Properties Evaluation of Fe95-xSi5Cx Under the Earth's Inner-Core Conditions: Insight from The Ab-Initio Investigation

Abstract

Under the Earth’s core conditions of pressure and temperature, the structural, electronic, and transport properties of Fe-Si-C ternary alloys based on Fe and 5% of Si with various concentrations 0%, 5%, 15%, 25%, and 40% of element C, through the calculations of First-principles, based on density functional theory (DFT) with Local Density Approximation (LDA) for adopting the exchange correlation potential. By using the Korringa-Kohn-Rostoker method along with coherent potential approximation (KKR-CPA) which includes in package Akai-KKR (machikaneyama), we performed the calculation of electronic property (density of states, band structure, and Fermi Surface) at 360 GPa. Afterward, by using the Kubo-Greenwood formula based on the relativistic polarized spin with the vertex correction using SPR-KKR code, we calculate the electrical resistivity of impurities. Then, by using the Wiedemann-Franz law and depending on the conditions of the Earth's inner core ICB, which are the range of 320-360 GPa of pressure and 4500-6000k of temperature, we model thermal conductivity by electrical resistivity for these two variables. Hence, our results suggest that 43–120 μΩ•cm and 120-280 μΩ•cm respectively at 0 K and 320-360 GPa then at 4500-6000 K and 360 GPa for electrical resistivity. And thermal conductivity of Earth’s inner core varies between 48-112 W•m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−1</sup> •K <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−1</sup> at 4500-6000 K and 360 GPa, supporting a present-day geodynamo driven by thermal and compositional convection.