Extension of the Law of Corresponding States to Rare-Gas Solids

It is shown that the law of corresponding states can be applied to sublimation pressure curves of rare-gas solids. The vapor pressure ($P$) and temperature ($T$) below the triple point are written in terms of the usual reduced variables $P^{*}=\frac{P{\sigma }^3}{\epsilon }$ and $T^{*}=\frac{\mathrm{kT}}{\epsilon }$, where $\epsilon$ and $\sigma$ are Lennard-Jones potential parameters. It is then demonstrated that a single curve fits the $P^{*}$, $T^{*}$ data for Ar, Kr, and Xe over the 5-decade range in $P^{*}$ for which measurements have been made, $2\times {10}^{-8\mathrm{}}\le P^{*}\le 2\times {10}^{-3\mathrm{}}$ and $0.36\le T^{*}\le 0.72$. The equation of the curve for Ar, Kr, and Xe is $\ln P^{*}=5.\mathrm{}302-\frac{8.206}{T^{*}}$. The sublimation pressure curve for Ne is different from that of the heavier rare gases because of zero-point energy effects. The equation of the Ne curve is $\ln P^{*}=4.\mathrm{}287-\frac{7.077}{T^{*}}$, over about 3 decades in $P^{*}$. The historical background of the law of corresponding states and its derivation by De Boer et al. from quantum-mechanical first principles are presented in a way natural to this problem. It is shown that extension of the law of corresponding states to the solid-vapor phase transition is natural and proper. As a corollary, the sublimation pressure for radon is predicted as ${log}_{10}P\left(\mathrm{Torr}\right)=7.868-\frac{1034}{T}$.