Total-energy study of hydrogen ordering in ${\mathrm{PdH}}_{\mathit{x}}$ (0⩽x⩽1)

We studied total energies of various ordered structures of ${\mathrm{PdH}}_{\mathit{x}}$ (in which hydrogen occupies the octahedral sites within the fcc Pd lattice) using the pseudopotential method and a plane-wave basis within the local-density-functional approximation. The structures considered include the (420)-plane ordering of hydrogen atoms at different concentrations. For x≥1/2 we found that the NiMo- and ${\mathrm{Ni}}_4$Mo (D$1_{\mathit{a}}$)-type structures at x=1/2 and x=4/5, respectively, were energetically favored phases, in agreement with the superlattice reflections found in previous neutron-scattering measurements. For the intermediate concentrations, linear variation of the formation energy as a function of x in several (420)-ordered structures explained the observed short-range order. In contrast to an earlier proposal, we did not find the Fermi surface imaging effect responsible in this case. The overall energy variation in different phases indicates the importance of going beyond pairwise interactions between interstitial hydrogen atoms in this system. © 1996 The American Physical Society.