Perturbation Theory of the Miscibility Gap in Metal Salt Solutions

  • G. Chabrier
Part of the NATO ASI Series book series (volume 154)

Abstract

The metal-salt solutions are regarded as being composed of N1 positive ions of charge Z1e and N2 negative ions of charge Z2e in a volume Ω; the corresponding number densities and concentrations are defined as p α = Nα/Ω and xα=Nα/N (α=1,2), with N=N1+N2. The excess of positive charge is compensated by the conduction electrons which are assumed to provide a rigid, uniform background of charge density ep o, ensuring overall charge neutrality:
$$ {\rho _1}{z_1} + {\rho _2}{z_2} + {\rho _{\rm{o}}} = 0 $$
(1)
This reference system will serve as a starting point for our perturbation expansion. In that case the ions are assumed to interact via the following potential:
$$ {{\rm{U}}_{\alpha \beta }}({\rm{r}}) = {{{{\rm{z}}_\alpha }{{\rm{z}}_\beta }{{\rm{e}}^2}} \over {\rm{r}}} + (1 - {\delta _{\alpha \beta }}){{\rm{V}}_{\rm{o}}}({\rm{r}}) $$
(2a)
where the short range repulsion, which acts only between oppositely charged ions, is taken to be of exponential form:
$$ {{\rm{V}}_{\rm{o}}}({\rm{r}}) = {{\rm{A}}_{{\rm{12}}}}\exp ( - {\alpha _{12}}{\rm{r}}) $$
(2b)
The potential (2) is a simplified version of the usual Born-Huggins-Mayer potential, retaining only its essential features. We have dropped the Van der Waals dispersion terms, as well as the short range repulsion between equally charged ions, since the Coulomb repulsion is sufficiently strong to keep them apart. The limiting situations of the potential (2) are: i) x-1, i.e. the pure metal, for which we recover the one component plasma (O.C.P.) model3,4; ii) x=0, i.e. the pure salt, reasonably well described by a Born-Huggins-Mayer rigid ion potential, provided ion polarizability effects are not too important.5 The pair correlation functions are calculated through the closed set of equations composed of the Qrnstein-Zernicke relation and the hypernetted-chain (H.N.C.) equations.2

Keywords

Enthalpy Compressibility 

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Copyright information

© Plenum Press, New York 1987

Authors and Affiliations

  • G. Chabrier
    • 1
  1. 1.Dpt. Physique des MateriauxUniversite Claude Bernard Lyon IVilleurbanne CedexFrance

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