The P‐V‐T equation of state and thermodynamic properties of liquid iron

Abstract

The equation of state (EoS) and thermodynamic properties of non-magnetic liquid iron were investigated from energy (E)-pressure (P)-volume (V)-temperature (T) relationships calculated by means of ab initio molecular dynamics simulations at 60-420 GPa and 4000-7000 K. Its internally consistent thermodynamic and elastic properties, in particular, density, adiabatic bulk modulus, and P wave velocity, were then analyzed. Compared to the seismological data of the Earth's outer core, pure liquid iron is found to have an 8-10% larger density and 3-10% larger bulk modulus than the Earth's values. Results also show that the P wave velocity of liquid iron has marginal temperature dependence as the bulk sound velocity of solid iron. The new EoS model and thermodynamic properties of liquid iron may serve as fundamental data for the thermochemical modeling of the Earth's core.

Constraints from material properties on the dynamics and evolution of Earth’s core

“…Ab initio calculations have found the specific heat C p = 700 − 800 J kg −1 K −1 independent of radius 54 , in agreement with theory 55 and hence α T is a decreasing function of depth 55,56 because of the factor ρ/K s . The compositional expansion coefficient α c is different for each element; values obtained at present ICB (P, T ) conditions 49 are given in Table 1.…”

“…The bulk modulus, K s , and gravity, g, are calculated directly in ab initio methods and are very similar to PREM. Ab initio calculations have found that γ ≈ 1.5 at the CMB and remains constant 17 (to within the accuracy of the calculations) or decreases slightly 53,54 with depth. The depth variation reduces ∂T a /∂r and increases τ = dT m /dP −∂T a /∂P , but makes little difference to T a .…”

“…Individually changing α c or L by ±10%, C p to the values of a previous study 55 , core density from PREM to AK135 71 , or the melting curve to a recent experimental profile 20 (denoted T A m ) each make little difference. Using a depth-variable γ (denoted γ I ) 54 makes a small change to the inner core age but barely changes T 3.5Ga . The biggest changes arise from varying k and allowing for the ±300 K uncertainty in T i .…”

“…T A m is a recent experimentally-determined melting curve 20 . Model γ I uses depth-dependent γ taken from a recent study 54 . Crosses show the youngest and oldest inner core ages that can be achieved by combining the other variations.…”

Small shear modulus of cubic CaSiO3 perovskite

“…FPMD was performed using a PWSCF code [Giannozzi et al, 2009] for electronic structure with an original implementation of the constant-temperature molecular dynamics (MD) solver [Usui and Tsuchiya, 2010;Kawai and Tsuchiya, 2014;Ichikawa et al, 2014]. Our FPMD simulations were within the canonical (NVT) ensemble, in which the number of atoms in the periodically repeating computational cell (N) and the cell volume (V) were fixed.…”