  Using combination of Density Functional Theory and Monte Carlo simulation, we
study the phase stability and electronic properties of two dimensional
hexagonal composites of boron nitride and graphene, with a goal to uncover the
role of the interface geometry formed between the two. Our study highlights
that preferential creation of extended armchair interfaces may facilitate
formation of solid solution of boron nitride and graphene within a certain
temperature range. We further find that for band-gap engineering, armchair
interfaces or patchy interfaces with mixed geometry are most suitable.
Extending the study to nanoribbon geometry shows that reduction of
dimensionality makes the tendency to phase segregation of the two phases even
stronger. Our thorough study should form an useful database in designing boron
nitride-graphene composites with desired properties.
