A High-Precision Reanalysis of the Thermal Equation of State of hcp-Iron

Abstract:

To address questions on the composition of the Earth’s core and to determine the structure and composition of the cores of recently discovered super-Earth exoplanets, there is a need to extrapolate measured equations of state (EsOS) of relevant materials, such as iron, well beyond the scope of experiments. As such, precise constraints on the density deficit of the Earth’s core are difficult to obtain due to the uncertainties in experimental measurements at high pressures and temperatures. Over the past 50 years, the development of the laser-heated diamond anvil cell (LHDAC) and in situ synchrotron technology have expanded the accessible pressures and temperatures. We present the results of high-precision experiments on hcp-iron using microfabricated samples designed to reduce uncertainties attributed to large temperature gradients and inconsistent sample geometries. We implement a new, azimuthally dependent method to improve the two-theta resolution of X-ray diffraction peaks by measuring the positions, widths, and intensities of each of the diffracting crystallites contributing to the X-ray diffraction pattern. This yields a more accurate determination of volume, and generates a more detailed statistical description of the precision in each of the lattice positions. We present a thermal equation of state of hcp-iron from these data between 20-80 GPa and 1200-2400 K, as well as a reanalysis of 9 published P-V-T data sets for hcp-iron up to 280 GPa and 3000 K using a Monte Carlo fitting routine which fully propagates uncertainties in volume and temperature measurements and pressure calculations to determine the covariance between each equation of state parameter. We obtained values of K₀ = 168(6) GPa, K’ = 4.89(14), and V₀ = 22.41(6) ų with a covariance between K₀ and K’ of -0.92. We use the same Monte Carlo approach to extrapolate uncertainties in the EOS and model uncertainty in the density of iron to place quantitative bounds on the density deficit of the Earth’s core. This work shows that diligent attention to statistics at every step, from data collection to extrapolation, is essential to tightly constrain the properties of iron at these conditions and appropriately address questions surrounding planetary cores in our solar system and beyond.