Distribution function for the orientational order parameters in solid H2 and D2.

Abstract

A model for the distribution function P(\ensuremath{\sigma},\ensuremath{\eta}) for the axial and eccentric orientational order parameters \ensuremath{\sigma} and \ensuremath{\eta} is proposed for a system of quadrupoles which represents the situation in solid ${\mathrm{H}}_{2}$ and ${\mathrm{D}}_{2}$. It is based on a plausible approximation to the exact one-particle orientational density matrix for J=1 molecules in the randomly distributed (J${=1)}_{X}$(J${=0)}_{(1\mathrm{\ensuremath{-}}X)}$ solid, where X is the molar concentration of the J=1 component. The properties of P(\ensuremath{\sigma},\ensuremath{\eta}) are described, and can be expressed as a function of a single parameter D. Three-dimensional representations of P(\ensuremath{\sigma},\ensuremath{\eta}) for several values of D are shown, where D\ensuremath{\ll}1 and D\ensuremath{\gg}1 represent the extreme situations for zero and complete ordering. By means of the P(\ensuremath{\sigma},\ensuremath{\eta}) model, the NMR line shape for an ortho-para-mixture polycrystalline sample is calculated and compared with experiments in ${\mathrm{H}}_{2}$. The correlation of the parameter D with a given ordering state in the temperature-concentration plane for ${\mathrm{H}}_{2}$, the effect of zero-point motion, and the effect of crystalline anisotropy on the line shape are discussed.