Discussion of “Legendre polynomial expansions of thermodynamic properties of binary solutions”

Abstract

In the paper quoted above enhancements to Legendre polynomial expansions for representing the excess thermodynamic properties of binary solutions are presented. Further, formulae are given for the conversion of the coefficients of simple power series or Redlich-Kister polynomials to Legendre coefficients. This discussion is directed toward these conversion formulae. Pelton and Bale I remark that the conversion between the Redlich-Kister and Legendre coefficients has been given previously by Hillert, 2 but neglect to mention that Van Tyne, Novotny, and Tarby 3 had derived a relationship for the conversion between simple power series and Legendre coefficients over ten years ago. The relationship which provides for the conversion of the coefficients is given by Van Tyne et al. 's Eq. [9], which is rewritten below using the nomenclature of Pelton and Bale for the Legendre coefficients (p) and the power series coefficients (q):