High-temperature ab initio calculations on FeSi and NiSi at conditions relevant to small planetary cores

Thermoelastic Properties of B2‐Type FeSi Under Deep Earth Conditions: Implications for the Compositions of the Ultralow‐Velocity Zones and the Inner Core

“…A trial fitting showed that n was statistically insignificant and therefore a density independent thermal pressure term P th = m(T T ref ) was used for the final fitting. The optimized parameters for ρ 0 , K T0 , K ′ T0 , and m were 5.67 ± 0.01 g/cm 3 , 132.30 ± 2.01 GPa, 4.53 ± 0.02, and (8.40 ± 0.03) × 10 3 , respectively, at 4,000 K, and 6.64 ± 0.01 g/cm 3 , 248.87 ± 1.45 GPa, 4.27 ± 0.01, and (8.40 ± 0.02) × 10 3 , respectively, at 300 K. Our fitting results are compared with those from previous works (Dobson et al, 2002;Ono et al, 2007;Qi et al, 2019;Sata et al, 2010;Wann et al, 2017) in Table S2 in Supporting Information S1 and Figure 1. Our EOS agrees well with recent experimental results from Yokoo et al (2023) at relatively low pressures (∼100 GPa) and 3,000 K. Static DFT calculations from Caracas and Wentzcovitch (2004) and Nagaya et al (2023) did not consider the effect of thermal pressure, thus yielding lower predicted pressure at a given density compared to this study.…”

“…For example, the EOS and elasticity of B2-FeSi have been determined by first-principles simulations up to 160 GPa but at 0 K (Caracas & Wentzcovitch, 2004). Wann et al (2017) and Nagaya et al (2023) investigated the effect of temperature on the EOS of B2-FeSi up to 400 GPa using ab initio lattice dynamics and quasi-harmonic approximation, respectively. However, these methods do not consider the anharmonic effect.…”

Thermofield Theory for Finite-Temperature Electronic Structure

“…On the other hand, for quantum systems with optical gaps comparable to, or smaller than, the thermal energy, the ground sate is no longer a sufficient description. Accounting for thermal effects becomes essential for an accurate understanding of the electronic structure under these conditions, which often arise in novel applications based on strongly correlated materials (e.g., high-Tc superconductors and transition metal complexes at room temperature). , Other examples include, but are not limited to, chemical reactions driven by hot-electrons and those in extreme geological environments. , …”

“…[1,2] Other examples include, but are not limited to, chemical reactions driven by hot-electrons [3] and those or in extreme geological environments. [4,5] Finite-temperature properties are defined as an average of all expected outcomes of an observable, weighted over an appropriate ensemble. For example, in the grandcanonical ensemble, the expectation value of an observable A at inverse temperature β = 1/k B T and chemical potential µ is defined as…”

“…For instance, Hartree−Fock (HF) theory is a mean-field method that generally provides a good qualitative result at n ( ) 3 computational scaling (n being a measure of the system size). Configuration interaction (CI) with singles and doubles (CISD) and second-order Møller−Plesset perturbation theory (MP2) improve upon HF but require increased computational effort ( n ( ) 6 for CISD and n ( ) 5 for MP2). Coupled cluster (CC) theory, 9,10 truncated at singles and doubles as well (CCSD), generally outperforms HF, CISD, and MP2 and scales as n ( ) 6 .…”