Validity of Brownian-motion theory of activated processes: Diffusion in solids
- 15 February 1982
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review B
- Vol. 25 (4) , 2324-2342
- https://doi.org/10.1103/physrevb.25.2324
Abstract
A scheme is presented for the calculation of an impurity diffusion rate in solids. "Activated" state theory usually used for this purpose fails because of the absence of quasi-equilibrium, and Brownian-motion theory cannot be used to correct it because of the absence of widely disparate time scales. We argue that a more nearly correct procedure in this case is based on random modulation of certain parameters of the problem. In harmonic approximation, the impurity either induces an isolated local phonon mode or else produces a resonance. In the former case the diffusion rate then differs widely from the usual absolute-rate theory result (both in activation energy and preexponential factor). In the latter case the effective activation energy comes very close to that of absolute rate theory. Comparison of the prefactors requires numerical analysis.Keywords
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