Инд. авторы: | Dorogokupets P.I., Sokolova T.S., Dymshits A.M., Litasov K.D. |
Заглавие: | Thermodynamic properties of rock-forming oxides, α-al2o3, cr2o3, α-fe2o3, and fe3o4 at high temperatures and pressures |
Библ. ссылка: | Dorogokupets P.I., Sokolova T.S., Dymshits A.M., Litasov K.D. Thermodynamic properties of rock-forming oxides, α-al2o3, cr2o3, α-fe2o3, and fe3o4 at high temperatures and pressures // Геодинамика и тектонофизика. - 2016. - Vol.7. - Iss. 3. - P.459-476. - EISSN 2078-502X. |
Внешние системы: | РИНЦ: 26902030; |
Реферат: | rus: На основе свободной энергии Гельмгольца построены уравнения состояния корунда (α-Al2O3), эсколаита (Cr2O3), гематита (α-Fe2O3) и магнетита (Fe3O4) путем одновременной оптимизации ультразвуковых, рентгеновских, дилатометрических данных и термохимических измерений теплоемкости при атмосферном давлении и при повышенных температурах и давлениях. Магнитный вклад в свободную энергию Гельмгольца для Cr2O3, α-Fe2O3 и Fe3O4 определен с помощью модели A.T. Динсдала [Dinsdale, 1991]. Предложенный подход к построению уравнений состояния хорошо описывает À-видную аномалию в теплоемкостях эсколаита, гематита и магнетита, которая связана с изменением магнитных свойств. Полная термодинамическая модель уравнений состояния α-Al2O3, Cr2O3, α-Fe2O3 и Fe3O4 содержит группу из семи фиксированных параметров и группу из девяти подгоночных параметров, значения которых определяются методом наименьших квадратов. Рассчитанные термодинамические функции породообразующих оксидов алюминия, хрома и железа хорошо согласуются со справочными данными и экспериментальными измерениями при атмосферном давлении, а также с современными P-V-T измерениями в алмазных наковальнях и многопуансонных аппаратах высокого давления. Приведена табуляция термодинамических функций (объем, коэффициент термического расширения, изобарная и изохорная теплоемкость, энтропия, адиабатический и изотермический модули сжатия, термодинамический параметр Грюнейзена и энергия Гиббса) корунда, эсколаита, гематита и магнетита до температуры 2000 K при разных давлениях (до 80, 70, 50 и 20 ГПа, соответственно). Таким образом, полученные уравнения состояния уточняют термодинамику оксидных фаз от стандартных условий до температур и давлений, соответствующих условиям мантии Земли. Рассчитанная энергия Гиббса породообразующих оксидов алюминия, хрома и железа может быть использована для построения фазовых диаграмм минеральных систем с их участием, имеющих принципиальное значение для интерпретации глобальных и промежуточных границ в земной мантии. eng: Equations of state of corundum (α-Al2O3), eskolaite (Cr2O3), hematite (α-Fe2O3), and magnetite (Fe3O4) are constructed based on the Helmholtz free energy by simultaneous optimization of ultrasonic, X-ray diffraction, dilatometric, and thermochemical measurements. The magnetic contribution to Cr2O3, α-Fe2O3, and Fe3O4 Helmholtz free energy was determined via the A.T. Dinsdale model [Dinsdale, 1991]. The calculated thermodynamic properties of rock-forming oxides of aluminum, chromium, and iron are in good agreement with the reference data and experimental measurements at room pressure, as well as with P-V-T measurements at high temperatures and pressures. Thermodynamic functions (x, α, S, CP, CV, KT, KS, γth, G) of corundum, eskolaite, hematite, and magnetite are calculated at different pressures (up to 80, 70, 50 and 20 GPa, respectively) and temperatures (up to 2000 K), and the results are tabulated. The calculated Gibbs energy of rock-forming oxides can be used to construct the phase diagrams of mineral systems, which include the oxides under the conditions of the Earth's mantle. |
Ключевые слова: | equation of state; Helmholtz free energy; oxide; corundum; Eskolaite; hematite; magnetite; mantle; мантия; магнетит; гематит; эсколаит; корунд; оксид; свободная энергия Гельмгольца; уравнение состояния; термодинамика; thermodynamics; |
Издано: | 2016 |
Физ. характеристика: | с.459-476 |
Цитирование: | 1. Aldebert P., Traverse J.P., 1984. α-Al2O3: A high temperature thermal expansion standard. High Temperatures. High Pressures 16 (2), 127-135. 2. Al'tshuler L.V., Brusnikin S.E., Kuz'menkov E.A., 1987. Isotherms and Grüneisen functions for 25 metals. Journal of Applied Mechanics and Technical Physics 28 (1), 129-141. http://dx.doi.org/10.1007/BF00918785. 3. d'Amour H., Schiferl D., Denner W., Schulz H., Holzapfel W.B., 1978. High-pressure single-crystal structure determinations for ruby up to 90 kbar using an automatic diffractometer. Journal of Applied Physics 49 (8), 4411-4416. http://dx.doi.org/10.1063/1.325494. 4. Anderson O.L., Isaak D.G., 1995. Elastic constants of mantle minerals at high temperature. In: T.J. Ahrens (Ed.), Mineral physics and crystallography. A Handbook of Physical Constants. AGU Reference Shelf 2. AGU, Washington, p. 64-97. http://dx.doi.org/10.1029/RF002p0064. 5. Archer D.G., 1993. Thermodynamic properties of synthetic sapphire (a-Al2Ü3), standard reference material 720 and the effect of temperature-scale differences on thermodynamic properties. Journal of Physical and Chemical Reference Data 22 (6), 1441-1453. http://dx.doi.org/10.1063/1.555931. 6. Aristova N.M., Gusarov A.V., 2008. ChemNet. Available from: http://www.chem.msu.su/Zn/Cr/welcome.html (last accessed July 14, 2016). 7. Brosh E., Shneck Z., Makov G., 2008. Explicit Gibbs free energy equation of state for solids. Journal of Physics and Chemistry of Solids 69 (8), 1912-1922. http://dx.doi.org/10.1016Zj.jpcs.2008.01.019. 8. Brown M.J., 1999. The NaCl pressure standard. Journal of Applied Physics 86 (10), 5801-5808. http://dx.doi.org/ 10.1063/1.371596. 9. Bruce R.H., Cannel D.S., 1977. Specific heat of Cr2Ü3 near the Neel temperature. Physical Review B 15 (9), 4451-4458. http://dx.doi.org/10.1103/PhysRevB.15.4451. 10. Chase M.W., 1998. NIST-JANAF thermochemical tables. Fourth Edition. Journal of Physical and Chemical Reference Data, Monograph 9. AIP, New York, 1951 p. 11. Chung D.H., Simmons G., 1968. Pressure and temperature dependences of the isotropic elastic moduli of polycrystalline alumina. Journal of Applied Physics 39 (11), 5316-5326. http://dx.doi.org/10.1063/1.1655961. 12. Decker D.L., 1971. High-pressure equation of state for NaCl, KCl, and CsCl. Journal of Applied Physics 42 (8), 3239-3244. http://dx.doi.org/10.1063/1.1660714. 13. Dera P., Lavina B., Meng Y., Prakapenka V.B., 2011. Structural and electronic evolution of Cr2Ü3 on compression to 55 GPa. Journal of Solid State Chemistry 184 (11), 3040-3049. http://dx.doi.org/10.1016/j.jssc.2011.09.021. 14. Dewaele A., Torrent M. 2013. Equation of state of α-Al2O3. Physical Review B 88 (6), 064107. http://dx.doi.org/ 10.1103/PhysRevB.88.064107. 15. Dinsdale A.T., 1991. SGTE data for pure elements. CALPHAD 15 (4), 317-425. http://dx.doi.org/10.1016/0364-5916(91)90030-N. 16. Dorogokupets P.I., 1995. Equation of state for lambda transition in quartz. Journal of Geophysical Research 100 (B5), 8489-8499. http://dx.doi.org/10.1029/94JB02917. 17. Dorogokupets P.I., 2010. P-V-T equations of state of MgÜ and thermodynamics. Physics and Chemistry of Minerals 37 (9), 677-684. http://dx.doi.org/10.1007/s00269-010-0367-2. 18. Dorogokupets P.I., Dewaele A., 2007. Equations of state of MgÜ, Au, Pt, NaCl-B1, and NaCl-B2: Internally consistent high-temperature pressure scales. High Pressure Research 27 (4), 431-446. http://dx.doi.org/10.1080/08957 950701659700. 19. Dorogokupets P.I., Dymshits A.M., Sokolova T.S., Danilov B.S., Litasov K.D., 2015. The equations of state of forsterite, wadsleyite, ringwoodite, akimotoite, MgSiÜ3-perovskite, and postperovskite and phase diagram for the Mg2SiO4 system at pressures of up to 130 GPa. Russian Geology and Geophysics 56 (1-2), 172-189. http://dx.doi.org/ 10.1016/j.rgg.2015.01.011. 20. Dorogokupets P.I., Oganov A.R., 2007. Ruby, metals, and MgÜ as alternative pressure scales: A semiempirical description of shock-wave, ultrasonic, x-ray, and thermochemical data at high temperatures and pressures. Physical Review B 75 (2), 024115. http://dx.doi.org/10.1103/PhysRevB.75.024115. 21. Dorogokupets P.I, Ponomarev E.M., Melekhova E.A., 1999. Üptimization of experimental data on the heat capacity, volume, and bulk moduli of minerals. Petrology 7 (6), 574-591 22. Дорогокупец П.И., Соколова Т.С., Данилов Б.С., Литасов К.Д. Почти абсолютные уравнения состояния алмаза, Ag, Al, Au, Cu, Mo, Nb, Pt, Ta, W для квазигидростатических условий // Геодинамика и тектонофизика. 2012. Т. 3. № 2. С. 129-166. dx.doi.org/10.5800/GT-2012-3-2-0067. 23. Дорогокупец П.И., Соколова Т.С., Литасов К.Д. Термодинамические свойства bcc-Fe до температуры плавления и до давления 15 ГПа // Геодинамика и тектонофизика. 2014. Т. 5. № 4. С. 1033-1044. dx.doi.org/10.5800/GT-2014-5-4-0166. 24. Dubrovinskaya N.A., Dubrovinsky L.S., Saxena S.K., 1997. Systematics of thermodynamic data on solids: Thermochemical and pressure-volume-temperature properties of some minerals. Geochimica et Cosmochimica Acta 61 (19), 4151-4158. http://dx.doi.org/10.1016/S0016-7037(97)00233-0. 25. Dubrovinsky L.S., Saxena S.K., Lazor P., 1998. High-pressure and high-temperature in situ X-ray diffraction study of iron and corundum to 68 GPa using an internally heated diamond anvil cell. Physical and Chemistry of Minerals 25 (6), 434-441. http://dx.doi.org/10.1007/s002690050133. 26. Dymshits A.M., Dorogokupets P.I., Sharygin I.S., Litasov K.D., Shatskiy A., Rashchenko S.V., Ohtani E., Suzuki A., Higo Y., 2016. Thermoelastic properties of chromium oxide Cr2Ü3 (eskolaite) at high pressures and temperatures. Physics and Chemistry of Minerals 43 (6), 447-458. http://dx.doi.org/10.1007/s00269-016-0808-7. 27. Finger L.W., Hazen R.M., 1978. Crystal structure and compression of ruby to 46 kbar. Journal of Applied Physics 49 (12), 5823-5826. http://dx.doi.org/10.1063A.324598. 28. Finger L.W., Hazen R.M., 1980. Crustal structure and isothermal compression of Fe2Ü3, Cr2Ü3, and V2Ü3 to 50 kbars. Journal of Applied Physics 51 (10), 5362-5367. http://dx.doi.org/10.1063A.327451. 29. Funamori N., Jeanloz R., 1997. High-pressure transformation of Al2Ü3. Science 278 (5340), 1109-1111. http://dx.doi. org/10.1126/science.278.5340.1109. 30. Gatta G.D., Kantor I., Ballaran T.B., Dubrovinsky L., McCammon C., 2007. Effect of non-hydrostatic conditions on the elastic behavior of magnetite: an in situ single-crystal X-ray diffraction study. Physical and Chemistry of Minerals 34 (9), 627-635. http://dx.doi.org/10.1007/s00269-007-0177-3. 31. Gerya T.V., Maresch W.V., Podlesskii K.K., Perchuk L.L., 2004. Semi-empirical Gibbs free energy formulations for minerals and fluids for use in thermodynamic databases of petrological interest. Physics and Chemistry of Minerals 31 (7), 429-455. http://dx.doi.org/10.1007/s00269-004-0409-8. 32. Gerya T.V., Podlesskii K.K., Perchuk L.L., Swamy V., Kosyakova N.A., 1998. Equations of state of minerals for thermodynamic databases used in petrology. Petrology 6 (6), 511-526. 33. Goto T., Anderson O.L., Ohno I., Yamamoto S., 1989. Elastic constants of corundum up to 1825 K. Journal of Geophysical Research 94 (B6), 7588-7602. http://dx.doi.org/10.1029/JB094iB06p07588. 34. Grevel K.-D., Burchard M., Fabhauer D.F., 2000. Pressure-volume-temperature behavior of diaspore and corundum: An in situ X-ray diffraction study comparing different pressure media. Journal of Geophysical Research 105 (B12), 27877-27887. http://dx.doi.org/10.1029/2000JB900323. 35. Gronvold F., Samuelsen E.J., 1975. Heat capacity and thermodynamic properties of a-Fe2Ü3 in the region 300-1050 K. Antiferromagnetic transition. Journal of Physics and Chemistry Solids 36 (4), 249-256. http://dx.doi.org/10.1016/ 0022-3697(75)90017-7. 36. Gronvold F., Sveen A., 1974. Heat capacity and thermodynamic properties of synthetic magnetite (Fe3Ü4) from 300 to 1050 K. Ferrimagnetic transition and zero-point entropy. Journal of Chemistry Thermodynamics 6 (9), 859-872. http://dx.doi.org/10.1016/0021-9614(74)90230-4. 37. Gronvold F., Westrum E.F., 1959. α-Ferric Oxide: low temperature heat capacity and thermodynamic functions. Journal of the American Chemical Society 81 (8), 1780-1783. http://dx.doi.org/10.1021/ja01517a002. 38. Gurevich V.M., Kuskov O.L., Smirnova N.N., Gavrichev K.S., Markin A.V., 2009. Thermodynamic functions of eskolaite Cr2Ü3(c) at 0-1800 K. Geochemistry International 47 (12), 1170-1179. http://dx.doi.org/10.1134/S0016702909120027. 39. Гурвич Л.В., Вейц И.В., Медведев В.А. Термодинамические свойства индивидуальных веществ. М.: Наука, 1981. Т. 3. 400 с. 40. Hemingway B.S., 1990. Thermodynamic properties for bunsenite, NiÜ, magnetite, Fe3Ü4, and hematite, Fe2O3 with comments on selected oxygen buffer reactions. American Mineralogist 75 (7-8), 781-790. 41. Hill A.H., Harrison A., Dickinson C., Zhou W., Kockelmann W., 2010. Crystallographic and magnetic studies of mesoporous eskolaite, Cr2O3. Microporous and Mesoporous Materials 130 (1-3), 280-286. http://dx.doi.org/10.1016/ j.micromeso.2009.11.021. 42. Holland T.J.B., Powell R., 2011. An improved and extended internally consistent thermodynamic dataset for phases of petrological interest, involving a new equation of state for solids. Journal of Metamorphic Geology 29 (3), 333-383. http://dx.doi.org/10.1111/j.1525-1314.2010.00923.x. 43. Ito E., Fukui H., Katsura T., Yamazaki D., Yoshino T., Aizawa Y., Kubo A., Yokoshi S., Kawabe K., Zhai S., Shatzkiy A., Okube M., Nozawa A., Funakoshi K.-I., 2009. Determination of high-pressure phase equilibria of Fe2O3 using the Kawai-type apparatus equipped with sintered diamond anvils. American Mineralogist 94 (2-3), 205-209. http:// dx.doi.org/10.2138/am.2009.2913. 44. Jacobs M.H.G., Oonk H.A.J., 2001. The Gibbs energy formulation of the a, ß, and y forms of Mg2SiÜ4 using Grover, Getting and Kennedy's empirical relation between volume and bulk modulus. Physics and Chemistry of Minerals 28 (8), 572-585. http://dx.doi.org/10.1007/s002690100180. 45. Jacobs M.H.G., Schmid-Fetzer R., 2010. Thermodynamic properties and equation of state of fcc aluminum and bcc iron, derived from a lattice vibrational method. Physics and Chemistry of Minerals 37 (10), 721-739. http://dx.doi.org/ 10.1007/s00269-010-0371-6. 46. Jacobs M.H.G., Schmid-Fetzer R., Berg A.P., 2013. An alternative use of Kieffer's lattice dynamics model using vibrational density of states for constructing thermodynamic databases. Physics and Chemistry of Minerals 40 (3), 207-227. http://dx.doi.org/10.1007/s00269-012-0562-4. 47. Jephcoat A.P., Hemley R.J., Mao H.K., 1988. X-ray diffraction of ruby (AhO3:Cr3+) to 175 GPa. Physica B+C 150 (1-2), 115-121. http://dx.doi.org/10.1016/0378-4363(88)90112-X. 48. Kantor A., Kantor I., Merlini M., Glazyrin K., Prescher C., Hanfland M., Dubrovinsky L., 2012. High-pressure structural studies of eskolaite by means of single-crystal X-ray diffraction. American Mineralogist 97 (10), 1764-1770. http://dx.doi.org/10.2138/am.2012.4103. 49. Kim-Zajonz J., Werner S., Shultz H., 1999. High pressure single crystal X-ray diffraction study on ruby up to 31 GPa. Zeitshrift fur Kristallographie 214 (6), 331-336. http://dx.doi.org/10.1524/zkri.1999.214.6.331. 50. Kirby R.K., Hahn T.A., Rothrock B.D., 1972. Thermal expansion. In: B.H. Billings, D.E. Gray (Eds.), American Institute of Physics Handbook, 3rd edition. McGraw-Hill, New York, p. 4119-4142. 51. Klemme S., O'Neill H.S.C., Schnelle W., Gmelin E., 2000. The heat capacity of MgCr2O4, FeCr2O4, and Cr2O3 at low temperatures and derived thermodynamic properties. American Mineralogist 85 (11-12), 1686-1693. http://dx.doi. org/10.2138/am-2000-11-1212. 52. Lin J.-F., Degtyareva O., Prewitt C.T., Dera P., Sata N., Gregoryanz E., Mao H-K., Hemley R.J., 2004. Crystal structure of a high-pressure/high-temperature phase of alumina by in situ X-ray diffraction. Nature Materials 3 (6), 389-393. http://dx.doi.org/10.1038/nmat1121. 53. Liu Y., Oganov A.R., Wang S., Zhu Q., Dong X., Kresse G., 2015. Prediction of new thermodynamically stable aluminum oxides. Scientific Reports 5, 9518. http://dx.doi.org/10.1038/srep09518. 54. Logvinova A.M., Wirth R., Sobolev N.V., Seryotkin Y.V., Yefimova E.S., Floss C., Taylor L.A., 2008. Eskolaite associated with diamond from the Udachnaya kimberlite pipe, Yakutia, Russia. American Mineralogist 93 (4), 685-690. http://dx. doi.org/10.2138/am.2008.2670. 55. Moore G.E., Kelly K.K., 1944. High-temperature heat contents of the chromium carbides and chromic oxide. In: US Bureau of Mines Technical Report, vol. 662, p. 10-15. 56. Muan A., Sömiya S., 1959. Phase equilibrium studies in the system iron oxide-A12Ü3-Cr2Ü3. Journal of the American Ceramic Society 42 (12), 603-613. http://dx.doi.org/10.1111/j.1151-2916.1959.tb13581.x. 57. Nakagiri N., Manghnani M.H., Ming L.C., Kimura S., 1986. Crystal structure of magnetite under pressure. Physical and Chemistry of Minerals 13 (4), 238-244. http://dx.doi.org/10.1007/BF00308275. 58. Oganov A.R., Ono S., 2005. The high-pressure phase of alumina and implications for Earth’s D" layer. Proceedings of the National Academy of Sciences 102 (31), 10828-10831. http://dx.doi.org/10.1073/pnas.0501800102. 59. Ono S., Ohishi Y., 2005. In situ X-ray observation of phase transformation in Fe2Ü3 at high pressures and high temperatures. Journal of Physics and Chemistry of Solids 66 (10), 1714-1720. http://dx.doi.org/10.1016/j.jpcs.2005.06. 010. 60. Otero-de-la-Roza A., Luana V., 2011. Equations of state and thermodynamics of solids using empirical corrections in the quasiharmonic approximation. Physical Review B 84 (18), 184103. http://dx.doi.org/10.1103/PhysRevB. 84.184103. 61. Пущаровский Ю.М., Пущаровский Д.Ю. Геология мантии Земли. М.: ГЕОС, 2010. 140 с 62. Reichmann H.J., Jacobsen S.D., 2004. High-pressure elasticity of a natural magnetite crystal. American Mineralogist 89 (7), 1061-1066. http://dx.doi.org/10.2138/am-2004-0718. 63. Richet P., Xu J.-A., Mao H.-K., 1988. Quasi-hydrostatic compression of ruby to 500 kbar. Physical and Chemistry of Minerals 16 (3), 207-211. http://dx.doi.org/10.1007/BF00220687. 64. Ricolleau A., Fei Y., 2016. Equation of state of the high-pressure Fe3Ü4 phase and a new structural transition at 70 GPa. American Mineralogist 101 (3), 719-725. http://dx.doi.org/10.2138/am-2016-5409. 65. Robie R.A., Hemingway B.S., Fisher J.R., 1978. Thermodynamic Properties of Minerals and Related Substances at 298.15 K and 1 Bar Pressure and at Higher Temperatures. Washington, 456 p. 66. Sato Y., Akimoto S., 1979. Hydrostatic compression of four corundum-type compounds: α-Al2O3, V2O3, Cr2O3, and α-Fe2O3. Journal of Applied Physics 50 (8), 5285. http://dx.doi.org/10.1063/1.326625. 67. Saxena S.K., Shen G., 1992. Assessed data on heat capacity, thermal expansion and compressibility for some oxides and silicates. Journal of Geophysical Research 97 (B13), 19813-19825. http://dx.doi.org/10.1029/92JB01555. 68. Schauer A., 1965. Thermal expansion, Grueneisen parameter, and temperature dependence of lattice vibration frequencies of aluminum oxide. Canadian Journal of Physics 43 (4), 523-531. http://dx.doi.org/10.1139/p65-049. 69. Schultz A.H., Stubican V.S., 1970. Separation of phases by spinodal decomposition in the systems Al2O3-Cr2O3, and Al2O3-Cr2O3-Fe2O3. Journal of the American Ceramic Society 53 (11), 613-616. http://dx.doi.org/10.1111/j.1151-2916.1970.tb15984.x. 70. Shebanova O.N., Lazor P., 2003. Vibrational modeling of the thermodynamic properties of magnetite (Fe3O4) at high pressure from Raman spectroscopic study. Journal of Chemical Physics 119 (12), 6100-6110. http://dx.doi.org/ 10.1063/1.1602072. 71. Shim S-H., Dufjy T.S., Jeanloz R., Yoo C.-S., Iota V., 2004. Raman spectroscopy and x-ray diffraction of phase transitions in Cr2Ü3 to 61 GPa. Physical Review B 69 (14), 144107. http://dx.doi.org/10.1103/PhysRevB.69.144107. 72. Sivasubramanian K., Raju S., Mohandas E., 2001. Estimating enthalpy and bulk modulus from thermal expansion data -a case study with a-AhÜ3 and SiC. Journal of the European Ceramic Society 21 (9), 1229-1235. http://dx.doi.org/ 10.1016/S0955-2219(00)00323-X. 73. Skinner B.J., 1966. Section 6: Thermal expansion. In: S.P. Clark (Ed.), Handbook of Physical Constants. Geological Society of America Memoirs, vol. 97, p. 75-96. http://dx.doi.org/10.1130/MEM97-p75. 74. Snow C.L., Lee C.R., Shi Q., Boerio-Goates J., Woodfield B.F., 2010. Size-dependence of the heat capacity and thermodynamic properties of hematite (a-Fe2Ü3). Journal of Chemical Thermodynamics 42 (9), 1142-1151. http://dx.doi. org/10.1016/j.jct.2010.04.009. 75. Sokolova T.S., Dorogokupets P.I., Dymshits A.M., Danilov B.S., Litasov K.D., 2016. Microsoft excel spreadsheets for calculation of P-V-T relations and thermodynamic properties from equations of state of MgÜ, diamond and nine metals as pressure markers in high-pressure and high-temperature experiments. Computers and Geosciences 94, 162-169. http://dx.doi.org/10.1016/j.cageo.2016.06.002. 76. Sokolova T.S., Dorogokupets P.I., Litasov K.D., 2013. Self-consistent pressure scales based on the equations of state for ruby, diamond, MgÜ, B2-NaCl, as well as Au, Pt, and other metals to 4 Mbar and 3000 K. Russian Geology and Geophysics 54 (2), 181-199. http://dx.doi.org/10.1016/j.rgg.2013.01.005. 77. Stixrude L., Lithgow-Bertelloni C., 2005. Thermodynamics of mantle minerals - I. Physical properties. Geophysical Journal International 162 (2), 610-632. http://dx.doi.org/10.1111/j.1365-246X.2005.02642.x. 78. Strässle T., Klotz S., Kunc K., Pomjakushin V., White J.S., 2014. Equation of state of lead from high-pressure neutron diffraction up to 8.9 GPa and its implication for the NaCl pressure scale. Physical Review B 90 (1), 014101. http:// dx.doi.org/10.1103/PhysRevB.90.014101. 79. Tucek J., Machala L., Ono S., Namai A., Yoshikiyo M., Imoto K., Tokoro H., Ohkoshi S., Zboril R., 2015. Zeta-Fe2O3 - A new stable polymorph in iron(III) oxide family. Scientific Reports 5, 15091. http://dx.doi.org/10.1038/srep15091. 80. Umemoto K., Wentzcovitch R.M., 2008. Prediction of an U2S3-type polymorph of Al2O3 at 3.7 Mbar. Proceedings of the National Academy of Sciences 105 (18), 6526-6530. http://dx.doi.org/10.1073/pnas.0711925105. 81. Vinet P., Ferrante J., Rose J.H., Smith J.R., 1987. Compressibility of solids. Journal of Geophysical Research 92 (B9), 9319-9325. http://dx.doi.org/10.1029/JB092iB09p09319. 82. Wachtman J.B., Scuderi T.G., Gleek G.W., 1962. Linear thermal expansion of aluminum oxide and thorium oxide from 100 to 1100 К Journal of the American Ceramic Society 45 (7), 319-323. http://dx.doi.org/10.1111/j.1151-2916.1962.tb11159.x. 83. Wessel C., Dronskowski R., 2013. A first-principles study on chromium sesquioxide, Cr2Ü3. Journal of Solid State Chemistry 199, 149-153. http://dx.doi.org/10.1016/j.jssc.2012.12.019 84. Westrum E.F., Gronvold F., 1969. Magnetite (Fe3Ü4) heat capacity and thermodynamic properties from 5 to 350 K, low-temperature transition. Journal of Chemical Thermodynamics 1 (6), 543-557. http://dx.doi.org/10.1016/0021-9614(69)90015-9. 85. White G.K., Roberts R.B., 1983. Thermal expansion of reference materials: Tungsten and a-AhÜ3. High Temperatures. High Pressures 15 (3), 321-328. 86. Wilburn D.R., Bassett W.A., Sato Y., Akimoto S., 1978. X ray diffraction compression studies of hematite under hydrostatic, isothermal conditions. Journal of Geophysical Research 83 (B7), 3509-3512. http://dx.doi.org/10.1029/ JB083iB07p03509. 87. Woodland A.B., Frost D.J., Trots D.M., Klimm K., Mezouar M., 2012. In situ observation of the breakdown of magnetite (Fe3Ü4) to Fe4Ü5 and hematite at high pressures and temperatures. American Mineralogist 97 (10), 1808-1811. http://dx.doi.org/10.2138/am.2012.4270. 88. Worlton T.G., Brugger R.M., Bennion R.B., 1968. Pressure dependence of the Néel temperature of Cr2Ü3. Journal of Physics and Chemistry of Solids 29 (3), 435-438. http://dx.doi.org/10.1016/0022-3697(68)90120-0. 89. Zharkov V.N., Kalinin V.A., 1971. Equations of State of Solids at High Pressures and Temperatures. Consultants Bureau, New York, 257 p. 90. Ziemniak S.E., Anovitz L.M., Castelli R.A., Porter W.D., 2007. Thermodynamics of Cr2O3, FeCr2O4, ZnCr2O4, and CoCr2O4. Journal of Chemistry Thermodynamics 39 (11), 1474-1492. http://dx.doi.org/10.1016/j.jct.2007.03.001. |