Equations of state and phase diagrams for dense multi-ionic mixture plasmas

Equations of state for dense binary-ionic mixture (BIM) plasmas with charge ratios ${\mathit{R}}_{\mathit{Z}}$≤4.5 are evaluated for both fluid and solid phases on the basis of internal energies calculated by the Monte Carlo (MC) simulation method. The accuracy of the results has been confirmed through a sum-rule analysis of the free energy with respect to screening potentials at zero separation in one-component plasmas. Phase diagrams for various BIM’s appropriate to white-dwarf interiors are constructed, including the effects of compressibility of the relativistically degenerate electrons. Eutectic diagrams, which result in significant chemical separation upon solidification, are predicted for BIM’s with ${\mathit{R}}_{\mathit{Z}}$≳1.6. Free energies for dense ternary-ionic mixtures are also derived for both fluid and solid phases through comparison of the corresponding MC internal energies and by a sum-rule analysis using BIM screening potentials at zero separation. We apply the results to the process of solidification of ${}_{}{}^{12}{}_{}{}^{}\mathrm{-}_{}^{16}{}_{}{}^{}$O${\mathrm{-}}^{22}$Ne mixtures in the interiors of white dwarfs. We find that chemical separation does indeed occur at solidification, and we obtain the result that nearly pure Ne cores are formed in such white dwarfs, even though Ne is only a trace element in the mixture.