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Title: Equation of State Measurements on Iron Near the Melting Curve at Planetary Core Conditions by Shock and Ramp Compressions

Journal Article · · Journal of Geophysical Research. Solid Earth
DOI:https://doi.org/10.1029/2020jb020008· OSTI ID:1772022

Abstract The outer core of the Earth is composed primarily of liquid iron, and the inner core boundary is governed by the intersection of the melt line and the geotherm. While there are many studies on the thermodynamic equation of state for solid iron, the equation of state of liquid iron is relatively unexplored. We use dynamic compression to diagnose the high‐pressure liquid equation of state of iron by utilizing the shock‐ramp capability at Sandia National Laboratories’ Z‐Machine. This technique enables measurements of material states off the Hugoniot by initially shocking samples and subsequently driving a further, shockless compression. Planetary studies benefit greatly from isentropic, off‐Hugoniot experiments since they can cover pressure‐temperature (P‐T) conditions that are close to adiabatic profiles found in planetary interiors. We used this method to drive iron to P‐T conditions similar to those of the Earth’s outer‐inner core boundary, along an elevated‐temperature isentrope in the liquid from 275 GPa to 400 GPa. We derive the equation of state using a hybrid backward integration – forward Lagrangian technique on particle velocity traces to determine the pressure‐density history of the sample. Our results are in excellent agreement with SESAME 92141, a previously published equation of state table. With our data and previous experimental data on liquid iron we provide new information on the iron melting line and derive new parameters for a Vinet‐based equation of state. The table and our parameterized equation of state are applied to provide an updated means of modeling the pressure, mass, and density of liquid iron cores in exoplanetary interiors.

Research Organization:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Organization:
USDOE National Nuclear Security Administration (NNSA); National Science Foundation (NSF)
Grant/Contract Number:
AC04-94AL85000; NA0003525
OSTI ID:
1772022
Alternate ID(s):
OSTI ID: 1786807
Report Number(s):
SAND-2021-2739J; 694630
Journal Information:
Journal of Geophysical Research. Solid Earth, Vol. 126, Issue 3; ISSN 2169-9313
Publisher:
American Geophysical UnionCopyright Statement
Country of Publication:
United States
Language:
English

References (70)

Thermal equation of state of hcp-iron: Constraint on the density deficit of Earth's solid inner core: THERMAL EQUATION OF STATE OF HCP-IRON journal July 2016
Shock-ramp compression of tin near the melt line
  • Seagle, Christopher T.; Porwitzky, Andrew J.
  • SHOCK COMPRESSION OF CONDENSED MATTER - 2017: Proceedings of the Conference of the American Physical Society Topical Group on Shock Compression of Condensed Matter, AIP Conference Proceedings https://doi.org/10.1063/1.5044783
conference January 2018
Melting curve of iron to 290 GPa determined in a resistance-heated diamond-anvil cell journal March 2019
Unified analyses for P - V - T equation of state of MgO: A solution for pressure-scale problems in high P - T experiments journal January 2009
Thermodynamics of melting relations in the system Fe-FeO at high pressure: Implications for oxygen in the Earth's core journal May 2014
Elasticity and constitution of the Earth's interior journal June 1952
Transiting exoplanets from the CoRoT space mission: VIII. CoRoT-7b: the first super-Earth with measured radius journal August 2009
Laser interferometer for measuring high velocities of any reflecting surface journal November 1972
Shock Compression and Melting of an Fe-Ni-Si Alloy: Implications for the Temperature Profile of the Earth's Core and the Heat Flux Across the Core-Mantle Boundary journal February 2018
The electronic thermodynamics of iron under Earth core conditions journal April 1986
Transiting Exoplanet Survey Satellite journal October 2014
Magnetically driven hyper-velocity launch capability at the Sandia Z accelerator journal June 2011
Experimental configuration for isentropic compression of solids using pulsed magnetic loading journal September 2001
Strength of lithium fluoride under shockless compression to 114 GPa journal November 2009
Ab initio lattice dynamics of MgSiO 3 perovskite at high pressure journal December 2000
Experimental measurement of the principal isentrope for aluminum 6061-T6 to 240GPa journal May 2006
Scaling the Earth: a Sensitivity Analysis of Terrestrial Exoplanetary Interior Models journal February 2016
Adiabatic temperature profile in the mantle journal November 2010
Measurement of the principal isentropes of lead and lead–antimony alloy to ∼400 kbar by quasi-isentropic compression journal February 2005
High pressure phase transformation in iron under fast compression journal December 2009
Equation of state of iron under core conditions of large rocky exoplanets journal April 2018
Planetary Radii across Five Orders of Magnitude in Mass and Stellar Insolation: Application to Transits journal April 2007
Iron under Earth’s core conditions: Liquid-state thermodynamics and high-pressure melting curve from ab initio calculations journal April 2002
Electrical conductivity and magnetic dynamos in magma oceans of Super-Earths journal September 2018
Seven temperate terrestrial planets around the nearby ultracool dwarf star TRAPPIST-1 journal February 2017
The Earth's core composition from high pressure density measurements of liquid iron alloys journal July 2013
Melting of iron at the physical conditions of the Earth's core journal January 2004
Properties of iron alloys under the Earth's core conditions journal May 2014
Solid Iron Compressed Up to 560 GPa journal August 2013
Ramp compression of iron to 273 GPa journal July 2013
The Mass-Radius Relation for Cold Spheres of Low Mass journal October 1969
Compressibility change in iron-rich melt and implications for core formation models journal June 2011
The role of high-pressure experiments on determining super-Earth properties journal May 2009
The Melting Curves and Entropy of Iron under High Pressure journal May 2011
The P-V-T equation of state and thermodynamic properties of liquid iron: The equation of state of liquid iron journal January 2014
Internal structure of massive terrestrial planets journal April 2006
Shock-ramp compression: Ramp compression of shock-melted tin journal June 2013
Phase transitions, Grüneisen parameter, and elasticity for shocked iron between 77 GPa and 400 GPa journal June 1986
Earth's Core and the Geodynamo journal June 2000
Solving Controversies on the Iron Phase Diagram Under High Pressure journal October 2018
Mechanical response of lithium fluoride under off-principal dynamic shock-ramp loading journal October 2016
A Study of the Accuracy of Mass-Radius Relationships for Silicate-Rich and Ice-Rich Planets up to 100 Earth Masses journal March 2009
Theorie des festen Zustandes einatomiger Elemente journal January 1912
A Framework for Quantifying the Degeneracies of Exoplanet Interior Compositions journal March 2010
Mass–Radius Relation for Rocky Planets Based on prem journal March 2016
KEPLER 'S FIRST ROCKY PLANET: KEPLER-10b journal February 2011
Universal features of the equation of state of solids journal March 1989
Mechanical and optical response of [100] lithium fluoride to multi-megabar dynamic pressures journal October 2016
Mass-Radius Relationships for Exoplanets journal December 2011
Mass–radius curve for extrasolar Earth-like planets and ocean planets journal November 2007
MASSES, RADII, AND ORBITS OF SMALL KEPLER PLANETS: THE TRANSITION FROM GASEOUS TO ROCKY PLANETS journal January 2014
Formation of the giant planets journal August 1982
Quantum molecular dynamics of warm dense iron and a five-phase equation of state journal May 2018
The Pressure and Temperature Limits of Likely Rocky Exoplanets journal July 2019
Quasihydrostatic Equation of State of Iron above 2 Mbar journal November 2006
Foundations of VISAR analysis. report June 2006
Experimental vibrational Grüneisen ratio values for ϵ-iron up to 330 GPa at 300 K journal January 2001
Mass‐Radius Relationships for Solid Exoplanets journal November 2007
Interior structure models of solid exoplanets using material laws in the infinite pressure limit journal August 2011
Direct measurement of thermal conductivity in solid iron at planetary core conditions journal June 2016
Shock Melting Curve of Iron: A Consensus on the Temperature at the Earth's Inner Core Boundary journal August 2020
Melting of Iron at Earth's Inner Core Boundary Based on Fast X-ray Diffraction journal April 2013
Experimental determination of the electrical resistivity of iron at Earth’s core conditions journal June 2016
Theoretical equation of state for aluminum journal January 1987
Determining the refractive index of shocked [100] lithium fluoride to the limit of transmissibility journal July 2014
Theoretical High-Pressure Equations of State including Correlation Energy journal June 1967
Generation of planetary magnetism by convection journal September 1976
First-principles thermal equation of state and thermoelasticity of hcp Fe at high pressures journal March 2010
Magnetically accelerated, ultrahigh velocity flyer plates for shock wave experiments journal October 2005
The extreme physical properties of the CoRoT-7b super-Earth journal May 2011