Microstructure and velocity of field-driven solid-on-solid interfaces moving under stochastic dynamics with local energy barriers

TL;DR

This study investigates the microscopic structure and velocity of driven solid-on-solid interfaces in an Ising model, comparing two Arrhenius dynamics, revealing how different stochastic rules influence interface behavior under force.

Contribution

It provides a detailed comparison of soft and hard Arrhenius dynamics on interface structure and velocity, highlighting their distinct responses to external driving forces.

Findings

Interface width increases with force under TDA dynamics.

OSD dynamics show weak force influence on interface structure.

Velocity and anisotropy depend on the type of stochastic dynamics.

Abstract

We study the microscopic structure and the stationary propagation velocity of (1+1)-dimensional solid-on-solid interfaces in an Ising lattice-gas model, which are driven far from equilibrium by an applied force, such as a magnetic field or a difference in (electro)chemical potential. We use an analytic nonlinear-response approximation [P.A. Rikvold and M. Kolesik, J. Stat. Phys. 100, 377 (2000)] together with kinetic Monte Carlo simulations. Here we consider interfaces that move under Arrhenius dynamics, which include a microscopic energy barrier between the allowed Ising/lattice-gas states. Two different dynamics are studied: the standard one-step dynamic (OSD) [H.C. Kang and W. Weinberg, J. Chem. Phys. 90, 2824 (1992)] and the two-step transition-dynamics approximation (TDA) [T. Ala-Nissila, J. Kjoll, and S.C. Ying, Phys. Rev. B 46, 846 (1992)]. In the OSD the effects of the applied force and the interaction energies in the model factorize in the transition rates (a soft dynamic), while in the TDA such factorization is not possible (a hard dynamic). In full agreement with previous general theoretical results we find that the local interface width under the TDA increases dramatically with the applied force. In contrast, the interface structure with the OSD is only weakly influenced by the force, in qualitative agreement with the theoretical expectations. Results are also obtained for the force-dependence and anisotropy of the interface velocity, which also show differences in good agreement with the theoretical expectations for the differences between soft and hard dynamics. Our results confirm that different stochastic interface dynamics that all obey detailed balance and the same conservation laws nevertheless can lead to radically different interface responses to an applied force.