High P-T experiments and first principles calculations of the diffusion of Si and Cr in liquid iron

Chemical diffusion rates of Si and Cr in liquid iron have been measured over the P-T range of 1-18 GPa and 1873-2428 K. The experiments were performed using a multi-anvil apparatus with diffusion couples comprised of pure iron and iron alloy placed end to end in a vertical orientation. In order to extend our dataset to the Earth's core-mantle boundary and to compare experimental data with theoretical diffusion rates calculated under laboratory-accessible conditions, we have also performed first principles molecular dynamic simulations (FP-MD) and calculated self-diffusion coefficients and activation parameters for Si, Cr, and Fe diffusion in liquid Fe, Fe0.92Si0.08 and Fe0.92Cr0.08 compositions over the P-T range of 1 bar-135 GPa and 2200-5500 K. Over the entire range of pressures and temperatures studied using both methods, diffusion coefficients are described well using an exponential function of the homologous temperature relation, D = Dhexp(−gTh), where Th = Tm/T, Tm is the melting temperature at the pressure of interest and g and Dh are constants. Our findings indicate constant diffusivities of approximately 4 × 10−9 m2 s−1 for Si and Cr and 5 × 10−9 m2 s−1 for Fe along the melting curve from ambient to core pressures in all liquid compositions studied, with an increase of ∼0.8 log units at T = 2Tm. Differences between experimental data and computational results are less than 0.1 log units. Structural properties of liquid iron alloys analyzed using partial radial distribution functions (RDFs) show the average distance between two Fe atoms, rFe-Fe, is identical to that of rFe-Si and rFe-Cr over the entire P-T range of study, which supports that the diffusion of Si and Cr (and thus likely other species of similar atomic radii) occurs via direct substitution with Fe. Diffusion coefficients and interatomic distances used to calculate liquid viscosities via the Stokes-Einstein relation yield constant viscosity along the melting curve of ∼6 mPa s for liquid Fe, ∼7 mPa s for liquid Fe0.92Cr0.08, and ∼8 mPa s for liquid Fe0.92Si0.08, with a decrease of ∼0.8 log units at T = 2Tm. The data can also be reproduced within <10% using the Arrhenian model with derivatives of the activation parameters determined over a very wide range of P-T conditions. Verification of a homologous temperature dependence of diffusion in liquid metals, as well as the excellent agreement between experimental results and FP-MD simulations, provides a new and simple framework for interpreting and modeling mass transport processes of liquid iron alloys in all planetary bodies regardless of size. Our results are used to evaluate the kinetics of metal-silicate chemical equilibration during core formation and diffusivity contrasts across a solid-liquid metal interface, i.e. at the inner core boundary.