Modeling diffusion and phase transitions by a uniform-acceptance force-bias Monte Carlo method

Abstract

The uniform-acceptance force-bias Monte Carlo ͑UFMC͒ method ͓G. Dereli, Mol. Simul. 8, 351 ͑1992͔͒ is a little-used atomistic simulation method that has strong potential as alternative or complementary technique to molecular dynamics ͑MD͒. We have applied UFMC to surface diffusion, amorphization, melting, glass transition, and crystallization, mainly of silicon. The purpose is to study the potential and the limitations of the method: to investigate its applicability, determine safe and effective values of the two UFMC parameters-a temperature and a maximum allowed atomic displacement per iteration step-that lead to reliable results for different types of simulations, assess the computational speed increase relative to MD, discover the microscopic mechanisms that make UFMC work, and show in what kind of simulations it can be useful and preferable over MD. It is found that in many simulations, UFMC can be a very efficient alternative to MD: it leads to analogous results in much fewer iteration steps. Due to the straightforward formalism of UFMC, it can be easily implemented in any MD code. Thus both methods can be combined and applied in turn, using UFMC for the acceleration of certain processes and MD for keeping precision and monitoring individual atom trajectories.

Uniform-acceptance force-bias Monte Carlo method with time scale to study solid-state diffusion

“…III). Note that, for the convenience of the reader, we remained consistent with the notation used in the prior paper of Timonova et al 18 …”

“…Although the obtained formalism differs slightly from the original one proposed by Dereli (uniform-acceptance force-bias Monte Carlo, UFMC), 15,18 it offers the advantage of providing an intuitive and solid derivation for the technique. The comparison between our time-stamped force-bias Monte Carlo (tfMC) and the MD formalism is carried out through the formulation of a statistically relevant time bound to the atomic displacement.…”

“…As pointed-out by Timonova et al, 18 the essence of the force-bias Monte Carlo approach relies on an iterative modification of the atomic positions in which only their atomic forces are accounted for. To be valid, such a stochastic displacement of the particles has to remain statistically consistent with the evolution of the system.…”

“…This approach recently has been shown to be successfully able to reproduce long-term events that take place in materials upon phase transition, surface diffusion, and growth. [17][18][19][20] The simplicity of the fbMC approach is not its only attractiveness, since, compared to a classical MD approach, it has been reported to require a reduced number of numerical iterations to access physical meaningful results. 18 Aside from this apparent gain in efficiency, a clear quantitative comparison between the MD and fbMC approaches turns out to be a difficult task due to the stochastic roots of fbMC and its lack of a time scale.…”

“…Although these force-bias Monte-Carlo (fbMC) methods have been little used in the past (see for instance Refs. 16 and 17) they recently regained attention through the works of Timonova 18 and Neyts et al 19,20 Contrary to MD algorithms, fbMC relies on a force-bias probabilistic description of the atomic motion. This approach recently has been shown to be successfully able to reproduce long-term events that take place in materials upon phase transition, surface diffusion, and growth.…”