Equilibrium hydrogen pressures in the V–H system from first principles

Equilibrium hydrogen pressures over hydrogenated vanadium, i.e., crystalline VH_x with 0≤x≤2, are estimated based on first-principles calculations to assess the suitability of V-based alloys for use as hydrogen storage materials. For intermediate H contents (x = 0.5 and 1) corresponding to partial site occupancies, a multistep process was used to determine the ground-state structures. First, a large number of configurations with H on tetrahedral (T) or octahedral (O) sites in bcc–type lattices were ranked in terms of energetical stability sans vibrational contributions. Next, phonon calculations were carried out for the lowest-energy structures identified in the first step and zero-point energies added to the electronic energies. Hydrogen pressures for V-VH_0.5 and VH-VH₂ equilibria were then calculated using these ground-state free energies and thermodynamic equations. Calculation of vibrational energies was simplified by identifying the linear relationship between H content and zero-point energy, which depends only on the type of sites occupied by H atoms. Whereas H atoms preferentially occupy T sites when vibrational terms are ignored, their inclusion leads to H atoms preferentially occupying O sites in both VH_0.5 and VH at 0 K. Inclusion of vibrational energy also leads to a better match with reported experimental hydrogen pressures highlighting its importance when assessing the stabilities of different H distributions in metal lattices. The method outlined consists of a more exhaustive configurational search than has been considered previously, and should be useful for systematic investigation of a wide variety of V-based alloys.