Theoretical models and experimental determination methods for equations of state of silicate melts: A review

  • Juntao Hou
  • Qiong LiuEmail author


Silicate melts are very active in the interior of the Earth and other terrestrial planets, and are important carriers for the transport of material and energy. The determination of the equation of state (EOS) for silicate melts and the acquisition of a precise quantitative relationship between molar volume (or density) and temperature, pressure, and composition is essential for simulating the generation, migration, and eruption processes of magmas and the evolution of the magma ocean stage during the early formation of the Earth and other terrestrial planets, for calculating and modeling the phase equilibria involving silicate melts, and for revealing the variation of the microstructure of silicate melts with pressure. However, it is experimentally challenging to determine the volumetric properties of silicate melts and the accumulated density data at high pressure are still very limited due to a series of problems such as: the high liquidus temperature of silicate rocks; proneness for silicate melts to react with sample capsules to change the melt composition; and proneness for melts to flow and leak during the high pressure and high temperature experiments. In recent years, there is rapid progress in the high pressure and high temperature experimental techniques, in terms of not only the extension of temperature and pressure ranges but also the improvement on the accuracy of measurements, and the emergence of new methods for in-situ measurements. Here, we review the widely-used theoretical models of ambient-pressure and high-pressure EOS for silicate melts, and illustrate some problems that need to be solved urgently: (1) the room pressure EOS for iron- and titanium-bearing silicate melts needs to be improved; (2) the partial molar properties of the H2O and CO2 components in silicate melts containing volatile components may vary markedly with the melt composition, which need to be addressed in high-pressure EOS; (3) how the formulation and applicable range of EOS correspond to changes in melt structure and compression mechanism requires further study. We highlight the basic principle and applicable range of various methods for determining the EOS for silicate melts, and compare the advantages and disadvantages of doublebob Archimedes method, fusion curve analysis, shock compression experiments, sink-float method, X-ray absorption, X-ray diffraction and ultrasonic interferometry. Future trends in this field are to develop experimental techniques for in situ measurements on melt density or sound velocity at high temperature and high pressure and to accumulate more experimental data, and on the other hand, to improve the theoretical models of the EOS for silicate melts by a combination of research on the microstructure and compression mechanisms of silicate melts.


Silicate melts Equations of state Theoretical models Determination methods Melt structure Compression mechanisms 


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Constructive comments made by Yongfei Zheng, the chief editor, two anonymous reviewers, and Haoran Ma from School of Earth and Space Sciences, Peking University, which greatly improved the quality of this manuscript, are highly appreciated. This work was supported by the National Natural Science Foundation of China (Grant Nos. 40972028, 41520104004, and 41672036).


  1. Agee C B. 1998. Crystal-liquid density inversions in terrestrial and lunar magmas. Phys Earth Planet Inter, 107: 63–74CrossRefGoogle Scholar
  2. Agee C B. 2008. Static compression of hydrous silicate melt and the effect of water on planetary differentiation. Earth Planet Sci Lett, 265: 641–654CrossRefGoogle Scholar
  3. Agee C B, Walker D. 1988. Static compression and olivine flotation in ultrabasic silicate liquid. J Geophys Res, 93: 3437–3449CrossRefGoogle Scholar
  4. Agee C B, Walker D. 1993. Olivine flotation in mantle melt. Earth Planet Sci Lett, 114: 315–324CrossRefGoogle Scholar
  5. Ahart M, Karandikar A, Gramsch S, Boehler R, Hemley R J. 2014. High PT Brillouin scattering study of H2O melting to 26 GPa. High Pressure Res, 34: 327–336CrossRefGoogle Scholar
  6. Ahrens T J. 1993. Equation of state. In: Asay J R, Shahinpoor M, eds. High-Pressure Shock Compression of Solids. New York: Springer-Verlag. 75–113CrossRefGoogle Scholar
  7. Ai Y H, Lange R. 2004a. An ultrasonic frequency sweep interferometer for liquids at high temperature: 1. Acoustic model. J Geophys Res, 109: 12203CrossRefGoogle Scholar
  8. Ai Y H, Lange R. 2004b. An ultrasonic frequency sweep interferometer for liquids at high temperature: 2. Mechanical assembly, signal processing, and application. J Geophys Res, 109: B12204CrossRefGoogle Scholar
  9. Ai Y, Lange R A. 2008. New acoustic velocity measurements on CaOMgO- Al2O3-SiO2 liquids: Reevaluation of the volume and compressibility of CaMgSi2O6-CaAl2Si2O8 liquids to 25 GPa. J Geophys Res, 113: 04203CrossRefGoogle Scholar
  10. Álvarez-Murga M, Perrillat J P, Le Godec Y, Bergame F, Philippe J, King A, Guignot N, Mezouar M, Hodeau J L. 2017. Development of synchrotron X-ray micro-tomography under extreme conditions of pressure and temperature. J Synchrotron Radiat, 24: 240–247CrossRefGoogle Scholar
  11. Angel R J. 2000. Equations of state. Rev Mineral Geochem, 41: 35–59CrossRefGoogle Scholar
  12. Angel R J, Gonzalez-Platas J, Alvaro M. 2014. EosFit7c and a Fortran module (library) for equation of state calculations. Z Krist-Cryst Mater, 229: 405–419Google Scholar
  13. Asimow P D. 2012. Shock compression of preheated silicate liquids: Apparent universality of increasing Grüneisen parameter upon compression. In: Elert M L, Buttler W T, Borg J P, Jordan J L, Vogler T J, eds. AIP Conference Proceedings. Melville: American Institute of Physics. 1426: 887–890CrossRefGoogle Scholar
  14. Asimow P D, Ahrens T J. 2010. Shock compression of liquid silicates to 125 GPa: The anorthite-diopside join. J Geophys Res, 115: B10209CrossRefGoogle Scholar
  15. Ayrinhac S, Gauthier M, Le Marchand G, Morand M, Bergame F, Decremps F. 2015. Thermodynamic properties of liquid gallium from picosecond acoustic velocity measurements. J Phys-Condens Matter, 27: 275103CrossRefGoogle Scholar
  16. Bajgain S, Ghosh D B, Karki B B. 2015. Structure and density of basaltic melts at mantle conditions from first-principles simulations. Nat Commun, 6: 8578CrossRefGoogle Scholar
  17. Bassett W A. 2009. Diamond anvil cell, 50th birthday. High Pressure Res, 29: 163–186CrossRefGoogle Scholar
  18. Boslough M B, Asay J R. 1993. Basic principles of shock compression. In: Asay J R, Shahinpoor M, eds. High-Pressure Shock Compression of Solids. New York: Springer-Verlag. 7–42CrossRefGoogle Scholar
  19. Carlson R W, Garnero E, Harrison T M, Li J, Manga M, McDonough W F, Mukhopadhyay S, Romanowicz B, Rubie D, Williams Q, Zhong S. 2014. How did early Earth become our modern world? Annu Rev Earth Planet Sci, 42: 151–178CrossRefGoogle Scholar
  20. Chantel J, Manthilake G, Andrault D, Novella D, Yu T, Wang Y. 2016. Experimental evidence supports mantle partial melting in the asthenosphere. Sci Adv, 2: e1600246CrossRefGoogle Scholar
  21. Chen G Q, Ahrens T J. 1998. Radio frequency heating coils for shock wave experiments. In: Wentzcovitch R M, Hemley R J, Nellis W J, Yu P Y, eds. High-Pressure Materials Research. Materials Research Society Symposium Proceedings. Warrendale: Materials Research Society. 499: 63–71CrossRefGoogle Scholar
  22. Chen G Q, Ahrens T J, Stolper E M. 2002. Shock-wave equation of state of molten and solid fayalite. Phys Earth Planet Inter, 134: 35–52CrossRefGoogle Scholar
  23. Chevrel M O, Giordano D, Potuzak M, Courtial P, Dingwell D B. 2013. Physical properties of CaAl2Si2O8-CaMgSi2O6-FeO-Fe2O3 melts: Analogues for extra-terrestrial basalt. Chem Geol, 346: 93–105CrossRefGoogle Scholar
  24. Circone S, Agee C B. 1996. Compressibility of molten high-Ti mare glass: Evidence for crystal-liquid density inversions in the lunar mantle. Geochim Cosmochim Acta, 60: 2709–2720CrossRefGoogle Scholar
  25. Cochain B, Sanloup C, Leroy C, Kono Y. 2017. Viscosity of mafic magmas at high pressures. Geophys Res Lett, 44: 818–826CrossRefGoogle Scholar
  26. Courtial P, Dingwell D B. 1999. Densities of melts in the CaO-MgO-Al2O3-SiO2 system. Am Miner, 84: 465–476CrossRefGoogle Scholar
  27. Courtial P. 2005. High-temperature density of lanthanide-bearing Na-silicate melts: Partial molar volumes for Ce2O3, Pr2O3, Nd2O3, Sm2O3, Eu2O3, Gd2O3, Tb2O3, Dy2O3, Ho2O3, Er2O3, Tm2O3, and Yb2O3. Am Miner, 90: 1597–1605CrossRefGoogle Scholar
  28. Crépisson C, Morard G, Bureau H, Prouteau G, Morizet Y, Petitgirard S, Sanloup C. 2014. Magmas trapped at the continental lithosphere-asthenosphere boundary. Earth Planet Sci Lett, 393: 105–112CrossRefGoogle Scholar
  29. Decremps F, Belliard L, Couzinet B, Vincent S, Munsch P, Le Marchand G, Perrin B. 2009. Liquid mercury sound velocity measurements under high pressure and high temperature by picosecond acoustics in a diamond anvils cell. Rev Sci Instrum, 80: 073902CrossRefGoogle Scholar
  30. Dubrovinsky L, Dubrovinskaia N, Prakapenka V B, Abakumov A M. 2012. Implementation of micro-ball nanodiamond anvils for high-pressure studies above 6 Mbar. Nat Commun, 3: 1163CrossRefGoogle Scholar
  31. Duncan M S, Agee C B. 2011. The partial molar volume of carbon dioxide in peridotite partial melt at high pressure. Earth Planet Sci Lett, 312: 429–436CrossRefGoogle Scholar
  32. Dziewonski A M, Anderson D L. 1981. Preliminary reference earth model. Phys Earth Planet Inter, 25: 297–356CrossRefGoogle Scholar
  33. Eggert J H, Weck G, Loubeyre P, Mezouar M. 2002. Quantitative structure factor and density measurements of high-pressure fluids in diamond anvil cells by X-ray diffraction: Argon and water. Phys Rev B, 65: 174105CrossRefGoogle Scholar
  34. Elkins-Tanton L T. 2012. Magma oceans in the inner solar system. Annu Rev Earth Planet Sci, 40: 113–139CrossRefGoogle Scholar
  35. Fortov V E, Lomonosov I V. 2010. Shock waves and equations of state of matter. Shock Waves, 20: 53–71CrossRefGoogle Scholar
  36. Funakoshi K, Nozawa A. 2012. Development of a method for measuring the density of liquid sulfur at high pressures using the falling-sphere technique. Rev Sci Instrum, 83: 103908CrossRefGoogle Scholar
  37. Funamori N, Sato T. 2010. Density contrast between silicate melts and crystals in the deep mantle: An integrated view based on static-compression data. Earth Planet Sci Lett, 295: 435–440CrossRefGoogle Scholar
  38. Ghiorso M S. 2004a. An equation of state for silicate melts. I. Formulation of a general model. Am J Sci, 304: 637–678CrossRefGoogle Scholar
  39. Ghiorso M S. 2004b. An equation of state for silicate melts. III. Analysis of stoichiometric liquids at elevated pressure: Shock compression data, molecular dynamics simulations and mineral fusion curves. Am J Sci, 304: 752–810CrossRefGoogle Scholar
  40. Ghiorso M S. 2004c. An equation of state for silicate melts. IV. Calibration of a multicomponent mixing model to 40 GPa. Am J Sci, 304: 811–838CrossRefGoogle Scholar
  41. Ghiorso M S, Kress V C. 2004. An equation of state for silicate melts. II. Calibration of volumetric properties at 105 Pa. Am J Sci, 304: 679–751CrossRefGoogle Scholar
  42. Ghosh S, Ohtani E, Litasov K, Suzuki A, Sakamaki T. 2007. Stability of carbonated magmas at the base of the Earth’s upper mantle. Geophys Res Lett, 34: L22312CrossRefGoogle Scholar
  43. Gonzalez-Platas J, Alvaro M, Nestola F, Angel R. 2016. EosFit7-GUI: A new graphical user interface for equation of state calculations, analyses and teaching. J Appl Crystlogr, 49: 1377–1382CrossRefGoogle Scholar
  44. Guo X. 2013. Density and compressibility of FeO-bearing silicate melt: Relevance to magma behavior in the Earth. Doctoral Dissertation. Ann Arbor: University of MichiganGoogle Scholar
  45. Guo X, Lange R A, Ai Y. 2013. The density and compressibility of CaOFeO- SiO2 liquids at one bar: Evidence for four-coordinated Fe2+ in the CaFeO2 component. Geochim Cosmochim Acta, 120: 206–219CrossRefGoogle Scholar
  46. Guo X, Lange R A, Ai Y. 2014. Density and sound speed measurements on model basalt (An-Di-Hd) liquids at one bar: New constraints on the partial molar volume and compressibility of the FeO component. Earth Planet Sci Lett, 388: 283–292CrossRefGoogle Scholar
  47. Harvey J P, Asimow P D. 2015. Current limitations of molecular dynamic simulations as probes of thermo-physical behavior of silicate melts. Am Miner, 100: 1866–1882CrossRefGoogle Scholar
  48. Hong X, Shen G, Prakapenka V B, Rivers M L, Sutton S R. 2007. Density measurements of noncrystalline materials at high pressure with diamond anvil cell. Rev Sci Instrum, 78: 103905CrossRefGoogle Scholar
  49. Huang F, Wu Z, Huang S, Wu F. 2014. First-principles calculations of equilibrium silicon isotope fractionation among mantle minerals. Geochim Cosmochim Acta, 140: 509–520CrossRefGoogle Scholar
  50. Jacobsen S D, Reichmann H J, Kantor A, Spetzler H A. 2005. A gigahertz ultrasonic interferometer for the diamond anvil cell and high-pressure elasticity of some iron-oxide minerals. In: Chen J, Wang Y, Duffy T S, Shen G, Dobrzhinetskaya L F, eds. Advances in High-Pressure Technology for Geophysical Applications. Amsterdam: Elsevier. 25–48CrossRefGoogle Scholar
  51. 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 USA, 101: 5867–5871CrossRefGoogle Scholar
  52. Jacobsen S D, Spetzler H A, Reichmann H J, Smyth J R, Mackwell S J, Angel R J, Bassett W A. 2002. Gigahertz ultrasonic interferometry at high P and T: New tools for obtaining a thermodynamic equation of state. J Phys-Condens Matter, 14: 11525–11530CrossRefGoogle Scholar
  53. Jing Z, Karato S. 2008. Compositional effect on the pressure derivatives of bulk modulus of silicate melts. Earth Planet Sci Lett, 272: 429–436CrossRefGoogle Scholar
  54. Jing Z, Karato S. 2009. The density of volatile bearing melts in the Earth’s deep mantle: The role of chemical composition. Chem Geol, 262: 100–107CrossRefGoogle Scholar
  55. Jing Z, Karato S. 2011. A new approach to the equation of state of silicate melts: An application of the theory of hard sphere mixtures. Geochim Cosmochim Acta, 75: 6780–6802CrossRefGoogle Scholar
  56. Jing Z, Karato S. 2012. Effect of H2O on the density of silicate melts at high pressures: Static experiments and the application of a modified hard-sphere model of equation of state. Geochim Cosmochim Acta, 85: 357–372CrossRefGoogle Scholar
  57. Jing Z, Wang Y, Kono Y, Yu T, Sakamaki T, Park C, Rivers M L, Sutton S R, Shen G. 2014. Sound velocity of Fe-S liquids at high pressure: Implications for the Moon’s molten outer core. Earth Planet Sci Lett, 396: 78–87CrossRefGoogle Scholar
  58. Jones A P, Genge M, Carmody L. 2013. Carbonate melts and carbonatites. Rev Mineral Geochem, 75: 289–322CrossRefGoogle Scholar
  59. Kanzaki M, Kurita K, Fujii T, Kato T, Shimomura O, Akimoto S. 1987. A new technique to measure the viscosity and density of silicate melts at high pressure. In: Manghnani M H, Syono Y, eds. High-Pressure Research in Mineral Physics. Tokyo: Terrapub. 195–200Google Scholar
  60. Karki B B. 2010. First-principles molecular dynamics simulations of silicate melts: Structural and dynamical properties. Rev Mineral Geochem, 71: 355–389CrossRefGoogle Scholar
  61. Karki B B. 2015. First-principles computation of mantle materials in crystalline and amorphous phases. Phys Earth Planet Inter, 240: 43–69CrossRefGoogle Scholar
  62. Katayama Y, Tsuji K, Chen J Q, Koyama N, Kikegawa T, Yaoita K, Shimomura O. 1993. Density of liquid tellurium under high pressure. J Non-Cryst Solids, 156–158: 687–690CrossRefGoogle Scholar
  63. Katayama Y, Tsuji K, Kanda H, Nosaka H, Yaoita K, Kikegawa T, Shimomura O. 1996. Density of liquid tellurium under pressure. J Non-Cryst Solids, 205–207: 451–454CrossRefGoogle Scholar
  64. Katayama Y, Tsuji K, Shimomura O, Kikegawa T, Mezouar M, Martinez-Garcia D, Besson J M, Häusermann D, Hanfland M. 1998. Density measurements of liquid under high pressure and high temperature. J Synchrotron Radiat, 5: 1023–1025CrossRefGoogle Scholar
  65. Knoche R, Luth R W. 1996. Density measurements on melts at high pressure using the sink/float method: Limitations and possibilities. Chem Geol, 128: 229–243CrossRefGoogle Scholar
  66. Kono Y, Kenney-Benson C, Shibazaki Y, Park C, Shen G, Wang Y. 2015. High-pressure viscosity of liquid Fe and FeS revisited by falling sphere viscometry using ultrafast X-ray imaging. Phys Earth Planet Inter, 241: 57–64CrossRefGoogle Scholar
  67. Kono Y, Park C, Kenney-Benson C, Shen G, Wang Y. 2014. Toward comprehensive studies of liquids at high pressures and high temperatures: Combined structure, elastic wave velocity, and viscosity measurements in the Paris-Edinburgh cell. Phys Earth Planet Inter, 228: 269–280CrossRefGoogle Scholar
  68. Kuwabara S, Terasaki H, Nishida K, Shimoyama Y, Takubo Y, Higo Y, Shibazaki Y, Urakawa S, Uesugi K, Takeuchi A, Kondo T. 2016. Sound velocity and elastic properties of Fe-Ni and Fe-Ni-C liquids at high pressure. Phys Chem Miner, 43: 229–236CrossRefGoogle Scholar
  69. Lange R A. 1994. The effect of H2O, CO2 and F on the density and viscosity of silicate melts. Rev Mineral, 30: 331–369Google Scholar
  70. Lange R A. 1996. Temperature independent thermal expansivities of sodium aluminosilicate melts between 713 and 1835 K. Geochim Cosmochim Acta, 60: 4989–4996CrossRefGoogle Scholar
  71. Lange R A. 1997. A revised model for the density and thermal expansivity of K2O-Na2O-CaO-MgO-Al2O3-SiO2 liquids from 700 to 1900 K: Extension to crustal magmatic temperatures. Contrib Mineral Petrol, 130: 1–11CrossRefGoogle Scholar
  72. Lange R A. 2003. The fusion curve of albite revisited and the compressibility of NaAlSi3O8 liquid with pressure. Am Miner, 88: 109–120CrossRefGoogle Scholar
  73. Lange R A. 2007. The density and compressibility of KAlSi3O8 liquid to 6.5 GPa. Am Miner, 92: 114–123CrossRefGoogle Scholar
  74. Lange R A, Carmichael I S E. 1987. Densities of Na2O-K2O-CaO-MgOFeO- Fe2O3-Al2O3-TiO2-SiO2 liquids: New measurements and derived partial molar properties. Geochim Cosmochim Acta, 51: 2931–2946CrossRefGoogle Scholar
  75. Lange R A, Carmichael I S E. 1990. Thermodynamic properties of silicate liquids with emphasis on density, thermal-expansion and compressibility. Rev Mineral, 24: 25–64Google Scholar
  76. Lesher, C E, Spera, F J. 2015. Chapter 5–thermodynamic and transport properties of silicate melts and magma. In: Sigurdsson H, ed. The Encyclopedia of Volcanoes, 113–141CrossRefGoogle Scholar
  77. 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: 559–574CrossRefGoogle Scholar
  78. Li B, Liebermann R C. 2007. Indoor seismology by probing the Earth’s interior by using sound velocity measurements at high pressures and temperatures. Proc Natl Acad Sci USA, 104: 9145–9150CrossRefGoogle Scholar
  79. 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: 135–153CrossRefGoogle Scholar
  80. Li B, Liu W. 2010. Advanced elasticity and density measurements on melts at mantle pressures using ultrasonic interferometry and synchrotron Xradiation. AGU Fall Meeting, abstract #MR44A-02Google Scholar
  81. Liebermann R C. 2011. Multi-anvil, high pressure apparatus: A half-century of development and progress. High Pressure Res, 31: 493–532CrossRefGoogle Scholar
  82. Liu L, Bi Y, Xu J A. 2016. Latest developments in experimental research on structural and physical properties of liquids under extreme conditions (in Chinese). Chin J High Pressure Phys, 30: 7–19Google Scholar
  83. Liu Q, Lange R A. 2001. The partial molar volume and thermal expansivity of TiO2 in alkali silicate melts: Systematic variation with Ti coordination. Geochim Cosmochim Acta, 65: 2379–2393CrossRefGoogle Scholar
  84. Liu Q, Lange R A. 2006. The partial molar volume of Fe2O3 in alkali silicate melts: Evidence for an average Fe3+ coordination number near five. Am Miner, 91: 385–393CrossRefGoogle Scholar
  85. Liu Q, Lange R A, Ai Y. 2007a. Acoustic velocity measurements on Na2OTiO2-SiO2 liquids: Evidence for a highly compressible TiO2 component related to five-coordinated Ti. Geochim Cosmochim Acta, 71: 4314–4326CrossRefGoogle Scholar
  86. Liu Q, Tenner T J, Lange R A. 2007b. Do carbonate liquids become denser than silicate liquids at pressure? Constraints from the fusion curve of K2CO3 to 3.2 GPa. Contrib Mineral Petrol, 153: 55–66CrossRefGoogle Scholar
  87. Malfait W J, Sanchez-Valle C, Ardia P, Medard E, Lerch P. 2011. Amorphous materials: Properties, structure, and durability: Compositional dependent compressibility of dissolved water in silicate glasses. Am Miner, 96: 1402–1409CrossRefGoogle Scholar
  88. Malfait W J, Seifert R, Petitgirard S, Mezouar M, Sanchez-Valle C. 2014a. The density of andesitic melts and the compressibility of dissolved water in silicate melts at crustal and upper mantle conditions. Earth Planet Sci Lett, 393: 31–38CrossRefGoogle Scholar
  89. Malfait W J, Seifert R, Petitgirard S, Perrillat J P, Mezouar M, Ota T, Nakamura E, Lerch P, Sanchez-Valle C. 2014b. Supervolcano eruptions driven by melt buoyancy in large silicic magma chambers. Nat Geosci, 7: 122–125CrossRefGoogle Scholar
  90. Matsukage K N, Jing Z, Karato S I. 2005. Density of hydrous silicate melt at the conditions of Earth’s deep upper mantle. Nature, 438: 488–491CrossRefGoogle Scholar
  91. Miller G H, Ahrens T J, Stolper E M. 1988. The equation of state of molybdenum at 1400°C. J Appl Phys, 63: 4469–4475CrossRefGoogle Scholar
  92. Miller G H, Stolper E M, Ahrens T J. 1991. The equation of state of a molten komatiite: 1. Shock wave compression to 36 GPa. J Geophys Res, 96: 11831–11848CrossRefGoogle Scholar
  93. Morard G, Garbarino G, Antonangeli D, Andrault D, Guignot N, Siebert J, Roberge M, Boulard E, Lincot A, Denoeud A, Petitgirard S. 2014. Density measurements and structural properties of liquid and amorphous metals under high pressure. High Pressure Res, 34: 9–21CrossRefGoogle Scholar
  94. Mueller H J, Roetzler K, Schilling F R, Lathe C, Wehber M. 2010. Techniques for measuring the elastic wave velocities of melts and partial molten systems under high pressure conditions. J Phys Chem Solids, 71: 1108–1117CrossRefGoogle Scholar
  95. Nakajima Y, Imada S, Hirose K, Komabayashi T, Ozawa H, Tateno S, Tsutsui S, Kuwayama Y, Baron A Q R. 2015. Carbon-depleted outer core revealed by sound velocity measurements of liquid iron-carbon alloy. Nat Commun, 6: 8942CrossRefGoogle Scholar
  96. Ni H. 2013. Advances and application in physicochemical properties of silicate melts. Chin Sci Bull, 58: 865–890CrossRefGoogle Scholar
  97. Ni H, Zhang L, Guo X. 2016. Water and partial melting of Earth’s mantle. Sci China Earth Sci, 59: 720–730CrossRefGoogle Scholar
  98. Nishida K, Kono Y, Terasaki H, Takahashi S, Ishii M, Shimoyama Y, Higo Y, Funakoshi K, Irifune T, Ohtani E. 2013. Sound velocity measurements in liquid Fe-S at high pressure: Implications for Earth’s and lunar cores. Earth Planet Sci Lett, 362: 182–186CrossRefGoogle Scholar
  99. Nishida K, Suzuki A, Terasaki H, Shibazaki Y, Higo Y, Kuwabara S, Shimoyama Y, Sakurai M, Ushioda M, Takahashi E, Kikegawa T, Wakabayashi D, Funamori N. 2016. Towards a consensus on the pressure and composition dependence of sound velocity in the liquid Fe-S system. Phys Earth Planet Inter, 257: 230–239CrossRefGoogle Scholar
  100. Ochs F A, Lange R A. 1997. The partial molar volume, thermal expansivity, and compressibility of H2O in NaAlSi3O8 liquid: New measurements and an internally consistent model. Contrib Mineral Petrol, 129: 155–165CrossRefGoogle Scholar
  101. Ochs F A, Lange R A. 1999. The density of hydrous magmatic liquids. Science, 283: 1314–1317CrossRefGoogle Scholar
  102. Ohira I, Murakami M, Kohara S, Ohara K, Ohtani E. 2016. Ultrahighpressure acoustic wave velocities of SiO2-Al2O3 glasses up to 200 GPa. Prog Earth Planet Sci, 3: 18CrossRefGoogle Scholar
  103. Ohtani E. 2009. Melting relations and the equation of state of magmas at high pressure: Application to geodynamics. Chem Geol, 265: 279–288CrossRefGoogle Scholar
  104. Ohtani E, Maeda M. 2001. Density of basaltic melt at high pressure and stability of the melt at the base of the lower mantle. Earth Planet Sci Lett, 193: 69–75CrossRefGoogle Scholar
  105. Ohtani E, Suzuki A, Ando R, Urakawa S, Funakoshi K, Katayama Y. 2005. Viscosity and density measurements of melts and glasses at high pressure and temperature by using the multi-anvil apparatus and synchrotron X-ray radiation. In: Chen J, Wang Y, Duffy T S, Shen G, Dobrzhinetskaya L F, eds. Advances in High-Pressure Technology for Geophysical Applications. Amsterdam: Elsevier. 195–209CrossRefGoogle Scholar
  106. Ohtani E, Suzuki A, Kato T. 1993. Flotation of olivine in the peridotite melt at high pressure. Proc Jpn Acad Ser B-Phys Biol Sci, 69: 23–28CrossRefGoogle Scholar
  107. Petitgirard S. 2017. Density and structural changes of silicate glasses under high pressure. High Pressure Res, 37: 200–213CrossRefGoogle Scholar
  108. Petitgirard S, Malfait W J, Sinmyo R, Kupenko I, Hennet L, Harries D, Dane T, Burghammer M, Rubie D C. 2015. Fate of MgSiO3 melts at core-mantle boundary conditions. Proc Natl Acad Sci USA, 112: 14186–14190CrossRefGoogle Scholar
  109. Poirier J. 2000. Introduction to the Physics of the Earth’s Interior. 2nd ed. Cambridge: Cambridge University Press. 312Google Scholar
  110. Reichmann H J, Jacobsen S D, Ballaran T B. 2013. Elasticity of franklinite and trends for transition-metal oxide spinels. Am Miner, 98: 601–608CrossRefGoogle Scholar
  111. Rigden S M, Ahrens T J, Stolper E M. 1984. Densities of liquid silicates at high pressures. Science, 226: 1071–1074CrossRefGoogle Scholar
  112. Rigden S M, Ahrens T J, Stolper E M. 1988. Shock compression of molten silicate: Results for a model basaltic composition. J Geophys Res, 93: 367–382CrossRefGoogle Scholar
  113. Rigden S M, Ahrens T J, Stolper E M. 1989. High-pressure equation of state of molten anorthite and diopside. J Geophys Res, 94: 9508–9522CrossRefGoogle Scholar
  114. Rivers M L, Carmichael I S E. 1987. Ultrasonic studies of silicate melts. J Geophys Res, 92: 9247–9270CrossRefGoogle Scholar
  115. Rowan L R. 1993. I. Equation of state of molten mid-ocean ridge basalt II. Structure of Kilauea volcano, Hawaii. Doctoral Dissertation. Pasadena: California Institute of TechnologyGoogle Scholar
  116. Sakamaki T, Ohtani E, Urakawa S, Suzuki A, Katayama Y. 2009. Measurement of hydrous peridotite magma density at high pressure using the X-ray absorption method. Earth Planet Sci Lett, 287: 293–297CrossRefGoogle Scholar
  117. Sakamaki T, Ohtani E, Urakawa S, Suzuki A, Katayama Y. 2010a. Density of dry peridotite magma at high pressure using an X-ray absorption method. Am Miner, 95: 144–147CrossRefGoogle Scholar
  118. Sakamaki T, Ohtani E, Urakawa S, Suzuki A, Katayama Y, Zhao D. 2010b. Density of high-Ti basalt magma at high pressure and origin of heterogeneities in the lunar mantle. Earth Planet Sci Lett, 299: 285–289CrossRefGoogle Scholar
  119. Sakamaki T, Ohtani E, Urakawa S, Terasaki H, Katayama Y. 2011. Density of carbonated peridotite magma at high pressure using an X-ray absorption method. Am Miner, 96: 553–557CrossRefGoogle Scholar
  120. Sakamaki T, Suzuki A, Ohtani E. 2006. Stability of hydrous melt at the base of the Earth’s upper mantle. Nature, 439: 192–194CrossRefGoogle Scholar
  121. Sakamaki T, Suzuki A, Ohtani E, Terasaki H, Urakawa S, Katayama Y, Funakoshi K I, Wang Y, Hernlund J W, Ballmer M D. 2013. Ponded melt at the boundary between the lithosphere and asthenosphere. Nat Geosci, 6: 1041–1044CrossRefGoogle Scholar
  122. Sanloup C. 2016. Density of magmas at depth. Chem Geol, 429: 51–59CrossRefGoogle Scholar
  123. Sanloup C, Drewitt J W E, Crépisson C, Kono Y, Park C, McCammon C, Hennet L, Brassamin S, Bytchkov A. 2013a. Structure and density of molten fayalite at high pressure. Geochim Cosmochim Acta, 118: 118–128CrossRefGoogle Scholar
  124. Sanloup C, Drewitt J W E, Konôpková Z, Dalladay-Simpson P, Morton D M, Rai N, van Westrenen W, Morgenroth W. 2013b. Structural change in molten basalt at deep mantle conditions. Nature, 503: 104–107CrossRefGoogle Scholar
  125. Sato T, Funamori N. 2008. Sixfold-coordinated amorphous polymorph of SiO2 under high pressure. Phys Rev Lett, 101: 255502CrossRefGoogle Scholar
  126. Schmandt B, Jacobsen S D, Becker T W, Liu Z, Dueker K G. 2014. Dehydration melting at the top of the lower mantle. Science, 344: 1265–1268CrossRefGoogle Scholar
  127. Schmerr N. 2012. The Gutenberg discontinuity: Melt at the lithosphereasthenosphere boundary. Science, 335: 1480–1483CrossRefGoogle Scholar
  128. Secco R A, Manghnani M H, Liu T C. 1991a. The bulk modulus-attenuation- viscosity systematics of diopside-anorthite melts. Geophys Res Lett, 18: 93–96CrossRefGoogle Scholar
  129. Secco R A, Manghnani M H, Liu T. 1991b. Velocities and compressibilities of komatiitic melts. Geophys Res Lett, 18: 1397–1400CrossRefGoogle Scholar
  130. Seifert R, Malfait W J, Lerch P, Sanchez-Valle C. 2013a. Partial molar volume and compressibility of dissolved CO2 in glasses with magmatic compositions. Chem Geol, 358: 119–130CrossRefGoogle Scholar
  131. Seifert R, Malfait W J, Petitgirard S, Sanchez-Valle C. 2013b. Density of phonolitic magmas and time scales of crystal fractionation in magma chambers. Earth Planet Sci Lett, 381: 12–20CrossRefGoogle Scholar
  132. Shen G, Mao H K. 2017. High-pressure studies with X-rays using diamond anvil cells. Rep Prog Phys, 80: 016101CrossRefGoogle Scholar
  133. Shen G, Sata N, Newville M, Rivers M L, Sutton S R. 2002. Molar volumes of molten indium at high pressures measured in a diamond anvil cell. Appl Phys Lett, 81: 1411–1413CrossRefGoogle Scholar
  134. Shen G, Wang Y. 2014. High-pressure apparatus integrated with synchrotron radiation. Rev Mineral Geochem, 78: 745–777CrossRefGoogle Scholar
  135. Shimoyama Y, Terasaki H, Urakawa S, Takubo Y, Kuwabara S, Kishimoto S, Watanuki T, Machida A, Katayama Y, Kondo T. 2016. Thermoelastic properties of liquid Fe-C revealed by sound velocity and density measurements at high pressure. J Geophys Res-Solid Earth, 121: 7984–7995CrossRefGoogle Scholar
  136. Smith J R, Agee C B. 1997. Compressibility of molten “green glass” and crystal-liquid density crossovers in low-Ti lunar magma. Geochim Cosmochim Acta, 61: 2139–2145CrossRefGoogle Scholar
  137. Stixrude L, de Koker N, Sun N, Mookherjee M, Karki B B. 2009. Thermodynamics of silicate liquids in the deep Earth. Earth Planet Sci Lett, 278: 226–232CrossRefGoogle Scholar
  138. Stolper E, Hager B H, Walker D, Hays J F. 1981. Melt segregation from partially molten source regions: The importance of melt density and source region size. J Geophys Res, 86: 6261–6271CrossRefGoogle Scholar
  139. Suzuki A, Ohtani E. 2003. Density of peridotite melts at high pressure. Phys Chem Miner, 30: 449–456CrossRefGoogle Scholar
  140. Suzuki A, Ohtani E, Kato T. 1995. Flotation of diamond in mantle melt at high pressure. Science, 269: 216–218CrossRefGoogle Scholar
  141. Suzuki A, Ohtani E, Kato T. 1998. Density and thermal expansion of a peridotite melt at high pressure. Phys Earth Planet Inter, 107: 53–61CrossRefGoogle Scholar
  142. Suzuki A, Ohtani E, Terasaki H, Sakamaki T, Nishida K, Funakoshi K. 2007. In situ buoyancy test for the density measurement of basaltic liquid at high pressure and high temperature. AGU Fall Meeting, abstracts #MR13B-1258Google Scholar
  143. Tauzin B, Debayle E, Wittlinger G. 2010. Seismic evidence for a global low-velocity layer within the Earth’s upper mantle. Nat Geosci, 3: 718–721CrossRefGoogle Scholar
  144. Tenner T J, Lange R A, Downs R T. 2007. The albite fusion curve reexamined: New experiments and the high-pressure density and compressibility of high albite and NaAlSi3O8 liquid. Am Miner, 92: 1573–1585CrossRefGoogle Scholar
  145. Thibodeau E, Gheribi A E, Jung I H. 2016a. A structural molar volume model for oxide melts part I: Li2O-Na2O-K2O-MgO-CaO-MnO-PbOAl2O3- SiO2 melts—Binary systems. Metall Mater Trans B, 47: 1147–1164CrossRefGoogle Scholar
  146. Thibodeau E, Gheribi A E, Jung I H. 2016b. A structural molar volume model for oxide melts part II: Li2O-Na2O-K2O-MgO-CaO-MnO-PbOAl2O3-SiO2 melts—Ternary and multicomponent systems. Metall Mater Trans B, 47: 1165–1186CrossRefGoogle Scholar
  147. Thibodeau E, Gheribi A E, Jung I H. 2016c. A structural molar volume model for oxide melts part III: Fe oxide-containing melts. Metall Mater Trans B, 47: 1187–1202CrossRefGoogle Scholar
  148. Thomas C W, Asimow P D. 2013a. Preheated shock experiments in the molten CaAl2Si2O8-CaFeSi2O6-CaMgSi2O6 ternary: A test for linear mixing of liquid volumes at high pressure and temperature. J Geophys Res-Solid Earth, 118: 3354–3365CrossRefGoogle Scholar
  149. Thomas C W, Asimow P D. 2013b. Direct shock compression experiments on premolten forsterite and progress toward a consistent high-pressure equation of state for CaO-MgO-Al2O3-SiO2-FeO liquids. J Geophys Res-Solid Earth, 118: 5738–5752CrossRefGoogle Scholar
  150. Thomas C W, Liu Q, Agee C B, Asimow P D, Lange R A. 2012. Multitechnique equation of state for Fe2SiO4 melt and the density of Febearing silicate melts from 0 to 161 GPa. J Geophys Res, 117: 10206CrossRefGoogle Scholar
  151. Ueki K, Iwamori H. 2016. Density and seismic velocity of hydrous melts under crustal and upper mantle conditions. Geochem Geophys Geosyst, 17: 1799–1814CrossRefGoogle Scholar
  152. Urakawa S, Sakamaki T, Ohtani E. 2006. Anomalous compression of basaltic magma: Implication to pressure-induced structural change in silicate melt. Spring-8 Res Front. 113–114Google Scholar
  153. van Kan Parker M, Agee C B, Duncan M S, van Westrenen W. 2011. Compressibility of molten Apollo 17 orange glass and implications for density crossovers in the lunar mantle. Geochim Cosmochim Acta, 75: 1161–1172CrossRefGoogle Scholar
  154. van Kan Parker M, Sanloup C, Sator N, Guillot B, Tronche E J, Perrillat J P, Mezouar M, Rai N, van Westrenen W. 2012. Neutral buoyancy of titanium-rich melts in the deep lunar interior. Nat Geosci, 5: 186–189CrossRefGoogle Scholar
  155. van Kan Parker M, Sanloup C, Tronche E J, Perrillat J P, Mezouar M, Rai N, van Westrenen W. 2010. Calibration of a diamond capsule cell assembly for in situ determination of liquid properties in the Paris- Edinburgh press. High Pressure Res, 30: 332–341CrossRefGoogle Scholar
  156. Vander Kaaden K E, Agee C B, McCubbin F M. 2015. Density and compressibility of the molten lunar picritic glasses: Implications for the roles of Ti and Fe in the structures of silicate melts. Geochim Cosmochim Acta, 149: 1–20CrossRefGoogle Scholar
  157. Wakabayashi D, Funamori N. 2013. Equation of state of silicate melts with densified intermediate-range order at the pressure condition of the Earth’s deep upper mantle. Phys Chem Miner, 40: 299–307CrossRefGoogle Scholar
  158. Wakabayashi D, Funamori N, Sato T, Sekine T. 2014. Equation of state for silicate melts: A comparison between static and shock compression. Geophys Res Lett, 41: 50–54CrossRefGoogle Scholar
  159. Wang Y. 2010. Large volume presses for high-pressure studies using synchrotron radiation. In: Boldyreva E, Dera P, eds. High-Pressure Crystallography. NATO Science for Peace and Security Series B: Physics and Biophysics. Dordrecht: Springer. 81–96Google Scholar
  160. Wang Y, Rivers M, Sutton S, Nishiyama N, Uchida T, Sanehira T. 2009. The large-volume high-pressure facility at GSECARS: A “Swiss-armyknife” approach to synchrotron-based experimental studies. Phys Earth Planet Inter, 174: 270–281CrossRefGoogle Scholar
  161. Wang Y, Shen G. 2014. High-pressure experimental studies on geo-liquids using synchrotron radiation at the Advanced Photon Source. J Earth Sci, 25: 939–958CrossRefGoogle Scholar
  162. Wang Y B. 2006. Combining the large-volume press with synchrotron radiation: Applications to in-situ studies of Earth materials under high pressure and temperature. Earth Sci Front, 13: 1–36Google Scholar
  163. Williams Q, Garnero E J. 1996. Seismic evidence for partial melt at the base of Earth’s mantle. Science, 273: 1528–1530CrossRefGoogle Scholar
  164. Wolf A S, Asimow P D, Stevenson D J. 2015. Coordinated Hard Sphere Mixture (CHaSM): A simplified model for oxide and silicate melts at mantle pressures and temperatures. Geochim Cosmochim Acta, 163: 40–58CrossRefGoogle Scholar
  165. Yamazaki D, Ito E, Yoshino T, Tsujino N, Yoneda A, Guo X, Xu F, Higo Y, Funakoshi K. 2014. Over 1Mbar generation in the Kawai-type multianvil apparatus and its application to compression of (Mg0.92Fe0.08)SiO3 perovskite and stishovite. Phys Earth Planet Inter, 228: 262–267CrossRefGoogle Scholar
  166. Yasuda A, Fujii T, Kurita K. 1994. Melting phase relations of an anhydrous mid-ocean ridge basalt from 3 to 20 GPa: Implications for the behavior of subducted oceanic crust in the mantle, J Geophys Res, 99: 9401–9414CrossRefGoogle Scholar
  167. Yu T, Wang Y, Rivers M L. 2016. Imaging in 3D under pressure: A decade of high-pressure X-ray microtomography development at GSECARS. Prog Earth Planet Sci, 3: 17CrossRefGoogle Scholar
  168. Zhang X, Liu Y G, Song W, Wang Z G, Xie H S. 2013. Research progress on ultrasonic velocity measurement of liquid materials under high pressure. Chin J High Pressure Phys, 27: 239–244Google Scholar
  169. Zinin P V, Prakapenka V B, Burgess K, Odake S, Chigarev N, Sharma S K. 2016. Combined laser ultrasonics, laser heating, and Raman scattering in diamond anvil cell system. Rev Sci Instrum, 87: 123908CrossRefGoogle Scholar

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© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.MOE Key Laboratory of Orogenic Belt and Crustal Evolution, School of Earth and Space SciencesPeking UniversityBeijingChina

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