Condensed Matter Physics, 2017, vol. 20, No. 1, 13201
DOI:10.5488/CMP.20.13201
arXiv:1703.10372
Title:
Diffusion equations in inhomogeneous solid having arbitrary gradient concentration
Author(s):

Y. Bilotsky
(Aalto University, School of Chemical Technology, Materials Processing, PO Box 16200 FI00076 AALTO Finland)
,


M. Gasik
(Aalto University, School of Chemical Technology, Materials Processing, PO Box 16200 FI00076 AALTO Finland)
,


B. Lev
(Bogolyubov Institute for Theoretical Physics of the National Academy of Sciences of Ukraine, 14b Metrolohichna St., 03143 Kyiv, Ukraine)

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 nonlinear diffusion equation. We derive conditions for which this equation can be reduced to Fick's or
Cahn equation.
Key words:
nonequilibrium statistical operator, solid state, diffusion process
PACS:
23.23.+x, 56.65.Dy
