Anomalous mobility of dislocation kink solitons in disordered solid solutions

Dislocation kink solitons in disordered solid solutions provide an example of quasiparticles showing anomalous kinetics-i.e., the nonlinear dependence of the displacement x on the time t , x approximately t(delta) (delta<1) . To describe the dynamic phase transition from the ordinary linear to anomalous regime, the dynamics of a quasiparticle in an energy landscape that performs a correlated random walk on the energy scale was theoretically studied. The phase diagram was characterized by the calculated temperature dependence of the threshold driving force F(th) below which the average velocity of quasiparticles vanishes. The exponent delta of the kinetic equation for the anomalous phase, x approximately t(delta), was determined by simple statistical arguments using the concepts of the "optimal fluctuation method." The dependence of the threshold driving force F(th) on the concentration of solute atoms and 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 F(th), thereby providing a qualitative explanation of experimental data on the dislocation pinning in solid solutions.