Abstract
Earth's inner core consists of iron (Fe) alloyed with minor light elements, predominantly silicon (Si), yet the crystal structure and seismic velocities of Fe-Si alloys at inner-core conditions remain poorly constrained. Ab-initio methods struggle with the alloy's vast configurational complexity, limiting reliable property predictions. To overcome this, here we integrate a hybrid Monte Carlo sampling algorithm with a deep-learning interatomic potential to compute the Fe-Si binary phase diagram and sound velocities at inner-core boundary pressures. A complex phase diagram emerges, featuring the re-entrance of a body-centered cubic (bcc) phase stabilized by pronounced short-range ordering of the Si atoms. The bcc phase reproduces key seismic features of the inner core, including low shear-wave velocities and seismic anisotropy, more faithfully than other competing close-packed structures, making it a leading candidate for the inner-core structure. Our results underscore the importance of accurately describing light-element effects on Earth's core properties.