Trends in Elasticity and Electronic Structure of Transition-Metal Nitrides and Carbides from First Principles

TL;DR

This study uses first-principles calculations to analyze elastic properties and electronic structure trends in transition-metal nitrides and carbides, revealing how these properties vary across the periodic table and with valence electrons.

Contribution

It provides a comprehensive first-principles analysis of elastic constants and electronic structure trends in transition-metal nitrides and carbides, including predictions of stability and maximum shear moduli.

Findings

Elastic constants agree with experimental data and numerical derivatives.

Bulk and shear moduli increase across the periodic table for certain substitutions.

Transition-metal nitrides with specific valence electron counts are predicted to be unstable.

Abstract

The elastic properties of the $B_1$-structured transition-metal nitrides and their carbide counterparts are studied using the {\it ab initio\} density functional perturbation theory. The linear response results of elastic constants are in excellent agreement with those obtained from numerical derivative methods, and are also consistent with measured data. We find the following trends: (1) Bulk moduli $B$ and tetragonal shear moduli $G^{\prime}=(C_{11}-C_{12})/2$, increase and lattice constants $a_{0}$ decrease rightward or downward on the Periodic Table for the metal component or if C is replaced by N; (2) The inequality $B > G^{\prime} > G > 0$ holds for $G=C_{44}$; (3) $G$ depends strongly on the number of valence electrons per unit cell ($Z_{V}$). From the fitted curve of $G$ as a function of $Z_{V}$, we can predict that MoN is unstable in $B_{1}$ structure, and transition-metal carbonitrides ($e.g.$ ZrC$_{x}$N$_{1-x}$) and di-transition-metal carbides ($e.g.$ Hf$_{x}$Ta$_{1-x}$C) have maximum $G$ at $Z_{V} \approx 8.3$.