =gt

y

Chapter 1 - 58


direction

a = 0405 nm

Linear Density


a

[110]


Number of atoms

atoms

length

1 35 nm

a 2

2 LD -

Adapted from

Fig 31(a)

CampR8e

Chapter 1 -

BCC vs simple cubic

59

Chapter 1 -

BCC vs Simple C





60

Chapter 1 -

On to HCP






c

Chapter 1 -

Reading


bull 4-1 ndash 4-7

bull 5-1 ndash 5-5

62

Chapter 1 - 63



through origin





[uvtw]

[ 1120 ] ex frac12 frac12 -1 0 =gt


CampR8e



a2

a3

-a3

2

a 2

2

a 1

- a3

a1

a2

z

Algorithm


Chapter 1 - 64




as follows

w w

t

v

u

) v u ( + -

) u v 2 ( 3

1 -

) v u 2 ( 3

1 -

] uvtw [ ] w v u [

Fig 38(a) CampR8e

- a3

a1

a2

z

Chapter 1 - 65



CampR8e

Chapter 1 - 66




Chapter 1 - 67


x

y a b

c


example a b c z

x

y a b

c


1 Intercepts 1 1


1 1 0 3 Reduction 1 1 0

1 Intercepts 12


2 0 0 3 Reduction 2 0 0

example a b c

Chapter 1 - 68


z

x

y a b

c



a b c


2 1 43

3 Reduction 6 3 4

(001) (010)


(100) (010) (001) Ex 100 = (100)

Chapter 1 - 69



used

example a1 a2 a3 c



1 0

-1

-1

1

1


a2

a3

a1

z


CampR8e

Chapter 1 - 70






important


for Fe


planes

Chapter 1 - 71



(100)


R 3

3 4 a


2D repeat unit


1

atoms

2D repeat unit

= nm2

atoms 121

m2

atoms = 12 x 1019

1

2

R 3

3 4 area

2D repeat unit

Chapter 1 - 72







others

-- diamond single


-- turbine blades




GE Superabrasives


permission)


Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 38


-metals

-many ceramics

-some polymers



-complex structures

-rapid cooling

crystalline SiO2


CampR8e


CampR8e


Si Oxygen

bull typical of

bull occurs for

Chapter 1 - 39




radii are the same








Chapter 1 - 40






Chapter 1 - 41


APF =

a 3

4

3 p (05a) 3 1

atoms

unit cell atom

volume

unit cell

volume



Volume of unit cell

assume hard spheres



a

R=05a


Chapter 1 - 42








Chapter 1 - 43


a

APF =

4

3 p ( 3 a4 ) 3 2

atoms

unit cell atom

volume

a 3

unit cell

volume

length = 4R =


3 a


a R Adapted from

Fig 32(a) CampR8e

a 2

a 3

Chapter 1 - 44









Chapter 1 - 45




APF =

4

3 p ( 2 a4 ) 3 4

atoms

unit cell atom

volume

a 3

unit cell

volume


length = 4R = 2 a


a

2 a

Adapted from

Fig 31(a)

CampR8e

Chapter 1 - 46

A sites

B B

B

B B

B B

C sites

C C

C A

B

B sites


bull 2D Projection

bull FCC Unit Cell


B B

B

B B

B B

B sites C C

C A

C C

C A

A B

C

Chapter 1 - 47



bull APF = 074



CampR8e


(HCP)

6 atomsunit cell

ex Cd Mg Ti Zn

bull ca = 1633

c

a

A sites

B sites


Middle layer

Top layer

Chapter 1 - 48



A = atomic weight




Density = r =

VC NA

n A r =



Chapter 1 - 49

bull Ex Cr (BCC)

A = 5200 gmol

R = 0125 nm


rtheoretical

a = 4R 3 = 02887 nm

ractual

a R

r = a3

5200 2

atoms

unit cell mol

g

unit cell

volume atoms

mol

6022 x 1023


= 718 gcm3

= 719 gcm3

Adapted from

Fig 32(a) CampR8e

Chapter 1 - 50



Why


r (g

cm

)

3


Metals Alloys

Composites fibers

Polymers

1

2

2 0




3

4

5

03

04

05

Magnesium

Aluminum

Steels

Titanium

CuNi

Tin Zinc

Silver Mo


G raphite

Silicon



Zirconia

H DPE PS PP LDPE

PC

PTFE

PET PVC Silicone

Wood

AFRE

CFRE

GFRE

Glass fibers

Carbon fibers

A ramid fibers


(metallic bonding)





(often amorphous)



In general

Chapter 1 - 51

Chapter 1 - 52

Chapter 1 - 53

Chapter 1 - 54

Fig 34 CampR8e

Crystal Systems

7 crystal systems

14 crystal lattices




Chapter 1 - 55

Chapter 1 - 56

Point Coordinates





z

x

y a b

c

000

111

y

z

2c

b

b

Chapter 1 - 57



through origin





[uvw]

ex 1 0 frac12 =gt 2 0 1 =gt [ 201 ]

-1 1 1


z

x

Algorithm


negative index

[ 111 ] =gt

y

Chapter 1 - 58


direction

a = 0405 nm

Linear Density


a

[110]


Number of atoms

atoms

length

1 35 nm

a 2

2 LD -

Adapted from

Fig 31(a)

CampR8e

Chapter 1 -

BCC vs simple cubic

59

Chapter 1 -

BCC vs Simple C





60

Chapter 1 -

On to HCP






c

Chapter 1 -

Reading


bull 4-1 ndash 4-7

bull 5-1 ndash 5-5

62

Chapter 1 - 63



through origin





[uvtw]

[ 1120 ] ex frac12 frac12 -1 0 =gt


CampR8e



a2

a3

-a3

2

a 2

2

a 1

- a3

a1

a2

z

Algorithm


Chapter 1 - 64




as follows

w w

t

v

u

) v u ( + -

) u v 2 ( 3

1 -

) v u 2 ( 3

1 -

] uvtw [ ] w v u [

Fig 38(a) CampR8e

- a3

a1

a2

z

Chapter 1 - 65



CampR8e

Chapter 1 - 66




Chapter 1 - 67


x

y a b

c


example a b c z

x

y a b

c


1 Intercepts 1 1


1 1 0 3 Reduction 1 1 0

1 Intercepts 12


2 0 0 3 Reduction 2 0 0

example a b c

Chapter 1 - 68


z

x

y a b

c



a b c


2 1 43

3 Reduction 6 3 4

(001) (010)


(100) (010) (001) Ex 100 = (100)

Chapter 1 - 69



used

example a1 a2 a3 c



1 0

-1

-1

1

1


a2

a3

a1

z


CampR8e

Chapter 1 - 70






important


for Fe


planes

Chapter 1 - 71



(100)


R 3

3 4 a


2D repeat unit


1

atoms

2D repeat unit

= nm2

atoms 121

m2

atoms = 12 x 1019

1

2

R 3

3 4 area

2D repeat unit

Chapter 1 - 72







others

-- diamond single


-- turbine blades




GE Superabrasives


permission)


Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 39




radii are the same








Chapter 1 - 40






Chapter 1 - 41


APF =

a 3

4

3 p (05a) 3 1

atoms

unit cell atom

volume

unit cell

volume



Volume of unit cell

assume hard spheres



a

R=05a


Chapter 1 - 42








Chapter 1 - 43


a

APF =

4

3 p ( 3 a4 ) 3 2

atoms

unit cell atom

volume

a 3

unit cell

volume

length = 4R =


3 a


a R Adapted from

Fig 32(a) CampR8e

a 2

a 3

Chapter 1 - 44









Chapter 1 - 45




APF =

4

3 p ( 2 a4 ) 3 4

atoms

unit cell atom

volume

a 3

unit cell

volume


length = 4R = 2 a


a

2 a

Adapted from

Fig 31(a)

CampR8e

Chapter 1 - 46

A sites

B B

B

B B

B B

C sites

C C

C A

B

B sites


bull 2D Projection

bull FCC Unit Cell


B B

B

B B

B B

B sites C C

C A

C C

C A

A B

C

Chapter 1 - 47



bull APF = 074



CampR8e


(HCP)

6 atomsunit cell

ex Cd Mg Ti Zn

bull ca = 1633

c

a

A sites

B sites


Middle layer

Top layer

Chapter 1 - 48



A = atomic weight




Density = r =

VC NA

n A r =



Chapter 1 - 49

bull Ex Cr (BCC)

A = 5200 gmol

R = 0125 nm


rtheoretical

a = 4R 3 = 02887 nm

ractual

a R

r = a3

5200 2

atoms

unit cell mol

g

unit cell

volume atoms

mol

6022 x 1023


= 718 gcm3

= 719 gcm3

Adapted from

Fig 32(a) CampR8e

Chapter 1 - 50



Why


r (g

cm

)

3


Metals Alloys

Composites fibers

Polymers

1

2

2 0




3

4

5

03

04

05

Magnesium

Aluminum

Steels

Titanium

CuNi

Tin Zinc

Silver Mo


G raphite

Silicon



Zirconia

H DPE PS PP LDPE

PC

PTFE

PET PVC Silicone

Wood

AFRE

CFRE

GFRE

Glass fibers

Carbon fibers

A ramid fibers


(metallic bonding)





(often amorphous)



In general

Chapter 1 - 51

Chapter 1 - 52

Chapter 1 - 53

Chapter 1 - 54

Fig 34 CampR8e

Crystal Systems

7 crystal systems

14 crystal lattices




Chapter 1 - 55

Chapter 1 - 56

Point Coordinates





z

x

y a b

c

000

111

y

z

2c

b

b

Chapter 1 - 57



through origin





[uvw]

ex 1 0 frac12 =gt 2 0 1 =gt [ 201 ]

-1 1 1


z

x

Algorithm


negative index

[ 111 ] =gt

y

Chapter 1 - 58


direction

a = 0405 nm

Linear Density


a

[110]


Number of atoms

atoms

length

1 35 nm

a 2

2 LD -

Adapted from

Fig 31(a)

CampR8e

Chapter 1 -

BCC vs simple cubic

59

Chapter 1 -

BCC vs Simple C





60

Chapter 1 -

On to HCP






c

Chapter 1 -

Reading


bull 4-1 ndash 4-7

bull 5-1 ndash 5-5

62

Chapter 1 - 63



through origin





[uvtw]

[ 1120 ] ex frac12 frac12 -1 0 =gt


CampR8e



a2

a3

-a3

2

a 2

2

a 1

- a3

a1

a2

z

Algorithm


Chapter 1 - 64




as follows

w w

t

v

u

) v u ( + -

) u v 2 ( 3

1 -

) v u 2 ( 3

1 -

] uvtw [ ] w v u [

Fig 38(a) CampR8e

- a3

a1

a2

z

Chapter 1 - 65



CampR8e

Chapter 1 - 66




Chapter 1 - 67


x

y a b

c


example a b c z

x

y a b

c


1 Intercepts 1 1


1 1 0 3 Reduction 1 1 0

1 Intercepts 12


2 0 0 3 Reduction 2 0 0

example a b c

Chapter 1 - 68


z

x

y a b

c



a b c


2 1 43

3 Reduction 6 3 4

(001) (010)


(100) (010) (001) Ex 100 = (100)

Chapter 1 - 69



used

example a1 a2 a3 c



1 0

-1

-1

1

1


a2

a3

a1

z


CampR8e

Chapter 1 - 70






important


for Fe


planes

Chapter 1 - 71



(100)


R 3

3 4 a


2D repeat unit


1

atoms

2D repeat unit

= nm2

atoms 121

m2

atoms = 12 x 1019

1

2

R 3

3 4 area

2D repeat unit

Chapter 1 - 72







others

-- diamond single


-- turbine blades




GE Superabrasives


permission)


Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 40






Chapter 1 - 41


APF =

a 3

4

3 p (05a) 3 1

atoms

unit cell atom

volume

unit cell

volume



Volume of unit cell

assume hard spheres



a

R=05a


Chapter 1 - 42








Chapter 1 - 43


a

APF =

4

3 p ( 3 a4 ) 3 2

atoms

unit cell atom

volume

a 3

unit cell

volume

length = 4R =


3 a


a R Adapted from

Fig 32(a) CampR8e

a 2

a 3

Chapter 1 - 44









Chapter 1 - 45




APF =

4

3 p ( 2 a4 ) 3 4

atoms

unit cell atom

volume

a 3

unit cell

volume


length = 4R = 2 a


a

2 a

Adapted from

Fig 31(a)

CampR8e

Chapter 1 - 46

A sites

B B

B

B B

B B

C sites

C C

C A

B

B sites


bull 2D Projection

bull FCC Unit Cell


B B

B

B B

B B

B sites C C

C A

C C

C A

A B

C

Chapter 1 - 47



bull APF = 074



CampR8e


(HCP)

6 atomsunit cell

ex Cd Mg Ti Zn

bull ca = 1633

c

a

A sites

B sites


Middle layer

Top layer

Chapter 1 - 48



A = atomic weight




Density = r =

VC NA

n A r =



Chapter 1 - 49

bull Ex Cr (BCC)

A = 5200 gmol

R = 0125 nm


rtheoretical

a = 4R 3 = 02887 nm

ractual

a R

r = a3

5200 2

atoms

unit cell mol

g

unit cell

volume atoms

mol

6022 x 1023


= 718 gcm3

= 719 gcm3

Adapted from

Fig 32(a) CampR8e

Chapter 1 - 50



Why


r (g

cm

)

3


Metals Alloys

Composites fibers

Polymers

1

2

2 0




3

4

5

03

04

05

Magnesium

Aluminum

Steels

Titanium

CuNi

Tin Zinc

Silver Mo


G raphite

Silicon



Zirconia

H DPE PS PP LDPE

PC

PTFE

PET PVC Silicone

Wood

AFRE

CFRE

GFRE

Glass fibers

Carbon fibers

A ramid fibers


(metallic bonding)





(often amorphous)



In general

Chapter 1 - 51

Chapter 1 - 52

Chapter 1 - 53

Chapter 1 - 54

Fig 34 CampR8e

Crystal Systems

7 crystal systems

14 crystal lattices




Chapter 1 - 55

Chapter 1 - 56

Point Coordinates





z

x

y a b

c

000

111

y

z

2c

b

b

Chapter 1 - 57



through origin





[uvw]

ex 1 0 frac12 =gt 2 0 1 =gt [ 201 ]

-1 1 1


z

x

Algorithm


negative index

[ 111 ] =gt

y

Chapter 1 - 58


direction

a = 0405 nm

Linear Density


a

[110]


Number of atoms

atoms

length

1 35 nm

a 2

2 LD -

Adapted from

Fig 31(a)

CampR8e

Chapter 1 -

BCC vs simple cubic

59

Chapter 1 -

BCC vs Simple C





60

Chapter 1 -

On to HCP






c

Chapter 1 -

Reading


bull 4-1 ndash 4-7

bull 5-1 ndash 5-5

62

Chapter 1 - 63



through origin





[uvtw]

[ 1120 ] ex frac12 frac12 -1 0 =gt


CampR8e



a2

a3

-a3

2

a 2

2

a 1

- a3

a1

a2

z

Algorithm


Chapter 1 - 64




as follows

w w

t

v

u

) v u ( + -

) u v 2 ( 3

1 -

) v u 2 ( 3

1 -

] uvtw [ ] w v u [

Fig 38(a) CampR8e

- a3

a1

a2

z

Chapter 1 - 65



CampR8e

Chapter 1 - 66




Chapter 1 - 67


x

y a b

c


example a b c z

x

y a b

c


1 Intercepts 1 1


1 1 0 3 Reduction 1 1 0

1 Intercepts 12


2 0 0 3 Reduction 2 0 0

example a b c

Chapter 1 - 68


z

x

y a b

c



a b c


2 1 43

3 Reduction 6 3 4

(001) (010)


(100) (010) (001) Ex 100 = (100)

Chapter 1 - 69



used

example a1 a2 a3 c



1 0

-1

-1

1

1


a2

a3

a1

z


CampR8e

Chapter 1 - 70






important


for Fe


planes

Chapter 1 - 71



(100)


R 3

3 4 a


2D repeat unit


1

atoms

2D repeat unit

= nm2

atoms 121

m2

atoms = 12 x 1019

1

2

R 3

3 4 area

2D repeat unit

Chapter 1 - 72







others

-- diamond single


-- turbine blades




GE Superabrasives


permission)


Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 41


APF =

a 3

4

3 p (05a) 3 1

atoms

unit cell atom

volume

unit cell

volume



Volume of unit cell

assume hard spheres



a

R=05a


Chapter 1 - 42








Chapter 1 - 43


a

APF =

4

3 p ( 3 a4 ) 3 2

atoms

unit cell atom

volume

a 3

unit cell

volume

length = 4R =


3 a


a R Adapted from

Fig 32(a) CampR8e

a 2

a 3

Chapter 1 - 44









Chapter 1 - 45




APF =

4

3 p ( 2 a4 ) 3 4

atoms

unit cell atom

volume

a 3

unit cell

volume


length = 4R = 2 a


a

2 a

Adapted from

Fig 31(a)

CampR8e

Chapter 1 - 46

A sites

B B

B

B B

B B

C sites

C C

C A

B

B sites


bull 2D Projection

bull FCC Unit Cell


B B

B

B B

B B

B sites C C

C A

C C

C A

A B

C

Chapter 1 - 47



bull APF = 074



CampR8e


(HCP)

6 atomsunit cell

ex Cd Mg Ti Zn

bull ca = 1633

c

a

A sites

B sites


Middle layer

Top layer

Chapter 1 - 48



A = atomic weight




Density = r =

VC NA

n A r =



Chapter 1 - 49

bull Ex Cr (BCC)

A = 5200 gmol

R = 0125 nm


rtheoretical

a = 4R 3 = 02887 nm

ractual

a R

r = a3

5200 2

atoms

unit cell mol

g

unit cell

volume atoms

mol

6022 x 1023


= 718 gcm3

= 719 gcm3

Adapted from

Fig 32(a) CampR8e

Chapter 1 - 50



Why


r (g

cm

)

3


Metals Alloys

Composites fibers

Polymers

1

2

2 0




3

4

5

03

04

05

Magnesium

Aluminum

Steels

Titanium

CuNi

Tin Zinc

Silver Mo


G raphite

Silicon



Zirconia

H DPE PS PP LDPE

PC

PTFE

PET PVC Silicone

Wood

AFRE

CFRE

GFRE

Glass fibers

Carbon fibers

A ramid fibers


(metallic bonding)





(often amorphous)



In general

Chapter 1 - 51

Chapter 1 - 52

Chapter 1 - 53

Chapter 1 - 54

Fig 34 CampR8e

Crystal Systems

7 crystal systems

14 crystal lattices




Chapter 1 - 55

Chapter 1 - 56

Point Coordinates





z

x

y a b

c

000

111

y

z

2c

b

b

Chapter 1 - 57



through origin





[uvw]

ex 1 0 frac12 =gt 2 0 1 =gt [ 201 ]

-1 1 1


z

x

Algorithm


negative index

[ 111 ] =gt

y

Chapter 1 - 58


direction

a = 0405 nm

Linear Density


a

[110]


Number of atoms

atoms

length

1 35 nm

a 2

2 LD -

Adapted from

Fig 31(a)

CampR8e

Chapter 1 -

BCC vs simple cubic

59

Chapter 1 -

BCC vs Simple C





60

Chapter 1 -

On to HCP






c

Chapter 1 -

Reading


bull 4-1 ndash 4-7

bull 5-1 ndash 5-5

62

Chapter 1 - 63



through origin





[uvtw]

[ 1120 ] ex frac12 frac12 -1 0 =gt


CampR8e



a2

a3

-a3

2

a 2

2

a 1

- a3

a1

a2

z

Algorithm


Chapter 1 - 64




as follows

w w

t

v

u

) v u ( + -

) u v 2 ( 3

1 -

) v u 2 ( 3

1 -

] uvtw [ ] w v u [

Fig 38(a) CampR8e

- a3

a1

a2

z

Chapter 1 - 65



CampR8e

Chapter 1 - 66




Chapter 1 - 67


x

y a b

c


example a b c z

x

y a b

c


1 Intercepts 1 1


1 1 0 3 Reduction 1 1 0

1 Intercepts 12


2 0 0 3 Reduction 2 0 0

example a b c

Chapter 1 - 68


z

x

y a b

c



a b c


2 1 43

3 Reduction 6 3 4

(001) (010)


(100) (010) (001) Ex 100 = (100)

Chapter 1 - 69



used

example a1 a2 a3 c



1 0

-1

-1

1

1


a2

a3

a1

z


CampR8e

Chapter 1 - 70






important


for Fe


planes

Chapter 1 - 71



(100)


R 3

3 4 a


2D repeat unit


1

atoms

2D repeat unit

= nm2

atoms 121

m2

atoms = 12 x 1019

1

2

R 3

3 4 area

2D repeat unit

Chapter 1 - 72







others

-- diamond single


-- turbine blades




GE Superabrasives


permission)


Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 42








Chapter 1 - 43


a

APF =

4

3 p ( 3 a4 ) 3 2

atoms

unit cell atom

volume

a 3

unit cell

volume

length = 4R =


3 a


a R Adapted from

Fig 32(a) CampR8e

a 2

a 3

Chapter 1 - 44









Chapter 1 - 45




APF =

4

3 p ( 2 a4 ) 3 4

atoms

unit cell atom

volume

a 3

unit cell

volume


length = 4R = 2 a


a

2 a

Adapted from

Fig 31(a)

CampR8e

Chapter 1 - 46

A sites

B B

B

B B

B B

C sites

C C

C A

B

B sites


bull 2D Projection

bull FCC Unit Cell


B B

B

B B

B B

B sites C C

C A

C C

C A

A B

C

Chapter 1 - 47



bull APF = 074



CampR8e


(HCP)

6 atomsunit cell

ex Cd Mg Ti Zn

bull ca = 1633

c

a

A sites

B sites


Middle layer

Top layer

Chapter 1 - 48



A = atomic weight




Density = r =

VC NA

n A r =



Chapter 1 - 49

bull Ex Cr (BCC)

A = 5200 gmol

R = 0125 nm


rtheoretical

a = 4R 3 = 02887 nm

ractual

a R

r = a3

5200 2

atoms

unit cell mol

g

unit cell

volume atoms

mol

6022 x 1023


= 718 gcm3

= 719 gcm3

Adapted from

Fig 32(a) CampR8e

Chapter 1 - 50



Why


r (g

cm

)

3


Metals Alloys

Composites fibers

Polymers

1

2

2 0




3

4

5

03

04

05

Magnesium

Aluminum

Steels

Titanium

CuNi

Tin Zinc

Silver Mo


G raphite

Silicon



Zirconia

H DPE PS PP LDPE

PC

PTFE

PET PVC Silicone

Wood

AFRE

CFRE

GFRE

Glass fibers

Carbon fibers

A ramid fibers


(metallic bonding)





(often amorphous)



In general

Chapter 1 - 51

Chapter 1 - 52

Chapter 1 - 53

Chapter 1 - 54

Fig 34 CampR8e

Crystal Systems

7 crystal systems

14 crystal lattices




Chapter 1 - 55

Chapter 1 - 56

Point Coordinates





z

x

y a b

c

000

111

y

z

2c

b

b

Chapter 1 - 57



through origin





[uvw]

ex 1 0 frac12 =gt 2 0 1 =gt [ 201 ]

-1 1 1


z

x

Algorithm


negative index

[ 111 ] =gt

y

Chapter 1 - 58


direction

a = 0405 nm

Linear Density


a

[110]


Number of atoms

atoms

length

1 35 nm

a 2

2 LD -

Adapted from

Fig 31(a)

CampR8e

Chapter 1 -

BCC vs simple cubic

59

Chapter 1 -

BCC vs Simple C





60

Chapter 1 -

On to HCP






c

Chapter 1 -

Reading


bull 4-1 ndash 4-7

bull 5-1 ndash 5-5

62

Chapter 1 - 63



through origin





[uvtw]

[ 1120 ] ex frac12 frac12 -1 0 =gt


CampR8e



a2

a3

-a3

2

a 2

2

a 1

- a3

a1

a2

z

Algorithm


Chapter 1 - 64




as follows

w w

t

v

u

) v u ( + -

) u v 2 ( 3

1 -

) v u 2 ( 3

1 -

] uvtw [ ] w v u [

Fig 38(a) CampR8e

- a3

a1

a2

z

Chapter 1 - 65



CampR8e

Chapter 1 - 66




Chapter 1 - 67


x

y a b

c


example a b c z

x

y a b

c


1 Intercepts 1 1


1 1 0 3 Reduction 1 1 0

1 Intercepts 12


2 0 0 3 Reduction 2 0 0

example a b c

Chapter 1 - 68


z

x

y a b

c



a b c


2 1 43

3 Reduction 6 3 4

(001) (010)


(100) (010) (001) Ex 100 = (100)

Chapter 1 - 69



used

example a1 a2 a3 c



1 0

-1

-1

1

1


a2

a3

a1

z


CampR8e

Chapter 1 - 70






important


for Fe


planes

Chapter 1 - 71



(100)


R 3

3 4 a


2D repeat unit


1

atoms

2D repeat unit

= nm2

atoms 121

m2

atoms = 12 x 1019

1

2

R 3

3 4 area

2D repeat unit

Chapter 1 - 72







others

-- diamond single


-- turbine blades




GE Superabrasives


permission)


Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 43


a

APF =

4

3 p ( 3 a4 ) 3 2

atoms

unit cell atom

volume

a 3

unit cell

volume

length = 4R =


3 a


a R Adapted from

Fig 32(a) CampR8e

a 2

a 3

Chapter 1 - 44









Chapter 1 - 45




APF =

4

3 p ( 2 a4 ) 3 4

atoms

unit cell atom

volume

a 3

unit cell

volume


length = 4R = 2 a


a

2 a

Adapted from

Fig 31(a)

CampR8e

Chapter 1 - 46

A sites

B B

B

B B

B B

C sites

C C

C A

B

B sites


bull 2D Projection

bull FCC Unit Cell


B B

B

B B

B B

B sites C C

C A

C C

C A

A B

C

Chapter 1 - 47



bull APF = 074



CampR8e


(HCP)

6 atomsunit cell

ex Cd Mg Ti Zn

bull ca = 1633

c

a

A sites

B sites


Middle layer

Top layer

Chapter 1 - 48



A = atomic weight




Density = r =

VC NA

n A r =



Chapter 1 - 49

bull Ex Cr (BCC)

A = 5200 gmol

R = 0125 nm


rtheoretical

a = 4R 3 = 02887 nm

ractual

a R

r = a3

5200 2

atoms

unit cell mol

g

unit cell

volume atoms

mol

6022 x 1023


= 718 gcm3

= 719 gcm3

Adapted from

Fig 32(a) CampR8e

Chapter 1 - 50



Why


r (g

cm

)

3


Metals Alloys

Composites fibers

Polymers

1

2

2 0




3

4

5

03

04

05

Magnesium

Aluminum

Steels

Titanium

CuNi

Tin Zinc

Silver Mo


G raphite

Silicon



Zirconia

H DPE PS PP LDPE

PC

PTFE

PET PVC Silicone

Wood

AFRE

CFRE

GFRE

Glass fibers

Carbon fibers

A ramid fibers


(metallic bonding)





(often amorphous)



In general

Chapter 1 - 51

Chapter 1 - 52

Chapter 1 - 53

Chapter 1 - 54

Fig 34 CampR8e

Crystal Systems

7 crystal systems

14 crystal lattices




Chapter 1 - 55

Chapter 1 - 56

Point Coordinates





z

x

y a b

c

000

111

y

z

2c

b

b

Chapter 1 - 57



through origin





[uvw]

ex 1 0 frac12 =gt 2 0 1 =gt [ 201 ]

-1 1 1


z

x

Algorithm


negative index

[ 111 ] =gt

y

Chapter 1 - 58


direction

a = 0405 nm

Linear Density


a

[110]


Number of atoms

atoms

length

1 35 nm

a 2

2 LD -

Adapted from

Fig 31(a)

CampR8e

Chapter 1 -

BCC vs simple cubic

59

Chapter 1 -

BCC vs Simple C





60

Chapter 1 -

On to HCP






c

Chapter 1 -

Reading


bull 4-1 ndash 4-7

bull 5-1 ndash 5-5

62

Chapter 1 - 63



through origin





[uvtw]

[ 1120 ] ex frac12 frac12 -1 0 =gt


CampR8e



a2

a3

-a3

2

a 2

2

a 1

- a3

a1

a2

z

Algorithm


Chapter 1 - 64




as follows

w w

t

v

u

) v u ( + -

) u v 2 ( 3

1 -

) v u 2 ( 3

1 -

] uvtw [ ] w v u [

Fig 38(a) CampR8e

- a3

a1

a2

z

Chapter 1 - 65



CampR8e

Chapter 1 - 66




Chapter 1 - 67


x

y a b

c


example a b c z

x

y a b

c


1 Intercepts 1 1


1 1 0 3 Reduction 1 1 0

1 Intercepts 12


2 0 0 3 Reduction 2 0 0

example a b c

Chapter 1 - 68


z

x

y a b

c



a b c


2 1 43

3 Reduction 6 3 4

(001) (010)


(100) (010) (001) Ex 100 = (100)

Chapter 1 - 69



used

example a1 a2 a3 c



1 0

-1

-1

1

1


a2

a3

a1

z


CampR8e

Chapter 1 - 70






important


for Fe


planes

Chapter 1 - 71



(100)


R 3

3 4 a


2D repeat unit


1

atoms

2D repeat unit

= nm2

atoms 121

m2

atoms = 12 x 1019

1

2

R 3

3 4 area

2D repeat unit

Chapter 1 - 72







others

-- diamond single


-- turbine blades




GE Superabrasives


permission)


Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 44









Chapter 1 - 45




APF =

4

3 p ( 2 a4 ) 3 4

atoms

unit cell atom

volume

a 3

unit cell

volume


length = 4R = 2 a


a

2 a

Adapted from

Fig 31(a)

CampR8e

Chapter 1 - 46

A sites

B B

B

B B

B B

C sites

C C

C A

B

B sites


bull 2D Projection

bull FCC Unit Cell


B B

B

B B

B B

B sites C C

C A

C C

C A

A B

C

Chapter 1 - 47



bull APF = 074



CampR8e


(HCP)

6 atomsunit cell

ex Cd Mg Ti Zn

bull ca = 1633

c

a

A sites

B sites


Middle layer

Top layer

Chapter 1 - 48



A = atomic weight




Density = r =

VC NA

n A r =



Chapter 1 - 49

bull Ex Cr (BCC)

A = 5200 gmol

R = 0125 nm


rtheoretical

a = 4R 3 = 02887 nm

ractual

a R

r = a3

5200 2

atoms

unit cell mol

g

unit cell

volume atoms

mol

6022 x 1023


= 718 gcm3

= 719 gcm3

Adapted from

Fig 32(a) CampR8e

Chapter 1 - 50



Why


r (g

cm

)

3


Metals Alloys

Composites fibers

Polymers

1

2

2 0




3

4

5

03

04

05

Magnesium

Aluminum

Steels

Titanium

CuNi

Tin Zinc

Silver Mo


G raphite

Silicon



Zirconia

H DPE PS PP LDPE

PC

PTFE

PET PVC Silicone

Wood

AFRE

CFRE

GFRE

Glass fibers

Carbon fibers

A ramid fibers


(metallic bonding)





(often amorphous)



In general

Chapter 1 - 51

Chapter 1 - 52

Chapter 1 - 53

Chapter 1 - 54

Fig 34 CampR8e

Crystal Systems

7 crystal systems

14 crystal lattices




Chapter 1 - 55

Chapter 1 - 56

Point Coordinates





z

x

y a b

c

000

111

y

z

2c

b

b

Chapter 1 - 57



through origin





[uvw]

ex 1 0 frac12 =gt 2 0 1 =gt [ 201 ]

-1 1 1


z

x

Algorithm


negative index

[ 111 ] =gt

y

Chapter 1 - 58


direction

a = 0405 nm

Linear Density


a

[110]


Number of atoms

atoms

length

1 35 nm

a 2

2 LD -

Adapted from

Fig 31(a)

CampR8e

Chapter 1 -

BCC vs simple cubic

59

Chapter 1 -

BCC vs Simple C





60

Chapter 1 -

On to HCP






c

Chapter 1 -

Reading


bull 4-1 ndash 4-7

bull 5-1 ndash 5-5

62

Chapter 1 - 63



through origin





[uvtw]

[ 1120 ] ex frac12 frac12 -1 0 =gt


CampR8e



a2

a3

-a3

2

a 2

2

a 1

- a3

a1

a2

z

Algorithm


Chapter 1 - 64




as follows

w w

t

v

u

) v u ( + -

) u v 2 ( 3

1 -

) v u 2 ( 3

1 -

] uvtw [ ] w v u [

Fig 38(a) CampR8e

- a3

a1

a2

z

Chapter 1 - 65



CampR8e

Chapter 1 - 66




Chapter 1 - 67


x

y a b

c


example a b c z

x

y a b

c


1 Intercepts 1 1


1 1 0 3 Reduction 1 1 0

1 Intercepts 12


2 0 0 3 Reduction 2 0 0

example a b c

Chapter 1 - 68


z

x

y a b

c



a b c


2 1 43

3 Reduction 6 3 4

(001) (010)


(100) (010) (001) Ex 100 = (100)

Chapter 1 - 69



used

example a1 a2 a3 c



1 0

-1

-1

1

1


a2

a3

a1

z


CampR8e

Chapter 1 - 70






important


for Fe


planes

Chapter 1 - 71



(100)


R 3

3 4 a


2D repeat unit


1

atoms

2D repeat unit

= nm2

atoms 121

m2

atoms = 12 x 1019

1

2

R 3

3 4 area

2D repeat unit

Chapter 1 - 72







others

-- diamond single


-- turbine blades




GE Superabrasives


permission)


Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 45




APF =

4

3 p ( 2 a4 ) 3 4

atoms

unit cell atom

volume

a 3

unit cell

volume


length = 4R = 2 a


a

2 a

Adapted from

Fig 31(a)

CampR8e

Chapter 1 - 46

A sites

B B

B

B B

B B

C sites

C C

C A

B

B sites


bull 2D Projection

bull FCC Unit Cell


B B

B

B B

B B

B sites C C

C A

C C

C A

A B

C

Chapter 1 - 47



bull APF = 074



CampR8e


(HCP)

6 atomsunit cell

ex Cd Mg Ti Zn

bull ca = 1633

c

a

A sites

B sites


Middle layer

Top layer

Chapter 1 - 48



A = atomic weight




Density = r =

VC NA

n A r =



Chapter 1 - 49

bull Ex Cr (BCC)

A = 5200 gmol

R = 0125 nm


rtheoretical

a = 4R 3 = 02887 nm

ractual

a R

r = a3

5200 2

atoms

unit cell mol

g

unit cell

volume atoms

mol

6022 x 1023


= 718 gcm3

= 719 gcm3

Adapted from

Fig 32(a) CampR8e

Chapter 1 - 50



Why


r (g

cm

)

3


Metals Alloys

Composites fibers

Polymers

1

2

2 0




3

4

5

03

04

05

Magnesium

Aluminum

Steels

Titanium

CuNi

Tin Zinc

Silver Mo


G raphite

Silicon



Zirconia

H DPE PS PP LDPE

PC

PTFE

PET PVC Silicone

Wood

AFRE

CFRE

GFRE

Glass fibers

Carbon fibers

A ramid fibers


(metallic bonding)





(often amorphous)



In general

Chapter 1 - 51

Chapter 1 - 52

Chapter 1 - 53

Chapter 1 - 54

Fig 34 CampR8e

Crystal Systems

7 crystal systems

14 crystal lattices




Chapter 1 - 55

Chapter 1 - 56

Point Coordinates





z

x

y a b

c

000

111

y

z

2c

b

b

Chapter 1 - 57



through origin





[uvw]

ex 1 0 frac12 =gt 2 0 1 =gt [ 201 ]

-1 1 1


z

x

Algorithm


negative index

[ 111 ] =gt

y

Chapter 1 - 58


direction

a = 0405 nm

Linear Density


a

[110]


Number of atoms

atoms

length

1 35 nm

a 2

2 LD -

Adapted from

Fig 31(a)

CampR8e

Chapter 1 -

BCC vs simple cubic

59

Chapter 1 -

BCC vs Simple C





60

Chapter 1 -

On to HCP






c

Chapter 1 -

Reading


bull 4-1 ndash 4-7

bull 5-1 ndash 5-5

62

Chapter 1 - 63



through origin





[uvtw]

[ 1120 ] ex frac12 frac12 -1 0 =gt


CampR8e



a2

a3

-a3

2

a 2

2

a 1

- a3

a1

a2

z

Algorithm


Chapter 1 - 64




as follows

w w

t

v

u

) v u ( + -

) u v 2 ( 3

1 -

) v u 2 ( 3

1 -

] uvtw [ ] w v u [

Fig 38(a) CampR8e

- a3

a1

a2

z

Chapter 1 - 65



CampR8e

Chapter 1 - 66




Chapter 1 - 67


x

y a b

c


example a b c z

x

y a b

c


1 Intercepts 1 1


1 1 0 3 Reduction 1 1 0

1 Intercepts 12


2 0 0 3 Reduction 2 0 0

example a b c

Chapter 1 - 68


z

x

y a b

c



a b c


2 1 43

3 Reduction 6 3 4

(001) (010)


(100) (010) (001) Ex 100 = (100)

Chapter 1 - 69



used

example a1 a2 a3 c



1 0

-1

-1

1

1


a2

a3

a1

z


CampR8e

Chapter 1 - 70






important


for Fe


planes

Chapter 1 - 71



(100)


R 3

3 4 a


2D repeat unit


1

atoms

2D repeat unit

= nm2

atoms 121

m2

atoms = 12 x 1019

1

2

R 3

3 4 area

2D repeat unit

Chapter 1 - 72







others

-- diamond single


-- turbine blades




GE Superabrasives


permission)


Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 46

A sites

B B

B

B B

B B

C sites

C C

C A

B

B sites


bull 2D Projection

bull FCC Unit Cell


B B

B

B B

B B

B sites C C

C A

C C

C A

A B

C

Chapter 1 - 47



bull APF = 074



CampR8e


(HCP)

6 atomsunit cell

ex Cd Mg Ti Zn

bull ca = 1633

c

a

A sites

B sites


Middle layer

Top layer

Chapter 1 - 48



A = atomic weight




Density = r =

VC NA

n A r =



Chapter 1 - 49

bull Ex Cr (BCC)

A = 5200 gmol

R = 0125 nm


rtheoretical

a = 4R 3 = 02887 nm

ractual

a R

r = a3

5200 2

atoms

unit cell mol

g

unit cell

volume atoms

mol

6022 x 1023


= 718 gcm3

= 719 gcm3

Adapted from

Fig 32(a) CampR8e

Chapter 1 - 50



Why


r (g

cm

)

3


Metals Alloys

Composites fibers

Polymers

1

2

2 0




3

4

5

03

04

05

Magnesium

Aluminum

Steels

Titanium

CuNi

Tin Zinc

Silver Mo


G raphite

Silicon



Zirconia

H DPE PS PP LDPE

PC

PTFE

PET PVC Silicone

Wood

AFRE

CFRE

GFRE

Glass fibers

Carbon fibers

A ramid fibers


(metallic bonding)





(often amorphous)



In general

Chapter 1 - 51

Chapter 1 - 52

Chapter 1 - 53

Chapter 1 - 54

Fig 34 CampR8e

Crystal Systems

7 crystal systems

14 crystal lattices




Chapter 1 - 55

Chapter 1 - 56

Point Coordinates





z

x

y a b

c

000

111

y

z

2c

b

b

Chapter 1 - 57



through origin





[uvw]

ex 1 0 frac12 =gt 2 0 1 =gt [ 201 ]

-1 1 1


z

x

Algorithm


negative index

[ 111 ] =gt

y

Chapter 1 - 58


direction

a = 0405 nm

Linear Density


a

[110]


Number of atoms

atoms

length

1 35 nm

a 2

2 LD -

Adapted from

Fig 31(a)

CampR8e

Chapter 1 -

BCC vs simple cubic

59

Chapter 1 -

BCC vs Simple C





60

Chapter 1 -

On to HCP






c

Chapter 1 -

Reading


bull 4-1 ndash 4-7

bull 5-1 ndash 5-5

62

Chapter 1 - 63



through origin





[uvtw]

[ 1120 ] ex frac12 frac12 -1 0 =gt


CampR8e



a2

a3

-a3

2

a 2

2

a 1

- a3

a1

a2

z

Algorithm


Chapter 1 - 64




as follows

w w

t

v

u

) v u ( + -

) u v 2 ( 3

1 -

) v u 2 ( 3

1 -

] uvtw [ ] w v u [

Fig 38(a) CampR8e

- a3

a1

a2

z

Chapter 1 - 65



CampR8e

Chapter 1 - 66




Chapter 1 - 67


x

y a b

c


example a b c z

x

y a b

c


1 Intercepts 1 1


1 1 0 3 Reduction 1 1 0

1 Intercepts 12


2 0 0 3 Reduction 2 0 0

example a b c

Chapter 1 - 68


z

x

y a b

c



a b c


2 1 43

3 Reduction 6 3 4

(001) (010)


(100) (010) (001) Ex 100 = (100)

Chapter 1 - 69



used

example a1 a2 a3 c



1 0

-1

-1

1

1


a2

a3

a1

z


CampR8e

Chapter 1 - 70






important


for Fe


planes

Chapter 1 - 71



(100)


R 3

3 4 a


2D repeat unit


1

atoms

2D repeat unit

= nm2

atoms 121

m2

atoms = 12 x 1019

1

2

R 3

3 4 area

2D repeat unit

Chapter 1 - 72







others

-- diamond single


-- turbine blades




GE Superabrasives


permission)


Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 47



bull APF = 074



CampR8e


(HCP)

6 atomsunit cell

ex Cd Mg Ti Zn

bull ca = 1633

c

a

A sites

B sites


Middle layer

Top layer

Chapter 1 - 48



A = atomic weight




Density = r =

VC NA

n A r =



Chapter 1 - 49

bull Ex Cr (BCC)

A = 5200 gmol

R = 0125 nm


rtheoretical

a = 4R 3 = 02887 nm

ractual

a R

r = a3

5200 2

atoms

unit cell mol

g

unit cell

volume atoms

mol

6022 x 1023


= 718 gcm3

= 719 gcm3

Adapted from

Fig 32(a) CampR8e

Chapter 1 - 50



Why


r (g

cm

)

3


Metals Alloys

Composites fibers

Polymers

1

2

2 0




3

4

5

03

04

05

Magnesium

Aluminum

Steels

Titanium

CuNi

Tin Zinc

Silver Mo


G raphite

Silicon



Zirconia

H DPE PS PP LDPE

PC

PTFE

PET PVC Silicone

Wood

AFRE

CFRE

GFRE

Glass fibers

Carbon fibers

A ramid fibers


(metallic bonding)





(often amorphous)



In general

Chapter 1 - 51

Chapter 1 - 52

Chapter 1 - 53

Chapter 1 - 54

Fig 34 CampR8e

Crystal Systems

7 crystal systems

14 crystal lattices




Chapter 1 - 55

Chapter 1 - 56

Point Coordinates





z

x

y a b

c

000

111

y

z

2c

b

b

Chapter 1 - 57



through origin





[uvw]

ex 1 0 frac12 =gt 2 0 1 =gt [ 201 ]

-1 1 1


z

x

Algorithm


negative index

[ 111 ] =gt

y

Chapter 1 - 58


direction

a = 0405 nm

Linear Density


a

[110]


Number of atoms

atoms

length

1 35 nm

a 2

2 LD -

Adapted from

Fig 31(a)

CampR8e

Chapter 1 -

BCC vs simple cubic

59

Chapter 1 -

BCC vs Simple C





60

Chapter 1 -

On to HCP






c

Chapter 1 -

Reading


bull 4-1 ndash 4-7

bull 5-1 ndash 5-5

62

Chapter 1 - 63



through origin





[uvtw]

[ 1120 ] ex frac12 frac12 -1 0 =gt


CampR8e



a2

a3

-a3

2

a 2

2

a 1

- a3

a1

a2

z

Algorithm


Chapter 1 - 64




as follows

w w

t

v

u

) v u ( + -

) u v 2 ( 3

1 -

) v u 2 ( 3

1 -

] uvtw [ ] w v u [

Fig 38(a) CampR8e

- a3

a1

a2

z

Chapter 1 - 65



CampR8e

Chapter 1 - 66




Chapter 1 - 67


x

y a b

c


example a b c z

x

y a b

c


1 Intercepts 1 1


1 1 0 3 Reduction 1 1 0

1 Intercepts 12


2 0 0 3 Reduction 2 0 0

example a b c

Chapter 1 - 68


z

x

y a b

c



a b c


2 1 43

3 Reduction 6 3 4

(001) (010)


(100) (010) (001) Ex 100 = (100)

Chapter 1 - 69



used

example a1 a2 a3 c



1 0

-1

-1

1

1


a2

a3

a1

z


CampR8e

Chapter 1 - 70






important


for Fe


planes

Chapter 1 - 71



(100)


R 3

3 4 a


2D repeat unit


1

atoms

2D repeat unit

= nm2

atoms 121

m2

atoms = 12 x 1019

1

2

R 3

3 4 area

2D repeat unit

Chapter 1 - 72







others

-- diamond single


-- turbine blades




GE Superabrasives


permission)


Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 48



A = atomic weight




Density = r =

VC NA

n A r =



Chapter 1 - 49

bull Ex Cr (BCC)

A = 5200 gmol

R = 0125 nm


rtheoretical

a = 4R 3 = 02887 nm

ractual

a R

r = a3

5200 2

atoms

unit cell mol

g

unit cell

volume atoms

mol

6022 x 1023


= 718 gcm3

= 719 gcm3

Adapted from

Fig 32(a) CampR8e

Chapter 1 - 50



Why


r (g

cm

)

3


Metals Alloys

Composites fibers

Polymers

1

2

2 0




3

4

5

03

04

05

Magnesium

Aluminum

Steels

Titanium

CuNi

Tin Zinc

Silver Mo


G raphite

Silicon



Zirconia

H DPE PS PP LDPE

PC

PTFE

PET PVC Silicone

Wood

AFRE

CFRE

GFRE

Glass fibers

Carbon fibers

A ramid fibers


(metallic bonding)





(often amorphous)



In general

Chapter 1 - 51

Chapter 1 - 52

Chapter 1 - 53

Chapter 1 - 54

Fig 34 CampR8e

Crystal Systems

7 crystal systems

14 crystal lattices




Chapter 1 - 55

Chapter 1 - 56

Point Coordinates





z

x

y a b

c

000

111

y

z

2c

b

b

Chapter 1 - 57



through origin





[uvw]

ex 1 0 frac12 =gt 2 0 1 =gt [ 201 ]

-1 1 1


z

x

Algorithm


negative index

[ 111 ] =gt

y

Chapter 1 - 58


direction

a = 0405 nm

Linear Density


a

[110]


Number of atoms

atoms

length

1 35 nm

a 2

2 LD -

Adapted from

Fig 31(a)

CampR8e

Chapter 1 -

BCC vs simple cubic

59

Chapter 1 -

BCC vs Simple C





60

Chapter 1 -

On to HCP






c

Chapter 1 -

Reading


bull 4-1 ndash 4-7

bull 5-1 ndash 5-5

62

Chapter 1 - 63



through origin





[uvtw]

[ 1120 ] ex frac12 frac12 -1 0 =gt


CampR8e



a2

a3

-a3

2

a 2

2

a 1

- a3

a1

a2

z

Algorithm


Chapter 1 - 64




as follows

w w

t

v

u

) v u ( + -

) u v 2 ( 3

1 -

) v u 2 ( 3

1 -

] uvtw [ ] w v u [

Fig 38(a) CampR8e

- a3

a1

a2

z

Chapter 1 - 65



CampR8e

Chapter 1 - 66




Chapter 1 - 67


x

y a b

c


example a b c z

x

y a b

c


1 Intercepts 1 1


1 1 0 3 Reduction 1 1 0

1 Intercepts 12


2 0 0 3 Reduction 2 0 0

example a b c

Chapter 1 - 68


z

x

y a b

c



a b c


2 1 43

3 Reduction 6 3 4

(001) (010)


(100) (010) (001) Ex 100 = (100)

Chapter 1 - 69



used

example a1 a2 a3 c



1 0

-1

-1

1

1


a2

a3

a1

z


CampR8e

Chapter 1 - 70






important


for Fe


planes

Chapter 1 - 71



(100)


R 3

3 4 a


2D repeat unit


1

atoms

2D repeat unit

= nm2

atoms 121

m2

atoms = 12 x 1019

1

2

R 3

3 4 area

2D repeat unit

Chapter 1 - 72







others

-- diamond single


-- turbine blades




GE Superabrasives


permission)


Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 49

bull Ex Cr (BCC)

A = 5200 gmol

R = 0125 nm


rtheoretical

a = 4R 3 = 02887 nm

ractual

a R

r = a3

5200 2

atoms

unit cell mol

g

unit cell

volume atoms

mol

6022 x 1023


= 718 gcm3

= 719 gcm3

Adapted from

Fig 32(a) CampR8e

Chapter 1 - 50



Why


r (g

cm

)

3


Metals Alloys

Composites fibers

Polymers

1

2

2 0




3

4

5

03

04

05

Magnesium

Aluminum

Steels

Titanium

CuNi

Tin Zinc

Silver Mo


G raphite

Silicon



Zirconia

H DPE PS PP LDPE

PC

PTFE

PET PVC Silicone

Wood

AFRE

CFRE

GFRE

Glass fibers

Carbon fibers

A ramid fibers


(metallic bonding)





(often amorphous)



In general

Chapter 1 - 51

Chapter 1 - 52

Chapter 1 - 53

Chapter 1 - 54

Fig 34 CampR8e

Crystal Systems

7 crystal systems

14 crystal lattices




Chapter 1 - 55

Chapter 1 - 56

Point Coordinates





z

x

y a b

c

000

111

y

z

2c

b

b

Chapter 1 - 57



through origin





[uvw]

ex 1 0 frac12 =gt 2 0 1 =gt [ 201 ]

-1 1 1


z

x

Algorithm


negative index

[ 111 ] =gt

y

Chapter 1 - 58


direction

a = 0405 nm

Linear Density


a

[110]


Number of atoms

atoms

length

1 35 nm

a 2

2 LD -

Adapted from

Fig 31(a)

CampR8e

Chapter 1 -

BCC vs simple cubic

59

Chapter 1 -

BCC vs Simple C





60

Chapter 1 -

On to HCP






c

Chapter 1 -

Reading


bull 4-1 ndash 4-7

bull 5-1 ndash 5-5

62

Chapter 1 - 63



through origin





[uvtw]

[ 1120 ] ex frac12 frac12 -1 0 =gt


CampR8e



a2

a3

-a3

2

a 2

2

a 1

- a3

a1

a2

z

Algorithm


Chapter 1 - 64




as follows

w w

t

v

u

) v u ( + -

) u v 2 ( 3

1 -

) v u 2 ( 3

1 -

] uvtw [ ] w v u [

Fig 38(a) CampR8e

- a3

a1

a2

z

Chapter 1 - 65



CampR8e

Chapter 1 - 66




Chapter 1 - 67


x

y a b

c


example a b c z

x

y a b

c


1 Intercepts 1 1


1 1 0 3 Reduction 1 1 0

1 Intercepts 12


2 0 0 3 Reduction 2 0 0

example a b c

Chapter 1 - 68


z

x

y a b

c



a b c


2 1 43

3 Reduction 6 3 4

(001) (010)


(100) (010) (001) Ex 100 = (100)

Chapter 1 - 69



used

example a1 a2 a3 c



1 0

-1

-1

1

1


a2

a3

a1

z


CampR8e

Chapter 1 - 70






important


for Fe


planes

Chapter 1 - 71



(100)


R 3

3 4 a


2D repeat unit


1

atoms

2D repeat unit

= nm2

atoms 121

m2

atoms = 12 x 1019

1

2

R 3

3 4 area

2D repeat unit

Chapter 1 - 72







others

-- diamond single


-- turbine blades




GE Superabrasives


permission)


Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 50



Why


r (g

cm

)

3


Metals Alloys

Composites fibers

Polymers

1

2

2 0




3

4

5

03

04

05

Magnesium

Aluminum

Steels

Titanium

CuNi

Tin Zinc

Silver Mo


G raphite

Silicon



Zirconia

H DPE PS PP LDPE

PC

PTFE

PET PVC Silicone

Wood

AFRE

CFRE

GFRE

Glass fibers

Carbon fibers

A ramid fibers


(metallic bonding)





(often amorphous)



In general

Chapter 1 - 51

Chapter 1 - 52

Chapter 1 - 53

Chapter 1 - 54

Fig 34 CampR8e

Crystal Systems

7 crystal systems

14 crystal lattices




Chapter 1 - 55

Chapter 1 - 56

Point Coordinates





z

x

y a b

c

000

111

y

z

2c

b

b

Chapter 1 - 57



through origin





[uvw]

ex 1 0 frac12 =gt 2 0 1 =gt [ 201 ]

-1 1 1


z

x

Algorithm


negative index

[ 111 ] =gt

y

Chapter 1 - 58


direction

a = 0405 nm

Linear Density


a

[110]


Number of atoms

atoms

length

1 35 nm

a 2

2 LD -

Adapted from

Fig 31(a)

CampR8e

Chapter 1 -

BCC vs simple cubic

59

Chapter 1 -

BCC vs Simple C





60

Chapter 1 -

On to HCP






c

Chapter 1 -

Reading


bull 4-1 ndash 4-7

bull 5-1 ndash 5-5

62

Chapter 1 - 63



through origin





[uvtw]

[ 1120 ] ex frac12 frac12 -1 0 =gt


CampR8e



a2

a3

-a3

2

a 2

2

a 1

- a3

a1

a2

z

Algorithm


Chapter 1 - 64




as follows

w w

t

v

u

) v u ( + -

) u v 2 ( 3

1 -

) v u 2 ( 3

1 -

] uvtw [ ] w v u [

Fig 38(a) CampR8e

- a3

a1

a2

z

Chapter 1 - 65



CampR8e

Chapter 1 - 66




Chapter 1 - 67


x

y a b

c


example a b c z

x

y a b

c


1 Intercepts 1 1


1 1 0 3 Reduction 1 1 0

1 Intercepts 12


2 0 0 3 Reduction 2 0 0

example a b c

Chapter 1 - 68


z

x

y a b

c



a b c


2 1 43

3 Reduction 6 3 4

(001) (010)


(100) (010) (001) Ex 100 = (100)

Chapter 1 - 69



used

example a1 a2 a3 c



1 0

-1

-1

1

1


a2

a3

a1

z


CampR8e

Chapter 1 - 70






important


for Fe


planes

Chapter 1 - 71



(100)


R 3

3 4 a


2D repeat unit


1

atoms

2D repeat unit

= nm2

atoms 121

m2

atoms = 12 x 1019

1

2

R 3

3 4 area

2D repeat unit

Chapter 1 - 72







others

-- diamond single


-- turbine blades




GE Superabrasives


permission)


Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 51

Chapter 1 - 52

Chapter 1 - 53

Chapter 1 - 54

Fig 34 CampR8e

Crystal Systems

7 crystal systems

14 crystal lattices




Chapter 1 - 55

Chapter 1 - 56

Point Coordinates





z

x

y a b

c

000

111

y

z

2c

b

b

Chapter 1 - 57



through origin





[uvw]

ex 1 0 frac12 =gt 2 0 1 =gt [ 201 ]

-1 1 1


z

x

Algorithm


negative index

[ 111 ] =gt

y

Chapter 1 - 58


direction

a = 0405 nm

Linear Density


a

[110]


Number of atoms

atoms

length

1 35 nm

a 2

2 LD -

Adapted from

Fig 31(a)

CampR8e

Chapter 1 -

BCC vs simple cubic

59

Chapter 1 -

BCC vs Simple C





60

Chapter 1 -

On to HCP






c

Chapter 1 -

Reading


bull 4-1 ndash 4-7

bull 5-1 ndash 5-5

62

Chapter 1 - 63



through origin





[uvtw]

[ 1120 ] ex frac12 frac12 -1 0 =gt


CampR8e



a2

a3

-a3

2

a 2

2

a 1

- a3

a1

a2

z

Algorithm


Chapter 1 - 64




as follows

w w

t

v

u

) v u ( + -

) u v 2 ( 3

1 -

) v u 2 ( 3

1 -

] uvtw [ ] w v u [

Fig 38(a) CampR8e

- a3

a1

a2

z

Chapter 1 - 65



CampR8e

Chapter 1 - 66




Chapter 1 - 67


x

y a b

c


example a b c z

x

y a b

c


1 Intercepts 1 1


1 1 0 3 Reduction 1 1 0

1 Intercepts 12


2 0 0 3 Reduction 2 0 0

example a b c

Chapter 1 - 68


z

x

y a b

c



a b c


2 1 43

3 Reduction 6 3 4

(001) (010)


(100) (010) (001) Ex 100 = (100)

Chapter 1 - 69



used

example a1 a2 a3 c



1 0

-1

-1

1

1


a2

a3

a1

z


CampR8e

Chapter 1 - 70






important


for Fe


planes

Chapter 1 - 71



(100)


R 3

3 4 a


2D repeat unit


1

atoms

2D repeat unit

= nm2

atoms 121

m2

atoms = 12 x 1019

1

2

R 3

3 4 area

2D repeat unit

Chapter 1 - 72







others

-- diamond single


-- turbine blades




GE Superabrasives


permission)


Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 52

Chapter 1 - 53

Chapter 1 - 54

Fig 34 CampR8e

Crystal Systems

7 crystal systems

14 crystal lattices




Chapter 1 - 55

Chapter 1 - 56

Point Coordinates





z

x

y a b

c

000

111

y

z

2c

b

b

Chapter 1 - 57



through origin





[uvw]

ex 1 0 frac12 =gt 2 0 1 =gt [ 201 ]

-1 1 1


z

x

Algorithm


negative index

[ 111 ] =gt

y

Chapter 1 - 58


direction

a = 0405 nm

Linear Density


a

[110]


Number of atoms

atoms

length

1 35 nm

a 2

2 LD -

Adapted from

Fig 31(a)

CampR8e

Chapter 1 -

BCC vs simple cubic

59

Chapter 1 -

BCC vs Simple C





60

Chapter 1 -

On to HCP






c

Chapter 1 -

Reading


bull 4-1 ndash 4-7

bull 5-1 ndash 5-5

62

Chapter 1 - 63



through origin





[uvtw]

[ 1120 ] ex frac12 frac12 -1 0 =gt


CampR8e



a2

a3

-a3

2

a 2

2

a 1

- a3

a1

a2

z

Algorithm


Chapter 1 - 64




as follows

w w

t

v

u

) v u ( + -

) u v 2 ( 3

1 -

) v u 2 ( 3

1 -

] uvtw [ ] w v u [

Fig 38(a) CampR8e

- a3

a1

a2

z

Chapter 1 - 65



CampR8e

Chapter 1 - 66




Chapter 1 - 67


x

y a b

c


example a b c z

x

y a b

c


1 Intercepts 1 1


1 1 0 3 Reduction 1 1 0

1 Intercepts 12


2 0 0 3 Reduction 2 0 0

example a b c

Chapter 1 - 68


z

x

y a b

c



a b c


2 1 43

3 Reduction 6 3 4

(001) (010)


(100) (010) (001) Ex 100 = (100)

Chapter 1 - 69



used

example a1 a2 a3 c



1 0

-1

-1

1

1


a2

a3

a1

z


CampR8e

Chapter 1 - 70






important


for Fe


planes

Chapter 1 - 71



(100)


R 3

3 4 a


2D repeat unit


1

atoms

2D repeat unit

= nm2

atoms 121

m2

atoms = 12 x 1019

1

2

R 3

3 4 area

2D repeat unit

Chapter 1 - 72







others

-- diamond single


-- turbine blades




GE Superabrasives


permission)


Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 53

Chapter 1 - 54

Fig 34 CampR8e

Crystal Systems

7 crystal systems

14 crystal lattices




Chapter 1 - 55

Chapter 1 - 56

Point Coordinates





z

x

y a b

c

000

111

y

z

2c

b

b

Chapter 1 - 57



through origin





[uvw]

ex 1 0 frac12 =gt 2 0 1 =gt [ 201 ]

-1 1 1


z

x

Algorithm


negative index

[ 111 ] =gt

y

Chapter 1 - 58


direction

a = 0405 nm

Linear Density


a

[110]


Number of atoms

atoms

length

1 35 nm

a 2

2 LD -

Adapted from

Fig 31(a)

CampR8e

Chapter 1 -

BCC vs simple cubic

59

Chapter 1 -

BCC vs Simple C





60

Chapter 1 -

On to HCP






c

Chapter 1 -

Reading


bull 4-1 ndash 4-7

bull 5-1 ndash 5-5

62

Chapter 1 - 63



through origin





[uvtw]

[ 1120 ] ex frac12 frac12 -1 0 =gt


CampR8e



a2

a3

-a3

2

a 2

2

a 1

- a3

a1

a2

z

Algorithm


Chapter 1 - 64




as follows

w w

t

v

u

) v u ( + -

) u v 2 ( 3

1 -

) v u 2 ( 3

1 -

] uvtw [ ] w v u [

Fig 38(a) CampR8e

- a3

a1

a2

z

Chapter 1 - 65



CampR8e

Chapter 1 - 66




Chapter 1 - 67


x

y a b

c


example a b c z

x

y a b

c


1 Intercepts 1 1


1 1 0 3 Reduction 1 1 0

1 Intercepts 12


2 0 0 3 Reduction 2 0 0

example a b c

Chapter 1 - 68


z

x

y a b

c



a b c


2 1 43

3 Reduction 6 3 4

(001) (010)


(100) (010) (001) Ex 100 = (100)

Chapter 1 - 69



used

example a1 a2 a3 c



1 0

-1

-1

1

1


a2

a3

a1

z


CampR8e

Chapter 1 - 70






important


for Fe


planes

Chapter 1 - 71



(100)


R 3

3 4 a


2D repeat unit


1

atoms

2D repeat unit

= nm2

atoms 121

m2

atoms = 12 x 1019

1

2

R 3

3 4 area

2D repeat unit

Chapter 1 - 72







others

-- diamond single


-- turbine blades




GE Superabrasives


permission)


Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 54

Fig 34 CampR8e

Crystal Systems

7 crystal systems

14 crystal lattices




Chapter 1 - 55

Chapter 1 - 56

Point Coordinates





z

x

y a b

c

000

111

y

z

2c

b

b

Chapter 1 - 57



through origin





[uvw]

ex 1 0 frac12 =gt 2 0 1 =gt [ 201 ]

-1 1 1


z

x

Algorithm


negative index

[ 111 ] =gt

y

Chapter 1 - 58


direction

a = 0405 nm

Linear Density


a

[110]


Number of atoms

atoms

length

1 35 nm

a 2

2 LD -

Adapted from

Fig 31(a)

CampR8e

Chapter 1 -

BCC vs simple cubic

59

Chapter 1 -

BCC vs Simple C





60

Chapter 1 -

On to HCP






c

Chapter 1 -

Reading


bull 4-1 ndash 4-7

bull 5-1 ndash 5-5

62

Chapter 1 - 63



through origin





[uvtw]

[ 1120 ] ex frac12 frac12 -1 0 =gt


CampR8e



a2

a3

-a3

2

a 2

2

a 1

- a3

a1

a2

z

Algorithm


Chapter 1 - 64




as follows

w w

t

v

u

) v u ( + -

) u v 2 ( 3

1 -

) v u 2 ( 3

1 -

] uvtw [ ] w v u [

Fig 38(a) CampR8e

- a3

a1

a2

z

Chapter 1 - 65



CampR8e

Chapter 1 - 66




Chapter 1 - 67


x

y a b

c


example a b c z

x

y a b

c


1 Intercepts 1 1


1 1 0 3 Reduction 1 1 0

1 Intercepts 12


2 0 0 3 Reduction 2 0 0

example a b c

Chapter 1 - 68


z

x

y a b

c



a b c


2 1 43

3 Reduction 6 3 4

(001) (010)


(100) (010) (001) Ex 100 = (100)

Chapter 1 - 69



used

example a1 a2 a3 c



1 0

-1

-1

1

1


a2

a3

a1

z


CampR8e

Chapter 1 - 70






important


for Fe


planes

Chapter 1 - 71



(100)


R 3

3 4 a


2D repeat unit


1

atoms

2D repeat unit

= nm2

atoms 121

m2

atoms = 12 x 1019

1

2

R 3

3 4 area

2D repeat unit

Chapter 1 - 72







others

-- diamond single


-- turbine blades




GE Superabrasives


permission)


Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 55

Chapter 1 - 56

Point Coordinates





z

x

y a b

c

000

111

y

z

2c

b

b

Chapter 1 - 57



through origin





[uvw]

ex 1 0 frac12 =gt 2 0 1 =gt [ 201 ]

-1 1 1


z

x

Algorithm


negative index

[ 111 ] =gt

y

Chapter 1 - 58


direction

a = 0405 nm

Linear Density


a

[110]


Number of atoms

atoms

length

1 35 nm

a 2

2 LD -

Adapted from

Fig 31(a)

CampR8e

Chapter 1 -

BCC vs simple cubic

59

Chapter 1 -

BCC vs Simple C





60

Chapter 1 -

On to HCP






c

Chapter 1 -

Reading


bull 4-1 ndash 4-7

bull 5-1 ndash 5-5

62

Chapter 1 - 63



through origin





[uvtw]

[ 1120 ] ex frac12 frac12 -1 0 =gt


CampR8e



a2

a3

-a3

2

a 2

2

a 1

- a3

a1

a2

z

Algorithm


Chapter 1 - 64




as follows

w w

t

v

u

) v u ( + -

) u v 2 ( 3

1 -

) v u 2 ( 3

1 -

] uvtw [ ] w v u [

Fig 38(a) CampR8e

- a3

a1

a2

z

Chapter 1 - 65



CampR8e

Chapter 1 - 66




Chapter 1 - 67


x

y a b

c


example a b c z

x

y a b

c


1 Intercepts 1 1


1 1 0 3 Reduction 1 1 0

1 Intercepts 12


2 0 0 3 Reduction 2 0 0

example a b c

Chapter 1 - 68


z

x

y a b

c



a b c


2 1 43

3 Reduction 6 3 4

(001) (010)


(100) (010) (001) Ex 100 = (100)

Chapter 1 - 69



used

example a1 a2 a3 c



1 0

-1

-1

1

1


a2

a3

a1

z


CampR8e

Chapter 1 - 70






important


for Fe


planes

Chapter 1 - 71



(100)


R 3

3 4 a


2D repeat unit


1

atoms

2D repeat unit

= nm2

atoms 121

m2

atoms = 12 x 1019

1

2

R 3

3 4 area

2D repeat unit

Chapter 1 - 72







others

-- diamond single


-- turbine blades




GE Superabrasives


permission)


Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 56

Point Coordinates





z

x

y a b

c

000

111

y

z

2c

b

b

Chapter 1 - 57



through origin





[uvw]

ex 1 0 frac12 =gt 2 0 1 =gt [ 201 ]

-1 1 1


z

x

Algorithm


negative index

[ 111 ] =gt

y

Chapter 1 - 58


direction

a = 0405 nm

Linear Density


a

[110]


Number of atoms

atoms

length

1 35 nm

a 2

2 LD -

Adapted from

Fig 31(a)

CampR8e

Chapter 1 -

BCC vs simple cubic

59

Chapter 1 -

BCC vs Simple C





60

Chapter 1 -

On to HCP






c

Chapter 1 -

Reading


bull 4-1 ndash 4-7

bull 5-1 ndash 5-5

62

Chapter 1 - 63



through origin





[uvtw]

[ 1120 ] ex frac12 frac12 -1 0 =gt


CampR8e



a2

a3

-a3

2

a 2

2

a 1

- a3

a1

a2

z

Algorithm


Chapter 1 - 64




as follows

w w

t

v

u

) v u ( + -

) u v 2 ( 3

1 -

) v u 2 ( 3

1 -

] uvtw [ ] w v u [

Fig 38(a) CampR8e

- a3

a1

a2

z

Chapter 1 - 65



CampR8e

Chapter 1 - 66




Chapter 1 - 67


x

y a b

c


example a b c z

x

y a b

c


1 Intercepts 1 1


1 1 0 3 Reduction 1 1 0

1 Intercepts 12


2 0 0 3 Reduction 2 0 0

example a b c

Chapter 1 - 68


z

x

y a b

c



a b c


2 1 43

3 Reduction 6 3 4

(001) (010)


(100) (010) (001) Ex 100 = (100)

Chapter 1 - 69



used

example a1 a2 a3 c



1 0

-1

-1

1

1


a2

a3

a1

z


CampR8e

Chapter 1 - 70






important


for Fe


planes

Chapter 1 - 71



(100)


R 3

3 4 a


2D repeat unit


1

atoms

2D repeat unit

= nm2

atoms 121

m2

atoms = 12 x 1019

1

2

R 3

3 4 area

2D repeat unit

Chapter 1 - 72







others

-- diamond single


-- turbine blades




GE Superabrasives


permission)


Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 57



through origin





[uvw]

ex 1 0 frac12 =gt 2 0 1 =gt [ 201 ]

-1 1 1


z

x

Algorithm


negative index

[ 111 ] =gt

y

Chapter 1 - 58


direction

a = 0405 nm

Linear Density


a

[110]


Number of atoms

atoms

length

1 35 nm

a 2

2 LD -

Adapted from

Fig 31(a)

CampR8e

Chapter 1 -

BCC vs simple cubic

59

Chapter 1 -

BCC vs Simple C





60

Chapter 1 -

On to HCP






c

Chapter 1 -

Reading


bull 4-1 ndash 4-7

bull 5-1 ndash 5-5

62

Chapter 1 - 63



through origin





[uvtw]

[ 1120 ] ex frac12 frac12 -1 0 =gt


CampR8e



a2

a3

-a3

2

a 2

2

a 1

- a3

a1

a2

z

Algorithm


Chapter 1 - 64




as follows

w w

t

v

u

) v u ( + -

) u v 2 ( 3

1 -

) v u 2 ( 3

1 -

] uvtw [ ] w v u [

Fig 38(a) CampR8e

- a3

a1

a2

z

Chapter 1 - 65



CampR8e

Chapter 1 - 66




Chapter 1 - 67


x

y a b

c


example a b c z

x

y a b

c


1 Intercepts 1 1


1 1 0 3 Reduction 1 1 0

1 Intercepts 12


2 0 0 3 Reduction 2 0 0

example a b c

Chapter 1 - 68


z

x

y a b

c



a b c


2 1 43

3 Reduction 6 3 4

(001) (010)


(100) (010) (001) Ex 100 = (100)

Chapter 1 - 69



used

example a1 a2 a3 c



1 0

-1

-1

1

1


a2

a3

a1

z


CampR8e

Chapter 1 - 70






important


for Fe


planes

Chapter 1 - 71



(100)


R 3

3 4 a


2D repeat unit


1

atoms

2D repeat unit

= nm2

atoms 121

m2

atoms = 12 x 1019

1

2

R 3

3 4 area

2D repeat unit

Chapter 1 - 72







others

-- diamond single


-- turbine blades




GE Superabrasives


permission)


Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 58


direction

a = 0405 nm

Linear Density


a

[110]


Number of atoms

atoms

length

1 35 nm

a 2

2 LD -

Adapted from

Fig 31(a)

CampR8e

Chapter 1 -

BCC vs simple cubic

59

Chapter 1 -

BCC vs Simple C





60

Chapter 1 -

On to HCP






c

Chapter 1 -

Reading


bull 4-1 ndash 4-7

bull 5-1 ndash 5-5

62

Chapter 1 - 63



through origin





[uvtw]

[ 1120 ] ex frac12 frac12 -1 0 =gt


CampR8e



a2

a3

-a3

2

a 2

2

a 1

- a3

a1

a2

z

Algorithm


Chapter 1 - 64




as follows

w w

t

v

u

) v u ( + -

) u v 2 ( 3

1 -

) v u 2 ( 3

1 -

] uvtw [ ] w v u [

Fig 38(a) CampR8e

- a3

a1

a2

z

Chapter 1 - 65



CampR8e

Chapter 1 - 66




Chapter 1 - 67


x

y a b

c


example a b c z

x

y a b

c


1 Intercepts 1 1


1 1 0 3 Reduction 1 1 0

1 Intercepts 12


2 0 0 3 Reduction 2 0 0

example a b c

Chapter 1 - 68


z

x

y a b

c



a b c


2 1 43

3 Reduction 6 3 4

(001) (010)


(100) (010) (001) Ex 100 = (100)

Chapter 1 - 69



used

example a1 a2 a3 c



1 0

-1

-1

1

1


a2

a3

a1

z


CampR8e

Chapter 1 - 70






important


for Fe


planes

Chapter 1 - 71



(100)


R 3

3 4 a


2D repeat unit


1

atoms

2D repeat unit

= nm2

atoms 121

m2

atoms = 12 x 1019

1

2

R 3

3 4 area

2D repeat unit

Chapter 1 - 72







others

-- diamond single


-- turbine blades




GE Superabrasives


permission)


Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 -

BCC vs simple cubic

59

Chapter 1 -

BCC vs Simple C





60

Chapter 1 -

On to HCP






c

Chapter 1 -

Reading


bull 4-1 ndash 4-7

bull 5-1 ndash 5-5

62

Chapter 1 - 63



through origin





[uvtw]

[ 1120 ] ex frac12 frac12 -1 0 =gt


CampR8e



a2

a3

-a3

2

a 2

2

a 1

- a3

a1

a2

z

Algorithm


Chapter 1 - 64




as follows

w w

t

v

u

) v u ( + -

) u v 2 ( 3

1 -

) v u 2 ( 3

1 -

] uvtw [ ] w v u [

Fig 38(a) CampR8e

- a3

a1

a2

z

Chapter 1 - 65



CampR8e

Chapter 1 - 66




Chapter 1 - 67


x

y a b

c


example a b c z

x

y a b

c


1 Intercepts 1 1


1 1 0 3 Reduction 1 1 0

1 Intercepts 12


2 0 0 3 Reduction 2 0 0

example a b c

Chapter 1 - 68


z

x

y a b

c



a b c


2 1 43

3 Reduction 6 3 4

(001) (010)


(100) (010) (001) Ex 100 = (100)

Chapter 1 - 69



used

example a1 a2 a3 c



1 0

-1

-1

1

1


a2

a3

a1

z


CampR8e

Chapter 1 - 70






important


for Fe


planes

Chapter 1 - 71



(100)


R 3

3 4 a


2D repeat unit


1

atoms

2D repeat unit

= nm2

atoms 121

m2

atoms = 12 x 1019

1

2

R 3

3 4 area

2D repeat unit

Chapter 1 - 72







others

-- diamond single


-- turbine blades




GE Superabrasives


permission)


Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 -

BCC vs Simple C





60

Chapter 1 -

On to HCP






c

Chapter 1 -

Reading


bull 4-1 ndash 4-7

bull 5-1 ndash 5-5

62

Chapter 1 - 63



through origin





[uvtw]

[ 1120 ] ex frac12 frac12 -1 0 =gt


CampR8e



a2

a3

-a3

2

a 2

2

a 1

- a3

a1

a2

z

Algorithm


Chapter 1 - 64




as follows

w w

t

v

u

) v u ( + -

) u v 2 ( 3

1 -

) v u 2 ( 3

1 -

] uvtw [ ] w v u [

Fig 38(a) CampR8e

- a3

a1

a2

z

Chapter 1 - 65



CampR8e

Chapter 1 - 66




Chapter 1 - 67


x

y a b

c


example a b c z

x

y a b

c


1 Intercepts 1 1


1 1 0 3 Reduction 1 1 0

1 Intercepts 12


2 0 0 3 Reduction 2 0 0

example a b c

Chapter 1 - 68


z

x

y a b

c



a b c


2 1 43

3 Reduction 6 3 4

(001) (010)


(100) (010) (001) Ex 100 = (100)

Chapter 1 - 69



used

example a1 a2 a3 c



1 0

-1

-1

1

1


a2

a3

a1

z


CampR8e

Chapter 1 - 70






important


for Fe


planes

Chapter 1 - 71



(100)


R 3

3 4 a


2D repeat unit


1

atoms

2D repeat unit

= nm2

atoms 121

m2

atoms = 12 x 1019

1

2

R 3

3 4 area

2D repeat unit

Chapter 1 - 72







others

-- diamond single


-- turbine blades




GE Superabrasives


permission)


Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 -

On to HCP






c

Chapter 1 -

Reading


bull 4-1 ndash 4-7

bull 5-1 ndash 5-5

62

Chapter 1 - 63



through origin





[uvtw]

[ 1120 ] ex frac12 frac12 -1 0 =gt


CampR8e



a2

a3

-a3

2

a 2

2

a 1

- a3

a1

a2

z

Algorithm


Chapter 1 - 64




as follows

w w

t

v

u

) v u ( + -

) u v 2 ( 3

1 -

) v u 2 ( 3

1 -

] uvtw [ ] w v u [

Fig 38(a) CampR8e

- a3

a1

a2

z

Chapter 1 - 65



CampR8e

Chapter 1 - 66




Chapter 1 - 67


x

y a b

c


example a b c z

x

y a b

c


1 Intercepts 1 1


1 1 0 3 Reduction 1 1 0

1 Intercepts 12


2 0 0 3 Reduction 2 0 0

example a b c

Chapter 1 - 68


z

x

y a b

c



a b c


2 1 43

3 Reduction 6 3 4

(001) (010)


(100) (010) (001) Ex 100 = (100)

Chapter 1 - 69



used

example a1 a2 a3 c



1 0

-1

-1

1

1


a2

a3

a1

z


CampR8e

Chapter 1 - 70






important


for Fe


planes

Chapter 1 - 71



(100)


R 3

3 4 a


2D repeat unit


1

atoms

2D repeat unit

= nm2

atoms 121

m2

atoms = 12 x 1019

1

2

R 3

3 4 area

2D repeat unit

Chapter 1 - 72







others

-- diamond single


-- turbine blades




GE Superabrasives


permission)


Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 -

Reading


bull 4-1 ndash 4-7

bull 5-1 ndash 5-5

62

Chapter 1 - 63



through origin





[uvtw]

[ 1120 ] ex frac12 frac12 -1 0 =gt


CampR8e



a2

a3

-a3

2

a 2

2

a 1

- a3

a1

a2

z

Algorithm


Chapter 1 - 64




as follows

w w

t

v

u

) v u ( + -

) u v 2 ( 3

1 -

) v u 2 ( 3

1 -

] uvtw [ ] w v u [

Fig 38(a) CampR8e

- a3

a1

a2

z

Chapter 1 - 65



CampR8e

Chapter 1 - 66




Chapter 1 - 67


x

y a b

c


example a b c z

x

y a b

c


1 Intercepts 1 1


1 1 0 3 Reduction 1 1 0

1 Intercepts 12


2 0 0 3 Reduction 2 0 0

example a b c

Chapter 1 - 68


z

x

y a b

c



a b c


2 1 43

3 Reduction 6 3 4

(001) (010)


(100) (010) (001) Ex 100 = (100)

Chapter 1 - 69



used

example a1 a2 a3 c



1 0

-1

-1

1

1


a2

a3

a1

z


CampR8e

Chapter 1 - 70






important


for Fe


planes

Chapter 1 - 71



(100)


R 3

3 4 a


2D repeat unit


1

atoms

2D repeat unit

= nm2

atoms 121

m2

atoms = 12 x 1019

1

2

R 3

3 4 area

2D repeat unit

Chapter 1 - 72







others

-- diamond single


-- turbine blades




GE Superabrasives


permission)


Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 63



through origin





[uvtw]

[ 1120 ] ex frac12 frac12 -1 0 =gt


CampR8e



a2

a3

-a3

2

a 2

2

a 1

- a3

a1

a2

z

Algorithm


Chapter 1 - 64




as follows

w w

t

v

u

) v u ( + -

) u v 2 ( 3

1 -

) v u 2 ( 3

1 -

] uvtw [ ] w v u [

Fig 38(a) CampR8e

- a3

a1

a2

z

Chapter 1 - 65



CampR8e

Chapter 1 - 66




Chapter 1 - 67


x

y a b

c


example a b c z

x

y a b

c


1 Intercepts 1 1


1 1 0 3 Reduction 1 1 0

1 Intercepts 12


2 0 0 3 Reduction 2 0 0

example a b c

Chapter 1 - 68


z

x

y a b

c



a b c


2 1 43

3 Reduction 6 3 4

(001) (010)


(100) (010) (001) Ex 100 = (100)

Chapter 1 - 69



used

example a1 a2 a3 c



1 0

-1

-1

1

1


a2

a3

a1

z


CampR8e

Chapter 1 - 70






important


for Fe


planes

Chapter 1 - 71



(100)


R 3

3 4 a


2D repeat unit


1

atoms

2D repeat unit

= nm2

atoms 121

m2

atoms = 12 x 1019

1

2

R 3

3 4 area

2D repeat unit

Chapter 1 - 72







others

-- diamond single


-- turbine blades




GE Superabrasives


permission)


Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 64




as follows

w w

t

v

u

) v u ( + -

) u v 2 ( 3

1 -

) v u 2 ( 3

1 -

] uvtw [ ] w v u [

Fig 38(a) CampR8e

- a3

a1

a2

z

Chapter 1 - 65



CampR8e

Chapter 1 - 66




Chapter 1 - 67


x

y a b

c


example a b c z

x

y a b

c


1 Intercepts 1 1


1 1 0 3 Reduction 1 1 0

1 Intercepts 12


2 0 0 3 Reduction 2 0 0

example a b c

Chapter 1 - 68


z

x

y a b

c



a b c


2 1 43

3 Reduction 6 3 4

(001) (010)


(100) (010) (001) Ex 100 = (100)

Chapter 1 - 69



used

example a1 a2 a3 c



1 0

-1

-1

1

1


a2

a3

a1

z


CampR8e

Chapter 1 - 70






important


for Fe


planes

Chapter 1 - 71



(100)


R 3

3 4 a


2D repeat unit


1

atoms

2D repeat unit

= nm2

atoms 121

m2

atoms = 12 x 1019

1

2

R 3

3 4 area

2D repeat unit

Chapter 1 - 72







others

-- diamond single


-- turbine blades




GE Superabrasives


permission)


Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 65



CampR8e

Chapter 1 - 66




Chapter 1 - 67


x

y a b

c


example a b c z

x

y a b

c


1 Intercepts 1 1


1 1 0 3 Reduction 1 1 0

1 Intercepts 12


2 0 0 3 Reduction 2 0 0

example a b c

Chapter 1 - 68


z

x

y a b

c



a b c


2 1 43

3 Reduction 6 3 4

(001) (010)


(100) (010) (001) Ex 100 = (100)

Chapter 1 - 69



used

example a1 a2 a3 c



1 0

-1

-1

1

1


a2

a3

a1

z


CampR8e

Chapter 1 - 70






important


for Fe


planes

Chapter 1 - 71



(100)


R 3

3 4 a


2D repeat unit


1

atoms

2D repeat unit

= nm2

atoms 121

m2

atoms = 12 x 1019

1

2

R 3

3 4 area

2D repeat unit

Chapter 1 - 72







others

-- diamond single


-- turbine blades




GE Superabrasives


permission)


Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 66




Chapter 1 - 67


x

y a b

c


example a b c z

x

y a b

c


1 Intercepts 1 1


1 1 0 3 Reduction 1 1 0

1 Intercepts 12


2 0 0 3 Reduction 2 0 0

example a b c

Chapter 1 - 68


z

x

y a b

c



a b c


2 1 43

3 Reduction 6 3 4

(001) (010)


(100) (010) (001) Ex 100 = (100)

Chapter 1 - 69



used

example a1 a2 a3 c



1 0

-1

-1

1

1


a2

a3

a1

z


CampR8e

Chapter 1 - 70






important


for Fe


planes

Chapter 1 - 71



(100)


R 3

3 4 a


2D repeat unit


1

atoms

2D repeat unit

= nm2

atoms 121

m2

atoms = 12 x 1019

1

2

R 3

3 4 area

2D repeat unit

Chapter 1 - 72







others

-- diamond single


-- turbine blades




GE Superabrasives


permission)


Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 67


x

y a b

c


example a b c z

x

y a b

c


1 Intercepts 1 1


1 1 0 3 Reduction 1 1 0

1 Intercepts 12


2 0 0 3 Reduction 2 0 0

example a b c

Chapter 1 - 68


z

x

y a b

c



a b c


2 1 43

3 Reduction 6 3 4

(001) (010)


(100) (010) (001) Ex 100 = (100)

Chapter 1 - 69



used

example a1 a2 a3 c



1 0

-1

-1

1

1


a2

a3

a1

z


CampR8e

Chapter 1 - 70






important


for Fe


planes

Chapter 1 - 71



(100)


R 3

3 4 a


2D repeat unit


1

atoms

2D repeat unit

= nm2

atoms 121

m2

atoms = 12 x 1019

1

2

R 3

3 4 area

2D repeat unit

Chapter 1 - 72







others

-- diamond single


-- turbine blades




GE Superabrasives


permission)


Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 68


z

x

y a b

c



a b c


2 1 43

3 Reduction 6 3 4

(001) (010)


(100) (010) (001) Ex 100 = (100)

Chapter 1 - 69



used

example a1 a2 a3 c



1 0

-1

-1

1

1


a2

a3

a1

z


CampR8e

Chapter 1 - 70






important


for Fe


planes

Chapter 1 - 71



(100)


R 3

3 4 a


2D repeat unit


1

atoms

2D repeat unit

= nm2

atoms 121

m2

atoms = 12 x 1019

1

2

R 3

3 4 area

2D repeat unit

Chapter 1 - 72







others

-- diamond single


-- turbine blades




GE Superabrasives


permission)


Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 69



used

example a1 a2 a3 c



1 0

-1

-1

1

1


a2

a3

a1

z


CampR8e

Chapter 1 - 70






important


for Fe


planes

Chapter 1 - 71



(100)


R 3

3 4 a


2D repeat unit


1

atoms

2D repeat unit

= nm2

atoms 121

m2

atoms = 12 x 1019

1

2

R 3

3 4 area

2D repeat unit

Chapter 1 - 72







others

-- diamond single


-- turbine blades




GE Superabrasives


permission)


Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 70






important


for Fe


planes

Chapter 1 - 71



(100)


R 3

3 4 a


2D repeat unit


1

atoms

2D repeat unit

= nm2

atoms 121

m2

atoms = 12 x 1019

1

2

R 3

3 4 area

2D repeat unit

Chapter 1 - 72







others

-- diamond single


-- turbine blades




GE Superabrasives


permission)


Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 71



(100)


R 3

3 4 a


2D repeat unit


1

atoms

2D repeat unit

= nm2

atoms 121

m2

atoms = 12 x 1019

1

2

R 3

3 4 area

2D repeat unit

Chapter 1 - 72







others

-- diamond single


-- turbine blades




GE Superabrasives


permission)


Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 72







others

-- diamond single


-- turbine blades




GE Superabrasives


permission)


Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 73

Polycrystals

Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 74






Data from Table 33


is RW Hertzberg

Deformation and




Sons 1989)

bull Polycrystals


vary with direction


oriented isotropic



anisotropic


414(b) CampR8e


of LC Smith and C

Brady the National

Bureau of Standards

Washington DC [now


Standards and

Technology

Gaithersburg MD])


E (edge) = 125 GPa

Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 75














Chang Albany)

1 mm

Polycrystals

Isotropic

Anisotropic

Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 76

Polymorphism



titanium

a -Ti

carbon

diamond graphite

BCC

FCC

BCC

1538ordmC

1394ordmC

912ordmC

-Fe

-Fe

a-Fe

liquid

iron system

Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 77

SUMMARY




HCP)








Chapter 1 - 78



allotropy)

SUMMARY








Chapter 1 - 78



allotropy)

SUMMARY








ucla mse104 chapter 1

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