Electronic structure and pairwise interactions in substoichiometric transition metal carbides and nitrides

In substoichiometric transition metal carbides and nitrides crystallizing with the NaCl structure, the vacancies, which appear on the metalloid FCC lattice only, may order under some conditions. The corresponding long range ordered phases are analogous to those predicted, for FCC substitutional alloys, by theoretical calculations using pair interactions limited to first and second neighbours (V1, V2). We show here that the ordering energy of these compounds can be expanded in terms of pairwise interactions calculated from the electronic structure of the disordered state and that this expansion can be limited to a good accuracy to first and second neighbours. From these calculated pair interactions we then derive a theoretical (V1, V2) diagram in which the domains of existence of ordered carbides and nitrides are well separated; more precisely carbides exist in the region (V2 > 0, V2 >> V1) whereas nitrides are found for (V1 ≳ V2, V1 > 0), in fair agreement with experiments.