It was noted that dislocation kink solitons, in disordered solid solutions, provided an example of quasi-particles exhibiting anomalous kinetics. That is, a non-linear dependence of the displacement upon the time. In order to describe the dynamic phase transition from the ordinary linear, to anomalous regime, the dynamics of a quasi-particle in an energy landscape that performed a correlated random walk on the energy scale was studied theoretically. The phase diagram was characterized by the calculated temperature dependence of the threshold driving force; below which the average velocity of the quasi-particles vanished. The exponent of the kinetic equation for the anomalous phase was determined by means of simple statistical arguments using the concept of the optimal fluctuation method. The dependence of the threshold driving force upon the concentration of solute atoms, and the statistical properties of a random energy landscape relevant to disordered solid solutions, was calculated. The correlations between steps of the random potential were shown to modify the concentration dependence of the threshold driving force; thereby providing a qualitative explanation of experimental data on dislocation pinning in solid solutions.

Anomalous Mobility of Dislocation Kink Solitons in Disordered Solid Solutions. B.V.Petukhov: Physical Review E, 2008, 77[2-II], 026601