Thermophysical properties of helium and hydrogen mixtures under high pressure predicted by ab-initio calculations: Implications for Saturn and Jupiter planets

The thermodynamic and physical properties of Helium (He) and Hydrogen (H) mixtures are crucial form an astrophysical perspective. Nowadays, it is well known that these two elements constitute roughly 95% of the matter in the solar system. The high-pressure equation of He state doped with H is calculated in the framework of density functional theory (DFT) for three crystallographic structures. Namely, the Body Centered Cubic (BCC), Face Centered Cubic (FCC), and hexagonal close packed (HCP) structures have been studied. The equations of state (EOS) are provided for the He0.90H0.10 and He0.70H0.30 mixtures and the energy of the same mixtures are calculated with the earlier structures. The band structure for pressures of 0, 75 and 150 GPa were estimated by our calculations for the presumed crystal structures in the case of pure He and He0.70H0.30 mixture for comparison. The k(x) - k(y) cuts of the Bloch Spectral Functions (BSF) are presented for the pure He and He0.70H0.30 mixture for the three structures to explore the impact of doping on electronic properties. In addition, electrical resistivity calculations of the mentioned structures were carried out for mixtures with 10, 15, 20 and 30% of H. At final stage, the enthalpy (Delta H) of these latest mixtures have been deduced for the three crystal structures.