The lattice kinetic Monte Carlo method (LKMC) is an efficient approach for simulating dynamical evolution in microscopic systems, because it coarse-grains out the details of atomic vibration that severely limits the scope of molecular dynamics (MD) simulations while retaining atomistic resolution. However, the confinement of atomic positions to a rigid lattice necessarily reduces the available configurational degrees of freedom in a system. This constraint can become very important at elevated temperatures.

In previous work, a bond-counting LKMC model for vacancy diffusion and aggregation in silicon was generated. It was shown that the lattice constraint led to large errors in the predicted dynamics of vacancy clustering at high temperature because off-lattice configurations could not be explicitly captured in the rigid lattice model [1]. The missing configurational degrees of freedom were implicitly accounted for by regressing the bond energies to data generated by MD simulations [2]. While this approach successfully captured important high temperature entropic contributions, the lack of transferability to different temperatures limits its application to realistic processes such as crystal growth.

In this work, we present a LKMC framework to simulate continuous systems. Previous Metropolis Monte Carlo modeling studies have shown that lattice representations are able to correctly capture the phase behavior of continuous fluids if the discretization is sufficiently fine [3]. Here, we investigate the effect of lattice spacing on the ability of a LKMC simulation to capture the correct dynamical behavior by making detailed comparisons to molecular dynamics simulations. We discuss the calculation of rate barriers from a prescribed interatomic potential such as the Lennard-Jones model. We show that it is possible to generate the correct dynamics with LKMC for sufficiently discretized grids.

[1] S. S. Kapur, M. Prasad, J. C. Crocker, T. Sinno, Role of configurational entropy in the thermo-dynamics of clusters of point defects in crystalline solids, Phys. Rev. B 72, 014119 (2005).

[2] J. Dai, W. D. Seider and T. Sinno, Lattice kinetic Monte Carlo simulations of defect evolution in crystals at elevated temperature. Molecular Simulation, 32, 305 (2006).

[3] A. Z. Panagiotopoulos, On the equivalence of continuum and lattice models for fluids. J. Chem. Phys., 112, 7132 (2000).