Theory of quantum and polaron effects in depinning of dislocation kinks

Abstract

A microscopic theory is presented of stress-assisted fluctuational breakaway of dislocation kinks from pinning centers. It is shown that a polaron lattice distortion near a pinned kink essentially affects the magnitude of energy fluctuation required to activate a jump over the pinning barrier. The effect of quantum lattice fluctuations on the low-temperature depinning rate is analyzed. The role played by the kink geometric width in depinning phenomenon is disclosed.PACS numbers: 61.70.Ga, 62.20.FeThe study of kinks on dislocations has proved fruitful in theories [1] of plastic flow and strength of crystalline materials. Although various aspects of kinetic behavior of kinks in pure crystals have received considerable attention [2], much work needs to be done to clarify the situation where the kink motion is hindered by local pinning agents (such as solute atoms, impurity clusters, radiation damage, etc.). In this connection, understanding of microscopic mechanisms which control the breakaway of kinks from efficient pinning centers is of fundamental importance.The phenomenological descriptions [3] of the depinning process rely on an assumption that in a wide range of temperatures 7\ a kink acted on by a stress x less than the Peierls stress xp breaks away from its pin with anwhere vo is a rather ill-defined attempt frequency, and E(T) is the activation energy (we set kg = 1). As regards the stress dependence of £(r), it is usually assumed that E(r) -IJ^ -t^x, where the pinning barrier height at x =0, £/n, is decreased by the work v>x done by the stress, and ^ is the activation volume of the process, maintained by environmental fluctuations.One cannot escape the feeling that the aforementioned absolute reaction-rate formula gives an oversimplified description of the breakaway process for at least two reasons: Clearly, the Arrhenius behavior of the rate will no longer be valid at sufficiently low temperatures, when quantum environmental fluctuations are expected to dominate. Moreover, the explicit form of the activation energy involved tells one nothing about the physical mechanism by which the energy is supplied to the activated kink. As is known from the classical work of Eshelby [4], an effective mechanism of energy gain from lattice fluctuations is provided by the kink-phonon coupling. A priori, it seems possible that this coupling, if strong enough, may be able to cause an appreciable distortion of the host lattice near a pinned kink. If this is the case, then there is a good reason to suspect that such a polaron effect can essentially modify the simple phenomenological picture of the depinning process.In view of all this, one concludes that environmental effects on depinning kinetics are only vaguely understood.In an attempt to clarify the situation we propose in this Letter a microscopic theory of the dislocation-kink depinning process. Our approach takes into account the coupling of the kink to phonons, the lattice distortions, and other pertinent processes that have not been appreciated in previous studies. ...