A Global Reanalysis of the Thermal Equation of State of hcp-Fe
Abstract
Quantifiable constraints on the composition and evolution of cores of the Earth and exoplanets require reliable equations of state (EsOS) at pressure (P) and temperature (T) conditions beyond the reach of most static compression experiments (>400 GPa and > 4000 K). High-precision EsOS of relevant core materials, such as hcp-Fe, rely on high-precision observations of volume (V), pressure, and temperature. Because extrapolation of these EsOS to the conditions of planetary cores is inevitable, measurements with realistic uncertainties and elimination of systematic errors are critical to constrain uncertainty in the EOS. We present an azimuthally dependent method to improve the two-theta resolution of X-Ray Diffraction (XRD) peaks in laser-heated diamond anvil cell (LHDAC) experiments by measuring the positions of each of the diffracting crystallites contributing to the XRD pattern, which yields a more precise determination of peak position than more traditional methods including fitting a Gaussian to an integrated, 1D XRD profile (0.005 A uncertainty compared to 0.01 A). This method produces a more robust statistical description of the precision in each of the lattice positions, allowing for a qualitative and quantitative determination of potential strain in a lattice or potential issues in the system calibration by looking at systematic differences in the peak position by azimuth. We also present a two-color pyrometry analysis of high temperature (1200 - 2500 K) spectroradiometric measurements to constrain systematic error in temperature resulting from wavelength-dependent emissivity. In parallel with high-precision measurements of iron, we re-evaluate the pressure uncertainties from internal pressure standards of 9 previously published data sets using a Monte Carlo analysis that fully propagates uncertainty in both the standard EOS and volume and temperature measurements. Using the same Monte Carlo analysis, we fit an EOS to the P-V-T data, fully propagating uncertainty in each measurement, and determine the full covariance matrix. We propagate this EOS and associated uncertainties to the conditions of Earths core, yielding a density of hcp-Fe of 13.30(9) g/cm3 at 363.9 GPa and 5000 K, providing quantitative bounds on the density deficit of the Earths core of 1.6(12)%.
- Publication:
-
AGU Fall Meeting Abstracts
- Pub Date:
- December 2021
- Bibcode:
- 2021AGUFMDI33A..04M