Reconciliation of Experiments and Theory on Transport Properties of Iron and the Geodynamo

Zhang, Youjun; Hou, Mingqiang; Liu, Guangtao; Zhang, Chengwei; Prakapenka, Vitali B; Greenberg, Eran; Fei, Yingwei; Cohen, R.  E.; Lin, Jung-Fu

doi:10.1103/physrevlett.125.078501

Title: Reconciliation of Experiments and Theory on Transport Properties of Iron and the Geodynamo

Abstract

We measure the electrical resistivity of hcp iron up to ~170 GPa and ~3000 K using a four-probe van der Pauw method coupled with homogeneous flattop laser heating in a DAC, and compute its electrical and thermal conductivity by first-principles molecular dynamics including electron-phonon and electron-electron scattering. We find that the measured resistivity of hcp iron increases almost linearly with temperature, and is consistent with our computations. Overall, the results constrain the resistivity and thermal conductivity of hcp iron to ~80±5 μΩ cm and ~100±10 W m^-1 K^-1, respectively, at conditions near the core-mantle boundary. Our results indicate an adiabatic heat flow of ~10±1 TW out of the core, supporting a present-day geodynamo driven by thermal and compositional convection.

Authors:

^[1];

^[2]; Liu, Guangtao ^[3]; Zhang, Chengwei ^[3];

^[4];

^[5];

^[5]

Sichuan Univ., Chengdu (China). Inst. of Atomic & Molecular Physics; Center for High Pressure Science and Technology Advanced Research (HPSTAR), Shanghai (China)
Center for High Pressure Science and Technology Advanced Research (HPSTAR), Shanghai (China); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Advanced Light Source (ALS)
Center for High Pressure Science and Technology Advanced Research (HPSTAR), Shanghai (China)
Univ. of Chicago, IL (United States). Center for Advanced Radiation Sources (CARS)
Carnegie Inst. of Science, Washington, DC (United States). Earth and Planets Lab., Extreme Materials Initiative

Publication Date:: Thu Aug 13 00:00:00 EDT 2020

Research Org.:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Basic Energy Sciences (BES); National Science Foundation (NSF); National Natural Science Foundation of China (NSFC)

OSTI Identifier:: 1782157

Grant/Contract Number:: AC02-05CH11231; 41804082; EAR-1901813; EAR-1901801; EAR-1634415; FG02-94ER1446

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review Letters

Additional Journal Information:: Journal Volume: 125; Journal Issue: 7; Journal ID: ISSN 0031-9007

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 58 GEOSCIENCES; Earth's interior; electrical conductivity; electron thermal conductivity; geomagnetism; transition metals; Boltzmann theory; DFT+DMFT; pressure techniques; resistivity measurements; x-ray diffraction

Citation Formats


                    Zhang, Youjun, Hou, Mingqiang, Liu, Guangtao, Zhang, Chengwei, Prakapenka, Vitali B, Greenberg, Eran, Fei, Yingwei, Cohen, R.  E., and Lin, Jung-Fu. Reconciliation of Experiments and Theory on Transport Properties of Iron and the Geodynamo.  United States: N. p., 2020. 
Web.  doi:10.1103/physrevlett.125.078501.

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                    Zhang, Youjun, Hou, Mingqiang, Liu, Guangtao, Zhang, Chengwei, Prakapenka, Vitali B, Greenberg, Eran, Fei, Yingwei, Cohen, R.  E., & Lin, Jung-Fu. Reconciliation of Experiments and Theory on Transport Properties of Iron and the Geodynamo.  United States.  https://doi.org/10.1103/physrevlett.125.078501

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                    Zhang, Youjun, Hou, Mingqiang, Liu, Guangtao, Zhang, Chengwei, Prakapenka, Vitali B, Greenberg, Eran, Fei, Yingwei, Cohen, R.  E., and Lin, Jung-Fu. Thu .  
"Reconciliation of Experiments and Theory on Transport Properties of Iron and the Geodynamo".  United States.  https://doi.org/10.1103/physrevlett.125.078501.  https://www.osti.gov/servlets/purl/1782157.

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@article{osti_1782157,

  title        = {Reconciliation of Experiments and Theory on Transport Properties of Iron and the Geodynamo},

  author       = {Zhang, Youjun and Hou, Mingqiang and Liu, Guangtao and Zhang, Chengwei and Prakapenka, Vitali B and Greenberg, Eran and Fei, Yingwei and Cohen, R.  E. and Lin, Jung-Fu},

  abstractNote = {We measure the electrical resistivity of hcp iron up to ~170 GPa and ~3000 K using a four-probe van der Pauw method coupled with homogeneous flattop laser heating in a DAC, and compute its electrical and thermal conductivity by first-principles molecular dynamics including electron-phonon and electron-electron scattering. We find that the measured resistivity of hcp iron increases almost linearly with temperature, and is consistent with our computations. Overall, the results constrain the resistivity and thermal conductivity of hcp iron to ~80±5 μΩ cm and ~100±10 W m-1 K-1, respectively, at conditions near the core-mantle boundary. Our results indicate an adiabatic heat flow of ~10±1 TW out of the core, supporting a present-day geodynamo driven by thermal and compositional convection.},

  doi          = {10.1103/physrevlett.125.078501},

  journal      = {Physical Review Letters},

  number       = 7,

  volume       = 125,

  place        = {United States},

  year         = {Thu Aug 13 00:00:00 EDT 2020},

  month        = {Thu Aug 13 00:00:00 EDT 2020}

}

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The origin of Earth's ancient magnetic field is an outstanding problem. It has recently been proposed that exsolution of MgO from the core may provide sufficient energy to drive an early geodynamo. Here, in this work, we present new experiments on Mg partitioning between iron-rich liquids and silicate/oxide melts. Our results indicate that Mg partitioning depends strongly on the oxygen content in the iron-rich liquid, in contrast to previous findings that it depends only on temperature. Consequently, MgO exsolution during core cooling is drastically reduced and insufficient to drive an early geodynamo alone. Using the new experimental data, our thermalmore »« less
Cited by 24
https://doi.org/10.1002/2017GL075283

Full Text Available
Melting and phase relations of Fe-Ni-Si determined by a multi-technique approach

Journal Article Dobrosavljevic, Vasilije V. ; Zhang, Dongzhou ; Sturhahn, Wolfgang ; ... - Earth and Planetary Science Letters

Many studies have suggested silicon as a candidate light element for the cores of Earth and Mercury. However, the effect of silicon on the melting temperatures of core materials and thermal profiles of cores is poorly understood, due to disagreements among melt detection techniques, uncertainties in sample pressure evolution during heating, and sparsity of studies investigating the combined effects of nickel and silicon on the phase diagram of iron. Here, in this study we develop a multi-technique approach for measuring the high-pressure melting and solid phase relations of iron alloys and apply it to Fe_0.8Ni_0.1Si_0.1 (Fe-11wt%Ni-5.3wt%Si), a composition compatible withmore »« less
https://doi.org/10.1016/j.epsl.2021.117358

Full Text Available
Chemical bonding and the incorporation of potassium into the Earth's core

Journal Article Sherman, D M - Geophysical Research Letters (American Geophysical Union); (USA)

It has been argued that most of the Earth's potassium was segregated into the outer core and that the radioactive decay of {sup 40}K provided the heat source for the geodynamo. This idea rests on the assumption that the affinity of potassium for sulfur or metallic iron is enhanced at high pressure. In this paper, the high pressure electronic structures of K in sulfide, iron sulfide and metallic iron coordination environments were determined from molecular orbital (SCF-X{alpha}-SW) calculations on (KS{sub 8}){sup 15{minus}}, (KS{sub 8}Fe{sub 6}){sup 3{minus}} and KFe{sub 14} clusters. It is shown that, even at high pressure, potassium cannotmore »« less
https://doi.org/10.1029/GL017i006p00693
Reduced lattice thermal conductivity of Fe-bearing bridgmanite in Earth's deep mantle

Journal Article Hsieh, Wen -Pin ; Deschamps, Frédéric ; Okuchi, Takuo ; ... - Journal of Geophysical Research. Solid Earth

Complex seismic, thermal, and chemical features have been reported in Earth's lowermost mantle. In particular, possible iron enrichments in the large low shear–wave velocity provinces (LLSVPs) could influence thermal transport properties of the constituting minerals in this region, altering the lower mantle dynamics and heat flux across core–mantle boundary (CMB). Thermal conductivity of bridgmanite is expected to partially control the thermal evolution and dynamics of Earth's lower mantle. Importantly, the pressure–induced lattice distortion and iron spin and valence states in bridgmanite could affect its lattice thermal conductivity, but these effects remain largely unknown. Here we precisely measured the lattice thermalmore »« less
Cited by 37
https://doi.org/10.1002/2017JB014339

Full Text Available

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Title: Reconciliation of Experiments and Theory on Transport Properties of Iron and the Geodynamo

Abstract

Citation Formats

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

Electrical resistivity of liquid Fe to 12 GPa: Implications for heat flow in cores of terrestrial bodies journal, July 2018

The New Core Paradox journal, October 2013

Geodynamo, Solar Wind, and Magnetopause 3.4 to 3.45 Billion Years Ago journal, March 2010

An Experimental Examination of Thermal Conductivity Anisotropy in hcp Iron journal, November 2018

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

Resistivity saturation of hcp Fe-Si alloys in an internally heated diamond anvil cell: A key to assessing the Earth's core conductivity journal, August 2020

QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials journal, September 2009

Thermal and electrical conductivity of iron at Earth’s core conditions journal, April 2012

Core–mantle boundary heat flow journal, January 2008

High-temperature electrical resistivity measurements of hcp iron to Mbar pressure in an internally resistive heated diamond anvil cell journal, October 2019

Optimal representation of source-sink fluxes for mesoscale carbon dioxide inversion with synthetic data: FLUX REPRESENTATION FOR CO journal, November 2011

Electrical and thermal transport properties of iron and iron-silicon alloy at high pressure: TRANSPORT PROPERTIES OF Fe AND Fe-Si journal, October 2013

Thermal Conductivity and Electrical Resistivity of Solid Iron at Earth’s Core Conditions from First Principles journal, August 2018

A numerical analysis of various cross sheet resistor test structures journal, January 1977

Geodynamo Conductivity Limits journal, July 2019

The plastic deformation of iron at pressures of the Earth's inner core journal, June 2000

Ioffe-Regel criterion and resistivity of metals journal, December 1981

Electron–electron scattering and thermal conductivity of ϵ -iron at Earth’s core conditions journal, July 2017

A revised estimate of the conductivity of iron alloy at high pressure and implications for the core energy balance journal, April 2007

Reduced lattice thermal conductivity of Fe-bearing bridgmanite in Earth's deep mantle: Reduced Conductivity of Fe-Bridgmanite journal, July 2017

Analytical model for solidification of the Earth's core journal, March 1992

Electrical resistivity and thermal conductivity of liquid Fe alloys at high P and T, and heat flux in Earth's core journal, February 2012

Powering Earth’s dynamo with magnesium precipitation from the core journal, January 2016

Electronic structure calculations with dynamical mean-field theory journal, August 2006

Thermal conductivity of hcp iron at high pressure and temperature journal, March 2011

Incoherent charge dynamics of La 2 − x Sr x CuO 4 : Dynamical localization and resistivity saturation journal, October 2003

The high conductivity of iron and thermal evolution of the Earth’s core journal, November 2013

Transport properties of iron at Earth's core conditions: The effect of spin disorder journal, July 2017

Electrical resistivity at large temperatures: Saturation and lack thereof journal, November 2002

High pressure and temperature electrical resistivity of iron and implications for planetary cores: HIGH PRESSURE AND TEMPERATURE ELECTRICAL RESISTIVITY journal, January 2013

Pseudopotentials for high-throughput DFT calculations journal, January 2014

Transport properties in correlated systems: An analytical model journal, October 2005

Electronic thermal conductivity at high temperatures: Violation of the Wiedemann-Franz law in narrow-band metals journal, December 2006

Effects of iron on the lattice thermal conductivity of Earth’s deep mantle and implications for mantle dynamics journal, April 2018

Infrared and dc conductivity in metals with strong scattering: Nonclassical behavior from a generalized Boltzmann equation containing band-mixing effects journal, May 1981

Lattice thermal conductivity of MgSiO3 perovskite and post-perovskite at the core–mantle boundary journal, October 2012

Elasticity and rheology of iron above 220 GPa and the nature of the Earth's inner core journal, December 1998

Palaeomagnetic field intensity variations suggest Mesoproterozoic inner-core nucleation journal, October 2015

An Experimental Study of Various Cross Sheet Resistor Test Structures journal, January 1978

Thermal conductivity and Seebeck coefficient of Fe and Fe-Si alloys: Implications for variable Lorenz number journal, April 2017

Young inner core inferred from Ediacaran ultra-low geomagnetic field intensity journal, January 2019

Thermal conductivity of ferropericlase in the Earth's lower mantle journal, May 2017

Thermal evolution of the core with a high thermal conductivity journal, October 2015

Advanced flat top laser heating system for high pressure research at GSECARS: application to the melting behavior of germanium journal, September 2008

Electrical resistivity of substitutionally disordered hcp Fe–Si and Fe–Ni alloys: Chemically-induced resistivity saturation in the Earth's core journal, October 2016

Advances in geodynamo modelling journal, March 2019

Colloquium : Saturation of electrical resistivity journal, October 2003

Shear wave anisotropy of textured hcp-Fe in the Earth's inner core journal, October 2010

Transport properties for liquid silicon-oxygen-iron mixtures at Earth's core conditions journal, January 2013

Experimental constraints on light elements in the Earth’s outer core journal, March 2016

Combination of pulsed light heating thermoreflectance and laser-heated diamond anvil cell for in-situ high pressure-temperature thermal diffusivity measurements journal, July 2019

Electrical conductivity of iron under shock compression up to 200 GPa journal, October 2002

Quasihydrostatic Equation of State of Iron above 2 Mbar journal, November 2006

The Thermal Conductivity of Earth's Core: A Key Geophysical Parameter's Constraints and Uncertainties journal, May 2018

Electrical Resistivity of Fe‐C Alloy at High Pressure: Effects of Carbon as a Light Element on the Thermal Conductivity of the Earth's Core journal, May 2018

Composition and State of the Core journal, May 2013

Thermal conductivity of MgO, MgSiO3 perovskite and post-perovskite in the Earth's deep mantle journal, November 2012

Constraints from material properties on the dynamics and evolution of Earth’s core journal, August 2015

On the thermal and magnetic histories of Earth and Venus: Influences of melting, radioactivity, and conductivity journal, November 2014

Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions journal, January 1996

How much potassium is in the Earth's core? New insights from partitioning experiments journal, April 2007

Lattice thermal conductivity of lower mantle minerals and heat flux from Earth's core journal, October 2011

Earth's core problem journal, June 2016

Inner Workings: Diamond anvils probe the origins of Earth’s magnetic field journal, February 2017

The influence of sulfur on the electrical resistivity of hcp iron: Implications for the core conductivity of Mars and Earth: Impurity Resistivity of S in hcp Iron journal, August 2017

Preliminary reference Earth model journal, June 1981

Direct measurement of thermal conductivity in solid iron at planetary core conditions journal, June 2016

Experimental determination of the electrical resistivity of iron at Earth’s core conditions journal, June 2016

Melting of Iron at Earth's Inner Core Boundary Based on Fast X-ray Diffraction journal, April 2013

The Iron Invariance: Implications for Thermal Convection in Earth's Core journal, October 2019

Influence of sulfur on the electrical resistivity of a crystallizing core in small terrestrial bodies journal, August 2018

Electrical resistivity and thermal conductivity of hcp Fe–Ni alloys under high pressure: Implications for thermal convection in the Earth’s core journal, October 2015

Lowermost mantle thermal conductivity constrained from experimental data and tomographic models journal, May 2019

Thermal and electrical conductivity of solid iron and iron–silicon mixtures at Earth's core conditions journal, May 2014

New method for solving Boltzmann's equation for electrons in metals journal, May 1978

Electrical and thermal conductivities of Fe–Ni–Si alloy under core conditions journal, August 2001

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

Electrical resistivity of liquid Fe to 12 GPa: Implications for heat flow in cores of terrestrial bodies
journal, July 2018

The New Core Paradox
journal, October 2013

Geodynamo, Solar Wind, and Magnetopause 3.4 to 3.45 Billion Years Ago
journal, March 2010

An Experimental Examination of Thermal Conductivity Anisotropy in hcp Iron
journal, November 2018

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

Resistivity saturation of hcp Fe-Si alloys in an internally heated diamond anvil cell: A key to assessing the Earth's core conductivity
journal, August 2020

QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials
journal, September 2009

Thermal and electrical conductivity of iron at Earth’s core conditions
journal, April 2012

Core–mantle boundary heat flow
journal, January 2008

High-temperature electrical resistivity measurements of hcp iron to Mbar pressure in an internally resistive heated diamond anvil cell
journal, October 2019

Optimal representation of source-sink fluxes for mesoscale carbon dioxide inversion with synthetic data: FLUX REPRESENTATION FOR CO
journal, November 2011

Electrical and thermal transport properties of iron and iron-silicon alloy at high pressure: TRANSPORT PROPERTIES OF Fe AND Fe-Si
journal, October 2013

Thermal Conductivity and Electrical Resistivity of Solid Iron at Earth’s Core Conditions from First Principles
journal, August 2018

A numerical analysis of various cross sheet resistor test structures
journal, January 1977

Geodynamo Conductivity Limits
journal, July 2019

The plastic deformation of iron at pressures of the Earth's inner core
journal, June 2000

Ioffe-Regel criterion and resistivity of metals
journal, December 1981

Electron–electron scattering and thermal conductivity of ϵ -iron at Earth’s core conditions
journal, July 2017

A revised estimate of the conductivity of iron alloy at high pressure and implications for the core energy balance
journal, April 2007

Reduced lattice thermal conductivity of Fe-bearing bridgmanite in Earth's deep mantle: Reduced Conductivity of Fe-Bridgmanite
journal, July 2017

Analytical model for solidification of the Earth's core
journal, March 1992

Electrical resistivity and thermal conductivity of liquid Fe alloys at high P and T, and heat flux in Earth's core
journal, February 2012

Powering Earth’s dynamo with magnesium precipitation from the core
journal, January 2016

Electronic structure calculations with dynamical mean-field theory
journal, August 2006

Thermal conductivity of hcp iron at high pressure and temperature
journal, March 2011

Incoherent charge dynamics of ${La}_{2 - x} {Sr}_{x} {CuO}_{4} :$ Dynamical localization and resistivity saturation
journal, October 2003

The high conductivity of iron and thermal evolution of the Earth’s core
journal, November 2013

Transport properties of iron at Earth's core conditions: The effect of spin disorder
journal, July 2017

Electrical resistivity at large temperatures: Saturation and lack thereof
journal, November 2002

High pressure and temperature electrical resistivity of iron and implications for planetary cores: HIGH PRESSURE AND TEMPERATURE ELECTRICAL RESISTIVITY
journal, January 2013

Pseudopotentials for high-throughput DFT calculations
journal, January 2014

Transport properties in correlated systems: An analytical model
journal, October 2005

Electronic thermal conductivity at high temperatures: Violation of the Wiedemann-Franz law in narrow-band metals
journal, December 2006

Effects of iron on the lattice thermal conductivity of Earth’s deep mantle and implications for mantle dynamics
journal, April 2018

Infrared and dc conductivity in metals with strong scattering: Nonclassical behavior from a generalized Boltzmann equation containing band-mixing effects
journal, May 1981

Lattice thermal conductivity of MgSiO3 perovskite and post-perovskite at the core–mantle boundary
journal, October 2012

Elasticity and rheology of iron above 220 GPa and the nature of the Earth's inner core
journal, December 1998

Palaeomagnetic field intensity variations suggest Mesoproterozoic inner-core nucleation
journal, October 2015

An Experimental Study of Various Cross Sheet Resistor Test Structures
journal, January 1978

Thermal conductivity and Seebeck coefficient of Fe and Fe-Si alloys: Implications for variable Lorenz number
journal, April 2017

Young inner core inferred from Ediacaran ultra-low geomagnetic field intensity
journal, January 2019

Thermal conductivity of ferropericlase in the Earth's lower mantle
journal, May 2017

Thermal evolution of the core with a high thermal conductivity
journal, October 2015

Advanced flat top laser heating system for high pressure research at GSECARS: application to the melting behavior of germanium
journal, September 2008

Electrical resistivity of substitutionally disordered hcp Fe–Si and Fe–Ni alloys: Chemically-induced resistivity saturation in the Earth's core
journal, October 2016

Advances in geodynamo modelling
journal, March 2019

Colloquium : Saturation of electrical resistivity
journal, October 2003

Shear wave anisotropy of textured hcp-Fe in the Earth's inner core
journal, October 2010

Transport properties for liquid silicon-oxygen-iron mixtures at Earth's core conditions
journal, January 2013

Experimental constraints on light elements in the Earth’s outer core
journal, March 2016

Combination of pulsed light heating thermoreflectance and laser-heated diamond anvil cell for in-situ high pressure-temperature thermal diffusivity measurements
journal, July 2019

Electrical conductivity of iron under shock compression up to 200 GPa
journal, October 2002

Quasihydrostatic Equation of State of Iron above 2 Mbar
journal, November 2006

The Thermal Conductivity of Earth's Core: A Key Geophysical Parameter's Constraints and Uncertainties
journal, May 2018

Electrical Resistivity of Fe‐C Alloy at High Pressure: Effects of Carbon as a Light Element on the Thermal Conductivity of the Earth's Core
journal, May 2018

Composition and State of the Core
journal, May 2013

Thermal conductivity of MgO, MgSiO3 perovskite and post-perovskite in the Earth's deep mantle
journal, November 2012

Constraints from material properties on the dynamics and evolution of Earth’s core
journal, August 2015

On the thermal and magnetic histories of Earth and Venus: Influences of melting, radioactivity, and conductivity
journal, November 2014

Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions
journal, January 1996

How much potassium is in the Earth's core? New insights from partitioning experiments
journal, April 2007

Lattice thermal conductivity of lower mantle minerals and heat flux from Earth's core
journal, October 2011

Earth's core problem
journal, June 2016

Inner Workings: Diamond anvils probe the origins of Earth’s magnetic field
journal, February 2017

The influence of sulfur on the electrical resistivity of hcp iron: Implications for the core conductivity of Mars and Earth: Impurity Resistivity of S in hcp Iron
journal, August 2017

Preliminary reference Earth model
journal, June 1981

Direct measurement of thermal conductivity in solid iron at planetary core conditions
journal, June 2016

Experimental determination of the electrical resistivity of iron at Earth’s core conditions
journal, June 2016

Melting of Iron at Earth's Inner Core Boundary Based on Fast X-ray Diffraction
journal, April 2013

The Iron Invariance: Implications for Thermal Convection in Earth's Core
journal, October 2019

Influence of sulfur on the electrical resistivity of a crystallizing core in small terrestrial bodies
journal, August 2018

Electrical resistivity and thermal conductivity of hcp Fe–Ni alloys under high pressure: Implications for thermal convection in the Earth’s core
journal, October 2015

Lowermost mantle thermal conductivity constrained from experimental data and tomographic models
journal, May 2019

Thermal and electrical conductivity of solid iron and iron–silicon mixtures at Earth's core conditions
journal, May 2014

New method for solving Boltzmann's equation for electrons in metals
journal, May 1978

Electrical and thermal conductivities of Fe–Ni–Si alloy under core conditions
journal, August 2001

Electrical conductivity, demagnetization, and the high-pressure phase transition in shock-compressed iron
journal, February 1969

The electrical resistivity of solid and liquid Fe at pressures up to 7 GPa
journal, January 1989

Advances in geodynamo modelling
journal, March 2019