A new generalized Frenkel-Kontorova (discrete sine-Gordon) model is proposed which treats a crystal as a set of one-dimensional atomic chains interacting with each other. Here, unlike earlier works, the model does not include the fixed field generated by an external rigid substrate. The two-dimensional version of the model is considered, but the three-dimensional generalization can be easily developed. On the basis of the present interacting atomic chain model a computer simulation of the crowdion (or the anticrowdion) in an anisotropic crystal is made. The calculated results completely agree with analytical results of the elasticity theory.

The “rolling disk” method is used for obtaining the distribution functions of the bow‐out angles and segment lengths for a dislocation pressed by an external stress to an array of point obstacles randomly distributed in the glide plane. Based on these distribution functions, the thermally activated motion of infinite as well as finite‐length dislocation lines through the random array of obstacles is considered. Formulas are obtained for evaluating the mean rates of glide as functions of stress and temperature. A rather good agreemeut of the results with those obtained with computer‐simulation technique substantiates the validity of the theory suggested.

The well-known Frenkel-Kontorova theoretical model is generalized by including the elastic properties of the three-dimensional medium surrounding the discrete atomic chain considered. The generalized sinuse-Gordon equation (SGE) and the integro-differential equation describing the crowdion in a highly anisotropic crystal are described. The numerical solution of these equations corroborates all the analytical estimates.

A new method of molecular dynamic computer simulation at constant temperature T and pressure P has been proposed. Unlike the earlier techniques of this sort, the new approach does not assume the volume V of the crystal to be an independent variable but the one that can be estimated from the coordinates of the atoms in the crystal. The new method was carefully tested on a finite hcp crystal whose Lennard-Jones potential of the two-atom interaction is known. The test proved the efficiency of the new method under different conditions including T=0 and P>0.

A method is suggested for taking into account the effect of inertial properties of dislocations on the velocity of their thermally activated motion. The method is based on the results of a statistical analysis of the dislocation motion through a random array of point obstacles. Because of the scatter in geometrical parameters, the dislocations interact with different obstacles at different angles α, even when all the obstacles in the crystal are identical. A fraction of the angles, g, can be higher than the critical value αc. The corresponding obstacles are surmounted by the dislocation in an unactivated way. The dislocation inertia manifests itself as an increase in the value of g, hence in the mean path length λ−; covered by the dislocation after each thermal activation event. Ultimately this results in an increase of velocity of the thermally activated motion. The equations suggested permit a numerical solution and comparison of the theoretical results with the experiment. A numerical example is given.