Full-potential linear-muffin-tin-orbital study of brittle fracture in titanium carbide

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Abstract
The inelastic behavior of the refractory transition-metal carbides is dominated, at low temperatures, by brittle fracture. We discuss in this article our theoretical study of both the elastic and fracture properties of titanium carbide under tensile stress. The calculations involved were performed using a full-potential linear-muffin-tin-orbital electronic structure method, with a repeated slab arrangement of atoms simulating an isolated cleavage plane. We report results for the elastic constants (excluding the shear modulus), the stress-strain relationship up to the point of fracture, and the ideal yield stress and strain for stoichiometric TiC. We relate these properties to the details of the electronic structure and to the breaking of metal-nonmetal covalent bonds at the cleavage plane. This includes a detailed pictorial analysis of the charge redistribution accompanying cleavage.