Theoretical investigation of solid solution states of Ti_1−xV_xH₂

The solution states of metal atoms in Ti_1−xV_xH₂, the stability of ordered ground-state structures, and the effect of metal-atom configurations on the bonding strength of H atoms are investigated by combining the cluster expansion method with first-principles calculations. Formation energies of all possible configurations of metal atoms in CaF₂-type structures with up to sixteen metal atoms calculated using an optimized set of clusters are reported. Nine ground-state structures with different compositions are identified, most of which are found to have layered structures containing V bilayers. Analysis of the component clusters suggests that, while pair clusters contribute to formation of the layered structures, the higher-body clusters contribute more to stabilization of V bilayers than Ti bilayers. Based on calculations of short-range order parameters for all configurations of composition x = 1/2, low-energy structures including the layered structures appear to have a tendency for phase separation at the atomic scale. Order-disorder transition temperatures of the ground-state structures are estimated from Monte Carlo simulations to be less than 460 K. Comparison of lattice constants with experimental values as well as the low transition temperatures suggests that disordered solutions will be predominantly formed under typical synthesis conditions. In addition, we examine the stability of H atoms in different coordination environments and find that the metal-atom ordering does not greatly affect the local bonding between H and surrounding metal atoms.