Bridging the Theoretical–Experimental Gap: A Study on Pressure-Corrected Fe-Si Alloys Under the Earth’s Outer Core

Determining the concentration of light elements in the Earth’s outer core is crucial for understanding the generation of the geomagnetic field, as well as the Earth’s internal dynamics and thermal evolution. However, as a potential dominant light element in the outer core, the precise composition of silicon (Si) is still a topic of intense debate. Due to the limited experimental data, significant controversies exist between theoretical models and experimental predictions regarding the Si content in the outer core. In this work, we have calculated pressure (P)–volume (V)–temperature (T) data of Fe-X wt.% Si, where X = 0, 2.4, 4.9, 7.5, and 10.3 at ~136–330 GPa and 4000–7000 K by first-principles molecular dynamics (FP-MD) simulations. We employed pressure correction to address the discrepancy between theoretical and experimental measurements. Based on the corrected data, we established an equation of state (EoS) for Fe-Si alloys. We calculated thermodynamic properties, including density (ρ), thermal expansivity, Grüneisen parameter, isothermal and adiabatic bulk moduli, and sound velocity (VP). To constrain the silicon content in the outer core, the ρ and VP of Fe-X wt.% Si computed along the outer core geotherm were compared with the Preliminary Reference Earth Model (PREM). Assuming Si is the only light element in the outer core and is constrained by PREM data, the maximum Si content at TICB = 5400 K is 2.4 ± 1.7 wt.%. Considering the uncertainty in TICB, the maximum Si content in the outer core ranges from 1.8 to 3.0 ± 1.7 wt.%. The fact that a homogeneous binary alloy cannot match all seismic observations provides evidence that the content of Si in the outer core may vary with depth. Besides, the work states that pressure correction helps bridge the gap between theoretical and experimental estimates of Si concentration. The pressure-corrected equation of state provides a robust benchmark for constraining multi-component core models.