Diffusion

· From Fick's first law: J_x = - D₀ exp(-Q/kT) (dc/dx)
· Writing the concentration gradient in terms of N_i and the lattice spacing, a, gives: (dc/dx) = - (N_C- N_Α)/a(a x 1 x 1)
· Substituting into the atomic expression for the net interstitial flux gives:
J_x = α(N_Α - N_C) ν exp(- ΔG_m /kT) = αa²ν exp (- ΔG_m /kT)(dc/dx)
· Comparison with Fick's law yields: D₀ = α a²ν and Q = ΔG_m
· For the vacancy mechanism: J_x = α(N_Α - N_C) ν exp(-[ ΔG_m + ΔG_V]/kT)
and the interpretation of D₀ and Q changes.
· Comparing the expression for the net flux with Fick's first law gives:
Q = [ ΔG_m + ΔG_V] and D₀ = ανa²
· The geometric parameter, α, must be determined before these quantities can be evaluated.