The theory of diffusion in strained systems

Louis A. Girifalco, Hubert H. Grimes
SEP 1958

Because the current theory of solid-state diffusion is limited to unstrained crystals and cannot be applied readily to strained systems, Fick's first and second laws were generalized to include the effects of strain on the diffusion rates. The nonhomogeneity introduced into the atomic jump frequency by strain was found to contribute strain-dependent terms to the diffusion equations in addition to the terms containing the concentration gradient. From a consideration of the effect of strain on the free energy of activation, it can be shown that for simple strains, such as those resulting from compression, tension, shear, and hydrostatic pressure, the diffusion coefficient is an exponential function of the lattice parameter. An examination of the available experimental data for the variation of diffusion coefficients with pressure confirms this theoretical prediction. The theory presented herein states that the magnitude of the variation of the diffusion coefficient with pressure depends on the interatomic forces as the diffusing atom moves from its equilibrium position to the activated position. On the basis of this theory, a parameter depending upon the interatomic forces can be computed from the experimental data. In all cases investigated, the magnitudes of this parameter were in agreement with the known characteristics of the interatomic potential-energy functions of the systems. The effect of plastic flow on the diffusion rate was also studied by considering the rate at which vacancies are produced by dislocation motion and the rate at which vacancies condense at inhomogeneities in the crystal. The resulting equations predict that for a vacancy mechanism the diffusion coefficient varies linearly with the strain rate. This conclusion is in agreement with experiment.

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