Kinetic Monte Carlo Simulations of Crystal Growth in Ferroelectric   Alloys
  The growth rates and chemical ordering of ferroelectric alloys are studied with kinetic Monte Carlo (KMC) simulations using an electrostatic model with long-range Coulomb interactions, as a function of temperature, chemical composition, and substrate orientation. Crystal growth is characterized by thermodynamic processes involving adsorption and evaporation, with solid-on-solid restrictions and excluding diffusion. A KMC algorithm is formulated to simulate this model efficiently in the presence of long-range interactions. Simulations were carried out on Ba(Mg_{1/3}Nb_{2/3})O_3 (BMN) type materials. Compared to the simple rocksalt ordered structures, ordered BMN grows only at very low temperatures and only under finely tuned conditions. For materials with tetravalent compositions, such as (1-x)Ba(Mg_{1/3}Nb_{2/3})O_3 + xBaZrO_3 (BMN-BZ), the model does not incorporate tetravalent ions at low-temperature, exhibiting a phase-separated ground state instead. At higher temperatures, tetravalent ions can be incorporated, but the resulting crystals show no chemical ordering in the absence of diffusive mechanisms. 
Malliga Suewattana, Henry Krakauer and Shiwei Zhang