material science and engineering

Chapter 6

DIFFUSION IN SOLIDS
• How does diffusion occur?
• Why is it an important part of processing?
• How can the rate of diffusion be predicted for some simple cases?
• How does diffusion depend on structure and temperature?

Driving force for movement
In general, force is a position derivative of energy (F = - dE/dr).
In other words, if there is any energy difference in space, there is a force which will act on matters - Force will move things.
(ex1) Potential energy by gravity:
Apple falls from high altitude (high potential energy) to low altitude (low potential energy).
(ex2) Drift current by battery (electrical potential energy).
(ex3) Atoms move from high concentration (high chemical potential) to low concentration (low chemical potential) → Diffusion!
* Concentration gradient is the driving force.
(well, it is chemical potential energy to be precise.
Concentration gradient is not sufficient condition for diffusion.)

Interdiffusion
• Interdiffusion: In an alloy, atoms tend to migrate from regions of large concentration.
Initially

Cu
100%

0

After some time

Ni

100%

Concentration Profiles

0
Concentration Profiles

DIFFUSION MECHANISMS
Substitutional diffusion and interstitial diffusion
(1) Substitutional (Vacancy) Diffusion:
• applies to substitutional impurities
• atoms exchange with vacancies
• rate depends on:
--number of vacancies
--activation energy to exchange.

increasing elapsed time

Vacancy Diffusion
• Simulation of interdiffusion across an interface:
• Rate of substitutional diffusion depends on:
--vacancy concentration
--frequency of jumping.

Temperature dependent.

(2) Interstitial Diffusion tetrahedral • Applies to interstitial
(small) impurities
(O, N, C, etc).
• More rapid than vacancy diffusion Why?

FCC

BCC

octahedral

Self-Diffusion
• Self-diffusion: In an elemental solid, atoms also migrate through diffusion. Driving force can be