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

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 $Z_V\approx 8.3$.

arXiv comment4 pages, 2 figures, submitted to PRL. 2 typos in ref. 15 were corrected

References in corpus (3)

• Phonons and related properties of extended systems from density-functional perturbation theory
• Metric Tensor Formulation of Strain in Density-Functional Perturbation Theory
• Transferable relativistic Dirac-Slater pseudopotentials

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