Estimation of the thermodynamic characteristics of the earth’s core using the embedded atom model

Abstract

Since there are only limited experimental data for the multicomponent composition of the Earth’s core, which may contain nickel, silicon, sulfur, oxygen, hydrogen, carbon, and other admixture elements, we applied the molecular dynamics method as an additional tool. This approach is currently limited to the analysis of one- and two-component systems. In order to estimate the validity of this method for modeling under the Earth’s core conditions, a hypothetical variant of core composition corresponding to the iron-sulfur binary system was considered, because there are sufficient experimental data for this system under low-pressure conditions. The proposed embedded atom potential allows adequate description of the thermodynamic properties of solid and liquid iron-sulfur solutions under the conditions of the Earth’s center, inner-outer core boundary, and core-mantle boundary. The calculations relied on the Preliminary Reference Earth Model (PREM) data for pressure and density of phases at the inner-outer core boundary. Molecular dynamics calculations showed that the hypothetical variant of iron-sulfur binary solutions can provide reasonable consistency with the PREM values of pressure, density, and sound velocity for all the above levels. For this variant, temperatures at the same levels and sulfur contents were determined. The sulfur content was constrained at 5 at % in the inner core and 11–12 at % in the outer core, and it is almost independent of coordinates in each part of the core. The uncertainty of the calculation of sulfur content is ±0.5%. For the accepted two-component variant, the calculated temperature is approximately 6700 K in the Earth’s center and 6325 K at the inner-outer core boundary; the temperature estimate for the core-mantle boundary is more uncertain and ranges from 3300 to 4325 K (the latter value is more probable). The deviation of the calculated sound velocity from the PREM data is 5–10%, and the calculated velocity is overestimated at the core-mantle boundary and underestimated at other levels. If sufficient experimental data are available, a similar computation method can be applied to other two-component models of the composition of the Earth’s core (for instance, iron-nickel, iron-silicon, iron-oxygen, etc.), whereas three- and multicomponent systems cannot currently be calculated using the molecular dynamics method. The calculations reported in this paper showed that the molecular dynamics method in combination with geophysical data allows us to analyze different hypothetical variants of the composition of the Earth’s core, provides additional information on the properties of the core material, and helps to reveal the variants of core composition that are inconsistent with the available natural data.