Self-Diffusion Coefficient in Solid Argon

Abstract

Self-diffusion in argon crystals is discussed on the basis of the mobility of vacancies, and in the scheme of the "absolute rate theory." Detailed calculations are made for the heat of activation $Q$ and for the pre-exponential factor $D_0$ including quantum corrections. The change of potential energy is evaluated first by minimizing the lattice energy with respect to the displacement of the four atoms around the diffusing particle, next by calculating first-order elastic relaxation of the entire lattice. The change of vibrational properties is evaluated in the Einstein approximation. Including the contributions for the hole formation, the values $D_0=4.20\mathrm{}\times {10}^{-4\mathrm{}}$ ${\mathrm{cm}}^2$ ${\sec }^{-1\mathrm{}}$, $Q=13.85\mathrm{}\times {10}^{-2\mathrm{}}$ ev, are found at $T=80\mathrm{}°$K; the zero-point energy contributes 5% to the heat of activation.