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Last Week Material Science Now. • Interplay of Processing, Structure, Properties and Performance.• Tailor the composition and atomic arrangements to achieve desired properties/functions.

Material Composition and Structures. • Valence electrons determines bonding types, and most material properties.

Chapter 4 - 1

• Three primary bonds: Ionic, Covalent and Metallic.• Solids can be amorphous, semicrystalline or crystalline. Crystalline materials have distinct crystal structure.

• Main metallic crystal structures: FCC, BCC and SC (rare due to its lower packing density).

• Identify crystal types, parameters and crystallographic directions and planes.• Calculate APF, Theoretical density, Line & Plane density.

Imperfections in Solids

There is no such thing as a perfect crystal.

• What are these imperfections?

• Why are they important?

Chapter 4 - 2

Many of the important properties of materials are due to the presence of imperfections.

• Vacancy atoms• Interstitial atoms• Substitutional atoms

Point defects (0 dimensional)

Types of Imperfections

• Dislocations Line defects (1 dimensional)

Chapter 4 - 3

Dislocations Line defects (1 dimensional)

• Grain Boundaries Area/planar defects (2 dimensional)

• Pores, Cracks Volume defects (3 dimensional)

• Vacancies:-vacant atomic sites in a structure.

Point Defects

Vacancydistortion of planes

Chapter 4 - 4

• Self-Interstitials:-"extra" atoms positioned between atomic sites.

self-interstitial

distortion of planes

Nv expQv

No. of defects

No of potential

Activation energy

• Equilibrium concentration varies with temperature!

Equilibrium Concentration:Point Defects

Chapter 4 - 5

Boltzmann's constant

(1.38 x 10 -23 J/atom-K)

(8.62 x 10-5 eV/atom-K)

Nexp

kT No. of potential defect sites. Temperature

Each lattice site is a potential vacancy site

• Find the equil. # of vacancies in 1 m3 of Cu at 1000C.• Given:

ACu = 63.5 g/mol = 8.4 g /cm3

Qv = 0.9 eV/atom NA = 6.02 x 1023 atoms/mol

Estimating Vacancy Concentration

Chapter 4 - 6

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• are line defects,• slip between crystal planes result when dislocations move,• produce permanent (plastic) deformation.

Dislocations:

Schematic of Zinc (HCP):• before deformation • after tensile elongation

Line Defects

Chapter 4 - 7

before deformation after tensile elongation

slip steps

Basic Types of Dislocations

Linear Defects (Dislocations)– Are one-dimensional defects around which atoms are

misaligned

• Edge dislocation:– extra half-plane of atoms inserted in a crystal structure– b to dislocation line

Chapter 4 - 8

b to dislocation line

• Screw dislocation:– spiral planar ramp resulting from shear deformation– b to dislocation line

Burger’s vector, b: magnitude and directions of lattice distortion

Dislocation line: line that defects centered around

b bb

Linear Dislocation

Chapter 4 -

Edge Edge Screw

9

Edge, Screw, and Mixed Dislocations

Mixed

Chapter 4 -

Adapted from Fig. 4.5, Callister 7e.

Edge

Screw

10

Imperfections in Solids

Chapter 4 - 11

Dislocations are visible in electron micrographs

Significance of Dislocations

• Plastic deformation is a result of motion of dislocations.

• If lots of plastic deformation can occur: material is ductile. If very little or no plastic

Chapter 4 -

deformation occurs before fracture, material is brittle.

• Experimentally, actual stress required to plastically deform a material is smaller than calculated theoretical stress. (Why? Presence of dislocations.)

12

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Dislocations & Materials Classes

• Covalent Ceramics

• Metals: Disl. motion easier.-non-directional bonding-close-packed directions

for slip. electron cloud ion cores

++

++

++++++++ + + + + +

+++++++

Chapter 4 -

(Si, diamond): Motion hard.-directional (angular) bonding

• Ionic Ceramics (NaCl):Motion hard.

-need to avoid ++ and - -neighbors.

+ + + ++++

+ + + +

- - -----

- - -

Dislocation MotionDislocations & plastic deformation

• Cubic & hexagonal metals - plastic deformation by plastic shear or slip where one plane of atoms slides over adjacent plane by defect motion (dislocations).

Chapter 4 -

• If dislocations don't move, deformation doesn't occur!

Dislocation Motion• Dislocation moves along slip plane in slip direction

perpendicular to dislocation line

• Slip direction same direction as Burgers vector

Edge dislocation

Chapter 4 -

Screw dislocation

Slip System– Slip plane - plane allowing easiest slippage

• Wide interplanar spacings - highest planar densities

– Slip direction - direction of movement - Highest linear densities – shortest moving distance

Deformation Mechanisms

Chapter 4 -

– FCC Slip occurs on {111} planes (close-packed) in <110> directions (close-packed)

=> total of 12 slip systems in FCC

– in BCC & HCP other slip systems occur

• Point, Line, and Area defects exist in solids.

• The number and type of defects can be variedand controlled (e.g., T controls vacancy conc.)

• Defects affect material properties (e.g., grain

Summary

Chapter 4 - 17

Defects affect material properties (e.g., grainboundaries control crystal slip).

• Defects may be desirable or undesirable(e.g., dislocations may be good or bad, dependingon whether plastic deformation is desirable or not.)

Diffusion

Diffusion - Mass transport by atomic motion

Mechanisms• Gases & Liquids – random (Brownian) motion

Solids vacancy diffusion or interstitial diffusion

Chapter 5 - 18

• Solids – vacancy diffusion or interstitial diffusion

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• Interdiffusion: In an alloy, atoms tend to migratefrom regions of high conc. to regions of low conc.

Initially

Diffusion

After some time

Chapter 5 - 19

• Self-diffusion: In an elemental solid, atomsalso migrate.

Label some atoms After some time

Diffusion

A

C

A

C

D

Chapter 5 - 20

B

DA

B

Diffusion Mechanisms

Vacancy Diffusion:

• atoms exchange with vacancies• applies to substitutional impurities atoms • rate depends on:

--number of vacancies--activation energy to exchange.

Chapter 5 - 21

gy g

increasing elapsed time

Diffusion Mechanisms

• Interstitial diffusion – smaller atoms can diffuse between atoms.

Chapter 5 - 22

More rapid than vacancy diffusion

• Case Hardening:--Diffuse carbon atoms

into the host iron atomsat the surface.

--Example of interstitialdiffusion is a casehardened gear

Processing Using Diffusion

Chapter 5 - 23

hardened gear.

• Result: The presence of C atoms makes iron (steel) harder.

• Doping silicon with phosphorus for n-type semiconductors:• Process:

Processing Using Diffusion

magnified image of a computer chip

0.5mm

1. Deposit P richlayers on surface.

silicon

Chapter 5 - 24

3. Result: Dopedsemiconductorregions.

silicon

light regions: Si atoms

light regions: Al atoms

2. Heat it.

silicon

Adapted from chapter-opening photograph, Chapter 18, Callister 7e.

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Diffusion• How do we quantify the amount or rate of diffusion?

• Measured empirically– Make thin film (membrane) of known surface area

sm

kgor

scm

mol

timearea surface

diffusing mass) (or molesFlux

22J

Chapter 5 - 25

– Impose concentration gradient– Measure how fast atoms or molecules diffuse through the

membrane

dt

dM

A

l

At

MJ

M =mass

diffused

time

J slope

Steady-State Diffusion

dC

Fick’s first law of diffusionC1C1

Rate of diffusion independent of time

Flux proportional to concentration gradient =dx

dC

Chapter 5 - 26

dx

dCDJ C2

x

C2

x1 x2

D diffusion coefficient

12

12 linear ifxx

CC

x

C

dx

dC

Example: Chemical Protective Clothing (CPC)

• Methylene chloride is a common ingredient of paint removers. Besides being an irritant, it also may be absorbed through skin. When using this paint remover, protective gloves should be worn.

• If butyl rubber gloves (0.04 cm thick) are used, what is the diffusive flux of methylene chloride through the

Chapter 5 - 27

is the diffusive flux of methylene chloride through the glove?

• Data:

– diffusion coefficient in butyl rubber: D = 110x10-8 cm2/s

– surface concentrations:

C2 = 0.02 g/cm2

C1 = 0.44 g/cm2

Chapter 5 - 28

Non-steady State Diffusion

• The concentration of diffucing species is a function of both time and position C = C(x,t)

• In this case Fick’s Second Law is used

Chapter 5 - 29

2

2

x

CD

t

C

Fick’s Second Law

Solve Partial Differential Equation, Set Boundary Conditions

Non-steady State Diffusion

• Copper diffuses into a bar of aluminum.

pre-existing conc., Co of copper atoms

Surface conc., C of Cu atoms bar

s

Cs • Assume semi-infinite solid with constant surface concentration of diffusing species.

Chapter 5 - 30

B.C. at t = 0, C = Co for 0 x

at t > 0, C = CS for x = 0 (const. surf. conc.)

C = Co for x =

• Assume a concentration of Co of the diffusing species in the solid (Co can be zero).

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Solution:

C(x,t) = Conc. at point x at time t

f ( ) f i

CS

Dt

x

CC

Ct,xC

os

o

2 erf1

Chapter 5 - 31

erf (z) = error function

erf(z) values are given in Table 5.1

Co

C(x,t)

dye yz 2

0

2

Non-steady State Diffusion

• Sample Problem: An FCC iron-carbon alloy initially containing 0.20 wt% C is carburized at an elevated temperature and in an atmosphere that gives a surface carbon concentration constant at 1.0 wt%. If after 49.5 h the concentration of carbon is 0.35 wt% at a position 4.0 mm below the surface, determine

Chapter 5 - 32

pthe diffusivity of carbon in iron at the treatment temperature.

• Solution: use Eqn. 5.5

Dt

x

CC

CtxC

os

o

2erf1

),(

Chapter 5 -

t01_05_pg116

Chapter 5 -

Chapter 5 -

Diffusion and Temperature

• Diffusion coefficient increases with increasing T.

D Do exp

Qd

RT

1ll

Q

DD d

D1

l

Chapter 5 - 36

= pre-exponential [m2/s]

= diffusion coefficient [m2/s]

= activation energy [J/mol or eV/atom]

= gas constant [8.314 J/mol-K]

= absolute temperature [K]

D

Do

Qd

R

T

1

lnln 0

TR

QDD d

T

D ln Ȣ

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Diffusion and Temperature

D has exponential dependence on T

Dinterstitial >> DsubstitutionalD (m2/s)

10-8T(C)

1500

1000

600

300

TD

1 ln Ȣ

Chapter 5 - 37

Adapted from Fig. 5.7, Callister 7e. (Date for Fig. 5.7 taken from E.A. Brandes and G.B. Brook (Ed.) Smithells Metals Reference Book, 7th ed., Butterworth-Heinemann, Oxford, 1992.)

C in -FeC in -Fe

Al in AlFe in -FeFe in -Fe

1000K/T0.5 1.0 1.510-20

10-14

Example: At 300ºC the diffusion coefficient and activation energy for Cu in Si are

D(300ºC) = 7.8 x 10-11 m2/sQd = 41.5 kJ/mol

What is the diffusion coefficient at 350ºC?

transformD ln D

Chapter 5 - 38

transform data

D

Temp = T

ln D

1/T

Chapter 5 - 39

Diffusion FASTER for...

• open crystal structures

• materials w/secondarybonding

Diffusion SLOWER for...

• close-packed structures

• materials w/covalentbonding

Summary

Chapter 5 - 40

• smaller diffusing atoms

• lower density materials

• larger diffusing atoms

• higher density materials