Equations of state for B2 and bcc Fe1-xSix

Composition, chemical disorder, and magnetism significantly affect the volume and bulk modulus of iron-silicon (Fe-Si) alloys at ambient pressure. Here we computed the equations of state for bcc-like (ordered B2 and disordered bcc) Fe-Si alloys up to the inner-core pressure using the first-principles Korringa-Kohn-Rostoker method. Ferromagnetic (FM) and nonmagnetic (NM) states were investigated over a wide compositional range from Fe to FeSi. The present static calculations revealed that magnetism and chemical disorder increased the volume and decreased the bulk modulus also at high pressures. In order to obtain their density and bulk sound velocity under high temperatures relevant to the inner core, we calculated the Helmholtz energy by using the quasi-harmonic approximation with the assumption that the Poisson's ratio of Fe-Si alloys is equivalent to that observed in the inner core. This assumption is valid when the inner core consists of bcc-like Fe-Si. Nevertheless, the obtained density and bulk sound velocity do not match seismological observations unless a temperature gradient inside the inner core is unrealistically large, indicating that the inner core is not a bcc-like Fe-Si alloy.