Orientational Order Parameter in CubicD2

We present a study of the orientational order parameter $\sigma$ for ${\mathrm{D}}_2$ molecules with both rotational angular momentum $J=1\mathrm{}$ (para-${\mathrm{D}}_2$) and $J=0\mathrm{}$ (ortho-${\mathrm{D}}_2$) in the orderrd cubic phase. Our study covers the temperature range between 0.4 and 4 K at mole fractions $X$ of ($J=1\mathrm{}$) molecules $0.55\le X\le 0.96$, The order parameters ${\sigma }_{\mathrm{}(J=1\mathrm{})\mathrm{}}(T, X)$ and ${\sigma }_{\mathrm{}(J=0\mathrm{})\mathrm{}}(T, X)$ are proportional to the respective doublet splitting observed in the NMR spectrum. In the ordered phase, two doublets spaced symmetrically around the central Larmor frequency are recorded. The outer one, with a splitting $\delta {\nu }_{\mathrm{}(J=1\mathrm{})\mathrm{}}$ up to about 78 kHz, represents the signal from the ($J=1\mathrm{}$) molecules. The inner one, with splitting $\delta {\nu }_{\mathrm{}(J=0\mathrm{})\mathrm{}}$ an order of magnitude smaller than $\delta {\nu }_{\mathrm{}(J=1\mathrm{})\mathrm{}}$, is caused by polarization of the ($J=0\mathrm{}$) molecules by the ($J=1\mathrm{}$) field. A description is presented of the line shape as a function of $T$ and $X$. Using the results from several samples, we obtain the extrapolated ($J=1\mathrm{}$) order parameter for $X=1\mathrm{}$ as a function of $T$. At the order-disorder transition temperature $T_{\lambda }$, the doublet structure suddenly disappears and is replaced by a sharp central line which is characteristic of the orientationally disordered phase. The first-order nature of the transition is thus clearly shown. The experimental order parameter for ($J=1\mathrm{}$) molecules ${\sigma }_{\mathrm{}(J=1\mathrm{})\mathrm{}}(X=1, T)$ is compared with predictions from a meanfield and a cluster-variation theory, and also with results from Raman spectroscopy. As $X$ decreases, the line structure shows a progressively greater temperature variation and becomes more smeared out as the order-disorder transition is approached. Below a critical mole fraction $X_c=0.54\mathrm{}$, obtained by extrapolation, no doublet structure is observed. The limiting value of both ${\sigma }_{\mathrm{}(J=1\mathrm{})\mathrm{}}$ and