Orientational Order in Solid Ortho-Hydrogen. I. Cubic Close-Packed Molecular Lattice

Abstract

Previous theories of the orientational ordering of the molecules in solid ortho-hydrogen have been based on the assumption that the lattice is hcp, and on a quantum-mechanical treatment that is not self-consistent. It now seems clear that a change from a fcc lattice to a hcp lattice is associated in some way with the thermal and NMR phenomena that indicate the occurrence of orientational reordering. This paper develops a self-consistent theory of orientational ordering of molecules on a rigid fcc lattice, assuming orientational coupling of the quadrupole-quadrupole form between nearest neighbors only, or throughout the lattice. It is shown how the special properties of hydrogen and its isotopes facilitate application of the self-consistent theory to solid hydrogen. It is found that at all temperatures, up to the transition temperature, the symmetry axes of the molecular orientation distributions are arranged like the equilibrium directions in the corresponding classical system. If one includes quadrupole-quadrupole couplings between all pairs of molecules, one finds that there would be a first-order transition to orientational disorder at 5.07°K in hydrogen, and at 6.37°K in deuterium, if the molecular lattice were fcc throughout. These values exceed the observed transition temperatures by more than a factor of 2—a discrepancy that is not surprising if the actual transition is one from a fcc lattice to a hcp lattice at a temperature determined by the properties of the two phases. Molecular energy levels and thermodynamic properties are given for the fcc phase up to the transition temperature.