Statistical mechanics of dense ionized matter. VII. Equation of state and phase separation of ionic mixtures in a uniform background

By solving the hypernetted chain (HNC) equation for the pair distribution functions, and by Monte Carlo simulations, we have calculated the equation of state and the pair structure of dense binary mixtures of classical point ions in a rigid, uniform background of opposite charge. All of our results indicate that the excess internal and free energies of mixing are negligible compared to the energies of the mixture or the pure phases, for ionic-charge ratios $\frac{{Z}_{2}}{{Z}_{1}}=2 \mathrm{and} 3$, in the strong coupling (high density or low temperature) regime. This feature allows us to write down a simple equation of state for such mixtures, which is used to determine the phase diagram of pressure-ionized H-He and H-Li mixtures in a rigid background of degenerate electrons. We then treat the polarization of the electron gas by the ionic-charge distribution by perturbation theory and include quantum corrections to the free energy of the ions. Both effects do not drastically modify the phase diagrams. The applicability of our results in astrophysical situations is discussed.