Sound velocity of liquid Fe–S alloy in diamond-anvil cell via inelastic X-ray scattering measurements

We have developed a new method and investigated sound velocity of liquid Fe-Ni-S alloys at high pressure up to 52 GPa in both externally-resistance-heated and laser-heated diamond-anvil cells using high-resolution inelastic X-ray scattering measurements (IXS) at SPring-8 with energy resolution of 2.8 meV at 17.79 keV. The X-ray beam was focused to 17 $\mu$$m^{2}$ area by a KB focusing mirror optics. At each $P$-$T$ condition, IXS spectra were collected at different momentum transfers ($Q$) using an array of twelve independent analyzers. The $Q$ range was 3.2 - 6.6 nm$^{-1}$ with resolution of 0.4 nm$^{-1}$ full width. Each spectrum was obtained in an energy range of -30 to 40 meV. Melting of the sample was determined by angle-dispersive X-ray diffraction spectra obtained before IXS measurements. We determined the elastic parameters of liquid Fe$_{47}$Ni$_{28}$S$_{25}$ to be $K_{SO}$ = 95.3 (27) GPa and $K_{SO}$’ = 3.98 (13), where $K_{SO}$ and $K_{SO}$’ are the adiabatic bulk modulus and its pressure derivative at zero pressure, when fixing the density at 5.58 g/cm$^{3}$ for 1 bar and 2000 K. Both sound velocity and density observed for the Earth's outer core can be explained by adding 5.8-7.0 wt. percent sulfur in the liquid iron.