Correlation functions between specific volume and stoichiometry for transition metal nitrides

A methodology is proposed to correlate the structural aspects of transition metal nitrides (TMN) to the stoichiometric ratio: x = [N]/[M]. The method is based on a numeric figure, υ, given by the difference between the atomic concentrations of nitride and parent metal normalized to the atomic concentration of parent metal. Numerical regression is used to construct interpolating functions for υ(x) using as input the available data for TMN in two well-recognized databases (ICDD and ICSD). In summary we obtain functions of x that describe the deformation caused in the parent metal lattice by the nitrogen assimilation. The results are attractive, since TMN show remarkable trends.