First-principles study of the atomic volume of hydrogen in palladium

The partial atomic volume of hydrogen, vH, is a fundamentally important thermodynamic parameter of interstitial metal hydrides in which dissociated H occupies interstices in the metal lattice. Such an important property should be able to be reliably calculated by a suitable theory or model in order to explain and understand its origin. In practice, vH is typically obtained by means of ab initio calculations founded on density functional theory (DFT), where the equilibrium lattice constant at zero temperature is found by minimising the Born-Oppenheimer energy. While the absolute lattice constants calculated in this way depend quite strongly on the DFT scheme employed, the present work showed that vH is rather robust against differing calculational approaches, thus making a meaningful comparison of theory and experiment possible. Comparing vH for PdnH (0<n<8) calculated with DFT and obtained from in-situ neutron diffraction measurements revealed a significant discrepancy when octahedral-only interstitial occupancy was assumed. Calculations for PdH with mixed octahedral and tetrahedral occupancy gave a value for vH in agreement with experiment assuming that PdH contains 15–20% tetrahedral H.