Part 8: Diffusion & Transport
Atomic Migration in Solids
Diffusion governs countless processes in materials science: heat treatment of metals, semiconductor doping, oxidation, sintering, and creep. Fick's laws provide the mathematical framework for describing how atoms move through solids, driven by concentration gradients and thermal activation.
$J = -D\frac{dC}{dx}$
Fick's First Law
$\frac{\partial C}{\partial t} = D\frac{\partial^2 C}{\partial x^2}$
Fick's Second Law
$D = D_0 e^{-Q/RT}$
Arrhenius Dependence