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

Understanding the thermal-chemical state of the Earth's core requires knowledge of the thermal expansion of iron-rich alloys at megabar pressures and high temperatures. Our survey of literature revealed a significant lack of such data. We have determined the unit-cell parameters of the iron-sulfur compound Fe(3)S by using synchrotron x-ray diffraction techniques and externally heated diamond-anvil cells at pressures up to 42.5 GPa and temperatures up to 900 K. The zero-pressure thermal expansivity of Fe(3)S is determined in the form alpha = a(1) + a(2)T, where a(1) = 3.0 +/- 1.3 x 10(-5) K(-1) and a(2) = 2.8 +/- 1.5 x 10(-8) K(-2). The temperature dependence of isothermal bulk modulus ((partial differential)K(T,0)/(partial differential)T)(P) is estimated at -3.75 +/- 1.80 x 10(-2) GPa K(-1). Our data at 42.5 GPa and 900 K suggest that approximately 2.1 at. % (1.2 wt. %) sulfur produces 1% density deficit in iron. We have also carried out energy-dispersive x-ray diffraction measurements on pure iron and Fe(0.864)Si(0.136) alloy samples that were placed symmetrically in the same multi-anvil cell assemblies, using the SPring-8 synchrotron facility in Japan. Based on direct comparison of unit cell volumes under presumably identical pressures and temperatures, our data suggest that at most 3.2 at. % (1.6 wt. %) silicon is needed to produce 1% density deficit with respect to pure iron.