First-Principles Calculations on the Origin of Mechanical Properties and Electronic Structures of 5d Transition Metal Monocarbides MC (M = Hf, Ta, W, Re, Os, Ir, and Pt)

Much is not systematically known about the origin of mechanical properties among 5d transition metal carbides including tungsten carbide. In order to understand the microscopic origin of hardness, the mechanical properties and electronic structures of 5d transition metal monocarbides MC (M = Hf, Ta, W, Re, Os, Ir, and Pt) in five different structures (NaCl, WC, ZnS, CsCl, and NiAs type) are analyzed using first-principles calculations based on the density functional theory. Our results would indicate that WC-type WC and NiAs-type ReC have the highest and second highest hardness among all of the MC, respectively, in terms of the Debye temperature. By examining the Debye temperature in the series, it is found that MC in the range of less and more than half filled 5d shells are brittle and ductile, respectively. Our results would indicate that filling in the bonding and anti-bonding states contributes to brittleness and ductility. The Debye temperature could be a key to understanding hardness in terms of bulk and shear moduli. In addition, we evaluate some other structural properties such as equilibrium volume, formation enthalpy, and elastic constant to investigate structural stability. Based on the theoretical findings, the microscopic mechanisms of hardness and brittleness in the transition metal carbides are discussed.