Phase separation of metallic hydrogen-helium alloys

Calculations are presented for the thermodynamic functions and phase-separation boundaries of solid metallic hydrogen-helium alloys at temperatures between 0 and ${19000}^{\mathrm{o}}$K and at pressures between 15 and 90 Mbar. Expressions for the band-structure energy of a randomly disordered alloy (including third order in the electron-ion interaction) are derived and evaluated. Short- and long-range order are included by the quasichemical method, and lattice dynamics in the virtual-crystal harmonic approximation. We conclude that at temperatures below ${4000}^{\mathrm{o}}$K there is essentially complete phase separation of hydrogen-helium alloys, and that a miscibility gap remains at the highest temperatures and pressures considered. The relevance of these results to models of the deep interior of Jupiter is briefly discussed.