Diffusion

� The net flux of impurity atoms, J_x, will depend on the jump rate, the atom concentrations on the reference planes, and a lattice geometry factor (α) which characterizes the number of equivalent paths between the reference planes:
J_x = {Net Flux} = {J_+x - J_-x} = α (N_Α - N_C) ν exp(-[ ΔG_m + ΔG_V]/kT)
� The Gibbs function barrier is symmetric for this case, and the diffusion flux is zero if: N_Α = N_C , i.e. a concentration gradient (chemical potential gradient) is needed for a vacancy diffusion mechanism
� The "energy" associated with the vacancy diffusion mechanism contains both the energy of motion, ΔG_m , and the vacancy formation energy, ΔG_V .
� Comparing either the interstitial or vacancy mechanism expressions for the net flux with Fick's first law permits D₀ and Q to be computed in atomic terms.