chapter 03 crystal structure

8/10/2019 Chapter 03 Crystal Structure

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3-1K. M. Flores

Materials Science & Engineering

CHAPTER 3: CRYSTAL

STRUCTURES & PROPERTIES

Why discuss crystal structure?

Density depends directly on atomic arrangement

Many properties depend on bond density and angle

(i.e. crystal orientation)

Crystal structure is basis for crystalline defects (Ch. 4)

3-2K. M. Flores


Non dense, random packing

Dense, regularpacking

Energy

r

typical neighborbond length

typical neighborbond energy

Energy

r

typical neighborbond length

typical neighborbond energy

ENERGY AND PACKING


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Crystalline materials...

atoms pack in periodic, 3D arrays

typical of: - metals

- many ceramics

- some polymers

Si Oxygen

crystalline SiO2Adapted from Fig. 3.18(a),

Callister 6e.

MATERIALS AND PACKING

Noncrystalline materials...

atoms have no periodic packing occurs for: complex structures

rapid cooling

"Amorphous" = Noncrystalline noncrystalline SiO2Adapted from Fig. 3.18(b),

Callister 6e.

3-4K. M. Flores


UNIT CELLSmall grouping of atoms that generate complete crystal

structure by repetitive displacement.

Edge of length a.

APF =

ATOMIC PACKING FACTOR

=

atoms

unit cell atomvolume

unit cell

volume

Relative density of atomic packing in unit cell, assuming

atoms are hard spheres.

a


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Have the simplest crystal structures

Tend to be densely packed:

Metallic bonding is not directional.

Typically, only one element is present:

all atomic radii are the same.

Nearest neighbor distances typically small to

lower bond energy.

We will look at foursuch structures...

METALLIC CRYSTALS

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(Courtesy P.M. Anderson)

SIMPLE CUBIC STRUCTURE (SC)

Rare due to poor packing (only Po has this structure)


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APF =Volume of atoms in unit cell

Volume of unit cell

APF =

a3

4

3

(a/2)31

atoms

unit cell

atom

volume

unit cell

volume

SC: close-packed directions

are cube edges

a

r

Unit cell contains 1/8th of 8 atoms (corners)

Adapted from Fig. 3.19,

Callister 6e.

ATOMIC PACKING FACTOR for SC

=

atoms

unit cell atomvolume

unit cell

volume

a3

(4/3)r3

Need: atoms/cell and r(a), relation between

atom radius and cube edge length:

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Callister 6e.


Close packed directions are cube diagonals.

BODY CENTERED CUBICSTRUCTURE (BCC)

--Note: All atoms are identical; the center atom is shaded

differently only for ease of viewing.


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ar

Close-packed direction are cube diagonals:

Unit cell contains:

1 (center) + 8 x 1/8 (corners)

Adapted from

Fig. 3.2,

Callister 6e.

ATOMIC PACKING FACTOR for BCC

APF =a3

4

3(a3/4)32

atoms

unit cell atom

volume

unit cell

volume

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Adapted from Fig. 3.1(a),

Callister 6e.


Close packed directions are face diagonals.

FACE CENTERED CUBICSTRUCTURE (FCC)

--Note: All atoms are identical; the face-centered atoms are shaded

differently only for ease of viewing.


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aAdapted from

Fig. 3.1(a),

Callister 6e.

APF =

a3

4

3

(a2/4)34

atoms

unit cell atom

volume

unit cell

volume

Unit cell contains of 6 atoms on face and

1/8th of 8 atoms on corners:

Close-packed directions are face diagonals:

ATOMIC PACKING FACTOR for FCC

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A

ABCABC... Stacking Sequence

2D Projection

A sites

B sites

C sites

B B

B

BB

B B

A

A

FCC Unit Cell

FCC STACKING SEQUENCE

B

C

C

C

C


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ABAB... Stacking Sequence Unit cell: 2D Projection

A sites

B sites

A sites Bottom layer

Middle layer

Top layer


Callister 6e.

HEXAGONAL CLOSE-PACKED

STRUCTURE (HCP)

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Example: Copper

= nA

VcNA

# atoms/unit cell Atomic weight (g/mol)

Volume/unit cell

(cm3/unit cell)

Avogadro's number

(6.023 x 1023 atoms/mol)

Data from Table inside front cover of Callister:

FCC crystal structure: n =

atomic weight:A =

atomic radius: r =

Vc = a3; For FCC, a = 4r/ 2 Vc =

Result: theoretical Cu =

THEORETICAL DENSITY,

actual Cu =


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Demonstrates "polymorphism"The same atoms can

have more than one

crystal structure.

DEMO: BCC FCC

TRANSFORMATION OF IRON

Temperature, C

BCC Stable

FCC Stable

914

1391

1536

shorter

longer!

shorter!

longer

Tc 768 magnet falls off

BCC Stable

Liquid

heat up

cool down

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Density will change because of change in crystal structure:

BCC FCC TRANSFORMATION OFIRON AT 914C

Ac

Fe

NV

nA=

FCCc,BCC

BCCc,FCC

FeBCC

ABCCc,

AFCCc,

FeFCC

BCC

FCC

Vn

Vn

An

NV

NV

An=

=

Vc,FCC =

Vc,BCC = 3BCCa

3FCCa


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Ionic compounds often have similar close-packed structures

Close-packed directions--along cube edges.

Structure of NaCl

Cl- anions are red

Na+ cations are grey


STRUCTURE OF CERAMICS (Ch. 12)

Cl- and Na+ ions sit on

interpenetratingFCC lattices.

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STRUCTURE OF POLYMERS (Ch. 14) Polymer= many mers

C C C C C C

HHHHHH

HHHHHH

Polyethylene (PE)

mer

ClCl Cl

C C C C C C

HHH

HHHHHH

Polyvinyl chloride (PVC)

mer

Polypropylene (PP)

CH3

C C C C C C

HHH

HHHHHH

CH3 CH3

mer

Covalent chain configurations and strength:

Direction of increasing strength

Adapted from Fig. 14.2, Callister 6e.

Branched Cross-Linked NetworkLinear

secondarybonding

Typically amorphous: difficult to align chains in 3D


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metals ceramics polymers

(g/cm

3)

Graphite/Ceramics/Semicond

Metals/

Alloys

Composites/

fibersPolymers

1

2

20

30Based on data in Table B1, Callister

*GFRE, CFRE, & AFRE are Glass,

Carbon, & Aramid Fiber-reinforced

epoxy composites (values based on

60% volume fraction of alignedfibers in an epoxy matrix).

10

3

4

5

0.3

0.4

0.5

Magnesium

Aluminum

Steels

Titanium

Cu,Ni

Tin, Zinc

Silver, Mo

TantalumGold, WPlatinum

Graphite

Silicon

Glass -sodaConcrete

Si nitrideDiamondAl oxide

Zirconia

HDPE, PSPP, LDPEPC

PTFE

PETPVCSilicone

Wood

AFRE*

CFRE*

GFRE*

Glass fibers

Carbon fibers

Aramid fibers

Why?

Metals have...

Ceramics have...

Polymers have...

Composites have...

Data from Table B1, Callister 6e.

DENSITIES OF MATERIAL CLASSES

> >

3-20K. M. Flores


Mostengineering materials are polycrystalline

If crystals are randomly oriented,overall component properties are not directional.

Crystal sizes typically range from 1 nm to 2 cm

(i.e., from a few to millions of atomic layers).

Adapted from Fig. K, color inset pages of

Callister 6e.

(Fig. K is courtesy of Paul E. Danielson,

Teledyne Wah Chang Albany)

1 mm

CRYSTALS AS BUILDING BLOCKS

grains = individual crystals

Nb-Hf-W plate with an electron beam weld.


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Some engineering applications require single crystals:

-- diamond single

crystals for abrasives

-- Ni superalloy turbine blades

for high performance enginesFig. 8.30(c), Callister 6e.

(Fig. 8.30(c) courtesy

of Pratt and Whitney).(Courtesy Martin Deakins,

GE Superabrasives,

Worthington, OH. Used with

permission.)

CRYSTALS AS ENGINEERING

STRUCTURES

Downloaded from

http://www.cstl.nist.gov/div837/Division/programs/microelect/microelect1.htm,

Sept. 7, 2005.

-- silicon wafer formicroelectronic devices

3-22K. M. Flores


Single Crystals

- Anisotropy: properties vary

with direction

- Example: the modulus of

elasticity (E) in BCC iron:

Polycrystals- Isotropy: properties same in

any direction

- Polycrystals are isotropicif

grains are randomly oriented

Epoly Fe =

- Polycrystals are anisotropicif

grains are textured

Ediagonal

Eedge

200 m

Data from Table 3.3, Callister 6e.

(Source of data is R.W. Hertzberg, Deformation

and Fracture Mechanics of Engineering

Materials, 3rd ed., John Wiley and Sons, 1989.)

Adapted from Fig. 4.12(b),Callister 6e.

(Fig. 4.12(b) is courtesy of L.C. Smith and C.

Brady, the National Bureau of Standards,

Washington, DC [now the National Institute of

Standards and Technology, Gaithersburg, MD].)

ISOTROPY vs. ANISOTROPY


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x-ray

intensity(fromdetector)

c

Incoming X-rays diffract off of crystal planes.

Measurement of:

Critical angles, c,for X-rays provideatomic spacing, d.

Adapted from Fig. 3.2W, Callister 6e.

X-RAYS TO CONFIRM CRYSTAL STRUCTURE

reflections mustbe in phase todetect signal

spacingbetweenplanes

d

incoming

X-rays

outgoing

X-rays

detec

tor

extradistancetraveledby wave 2

12

1

2

d = n/(2 sinc)

3-24K. M. Flores


Atoms can be arranged and imaged!

Carbon monoxide

molecules arranged

on a platinum (111)

surface.

Photos produced from the work of C.P. Lutz,

Zeppenfeld, and D.M. Eigler. Reprinted with

permission from International Business Machines

Corporation, copyright 1995.

Iron atoms arranged

on a copper (111)

surface. These Kanji

characters represent

the word atom.

SCANNING TUNNELINGMICROSCOPY


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Atoms may assemble into crystalline oramorphous structures.

We can predict the density of a material,

provided we know the atomic weight, atomic

radius, and crystal structure (e.g., FCC,

BCC, HCP).

Material properties generally vary with single

crystal orientation (i.e., they are anisotropic),

but properties are generally non-directional

(i.e., they are isotropic) in polycrystals withrandomly oriented grains.

SUMMARY

chapter 03 crystal structure

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