Dynamic Atomic Displacements and Athermal Dislocation Glide in Crystals

Abstract

A dislocation glide mechanism at low temperatures is proposed. The mechanism is based on the inclusion of dynamic atomic displacements, i.e., those caused by nonadiabatic transitions of atoms in a crystal with a dislocation under action of an external force. The dynamic displacements initiate the instability of a rectilinear dislocation with respect to low-amplitude displacements during atomic vibrations. The instability development leads to the formation of a double kink and the dislocation displacement by one interatomic distance.

APPENDIX

The numerical solution of Eqs. (3), (4), and (6)–(8) was performed by an implicit scheme. We introduced dimensionless variables

$$x = x{\text{/}}{{l}_{\eta }},\quad t = t{\text{/}}{{t}_{\eta }},\quad l = {{l}_{q}}{\text{/}}{{l}_{\eta }},\quad \theta = {{t}_{q}}{\text{/}}{{t}_{\eta }}.$$

(A.1)

The boundary conditions:

$$0 \leqslant x \leqslant X,\quad X = 100,$$

(A.2)

$${{\left. {\frac{{d\eta }}{{dx}}} \right|}_{{x = 0}}} = {{\left. {\frac{{d\eta }}{{dx}}} \right|}_{{x = X}}} = 0,\quad {{\left. {\frac{{dq}}{{dx}}} \right|}_{{x = 0}}} = {{\left. {\frac{{dq}}{{dx}}} \right|}_{{x = X}}} = 0,$$

(A.3)

$$\begin{gathered} q(x = 0,t) = q(x = X,t) = 0, \\ \eta (x = 0,t) = \eta (x = X,t) = 0. \\ \end{gathered} $$

(A.4)

The initial conditions

$$1.\;\;\eta (x,t = 0) = 0,\quad q(x,t = 0) = 0;$$

(A.5)

$$2.\;\;\eta (x,t = 0) = 0,\quad q(x,t = 0) = {{q}_{s}}.$$

(A.6)

The localized perturbations were given in the form

$$\Delta \eta = \Delta {{\eta }_{0}}\exp [ - {{\sigma }_{\eta }}{{(x - {{x}_{0}})}^{2}}],$$

(A.7)

$$\Delta q = \Delta {{q}_{0}}\exp [ - {{\sigma }_{q}}{{(x - {{x}_{0}})}^{2}}],$$

(A.8)

where Δη₀ and Δq₀ are the amplitudes, x₀ is the initial position, σ_η, σ_q are the dispersions of the perturbations of variables η and q, respectively.

The stochastic perturbation Δq in each site of the calculation mesh was taken a random value in the range

$$0 \leqslant \Delta q(x) \leqslant 0.001.$$

(A.9)

$$\Delta {{q}_{0}} = 0.01,\quad {{\sigma }_{q}} = 5,\quad {{x}_{0}} = 50.$$

(A.10)

$${{\eta }_{1}} = 0.2,\quad d = 0.3,\quad \alpha = 0.3,\quad c = 0.8.$$

(A.11)

$$\Delta {{\eta }_{0}} = 0.01,\quad {{\sigma }_{\eta }} = 15,\quad {{x}_{0}} = 50.$$

(A.12)

$${{\eta }_{1}} = 0.2,\quad d = 0.3,\quad \alpha = 0.7,\quad c = 0.8.$$

(A.13)