chapter 4b

Understanding atomic structure

and arrangement will allow us

to better understand how to

control the microstructure and

properties of materials.

Bohr Model

Electrons display characteristics

of both. Not all observed

phenomena can be explained by

the particle definition of electrons.

Particle theory cannot explain

specific heat, tunnel diodes,

scanning electron microscopes,

etc.

Electrons - Wave or Particle?

• The motion of the electron is

described by mathematics that

describe wave motion

• The energy/position of an electron is

described by a probability distribution

(Fermi-Dirac Statistics)

• Heisenberg Uncertainty Principle: the

closer we know the momentum of the

electron, the larger the uncertainty in

the position of the electron. z p = h

Wave Mechanics

The energy/position of an electron is described by a

probability distribution (Fermi-Dirac Statistics)

The energy/position of an electron is described exactly by

the Bohr particle model

• Electrons are transferred to form a bond

• Often found in compounds composed

of electropositive elements (metals)

and electronegative elements (non-

metals)

Na

Valence +1 Cl

Valence -1

Ionic Bonding

• Bonding Energy: 150-370 Kcal/mol

• Nondirectional Bond - strength of

bond equal in all directions

• Low electrical conductivity - entire

ion must move to conduct electricity

• Transparent, brittle, high melting

temperature

• Examples: NaCl 183 Kcal/mol, LiF

240 Kcal/mol

Ionic Bonding

General Characteristics

Electrons are shared to form a bond

Covalent Bonding

• Bonding Energy: 75-300 Kcal/mol

• Directional Bond - strength of bond is

not equal in all directions

• Low electrical conductivity

• Very hard, high melting temperature

• Examples: Si 84 Kcal/mol, GaAs 75

Kcal/mol, Diamond 170 Kcal/mol

Covalent Bonding

General Characteristics

Metallic Bonding

Valence

electrons form

an electron

cloud for

bonding

• Bonding Energy: 25-200 Kcal/mol

• Nondirectional Bond - strength of

bond is equal in all directions

• Good electrical conductivity - cloud of

electrons are free to move to conduct

electricity

• Ductile, opaque

• Examples: Na 26 Kcal/mol, Al 74

Kcal/mol, Cu 81 Kcal/mol

Metallic Bonding

General Characteristics

Van der Waals Bonding

• Weak secondary bond (<10 Kcal/mol)

• Often bonding force between molecules

• Example - PVC can be deformed by breaking

Van der Waals bonds between the molecules

that have strong covalent bonds

Hydrogen Bonding

• Special type of secondary bond between

some molecules containing H

• Example - bonds between molecules of water

Secondary Bonding

Cohesive Energy

Figure 4.19

Atoms are held together by bonds

that behave like springs

Cohesive energy is a measure of

the strength of the bonds

Bond Stiffness

Coulombic Attractive

Force 1/r2FA

Nuclear Repulsive

Force 1/r10FR

Energy=Force dr

a0

Potential Well Concept Ionic Bonding

distance

Ionic

Covalent

Metallic

Van der Waals

Relative Strength of Bonding Types

Table 4.1

Bond stiffness largely determines the value

of the modulus - E

Modulus of Elasticity

distance

Based on the bond energy curve

shown, determine which material

should be used for the applications

given below.

1) Beam that shows little deflection

under load

2) A crucible to be used at high

temperatures

3) A device designed to sense

temperature changes by changing its

dimension

What Determines Density

Density is mostly dependent on atomic weight

• Metals are dense because their atoms are heavy – iron

has an atomic weight of 56

• Polymers have low densities because they are made of

light atoms – carbon has an atomic weight of 12 while

hydrogen has an atomic weight of 1

The size of atoms and the way in which they are packed

also influence density, but to a much lesser degree

Atomic Packing

Most materials are crystalline – have a regularly

repeating pattern of structural units

Atoms often behave as if they are

hard and spherical

Layer A represents the close-packed

layer – there is no way to pack the atoms

more closely than this

Short-Range Order versus

Long-Range Order

1. No Order

Example: gases where atoms randomly fill whatever space is

available

2. Short-Range Order (SRO)

Example: glasses and many polymers where order only extends

to first nearest neighbors. Also called noncrystalline or

amorphous

3. Long-Range Order (LRO)

Example: atomic order that extends to large distances (> 100

nm) typical of metals and all “crystalline” materials

4. Liquid Crystals

Example: LCD’s where the material can change from amorphous

(SRO) to crystalline (LRO) under stimulus

Figure 4.8

Atomic structures are close-packed in three dimensions

Close-packed hexagonal: ABABAB stacking sequence

Face-centered cubic: ABCABC stacking sequence

Packing fraction for CPH and FCC structures is 0.74 – meaning

spheres occupy 74% of all available space

B and C represent alternative

positions for atoms in the next close-

packed plane

If the next plane of atoms lie in the same

position as the A atoms, the stacking sequence will be ABABAB. If the

next plane instead occupy the depressions marked C, the stacking

sequence will be ABCABC.

Unit Cell

Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon

Figure 4.11

Red lines define the cell while spheres represent

individual atoms

Shaded regions represent close or closest packed plane

Face-Centered Cubic Crystal

Body-Centered Cubic Crystal

Close-Packed Hexagonal Crystal

Crystal Lattice

Figure 4.12

Lattice points are the

points at which cell

edges meet

(a): hexagonal cell

(b): cubic cell

(c): cell with different

length edges

Non Close-Packed Structures

Body-centered cubic:

ABABAB packing sequence

Packing fraction = 0.68

Amorphous structure:

Packing fraction ≤ 0.64

Figure 4.9

Figure 4.10

Atomic Packing in Ceramics

Figure 4.13

(a): Hexagonal unit cell with a W-C atom pair associated

with each lattice point

(b): Cubic unit cell with a Si-C atom pair associated with each

lattice point

Atomic Packing in Glasses

Figure 4.14

Amorphous silica is the bases of most glasses

Rapid cooling allows material to maintain amorphous

structure achieved after melting

Atomic Packing

in Polymers

Figure 4.15

Figure 4.16

Polymers have a

carbon-carbon

backbone with

varying side-groups

Figure 4.17

Polymer chains bond to each other through weak hydrogen

bonds

Red lines indicate strong cross-linked carbon-carbon bonds

Polymer Structure

Figure 4.18

(a): No regular repeating pattern of

polymer chains – results in a

glassy or amorphous structure

(b): Regions in which polymer chains

line up and register – forms

crystalline patches

(c): Occasional cross-linking allowing

they polymer to stretch – typical

of elastomers

(d): Heavily cross-linked polymers

exhibit chain sliding – typical of

epoxy

Elastic Moduli of Elastomers

Figure 4.20

Undeformed polymer chains

has high randomness (entropy)

Stretched polymer chains

resemble more of a crystalline

structure and has a lower

entropy

Moduli of elastomers is

generally low and unlike

metals, increases with

temperature

Rule of Mixtures

f volume fraction of material or element A

ρA density of material or element A

ρB density of material or element B

Modifying the modulus and density is most effective when

done at a macro scale such as creating a hybrid rather than

a micro scale such as alloying a metal

Density of solid solution or hybrid material

Composites –

Density and Modulus

Figure 4.21

Polymer matrix composite (PMC)

Ceramic matrix composite (CMC)

Metal matrix composite (MMC)

Modulus can be altered by

combining stiff fibers with a

less-stiff matrix

ρr – density of reinforcement

ρm – density of matrix

Modulus of composite bracketed by two bounds:

• Upper bound: assumes that, on loading, both components strain

by the same amount, like springs in parallel

• Lower Bound: assumes that, on loading, each component carries

the same stress, like springs in series

Figure 4.22

Range of modulus and density properties for composites

with a ceramic reinforcement and polymeric matrix