Vibration of a pinned dislocation segment in an atomistic model

Abstract

The dynamic behavior of a freely-vibrating straight edge dislocation, pinned at equal distances along its length, in an idealized, atomistic crystal model is studied by computer simulation. The model, which represents the slip plane of the crystal, is a two-dimensional version of the Frenkel-Kontorowa model as modified by Kratochvil and Indenbom, and by Weiner and Sanders to be piecewise quadratic, and was utilized by Sanders in his study of dislocation kinks. By use of the convolution theorem, it is found possible to simulate an infinite strip of the slip plane while treating explicitly only a finite number of atoms. The model contains no phenomenological damping or viscosity; the dislocation loses energy solely by energy transfer to other lattice modes. The damping of the dislocation motion is determined by observing the decay in its amplitude of vibration. The behavior of the atomistic model is compared, based on a limited number of computer-simulation runs, with the string model of Koehler and of Granato and L\ucke. In agreement with that model, it is found that the frequency of free vibration, ${\mathrm{\ensuremath{\omega}}}_{0}$, is proportional to the square root of the shear modulus and inversely proportional to the loop length. For the case of model parameters leading to zero Peierls stress (${\ensuremath{\sigma}}_{P}=0$), the amplitude of dislocation vibration in the atomistic model for sufficiently large loop length decays exponentially as in the string model with linear damping. Furthermore, it is found that the logarithmic decrement, $\ensuremath{\Delta}$, of the decay of free vibrations in independent of ${\ensuremath{\omega}}_{0}$. A few runs with suitably-generated random initial atomic velocities simulate, on the basis of classical statistics, the effect of temperature, $T$. It is found that $\ensuremath{\Delta}$ decreases with increasing $T$, apparently due to the phenomenon of thermal energy trapping by the moving dislocation. For parameters leading to ${\ensuremath{\sigma}}_{P}g0$ it is found that at $T=0$ the vibrating dislocation becomes trapped in a single Peierls valley and, in this model with piecewise quadratic potential, ceases to lose energy.