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+1͒-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 ͑electro͒chemical potential, are studied by an analytic nonlinear-response approximation ͓P. A. Rikvold and M. Kolesik, J. Stat. Phys. 100, 377 ͑2000͔͒ 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 ͑2000͒; K. Park and M. A. Novotny, Comput. Phys. Commun. 147, 737 ͑2002͔͒, 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 dynamic͒. 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.

Field-driven solid-on-solid interfaces moving under a stochastic Arrhenius dynamics: Effects of the barrier height

“…When applied to kinetic Ising lattice-gas models, soft and hard Arrhenius dynamics give very different nucleation rates [11]. It has also recently been shown that SOS interfaces evolving under soft Arrhenius dynamics have quite different structures that those evolving under hard Arrhenius dynamics [7]. In soft Arrhenius dynamics, the barrier height only results in a change in the overall time scale of the simulation and has no effect on the interface microstructure [7].…”

“…Until recently it was commonly believed that dynamics that respect the same conservation laws and all obey detailed balance, give essentially the same qualitative behavior. However, recent results clearly show that there are nonconservative dynamics that, although they all obey detailed balance and the same conservation laws, lead to very different interface microstructures [3,4,5,6,7]. Since many interface properties, such as mobility and chemical activity, are determined by the microstructure, great care must therefore be taken in selecting the appropriate dynamic for the physical or chemical system of interest.…”

Transition rates for aS≥1spin model coupled to ad-dimensional phonon bath

“…A similar feature was reported in the time evolution of field-driven solid-on-solid interfaces using the d = 2 phonon-assisted transition rate. 22 Monte Carlo simulations are performed for D =4J and H = 0 with periodic boundary conditions and a random initial state. Spins at sites are updated in a regular typewriter fashion.…”

“…Very recently, the derived phonon-assisted transition rates were used to examine the nanostructure of field-driven solid-on-solid interfaces. 22 It was found that the phonon-assisted rates provide significant differences from other types of transition rates, such as the Glauber dynamics.…”

Metastability for the Blume-Capel model with distribution of magnetic anisotropy using different dynamics

“…Other commonly used dynamics are Metropolis [27] and soft stochastic dynamics [28]. It has been shown that different dynamics demand even different interpretations of the Arrhenius law [29] as well as different nonequilibrium properties [30] in the Ising model and nanostructures of field-driven solid-on-solid interfaces. One of us derived a transition rate or dynamic from a microscopic model where a spin system (S 1 generalized BC model) is weakly coupled to a d-dimensional phonon bath [31].…”