Diffusion equations in inhomogeneous solid having arbitrary gradient concentration

Abstract

A quantum kinetic equation is obtained for an inhomogeneous solid having arbitrary gradient concentration and chemical potential. We find, starting from nonequilibrium statistical operator, a new equation to describe atom migration in solid states. In continuous approximation, this equation turns into a non-linear diffusion equation. We derive conditions for which this equation can be reduced to Fick's or Cahn equation.