Clusters of J = 1 Impurities in J = 0 Solids

Abstract

For a random distribution of NX impurities over the N sites of a close-packed lattice, the average size of clusters of impurities connected by nn separations is finite for X ≲ 20%, as discussed in section 3.4. At sufficiently low concentrations X, it is therefore appropriate to analyze the properties of these solids in terms of clusters containing small numbers of J = 1 molecules, such as singles, nn pairs, triples with at least two nn separations, etc.1, 2 The distribution of the impurities over the lattice may be random, as realized after quick freezing of a liquid sample, or may correspond to the true equilibrium distribution, attained after a time long compared to the diffusion time constant. Valuable information on various cluster properties has been obtained from measurements of the specific heat of solid H2, D2, and their mixtures for J = 1 concentrations in the range 0.1–1%.2–4 The finer details of the effective interaction between the J = 1 impurities have been revealed by the Raman,5 NMR,6,7 and microwave (MW)8 spectroscopy of pairs of J = 1 molecules.