diffusion in solids’’  5 diffusion  mass transport by atomic motion mechanisms
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DIFFUSION IN SOLIDS
MSE225 Introduction to Materials Science Lecture5
Diffusion Diffusion  Mass transport by atomic motion
Mechanisms Gases & Liquids Brownian motion Solids vacancy diffusion or interstitial
diffusion.
Interdiffusion (impurity diffusion): In an alloy, atoms tend to migrate from regions of high concentration to regions of low concentration.
Initially
Interdiffusion
After some time
Selfdiffusion: In an elemental solid, atoms also migrate.
Label some atoms After some time
A
B
C
D
Selfdiffusion
Diffusion Mechanisms Atoms in solid materials are in constant motion, rapidly
changing positions. For an atom to move, 2 conditions must be met:
1. There must be an empty adjacent site, and 2. The atom must have sufficient (vibrational) energy to
break bonds with its neighboring atoms and then cause lattice distortion during the displacement. At a specific temperature, only a small fraction of the atoms is capable of motion by diffusion. This fraction increases with rising temperature.
There are 2 dominant models for metallic diffusion: 1. Vacancy Diffusion 2. Interstitial Diffusion
Vacancy Diffusion Vacancy Diffusion:
atoms exchange with vacancies
both self diffusion and interdiffusion occur by this mechanism rate depends on:  number of vacancies  activation energy to exchange.
increasing elapsed time
Atom needs enough thermal energy to break bonds and squeeze through its neighbors. Energy needed energy barrier Called the activation energy Q or Qd
Diffusion Thermally Activated Process
Atom
Vacancy
Qd
Distance
Ener
gy
Qsurface < Qgrain boundary < Qlattice
Experimentally determined activation energies for diffusion
Lower activation energy automatically implies higher diffusivity
Diffusion Paths with less Resistance
Simulation of interdiffusion across an interface:
Rate of vacancy diffusion depends on: vacancy concentration frequency of jumping.
(Courtesy P.M. Anderson)
DIFFUSION SIMULATION
Interstitial Diffusion
Interstitial diffusion smaller atoms (H, C, O, N) can diffuse between atoms.
More rapid than vacancy diffusion due to more mobile small atoms and more empty interstitial sites.
(Courtesy P.M. Anderson)
Applies to interstitial impurities. More rapid than vacancy diffusion. Simulation: shows the jumping of a smaller atom (gray) from one interstitial site to another in a BCC structure. The interstitial sites considered here are at midpoints along the unit cell edges.
INTERSTITIAL SIMULATION
Case Hardening: Diffuse carbon atoms into the host iron atoms at the surface. Example of interstitial diffusion is a case hardened gear.
Result: The "Case" is hard to deform: C atoms "lock" planes from shearing. hard to crack: C atoms put the surface in compression.
Fig. 5.0, Callister 6e. (Fig. 5.0 is courtesy of Surface Division, MidlandRoss.)
PROCESSING USING DIFFUSION
Diffusion How do we quantify the rate of diffusion?
J Flux moles (or mass) diffusingsurface area( ) time( )
=molm2s
or kgm2s
Measured empirically Make thin film (membrane) of known surface area Impose concentration gradient Measure how fast atoms or molecules diffuse through the
membrane
Rate of diffusion is independent of time; the diffusion flux does not change with time.
The concentration profile shows the concentration (C) vs the position within the solid (x); the slope at a particular point is the concentration gradient.
Steadystate diffusion across a thin plate
SteadyState Diffusion
dxdC
DJ =
Ficks first law of diffusion C1
C2
x
C1
C2
x1 x2 D diffusion coefficient
12
12 linear ifxxCC
xC
dxdC
=
Crosssectional area dndt= DA dC
dxNo. of atoms
crossing area A per unit time Concentration gradient
Matter transport is down the concentration gradient
Diffusion coefficient/ diffusivity
A Flow direction
J = D dCdx
Diffusion and Temperature
Diffusion coefficient increases with increasing T.
D =
Do exp

Qd R T
= preexponential [m2/s] = diffusion coefficient [m2/s]
= activation energy [J/mol or eV/atom] = gas constant [8.314 J/molK] = absolute temperature [K]
D Do Qd R T
The diffusing species, host material and temperature influence the diffusion coefficient.
For example, there is a significant difference in magnitude between selfdiffusion and carbon interdiffusion in iron at 500 C.
Factors that influence diffusion
Nonsteady State Diffusion The concentration of diffusing species is a
function of both time and position C = C(x,t). In this case, Ficks Second Law is used.
2
2
xC
DtC
=
Ficks Second Law
Nonsteady State Diffusion Copper diffuses into a bar of aluminum.
preexisting conc., Co of copper atoms Surface conc., C of Cu atoms bar s
General solution:
"error function
Co
Cs
position, x
C(x,t)
tot1
t2t3 Adapted from Fig. 5.5,
Callister 6e.
Factors that Influence Diffusion
Temperature  diffusion rate increases very rapidly with increasing temperature
Diffusion mechanism  interstitial is usually faster than vacancy
Diffusing and host species  Do, Qd is different for every solute, solvent pair
Microstructure  diffusion faster in polycrystalline vs. single crystal materials because of the rapid diffusion along grain boundaries and dislocation cores.
Diffusion FASTER for... open crystal structures lower melting T materials materials w/secondary bonding smaller diffusing atoms cations lower density materials
Diffusion SLOWER for... closepacked structures higher melting T materials materials w/covalent bonding larger diffusing atoms anions higher density materials
SUMMARY: STRUCTURE & DIFFUSION