Инд. авторы:	Дорогокупец П.И., Дымшиц А.М, Соколова Т.С., Данилов Б.С., Литасов К.Д.
Заглавие:	Уравнения состояния форстерита, вадслеита, рингвудита, акимотоита, mgsio 3-перовскита и постперовскита и фазовая диаграмма системы mg 2sio 4 при давлениях до 130 гпа
Библ. ссылка:	Дорогокупец П.И., Дымшиц А.М, Соколова Т.С., Данилов Б.С., Литасов К.Д. Уравнения состояния форстерита, вадслеита, рингвудита, акимотоита, mgsio 3-перовскита и постперовскита и фазовая диаграмма системы mg 2sio 4 при давлениях до 130 гпа // Геология и геофизика. - 2015. - Т.56. - № 1-2. - С.224-246. - ISSN 0016-7886.
Внешние системы:	РИНЦ: 23063217;
Реферат:	rus: Путем совместного анализа существующих экспериментальных измерений изобарной теплоемкости, модулей сжатия, термического расширения в зависимости от температуры при атмосферном давлении, а также объема на комнатной изотерме и при повышенных температурах построены уравнения состояния форстерита, вадслеита, рингвудита, MgSiO 3-перовскита, акимотоита и MgSiO 3-постперовскита. В качестве термодинамической модели были использованы модифицированные уравнения состояния на основе свободной энергии Гельмгольца. Полученные уравнения состояния позволяют рассчитать любые термодинамические функции рассматриваемых минералов в зависимости от температуры и объема или от температуры и давления. По реперным экспериментальным точкам определена разница в энергии Гиббса между этими фазами и построена фазовая диаграмма в системе MgSiO 3-MgO. На основании фазовых переходов были интерпретированы сейсмические границы Земли на глубинах 410 и 520 км, а также в области зоны D″. Под вопросом остается глобальный раздел верхней и нижней мантии на границе 660 км, который плохо согласуется с экспериментальными и расчетными данными по диссоциации рингвудита на перовскит и периклаз. eng: The equations of state of forsterite, wadsleyite, ringwoodite, MgSiO 3-perovskite, akimotoite, and postperovskite are set up by joint analysis of experimentally measured isobaric heat capacity, bulk moduli, thermal expansion depending on temperature at ambient pressure, and volume at room and higher temperatures. Modified equations of state based on the Helmholtz free energy are used to construct a thermodynamic model. The derived equations of state permit calculation of all thermodynamic functions for the minerals depending on temperature and volume or temperature and pressure. A phase diagram of the system MgSiO 3-MgO is constructed based on the differences in the Gibbs energy calibrated using the referred experimental points. The seismic boundaries at depths of 410 and 520 km and in the zone D ″ are interpreted on the basis of the phase transitions. The global upper/lower mantle discontinuity at a depth of 660 km remains debatable; it is in poor agreement with experimental and computational data on the dissociation of ringwoodite to perovskite and periclase.
Ключевые слова:	акимотоит; рингвудит; вадслеит; форстерит; энергия Гиббса; уравнения состояния; periclase; Akimotoite; ringwoodite; Wadsleyite; forsterite; Gibbs energy; equation of state; Helmholtz free energy; MgSiO 3-postperovskite; MgSiO 3-perovskite; MgSiO 3-постперовскит; MgSiO 3-перовскит; периклаз;
Издано:	2015
Физ. характеристика:	с.224-246
Цитирование:	1. Альтшулер Л.В., Брусникин С.Е., Кузьменков Е.А. Изотермы и функции Грюнейзена 25 металлов // Прикладная механика и теоретическая физика, 1987, т. 161, с. 134-146. 2. Дорогокупец П.И., Пономарев Е.М., Мелехова Е.А. Оптимизация экспериментальных данных по теплоемкости, объему и модулям сжатия минералов // Петрология, 1999, т. 7, с. 611-630. 3. Жарков В.Н. Физика земных недр. М., Наука и образование, 2012, 384 с. 4. Жарков В.Н., Калинин В.А. Уравнения состояния твердых веществ при высоких давлениях и температурах. М., Наука, 1968, 311 с. 5. Калачников А.А., Калинин В.А., Паньков В.Л. Термодинамические расчеты фазовой диаграммы системы Mg-SiO2 // Изв. АН СССР, Сер. Физика Земли, 1991, № 7, с. 3-11. 6. Кусков О.Л., Панферов А.Б. Профили упругих параметров и плотности для оливиновой модели мантии на глубинах 350-550 км // Изв. АН СССР, Сер. Физика Земли, 1989, № 1, с. 13-19. 7. Паньков В.Л., Калинин В.А., Калачников А.А. Фазовые соотношения краевых мантийных систем и особенности состава мантии // Изв. АН СССР, Сер. Физика Земли, 1996, № 6, с. 17-29. 8. Поляков В.Б., Кусков О.Л. Самосогласованная модель для расчета термоупругих и калорических свойств минералов // Геохимия, 1994, № 7, с. 1096-1121. 9. Соколова Т.С., Дорогокупец П.И., Литасов К.Д. Взаимосогласованные шкалы давлений на основании уравнений состояния рубина, алмаза, MgO, B2-NaCl, а также Au, Pt и других металлов до 4 Mбар и 3000 К // Геология и геофизика, 2013, т. 54 (2), с. 237-261. 10. Abramson E.H., Brown J.M., Slutsky L.J., Zaug J. The elastic constants of San Carlos olivine to 17 GPa // J. Geophys. Res.: Solid Earth, 1997, v. 102, p. 12253-12263. 11. Agee C.B. Phase transformations and seismic structure in the upper mantle and transition zone // Rev. Miner. Geochem., 1998, v. 37, p. 165-203. 12. Akaogi M., Ito E. Refinement of enthalpy measurement of MgSiO3 perovskite and negative pressure-temperature slopes for perovskite-forming reactions // Geophys. Res. Lett., 1993, v. 20, p. 1839-1842. 13. Akaogi M., Ito E., Navrotsky A. Olivine-modified spinel-spinel transitions in the system Mg2SiO4- 14. Fe2SiO4: Calorimetric measurements, thermochemical calculation, and geophysical application // J. Geophys. Res.: Solid Earth, 1989, v. 94, p. 15671-15685. 15. Akaogi M., Takayama H., Kojitani H., Kawaji H., Atake T. Low-temperature heat capacities, entropies and enthalpies of Mg2SiO4 polymorphs, and α-β-γ and post-spinel phase relations at high pressure // Phys. Chem. Miner., 2007, v. 34, p. 169-183. 16. Akaogi M., Kojitani H., Morita T., Kawaji H., Atake T. Low-temperature heat capacities, entropies and high-pressure phase relations of MgSiO3 ilmenite and perovskite // Phys. Chem. Miner., 2008, v. 35, p. 287-297. 17. Akimoto S. High-pressure research in geophysics: past, present and future // High-pressure research in mineral physics: A volume in honor of Syun-iti Akimoto, 1987, p. 1-13. 18. Anderson D.L. Chemical stratification of the mantle // J. Geophys. Res.: Solid Earth, 1979, v. 84, p. 6297-6298. 19. Anderson D.L., Bass J.D. Mineralogy and composition of the upper mantle // Geophys. Res. Lett., 1984, v. 11, p. 637-640. 20. Angel R., Allan D., Miletich R., Finger L. The use of quartz as an internal pressure standard in high-pressure crystallography // J. Appl. Crystallogr., 1997, v. 30, p. 461-466. 21. Ashida T., Kume S., Ito E., Navrotsky A. MgSiO3 ilmenite: heat capacity, thermal expansivity, and enthalpy of transformation // Phys. Chem. Miner., 1988, v. 16, p. 239-245. 22. Birch F. Finite strain isotherm and velocities for single-crystal and polycrystalline NaCl at high pressure and 300 K // J. Geophys. Res.: Solid Earth, 1978, v. 83, p. 1257-1268. 23. Boehler R., Chopelas A. A new approach to laser heating in high pressure mineral physics // Geophys. Res. Lett., 1991, v. 18, p. 1147-1150. 24. Chase M.W. NIST-JANAF thermochemical tables // J. Phys. Chem. Ref. Data, 1998, v. 9, 1951. 25. Chopelas A. Thermal properties of β-Mg2SiO4 at mantle pressures derived from vibrational spectroscopy: Implications for the mantle at 400 km depth // J. Geophys. Res.: Solid Earth (1978-2012), 1991, v. 96, p. 11817-11829. 26. Chudinovskikh L., Boehler R. High-pressure polymorphs of olivine and the 660-km seismic discontinuity // Nature, 2001, v. 411, p. 574-577. 27. Couvy H., Chen J., Drozd V. Compressibility of nanocrystalline forsterite // Phys. Chem. Miner., 2010, v. 37, p. 343-351. 28. Dachs E., Geiger C.A., Seckendorff V., Grodzicki M. A low-temperature calorimetric study of synthetic (forsterite + fayalite){(Mg2SiO4 + Fe2SiO4)} solid solutions: An analysis of vibrational, magnetic, and electronic contributions to the molar heat capacity and entropy of mixing // J. Chem. Thermodyn., 2007, v. 39, p.906-933. 29. Decker D. High-pressure equation of state for NaCl, KCl, and CsCl // J. Appl. Phys., 1971, v. 42, p. 3239-3244. 30. Dorogokupets P.I. Critical analysis of equations of state for NaCl // Geochem. Int., 2002, v. 40, p. S132-S144. 31. Dorogokupets P.I., Oganov A.R. Ruby, metals, and MgO as alternative pressure scales: A semiempirical description of shock-wave, ultrasonic, X-ray, and thermochemical data at high temperatures and pressures // Phys. Rev. B, 2007, v. 75, p. 024115. 32. Dorogokupets P.I., Sokolova T.S., Danilov B.S., Litasov K.D. Near-absolute equations of state of diamond, Ag, Al, Cu, Mo, Nb, Pt, Ta, and W for quasi-hydrostatic conditions // Geodyn. Tectonophys., 2012, v. 3, p. 129-166. 33. Downs R.T., Zha C.-S., Duffy T.S., Finger L.W. The equation of state of forsterite to 17.2 GPa and effects of pressure media // Amer. Mineral., 1996, v. 81, p. 51-55. 34. Duffy T.S., Hemley R.J., Mao H.-K. Equation of state and shear strength at multimegabar pressures: magnesium oxide to 227 GPa // Phys. Rev. Lett., 1995, v. 74, p. 1371-1374. 35. Dziewonski A.M., Anderson D.L. Preliminary reference Earth model // Phys. Earth Planet. Int., 1981, v. 25, p. 297-356. 36. Fabrichnaya O.B. Thermodynamic data for phases in the FeO-MgO-SiO2 system and phase relations in the mantle transition zone // Phys. Chem. Miner., 1995, v. 22, p. 323-332. 37. Fabrichnaya O. Thermodynamic data, models, and phase diagrams in multicomponent oxide systems: 38. an assessment for materials and planetary scientists based on calorimetric, volumetric and phase equilibrium data. Berlin, Springer Verlag, 2004, 198 p. 39. Fei Y., Saxena S.K. A thermochemical data base for phase equilibria in the system Fe-Mg-Si-O at high pressure and temperature // Phys. Chem. Miner., 1986, v. 13, p. 311-324. 40. Fei Y., Mao H.-K., Shu J., Parthasarathy G., Bassett W., Ko J. Simultaneous high-P, high-T X-ray diffraction study of β-(Mg,Fe)2SiO4 to 26 GPa and 900 K // J. Geophys. Res.: Solid Earth, 1992, v. 97, p. 4489-4495. 41. Fei Y., van Orman J., Li J., van Westrenen W., Sanloup C., Minarik W., Hirose K., Komabayashi T., Walter M., Funakoshi K.-I. Experimentally determined postspinel transformation boundary in Mg2SiO4 using MgO as an internal pressure standard and its geophysical implications // J. Geophys. Res.: Solid Earth, 2004, v. 109, B02305, doi:10.1029/2003JB002562. 42. Finkelstein G.J., Dera P.K., Jahn S., Oganov A.R., Holl C.M., Meng Y., Duffy T.S. Phase transitions and equation of state of forsterite to 90 GPa from single-crystal X-ray diffraction and molecular modeling // Amer. Mineral., 2014, v. 99, p. 35-43. 43. Fiquet G., Dewaele A., Andrault D., Kunz M., Le Bihan T. Thermoelastic properties and crystal structure of MgSiO3 perovskite at lower mantle pressure and temperature conditions // Geophys. Res. Lett., 2000, v. 27, p. 21-24. 44. Frost D.J., Dolejš D. Experimental determination of the effect of H2O on the 410-km seismic discontinuity // Earth Planet. Sci. Lett., 2007, v. 256, p. 182-195. 45. Frost D.J., Liebske C., Langenhorst F., McCammon C.A., Trønnes R.G., Rubie D.C. Experimental evidence for the existence of iron-rich metal in the Earth’s lower mantle // Nature, 2004, v. 428, p. 409-412. 46. Funamori N., Yagi T., Utsumi W., Kondo T., Uchida T., Funamori M. Thermoelastic properties of MgSiO3 perovskite determined by in situ X-ray observations up to 30 GPa and 2000 K // J. Geophys. Res., 1996, v. 101, p. 8257-8269. 47. Geophysical constraints on mantle composition // Treatise on geochemistry / Eds. C. Bina, G. Helffrich. Second Ed. Elsevier, Oxford, 2014, p. 41-65. 48. Gillet P., Richet P., Guyot F., Fiquet G. High-temperature thermodynamic properties of forsterite // J. Geophys. Res.: Solid Earth, 1991, v. 96, p. 11805-11816. 49. Guignot N., Andrault D., Morard G., Bolfan-Casanova N., Mezouar M. Thermoelastic properties of post-perovskite phase MgSiO3 determined experimentally at core-mantle boundary P-T conditions // Earth Planet. Sci. Lett., 2007, v. 256, p. 162-168. 50. Guyot F., Wang Y., Gillet P., Ricard Y. Quasi-harmonic computations of thermodynamic parameters of olivines at high pressure and high temperature. A comparison with experiment data // Phys. Earth Planet. Int., 1996, v. 98, p. 17-29. 51. Hirose K. Postperovskite phase transition and its geophysical implications // Rev. Geophys., 2006, v. 44, RG3001, doi:10.1029/2005RG000186. 52. Hirose K., Komabayashi T., Murakami M., Funakoshi K.-I. In situ measurements of the majorite-akimotoite-perovskite phase transition boundaries in MgSiO3 // Geophys. Res. Lett., 2001, v. 28, p. 4351-4354. 53. Hirose K., Sinmyo R., Sata N., Ohishi Y. Determination of post-perovskite phase transition boundary in MgSiO3 using Au and MgO pressure standards // Geophys. Res. Lett., 2006, v. 33, L01310, doi:10.1029/2005GL024468. 54. Holl C.M., Smyth J.R., Jacobsen S.D., Frost D.J. Effects of hydration on the structure and compressibility of wadsleyite, β-(Mg2SiO4) // Amer. Miner., 2008, v. 93, p. 598-607. 55. Holland T., Powell R. An improved and extended internally consistent thermodynamic dataset for phases of petrological interest, involving a new equation of state for solids // J. Metamorph. Geol., 2011, v. 29, p. 333-383. 56. Inoue T., Tanimoto Y., Irifune T., Suzuki T., Fukui H., Ohtaka O. Thermal expansion of wadsleyite, ringwoodite, hydrous wadsleyite and hydrous ringwoodite // Phys. Earth Planet. Int., 2004, v. 143, p. 279-290. 57. Inoue T., Irifune T., Higo Y., Sanehira T., Sueda Y., Yamada A., Shinmei T., Yamazaki D., Ando J., Funakoshi K. The phase boundary between wadsleyite and ringwoodite in Mg2SiO4 determined by in situ X-ray diffraction // Phys. Chem. Miner., 2006, v. 33, p. 106-114. 58. Irifune T., Sekine T., Ringwood A.E., Hibberson W.O. The eclogite-garnetite transformation at high pressure and some geophysical implications // Earth Planet. Sci. Lett., 1986, v. 77, p. 245-256. 59. Irifune T., Nishiyama N., Kuroda K., Inoue T., Isshiki M., Utsumi W., Funakoshi K.-I., Urakawa S., Uchida T., Katsura T. The postspinel phase boundary in Mg2SiO4 determined by in situ X-ray diffraction // Science, 1998, v. 279, p. 1698-1700. 60. Isaak D.G., Anderson O.L., Goto T. Elasticity of single-crystal forsterite measured to 1700 K // J. Geophys. Res.: Solid Earth, 1989, v. 94, p. 5895-5906. 61. Isaak D.G., Gwanmesia G.D., Falde D., Davis M.G., Triplett R.S., Wang L. The elastic properties of β-Mg2SiO4 from 295 to 660 K and implications on the composition of Earth’s upper mantle // Phys. Earth Planet. Int., 2007, v. 162, p. 22-31. 62. Ita J., Stixrude L. Petrology, elasticity, and composition of the mantle transition zone // J. Geophys. Res.: Solid Earth, 1992, v. 97, p. 6849-6866. 63. Jackson J.M., Sinogeikin S.V., Bass J.D. Sound velocities and elastic properties of γ-Mg2SiO4 to 873 K by Brillouin spectroscopy // Amer. Miner., 2000, v. 85, p. 296-303. 64. Jacobs M., Oonk H. The Gibbs energy formulation of the α, β, and γ forms of Mg2SiO4 using Grover, Getting and Kennedy’s empirical relation between volume and bulk modulus // Phys. Chem. Miner., 2001, v. 28, p. 572-585. 65. Jacobs M.H., De Jong B.H. An investigation into thermodynamic consistency of data for the olivine, wadsleyite and ringwoodite form of (Mg,Fe)2SiO4 // Geochim. Cosmochim. Acta, 2005, v. 69, p. 4361-4375. 66. Jacobs M.H., Schmid-Fetzer R., van den Berg A.P. An alternative use of Kieffer’s lattice dynamics model using vibrational density of states for constructing thermodynamic databases // Phys. Chem. Miner., 2013, v. 40, p. 1-21. 67. Jahn S., Rahner R., Dachs E., Mrosko M., Koch-Müller M. Thermodynamic properties of anhydrous and hydrous wadsleyite, β-Mg2SiO4 // High Press. Res., 2013, v. 33, p. 584-594. 68. Jamieson J., Fritz J., Manghnani M. Pressure measurement at high temperature in X-ray diffraction studies: gold as a primary standard // High Press. Res. Geophys., 1982, v. 12, p. 27-48. 69. Jeanloz R., Thompson A.B. Phase transitions and mantle discontinuities // Rev. Geophys., 1983, v. 21, p. 51-74. 70. Jeanloz R., Morris S. Temperature distribution in the crust and mantle // Ann. Rev. Earth Planet. Sci., 1986, v. 14, p. 377-415. 71. Katsura T. Phase-relation studies of mantle minerals by in situ X-ray diffraction using multianvil apparatus // Advances in high-pressure mineralogy / Ed. E. Ohtani. Special Papers, Geol. Soc. Amer., 2007, v. 421, p. 189-205. 72. Katsura T., Ito E. The system Mg2SiO4-Fe2SiO4 at high pressures and temperatures: Precise determination of stabilities of olivine, modified spinel, and spinel // J. Geophys. Res.: Solid Earth, 1989, v. 94, p. 15663-15670. 73. Katsura T., Yamada H., Shinmei T., Kubo A., Ono S., Kanzaki M., Yoneda A., Walter M.J., Ito E., Urakawa S. Post-spinel transition in Mg2SiO4 determined by high P-T in situ X-ray diffractometry // Phys. Earth Planet. Int., 2003, v. 136, p. 11-24. 74. Katsura T., Yamada H., Nishikawa O., Song M., Kubo A., Shinmei T., Yokoshi S., Aizawa Y., Yoshino T., Walter M.J. Olivine-wadsleyite transition in the system (Mg,Fe)2SiO4 // J. Geophys. Res.: Solid Earth, 2004a, v. 109, B02209, doi:10.1029/2003JB002438. 75. Katsura T., Yokoshi S., Song M., Kawabe K., Tsujimura T., Kubo A., Ito E., Tange Y., Tomioka N., Saito K. Thermal expansion of Mg2SiO4 ringwoodite at high pressures // J. Geophys. Res.: Solid Earth, 2004b, v. 109, B12209, doi:10.1029/2004JB003094. 76. Katsura T., Shatskiy A., Manthilake M., Zhai S., Fukui H., Yamazaki D., Matsuzaki T., Yoneda A., Ito E., Kuwata A. Thermal expansion of forsterite at high pressures determined by in situ X-ray diffraction: The adiabatic geotherm in the upper mantle // Phys. Earth Planet. Int., 2009a, v. 174, p. 86-92. 77. Katsura T., Yokoshi S., Kawabe K., Shatskiy A., Manthilake M., Zhai S., Fukui H., Hegoda H., Yoshino T., Yamazaki D. Correction to «P-V-T relations of the MgSiO3 perovskite determined by in situ X-ray 78. diffraction using a large-volume high-pressure apparatus» // Geophys. Res. Lett., 2009b, v. 36, L01305, doi:10.1029/2009GL039318. 79. Katsura T., Yokoshi S., Kawabe K., Shatskiy A., Manthilake M., Zhai S., Fukui H., Hegoda H., Yoshino T., Yamazaki D. P-V-T relations of MgSiO3 perovskite determined by in situ X-ray diffraction using a large-volume high-pressure apparatus // Geophys. Res. Lett., 2009c, v. 36, L01305, doi:10.1029/2008GL035658. 80. Katsura T., Yoneda A., Yamazaki D., Yoshino T., Ito E. Adiabatic temperature profile in the mantle // Phys. Earth Planet. Int., 2010, v. 183, p. 212-218. 81. Kawada K. The system Mg2SiO4-Fe2SiO4 at high pressures and temperatures and the Earth’s interior. Tokyo, Institute for Solid State Physics, University of Tokyo, Ph. D thesis, 1977, p. 1-187. 82. Kawai K., Yamamoto S., Tsuchiya T., Maruyama S. The second continent: existence of granitic continental materials around the bottom of the mantle transition zone // Geosci. Front., 2013, v. 4, p. 1-6. 83. Knittle E., Jeanloz R., Smith G.L. Thermal expansion of silicate perovskite and stratification of the Earth’s mantle // Nature, 1986, v. 319, p. 214-216. 84. Kojitani H., Oohata M., Inoue T., Akaogi M. Redetermination of high-temperature heat capacity of Mg2SiO4 ringwoodite: Measurement and lattice vibrational model calculation // Amer. Miner., 2012, v. 97, p. 1314-1319. 85. Komabayashi T., Hirose K., Sugimura E., Sata N., Ohishi Y., Dubrovinsky L.S. Simultaneous volume measurements of post-perovskite and perovskite in MgSiO3 and their thermal equations of state // Earth Planet. Sci. Lett., 2008, v. 265, p. 515-524. 86. Kunc K., Loa I., Syassen K. Equation of state and phonon frequency calculations of diamond at high pressures // Phys. Rev., 2003, № B 68, doi:094110.091103/PhysRevB.094168.094107. 87. Lawrence J.F., Shearer P.M. A global study of transition zone thickness using receiver functions // J. Geophys. Res.: Solid Earth, 2006, v. 111, B06307, doi:10.1029/2005JB003973. 88. Li B., Gwanmesia G.D., Liebermann R.C. Sound velocities of olivine and beta polymorphs of Mg2SiO4 at Earth’s transition zone pressures // Geophys. Res. Lett., 1996, v. 23, p. 2259-2262. 89. Li B., Liebermann R.C., Weidner D.J. P-V-VP-VS-T measurements on wadsleyite to 7 GPa and 873 K: Implications for the 410-km seismic discontinuity // J. Geophys. Res.: Solid Earth, 2001, v. 106, p. 30579-30591. 90. Litasov K.D., Ohtani E. Effect of water on the phase relations in Earth’s mantle and deep water cycle // Special papers, Geol. Soc. Amer., 2007, v. 421, p. 115-156. 91. Liu L.-G. Calculations of high-pressure phase transitions in the system MgO-SiO2 and implications for mantle discontinuities // Phys. Earth Planet. Int., 1979, v. 19, p. 319-330. 92. Mao H., Xu J.-A., Bell P. Calibration of the ruby pressure gauge to 800 kbar under quasi-hydrostatic conditions // J. Geophys. Res.: Solid Earth, 1986, v. 91, p. 4673-4676. 93. Matsui T., Manghnani M.H. Thermal expansion of single-crystal forsterite to 1023 K by Fizeau interferometry // Phys. Chem. Miner., 1985, v. 12, p. 201-210. 94. Matsui M., Parker S.C., Leslie M. The MD simulation of the equation of state of MgO: Application as a pressure calibration standard at high temperature and high pressure // Amer. Miner., 2000, v. 85, p. 312-316. 95. Mayama N., Suzuki I., Saito T., Ohno I., Katsura T., Yoneda A. Temperature dependence of elastic moduli of β-(Mg,Fe)2SiO4 // Geophys. Res. Lett., 2004, v. 31, L04612, doi:10.1029/2003GL019247. 96. Meng Y., Weidner D., Gwanmesia G., Liebermann R., Vaughan M., Wang Y., Leinenweber K., Pacalo R., Yeganeh-Haeri A., Zhao Y. In situ high P-TX ray diffraction studies on three polymorphs (α, β, γ) of Mg2SiO4 // J. Geophys. Res.: Solid Earth, 1993, v. 98, p. 22199-22207. 97. Meng Y., Fei Y., Weidner D., Gwanmesia G., Hu J. Hydrostatic compression of γ-Mg2SiO4 to mantle pressures and 700 K: Thermal equation of state and related thermoelastic properties // Phys. Chem. Miner., 1994, v. 21, p. 407-412. 98. Morishima H., Kato T., Suto M., Ohtani E., Urakawa S., Utsumi W., Shimomura O., Kikegawa T. The phase boundary between α-and β-Mg2SiO4 determined by in situ X-ray observation // Science, 1994, v. 265, p. 1202-1203. 99. Murakami M., Hirose K., Kawamura K., Sata N., Ohishi Y. Post-perovskite phase transition in MgSiO3 // Science, 2004, v. 304, p. 855-858. 100. Murakami M., Hirose K., Sata N., Ohishi Y. Post-perovskite phase transition and mineral chemistry in the pyrolitic lowermost mantle // Geophys. Res. Lett., 2005, v. 32, L03304, doi:10.1029/2004GL021956. 101. Murakami M., Sinigeikin S.V., Bass J.D., Sata N., Ohishi Y., Hirose K. Sound velocity of MgSiO3 post-perovskite phase: A constraint on the D″ discontinuity // Earth Planet. Sci. Lett., 2007, v. 259, p. 18-23. 102. Murakami M., Ohishi Y., Hirao N., Hirose K. A perovskitic lower mantle inferred from high-pressure, high-temperature sound velocity data // Nature, 2012, v. 485, p. 90-94. 103. Oganov A.R., Brodholt J.P. High-pressure phases in the Al2SiO5 system and the problem of aluminous phase in the Earth’s lower mantle: ab initio calculations // Phys. Chem. Miner., 2000, v. 27, p. 430-439. 104. Oganov A.R., Ono S. Theoretical and experimental evidence for a post-perovskite phase of MgSiO3 in Earth’s D″ layer // Nature, 2004, v. 430, p. 445-448. 105. Oganov A.R., Price G.D. Ab initio thermodynamics of MgSiO3 perovskite at high pressures and temperatures // J. Chem. Phys., 2005, v. 122, p. 124501. 106. Oganov A.R., Martonak R., Laio A., Raiteri P., Parrinello M. Anisotropy of Earth’s D″ layer and stacking faults in the MgSiO3 post-perovskite phase // Nature, 2005, v. 438, p. 1142-1144. 107. Ono S., Oganov A.R. In situ observations of phase transition between perovskite and CaIrO3 type phase in MgSiO3 and pyrolitic mantle composition // Earth Planet. Sci. Lett., 2005, v. 236, p. 914-932. 108. Ono S., Katsura T., Ito E., Kanzaki M., Yoneda A., Walter M., Urakawa S., Utsumi W., Funakoshi K. In situ observation of ilmenite-perovskite phase transition in MgSiO3 using synchrotron radiation // Geophys. Res. Lett., 2001, v. 28, p. 835-838. 109. Ono S., Kikegawa T., Ohishi Y. Equation of state of CaIrO3-type MgSiO3 up to 144 GPa // Amer. Miner., 2006, v. 91, p. 475-478. 110. Ottonello G., Civalleri B., Ganguly J., Zuccolini M.V., Noel Y. Thermophysical properties of the α-β-γ polymorphs of Mg2SiO4: a computational study // Phys. Chem. Miner., 2009, v. 36, p. 87-106. 111. Piazzoni A., Steinle-Neumann G., Bunge H.P., Dolejš D. A mineralogical model for density and elasticity of the Earth’s mantle // Geochem. Geophys. Geosyst., 2007, v. 8, Q11010, doi:10.1029/2007GC001697. 112. Price G.D., Parker S.C., Leslie M. The lattice dynamics and thermodynamics of the Mg2SiO4 polymorphs // Phys. Chem. Miner., 1987, v. 15, p. 181-190. 113. Pushcharovsky D.Y., Pushcharovsky Y.M. The mineralogy and the origin of deep geospheres: A review // Earth-Science Rev., 2012, v. 113, p. 94-109. 114. Reynard B., Fiquet G., Itie J.-P., Rubie D.C. High-pressure X-ray diffraction study and equation of state of MgSiO3 ilmenite // Amer. Miner., 1996, v. 81, p. 45-50. 115. Ringwood A.E. Composition and petrology of the Earth’s mantle. New York, McGraw-Hill, 1975, 618 p. 116. Ringwood A.E., Major A. The system Mg2SiO4-Fe2SiO4 at high pressures and temperatures // Phys. Earth Planet. Int., 1970, v. 3, p. 89-108. 117. Robie R.A., Hemingway B.C., Takei H. Heat capacities and entropies of Mg2SiO4, Mn2SiO4, and 118. Co2SiO4 between 5 and 380 K // Amer. Miner., 1982, v. 67, p. 470-482. 119. Ross N.L., Hazen R.M. Single crystal X-ray diffraction study of MgSiO3 perovskite from 77 to 400 K // Phys. Chem. Miner., 1989, v. 16, p. 415-420. 120. Saxena S.K., Dubrovinsky L.S., Tutti F., Le Bihan T. Equation of state of MgSiO3 with the perovskite structure based on experimental measurement // Amer. Miner., 1999, v. 84, p. 226-232. 121. Senshu H., Maruyama S., Rino S., Santosh M. Role of tonalite-trodhjemite-granite (TTG) crust subduction on the mechanism of supercontinent breakup // Gondwana Res., 2009, v. 15, p. 433-442. 122. Shim S.-H. The postperovskite transition // Ann. Rev. Earth Planet. Sci., 2008, v. 36, p. 569-599. 123. Sinmyo R., Hirose K., Muto S., Ohishi Y., Yasuhara A. The valence state and partitioning of iron in the Earth’s lowermost mantle // J. Geophys. Res.: Solid Earth, 2011, v. 116, № B07205, doi:07210.01029/02010JB008179. 124. Stacey F., Davis P. High pressure equations of state with applications to the lower mantle and core // Phys. Earth Planet. Int., 2004, v. 142, p. 137-184. 125. Stixrude L., Lithgow-Bertelloni C. Mineralogy and elasticity of the oceanic upper mantle: Origin of the low-velocity zone // J. Geophys. Res.: Solid Earth, 2005, v. 110, B03204, doi:10.1029/2004JB002965. 126. Suito K. Phase relations of pure Mg2SiO4 up to 200 kilobars // High Press. Res.: Appl. Geophys. / Eds. M.H. Manghnani, S. Akimoto, 1977, p. 255-266. 127. Sumino Y., Nishizawa O., Goto T., Ohno I., Ozima M. Temperature variation of elastic constants of single-crystal forsterite between 190° and 400 °C // J. Phys. Earth, 1977, v. 25, p. 377-392. 128. Suzuki I., Ohtani E., Kumazawa M. Thermal expansion of γ-Mg2SiO4 // J. Phys. Earth, 1979, v. 27, p. 53-61. 129. Suzuki I., Ohtani E., Kumazawa M. Thermal expansion of modified spinel, β-Mg2SiO4 // J. Phys. Earth, 1980, v. 28, p. 273-280. 130. Suzuki I., Anderson O.L., Sumino Y. Elastic properties of a single-crystal forsterite Mg2SiO4, up to 1200 K // Phys. Chem. Miner., 1983, v. 10, p. 38-46. 131. Suzuki A., Ohtani E., Morishima H., Kubo T., Kanbe Y., Kondo T., Okada T., Terasaki H., Kato T., Kikegawa T. In situ determination of the phase boundary between wadsleyite and ringwoodite in Mg2SiO4 // Geophys. Res. Lett., 2000, v. 27, p. 803-806. 132. Takemura K., Dewaele A. Isothermal equation of state for gold with a He-pressure medium // Phys. Rev. B, 2008, v. 78, 104119, doi:10.1103/PhysRevB.78.104119. 133. Tange Y., Kuwayama Y., Irifune T., Funakoshi K.-I., Ohishi Y. P-V-T equation of state of MgSiO3 perovskite based on the MgO pressure scale: A comprehensive reference for mineralogy of the lower mantle // J. Geophys. Res.: Solid Earth, 2012, v. 117, B06201, doi:10.1029/2011JB008988. 134. Tateno S., Hirose K., Sata N., Ohishi Y. Determination of post-perovskite phase transition boundary up to 4400 K and implications for thermal structure in D″ layer // Earth Planet. Sci. Lett., 2009, v. 277, p. 130-136. 135. Trots D.M., Kurnosov A., Ballaran T.B., Frost D.J. High-temperature structural behaviors of anhydrous wadsleyite and forsterite // Amer. Miner., 2012, v. 97, p. 1582-1590. 136. Tsuchiya T., Tsuchiya J., Umemoto K., Wentzcovitch R.M. Phase transition in MgSiO3 perovskite in the Earth’s lower mantle // Earth Planet. Sci. Lett., 2004, v. 224, p. 241-248. 137. Utsumi W., Funamori N., Yagi T. Thermal expansivity of MgSiO3 perovskite under high pressures up to 20 GPa // Geophys. Res. Lett., 1995, v. 22, p. 1005-1008. 138. Vacher P., Mocquet A., Sotin C. Computation of seismic profiles from mineral physics: the importance of the non-olivine components for explaining the 660 km depth discontinuity // Phys. Earth Planet. Int., 1998, v. 106, p. 275-298. 139. Vanpeteghem C., Angel R., Ross N., Jacobsen S., Dobson D., Litasov K., Ohtani E. Al, Fe substitution in the MgSiO3 perovskite structure: A single-crystal X-ray diffraction study // Phys. Earth Planet. Int., 2006, v. 155, p. 96-103. 140. Vinet P., Ferrante J., Rose J., Smith J. Compressibility of solids // J. Geophys. Res.: Solid Earth, 1987, v. 92, p. 9319-9325. 141. Wang Y., Weidner D.J., Liebermann R.C., Zhao Y. P-V-T equation of state of (Mg,Fe)SiO3 perovskite: constraints on composition of the lower mantle // Phys. Earth Planet. Int., 1994, v. 83, p. 13-40. 142. Wang Y., Uchida T., Zhang J., Rivers M.L., Sutton S.R. Thermal equation of state of akimotoite 143. MgSiO3 and effects of the akimotoite-garnet transformation on seismic structure near the 660 km discontinuity // Phys. Earth Planet. Int., 2004, v. 143, p. 57-80. 144. Weidner D.J. A mineral physics test of a pyrolite mantle // Geophys. Res. Lett., 1985, v. 12, p. 417-420. 145. Yagi T., Bell P., Mao H. Phase relations in the system MgO-FeO-SiO2 between 150 and 700 kbar at 1000 °C // Year Book Carnegie Inst., Washington, 1979, v. 78, p. 614-618. 146. Ye Y., Schwering R.A., Smyth J.R. Effects of hydration on thermal expansion of forsterite, wadsleyite, and ringwoodite at ambient pressure // Amer. Miner., 2009, v. 94, p. 899-904. 147. Yoneda A., Morioka M. Pressure derivatives of elastic constants of single crystal forsterite // AGU Geophys. Monograph. Ser. 67, 1992, p. 207-214. 148. Yoshino T., Manthilake G., Matsuzaki T., Katsura T. Dry mantle transition zone inferred from the conductivity of wadsleyite and ringwoodite // Nature, 2008, v. 451, p. 326-329. 149. Yu Y.G., Wu Z., Wentzcovitch R.M. α-β-γ transformations in Mg2SiO4 in Earth’s transition zone // Earth Planet. Sci. Lett., 2008, v. 273, p. 115-122. 150. Yu Y.G., Vinograd V.L., Winkler B., Wentzcovitch R.M. Phase equilibria of (Mg,Fe)2SiO4 at the Earth’s upper mantle conditions from first-principles studies // Phys. Earth Planet. Int., 2013, v. 217, p. 36-47. 151. Zha C.-S., Duffy T.S., Downs R.T., Mao H.-K., Hemley R.J. Sound velocity and elasticity of single-crystal forsterite to 16 GPa // J. Geophys. Res.: Solid Earth, 1996, v. 101, p. 17535-17545. 152. Zha C.-S., Duffy T.S., Mao H.-K., Downs R.T., Hemley R.J., Weidner D.J. Single-crystal elasticity of β-Mg2SiO4 to the pressure of the 410 km seismic discontinuity in the Earth’s mantle // Earth Planet. Sci. Lett., 1997, v. 147, p. E9-E15. 153. Zhang L. Single crystal hydrostatic compression of (Mg,Mn,Fe,Co)2SiO4 olivines // Phys. Chem. Miner., 1998, v. 25, p. 308-312. 154. Zhou C., Gréaux S., Nishiyama N., Irifune T., Higo Y. Sound velocities measurement on MgSiO3 akimotoite at high pressures and high temperatures with simultaneous in situ X-ray diffraction and ultrasonic study // Phys. Earth Planet. Int., 2014, v. 228, p. 97-105.