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1 Abramson, E.H., Brown, J.M., & Slutsky, L.J. (1999). Applications of impulsive stimulated scattering in the Earth and planetary sciences. Annu. Rev. Phys. Chem., 50, 279–313. https://doi.org/10.1146/annurev.physchem.50.1.279

2 Abu‐Eid, R.M., & Burns, R.G. (1976). The effect of pressure on the degree of covalency of the cation‐oxygen bond in minerals. Am. Mineral., 61, 391–397.

3 Andrault, D., Angel, R.J., Mosenfelder, J.L., & Bihan, T.L. (2003). Equation of state of stishovite to lower mantle pressures. Am. Mineral., 88, 301–307. https://doi.org/10.2138/am‐2003‐2‐307

4 Andrault, D., & Fiquet, G. (2001). Synchrotron radiation and laser heating in a diamond anvil cell. Rev. Sci. Instrum., 72, 1283–1288. https://doi.org/10.1063/1.1343866

5 Andrault, D., Fiquet, G., Guyot, F., & Hanfland, M. (1998). Pressure‐induced Landau‐type transition in stishovite. Science, 282, 720–724. https://doi.org/10.1126/science.282.5389.720

6 Andrault, D., Petitgirard, S., Lo Nigro, G., Devidal, J.‐L., Veronesi, G., Garbarino, G., & Mezouar, M. (2012). Solid–liquid iron partitioning in Earth’s deep mantle. Nature, 487, 354–357. https://doi.org/10.1038/nature11294

7 Angel, R.J. (2000). Equations of state. Rev. Mineral. Geochem., 41, 35–59. https://doi.org/10.2138/rmg.2000.41.2

8  Angel, R.J., Alvaro, M., & Gonzalez‐Platas, J. (2014). EosFit7c and a Fortran module (library) for equation of state calculations. Z. Kristallogr. – Cryst. Mater., 229, 405–419. https://doi.org/10.1515/zkri‐2013‐1711

9 Angel, R.J., Downs, R.T., & Finger, L.W. (2000). High‐temperature–high‐pressure diffractometry. Rev. Mineral. Geochem., 41, 559–597. https://doi.org/10.2138/rmg.2000.41.16

10 Angel, R.J., Jackson, J.M., Reichmann, H.J., & Speziale, S. (2009). Elasticity measurements on minerals: a review. Eur. J. Mineral., 21, 525–550. https://doi.org/10.1127/0935‐1221/2009/0021‐1925

11 Anisimov, V.I., Aryasetiawan, F., & Lichtenstein, A.I. (1997). First‐principles calculations of the electronic structure and spectra of strongly correlated systems: the LDA + U method. J. Phys: Condens. Matter, 9, 767–808. https://doi.org/10.1088/0953‐8984/9/4/002

12 Anisimov, V.I., Zaanen, J., & Andersen, O.K. (1991). Band theory and Mott insulators: Hubbard U instead of Stoner I. Phys. Rev. B, 44, 943–954. https://doi.org/10.1103/PhysRevB.44.943

13 Antonangeli, D., Komabayashi, T., Occelli, F., Borissenko, E., Walters, A.C., Fiquet, G., & Fei, Y. (2012). Simultaneous sound velocity and density measurements of hcp iron up to 93 GPa and 1100 K: An experimental test of the Birch’s law at high temperature. Earth Planet. Sci. Lett., 331–332, 210–214. https://doi.org/10.1016/j.epsl.2012.03.024

14 Antonangeli, D., Siebert, J., Aracne, C.M., Farber, D.L., Bosak, A., Hoesch, M., et al. (2011). Spin crossover in ferropericlase at high pressure: a seismologically transparent transition? Science, 331, 64–67. https://doi.org/10.1126/science.1198429

15 Auzende, A.‐L., Badro, J., Ryerson, F.J., Weber, P.K., Fallon, S.J., Addad, A., et al. (2008). Element partitioning between magnesium silicate perovskite and ferropericlase: New insights into bulk lower‐mantle geochemistry. Earth Planet. Sci. Lett., 269, 164–174. https://doi.org/10.1016/j.epsl.2008.02.001

16 Badro, J. (2014). Spin transitions in mantle minerals. Annu. Rev. Earth Planet. Sci., 42, 231–248. https://doi.org/10.1146/annurev‐earth‐042711‐105304

17 Badro, J., Fiquet, G., & Guyot, F. (2005). Thermochemical state of the lower mantle: New insights from mineral physics. In van der Hilst, R.D., Bass, J.D., Matas, J., Trampert, J. (Eds.), Earth’s Deep Mantle: Structure, Composition, and Evolution. American Geophysical Union, Washington, D.C., pp. 241–260. https://doi.org/10.1029/160GM15

18 Badro, J., Fiquet, G., Guyot, F., Gregoryanz, E., Occelli, F., Antonangeli, D., & d’Astuto, M. (2007). Effect of light elements on the sound velocities in solid iron: Implications for the composition of Earth’s core. Earth Planet. Sci. Lett., 254, 233–238. https://doi.org/10.1016/j.epsl.2006.11.025

19 Badro, J., Fiquet, G., Guyot, F., Rueff, J.‐P., Struzhkin, V.V., Vankó, G., & Monaco, G. (2003). Iron partitioning in Earth’s mantle: toward a deep lower mantle discontinuity. Science, 300, 789–791. https://doi.org/10.1126/science.1081311

20 Badro, J., Rueff, J.‐P., Vankó, G., Monaco, G., Fiquet, G., & Guyot, F. (2004). Electronic transitions in perovskite: possible nonconvecting layers in the lower mantle. Science, 305, 383–386. https://doi.org/10.1126/science.1098840

21 Ballmer, M.D., Houser, C., Hernlund, J.W., Wentzcovitch, R.M., & Hirose, K. (2017a). Persistence of strong silica‐enriched domains in the Earth’s lower mantle. Nat. Geosci., 10, 236–240. https://doi.org/10.1038/ngeo2898

22 Ballmer, M.D., Lourenço, D.L., Hirose, K., Caracas, R., & Nomura, R. (2017b). Reconciling magma‐ocean crystallization models with the present‐day structure of the Earth’s mantle. Geochem. Geophys. Geosystems, 18, 2785–2806. https://doi.org/10.1002/2017GC006917

23 Ballmer, M.D., Schmerr, N.C., Nakagawa, T., & Ritsema, J. (2015). Compositional mantle layering revealed by slab stagnation at ~1000‐km depth. Sci. Adv., 1, e1500815. https://doi.org/10.1126/sciadv.1500815

24 Baroni, S., de Gironcoli, S., Dal Corso, A., & Giannozzi, P. (2001). Phonons and related crystal properties from density‐functional perturbation theory. Rev. Mod. Phys., 73, 515–562. https://doi.org/10.1103/RevModPhys.73.515

25 Baroni, S., Giannozzi, P., & Testa, A. (1987a). Elastic constants of crystals from linear‐response theory. Phys. Rev. Lett., 59, 2662–2665. https://doi.org/10.1103/PhysRevLett.59.2662

26 Baroni, S., Giannozzi, P., & Testa, A. (1987b). Green’s‐function approach to linear response in solids. Phys. Rev. Lett., 58, 1861–1864. https://doi.org/10.1103/PhysRevLett.58.1861

27 Bass, J.D., & Anderson, D.L. (1984). Composition of the upper mantle: geophysical tests of two petrological models. Geophys. Res. Lett., 11, 229–232. https://doi.org/10.1029/GL011i003p00229

28 Bassett, W.A., Reichmann, H.‐J., Angel, R.J., Spetzler, H., & Smyth, J.R. (2000). New diamond anvil cells for gigahertz ultrasonic interferometry and X‐ray diffraction. Am. Mineral., 85, 283–287. https://doi.org/10.2138/am‐2000‐2‐303

29 Birch, F. (1964). Density and composition of mantle and core. J. Geophys. Res., 69, 4377–4388. https://doi.org/10.1029/JZ069i020p04377

30 Birch, F. (1952). Elasticity and constitution of the Earth’s interior. J. Geophys. Res., 57, 227–286. https://doi.org/10.1029/JZ057i002p00227

31 Birch, F. (1947). Finite elastic strain of cubic crystals. Phys. Rev., 71, 809–824. https://doi.org/10.1103/PhysRev.71.809

32 Birch, F. (1939). The variation of seismic velocities within a simplified Earth model, in accordance with the theory of finite strain. Bull. Seismol. Soc. Am., 29, 463–479.

33 Birch, F. (1938). The effect of pressure upon the elastic parameters of isotropic solids, according to Murnaghan’s theory of finite strain. J. Appl. Phys., 9, 279–288. https://doi.org/10.1063/1.1710417

34 Boffa Ballaran, T., Kurnosov, A., Glazyrin, K., Frost, D.J., Merlini, M., Hanfland, M., & Caracas, R. (2012). Effect of chemistry on the compressibility of silicate perovskite in the lower mantle. Earth Planet. Sci. Lett., 333–334, 181–190. https://doi.org/10.1016/j.epsl.2012.03.029

35 Boffa Ballaran, T., Kurnosov, A., & Trots, D. (2013). Single‐crystal X‐ray diffraction at extreme conditions: a review. High Press. Res., 33, 453–465. https://doi.org/10.1080/08957959.2013.834052

36  Bolfan‐Casanova, N., Andrault, D., Amiguet, E., & Guignot, N. (2009). Equation of state and post‐stishovite transformation of Al‐bearing silica up to 100 GPa and 3000 K. Phys. Earth Planet. Inter., 174, 70–77. https://doi.org/10.1016/j.pepi.2008.06.024

37 Boukaré, C.‐E., Ricard, Y., & Fiquet, G. (2015). Thermodynamics of the MgO‐FeO‐SiO2 system up to 140 GPa: Application to the crystallization of Earth’s magma ocean. J. Geophys. Res. – Solid Earth, 120, 6085–6101. https://doi.org/10.1002/2015JB011929

38 Bower, D.J., Wicks, J.K., Gurnis, M., & Jackson, J.M. (2011). A geodynamic and mineral physics model of a solid‐state ultralow‐velocity zone. Earth Planet. Sci. Lett., 303, 193–202. https://doi.org/10.1016/j.epsl.2010.12.035

39 Brandenburg, J.P., v& an Keken, P.E. (2007). Deep storage of oceanic crust in a vigorously convecting mantle. J. Geophys. Res. – Solid Earth, 112, B06403. https://doi.org/10.1029/2006JB004813

40 Buchen, J., Marquardt, H., Ballaran, T.B., Kawazoe, T., & McCammon, C. (2017). The equation of state of wadsleyite solid solutions: constraining the effects of anisotropy and crystal chemistry. Am. Mineral., 102, 2494–2504. https://doi.org/10.2138/am‐2017‐6162

41 Buchen, J., Marquardt, H., Schulze, K., Speziale, S., Boffa Ballaran, T., Nishiyama, N., & Hanfland, M. (2018a). Equation of state of polycrystalline stishovite across the tetragonal‐orthorhombic phase transition. J. Geophys. Res. – Solid Earth, 123, 7347–7360. https://doi.org/10.1029/2018JB015835

42 Buchen, J., Marquardt, H., Speziale, S., Kawazoe, T., Boffa Ballaran, T., & Kurnosov, A. (2018b). High‐pressure single‐crystal elasticity of wadsleyite and the seismic signature of water in the shallow transition zone. Earth Planet. Sci. Lett., 498, 77–87. https://doi.org/10.1016/j.epsl.2018.06.027

43 Burkel, E. (2000). Phonon spectroscopy by inelastic x‐ray scattering. Rep. Prog. Phys., 63, 171–232. https://doi.org/10.1088/0034‐4885/63/2/203

44 Burns, R.G. (1993). Mineralogical Applications of Crystal Field Theory, 2nd ed., Cambridge University Press, Cambridge. https://doi.org/10.1017/CBO9780511524899

45 Burns, R.G. (1985). Thermodynamic data from crystal field spectra. Rev. Mineral. Geochem., 14, 277–316.

46 Cammarano, F., Deuss, A., Goes, S., & Giardini, D. (2005a). One‐dimensional physical reference models for the upper mantle and transition zone: Combining seismic and mineral physics constraints. J. Geophys. Res. – Solid Earth, 110, B01306. https://doi.org/10.1029/2004JB003272

47 Cammarano, F., Goes, S., Deuss, A., & Giardini, D. (2005b). Is a pyrolitic adiabatic mantle compatible with seismic data? Earth Planet. Sci. Lett., 232, 227–243. https://doi.org/10.1016/j.epsl.2005.01.031

48 Cammarano, F., Goes, S., Vacher, P., & Giardini, D. (2003). Inferring upper‐mantle temperatures from seismic velocities. Phys. Earth Planet. Inter., 138, 197–222. https://doi.org/10.1016/S0031‐9201(03)00156‐0

49 Cammarano, F., Marquardt, H., Speziale, S., & Tackley, P.J. (2010). Role of iron‐spin transition in ferropericlase on seismic interpretation: A broad thermochemical transition in the mid mantle? Geophys. Res. Lett., 37, L03308. https://doi.org/10.1029/2009GL041583

50 Cammarano, F., Romanowicz, B., Stixrude, L., Lithgow‐Bertelloni, C., & Xu, W. (2009). Inferring the thermochemical structure of the upper mantle from seismic data. Geophys. J. Int., 179, 1169–1185. https://doi.org/10.1111/j.1365‐246X.2009.04338.x

51 Campbell, A.J. (2008). Measurement of temperature distributions across laser heated samples by multispectral imaging radiometry. Rev. Sci. Instrum., 79, 015108. https://doi.org/10.1063/1.2827513

52 Car, R., Parrinello, M. (1985). Unified approach for molecular dynamics and density‐functional theory. Phys. Rev. Lett., 55, 2471–2474. https://doi.org/10.1103/PhysRevLett.55.2471

53 Caracas, R. (2010). Spin and structural transitions in AlFeO3 and FeAlO3 perovskite and post‐perovskite. Phys. Earth Planet. Inter., 182, 10–17. https://doi.org/10.1016/j.pepi.2010.06.001

54 Caracas, R., & Cohen, R.E. (2005). Effect of chemistry on the stability and elasticity of the perovskite and post‐perovskite phases in the MgSiO3‐FeSiO3‐Al2O3 system and implications for the lowermost mantle. Geophys. Res. Lett., 32, L16310. https://doi.org/10.1029/2005GL023164

55 Carpenter, M.A. (2006). Elastic properties of minerals and the influence of phase transitions. Am. Mineral., 91, 229–246. https://doi.org/10.2138/am.2006.1979

56 Carpenter, M.A., Hemley, R.J., & Mao, H. (2000). High‐pressure elasticity of stishovite and the P42/mnm ⇌ Pnnm phase transition. J. Geophys. Res. – Solid Earth, 105, 10807–10816. https://doi.org/10.1029/1999JB900419

57 Carpenter, M.A., & Salje, E.K.H. (1998). Elastic anomalies in minerals due to structural phase transitions. Eur. J. Mineral., 10, 693–812. https://doi.org/10.1127/ejm/10/4/0693

58 Carpenter, M.A., Salje, E.K.H., & Graeme‐Barber, A. (1998). Spontaneous strain as a determinant of thermodynamic properties for phase transitions in minerals. Eur. J. Mineral., 10, 621–691. https://doi.org/10.1127/ejm/10/4/0621

59 Carrier, P., Wentzcovitch, R., & Tsuchiya, J. (2007). First‐principles prediction of crystal structures at high temperatures using the quasiharmonic approximation. Phys. Rev. B, 76, 064116. https://doi.org/10.1103/PhysRevB.76.064116

60 Catalli, K., Shim, S.‐H., Prakapenka, V.B., Zhao, J., Sturhahn, W., Chow, P., et al. (2010). Spin state of ferric iron in MgSiO3 perovskite and its effect on elastic properties. Earth Planet. Sci. Lett., 289, 68–75. https://doi.org/10.1016/j.epsl.2009.10.029

61 Chantel, J., Frost, D.J., McCammon, C.A., Jing, Z., & Wang, Y. (2012). Acoustic velocities of pure and iron‐bearing magnesium silicate perovskite measured to 25 GPa and 1200 K. Geophys. Res. Lett., 39, L19307. https://doi.org/10.1029/2012GL053075

62 Chen, B., Jackson, J.M., Sturhahn, W., Zhang, D., Zhao, J., Wicks, J.K., & Murphy, C.A. (2012). Spin crossover equation of state and sound velocities of (Mg0.65Fe0.35)O ferropericlase to 140 GPa. J. Geophys. Res. – Solid Earth, 117, B08208. https://doi.org/10.1029/2012JB009162

63 Chung, D.H., & Buessem, W.R. (1967). The Voigt‐Reuss‐Hill approximation and elastic moduli of polycrystalline MgO, CaF2, β‐ZnS, ZnSe, and CdTe. J. Appl. Phys., 38, 2535–2540. https://doi.org/10.1063/1.1709944

64 Chust, T.C., Steinle‐Neumann, G., Dolejš, D., Schuberth, B.S.A., & Bunge, H.‐P. (2017). MMA‐EoS: a computational framework for mineralogical thermodynamics. J. Geophys. Res. – Solid Earth, 122, 9881–9920. https://doi.org/10.1002/2017JB014501

65 Cobden, L., Goes, S., Cammarano, F., & Connolly, J.A.D. (2008). Thermochemical interpretation of one‐dimensional seismic reference models for the upper mantle: evidence for bias due to heterogeneity. Geophys. J. Int., 175, 627–648. https://doi.org/10.1111/j.1365‐246X.2008.03903.x

66 Cobden, L., Goes, S., Ravenna, M., Styles, E., Cammarano, F., Gallagher, K., & Connolly, J.A.D. (2009). Thermochemical interpretation of 1‐D seismic data for the lower mantle: The significance of nonadiabatic thermal gradients and compositional heterogeneity. J. Geophys. Res. – Solid Earth, 114, B11309. https://doi.org/10.1029/2008JB006262

67 Cococcioni, M. (2010). Accurate and efficient calculations on strongly correlated minerals with the LDA+U method: Review and perspectives. Rev. Mineral. Geochem., 71, 147–167. https://doi.org/10.2138/rmg.2010.71.8

68 Cococcioni, M., & de Gironcoli, S. (2005). Linear response approach to the calculation of the effective interaction parameters in the LDA+U method. Phys. Rev. B, 71, 035105. https://doi.org/10.1103/PhysRevB.71.035105

69 Connolly, J.A.D. (2005). Computation of phase equilibria by linear programming: A tool for geodynamic modeling and its application to subduction zone decarbonation. Earth Planet. Sci. Lett., 236, 524–541. https://doi.org/10.1016/j.epsl.2005.04.033

70 Cox, P.A. (1987). The Electronic Structure and Chemistry of Solids. Oxford University Press, Oxford.

71 Crowhurst, J.C., Brown, J.M., Goncharov, A.F., & Jacobsen, S.D. (2008). Elasticity of (Mg,Fe)O through the spin transition of iron in the lower mantle. Science, 319, 451–453. https://doi.org/10.1126/science.1149606

72 Cummins, H.Z., & Schoen, P.E. (1972). Linear scattering from thermal fluctuations. In Arecchi, F.T., Schulz‐DuBois, E.O. (Eds.), Laser Handbook. North‐Holland Publishing Company, Amsterdam, pp. 1029–1075.

73 Dai, L., Kudo, Y., Hirose, K., Murakami, M., Asahara, Y., Ozawa, H., et al. (2013). Sound velocities of Na0.4Mg0.6Al1.6Si0.4O4 NAL and CF phases to 73 GPa determined by Brillouin scattering method. Phys. Chem. Miner., 40, 195–201. https://doi.org/10.1007/s00269‐012‐0558‐0

74 Davies, D.R., Goes, S., Davies, J.H., Schuberth, B.S.A., Bunge, H.‐P., & Ritsema, J. (2012). Reconciling dynamic and seismic models of Earth’s lower mantle: The dominant role of thermal heterogeneity. Earth Planet. Sci. Lett., 353–354, 253–269. https://doi.org/10.1016/j.epsl.2012.08.016

75 Davies, G.F. (1974). Effective elastic moduli under hydrostatic stress—I. Quasi‐harmonic theory. J. Phys. Chem. Solids, 35, 1513–1520. https://doi.org/10.1016/S0022‐3697(74)80279‐9

76 Davies, G.F., & Dziewonski, A.M. (1975). Homogeneity and constitution of the earth’s lower mantle and outer core. Phys. Earth Planet. Inter., 10, 336–343. https://doi.org/10.1016/0031‐9201(75)90060‐6

77 Decremps, F., Antonangeli, D., Gauthier, M., Ayrinhac, S., Morand, M., Marchand, et al. (2014). Sound velocity of iron up to 152 GPa by picosecond acoustics in diamond anvil cell. Geophys. Res. Lett., 41, 1459–1464. https://doi.org/10.1002/2013GL058859

78 Decremps, F., Belliard, L., Gauthier, M., & Perrin, B. (2010). Equation of state, stability, anisotropy and nonlinear elasticity of diamond‐cubic (ZB) silicon by phonon imaging at high pressure. Phys. Rev. B, 82, 104119. https://doi.org/10.1103/PhysRevB.82.104119

79 Decremps, F., Belliard, L., Perrin, B., & Gauthier, M. (2008). Sound velocity and absorption measurements under high pressure using picosecond ultrasonics in a diamond anvil cell: Application to the stability study of AlPdMn. Phys. Rev. Lett., 100, 035502. https://doi.org/10.1103/PhysRevLett.100.035502

80 Deschamps, F., Cobden, L., & Tackley, P.J. (2012). The primitive nature of large low shear‐wave velocity provinces. Earth Planet. Sci. Lett., 349–350, 198–208. https://doi.org/10.1016/j.epsl.2012.07.012

81 Deschamps, F., & Trampert, J. (2004). Towards a lower mantle reference temperature and composition. Earth Planet. Sci. Lett., 222, 161–175. https://doi.org/10.1016/j.epsl.2004.02.024

82 Dil, J.G. (1982). Brillouin scattering in condensed matter. Rep. Prog. Phys., 45, 285–334. https://doi.org/10.1088/0034‐4885/45/3/002

83 Drickamer, H.G., & Frank, C.W. (1973). Electronic Transitions and the High Pressure Chemistry and Physics of Solids. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-6896-0.

84 Duffy, T.S., & Anderson, D.L. (1989). Seismic velocities in mantle minerals and the mineralogy of the upper mantle. J. Geophys. Res. – Solid Earth, 94, 1895–1912. https://doi.org/10.1029/JB094iB02p01895

85 Durand, S., Debayle, E., Ricard, Y., Zaroli, C., & Lambotte, S. (2017). Confirmation of a change in the global shear velocity pattern at around 1000 km depth. Geophys. J. Int., 211, 1628–1639. https://doi.org/10.1093/gji/ggx405

86 Dziewonski, A.M., & Anderson, D.L. (1981). Preliminary reference Earth model. Phys. Earth Planet. Inter., 25, 297–356. https://doi.org/10.1016/0031‐9201(81)90046‐7

87 Fayer, M.D. (1982). Dynamics of molecules in condensed phases: picosecond holographic grating experiments. Annu. Rev. Phys. Chem., 33, 63–87. https://doi.org/10.1146/annurev.pc.33.100182.000431

88 Fei, Y., Zhang, L., Corgne, A., Watson, H., Ricolleau, A., Meng, Y., & Prakapenka, V. (2007). Spin transition and equations of state of (Mg, Fe)O solid solutions. Geophys. Res. Lett., 34, L17307. https://doi.org/10.1029/2007GL030712

89 Finkelstein, G.J., Jackson, J.M., Said, A., Alatas, A., Leu, B.M., Sturhahn, W., & Toellner, T.S. (2018). Strongly anisotropic magnesiowüstite in Earth’s lower mantle. J. Geophys. Res. – Solid Earth, 123, 4740–4750. https://doi.org/10.1029/2017JB015349

90 Fiquet, G., Auzende, A.L., Siebert, J., Corgne, A., Bureau, H., Ozawa, H., & Garbarino, G. (2010). Melting of peridotite to 140 gigapascals. Science, 329, 1516–1518. https://doi.org/10.1126/science.1192448

91  Fiquet, G., Badro, J., Guyot, F., Bellin, C., Krisch, M., Antonangeli, D., et al. (2004). Application of inelastic X‐ray scattering to the measurements of acoustic wave velocities in geophysical materials at very high pressure. Phys. Earth Planet. Inter., 143–144, 5–18. https://doi.org/10.1016/j.pepi.2003.10.005

92 Fiquet, G., Badro, J., Guyot, F., Requardt, H., & Krisch, M. (2001). Sound velocities in iron to 110 gigapascals. Science, 291, 468–471. https://doi.org/10.1126/science.291.5503.468

93 Fiquet, G., Dewaele, A., Andrault, D., Kunz, M., Bihan, T.L. (2000). Thermoelastic properties and crystal structure of MgSiO3 perovskite at lower mantle pressure and temperature conditions. Geophys. Res. Lett., 27, 21–24. https://doi.org/10.1029/1999GL008397

94 Fischer, R.A., Campbell, A.J., Chidester, B.A., Reaman, D.M., Thompson, E.C., Pigott, J.S., et al. (2018). Equations of state and phase boundary for stishovite and CaCl2‐type SiO2. Am. Mineral., 103, 792–802. https://doi.org/10.2138/am‐2018‐6267

95 Frost, D.A., Rost, S., Garnero, E.J., & Li, M. (2017). Seismic evidence for Earth’s crusty deep mantle. Earth Planet. Sci. Lett., 470, 54–63. https://doi.org/10.1016/j.epsl.2017.04.036

96 Frost, D.J., & Langenhorst, F. (2002). The effect of Al2O3 on Fe‐Mg partitioning between magnesiowüstite and magnesium silicate perovskite. Earth Planet. Sci. Lett., 199, 227–241.

97 Frost, D.J., Liebske, C., Langenhorst, F., McCammon, C.A., Trønnes, R.G., & Rubie, D.C. (2004). Experimental evidence for the existence of iron‐rich metal in the Earth’s lower mantle. Nature, 428, 409–412. https://doi.org/10.1038/nature02413

98 Fu, S., Yang, J., Tsujino, N., Okuchi, T., Purevjav, N., & Lin, J.‐F. (2019). Single‐crystal elasticity of (Al,Fe)‐bearing bridgmanite and seismic shear wave radial anisotropy at the topmost lower mantle. Earth Planet. Sci. Lett., 518, 116–126. https://doi.org/10.1016/j.epsl.2019.04.023

99 Fu, S., Yang, J., Zhang, Y., Okuchi, T., McCammon, C., Kim, H.‐I., et al. (2018). Abnormal elasticity of Fe‐bearing bridgmanite in the Earth’s lower mantle. Geophys. Res. Lett., 45, 4725–4732. https://doi.org/10.1029/2018GL077764

100 Fujino, K., Nishio‐Hamane, D., Suzuki, K., Izumi, H., Seto, Y., & Nagai, T. (2009). Stability of the perovskite structure and possibility of the transition to the post‐perovskite structure in CaSiO3, FeSiO3, MnSiO3 and CoSiO3. Phys. Earth Planet. Inter., 177, 147–151. https://doi.org/10.1016/j.pepi.2009.08.009

101 Fukao, Y., & Obayashi, M. (2013). Subducted slabs stagnant above, penetrating through, and trapped below the 660 km discontinuity. J. Geophys. Res. – Solid Earth, 118, 5920–5938. https://doi.org/10.1002/2013JB010466

102 Funamori, N., & Jeanloz, R. (1997). High‐pressure transformation of Al2O3. Science, 278, 1109–1111. https://doi.org/10.1126/science.278.5340.1109

103 Funamori, N., Jeanloz, R., Miyajima, N., & Fujino, K. (2000). Mineral assemblages of basalt in the lower mantle. J. Geophys. Res. – Solid Earth, 105, 26037–26043. https://doi.org/10.1029/2000JB900252

104 Gaffney, E.S. (1972). Crystal field effects in mantle minerals. Phys. Earth Planet. Inter., 6, 385–390. https://doi.org/10.1016/0031‐9201(72)90062‐3

105 Gaffney, E.S., & Anderson, D.L. (1973). Effect of low‐spin Fe2+ on the composition of the lower mantle. J. Geophys. Res., 78, 7005–7014. https://doi.org/10.1029/JB078i029p07005

106 Garnero, E.J., McNamara, A.K., & Shim, S.‐H. (2016). Continent‐sized anomalous zones with low seismic velocity at the base of Earth’s mantle. Nat. Geosci., 9, 481–489. https://doi.org/10.1038/ngeo2733

107 Giannozzi, P., de Gironcoli, S., Pavone, P., & Baroni, S. (1991). Ab initio calculation of phonon dispersions in semiconductors. Phys. Rev. B, 43, 7231–7242. https://doi.org/10.1103/PhysRevB.43.7231

108 Giura, P., Paulatto, L., He, F., Lobo, R.P.S.M., Bosak, A., Calandrini, E., et al. (2019). Multiphonon anharmonicity of MgO. Phys. Rev. B, 99, 220304. https://doi.org/10.1103/PhysRevB.99.220304

109 Glazyrin, K., Boffa Ballaran, T., Frost, D.J., McCammon, C., Kantor, A., Merlini, M., et al. (2014). Magnesium silicate perovskite and effect of iron oxidation state on its bulk sound velocity at the conditions of the lower mantle. Earth Planet. Sci. Lett., 393, 182–186. https://doi.org/10.1016/j.epsl.2014.01.056

110 Gréaux, S., Irifune, T., Higo, Y., Tange, Y., Arimoto, T., Liu, Z., & Yamada, A. (2019). Sound velocity of CaSiO3 perovskite suggests the presence of basaltic crust in the Earth’s lower mantle. Nature, 565, 218–221. https://doi.org/10.1038/s41586‐018‐0816‐5

111 Gréaux, S., Kono, Y., Wang, Y., Yamada, A., Zhou, C., Jing, Z., et al. (2016). Sound velocities of aluminum‐bearing stishovite in the mantle transition zone. Geophys. Res. Lett., 43, 4239–4246. https://doi.org/10.1002/2016GL068377

112 Gwanmesia, G.D., Liebermann, R.C., & Guyot, F. (1990). Hot‐pressing and characterization of polycrystals of β‐Mg2SiO4, for acoustic velocity measurements. Geophys. Res. Lett., 17, 1331–1334. https://doi.org/10.1029/GL017i009p01331

113 Haussühl, S. (2007). Physical Properties of Crystals: An Introduction. Wiley‐VCH, Weinheim. https://doi.org/10.1002/9783527621156

114 Hill, R. (1952). The elastic behaviour of a crystalline aggregate. Proc. Phys. Soc., A65, 349–354. https://doi.org/10.1088/0370‐1298/65/5/307

115 Hirose, K., Fei, Y., Ma, Y., & Mao, H.‐K. (1999). The fate of subducted basaltic crust in the Earth’s lower mantle. Nature, 397, 53–56. https://doi.org/10.1038/16225

116 Hirose, K., Takafuji, N., Sata, N., & Ohishi, Y. (2005). Phase transition and density of subducted MORB crust in the lower mantle. Earth Planet. Sci. Lett., 237, 239–251. https://doi.org/10.1016/j.epsl.2005.06.035

117 Hofmann, A.W. (1997). Mantle geochemistry: the message from oceanic volcanism. Nature, 385, 219–229. https://doi.org/10.1038/385219a0

118 Hohenberg, P., & Kohn, W. (1964). Inhomogeneous electron gas. Phys. Rev., 136, B864–B871. https://doi.org/10.1103/PhysRev.136.B864

119 Holland, T.J.B., Hudson, N.F.C., Powell, R., & Harte, B. (2013). New thermodynamic models and calculated phase equilibria in NCFMAS for basic and ultrabasic compositions through the transition zone into the uppermost lower mantle. J. Petrol., 54, 1901–1920. https://doi.org/10.1093/petrology/egt035

120 Holmström, E., & Stixrude, L. (2015). Spin crossover in ferropericlase from first‐principles molecular dynamics. Phys. Rev. Lett., 114, 117202. https://doi.org/10.1103/PhysRevLett.114.117202

121 Holzapfel, W. (2009). Equations of state for solids under strong compression. Z. Kristallogr. – Cryst. Mater., 216, 473–488. https://doi.org/10.1524/zkri.216.9.473.20346

122 Hosseini, K., Sigloch, K., Tsekhmistrenko, M., Zaheri, A., Nissen‐Meyer, T., & Igel, H. (2020). Global mantle structure from multifrequency tomography using P, PP and P‐diffracted waves. Geophys. J. Int., 220, 96–141. https://doi.org/10.1093/gji/ggz394

123 Hsu, H., Blaha, P., Cococcioni, M., & Wentzcovitch, R.M. (2011). Spin‐state crossover and hyperfine interactions of ferric iron in MgSiO3 perovskite. Phys. Rev. Lett., 106, 118501. https://doi.org/10.1103/PhysRevLett.106.118501

124 Hsu, H., Umemoto, K., Blaha, P., & Wentzcovitch, R.M. (2010a). Spin states and hyperfine interactions of iron in (Mg,Fe)SiO3 perovskite under pressure. Earth Planet. Sci. Lett., 294, 19–26. https://doi.org/10.1016/j.epsl.2010.02.031

125 Hsu, H., Umemoto, K., Wu, Z., & Wentzcovitch, R.M. (2010b). Spin‐state crossover of iron in lower‐mantle minerals: Results of DFT+U investigations. Rev. Mineral. Geochem, 71, 169–199. https://doi.org/10.2138/rmg.2010.71.09

126 Hubbard, J. (1963). Electron correlations in narrow energy bands. Proc. R. Soc. Lond. A, 276, 238–257. https://doi.org/10.1098/rspa.1963.0204

127 Hyung, E., Huang, S., Petaev, M.I., Jacobsen, S.B. (2016). Is the mantle chemically stratified? Insights from sound velocity modeling and isotope evolution of an early magma ocean. Earth Planet. Sci. Lett., 440, 158–168. https://doi.org/10.1016/j.epsl.2016.02.001

128 Imada, S., Hirose, K., Komabayashi, T., Suzuki, T., & Ohishi, Y. (2012). Compression of Na0.4Mg0.6Al1.6Si0.4O4 NAL and Ca‐ferrite‐type phases. Phys. Chem. Miner., 39, 525–530. https://doi.org/10.1007/s00269‐012‐0508‐x

129 Immoor, J., Marquardt, H., Miyagi, L., Speziale, S., Merkel, S., Schwark, I., et al. (2020). An improved setup for radial diffraction experiments at high pressures and high temperatures in a resistive graphite‐heated diamond anvil cell. Rev. Sci. Instrum., 91, 045121. https://doi.org/10.1063/1.5143293

130 Irifune, T., Shinmei, T., McCammon, C.A., Miyajima, N., Rubie, D.C., & Frost, D.J. (2010). Iron partitioning and density changes of pyrolite in Earth’s lower mantle. Science, 327, 193–195. https://doi.org/10.1126/science.1181443

131 Isaak, D.G. (1992). High‐temperature elasticity of iron‐bearing olivines. J. Geophys. Res. – Solid Earth, 97, 1871–1885. https://doi.org/10.1029/91JB02675

132 Isaak, D.G., Anderson, O.L., Goto, T., & Suzuki, I. (1989). Elasticity of single‐crystal forsterite measured to 1700 K. J. Geophys. Res. – Solid Earth, 94, 5895–5906. https://doi.org/10.1029/JB094iB05p05895

133 Ishii, M., & Tromp, J. (1999). Normal‐mode and free‐air gravity constraints on lateral variations in velocity and density of Earth’s mantle. Science, 285, 1231–1236. https://doi.org/10.1126/science.285.5431.1231

134 Ishii, T., Liu, Z., & Katsura, T. (2019). A breakthrough in pressure generation by a Kawai‐type multi‐anvil apparatus with tungsten carbide anvils. Engineering, 5, 434–440. https://doi.org/10.1016/j.eng.2019.01.013

135 Ita, J., & Stixrude, L. (1992). Petrology, elasticity, and composition of the mantle transition zone. J. Geophys. Res. – Solid Earth, 97, 6849–6866. https://doi.org/10.1029/92JB00068

136 Jackson, I. (2015). Properties of rocks and minerals: Physical origins of anelasticity and attenuation in rock. In Schubert, G. (Ed.), Treatise on Geophysics, 2nd ed., Elsevier, Amsterdam, pp. 539–571. https://doi.org/10.1016/B978‐0‐444‐53802‐4.00045‐2

137 Jackson, I. (1998). Elasticity, composition and temperature of the Earth’s lower mantle: a reappraisal. Geophys. J. Int., 134, 291–311. https://doi.org/10.1046/j.1365‐246x.1998.00560.x

138 Jackson, J.M., Sturhahn, W., Shen, G., Zhao, J., Hu, M.Y., Errandonea, D., et al. (2005a). A synchrotron Mössbauer spectroscopy study of (Mg,Fe)SiO3 perovskite up to 120 GPa. Am. Mineral., 90, 199–205. https://doi.org/10.2138/am.2005.1633

139 Jackson, J.M., Zhang, J., Shu, J., Sinogeikin, S.V., Bass, J.D. (2005b). High‐pressure sound velocities and elasticity of aluminous MgSiO3 perovskite to 45 GPa: Implications for lateral heterogeneity in Earth’s lower mantle. Geophys. Res. Lett., 32, L21305. https://doi.org/10.1029/2005GL023522

140 Jacobsen, S.D., Reichmann, H.‐J., Spetzler, H.A., Mackwell, S.J., Smyth, J.R., et al. (2002). Structure and elasticity of single‐crystal (Mg,Fe)O and a new method of generating shear waves for gigahertz ultrasonic interferometry. J. Geophys. Res. – Solid Earth, 107, ECV 4‐1–ECV 4‐14. https://doi.org/10.1029/2001JB000490

141 Jacobsen, S.D., Spetzler, H., Reichmann, H.J., & Smyth, J.R. (2004). Shear waves in the diamond‐anvil cell reveal pressure‐induced instability in (Mg,Fe)O. Proc. Natl. Acad. Sci. U.S.A., 101, 5867–5871. https://doi.org/10.1073/pnas.0401564101

142 Jiang, F., Gwanmesia, G.D., Dyuzheva, T.I., & Duffy, T.S. (2009). Elasticity of stishovite and acoustic mode softening under high pressure by Brillouin scattering. Phys. Earth Planet. Inter., 172, 235–240. https://doi.org/10.1016/j.pepi.2008.09.017

143 Kaneshima, S., Helffrich, G. (2009). Lower mantle scattering profiles and fabric below Pacific subduction zones. Earth Planet. Sci. Lett., 282, 234–239. https://doi.org/10.1016/j.epsl.2009.03.024

144 Kantor, I., Prakapenka, V., Kantor, A., Dera, P., Kurnosov, A., Sinogeikin, S., et al. (2012). BX90: A new diamond anvil cell design for X‐ray diffraction and optical measurements. Rev. Sci. Instrum., 83, 125102. https://doi.org/10.1063/1.4768541

145 Karato, S. (2008). Deformation of Earth Materials: An Introduction to the Rheology of Solid Earth. Cambridge University Press, Cambridge. https://doi.org/10.1017/CBO9780511804892

146 Karato, S. (1993). Importance of anelasticity in the interpretation of seismic tomography. Geophys. Res. Lett., 20, 1623–1626. https://doi.org/10.1029/93GL01767

147 Karki, B.B., Stixrude, L., & Crain, J. (1997a). Ab initio elasticity of three high‐pressure polymorphs of silica. Geophys. Res. Lett., 24, 3269–3272. https://doi.org/10.1029/97GL53196

148  Karki, B.B., Stixrude, L., & Wentzcovitch, R.M. (2001a). High‐pressure elastic properties of major materials of Earth’s mantle from first principles. Rev. Geophys., 39, 507–534. https://doi.org/10.1029/2000RG000088

149 Karki, B.B., Warren, M.C., Stixrude, L., Ackland, G.J., & Crain, J. (1997b). Ab initio studies of high‐pressure structural transformations in silica. Phys. Rev. B, 55, 3465–3471. https://doi.org/10.1103/PhysRevB.55.3465

150 Karki, B.B., Wentzcovitch, R.M., de Gironcoli, S., & Baroni, S. (2000). High‐pressure lattice dynamics and thermoelasticity of MgO. Phys. Rev. B, 61, 8793–8800. https://doi.org/10.1103/PhysRevB.61.8793

151 Karki, B.B., Wentzcovitch, R.M., de Gironcoli, S., & Baroni, S. (2001b). First principles thermoelasticity of MgSiO3‐perovskite: consequences for the inferred properties of the lower mantle. Geophys. Res. Lett., 28, 2699–2702. https://doi.org/10.1029/2001GL012910

152 Karki, B.B., Wentzcovitch, R.M., de Gironcoli, S., & Baroni, S. (1999). First‐principles determination of elastic anisotropy and wave velocities of MgO at lower mantle conditions. Science, 286, 1705–1707. https://doi.org/10.1126/science.286.5445.1705

153 Kato, J., Hirose, K., Ozawa, H., & Ohishi, Y. (2013). High‐pressure experiments on phase transition boundaries between corundum, Rh2O3(II)‐and CaIrO3‐type structures in Al2O3. Am. Mineral., 98, 335–339. https://doi.org/10.2138/am.2013.4133

154 Katsura, T., Yoneda, A., Yamazaki, D., Yoshino, T., & Ito, E. (2010). Adiabatic temperature profile in the mantle. Phys. Earth Planet. Inter., 183, 212–218. https://doi.org/10.1016/j.pepi.2010.07.001

155 Kavner, A., & Nugent, C. (2008). Precise measurements of radial temperature gradients in the laser‐heated diamond anvil cell. Rev. Sci. Instrum., 79, 024902. https://doi.org/10.1063/1.2841173

156 Kawai, K., & Tsuchiya, T. (2015). Small shear modulus of cubic CaSiO3 perovskite. Geophys. Res. Lett., 42, 2718–2726. https://doi.org/10.1002/2015GL063446

157 Kennett, B.L.N., & Engdahl, E.R. (1991). Traveltimes for global earthquake location and phase identification. Geophys. J. Int., 105, 429–465. https://doi.org/10.1111/j.1365‐246X.1991.tb06724.x

158 Kennett, B.L.N., Engdahl, E.R., & Buland, R. (1995). Constraints on seismic velocities in the Earth from traveltimes. Geophys. J. Int., 122, 108–124. https://doi.org/10.1111/j.1365‐246X.1995.tb03540.x

159 Keppler, H., Kantor, I., & Dubrovinsky, L.S. (2007). Optical absorption spectra of ferropericlase to 84 GPa. Am. Mineral., 92, 433–436. https://doi.org/10.2138/am.2007.2454

160 Kesson, S.E., Gerald, J.D.F., & Shelley, J.M. (1998). Mineralogy and dynamics of a pyrolite lower mantle. Nature, 393, 252–255. https://doi.org/10.1038/30466

161 Kesson, S.E., Gerald, J.D.F., & Shelley, J.M.G. (1994). Mineral chemistry and density of subducted basaltic crust at lower‐mantle pressures. Nature, 372, 767–769. https://doi.org/10.1038/372767a0

162 Khan, A., Connolly, J.A.D., & Taylor, S.R. (2008). Inversion of seismic and geodetic data for the major element chemistry and temperature of the Earth’s mantle. J. Geophys. Res. – Solid Earth, 113, B09308. https://doi.org/10.1029/2007JB005239

163 Kobayashi, Y., Kondo, T., Ohtani, E., Hirao, N., Miyajima, N., Yagi, T., et al. (2005). Fe‐Mg partitioning between (Mg, Fe)SiO3 post‐perovskite, perovskite, and magnesiowüstite in the Earth’s lower mantle. Geophys. Res. Lett., 32, L19301. https://doi.org/10.1029/2005GL023257

164 Koelemeijer, P., Ritsema, J., Deuss, A., & van Heijst, H.‐J. (2016). SP12RTS: a degree‐12 model of shear‐ and compressional‐wave velocity for Earth’s mantle. Geophys. J. Int., 204, 1024–1039. https://doi.org/10.1093/gji/ggv481

165 Kohn, W., & Sham, L.J. (1965). Self‐consistent equations including exchange and correlation effects. Phys. Rev., 140, A1133–A1138. https://doi.org/10.1103/PhysRev.140.A1133

166 Komabayashi, T., Hirose, K., Nagaya, Y., Sugimura, E., & Ohishi, Y. (2010). High‐temperature compression of ferropericlase and the effect of temperature on iron spin transition. Earth Planet. Sci. Lett., 297, 691–699. https://doi.org/10.1016/j.epsl.2010.07.025

167 Komabayashi, T., & Omori, S. (2006). Internally consistent thermodynamic data set for dense hydrous magnesium silicates up to 35GPa, 1600°C: Implications for water circulation in the Earth’s deep mantle. Phys. Earth Planet. Inter., 156, 89–107. https://doi.org/10.1016/j.pepi.2006.02.002

168 Krebs, J.J., & Maisch, W.G. (1971). Exchange effects in the optical‐absorption spectrum of Fe3+ in Al2O3. Phys. Rev. B, 4, 757–769. https://doi.org/10.1103/PhysRevB.4.757

169 Kurnosov, A., Marquardt, H., Dubrovinsky, L., & Potapkin, V. (2019). A waveguide‐based flexible CO2‐laser heating system for diamond‐anvil cell applications. Comptes Rendus Geosci., 351, 280–285. https://doi.org/10.1016/j.crte.2018.09.008

170 Kurnosov, A., Marquardt, H., Frost, D.J., Ballaran, T.B., & Ziberna, L. (2017). Evidence for a Fe3+‐rich pyrolitic lowermantle from (Al,Fe)‐bearing bridgmanite elasticity data. Nature, 543, 543–546. https://doi.org/10.1038/nature21390

171 Labrosse, S., Hernlund, J.W., & Hirose, K. (2015). Fractional melting and freezing in the deep mantle and implications for the formation of a basal magma ocean. In Badro, J., Walter, M. (Eds.), The Early Earth: Accretion and Differentiation. American Geophysical Union, Washington, D.C., pp. 123–142. https://doi.org/10.1002/9781118860359.ch7

172 Lakshtanov, D.L., Sinogeikin, S.V., Litasov, K.D., Prakapenka, V.B., & Hellwig, H., Wang, J., et al. (2007). The post‐stishovite phase transition in hydrous alumina‐bearing SiO2 in the lower mantle of the earth. Proc. Natl. Acad. Sci. U.S.A., 104, 13588–13590. https://doi.org/10.1073/pnas.0706113104

173 Lehmann, G., Harder, H. (1970). Optical spectra of di‐ and trivalent iron in corundum. Am. Mineral., 55, 98–105.

174 Li, B., Kung, J., & Liebermann, R.C. (2004). Modern techniques in measuring elasticity of Earth materials at high pressure and high temperature using ultrasonic interferometry in conjunction with synchrotron X‐radiation in multi‐anvil apparatus. Phys. Earth Planet. Inter., 143–144, 559–574. https://doi.org/10.1016/j.pepi.2003.09.020

175 Li, B., Liebermann, R.C. (2014). Study of the Earth’s interior using measurements of sound velocities in minerals by ultrasonic interferometry. Phys. Earth Planet. Inter., 233, 135–153. https://doi.org/10.1016/j.pepi.2014.05.006

176 Li, J., Struzhkin, V.V., Mao, H., Shu, J., Hemley, R.J., Fei, Y., Mysen, B., et al. (2004). Electronic spin state of iron in lower mantle perovskite. Proc. Natl. Acad. Sci. U.S.A., 101, 14027–14030. https://doi.org/10.1073/pnas.0405804101

177 Li, X., Mao, Z., Sun, N., Liao, Y., Zhai, S., Wang, Y., et al. (2016). Elasticity of single‐crystal superhydrous phase B at simultaneous high pressure‐temperature conditions. Geophys. Res. Lett., 43, 8458–8465. https://doi.org/10.1002/2016GL070027

178 Liermann, H.‐P., Merkel, S., Miyagi, L., Wenk, H.‐R., Shen, G., Cynn, H., & Evans, W.J. (2009). Experimental method for in situ determination of material textures at simultaneous high pressure and high temperature by means of radial diffraction in the diamond anvil cell. Rev. Sci. Instrum., 80, 104501. https://doi.org/10.1063/1.3236365

179 Lin, J.‐F., Degtyareva, O., Prewitt, C.T., Dera, P., Sata, N., Gregoryanz, E., et al. (2004). Crystal structure of a high‐pressure/high‐temperature phase of alumina by in situ X‐ray diffraction. Nat. Mater., 3, 389–393. https://doi.org/10.1038/nmat1121

180 Lin, J.‐F., Jacobsen, S.D., Sturhahn, W., Jackson, J.M., Zhao, J., & Yoo, C.‐S. (2006). Sound velocities of ferropericlase in the Earth’s lower mantle. Geophys. Res. Lett., 33, L22304. https://doi.org/10.1029/2006GL028099

181 Lin, J.‐F., Mao, Z., Yang, J., Liu, J., Xiao, Y., Chow, P., & Okuchi, T. (2016). High‐spin Fe2+ and Fe3+ in single‐crystal aluminous bridgmanite in the lower mantle. Geophys. Res. Lett., 43, 6952–6959. https://doi.org/10.1002/2016GL069836

182 Lin, J.‐F., Speziale, S., Mao, Z., & Marquardt, H. (2013). Effects of the electronic spin transitions of iron in lower mantle minerals: Implications for deep mantle geophysics and geochemistry. Rev. Geophys., 51, 244–275. https://doi.org/10.1002/rog.20010

183 Lin, J.‐F., Struzhkin, V.V., Jacobsen, S.D., Hu, M.Y., Chow, P., Kung, J., et al. (2005). Spin transition of iron in magnesiowüstite in the Earth’s lower mantle. Nature, 436, 377–380. https://doi.org/10.1038/nature03825

184 Lin, J.‐F., & Tsuchiya, T. (2008). Spin transition of iron in the Earth’s lower mantle. Phys. Earth Planet. Inter., 170, 248–259. https://doi.org/10.1016/j.pepi.2008.01.005

185 Lin, J.‐F., Vanko, G., Jacobsen, S.D., Iota, V., Struzhkin, V.V., Prakapenka, V.B., et al. (2007). Spin transition zone in Earth’s lower mantle. Science, 317, 1740–1743. https://doi.org/10.1126/science.1144997

186 Liu, J., Dorfman, S.M., Zhu, F., Li, J., Wang, Y., Zhang, D., Xiao, Y., et al. (2018). Valence and spin states of iron are invisible in Earth’s lower mantle. Nat. Commun., 9, 1284. https://doi.org/10.1038/s41467‐018‐03671‐5

187 Mainprice, D. (2015). Seismic anisotropy of the deep Earth from a mineral and rock physics perspective. In Schubert, G. (Ed.), Treatise on Geophysics, 2nd ed., Elsevier, Amsterdam, pp. 487–538. https://doi.org/10.1016/B978-0-444-53802-4.00044-0

188 Mainprice, D., Barruol, G., Ismail, W.B. (2000). The seismic anisotropy of the Earth’s mantle: from single crystal to polycrystal. In Karato, S.‐I., Forte, A., Liebermann, R., Masters, G., Stixrude, L. (Eds.), Earth’s Deep Interior: Mineral Physics and Tomography From the Atomic to the Global Scale. American Geophysical Union, Washington, D.C., pp. 237–264. https://doi.org/10.1029/GM117p0237

189 Mao, Z., Fan, D., Lin, J.‐F., Yang, J., Tkachev, S.N., Zhuravlev, K., & Prakapenka, V.B. (2015). Elasticity of single‐crystal olivine at high pressures and temperatures. Earth Planet. Sci. Lett., 426, 204–215. https://doi.org/10.1016/j.epsl.2015.06.045

190 Mao, Z., Lin, J.‐F., Jacobsen, S.D., Duffy, T.S., Chang, Y.‐Y., Smyth, J.R., et al. (2012). Sound velocities of hydrous ringwoodite to 16 GPa and 673 K. Earth Planet. Sci. Lett., 331–332, 112–119. https://doi.org/10.1016/j.epsl.2012.03.001

191 Mao, Z., Lin, J.‐F., Liu, J., & Prakapenka, V.B. (2011). Thermal equation of state of lower‐mantle ferropericlase across the spin crossover. Geophys. Res. Lett., 38, L23308. https://doi.org/10.1029/2011GL049915

192 Marquardt, H., Buchen, J., Méndez, A.S.J., Kurnosov, A., Wendt, M., Rothkirch, A., et al. (2018). Elastic softening of (Mg0.8Fe0.2)O ferropericlase across the iron spin crossover measured at seismic frequencies. Geophys. Res. Lett., 45, 6862–6868. https://doi.org/10.1029/2018GL077982

193 Marquardt, H., Speziale, S., Jahn, S., Ganschow, S., & Schilling, F.R. (2009a). Single‐crystal elastic properties of (Y,Yb)3Al5O12. J. Appl. Phys., 106, 093519. https://doi.org/10.1063/1.3245285

194 Marquardt, H., Speziale, S., Reichmann, H.J., Frost, D.J., & Schilling, F.R. (2009b). Single‐crystal elasticity of (Mg0.9Fe0.1)O to 81 GPa. Earth Planet. Sci. Lett., 287, 345–352. https://doi.org/10.1016/j.epsl.2009.08.017

195 Marquardt, H., Speziale, S., Reichmann, H.J., Frost, D.J., Schilling, F.R., & Garnero, E.J. (2009c). Elastic shear anisotropy of ferropericlase in Earth’s lower mantle. Science, 324, 224–226. https://doi.org/10.1126/science.1169365

196 Masters, G., Laske, G., Bolton, H., & Dziewonski, A. (2000). The relative behavior of shear velocity, bulk sound speed, and compressional velocity in the mantle: Implications for chemical and thermal structure. In Karato, S.‐I., Forte, A., Liebermann, R., Masters, G., Stixrude, L. (Eds.), Earth’s Deep Interior: Mineral Physics and Tomography From the Atomic to the Global Scale. American Geophysical Union, Washington, D.C., pp. 63–87. https://doi.org/10.1029/GM117p0063

197 Matas, J., Bass, J., Ricard, Y., Mattern, E., & Bukowinski, M.S.T. (2007). On the bulk composition of the lower mantle: predictions and limitations from generalized inversion of radial seismic profiles. Geophys. J. Int., 170, 764–780. https://doi.org/10.1111/j.1365‐246X.2007.03454.x

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

199 McDonough, W.F., & Sun, S. ‐s. (1995). The composition of the Earth. Chem. Geol., 120, 223–253. https://doi.org/10.1016/0009‐2541(94)00140‐4

200 McNamara, A.K. (2019). A review of large low shear velocity provinces and ultra low velocity zones. Tectonophysics, 760, 199–220. https://doi.org/10.1016/j.tecto.2018.04.015

201 Méndez, A.S.J., Marquardt, H., Husband, R.J., Schwark, I., Mainberger, J., Glazyrin, K., et al. (2020). A resistively‐heated dynamic diamond anvil cell (RHdDAC) for fast compression x‐ray diffraction experiments at high temperatures. Rev. Sci. Instrum., 91, 073906. https://doi.org/10.1063/5.0007557.

202 Miletich, R., Hejny, C., Krauss, G., & Ullrich, A. (2005). Diffraction techniques: Shedding light on structural changes at extreme conditions. In Miletich, R. (Ed.), Mineral Behaviour at Extreme Conditions. European Mineralogical Union, pp. 281–338. https://doi.org/10.1180/EMU‐notes.7.13

203 Mookherjee, M. (2011). Mid‐mantle anisotropy: Elasticity of aluminous phases in subducted MORB. Geophys. Res. Lett., 38, L14302. https://doi.org/10.1029/2011GL047923

204 Morgan, J.P., & Morgan, W.J. (1999). Two‐stage melting and the geochemical evolution of the mantle: a recipe for mantle plum‐pudding. Earth Planet. Sci. Lett., 170, 215–239. https://doi.org/10.1016/S0012‐821X(99)00114‐4

205 Muir, J.M.R., & Brodholt, J.P. (2016). Ferrous iron partitioning in the lower mantle. Phys. Earth Planet. Inter., 257, 12–17. https://doi.org/10.1016/j.pepi.2016.05.008

206 Muir, J.M.R., & Brodholt, J.P. (2015a). Elastic properties of ferrous bearing MgSiO3 and their relevance to ULVZs. Geophys. J. Int., 201, 496–504. https://doi.org/10.1093/gji/ggv045

207 Muir, J.M.R., & Brodholt, J.P. (2015b). Elastic properties of ferropericlase at lower mantle conditions and its relevance to ULVZs. Earth Planet. Sci. Lett., 417, 40–48. https://doi.org/10.1016/j.epsl.2015.02.023

208 Murakami, M., Asahara, Y., Ohishi, Y., Hirao, N., & Hirose, K. (2009a). Development of in situ Brillouin spectroscopy at high pressure and high temperature with synchrotron radiation and infrared laser heating system: Application to the Earth’s deep interior. Phys. Earth Planet. Inter., 174, 282–291. https://doi.org/10.1016/j.pepi.2008.07.030

209 Murakami, M., Hirose, K., Kawamura, K., Sata, N., & Ohishi, Y. (2004). Post‐perovskite phase transition in MgSiO3. Science, 304, 855–858. https://doi.org/10.1126/science.1095932

210 Murakami, M., Hirose, K., Sata, N., & Ohishi, Y. (2005). Post‐perovskite phase transition and mineral chemistry in the pyrolitic lowermost mantle. Geophys. Res. Lett., 32, L03304. https://doi.org/10.1029/2004GL021956

211 Murakami, M., Ohishi, Y., Hirao, N., & Hirose, K. (2012). A perovskitic lower mantle inferred from high‐pressure, high‐temperature sound velocity data. Nature, 485, 90–94. https://doi.org/10.1038/nature11004

212 Murakami, M., Ohishi, Y., Hirao, N., & Hirose, K. (2009b). Elasticity of MgO to 130 GPa: Implications for lower mantle mineralogy. Earth Planet. Sci. Lett., 277, 123–129. https://doi.org/10.1016/j.epsl.2008.10.010

213 Murakami, M., Sinogeikin, S.V., Hellwig, H., Bass, J.D., & Li, J. (2007). Sound velocity of MgSiO3 perovskite to Mbar pressure. Earth Planet. Sci. Lett., 256, 47–54. https://doi.org/10.1016/j.epsl.2007.01.011

214 Murnaghan, F.D. (1937). Finite deformations of an elastic solid. Am. J. Math., 59, 235–260. https://doi.org/10.2307/2371405

215 Nagai, T., Hamane, D., Devi, P.S., Miyajima, N., Yagi, T., Yamanaka, T., & Fujino, K. (2005). A new polymorph of FeAlO3 at high pressure. J. Phys. Chem. B, 109, 18226–18229. https://doi.org/10.1021/jp054409s

216 Nakagawa, T., Tackley, P.J., Deschamps, F., & Connolly, J.A.D. (2010). The influence of MORB and harzburgite composition on thermo‐chemical mantle convection in a 3‐D spherical shell with self‐consistently calculated mineral physics. Earth Planet. Sci. Lett., 296, 403–412. https://doi.org/10.1016/j.epsl.2010.05.026

217 Nakajima, Y., Frost, D.J., & Rubie, D.C. (2012). Ferrous iron partitioning between magnesium silicate perovskite and ferropericlase and the composition of perovskite in the Earth’s lower mantle. J. Geophys. Res. – Solid Earth, 117, B08201. https://doi.org/10.1029/2012JB009151

218 Nielsen, O.H., & Martin, R.M. (1985). Quantum‐mechanical theory of stress and force. Phys. Rev. B, 32, 3780–3791. https://doi.org/10.1103/PhysRevB.32.3780

219 Nomura, R., Hirose, K., Sata, N., & Ohishi, Y. (2010). Precise determination of post‐stishovite phase transition boundary and implications for seismic heterogeneities in the mid‐lower mantle. Phys. Earth Planet. Inter., 183, 104–109. https://doi.org/10.1016/j.pepi.2010.08.004

220 Norby, P., & Schwarz, U. (2008). Powder diffraction under non‐ambient conditions. In Dinnebier, R.E., Billinge, S.J.L. (Eds.), Powder Diffraction: Theory and Practice. Royal Society of Chemistry, Cambridge, pp. 439–463. https://doi.org/10.1039/9781847558237‐00439

221 Nye, J.F. (1985). Physical Properties of Crystals: Their Representation by Tensors and Matrices. Oxford University Press, Oxford.

222 Oganov, A.R., Brodholt, J.P., & Price, G.D. (2001). The elastic constants of MgSiO3 perovskite at pressures and temperatures of the Earth’s mantle. Nature, 411, 934–937. https://doi.org/10.1038/35082048

223 Oganov, A.R., & Dorogokupets, P.I. (2004). Intrinsic anharmonicity in equations of state and thermodynamics of solids. J. Phys.: Condens. Matter, 16, 1351–1360. https://doi.org/10.1088/0953‐8984/16/8/018

224 Oganov, A.R., & Dorogokupets, P.I. (2003). All‐electron and pseudopotential study of MgO: Equation of state, anharmonicity, and stability. Phys. Rev. B, 67, 224110. https://doi.org/10.1103/PhysRevB.67.224110

225 Ohnishi, S. (1978). A theory of the pressure‐induced high‐spin–low‐spin transition of transition‐metal oxides. Phys. Earth Planet. Inter., 17, 130–139. https://doi.org/10.1016/0031‐9201(78)90054‐7

226 Ohnishi, S., & Sugano, S. (1981). Strain interaction effects on the high‐spin–low‐spin transition of transition‐metal compounds. J. Phys. C; Solid State Phys., 14, 39–55. https://doi.org/10.1088/0022‐3719/14/1/007

227 Ono, S., Ito, E., & Katsura, T. (2001). Mineralogy of subducted basaltic crust (MORB) from 25 to 37 GPa, and chemical heterogeneity of the lower mantle. Earth Planet. Sci. Lett., 190, 57–63. https://doi.org/10.1016/S0012‐821X(01)00375‐2

228 Perdew, J.P., & Ruzsinszky, A. (2010). Density functional theory of electronic structure: a short course for mineralogists and geophysicists. Rev. Mineral. Geochem., 71, 1–18. https://doi.org/10.2138/rmg.2010.71.1

229 Perrillat, J.‐P., Ricolleau, A., Daniel, I., Fiquet, G., Mezouar, M., Guignot, N., & Cardon, H. (2006). Phase transformations of subducted basaltic crust in the upmost lower mantle. Phys. Earth Planet. Inter., 157, 139–149. https://doi.org/10.1016/j.pepi.2006.04.001

230  Persson, K., Bengtson, A., Ceder, G., & Morgan, D. (2006). Ab initio study of the composition dependence of the pressure‐induced spin transition in the (Mg1‐x,Fe x)O system. Geophys. Res. Lett., 33, L16306. https://doi.org/10.1029/2006GL026621

231 Piet, H., Badro, J., Nabiei, F., Dennenwaldt, T., Shim, S.‐H., Cantoni, M., Hébert, C., & Gillet, P. (2016). Spin and valence dependence of iron partitioning in Earth’s deep mantle. Proc. Natl. Acad. Sci. U.S.A., 113, 11127–11130. https://doi.org/10.1073/pnas.1605290113

232 Prescher, C., Langenhorst, F., Dubrovinsky, L.S., Prakapenka, V.B., & Miyajima, N. (2014). The effect of Fe spin crossovers on its partitioning behavior and oxidation state in a pyrolitic Earth’s lower mantle system. Earth Planet. Sci. Lett., 399, 86–91. https://doi.org/10.1016/j.epsl.2014.05.011

233 Rainey, E.S.G., & Kavner, A. (2014). Peak scaling method to measure temperatures in the laser‐heated diamond anvil cell and application to the thermal conductivity of MgO. J. Geophys. Res. – Solid Earth, 119, 8154–8170. https://doi.org/10.1002/2014JB011267

234 Reichmann, H.J., Angel, R.J., Spetzler, H., & Bassett, W.A. (1998). Ultrasonic interferometry and X‐ray measurements on MgO in a new diamond anvil cell. Am. Mineral., 83, 1357–1360. https://doi.org/10.2138/am‐1998‐11‐1226

235 Reichmann, H.J., & Jacobsen, S.D. (2004). High‐pressure elasticity of a natural magnetite crystal. Am. Mineral., 89, 1061–1066. https://doi.org/10.2138/am‐2004‐0718

236 Reuss, A. (1929.) Berechnung der Fließgrenze von Mischkristallen auf Grund der Plastizitätsbedingung für Einkristalle. Z. Angew. Math. Mech., 9, 49–58 (in German). https://doi.org/10.1002/zamm.19290090104

237 Richards, M.A., & Engebretson, D.C. (1992). Large‐scale mantle convection and the history of subduction. Nature, 355, 437–440. https://doi.org/10.1038/355437a0

238 Richmond, N.C., & Brodholt, J.P. (1998). Calculated role of aluminum in the incorporation of ferric iron into magnesium silicate perovskite. Am. Mineral., 83, 947–951. https://doi.org/10.2138/am‐1998‐9‐1003

239 Ricolleau, A., Perrillat, J.‐P., Fiquet, G., Daniel, I., Matas, J., Addad, A., et al. (2010). Phase relations and equation of state of a natural MORB: Implications for the density profile of subducted oceanic crust in the Earth’s lower mantle. J. Geophys. Res. – Solid Earth, 115, B08202. https://doi.org/10.1029/2009JB006709

240 Rost, S., Garnero, E.J., & Williams, Q. (2008). Seismic array detection of subducted oceanic crust in the lower mantle. J. Geophys. Res. – Solid Earth, 113, B06303. https://doi.org/10.1029/2007JB005263

241 Sakai, T., Ohtani, E., Terasaki, H., Sawada, N., Kobayashi, Y., Miyahara, M., et al. (2009). Fe‐Mg partitioning between perovskite and ferropericlase in the lower mantle. Am. Mineral., 94, 921–925. https://doi.org/10.2138/am.2009.3123

242 Sammis, C., Anderson, D., & Jordan, T. (1970). Application of isotropic finite strain theory to ultrasonic and seismological data. J. Geophys. Res., 75, 4478–4480. https://doi.org/10.1029/JB075i023p04478

243 Schreuer, J., & Haussühl, S. (2005). Elastic and piezoelectric properties of minerals I. Principles and experimental approaches. In Miletich, R. (Ed.), Mineral Behaviour at Extreme Conditions. European Mineralogical Union, pp. 95–116. https://doi.org/10.1180/EMU‐notes.7.4

244 Schuberth, B.S.A., Bunge, H.‐P., & Ritsema, J. (2009a). Tomographic filtering of high‐resolution mantle circulation models: Can seismic heterogeneity be explained by temperature alone? Geochem. Geophys. Geosystems, 10, Q05W03. https://doi.org/10.1029/2009GC002401

245 Schuberth, B.S.A., Bunge, H.‐P., Steinle‐Neumann, G., Moder, C., Oeser, J. (2009). Thermal versus elastic heterogeneity in high‐resolution mantle circulation models with pyrolite composition: High plume excess temperatures in the lowermost mantle. Geochem. Geophys. Geosystems, 10, Q01W01. https://doi.org/10.1029/2008GC002235

246 Schulze, K., Marquardt, H., Kawazoe, T., Boffa Ballaran, T., McCammon, C., Koch‐Müller, M., et al. (2018). Seismically invisible water in Earth’s transition zone? Earth Planet. Sci. Lett., 498, 9–16. https://doi.org/10.1016/j.epsl.2018.06.021

247 Sherman, D.M. (1991). The high‐pressure electronic structure of magnesiowustite (Mg, Fe)O: Applications to the physics and chemistry of the lower mantle. J. Geophys. Res. – Solid Earth, 96, 14299–14312. https://doi.org/10.1029/91JB01202

248 Sherman, D.M. (1985). The electronic structures of Fe3+ coordination sites in iron oxides: Applications to spectra, bonding, and magnetism. Phys. Chem. Miner., 12, 161–175. https://doi.org/10.1007/BF00308210

249 Shim, S.‐H., Duffy, T.S., Jeanloz, R., & Shen, G. (2004). Stability and crystal structure of MgSiO3 perovskite to the core–mantle boundary. Geophys. Res. Lett., 31, L10603. https://doi.org/10.1029/2004GL019639

250 Shim, S.‐H., Jeanloz, R., & Duffy, T.S. (2002). Tetragonal structure of CaSiO3 perovskite above 20 GPa. Geophys. Res. Lett., 29, 2166. https://doi.org/10.1029/2002GL016148

251 Shukla, G., Cococcioni, M., & Wentzcovitch, R.M. (2016). Thermoelasticity of Fe3+‐ and Al‐bearing bridgmanite: Effects of iron spin crossover. Geophys. Res. Lett., 43, 5661–5670. https://doi.org/10.1002/2016GL069332

252 Shukla, G., Wu, Z., Hsu, H., Floris, A., Cococcioni, M., & Wentzcovitch, R.M. (2015). Thermoelasticity of Fe2+‐bearing bridgmanite. Geophys. Res. Lett., 42, 1741–1749. https://doi.org/10.1002/2014GL062888

253 Sigloch, K., McQuarrie, N., & Nolet, G. (2008). Two‐stage subduction history under North America inferred from multiple‐frequency tomography. Nat. Geosci., 1, 458–462. https://doi.org/10.1038/ngeo231

254 Simmons, N.A., Myers, S.C., Johannesson, G., Matzel, E., & Grand, S.P. (2015). Evidence for long‐lived subduction of an ancient tectonic plate beneath the southern Indian Ocean. Geophys. Res. Lett., 42, 9270–9278. https://doi.org/10.1002/2015GL066237

255 Sinmyo, R., & Hirose, K. (2013). Iron partitioning in pyrolitic lower mantle. Phys. Chem. Miner., 40, 107–113. https://doi.org/10.1007/s00269‐012‐0551‐7

256 Sinmyo, R., & Hirose, K. (2010). The Soret diffusion in laser‐heated diamond‐anvil cell. Phys. Earth Planet. Inter., 180, 172–178. https://doi.org/10.1016/j.pepi.2009.10.011

257 Sinmyo, R., Hirose, K., Nishio‐Hamane, D., Seto, Y., Fujino, K., Sata, N., & Ohishi, Y. (2008). Partitioning of iron between perovskite/postperovskite and ferropericlase in the lower mantle. J. Geophys. Res. – Solid Earth, 113, B11204. https://doi.org/10.1029/2008JB005730

258 Sinogeikin, S., Bass, J., Prakapenka, V., Lakshtanov, D., Shen, G., Sanchez‐Valle, C., & Rivers, M. (2006). Brillouin spectrometer interfaced with synchrotron radiation for simultaneous x‐ray density and acoustic velocity measurements. Rev. Sci. Instrum., 77, 103905. https://doi.org/10.1063/1.2360884

259 Sinogeikin, S.V., & Bass, J.D. (2000). Single‐crystal elasticity of pyrope and MgO to 20 GPa by Brillouin scattering in the diamond cell. Phys. Earth Planet. Inter., 120, 43–62. https://doi.org/10.1016/S0031‐9201(00)00143‐6

260 Sinogeikin, S.V., Katsura, T., & Bass, J.D. (1998). Sound velocities and elastic properties of Fe‐bearing wadsleyite and ringwoodite. J. Geophys. Res. – Solid Earth, 103, 20819–20825. https://doi.org/10.1029/98JB01819

261 Sinogeikin, S.V., Lakshtanov, D.L., Nicholas, J.D., & Bass, J.D. (2004). Sound velocity measurements on laser‐heated MgO and Al2O3. Phys. Earth Planet. Inter., 143–144, 575–586. https://doi.org/10.1016/j.pepi.2003.09.017

262 Sobolev, A.V., Hofmann, A.W., Kuzmin, D.V., Yaxley, G.M., Arndt, N.T., Chung, S.‐L., et al. (2007). The amount of recycled crust in sources of mantle‐derived melts. Science, 316, 412–417. https://doi.org/10.1126/science.1138113

263 Solomatova, N.V., Jackson, J.M., Sturhahn, W., Wicks, J.K., Zhao, J., Toellner, T.S., et al. (2016). Equation of state and spin crossover of (Mg,Fe)O at high pressure, with implications for explaining topographic relief at the core–mantle boundary. Am. Mineral., 101, 1084–1093. https://doi.org/10.2138/am‐2016‐5510

264 Spasojevic, S., Gurnis, M., & Sutherland, R. (2010). Mantle upwellings above slab graveyards linked to the global geoid lows. Nat. Geosci., 3, 435–438. https://doi.org/10.1038/ngeo855

265 Spetzler, H. (1970). Equation of state of polycrystalline and single‐crystal MgO to 8 kilobars and 800°K. J. Geophys. Res., 75, 2073–2087. https://doi.org/10.1029/JB075i011p02073

266 Spetzler, H., Shen, A., Chen, G., Herrmannsdoerfer, G., Schulze, H., & Weigel, R. (1996). Ultrasonic measurements in a diamond anvil cell. Phys. Earth Planet. Inter., 98, 93–99. https://doi.org/10.1016/S0031‐9201(96)03171‐8

267 Speziale, S., Lee, V.E., Clark, S.M., Lin, J.F., Pasternak, M.P., & Jeanloz, R. (2007). Effects of Fe spin transition on the elasticity of (Mg, Fe)O magnesiowüstites and implications for the seismological properties of the Earth’s lower mantle. J. Geophys. Res. – Solid Earth, 112, B10212. https://doi.org/10.1029/2006JB004730

268 Speziale, S., Marquardt, H., & Duffy, T.S. (2014). Brillouin scattering and its application in geosciences. Rev. Mineral. Geochem., 78, 543–603. https://doi.org/10.2138/rmg.2014.78.14

269 Speziale, S., Milner, A., Lee, V.E., Clark, S.M., Pasternak, M.P., & Jeanloz, R. (2005). Iron spin transition in Earth’s mantle. Proc. Natl. Acad. Sci. U.S.A., 102, 17918–17922. https://doi.org/10.1073/pnas.0508919102

270 Stacey, F.D., & Davis, P.M. (2004). High pressure equations of state with applications to the lower mantle and core. Phys. Earth Planet. Inter., 142, 137–184. https://doi.org/10.1016/j.pepi.2004.02.003

271 Stackhouse, S., Brodholt, J.P., & Price, G.D. (2006). Elastic anisotropy of FeSiO3 end‐members of the perovskite and post‐perovskite phases. Geophys. Res. Lett., 33, L01304. https://doi.org/10.1029/2005GL023887

272 Stackhouse, S., Brodholt, J.P., & Price, G.D. (2005a). High temperature elastic anisotropy of the perovskite and post‐perovskite polymorphs of Al2O3. Geophys. Res. Lett., 32, L13305. https://doi.org/10.1029/2005GL023163

273 Stackhouse, S., Brodholt, J.P., Wookey, J., Kendall, J.‐M., & Price, G.D. (2005b). The effect of temperature on the seismic anisotropy of the perovskite and post‐perovskite polymorphs of MgSiO3. Earth Planet. Sci. Lett., 230, 1–10. https://doi.org/10.1016/j.epsl.2004.11.021

274 Stackhouse, S., Stixrude, L., & Karki, B.B. (2010). Determination of the high‐pressure properties of fayalite from first‐principles calculations. Earth Planet. Sci. Lett., 289, 449–456. https://doi.org/10.1016/j.epsl.2009.11.033

275 Steinberger, B. (2000). Slabs in the lower mantle — results of dynamic modelling compared with tomographic images and the geoid. Phys. Earth Planet. Inter., 118, 241–257. https://doi.org/10.1016/S0031‐9201(99)00172‐7

276 Stephens, D.R., & Drickamer, H.G. (1961a). Effect of pressure on the spectrum of ruby. J. Chem. Phys., 35, 427–429. https://doi.org/10.1063/1.1731945

277 Stephens, D.R., & Drickamer, H.G. (1961b). Effect of pressure on the spectra of five nickel complexes. J. Chem. Phys., 34, 937–940. https://doi.org/10.1063/1.1731696

278 Stixrude, L., Cohen, R.E., & Hemley, R.J. (1998). Theory of minerals at high pressure. Rev. Mineral. Geochem., 37, 639–671.

279 Stixrude, L., & Lithgow‐Bertelloni, C. (2012). Geophysics of chemical heterogeneity in the mantle. Annu. Rev. Earth Planet. Sci., 40, 569–595. https://doi.org/10.1146/annurev.earth.36.031207.124244

280 Stixrude, L., & Lithgow‐Bertelloni, C. (2011). Thermodynamics of mantle minerals — II. Phase equilibria. Geophys. J. Int., 184, 1180–1213. https://doi.org/10.1111/j.1365‐246X.2010.04890.x

281 Stixrude, L., & Lithgow‐Bertelloni, C. (2005). Thermodynamics of mantle minerals — I. Physical properties. Geophys. J. Int., 162, 610–632. https://doi.org/10.1111/j.1365‐246X.2005.02642.x

282 Stixrude, L., Lithgow‐Bertelloni, C., Kiefer, B., & Fumagalli, P. (2007). Phase stability and shear softening in CaSiO3 perovskite at high pressure. Phys. Rev. B, 75, 024108. https://doi.org/10.1103/PhysRevB.75.024108

283 Stracke, A. (2012). Earth’s heterogeneous mantle: A product of convection‐driven interaction between crust and mantle. Chem. Geol., 330–331, 274–299. https://doi.org/10.1016/j.chemgeo.2012.08.007

284 Sturhahn, W. (2004). Nuclear resonant spectroscopy. J. Phys.: Condens. Matter, 16, S497–S530. https://doi.org/10.1088/0953‐8984/16/5/009

285 Sturhahn, W., Jackson, J.M. (2007). Geophysical applications of nuclear resonant spectroscopy. In Ohtani, E. (Ed.), Advances in High‐Pressure Mineralogy, Geological Society of America, Boulder, CO, pp. 157–174. https://doi.org/10.1130/2007.2421(09)

286  Sturhahn, W., Jackson, J.M., Lin, J.‐F. (2005). The spin state of iron in minerals of Earth’s lower mantle. Geophys. Res. Lett., 32, L12307. https://doi.org/10.1029/2005GL022802

287 Sun, N., Wei, W., Han, S., Song, J., Li, X., Duan, Y., Prakapenka, V.B., & Mao, Z. (2018). Phase transition and thermal equations of state of (Fe,Al)‐bridgmanite and post‐perovskite: Implication for the chemical heterogeneity at the lowermost mantle. Earth Planet. Sci. Lett., 490, 161–169. https://doi.org/10.1016/j.epsl.2018.03.004

288 Tanabe, Y., & Sugano, S. (1954a). On the absorption spectra of complex ions I. J. Phys. Soc. Jpn., 9, 753–766. https://doi.org/10.1143/JPSJ.9.753

289 Tanabe, Y., & Sugano, S. (1954b). On the absorption spectra of complex ions II. J. Phys. Soc. Jpn., 9, 766–779. https://doi.org/10.1143/JPSJ.9.766

290 Thomsen, L. (1972a). The fourth‐order anharmonic theory: Elasticity and stability. J. Phys. Chem. Solids, 33, 363–378. https://doi.org/10.1016/0022‐3697(72)90018‐2

291 Thomsen, L. (1972b). Elasticity of polycrystals and rocks. J. Geophys. Res., 77, 315–327. https://doi.org/10.1029/JB077i002p00315

292 Thomson, A.R., Crichton, W.A., Brodholt, J.P., Wood, I.G., Siersch, N.C., Muir, J.M.R., et al. (2019). Seismic velocities of CaSiO3 perovskite can explain LLSVPs in Earth’s lower mantle. Nature, 572, 643–647. https://doi.org/10.1038/s41586‐019‐1483‐x

293 Trampert, J., Deschamps, F., Resovsky, J., & Yuen, D. (2004). Probabilistic tomography maps chemical heterogeneities throughout the lower mantle. Science, 306, 853–856. https://doi.org/10.1126/science.1101996

294 Tröster, A., Ehsan, S., Belbase, K., Blaha, P., Kreisel, J., & Schranz, W. (2017). Finite‐strain Landau theory applied to the high‐pressure phase transition of lead titanate. Phys. Rev. B, 95, 064111. https://doi.org/10.1103/PhysRevB.95.064111

295 Tröster, A., Schranz, W., Karsai, F., & Blaha, P. (2014). Fully consistent finite‐strain Landau theory for high‐pressure phase transitions. Phys. Rev. X, 4, 031010. https://doi.org/10.1103/PhysRevX.4.031010

296 Tröster, A., Schranz, W., & Miletich, R. (2002). How to couple Landau theory to an equation of state. Phys. Rev. Lett., 88, 055503. https://doi.org/10.1103/PhysRevLett.88.055503

297 Tsuchiya, T., Wentzcovitch, R.M., da Silva, C.R.S., & de Gironcoli, S. (2006). Spin transition in magnesiowüstite in Earth’s lower mantle. Phys. Rev. Lett., 96. https://doi.org/10.1103/PhysRevLett.96.198501

298 van der Hilst, R.D., Widiyantoro, S., & Engdahl, E.R. (1997). Evidence for deep mantle circulation from global tomography. Nature, 386, 578–584. https://doi.org/10.1038/386578a0

299 Voigt, W. (1928). Lehrbuch der Kristallphysik. Teubner, Leipzig (in German).

300 Wadhawan, V.K. (1982). Ferroelasticity and related properties of crystals. Phase Transitions, 3, 3–103. https://doi.org/10.1080/01411598208241323

301 Wang, X., Tsuchiya, T., & Hase, A. (2015). Computational support for a pyrolitic lower mantle containing ferric iron. Nat. Geosci., 8, 556–559. https://doi.org/10.1038/ngeo2458

302 Waszek, L., Schmerr, N.C., & Ballmer, M.D. (2018). Global observations of reflectors in the mid‐mantle with implications for mantle structure and dynamics. Nat. Commun., 9, 385. https://doi.org/10.1038/s41467‐017‐02709‐4

303 Watt, J.P., Davies, G.F., & O’Connell, R.J. (1976). The elastic properties of composite materials. Rev. Geophys., 14, 541–563. https://doi.org/10.1029/RG014i004p00541

304 Weidner, D.J., Sawamoto, H., Sasaki, S., & Kumazawa, M. (1984). Single‐crystal elastic properties of the spinel phase of Mg2SiO4. J. Geophys. Res. – Solid Earth, 89, 7852–7860. https://doi.org/10.1029/JB089iB09p07852

305 Wentzcovitch, R.M., Justo, J.F., Wu, Z., Silva, C.R.S. da, Yuen, D.A., & Kohlstedt, D. (2009). Anomalous compressibility of ferropericlase throughout the iron spin cross‐over. Proc. Natl. Acad. Sci. U.S.A., 106, 8447–8452. https://doi.org/10.1073/pnas.0812150106

306 Wentzcovitch, R.M., Karki, B.B., Cococcioni, M., & de Gironcoli, S. (2004). Thermoelastic properties of MgSiO3‐perovskite: Insights on the nature of the Earth’s lower mantle. Phys. Rev. Lett., 92, 018501. https://doi.org/10.1103/PhysRevLett.92.018501

307 Wentzcovitch, R.M., Martins, J.L., & Price, G.D. (1993). Ab initio molecular dynamics with variable cell shape: Application to MgSiO3. Phys. Rev. Lett., 70, 3947–3950. https://doi.org/10.1103/PhysRevLett.70.3947

308 Wentzcovitch, R.M., Ross, N.L., & Price, G.D. (1995). Ab initio study of MgSiO3 and CaSiO3 perovskites at lower‐mantle pressures. Phys. Earth Planet. Inter., 90, 101–112. https://doi.org/10.1016/0031‐9201(94)03001‐Y

309 Wentzcovitch, R.M., Tsuchiya, T., & Tsuchiya, J. (2006). MgSiO3 postperovskite at D” conditions. Proc. Natl. Acad. Sci. U.S.A., 103, 543–546. https://doi.org/10.1073/pnas.0506879103

310 Wentzcovitch, R.M., Wu, Z., & Carrier, P. (2010a). First principles quasiharmonic thermoelasticity of mantle minerals. Rev. Mineral. Geochem., 71, 99–128. https://doi.org/10.2138/rmg.2010.71.5

311 Wentzcovitch, R.M., Yu, Y.G., & Wu, Z. (2010b). Thermodynamic properties and phase relations in mantle minerals investigated by first principles quasiharmonic theory. Rev. Mineral. Geochem., 71, 59–98. https://doi.org/10.2138/rmg.2010.71.4

312 Wicks, J.K., Jackson, J.M., & Sturhahn, W. (2010). Very low sound velocities in iron‐rich (Mg,Fe)O: Implications for the core–mantle boundary region. Geophys. Res. Lett., 37, L15304. https://doi.org/10.1029/2010GL043689

313 Wicks, J.K., Jackson, J.M., Sturhahn, W., & Zhang, D. (2017). Sound velocity and density of magnesiowüstites: Implications for ultralow‐velocity zone topography. Geophys. Res. Lett., 44, 2148–2158. https://doi.org/10.1002/2016GL071225

314 Workman, R.K., & Hart, S.R. (2005). Major and trace element composition of the depleted MORB mantle (DMM). Earth Planet. Sci. Lett., 231, 53–72. https://doi.org/10.1016/j.epsl.2004.12.005

315 Wu, Y., Qin, F., Wu, X., Huang, H., McCammon, C.A., Yoshino, T., et al. (2017). Spin transition of ferric iron in the calcium‐ferrite type aluminous phase. J. Geophys. Res. – Solid Earth, 122, 5935–5944. https://doi.org/10.1002/2017JB014095

316  Wu, Y., Wu, X., Lin, J.‐F., McCammon, C.A., Xiao, Y., Chow, P., et al. (2016). Spin transition of ferric iron in the NAL phase: Implications for the seismic heterogeneities of subducted slabs in the lower mantle. Earth Planet. Sci. Lett., 434, 91–100. https://doi.org/10.1016/j.epsl.2015.11.011

317 Wu, Z., Justo, J.F., da Silva, C.R.S., de Gironcoli, S., & Wentzcovitch, R.M. (2009). Anomalous thermodynamic properties in ferropericlase throughout its spin crossover. Phys. Rev. B, 80, 014409. https://doi.org/10.1103/PhysRevB.80.014409

318 Wu, Z., Justo, J.F., & Wentzcovitch, R.M. (2013). Elastic anomalies in a spin‐crossover system: Ferropericlase at lower mantle conditions. Phys. Rev. Lett., 110, 228501. https://doi.org/10.1103/PhysRevLett.110.228501

319 Wu, Z., & Wentzcovitch, R.M. (2014). Spin crossover in ferropericlase and velocity heterogeneities in the lower mantle. Proc. Natl. Acad. Sci. U.S.A., 111, 10468–10472. https://doi.org/10.1073/pnas.1322427111

320 Wu, Z., & Wentzcovitch, R.M. (2011). Quasiharmonic thermal elasticity of crystals: an analytical approach. Phys. Rev. B, 83, 184115. https://doi.org/10.1103/PhysRevB.83.184115

321 Wu, Z., & Wentzcovitch, R.M. (2009). Effective semiempirical ansatz for computing anharmonic free energies. Phys. Rev. B, 79, 104304. https://doi.org/10.1103/PhysRevB.79.104304

322 Xu, S., Lin, J.‐F., & Morgan, D. (2017). Iron partitioning between ferropericlase and bridgmanite in the Earth’s lower mantle. J. Geophys. Res. – Solid Earth, 122, 1074–1087. https://doi.org/10.1002/2016JB013543

323 Xu, W., Lithgow‐Bertelloni, C., Stixrude, L., & Ritsema, J. (2008). The effect of bulk composition and temperature on mantle seismic structure. Earth Planet. Sci. Lett., 275, 70–79. https://doi.org/10.1016/j.epsl.2008.08.012

324 Yamazaki, D., Ito, E., Yoshino, T., Tsujino, N., Yoneda, A., Gomi, H., et al. (2019). High‐pressure generation in the Kawai‐type multianvil apparatus equipped with tungsten‐carbide anvils and sintered‐diamond anvils, and X‐ray observation on CaSnO3 and (Mg,Fe)SiO3. Comptes Rendus Geosci., 351, 253–259. https://doi.org/10.1016/j.crte.2018.07.004

325 Yang, J., Lin, J.‐F., Jacobsen, S.D., Seymour, N.M., Tkachev, S.N., & Prakapenka, V.B. (2016). Elasticity of ferropericlase and seismic heterogeneity in the Earth’s lower mantle. J. Geophys. Res. – Solid Earth, 121, 8488–8500. https://doi.org/10.1002/2016JB013352

326 Yang, J., Tong, X., Lin, J.‐F., Okuchi, T., & Tomioka, N. (2015). Elasticity of ferropericlase across the spin crossover in the Earth’s lower mantle. Sci. Rep., 5, 17188. https://doi.org/10.1038/srep17188

327 Yang, R., & Wu, Z. (2014). Elastic properties of stishovite and the CaCl2‐type silica at the mantle temperature and pressure: an ab initio investigation. Earth Planet. Sci. Lett., 404, 14–21. https://doi.org/10.1016/j.epsl.2014.07.020

328 Yu, S., & Garnero, E.J. (2018). Ultralow velocity zone locations: a global assessment. Geochem. Geophys. Geosystems, 19, 396–414. https://doi.org/10.1002/2017GC007281

329 Zha, C., Duffy, T.S., Downs, R.T., Mao, H., & Hemley, R.J. (1998). Brillouin scattering and X‐ray diffraction of San Carlos olivine: direct pressure determination to 32 GPa. Earth Planet. Sci. Lett., 159, 25–33. https://doi.org/10.1016/S0012‐821X(98)00063‐6

330 Zha, C.‐S., Mao, H.‐K., & Hemley, R.J. (2000). Elasticity of MgO and a primary pressure scale to 55 GPa. Proc. Natl. Acad. Sci. U.S.A., 97, 13494–13499. https://doi.org/10.1073/pnas.240466697

331 Zhang, F., Oganov, A.R. (2006). Valence state and spin transitions of iron in Earth’s mantle silicates. Earth Planet. Sci. Lett., 249, 436–443. https://doi.org/10.1016/j.epsl.2006.07.023

332 Zhang, J.S., & Bass, J.D. (2016). Sound velocities of olivine at high pressures and temperatures and the composition of Earth’s upper mantle. Geophys. Res. Lett., 43, 9611–9618. https://doi.org/10.1002/2016GL069949

333 Zhang, J.S., Bass, J.D., & Zhu, G. (2015). Single‐crystal Brillouin spectroscopy with CO2 laser heating and variable q. Rev. Sci. Instrum., 86, 063905. https://doi.org/10.1063/1.4922634

334 Zhang, S., Cottaar, S., Liu, T., Stackhouse, S., & Militzer, B. (2016). High‐pressure, temperature elasticity of Fe‐ and Al‐bearing MgSiO3: Implications for the Earth’s lower mantle. Earth Planet. Sci. Lett., 434, 264–273. https://doi.org/10.1016/j.epsl.2015.11.030

335 Zhang, Y., Fu, S., Wang, B., & Lin, J.-F. (2021). Elasticity of a pseudoproper ferroelastic transition from stishovite to post-stishovite at high pressure. Phys. Rev. Lett., 126, 025701. https://doi.org/10.1103/PhysRevLett.126.025701

336 Zhang, Z., Stixrude, L., & Brodholt, J. (2013). Elastic properties of MgSiO3‐perovskite under lower mantle conditions and the composition of the deep Earth. Earth Planet. Sci. Lett., 379, 1–12. https://doi.org/10.1016/j.epsl.2013.07.034

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