Orientational Order in Solid Ortho-Hydrogen. II. Hexagonal Close-Packed Molecular Lattice

Abstract

The orientational ordering of the molecules in solid hcp ortho-${\mathrm{H}}_{2}$ is studied theoretically, using the internal-field approximation and neglecting lattice vibrations. A relaxation method suitable for use with a high-speed computer is employed in a search for molecular orderings that might occur in stable or metastable phases; numerical characterizations of the molecular states and the thermodynamic properties of these phases are then obtained for appropriate ranges of temperature. Orders describable in terms of four or eight sublattices are studied. On the assumption that there is quadrupole-quadrupole coupling only between nearest-neighbor molecules, it is concluded that as $T$ arises the phase (space group $\mathrm{Pca}{2}_{1}$) stable at the lowest temperatures undergoes a first-order into a $\frac{P{2}_{1}}{c}$ phase, followed by second-order transitions into a $\mathrm{Pnma}$ phase and then into an orientationally disordered phase. A model that includes quadrupole-quadrupole couplings between all molecules shows a first-order from the $\mathrm{Pca}{2}_{1}$ phase into a $\frac{P{6}_{3}}{m}$ phase, followed by a second-order into the orientationally disordered phase. It is concluded that the $\ensuremath{\lambda}$ transition in pure ortho-${\mathrm{H}}_{2}$ and in ortho-para mixtures sufficiently rich in ortho-${\mathrm{H}}_{2}$ will consist of a first-order from an orientationally ordered phase with fcc lattice ($\mathrm{Pa}3$) to an orientationally ordered phase with hcp lattice, followed by orientational transitions on the hcp lattice that give rise to the finer structure in the specific-heat curve observed by Ahlers and Orttung. In the case of solid deuterium rich in para-${\mathrm{D}}_{2}$, one can expect the to be a simple one from the orientationally ordered fcc phase to an orientationally disordered hcp phase, with no fine structure in the specific-heat curve.