Thermodynamic Analysis of Ar_<i>x</i>Xe₁_-_<i>x</i> Solid Solutions Based on Kirkwood–Buff Theory

Abstract

Kirkwood–Buff Integral (KBI) theory is an important method for the analysis of the structural and thermodynamic properties of liquid solutions. For solids, the calculation of KBIs has become possible only recently through the finite-volume generalisation of KBI theory, but it has so far only been applied to monoatomic crystals. Here, we show that KBI theory can be applied to solid mixtures and compute the KBIs of a ArxXe1−x solid solution, for 0x0.1 and temperature T=84−86 K, from pair distribution functions obtained by Monte Carlo simulation. From the KBIs, the isothermal compressibility, partial molar volumes, and thermodynamic factors are calculated and found to be in good agreement with alternative theoretical methods. The analysis of the KBIs and the partial molar volumes give insight into the structure of the mixture. The KBI of Ar pairs is much larger than that of Xe pairs, which indicates the tendency of Ar impurities to accumulate. The evolution of the partial molar volumes with increasing Ar molar fraction x shows a transition at x≈0.06, which reflects the formation of Ar clusters, precursors of the Ar-rich liquid phase. The calculated thermodynamic factors show that the solid(Xe) phase becomes unstable at x≈0.1, indicating the start of the solid (Xe)–liquid (Ar) equilibrium. The chemical potentials of Ar and Xe are obtained from the thermodynamic factor by integration over lnx, and by fitting the data to the Margules equations, the activity coefficients can be estimated over the whole composition range. The present findings extend the domain of applicability of the KBI solution theory from liquids to solids.

Keywords

• solid solution
• argon
• xenon
• Kirkwood–Buff Integral
• Monte Carlo simulation