Abstract

A first-principles-based lattice model is applied to investigate the ordered phases of mixed group-III nitride ternary alloys. The model surveys the atomistic configurations with the lowest formation enthalpy for a wide range of compositions. We found novel ordered phases in wurtzite structures having specific compositions of three- and four-sevenths molar fractions of group-III cations. The configurations of group–III atoms on cation sites in those phases consist of a characteristic fragment of the ordered phases of one-third and one-half ordered phases that were previously reported. The simulation results indicate that group-III cations in ternary nitrides follow spatial positioning “atomistic distancing rules” that can be described by the pairwise interaction energy of group-III cations to realize the stabilities of the ordered structures. To minimize the formation enthalpy of a mixed crystal, the minor B, Al, Ga, and In atoms on cation sites remain neither too close to nor too distant from each other, allowing those ordered phases to be realized.