Nanostructure and velocity of field-driven solid-on-solid interfaces moving under a phonon-assisted dynamic

Abstract

The nanoscopic 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, are studied by 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 the case that the system is coupled to a two-dimensional phonon bath. In the resulting dynamic [K. Saito et al., Phys. Rev. E 61, 2397 (2000); K. Park and M. A. Novotny, Comput. Phys. Commun. 147, 737 (2002)], transitions that conserve the system energy are forbidden, and the effects of the applied force and the interaction energies do not factorize (a so-called hard dynamic). In full agreement with previous general theoretical results, we find that the local interface width changes dramatically with the applied force. However, in contrast with other hard dynamics, this change is nonmonotonic in the driving force. 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. However, significant differences between theory and simulation are found near two special values of the driving force, where certain transitions allowed by the solid-on-solid model become forbidden by the phonon-assisted dynamic. Our results show 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. Thus, they represent a significant step toward providing a solid physical foundation for kinetic Monte Carlo simulations.