On the Theory of Vacancy Diffusion in Alloys

Abstract

The theory of diffusion in alloys is discussed on the basis of the migration of lattice vacancies in an attempt to interpret the experiments of W. A. Johnson on diffusion in gold-silver alloys. It is assumed that the lattice network preserves its identity during the diffusion even though there is a resultant vacancy current passing through any region. It is also assumed that two types of atom, designated as $A$ and $B$ atoms, are present in the lattice. The diffusion coefficients are expressed in terms of a function $p(n_{a1\mathrm{}},n_{a2\mathrm{}})$ giving the probability that a vacancy in jumping from one atomic plane (designated as plane 2) to a neighboring plane (designated as plane 1) will interchange places with an $A$ atom if there are $n_{a1\mathrm{}}A$ atoms per unit area of plane 1 and $n_{a2\mathrm{}}A$ atoms in plane 2. It is found that the chemical diffusion coefficient is related to the function $p$ in a very different way from the diffusion coefficients for radioactive tracers if the latter migrate when no chemical gradient is present. Models of increasing complexity are employed to derive explicit expressions for the function $p$. It is found that Johnson's experiments can be explained only with the use of models that are more complex than those commonly used. The theory of vacancy diffusion is also employed to interpret the experiments of Smigelskas and Kirkendall concerning the relative displacement during diffusion of fiducial markers placed at the interface between copper and brass. An experiment which could provide an absolute test for vacancy diffusion is proposed.