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

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

2004-12-14

arxiv.org/abs/cond-mat/0412374v2

Phys. Rev. B 71, 214103 (2005)

Physics

Condensed Matter

Materials Science

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

Scientific paper

10.1103/PhysRevB.71.214103

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 $Z_{V} \approx 8.3$.

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