Anisotropic elasticity of IVB transition-metal mononitrides determined by ab initio calculations

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Shijo Nagao
Nordic Hysitron Laboratory, Department of Materials Science and Engineering, Helsinki University of Technology, P. O. Box 6200, 02015 HUT, Finland

K. Nordlund
Accelerator Laboratory, University of Helsinki, P. O. Box 43, FIN-00014, Finland

R. Nowak
Nordic Hysitron Laboratory, Department of Materials Science and Engineering, Helsinki University of Technology, P. O. Box 6200, 02015 HUT, Finland

Received 10 February 2006; published 27 April 2006

Elasticparameters of IVB transition-metal mononitrides, TiN, ZrN, and HfN inthe cubic NaCl crystal structure have been calculated by meansof density-functional theory with the generalized gradient approximation. The elasticconstants c₁₁, c₁₂, and c₄₄ were shown to be sufficientlyconverged with the density of the k-point mesh in thedeformed Brillouin zone to discuss the elastic anisotropy of thesystems. It was found that the anisotropy coefficient kappa [equivalent] (c₁₁–c₁₂)/2c₄₄ increaseswith the atomic number of the metal element, i.e., HfNexhibits as strong anisotropy as kappa =2.02. The Young's modulus ofHfN along 100 is approximately two times higher than thatalong 111. Moreover, analysis of the deformation energy by theapplied strain modes shows that this elastic anisotropy originates fromthe strong covalent bonding between metal and nitrogen atoms along100.

URL:	http://link.aps.org/doi/10.1103/PhysRevB.73.144113
DOI:	10.1103/PhysRevB.73.144113
PACS:	62.20.Dc; 81.40.Jj; 46.25.-y; 81.05.Je 62.20.Dc Elasticity, elastic constants 81.40.Jj Elasticity and anelasticity, stress-strain relations 46.25.-y Static elasticity 81.05.Je Ceramics and refractories: fabrication, treatment, testing and analysis including borides, carbides, hydrides, nitrides, oxides, and silicides YEAR: 2006
KEYWORDS:	elasticity, ab initio calculations, titanium compounds, zirconium compounds, hafnium compounds, density functional theory, elastic constants, Brillouin zones, Young's modulus, deformation