A simple model for calculating the compressibility of the transition-metal carbides and nitrides alloys ZrxNb1−xC and ZrxNb1−xN

Abstract

The 4d-transition-metals carbides (ZrC, NbC) and nitrides (ZrN, NbN) in the rocksalt structure, as well as their ternary alloys, have been recently studied by means of a first-principles full potential linearized augmented plane waves method within the local density approximation. These materials are important because of their interesting mechanical and physical properties, which make them suitable for many technological applications. Here, by using a simple theoretical model, we estimate the bulk moduli of their ternary alloys ZrxNb1−xC and ZrxNb1−xN in terms of the bulk moduli of the end members alone. The results are comparable to those deduced from the first-principles calculations.

Strengths of covalent bonds in LnO2 determined from O K-edge XANES spectra using a Hubbard model

“…The values of the Born exponent, n, were determined from the derivative of the bulk modulus, B, with respect to pressure, dB/dP, using eqn (8), where n is the Born exponent. 77 Measured values of dB/dP for CeO 2 and PrO 2 were reported by Gerward et al, and dB/dP for TbO 2 was determined from the pressure dependence calculated by Miran et al 78,79 As is clear from the values of E BL , the stabilization due to electrostatic effects is much larger than the stabilization due to orbital overlap; as in trivalent lanthanide compounds, bonding in LnO 2 is best described as ionic with a small contribution from orbital interactions (covalent bonding). The rationale for determining E BL was to determine whether the trends in 4f and 5d bonding among the LnO 2 were reected in lattice energy once the effect of ionic bonding had been accounted for.…”