First-principles calculations of structural energetics of Cu–TM (TM = Ti, Zr, Hf) intermetallics

A systematic and comprehensive study of cohesive properties of Cu–TM (TM = Ti, Zr, Hf) intermetallics is carried out using a first-principles method. Specifically, the total energies and equilibrium cohesive properties of 95 intermetallics in the Cu–TM (TM = Ti, Zr, Hf) systems are calculated employing electronic density-functional theory (DFT), ultrasoft pseudopotentials and the generalized gradient approximation for the exchange-correlation energy. The intermetallic phases considered in our first-principles investigation are classified as stable, metastable and virtual types. The concentration dependence of the heat of formation (ΔEf) in the Cu–Ti system is only slightly asymmetric, while in the Cu–Zr and Cu–Hf systems they are distinctly asymmetric, being skewed towards the Cu-rich side with a minimum in ΔEf at Cu10TM7. Based on the observed differences between ab initio and calorimetric heat of formation, we conclude that additional careful experiments are needed to validate ab initio alloy energetics. We also note that the calphad model parameters representing alloy energetics vary significantly from one assessment to another in these systems. For the stable intermetallics, the calculated zero-temperature lattice parameters agree to within ±1% of experimental data at ambient temperature. For the stable phases with unit cell-internal degree(s) of freedom, the results of ab initio calculations show a good agreement when such data are available from X-ray and other diffraction results. For intermetallic compounds where no such experimental data are available, we provide optimized unit cell geometries which may be verified in future experiments. For most structures we also provide zero-temperature bulk moduli and their pressure derivatives, as defined by the equation of state. The bonding between Cu and Zr is discussed based on the analyses of density of states and bonding charge densities in Cu5Zr and CuZr.