Dislocation mobility in crystals containing small amounts of impurities

An expression is given for the dislocation velocity in crystals containing small amounts of impurities. It is of the form where U(σ) is the activation energy as a function of applied stress σ, x is the average displacement between impurities in a direction perpendicular to the dislocation, v is a frequency factor, and the other terms are defined below or have their usual meanings. The terms U(σ), x and v are represented in terms of the Friedel relation. The concentration and the temperature dependence of the velocity obtained from this formula are in agreement with available data. The stress dependence of the velocity is compared with data for the alkali halide crystals; NaCl, KBr and LiF. It is shown that the calculated values fit the measured data over many orders of magnitude, with reasonable values for the internal stress σi, the drag coefficient B, the binding energy of a dislocation with an impurity atom, and the concentration of impurity atoms.