Transmission electron microscopy and first-principles calculations of hydrogen ordering in β -YH_2+x

In YH_2+x hydrides stoichiometric deviations are associated with various interesting phenomena such as magnetic transitions and metal-insulator transitions; ordering of hydrogen on the octahedral sites (O sites) was suggested to be responsible. Long-range order was discovered in hydrogenated Y films by electron diffraction and high-resolution transmission electron microscopy. Ordering on interstitial O sites in the fcc-based Y_fcc H_2+x solid solution (0<x<1) was investigated with computational tools from the Alloy Theoretic Automated Toolkit. The resulting set of 94 structure energies was fit to a cluster-expansion Hamiltonian that was used to perform a ground-state analysis for the mostly metastable fcc-based solid solution and for the more stable Y_fcc H_2+x + Y _hcp H_2+x two-phase mixture. The calculated structures were tested by the observed diffraction conditions and two possible ordered structures were suggested, a ground-state triclinic x=0.0625 and an I-centered cubic x=0.375.