Anharmonic thermodynamic properties and phase boundary across the postperovskite transition in MgSiO3

Zhang, Zhen; Wentzcovitch, Renata M.

doi:10.1103/physrevb.106.054103

Anharmonic thermodynamic properties and phase boundary across the postperovskite transition in MgSi O3

Journal Article · Mon Aug 15 00:00:00 EDT 2022 · Physical Review. B

DOI:https://doi.org/10.1103/physrevb.106.054103· OSTI ID:1979794

Zhang, Zhen ^[1]; ^[2]

Columbia Univ., New York, NY (United States); OSTI
Columbia Univ., New York, NY (United States)

To address the effects of lattice anharmonicity across the perovskite to postperovskite transition in MgSiO₃, we conduct calculations using the phonon quasiparticle (PHQ) approach. The PHQ is based on abinitio molecular dynamics and, in principle, captures full anharmonicity. Free energies in the thermodynamic limit (N → ∞) are computed using temperature-dependent quasiparticle dispersions within the phonon gas model. Systematic results on anharmonic thermodynamic properties and phase boundary are reported. Both the local density approximation and the generalized gradient approximation calculations are performed to provide confident constraints on these properties. Anharmonic effects are demonstrated by comparing results with those obtained using the quasiharmonic approximation (QHA). The inadequacy of the QHA is indicated by its overestimation of thermal expansivity and thermodynamic Grüneisen parameter and its converged isochoric heat capacity in the high-temperature limit. The PHQ phase boundary has a Clapeyron slope (dP/dT) that increases with temperature. This result contrasts with the nearly zero curvature of the QHA phase boundary. Anharmonicity bends the phase boundary to lower temperatures at high pressures. Implications for the double-crossing of the phase boundary by the mantle geotherm are discussed.

View Accepted Manuscript (DOE)

Research Organization:: Columbia Univ., New York, NY (United States)

Sponsoring Organization:: National Science Foundation (NSF); USDOE Office of Science (SC)

Grant/Contract Number:: SC0019759

OSTI ID:: 1979794

Journal Information:: Physical Review. B, Journal Name: Physical Review. B Journal Issue: 5 Vol. 106; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (80)

Recent developments in ab initio thermodynamics Alf�, D.; de Wijs, G. A.; Kresse, G. International Journal of Quantum Chemistry, Vol. 77, Issue 5 https://doi.org/10.1002/(SICI)1097-461X(2000)77:5%3C871::AID-QUA8%3E3.0.CO;2-3	journal	January 2000
Influence of the iron spin crossover in ferropericlase on the lower mantle geotherm: SPIN CROSSOVER AND MANTLE TEMPERATURE Valencia-Cardona, Juan J.; Shukla, Gaurav; Wu, Zhongqing Geophysical Research Letters, Vol. 44, Issue 10 https://doi.org/10.1002/2017GL073294	journal	May 2017
High-pressure crystal chemistry of MgSiO3 perovskite Ross, NancyL.; Hazen, RobertM. Physics and Chemistry of Minerals, Vol. 17, Issue 3 https://doi.org/10.1007/BF00201454	journal	June 1990
Structure and crystal chemistry of perovskite-type MgSiO3 Yagi, Takehiko; Mao, Ho-Kwang; Bell, Peter M. Physics and Chemistry of Minerals, Vol. 3, Issue 2 https://doi.org/10.1007/BF00308114	journal	January 1978
Effect of pressure on the crystal structure of perovskite-type MgSiO3 Kudoh, Y.; Ito, E.; Takeda, H. Physics and Chemistry of Minerals, Vol. 14, Issue 4 https://doi.org/10.1007/BF00309809	journal	May 1987
P-V-T equation of state of (Mg,Fe)SiO3 perovskite: constraints on composition of the lower mantle Wang, Yanbin; Weidner, Donald J.; Liebermann, Robert C. Physics of the Earth and Planetary Interiors, Vol. 83, Issue 1 https://doi.org/10.1016/0031-9201(94)90109-0	journal	April 1994
Equation of state of gold and its application to the phase boundaries near 660 km depth in Earth’s mantle Shim, Sang-Heon; Duffy, Thomas S.; Takemura, Kenichi Earth and Planetary Science Letters, Vol. 203, Issue 2 https://doi.org/10.1016/S0012-821X(02)00917-2	journal	October 2002
P-V-T equation of state of MgSiO3 perovskite Fiquet, Guillaume; Andrault, Denis; Dewaele, Agnès Physics of the Earth and Planetary Interiors, Vol. 105, Issue 1-2 https://doi.org/10.1016/S0031-9201(97)00077-0	journal	January 1998
A thermodynamic model for MgSiO3-perovskite derived from pressure, temperature and volume dependence of the Raman mode frequencies Gillet, Philippe; Daniel, Isabelle; Guyot, François Physics of the Earth and Planetary Interiors, Vol. 117, Issue 1-4 https://doi.org/10.1016/S0031-9201(99)00107-7	journal	January 2000
phq: A Fortran code to compute phonon quasiparticle properties and dispersions Zhang, Z.; Zhang, D. -B.; Sun, T. Computer Physics Communications, Vol. 243 https://doi.org/10.1016/j.cpc.2019.05.003	journal	October 2019
Phase transition in MgSiO3 perovskite in the earth's lower mantle Tsuchiya, Taku; Tsuchiya, Jun; Umemoto, Koichiro Earth and Planetary Science Letters, Vol. 224, Issue 3-4 https://doi.org/10.1016/j.epsl.2004.05.017	journal	August 2004
In situ observations of phase transition between perovskite and CaIrO-type phase in MgSiO and pyrolitic mantle composition Ono, S.; Oganov, A. Earth and Planetary Science Letters, Vol. 236, Issue 3-4 https://doi.org/10.1016/j.epsl.2005.06.001	journal	August 2005
Thermoelastic properties of post-perovskite phase MgSiO3 determined experimentally at core–mantle boundary P–T conditions Guignot, N.; Andrault, D.; Morard, G. Earth and Planetary Science Letters, Vol. 256, Issue 1-2 https://doi.org/10.1016/j.epsl.2007.01.025	journal	April 2007
Simultaneous volume measurements of post-perovskite and perovskite in MgSiO3 and their thermal equations of state Komabayashi, Tetsuya; Hirose, Kei; Sugimura, Emiko Earth and Planetary Science Letters, Vol. 265, Issue 3-4 https://doi.org/10.1016/j.epsl.2007.10.036	journal	January 2008
Lattice thermal conductivity of MgSiO3 perovskite and post-perovskite at the core–mantle boundary Ohta, Kenji; Yagi, Takashi; Taketoshi, Naoyuki Earth and Planetary Science Letters, Vol. 349-350 https://doi.org/10.1016/j.epsl.2012.06.043	journal	October 2012
Direct shock wave loading of MgSiO3 perovskite to lower mantle conditions and its equation of state Deng, Liwei; Gong, Zizheng; Fei, Yingwei Physics of the Earth and Planetary Interiors, Vol. 170, Issue 3-4 https://doi.org/10.1016/j.pepi.2008.07.043	journal	November 2008
High-pressure experiments and the phase diagram of lower mantle and core materials Boehler, R. Reviews of Geophysics, Vol. 38, Issue 2 https://doi.org/10.1029/1998RG000053	journal	May 2000
Thermoelastic properties and crystal structure of MgSiO ₃ perovskite at lower mantle pressure and temperature conditions Fiquet, G.; Dewaele, A.; Andrault, D. Geophysical Research Letters, Vol. 27, Issue 1 https://doi.org/10.1029/1999GL008397	journal	January 2000
Quasi-hydrostatic compression of magnesium oxide to 52 GPa: Implications for the pressure-volume-temperature equation of state Speziale, Sergio; Zha, Chang-Sheng; Duffy, Thomas S. Journal of Geophysical Research: Solid Earth, Vol. 106, Issue B1 https://doi.org/10.1029/2000JB900318	journal	January 2001
First-principles prediction of the P - V - T equation of state of gold and the 660-km discontinuity in Earth's mantle : FIRST-PRINCIPLES PREDICTION OF EQUATION OF STATE OF GOLD Tsuchiya, Taku Journal of Geophysical Research: Solid Earth, Vol. 108, Issue B10 https://doi.org/10.1029/2003JB002446	journal	October 2003
Vibrational and thermodynamic properties of MgSiO ₃ postperovskite : THERMODYNAMIC PROPERTIES OF POSTPEROVSKITE Tsuchiya, Jun; Tsuchiya, Taku; Wentzcovitch, Renata M. Journal of Geophysical Research: Solid Earth, Vol. 110, Issue B2 https://doi.org/10.1029/2004JB003409	journal	February 2005
Phase relations in Mg ₃ Al ₂ Si ₃ O ₁₂ to 180 GPa: Effect of Al on post-perovskite phase transition Tateno, Shigehiko Geophysical Research Letters, Vol. 32, Issue 15 https://doi.org/10.1029/2005GL023309	journal	January 2005
Postperovskite phase transition and its geophysical implications Hirose, Kei Reviews of Geophysics, Vol. 44, Issue 3 https://doi.org/10.1029/2005RG000186	journal	January 2006
Unsolved problems in the lowermost mantle Hirose, Kei; Karato, Shun-ichiro; Cormier, Vernon F. Geophysical Research Letters, Vol. 33, Issue 12 https://doi.org/10.1029/2006GL025691	journal	January 2006
The valence state and partitioning of iron in the Earth's lowermost mantle Sinmyo, Ryosuke; Hirose, Kei; Muto, Shunsuke Journal of Geophysical Research, Vol. 116, Issue B7 https://doi.org/10.1029/2010JB008179	journal	January 2011
Low Melting Temperature of Anhydrous Mantle Materials at the Core‐Mantle Boundary Kim, Taehyun; Ko, Byeongkwan; Greenberg, Eran Geophysical Research Letters, Vol. 47, Issue 20 https://doi.org/10.1029/2020GL089345	journal	October 2020
Post‐Perovskite Phase Transition in the Pyrolitic Lowermost Mantle: Implications for Ubiquitous Occurrence of Post‐Perovskite Above CMB Kuwayama, Yasuhiro; Hirose, Kei; Cobden, Laura Geophysical Research Letters, Vol. 49, Issue 1 https://doi.org/10.1029/2021GL096219	journal	January 2022
Effect of pressure, temperature, and composition on lattice parameters and density of (Fe,Mg)SiO ₃ -perovskites to 30 GPa Mao, H. K.; Hemley, R. J.; Fei, Y. Journal of Geophysical Research, Vol. 96, Issue B5 https://doi.org/10.1029/91JB00176	journal	January 1991
High-temperature thermodynamic properties of forsterite Gillet, Philippe; Richet, Pascal; Guyot, François Journal of Geophysical Research, Vol. 96, Issue B7 https://doi.org/10.1029/91JB00680	journal	January 1991
Thermal expansivity of MgSiO ₃ perovskite under high pressures up to 20 GPa Utsumi, Wataru; Funamori, Nobumasa; Yagi, Takehiko Geophysical Research Letters, Vol. 22, Issue 9 https://doi.org/10.1029/95GL00584	journal	May 1995
Thermoelastic properties of MgSiO ₃ perovskite determined by in situ X ray observations up to 30 GPa and 2000 K Funamori, Nobumasa; Yagi, Takehiko; Utsumi, Wataru Journal of Geophysical Research: Solid Earth, Vol. 101, Issue B4 https://doi.org/10.1029/95JB03732	journal	April 1996
Microscopic anharmonicity and equation of state of MgSiO ₃ -perovskite Gillet, Philippe; Guyot, François; Wang, Yanbin Geophysical Research Letters, Vol. 23, Issue 21 https://doi.org/10.1029/96GL02771	journal	October 1996
Stability of orthorhombic MgSiO3 perovskite in the Earth's lower mantle Stixrude, Lars; Cohen, R. E. Nature, Vol. 364, Issue 6438 https://doi.org/10.1038/364613a0	journal	August 1993
Theoretical and experimental evidence for a post-perovskite phase of MgSiO3 in Earth's D″ layer Oganov, Artem R.; Ono, Shigeaki Nature, Vol. 430, Issue 6998 https://doi.org/10.1038/nature02701	journal	July 2004
A doubling of the post-perovskite phase boundary and structure of the Earth's lowermost mantle Hernlund, John W.; Thomas, Christine; Tackley, Paul J. Nature, Vol. 434, Issue 7035 https://doi.org/10.1038/nature03472	journal	April 2005
Thickness and Clapeyron slope of the post-perovskite boundary Catalli, Krystle; Shim, Sang-Heon; Prakapenka, Vitali Nature, Vol. 462, Issue 7274 https://doi.org/10.1038/nature08598	journal	December 2009
Core–mantle boundary heat flow Lay, Thorne; Hernlund, John; Buffett, Bruce A. Nature Geoscience, Vol. 1, Issue 1 https://doi.org/10.1038/ngeo.2007.44	journal	January 2008
Lattice Thermal Conductivity of MgSiO3 Perovskite from First Principles Ghaderi, Nahid; Zhang, Dong-Bo; Zhang, Huai Scientific Reports, Vol. 7, Issue 1 https://doi.org/10.1038/s41598-017-05523-6	journal	July 2017
Anharmonicity and the equation of state for gold Anderson, Orson L.; Isaak, Donald G.; Yamamoto, Shigeru Journal of Applied Physics, Vol. 65, Issue 4 https://doi.org/10.1063/1.342969	journal	February 1989
The equation of state of platinum to 660 GPa (6.6 Mbar) Holmes, N. C.; Moriarty, J. A.; Gathers, G. R. Journal of Applied Physics, Vol. 66, Issue 7 https://doi.org/10.1063/1.344177	journal	October 1989
A unified formulation of the constant temperature molecular dynamics methods Nosé, Shuichi The Journal of Chemical Physics, Vol. 81, Issue 1 https://doi.org/10.1063/1.447334	journal	July 1984
Iron-rich silicates in the Earth's D'' layer Mao, W. L.; Meng, Y.; Shen, G. Proceedings of the National Academy of Sciences, Vol. 102, Issue 28 https://doi.org/10.1073/pnas.0503737102	journal	June 2005
Equation of state of the postperovskite phase synthesized from a natural (Mg,Fe)SiO3 orthopyroxene Shieh, S. R.; Duffy, T. S.; Kubo, A. Proceedings of the National Academy of Sciences, Vol. 103, Issue 9 https://doi.org/10.1073/pnas.0506811103	journal	February 2006
Mineralogical effects on the detectability of the postperovskite boundary Grocholski, B.; Catalli, K.; Shim, S. -H. Proceedings of the National Academy of Sciences, Vol. 109, Issue 7 https://doi.org/10.1073/pnas.1109204109	journal	February 2012
QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials Giannozzi, Paolo; Baroni, Stefano; Bonini, Nicola Journal of Physics: Condensed Matter, Vol. 21, Issue 39, Article No. 395502 https://doi.org/10.1088/0953-8984/21/39/395502	journal	September 2009
Anharmonic Contributions to Specific Heat Keller, Joseph M.; Wallace, Duane C. Physical Review, Vol. 126, Issue 4 https://doi.org/10.1103/PhysRev.126.1275	journal	May 1962
Thermal Expansion and Other Anharmonic Properties of Crystals Wallace, Duane C. Physical Review, Vol. 139, Issue 3A https://doi.org/10.1103/PhysRev.139.A877	journal	August 1965
Canonical dynamics: Equilibrium phase-space distributions Hoover, William G. Physical Review A, Vol. 31, Issue 3 https://doi.org/10.1103/PhysRevA.31.1695	journal	March 1985
Ab initio anharmonic thermodynamic properties of cubic CaSiO3 perovskite Zhang, Zhen; Wentzcovitch, Renata M. Physical Review B, Vol. 103, Issue 10 https://doi.org/10.1103/PhysRevB.103.104108	journal	March 2021
Ab initio lattice thermal conductivity of MgSiO3 across the perovskite-postperovskite phase transition Zhang, Zhen; Wentzcovitch, Renata M. Physical Review B, Vol. 103, Issue 14 https://doi.org/10.1103/PhysRevB.103.144103	journal	April 2021
Self-interaction correction to density-functional approximations for many-electron systems Perdew, J. P.; Zunger, Alex Physical Review B, Vol. 23, Issue 10, p. 5048-5079 https://doi.org/10.1103/PhysRevB.23.5048	journal	May 1981
Projector augmented-wave method Blöchl, P. E. Physical Review B, Vol. 50, Issue 24, p. 17953-17979 https://doi.org/10.1103/PhysRevB.50.17953	journal	December 1994
Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set Kresse, G.; Furthmüller, J. Physical Review B, Vol. 54, Issue 16, p. 11169-11186 https://doi.org/10.1103/PhysRevB.54.11169	journal	October 1996
High-pressure lattice dynamics and thermoelasticity of MgO Karki, B. B.; Wentzcovitch, R. M.; de Gironcoli, S. Physical Review B, Vol. 61, Issue 13 https://doi.org/10.1103/PhysRevB.61.8793	journal	April 2000
Ab initio lattice dynamics of MgSiO 3 perovskite at high pressure Karki, B. B.; Wentzcovitch, R. M.; de Gironcoli, S. Physical Review B, Vol. 62, Issue 22 https://doi.org/10.1103/PhysRevB.62.14750	journal	December 2000
Vibrational and quasiharmonic thermal properties of CaO under pressure Karki, Bijaya B.; Wentzcovitch, Renata M. Physical Review B, Vol. 68, Issue 22 https://doi.org/10.1103/PhysRevB.68.224304	journal	December 2003
First-principles prediction of crystal structures at high temperatures using the quasiharmonic approximation Carrier, Pierre; Wentzcovitch, Renata; Tsuchiya, Jun Physical Review B, Vol. 76, Issue 6 https://doi.org/10.1103/PhysRevB.76.064116	journal	August 2007
Phonon quasiparticles and anharmonic perturbation theory tested by molecular dynamics on a model system Sun, Tao; Shen, Xiao; Allen, Philip B. Physical Review B, Vol. 82, Issue 22 https://doi.org/10.1103/PhysRevB.82.224304	journal	December 2010
Dynamic stabilization of cubic Ca Si O 3 perovskite at high temperatures and pressures from ab initio molecular dynamics Sun, Tao; Zhang, Dong-Bo; Wentzcovitch, Renata M. Physical Review B, Vol. 89, Issue 9 https://doi.org/10.1103/PhysRevB.89.094109	journal	March 2014
Equations of state and stability of MgSiO 3 perovskite and post-perovskite phases from quantum Monte Carlo simulations Lin, Yangzheng; Cohen, R. E.; Stackhouse, Stephen Physical Review B, Vol. 90, Issue 18 https://doi.org/10.1103/PhysRevB.90.184103	journal	November 2014
Thermal conductivity from phonon quasiparticles with subminimal mean free path in the MgSiO 3 perovskite Zhang, Dong-Bo; Allen, Philip B.; Sun, Tao Physical Review B, Vol. 96, Issue 10 https://doi.org/10.1103/PhysRevB.96.100302	journal	September 2017
Thermodynamic properties of MgSiO 3 at super-Earth mantle conditions Fratanduono, D. E.; Millot, M.; Kraus, R. G. Physical Review B, Vol. 97, Issue 21 https://doi.org/10.1103/PhysRevB.97.214105	journal	June 2018
Effect of anharmonicity on the hcp to bcc transition in beryllium at high-pressure and high-temperature conditions Xian, Jia-Wei; Yan, Jun; Liu, Hai-Feng Physical Review B, Vol. 99, Issue 6 https://doi.org/10.1103/PhysRevB.99.064102	journal	February 2019
Phonon Quasiparticles and Anharmonic Free Energy in Complex Systems Zhang, Dong-Bo; Sun, Tao; Wentzcovitch, Renata M. Physical Review Letters, Vol. 112, Issue 5 https://doi.org/10.1103/PhysRevLett.112.058501	journal	February 2014
Premelting hcp to bcc Transition in Beryllium Lu, Y.; Sun, T.; Zhang, Ping Physical Review Letters, Vol. 118, Issue 14 https://doi.org/10.1103/PhysRevLett.118.145702	journal	April 2017
Generalized Gradient Approximation Made Simple Perdew, John P.; Burke, Kieron; Ernzerhof, Matthias Physical Review Letters, Vol. 77, Issue 18, p. 3865-3868 https://doi.org/10.1103/PhysRevLett.77.3865	journal	October 1996
Thermoelastic Properties of M g S i O 3 -Perovskite: Insights on the Nature of the Earth’s Lower Mantle Wentzcovitch, R. M.; Karki, B. B.; Cococcioni, M. Physical Review Letters, Vol. 92, Issue 1 https://doi.org/10.1103/PhysRevLett.92.018501	journal	January 2004
High-Pressure Melting of MgSiO 3 Belonoshko, A. B.; Skorodumova, N. V.; Rosengren, A. Physical Review Letters, Vol. 94, Issue 19 https://doi.org/10.1103/PhysRevLett.94.195701	journal	May 2005
Phonons and related crystal properties from density-functional perturbation theory Baroni, Stefano; de Gironcoli, Stefano; Dal Corso, Andrea Reviews of Modern Physics, Vol. 73, Issue 2 https://doi.org/10.1103/RevModPhys.73.515	journal	July 2001
A lower mantle S-wave triplication and the shear velocity structure of D'' Lay, T.; Helmberger, D. V. Geophysical Journal International, Vol. 75, Issue 3 https://doi.org/10.1111/j.1365-246X.1983.tb05010.x	journal	December 1983
Self-consistent thermodynamic description of silicate liquids, with application to shock melting of MgO periclase and MgSiO ₃ perovskite de Koker, Nico; Stixrude, Lars Geophysical Journal International, Vol. 178, Issue 1 https://doi.org/10.1111/j.1365-246X.2009.04142.x	journal	July 2009
Post-Perovskite Phase Transition in MgSiO3 Murakami, M. Science, Vol. 304, Issue 5672 https://doi.org/10.1126/science.1095932	journal	May 2004
Structure and Freezing of MgSiO3 Liquid in Earth's Lower Mantle Stixrude, L. Science, Vol. 310, Issue 5746 https://doi.org/10.1126/science.1116952	journal	October 2005
Low Core-Mantle Boundary Temperature Inferred from the Solidus of Pyrolite Nomura, R.; Hirose, K.; Uesugi, K. Science, Vol. 343, Issue 6170 https://doi.org/10.1126/science.1248186	journal	January 2014
Synthesis and Equation of State of (Mg,Fe) SiO3 Perovskite to Over 100 Gigapascals Knittle, E.; Jeanloz, R. Science, Vol. 235, Issue 4789 https://doi.org/10.1126/science.235.4789.668	journal	February 1987
First-Principles Determination of Elastic Anisotropy and Wave Velocities of MgO at Lower Mantle Conditions Karki, B. B. Science, Vol. 286, Issue 5445 https://doi.org/10.1126/science.286.5445.1705	journal	November 1999
Equation of state of MgSiO ₃ with the perovskite structure based on experimental measurement Saxena, Surendra K.; Dubrovinsky, Leonid S.; Tutti, Faramarz American Mineralogist, Vol. 84, Issue 3 https://doi.org/10.2138/am-1999-0303	journal	March 1999
Equation of state of CaIrO3-type MgSiO3 up to 144 GPa Ono, S. American Mineralogist, Vol. 91, Issue 2-3 https://doi.org/10.2138/am.2006.2118	journal	February 2006
Iron partitioning between perovskite and post-perovskite: A transmission electron microscope study Hirose, K.; Takafuji, N.; Fujino, K. American Mineralogist, Vol. 93, Issue 10 https://doi.org/10.2138/am.2008.3001	journal	October 2008
Thermodynamic Properties and Phase Relations in Mantle Minerals Investigated by First Principles Quasiharmonic Theory Wentzcovitch, R. M.; Yu, Y. G.; Wu, Z. Reviews in Mineralogy and Geochemistry, Vol. 71, Issue 1 https://doi.org/10.2138/rmg.2010.71.4	journal	January 2010

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Anharmonic thermodynamic properties and phase boundary across the postperovskite transition in MgSi O3

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