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

TL;DR

The paper tackles how the local nitrogen environment governs vacancy formation energies in high-entropy metal nitrides. By constructing 10 optimized 64-atom supercells to maximize nitrogen-environment sampling and applying the energy density method alongside DFT, the authors show that vacancy energetics correlate with local nearest-neighbor chemistry, enabling a simple, interpretable linear model with MAE ≈ 0.149 eV that predominantly relies on first-neighbor composition. While EDM trends qualitatively align across binary, ternary, and HE nitride systems, transfer to less-ordered families is imperfect, and triplet corrections provide only modest improvements. The work provides a computationally efficient approach to predict vacancy energetics and offers guidance for designing HEMN coatings with tailored mechanical properties.

Abstract

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.

Figures (10)

• Figure 1: (Left) a single B1 high entropy metal nitride (HEMN) supercell used in this study, with the supercell boundary in red; (right) prototype nitrogen environments in this supercell. The prototypes are ordered from top to bottom as quinary, quaternary, ternary, and binary environments. A nitrogen environment is defined as the octahedron of six metal atoms in the first nearest-neighbor shell of a nitrogen site. The prototype environments are A$_3$B$_3$, A4B2, A2B2C2, A4BC, A$_3$B2C, A2B2CD, A$_3$BCD, A2BCDE. A--E represent the 5 different metal cations contained in each supercell.
• Figure 2: Average density of states (DOS) of all 10 supercells for each of the HEMNs. Energy values are in reference to the average fermi energy, which is represented by the dashed line. The average DOS for each HEMN is taken by interpolating each supercell's DOS onto a common energy spectrum per HEMN, and then averaging the interpolated DOS across all 10 supercells.
• Figure 3: EDM energies of all the HEMN nitrogen sites as a function of the atomic fraction of each metal cation in the site's first nearest-neighbor shell. The top and bottom end of the whiskers in the plots represent the maximum and minimum EDM energy, and the orange line is the median.
• Figure 4: EDM energies of all nitrogen sites in (CrNb)N, (CrTi)N, (MoHf)N, and (TiNb)N as a function of the nearest neighbor composition in the nitride. The red endpoints are the EDM energy of the binary nitrides, with a dashed line interpolation.
• Figure 5: EDM and vacancy formation energies ($E_\text{vf}$) for HEMN, ternary, and binary nitride nitrogen sites. A linear fit (dashed line) of the EDM values to the $E_\text{vf}$ values shows a negative correlation with an $R^2=0.534$.