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Investigating the effects of local environment on nitrogen vacancies in high entropy metal nitrides

High entropy metal nitrides are an important material class in a variety of applications, and the role of nitrogen vacancies is of great importance for understanding their stability and mechanical properties. We study six different high entropy nitrides with eight different metal species to build a predictive model of the nitrogen vacancy formation energy. We construct sets of supercells that maximize the number of unique nitrogen environments for a given chemistry, and then use density-functional theory to calculate the energy density for all nitrogen sites, and the vacancy formation energies for the highest, lowest, and a median subset based on the energy densities. The energy density of nitrogen sites correlates with the vacancy formation energies, for binary, ternary and high entropy nitrides. A linear regression model predicts the vacancy formation energies using only the nearest-neighbor composition; across our eight metals, we find the largest vacancy formation energies next to Hf, then Zr, Ti, V, Cr, Ta, Nb, and the lowest near Mo. Additionally, we see that binary nitride data shows qualitatively similar vacancy formation energy trends for high entropy nitrides; however, the binary data alone is insufficient to predict the complex nitride behavior. Our model is both predictive and easily interpretable, and correlates with experimental data.