Second virial coefficients of alkali metals from diatom fractions and assessment of ISM EOS by real data

Abstract

In this paper, the calculation of mean second virial coefficients 〈 B 2〉 of alkali metals by using diatom fractions at pressure 10 −5 bar is reported. A corresponding states description of the alkalis in terms of reduced second virial coefficients versus the new reduced temperature T q ∗=T q ∗(T,γ f ,ρ f ,Λ) follows, where T is the absolute temperature, γ f and ρ f the surface tension and liquid density at freezing temperature, respectively, and Λ accounts for the quantum effects that are highly essential in metals. The form of T q ∗ defines a semi-empirical description of a quantum mechanical law of corresponding states. We use the second virial coefficients to apply the Ihm–Song–Mason (ISM) equation of state (EOS) to molten alkali metals. Two other temperature-dependent coefficients α and b of the EOS are calculated by integration using the Rydberg potential function. To bring the highly attractive polarizable alkali metals in the ISM regime, which considers only small perturbation interaction potentials, a cofactor is applied by normalizing the potential well-depth of a metal to the noble of the preceding period. Application of the ISM EOS to molten alkali metals by our method is theoretically advantageous in that we have used real data. It reproduces the liquid densities within <8% of the experimental values in the temperature range 250–300 K around the boiling temperature. Diatom formations of Li, Na, and K turn over at 1410, 975, and 915 K, respectively, suggesting possible corresponding changes across the liquid–vapor phase transition boundaries.