Moving discommensurations interacting with diffusing impurities

We present an analytical description of the interaction between moving discommensurations and diffusing impurities for a realistic form of the impurity-discommensuration interaction energy. This interaction energy is derived within the framework of the modified sine-Gordon model with either misfit impurities (coupling to the gradient of the order parameter) or elastic-modulus impurities (coupling directly to the order parameter). This interaction potential is then employed in calculating the steady-state impurity concentration profile about the moving discommensuration for arbitrary discommensuration velocity and impurity diffusivity. The impurities provide a drag force on the moving discommensuration, which may lead to hysteresis in the relation between the applied force and the discommensuration velocity. Analytic results for the onset of hysteresis, as well as for the velocities and forces delimiting the hysteretic regime, are presented. Finally, we apply these results to charge-density waves, ferroelectric domain walls, and grain boundaries