A series of models was used to analyze the motion of super-dislocations in L12 intermetallic compounds which exhibited an anomalous increase in strength with increasing temperature. The models were in the form of stochastic finite-difference equations of motion, were based upon physical arguments, and took account of both dynamic and thermal annihilation of Kear-Wilsdorf locks. The use of the models revealed the occurrence of a pinning-depinning transition with increasing stress. The pinned phase was shown to have a large number of possible configurations. The simplest model could be solved exactly. This solution, presented in terms of the advancement probability, indicated the existence of a critical point at zero advancement probability. In the case of more complicated models, an exact solution could no longer be easily obtained. Instead, such models were studied by using the mean-field approximation and exact numerical techniques. It was noted that zero-temperature (no thermal annihilation of Kear-Wilsdorf locks) mean-field solutions indicated the existence of a non-zero value of the advancement probability; below which all of the super-dislocations eventually became pinned. Above this critical probability, an infinite dislocation remained mobile for all times. The mean-field solution suggested that there existed a broad spectrum of accessible configurations of the super-dislocations, when below the critical probability. However, above the critical value, the dynamics selected a particular configuration to be the mobile one. The spectrum of accessible states also appeared to narrow continuously as the critical value was approached from below. The inclusion of thermal annihilation of Kear-Wilsdorf locks considerably altered the manner in which the configurations competed. Within the mean-field solution, the dislocation assumed a particular mobile configuration for all values of the advancement probability. At the same time, the pinning-depinning transition moved to a zero advancement probability.

D.C.Chrzan, M.S.Daw: Physical Review B, 1997, 55[2], 798-811