O. L. Anderson. The Earth's Core and the Phase Diagram of Iron. Philos. T. Roy. Soc. A, 306(1492):21–35, 1982. URL:


D Antonangeli, J Siebert, CM Aracne, D Farber, A Bosak, M Hoesch, M Krisch, F Ryerson, G Fiquet, and J Badro. Spin crossover in ferropericlase at high pressure: a seismologically transparent transition? Science, 331(6031):64–67, 2011. URL:


T. H. K. Barron and R. W. Munn. Analysis of the thermal expansion of anisotropic solids: application to zinc. The Philosophical Magazine: A Journal of Theoretical Experimental and Applied Physics, 15(133):85–103, 1967. URL:, arXiv:, doi:10.1080/14786436708230352.


Eli Brosh, Guy Makov, and Roni Z. Shneck. Application of CALPHAD to high pressures. Calphad, 31(2):173–185, 2007. URL:, doi:


JM Brown and TJ Shankland. Thermodynamic parameters in the Earth as determined from seismic profiles. Geophys. J. Int., 66(3):579–596, 1981. URL:


F Cammarano, S Goes, A Deuss, and D Giardini. Is a pyrolitic adiabatic mantle compatible with seismic data? Earth Planet. Sci. Lett., 232(3):227–243, 2005. URL:


F. Cammarano. A short note on the pressure-depth conversion for geophysical interpretation. Geophysical Research Letters, 40(18):4834–4838, 2013. URL:, doi:10.1002/grl.50887.


CP Chin, S Hertzman, and B Sundman. An evaluation of the composition dependence of the magnetic order-disorder transition in cr-fe-co-ni alloys. Materials Research Center, The Royal Institute of Technology (Stockholm, Sweden), Report TRITA-MAC, 1987.


L Cobden, S Goes, M Ravenna, E Styles, F Cammarano, K Gallagher, and JA Connolly. Thermochemical interpretation of 1-D seismic data for the lower mantle: The significance of nonadiabatic thermal gradients and compositional heterogeneity. J. Geophys. Res., 114:B11309, 2009. URL:


JAD Connolly. Computation of phase equilibria by linear programming: a tool for geodynamic modeling and its application to subduction zone decarbonation. Earth Planet. Sci. Lett., 236(1):524–541, 2005. URL:


Sanne Cottaar, Timo Heister, Ian Rose, and Cayman Unterborn. Burnman: a lower mantle mineral physics toolkit. Geochemistry, Geophysics, Geosystems, 15(4):1164–1179, 2014. URL:, doi:10.1002/2013GC005122.


DR Davies, S Goes, JH Davies, BSA Shuberth, H-P Bunge, and J Ritsema. Reconciling dynamic and seismic models of Earth's lower mantle: The dominant role of thermal heterogeneity. Earth Planet. Sci. Lett., 353:253–269, 2012. URL:


F Deschamps, L Cobden, and PJ Tackley. The primitive nature of large low shear-wave velocity provinces. Earth Planet. Sci. Lett., 349-350:198–208, 2012. URL:


Frédéric Deschamps and Jeannot Trampert. Mantle tomography and its relation to temperature and composition. Phys. Earth Planet. Int., 140(4):277–291, December 2003. URL:, doi:10.1016/j.pepi.2003.09.004.


J. F. A. Diener, R. Powell, R. W. White, and T. J. B. Holland. A new thermodynamic model for clino- and orthoamphiboles in the system Na$_2$O–CaO–FeO–MgO–Al$_2$O$_3$–SiO$_2$–H$_2$O–O. Journal of Metamorphic Geology, 25(6):631–656, 2007. URL:, doi:10.1111/j.1525-1314.2007.00720.x.


A M Dziewonski and D L Anderson. Preliminary reference Earth model. Phys. Earth Planet. Int., 25(4):297–356, 1981.


Y He and L Wen. Geographic boundary of the “Pacific Anomaly” and its geometry and transitional structure in the north. J. Geophys. Res.-Sol. Ea., 2012. URL:, doi:DOI: 10.1029/2012JB009436.


George Helffrich and Bernard J Wood. Subregular model for multicomponent solutions. American Mineralogist, 74(9-10):1016–1022, 1989.


ER Hernández, D Alfè, and J Brodholt. The incorporation of water into lower-mantle perovskites: A first-principles study. Earth Planet. Sci. Lett., 364:37–43, 2013. URL:


T. J. B. Holland, N. F. C. Hudson, R. Powell, and B. Harte. New Thermodynamic Models and Calculated Phase Equilibria in NCFMAS for Basic and Ultrabasic Compositions through the Transition Zone into the Uppermost Lower Mantle. Journal of Petrology, 54(9):1901–1920, July 2013. URL:, doi:10.1093/petrology/egt035.


T. J. B. Holland and R. Powell. An enlarged and updated internally consistent thermodynamic dataset with uncertainties and correlations: the system K2O-Na$_2$O-CaO-MgO-MnO-FeO-Fe$_2$O$_3$-Al$_2$O$_3$-TiO$_2$-SiO$_2$-C-H$_2$-O$_2$. Journal of Metamorphic Geology, 8(1):89–124, 1990. URL:, doi:10.1111/j.1525-1314.1990.tb00458.x.


T. J. B. Holland and R. Powell. Mineral activity–composition relations and petrological calculations involving cation equipartition in multisite minerals: a logical inconsistency. Journal of Metamorphic Geology, 24(9):851–861, 2006. URL:, doi:10.1111/j.1525-1314.2006.00672.x.


Tim Holland and Roger Powell. A Compensated-Redlich-Kwong (CORK) equation for volumes and fugacities of CO2 and H2O in the range 1 bar to 50 kbar and 100–1600°C. Contributions to Mineralogy and Petrology, 109(2):265–273, 1991. URL:, doi:10.1007/BF00306484.


Tim Holland and Roger Powell. Thermodynamics of order-disorder in minerals; ii, symmetric formalism applied to solid solutions. American Mineralogist, 81(11-12):1425–1437, 1996. URL:, arXiv:, doi:10.2138/am-1996-11-1215.


Tim J.B. Holland, Neil F.C. Hudson, Roger Powell, and Ben Harte. New thermodynamic models and calculated phase equilibria in NCFMAS for basic and ultrabasic compositions through the transition zone into the uppermost lower mantle. Journal of Petrology, 54(9):1901–1920, 2013. URL:, arXiv:, doi:10.1093/petrology/egt035.


C Houser, G Masters, P Shearer, and G Laske. Shear and compressional velocity models of the mantle from cluster analysis of long-period waveforms. Geophys. J. Int., 174(1):195–212, 2008.


T Inoue, T Wada, R Sasaki, and H Yurimoto. Water partitioning in the Earth's mantle. Phys. Earth Planet. Int., 183(1):245–251, 2010. URL:


Joel Ita and Lars Stixrude. Petrology, elasticity, and composition of the mantle transition zone. Journal of Geophysical Research, 97(B5):6849, 1992. URL:, doi:10.1029/92JB00068.


Ian Jackson. Elasticity, composition and temperature of the Earth’s lower mantle: a reappraisal. Geophys. J. Int., 134(1):291–311, July 1998. URL:, doi:10.1046/j.1365-246x.1998.00560.x.


Matthew G Jackson, Richard W Carlson, Mark D Kurz, Pamela D Kempton, Don Francis, and Jerzy Blusztajn. Evidence for the survival of the oldest terrestrial mantle reservoir. Nature, 466(7308):853–856, 2010.


SI Karato and HA Spetzler. Defect microdynamics in minerals and solid-state mechanisms of seismic wave attenuation and velocity dispersion in the mantle. Rev. Geophys., 28(4):399–421, 1990. URL:


A Keane. An Investigation of Finite Strain in an Isotropic Material Subjected to Hydrostatic Pressure and its Seismological Applications. Australian Journal of Physics, 7(2):322, 1954. URL:, doi:10.1071/PH540322.


BLN Kennett, E R Engdahl, and R Buland. Constraints on seismic velocities in the Earth from traveltimes. Geophys. J. Int., 122(1):108–124, 1995. URL:


BLN Kennett and ER Engdahl. Traveltimes for global earthquake location and phase identification. Geophysical Journal International, 105(2):429–465, 1991.


Y Kudo, K Hirose, M Murakami, Y Asahara, H Ozawa, Y Ohishi, and N Hirao. Sound velocity measurements of CaSiO_3 perovskite to 133 GPa and implications for lowermost mantle seismic anomalies. Earth Planet. Sci. Lett., 349:1–7, 2012. URL:


B Kustowski, G Ekstrom, and AM Dziewonski. Anisotropic shear-wave velocity structure of the Earth's mantle: a global model. J. Geophys. Res., 113(B6):B06306, 2008. URL:


V Lekic, S Cottaar, A M Dziewonski, and B Romanowicz. Cluster analysis of global lower mantle tomography: A new class of structure and implications for chemical heterogeneity. Earth Planet. Sci. Lett., 357-358:68–77, 2012. URL:


C Li and RD van der Hilst. A new global model for P wave speed variations in Earth's mantle. Geochem. Geophys. Geosyst., 2008. URL:


JF Lin, S Speziale, Z Mao, and H Marquardt. Effects of the electronic spin transitions of iron in lower mantle minerals: Implications for deep mantle geophysics and geochemistry. Rev. Geophys., 2013. URL:


Jung-Fu Lin, György Vankó, Steven D. Jacobsen, Valentin Iota, Viktor V. Struzhkin, Vitali B. Prakapenka, Alexei Kuznetsov, and Choong-Shik Yoo. Spin transition zone in Earth's lower mantle. Science, 317(5845):1740–1743, 2007. URL:, arXiv:


C Mégnin and B Romanowicz. The three-dimensional shear velocity structure of the mantle from the inversion of body, surface and higher-mode waveforms. Geophys. J. Int., 143(3):709–728, 2000.


David Mainprice, Ralf Hielscher, and Helmut Schaeben. Calculating anisotropic physical properties from texture data using the MTEX open-source package. Geological Society, London, Special Publications, 360(1):175–192, 2011.


Z Mao, JF Lin, HP Scott, HC Watson, VB Prakapenka, Y Xiao, P Chow, and C McCammon. Iron-rich perovskite in the Earth's lower mantle. Earth Planet. Sci. Lett., 309(3):179–184, 2011. URL:


G. Masters, J.H. Woodhouse, and G. Freeman. Mineos v1.0.2 [software]. Computational Infrastructure for Geodynamics, :99, 2011. URL:


J Matas, J Bass, Y Ricard, E Mattern, and MST Bukowinski. On the bulk composition of the lower mantle: predictions and limitations from generalized inversion of radial seismic profiles. Geophys. J. Int., 170(2):764–780, 2007. URL:


J Matas and MST Bukowinski. On the anelastic contribution to the temperature dezpendence of lower mantle seismic velocities. Earth Planet. Sci. Lett., 259(1):51–65, 2007. URL:


E. Mattern, J. Matas, Y. Ricard, and J. Bass. Lower mantle composition and temperature from mineral physics and thermodynamic modelling. Geophys. J. Int., 160(3):973–990, March 2005. URL:, doi:10.1111/j.1365-246X.2004.02549.x.


WF McDonough and SS Sun. The composition of the Earth. Chem. Geol., 120(3):223–253, 1995. URL:


JB Minster and DL Anderson. A model of dislocation-controlled rheology for the mantle. Phil. Trans. R. Soc. Lond., 299(1449):319–359, 1981. URL:


I Mosca, L Cobden, A Deuss, J Ritsema, and J Trampert. Seismic and mineralogical structures of the lower mantle from probabilistic tomography. J. Geophys. Res.: Solid Earth, 2012. URL:


M Murakami. 6 Chemical Composition of the Earth's Lower Mantle: Constraints from Elasticity. In Physics and Chemistry of the Deep Earth (ed S.-I. Karato), pages 183–212. John Wiley & Sons, Ltd, Chichester, UK, 2013. URL:\&lr=\&id=7z9yES2XNyEC\&pgis=1.


M Murakami, Y Ohishi, N Hirao, and K Hirose. A perovskitic lower mantle inferred from high-pressure, high-temperature sound velocity data. Nature, 485(7396):90–94, 2012.


M Murakami, S Sinogeikin, H Hellwig, J Bass, and J Li. Sound velocity of MgSiO3 perovskite to Mbar pressure. Earth Planet. Sci. Lett., 256(1-2):47–54, April 2007. URL:, doi:10.1016/j.epsl.2007.01.011.


Motohiko Murakami, Yasuo Ohishi, Naohisa Hirao, and Kei Hirose. Elasticity of MgO to 130 GPa: Implications for lower mantle mineralogy. Earth Planet. Sci. Lett., 277(1-2):123–129, January 2009. URL:, doi:10.1016/j.epsl.2008.10.010.


F. D. Murnaghan. The compressibility of media under extreme pressures. Proceedings of the National Academy of Sciences, 30(9):244–247, 1944. URL:, arXiv:, doi:10.1073/pnas.30.9.244.


T Nakagawa, PJ Tackley, F Deschamps, and JAD Connolly. Radial 1-D seismic structures in the deep mantle in mantle convection simulations with self-consistently calculated mineralogy. Geochem. Geophys. Geosyst., 2012. URL:


Y Nakajima, DJ Frost, and DC Rubie. Ferrous iron partitioning between magnesium silicate perovskite and ferropericlase and the composition of perovskite in the Earth's lower mantle. J. Geophys. Res., 2012. URL:


M Noguchi, T Komabayashi, K Hirose, and Y Ohishi. High-temperature compression experiments of CaSiO_3 perovskite to lowermost mantle conditions and its thermal equation of state. Phys. Chem. Miner., 40(1):81–91, 2013. URL:


R Nomura, H Ozawa, S Tateno, K Hirose, J Hernlund, S Muto, H Ishii, and N Hiraoka. Spin crossover and iron-rich silicate melt in the Earth's deep mantle. Nature, 473(7346):199–202, 2011. URL:


M Panning and B Romanowicz. A three-dimensional radially anisotropic model of shear velocity in the whole mantle. Geophys. J. Int., 167(1):361–379, 2006.


JP Poirier. Introduction to the Physics of the Earth. Cambridge Univ. Press, Cambridge, England, 1991.


R. Powell and T. J. B. Holland. An internally consistent thermodynamic dataset with uncertainties and correlations: 1. methods and a worked example. Journal of Metamorphic Geology, 3(4):327–342, 1985. URL:, doi:10.1111/j.1525-1314.1985.tb00324.x.


Roger Powell. Darken's quadratic formalism and the thermodynamics of minerals. American Mineralogist, 72(1-2):1–11, 1987. URL:


Roger Powell and Tim Holland. On the formulation of simple mixing models for complex phases. American Mineralogist, 78(11-12):1174–1180, 1993. URL:


Roger Powell and Tim Holland. Relating formulations of the thermodynamics of mineral solid solutions; activity modeling of pyroxenes, amphiboles, and micas. American Mineralogist, 84(1-2):1–14, 1999. URL:, arXiv:


Frank M. Richter and Dan P. McKenzie. Parameterizations for the horizontally averaged temperature of infinite prandtl number convection. Journal of Geophysical Research: Solid Earth, 86(B3):1738–1744, 1981. URL:, arXiv:, doi:


J Ritsema, A Deuss, H. J. van Heijst, and J.H. Woodhouse. S40RTS: a degree-40 shear-velocity model for the mantle from new Rayleigh wave dispersion, teleseismic traveltime and normal-mode splitting function. Geophys. J. Int., 184(3):1223–1236, 2011. URL:


S. Saxena and G. Eriksson. Thermodynamics of Fe–S at ultra-high pressure. Calphad, 51:202–205, 2015. URL:, doi:


F. A. H. Schreinemakers. In-, mono-, and di-variant equilibria. VIII. Further consideration of the bivariant regions; the turning lines. Proc. K. Akad. Wet. (Netherlands), 18:1539–1552, 1916.


BSA Schuberth, C Zaroli, and G Nolet. Synthetic seismograms for a synthetic Earth: long-period P- and S-wave traveltime variations can be explained by temperature alone. Geophys. J. Int., 188(3):1393–1412, 2012. URL:


NA Simmons, AM Forte, L Boschi, and SP Grand. GyPSuM: A joint tomographic model of mantle density and seismic wave speeds. J. Geophys. Res., 115(B12):B12310, 2010. URL:


NA Simmons, SC Myers, G Johanneson, and E Matzel. LLNL-G3Dv3: Global P wave tomography model for improved regional and teleseismic travel time prediction. J. Geophys. Res., 2012. URL:


F.D. Stacey and P.M. Davis. High pressure equations of state with applications to the lower mantle and core. Physics of the Earth and Planetary Interiors, 142(3-4):137–184, may 2004. URL:, doi:10.1016/j.pepi.2004.02.003.


Frank D. Stacey. A thermal model of the Earth. Physics of the Earth and Planetary Interiors, 15(4):341–348, 1977. URL:, doi:


Frank D. Stacey and Frank D. The K-primed approach to high-pressure equations of state. Geophysical Journal International, 143(3):621–628, dec 2000. URL:, doi:10.1046/j.1365-246X.2000.00253.x.


L Stixrude and C Lithgow-Bertelloni. Thermodynamics of mantle minerals–I. Physical properties. Geophys. J. Int., 162(2):610–632, 2005. URL:


L Stixrude and C Lithgow-Bertelloni. Thermodynamics of mantle minerals–II. Phase equilibria. Geophys. J. Int., 184(3):1180–1213, 2011. URL:


L Stixrude and C Lithgow-Bertelloni. Geophysics of chemical heterogeneity in the mantle. Annu. Rev. Earth Planet. Sci., 40:569–595, 2012. URL:


Elinor Styles, D. Rhodri Davies, and Saskia Goes. Mapping spherical seismic into physical structure: biases from 3-D phase-transition and thermal boundary-layer heterogeneity. Geophys. J. Int., 184(3):1371–1378, March 2011. URL:, doi:10.1111/j.1365-246X.2010.04914.x.


B. Sundman. An assessment of the fe-o system. Journal of Phase Equilibria, 12(2):127–140, 1991. URL:, doi:10.1007/BF02645709.


PJ Tackley. Mantle convection and plate tectonics: Toward an integrated physical and chemical theory. Science, 288(5473):2002–2007, 2000. URL:


Mo Temkin. Mixtures of fused salts as ionic solutions. Acta Phys. Chem., USSR, 20:411, 1945.


A To, B Romanowicz, Y Capdeville, and N Takeuchi. 3D effects of sharp boundaries at the borders of the African and Pacific Superplumes: Observation and modeling. Earth Planet. Sci. Lett., 233(1-2):1447–1460, 2005.


Jeannot Trampert, Frédéric Deschamps, Joseph Resovsky, and Dave Yuen. Probabilistic tomography maps chemical heterogeneities throughout the lower mantle. Science (New York, N.Y.), 306(5697):853–6, October 2004. URL:, doi:10.1126/science.1101996.


Jeannot Trampert, Pierre Vacher, and Nico Vlaar. Sensitivities of seismic velocities to temperature, pressure and composition in the lower mantle. Phys. Earth Planet. Int., 124(3-4):255–267, August 2001. URL:, doi:10.1016/S0031-9201(01)00201-1.


Pascal Vinet, John R Smith, John Ferrante, and James H Rose. Temperature effects on the universal equation of state of solids. Physical Review B, 35(4):1945, 1987. doi:10.1103/PhysRevB.35.1945.


PJJR Vinet, J Ferrante, JR Smith, and JH Rose. A universal equation of state for solids. Journal of Physics C: Solid State Physics, 19(20):L467, 1986. doi:10.1088/0022-3719/19/20/001.


E. Bruce Watson and Ethan F. Baxter. Diffusion in solid-earth systems. Earth and Planetary Science Letters, 253(3–4):307 – 327, 2007. URL:, doi:


JP Watt, GF Davies, and RJ O'Connell. The elastic properties of composite materials. Rev. Geophys., 14(4):541–563, 1976. URL:


R. W. White, R. Powell, and J. A. Baldwin. Calculated phase equilibria involving chemical potentials to investigate the textural evolution of metamorphic rocks. Journal of Metamorphic Geology, 26(2):181–198, 2008. URL:, doi:10.1111/j.1525-1314.2008.00764.x.


RW White and R Powell. On the interpretation of retrograde reaction textures in granulite facies rocks. Journal of Metamorphic Geology, 29(1):131–149, 2011.


Z Wu, JF Justo, and RM Wentzcovitch. Elastic Anomalies in a Spin-Crossover System: Ferropericlase at Lower Mantle Conditions. Phys. Rev. Lett., 110(22):228501, 2013. URL:


Zhigang Zhang, Lars Stixrude, and John Brodholt. Elastic properties of MgSiO3-perovskite under lower mantle conditions and the composition of the deep Earth. Earth Planet. Sci. Lett., 379:1–12, October 2013. URL:, doi:10.1016/j.epsl.2013.07.034.


G. M. Anderson and D. A. Crerar. Thermodynamics in geochemistry: The equilibrium model. Oxford University Press, 1989.


W. W. Anderson and T. J. Ahrens. An equation of state for liquid iron and implications for the Earth's core. Journal of Geophysical Research, 99:4273–4284, March 1994. doi:10.1029/93JB03158.


L. S. Darken. Thermodynamics of binary metallic solutions. Metallurgical Society of AIME Transactions, 239:80–89, 1967.


N. de Koker, B. B. Karki, and L. Stixrude. Thermodynamics of the MgO-SiO$_2$ liquid system in Earth's lowermost mantle from first principles. Earth and Planetary Science Letters, 361:58–63, January 2013. doi:10.1016/j.epsl.2012.11.026.


J. Hama and K. Suito. High-temperature equation of state of CaSiO $_3$ perovskite and its implications for the lower mantle. Physics of the Earth and Planetary Interiors, 105:33–46, February 1998. doi:10.1016/S0031-9201(97)00074-5.


T. Holland and R. Powell. Activity-composition relations for phases in petrological calculations: an asymmetric multicomponent formulation. Contributions to Mineralogy and Petrology, 145:492–501, 2003. doi:10.1007/s00410-003-0464-z.


T. J. B. Holland and R. Powell. An internally consistent thermodynamic data set for phases of petrological interest. Journal of Metamorphic Geology, 16(3):309–343, 1998. URL:, doi:10.1111/j.1525-1314.1998.00140.x.


T. J. B. Holland and R. Powell. An improved and extended internally consistent thermodynamic dataset for phases of petrological interest, involving a new equation of state for solids. Journal of Metamorphic Geology, 29(3):333–383, 2011. URL:, doi:10.1111/j.1525-1314.2010.00923.x.


Y. K. Huang and C. Y. Chow. The generalized compressibility equation of Tait for dense matter. Journal of Physics D Applied Physics, 7:2021–2023, October 1974. doi:10.1088/0022-3727/7/15/305.


R. Myhill. The elastic solid solution model for minerals at high pressures and temperatures. Contributions to Mineralogy and Petrology, 173(2):12, February 2018. doi:10.1007/s00410-017-1436-z.


R. Myhill. An anisotropic equation of state for high pressure, high temperature applications. Geophysical Journal International, May 2022. doi:10.1093/gji/ggac180.


T. Nissen-Meyer, M. van Driel, S. C. Stähler, K. Hosseini, S. Hempel, L. Auer, A. Colombi, and A. Fournier. AxiSEM: broadband 3-D seismic wavefields in axisymmetric media. Solid Earth, 5:425–445, June 2014. doi:10.5194/se-5-425-2014.


A. Putnis. An Introduction to Mineral Sciences. Cambridge University Press, November 1992.


R. Rydberg. Graphische Darstellung einiger bandenspektroskopischer Ergebnisse. Zeitschrift fur Physik, 73:376–385, May 1932. doi:10.1007/BF01341146.


F. D. Stacey, B. J. Brennan, and R. D. Irvine. Finite strain theories and comparisons with seismological data. Geophysical Surveys, 4:189–232, April 1981. doi:10.1007/BF01449185.


J. J. van Laar. Sechs vorträge über das thermodynamischer potential. Vieweg, Brunswick, 1906.