The thermodynamics of solid solutions of argon and methane

Abstract

The primary concern of this paper is with the estimation of the excess Gibbs energy G E, S for solid solutions of two molecularly simple components which are completely miscible in the solid state. The method depends on combining information on the excess thermodynamic functions of liquid mixtures of the two components with a knowledge of the liquidus and solidus lines on the temperature-composition phase diagram. It is applied to the particular case of argon-methane. For this system, unit cell sizes and some heat of fusion measurements are also available, from which V E, S and H E, S have been calculated. A solid solution of argon and methane departs much more from ideality than does a liquid mixture of the same composition at the same temperature, the ratio r, = G E, S / G E, L , being about 3. Moreover, the concentration dependence of G E, S is less symmetrical than that of G E, L , and the ratio r increases markedly with increasing argon mole fraction. A dilute solution of methane (which has the larger molecules) in argon has a larger G E, S than the corresponding dilute solution of argon in methane. For a solid solution at 71 K with an argon mole fraction of 0.60, H E, S is ≈4801 Jmol −1. This gives TS E, S ≈ 220 J mol −1, which is about the same as G E, S . The solid solutions cannot therefore be regarded as even approximating to regular solutions. From the calculated G E, S results, it is predicted that the face-centred cubic solid solutions of argon and methane should separate into two phases on cooling. The calculated coordinates of the upper critical solution point are T = 67 K and an argon mole fraction of 0.63, in reasonable agreement with the experimental values of 63 K and 0.65 respectively.