Volume–temperature relationship for iron at 330 GPa and the Earth's core density deficit

Abstract

Estimates of core density deficit (cdd) of the Earth's outer core recently reported by Anderson and Isaak [Another look at the core density deficit of Earth's outer core, Phys. Earth Planet Int. 131 (2002) 19–27] are questionable in view of the serious errors in the pressure–volume and bulk modulus data due to an inadequacy in the calibration process used by Mao et al. [Static compression of iron to 300GPa and Fe0.8Ni0.2 alloy to 200GPa: implications for the core, J. Geophys. Res. 94 (1990) 21737–21742]. The data used by Anderson and Isaak deviate significantly from the corresponding values derived from seismology. In the present study we have used the input data on density, isothermal bulk modulus and its pressure derivative from Stacey and Davis [High pressure equations of state with application to lower mantle and core, Phys. Earth Planet Int. 142 (2004) 137–184] which are consistent with the seismological data. Volumes of hexagonal close-packed iron have been calculated at different temperatures under isobaric conditions at P = 330GPa, the inner core boundary (ICB) pressure using the relationship between thermal pressure and volume expansion based on the lattice potential theory originally due to Born and Huang [Dynamical Theory of Crystal Lattices, Oxford University Press, Oxford, 1954, p. 50]. The formulation for thermal pressure used by Anderson and Isaak has been modified by taking into account the variations of thermal expansivity α and isothermal bulk modulus KT with temperature. Values of cdd are then estimated corresponding to different temperatures ranging from 4000 to 8000K. The results for cdd at different temperatures obtained in the present study are significantly higher than those estimated by Anderson and Isaak suggesting that the cdd for the Earth's outer core is nearly 10%. The effects of nickel when an Fe–Ni alloy replaces Fe are estimated and found to be insignificant.