Melting of Iron under Earth’s Core Conditions from Diffusion Monte Carlo Free Energy Calculations

The temperature of Earth’s core is a parameter of critical importance to model the thermal structure of Earth. Since the core is mainly made of iron, with a solid liquid boundary (the inner core boundary) at 1220 km from the center of the Earth, the melting temperature of iron at the pressure of the ICB provides constraints on the temperature of the core. These constraints are based either on extrapolations to ICB pressure of experimental measurements, or on theoretical calculations which employed various flavors of quantum mechanics, most notably density functional theory. Significant disagreement between estimates obtained with different methods calls for calculations based on more accurate techniques. Here we used quantum Monte Carlo techniques to compute the free energies of solid and liquid iron at ICB conditions. We obtained an iron melting temperature at 330 GPa of $6900\pm 400\mathrm{K}$.

Figure 1

Top panel: DMC energies corresponding to configurations representative of solid (blue triangles) and liquid (red dots) iron, generated with DFT molecular dynamics on 64-atom systems. Red solid line and blue dashed line connect DFT energies calculated on the same set of configurations. An offset is added to the energies so that the average value of the DMC and DFT energies is the same, separately in the solid and the liquid. Bottom panel: DMC—DFT energy differences on the same configurations. The average DMC-DFT energy difference for the solid is subtracted from all points. Lines represent the average of the energy differences between DMC and DFT in the solid (line at zero energy) and the liquid.

Figure 2

Same as Fig. 1 but for 96-atom systems.

Figure 3

Comparison of melting temperatures (T) of Fe as function of pressure (P) from present calculations with experiments and other ab initio results. Black filled circle: present DMC results; blue filled square: melting point from DFT coexistence [14]; solid black line: melting curve from DFT free energies [11]; dashed blue curve: theoretical results from Ref. 13; light purple solid curve: theoretical results from Ref. 12; black chained and maroon dotted curves: DAC measurements of Refs. 2, 3; green open diamonds: DAC measurements of Ref. 4; green plus: DAC measurement of Ref. 6; green filled triangle: DAC measurement of Ref. 5; black stars, black open circle and pink filled diamond: shock experiments of Refs. 7, 8, 9. Error bars are those quoted in original references.