Thermal expansion of iron-rich alloys and implications for the Earth's core

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   Fig. 1.

   Isothermal compression data of Fe₃S at 300, 600, and 900 K. (a) Open circles represent compression data at room temperature (300 K) from Fei et al. (22). Filled squares, triangles, and diamonds represent the compression data at 300, 600, and 900 K, respectively. The three lines are the third-order Birch–Murnaghan EOS fits to the compression data. The error bars are estimated from multiple x-ray measurements at the same condition. Where duplicate measurements were not made, uncertainties estimated from multiple diffraction lines in a single measurement are slightly smaller than the symbols. A typical error bar is shown in the lower left corner. (b) f − F plot of the compression data at 300 K. The data can be fitted by an inclined straight line, suggesting that the compression of Fe₃S can be adequately described by a third-order Birch–Murnaghan EOS. The error bars are based on multiple diffraction lines in a single measurement.

   
   
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   Fig. 2.

   Density deficits in Fe–Si alloys and Si content in the Earth's core. (a) Minimum density deficit between hcp–Fe_0.864Si_0.136 and hcp–Fe under different experimental conditions. Density deficit is defined as (1 − ρ_Fe-Si/ρ_Fe) × 100%, where ρ represents the density. These data are listed in SI Table 4. Numbers next to symbols denote temperatures in Kelvin. (b) Density deficit versus maximum Si content in Fe–Si alloy with hcp structure. Gray regions labeled “OC” and “IC” indicate density deficit of the outer and inner core compared with pure Fe, respectively (ref. 16 and references therein). The filled circle represents the minimum density deficit produced by 13.6 at. % Si, based on data in a. The solid line represents a linear relationship between density deficit and Si content; dotted and dashed lines enclose the ranges of maximum Si content in the IC and OC, respectively.

   
   
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   Fig. 3.

   Density deficit in Fe₃S and S content in the Earth's core (a) Density deficit between Fe₃S and Fe, (1 − ρ_Fe3S/ρ_Fe) × 100% versus pressure. (b) Density deficit versus S content in an Fe–S alloy. The open circle denotes the density deficits of Fe₃S with respect to Fe at 1 bar and 300 K. The filled circle denotes the deficits at 42.5 GPa and 900 K. Gray regions labeled “OC” and “IC” indicate density deficits of the outer and inner core with respect to pure Fe, respectively (ref. 16 and references therein). The solid lines represent linear relationships between density deficit and S content; dotted and dashed lines enclose the ranges of S contents in the IC and OC, respectively.

   
   
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   Fig. 4.

   Lattice parameters of Fe₃S versus pressure at 300 and 600 K. (a) Lattice parameter c versus pressure at 300 K. (b) Lattice parameter a versus pressure at 300 K. (c) c/a ratio versus pressure at 300 and 600 K. For clarity, the c and a data at 600 K are not shown. The solid arrow indicates the valley in the 300 K data. The dotted arrow indicates the valley in the 600 K data. The error bars are estimated from multiple x-ray measurements.