Mantle Convection and Surface Expressions

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