  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.
