Abrupt-Kink Model of Dislocation Motion. II

The abrupt-kink model of dislocation motion is generalized to describe the dynamics of a dislocation at temperatures where the barrier to kink diffusion is negligible compared with the thermal energy, and where generation of double kinks is still unimportant. It is assumed that kinks may be treated as a one-dimensional gas of particles which interact through their long-range stress fields. The interaction energy, $U\left(x\right)\mathrm{}$, at a separation $x$ is derived. For $x$ greater than a few lattice spacings, $U\left(x\right)\mathrm{}\sim {\mathrm{}\left|x\right|\mathrm{}}^{-1\mathrm{}}$, like the interaction between point charges. The equations of motion of a dislocation are obtained for a general $U\left(x\right)\mathrm{}$. It is shown that the well-known string model is equivalent to assuming an incorrect short-range interaction $U\left(x\right)\mathrm{}\sim \delta \mathrm{}\left(x\right)\mathrm{}$ and ignoring the variation of the effective mass of a dislocation with its orientation relative to a close-packed crystal direction. While the equations of motion have not been solved with the true interaction, possible effects of its long-range character are investigated with an interaction of the form $U\left(x\right)\mathrm{}\sim -\ln \mathrm{}\left|x\right|\mathrm{}$. The behavior of the dislocation under a static stress is discussed according to this model and, in addition, the fundamental frequency of vibration about the equilibrium configuration is derived.