The effects of vacancy ordering on diffusion: a statistical study

In this paper we investigate the interconnection between vacancy-ordered phases and vacancy self-diffusion. Here, we investigate three ordered phases on a square lattice with energetics defined by two separate Hamiltonians. In the first case we used a classical antiferromagnetic Ising model Hamiltonian in order to generate a 'checkerboard' type ordered structure. In the second case, we used a modified Ising model with competing influence of second and third nearest-neighbors, which resulted in both 'hatch' and 'labyrinthine' structures, depending on concentration. To understand how vacancy-ordering affects diffusion, we determined the tracer diffusivity using rejection-free kinetic Monte Carlo and compared disordered and ordered structures. Finally, we developed an analytical model describing diffusion in the ordered 'checkerboard' structure and found that it was able to predict apparent activation energies in the ordered and disordered structures. Our results suggest that it is short-range order rather than long-range order that most significantly affects tracer diffusion.