Diffusion

· The jump geometry for a vacancy mechanism in an fcc lattice is shown opposite. The yellow sites indicate locations at which a vacancy could be situated and be a nearest neighbor to the jumping atom (red)
· The fraction of atoms in red locations that can jump = 1.

· The number of equivalent paths that such a jump could take = 4, (to each of the yellow sites).
· For this lattice and the vacancy mechanism the geometric jump factor is 4.
· Comparing the expression for the net flux with Fick's first law gives:
D₀ = 4νa²