Speed-up of Monte Carlo simulations by preparing starting off-lattice structures that are close to equilibrium.

The Monte Carlo (MC) technique is an important tool for studying equilibrium properties of materials. When the starting configuration provided as an input to a MC calculation is far from equilibrium, an inordinate amount of computational effort may be required to bring the system closer to equilibrium in the pre-equilibration step of the MC calculation. In order to alleviate this cost, a new computational strategy is presented with the aim of rapidly generating starting off-lattice atomic structures that are already close to equilibrium. The method involves preparing a collection of on-lattice configurations using fast reverse MC calculations. Each configuration corresponds to a different value of short-range order parameter(s). Next, by performing short MC calculations with each starting structure, one measures the extent to which the distribution of local atomic arrangements has changed. The optimal configuration exhibits the smallest change in the distribution. While the optimal configuration can serve as an input to longer MC calculations, in many situations, the resulting structure may be directly used for the estimation of thermodynamic properties. Application of our approach to several off-lattice binary and ternary metal alloy systems with phase separation, good mixing, ordering, and surface segregation is demonstrated. A speed-up of >100-1000 times over the standard MC approach is achieved even with small systems containing a few thousand particles, and close-to-equilibrium structures containing million atoms can be rapidly prepared using our method within a day on a standard desktop computer.

Thermodynamic calculations using reverse Monte Carlo.

We introduce the theoretical background needed to perform thermodynamic calculations using reverse Monte Carlo (RMC). The theory is developed for binary A_{x}B_{1-x} lattice systems. The main assumption is that the arrangement of A and B atoms can be described using short-ranged order (SRO) parameters. The detailed balance equation, which is expressed in terms of SRO parameters, is solved to obtain the equilibrium SRO parameter value for the given material interactions, temperature, and composition. Thermodynamic properties, such as the chemical potential, are evaluated using the equilibrium SRO parameter value. RMC enables the calculation of the probability distribution of the local atomic environments, which is needed in the detailed balance equation. We illustrate the application of our method to bulk lattice materials with different first nearest neighbor pair interactions. The main advantage of our approach is that the probability distribution from RMC can be stored in form of look-up tables, and used with a variety of interaction strengths and temperature for rapid estimation of thermodynamic properties. In all examples, the chemical potential is accurately evaluated in the matter of a few seconds on a desktop computer.