The Grain-Scale Distribution of Silicate, Carbonate and Metallosulfide Partial Melts: a Review of Theory and Experiments

  • Didier Laporte
  • Ariel Provost
Part of the Petrology and Structural Geology book series (PESG, volume 11)


In a partially molten rock containing a low melt fraction, the permeability and consequently the dynamics of melt segregation are strongly sensitive to the distribution of the melt at the grain scale. Melt distribution is controlled by a variety of factors such as the minimization of interfacial energies, the stress regime and different aspects of the melting reaction (melting rate, volume change on melting, spatial distribution of the reactants). Due to the long duration of large-scale melting events, an equilibrium melt configuration corresponding to a minimum total interfacial energy per unit volume should commonly be approached. In this chapter, we review the theoretical and experimental studies devoted to the equilibrium distribution of melt in a partially molten rock.

At low melt fraction, the ratio of grain-boundary energy to solid-melt interfacial energy, γ SS/γ SL, is the fundamental physical property that determines the equilibrium melt geometry, including the dihedral angle θ at the junction of melt with two grains and the interconnection threshold ϕ c (ϕ c is the melt fraction at which melt interconnection is established). The trends of increasing θ and ϕ c with decreasing γ SS/γ SL are well demonstrated in the idealized case of a monomineralic system with isotropic interfacial energies and that is subjected to hydrostatic stress. Recent experimental and theoretical studies indicate that these general trends must hold in natural systems: (1) low values of γ SS/γ SL (for instance ≈1) give rise to large average dihedral angles, a high proportion of dry grain edges and a non-interconnected melt geometry (at low melt fraction); (2) larger values of γ SS/γ SL result in low average dihedral angles, a large proportion of wetted grain edges and interconnection at a very low melt fraction; and (3) for large ratios γ SS/γ SL (> 2), generalized wetting of grain boundaries is expected.

The possibility of predicting the type of melt distribution as well as the interconnection threshold and the permeability from dihedral angle measurements has motivated numerous experimental studies of the grain-scale distribution of geological fluids. The data for silicate, carbonate and metallosulfide melts are reviewed and the implications for the movement of low melt fractions are discussed.

Key words

partial melting wetting behaviour dihedral angle interconnection threshold 


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  1. Agee, C. B., Li J., M.C. Shannon, and S. Circone, P-T phase diagram for the Allende meteorite, J. Geophys. Res., 100, 17725–17740, 1995.CrossRefGoogle Scholar
  2. Ballhaus, C., and D.J. Ellis, Mobility of core melts during Earth’s accretion, Earth Planet Sci. Lett., 143, 137–145, 1996.CrossRefGoogle Scholar
  3. Bourbié, T., and B. Zinszner, Hydraulic and acoustic properties as a function of porosity in Fontainebleau sandstone, J. Geophys. Res., 90, 11524–1532, 1985.CrossRefGoogle Scholar
  4. Brace, W. F., and J.B. Walsh, Some direct measurements of the surface energy of quartz and orthoclase, Amer. Mineral., 47, 1111–1122, 1962.Google Scholar
  5. Brenan, J. M., Diffusion of chlorine in fluid-bearing quartzite: effects of fluid composition and total porosity, Contrib. Mineral. Petrol., 115, 215–224, 1993.CrossRefGoogle Scholar
  6. Brown, M., Y.A. Averkin, and E.L. McLellan, Melt segregation in migmatites, J. Geophys. Res., 100, 15655–15679, 1995.CrossRefGoogle Scholar
  7. Bruhat, G., Thermodynamique, 428 pp., 4e édition. Masson & Cie, Paris, 1947.Google Scholar
  8. Bulau, J. R., H.S. Waff, and J.A. Tyburczy, Mechanical and thermodynamical constraints on fluid distribution in partial melts, J. Geophys. Res., 84, 6102–6108, 1979.CrossRefGoogle Scholar
  9. Busch, W., G. Schneider, and K.R. Mehnert, Initial melting at grain boundaries. Part II: melting in rocks of granodioritic, quartz-dioritic and tonalitic composition, N. Jahr. Mineral. Monatsh., 8, 345–370, 1974.Google Scholar
  10. Bussod, G.Y., and J.M. Christie, Textural development annd melt topology in spinel lherzolite experimentally deformed at hypersolidus conditions, J. Petrol. Special Lherzolite Issue, 17–39, 1991.Google Scholar
  11. Clemm, P.J., and J.C. Fisher, The influence of grain boundaries on the nucleation of secondary phases, Acta Metall., 3, 70–73, 1955.CrossRefGoogle Scholar
  12. Cmíral, M., J.D. Fitz Gerald, U.H. Faul, and D.H. Green, A close look at dihedral angles and melt geometry in olivine-basalt aggregates: a TEM study, Contrib. Mineral. Petrol, 130, 336–345, 1998.CrossRefGoogle Scholar
  13. Conrad, E. H., Surface roughening, melting and faceting, Progress in Surface Science, 39, 65–116, 1992.CrossRefGoogle Scholar
  14. Cooper, R. F., and D.L. Kohlstedt, Interfacial energies in the olivine-basalt system, in: High pressure research in geophysics, Adv. Earth Planet. Sci. 12., edited by S. Akimoto and M.H. Manghnani, pp. 217–228, Centre for Academic Publication, Tokyo, 1982CrossRefGoogle Scholar
  15. Cooper, R.F., and Kohlstedt D.L., Solution-precipitation enhanced diffusional creep of partially molten olivine-basalt aggregates during hot-pressing, Tectonophysics, 107, 207–233, 1984.CrossRefGoogle Scholar
  16. Cooper, R.F., and D.L. Kohlstedt, Rheology and structure of olivine-basalt partial melts, J. Geophys. Res., 91, 9315–9323, 1986.CrossRefGoogle Scholar
  17. Daines M. J., and D.L. Kohlstedt, Influence of deformation on melt topology in peridotites, J. Geophys. Res., 102, 10257–10271, 1997.CrossRefGoogle Scholar
  18. Daines, M. J., and F.M. Richter, An experimental method for directly determining the interconnectivity of melt in a partially molten system, Geophys. Res. Lett., 15, 1459–1462, 1988.CrossRefGoogle Scholar
  19. Dell’Angelo, L. N., and J. Tullis, Experimental deformation of partially melted granitic aggregates, J. Metam. Geol., 6, 495–515, 1988.CrossRefGoogle Scholar
  20. Defay, R. and I. Prigogine, Tension superficielle et adsorption, 295 pp., Editions Desser, Liège (Belgium), 1951.Google Scholar
  21. Faul, U. H., Permeability of partially molten upper mantle rocks from experiments and percolation theory, J. Geophys. Res., 102, 10299–10311, 1997.CrossRefGoogle Scholar
  22. Faul, U. H., Constraints on the melt distribution in anisotropic polycrystalline aggregates undergoing grain growth. This volume, 1999.Google Scholar
  23. Frank, C. F., Two-component flow model for convection in the Earth’s upper mantle, Nature, 220, 350–352, 1968.CrossRefGoogle Scholar
  24. Fujii, N., K. Osamura, and E. Takahashi, Effect of water saturation on the distribution of partial melt in the olivine-pyroxene-plagioclase system, J. Geophys. Res., 91, 9253–9259, 1986.CrossRefGoogle Scholar
  25. Gaetani, G. A., and T.L. Grove, The effect of variable f O2 / f S2 conditions on wetting angles in olivine/sulfide melt aggregates: mobility of sulfide melts in the Earth’s upper mantle, Lunar Planet Sci. Conf., 27, 389–390, 1996.Google Scholar
  26. Gibbs, J. W., Collected works, Longmans Green & Co., (1928), 2 vol., p. 219, 1877.Google Scholar
  27. Harker, D. and E.R. Parker, Grain shape and grain growth, Trans ASM, 34, 156–195, 1945.Google Scholar
  28. Harris, C, and J.D. Bell,. Natural partial melting of syenite blocks from Ascension Island, Contrib. Mineral Petrol., 79, 107–113, 1982.CrossRefGoogle Scholar
  29. Harte, B., R.H. Hunter, and P.D. Kinny,. Melt geometry, movement and crystallization, in relation to mantle dykes, veins and metasomatism, Phil. Trans. R. Soc. Lond. A, 342, 1–21, 1993.CrossRefGoogle Scholar
  30. Herpfer, M. A., Solid-state diffusion and melt microstructures in metal-silicate systems, PhD thesis, Arizona State University, 1992.Google Scholar
  31. Herpfer, M. A., and J.W. Larimer, Core formation: an experimental study of metallic melt-silicate segregation, Meteoritics, 28, 362, 1993.Google Scholar
  32. Herring, C, Some theorems on the free energies of crystal surfaces, Phys. Rev., 82, 87–93, 1951a.CrossRefGoogle Scholar
  33. Herring, C, Surface tension as a motivation for sintering, in: Physics of powder metallurgy, edited by W.E. Kingston, pp. 143–179, McGraw-Hill, New York, 1951b.Google Scholar
  34. Hirth, G., and Kohlstedt D. L., 1995. Experimental constraints on the dynamics of the partially molten mantle: deformation in the diffusion creep regime, J. Geophys. Res., 100, 1981–2001.CrossRefGoogle Scholar
  35. Hoffman, D.W., and J.W. Cahn, A vector thermodynamics for anisotropic surfaces. I: fundamentals and application to plane surface junctions, Surf. Sci., 31, 368–388, 1972.CrossRefGoogle Scholar
  36. Holness, M. B., Temperature and pressure dependence of quartz-aqueous fluid dihedral angles: the control of adsorbed H2O on the permeability of quartzites, Earth Planet. Sci. Lett., 117, 363–377, 1993.CrossRefGoogle Scholar
  37. Holness, M. B., The effect of feldspar on quartz-H2O−CO2 dihedral angles at 4 kbar, with consequences for the behaviour of aqueous fluids in migmatites, Contrib. Mineral. Petrol., 118, 356–364, 1995.CrossRefGoogle Scholar
  38. Holness, M. B., Surface chemical controls on pore fluid connectivity in texturally equilibrated materials, in: Fluid flow and transport in rocks: Mechanisms and effects, edited by B.D. Jamtveit B. D. and B.W.D. Yardley, pp. 149–170, Chapman & Hall, London, 1996.Google Scholar
  39. Holness M. B., The permeability of non-deforming rock, in: Deformation-enhanced fluid transport in the Earth’s crust and mantle, edited by M.B. Holness, pp. 9–39, Chapman & Hall, London, 1997.Google Scholar
  40. Hunter, R. H., and D. McKenzie, The equilibrium geometry of carbonate melts in rocks of mantle composition, Earth Planet. Sci. Lett., 92, 347–356, 1989.CrossRefGoogle Scholar
  41. Iida, T., and R.L. Guthrie, The physical properties of liquid metals, Oxford Science Pub., Clarendon Press, Oxford, 1988.Google Scholar
  42. Jarosewich, E., Chemical analyses of meteorites: A compilation of stony and iron meteorite analyses, Meteoritics, 25, 323–337, 1990.Google Scholar
  43. Jin, Z.-M., H.W. II Green, and Y. Zhou, Melt topology in partially molten mantle peridotite during ductile deformation, Nature, 372, 164–167, 1994.CrossRefGoogle Scholar
  44. Jung, H., and H.S. Waff, Olivine crystallographic control and anisotropic melt distribution in ultramafic partial melts, Geophys. Res. Lett., 25, 2901–2904, 1998.CrossRefGoogle Scholar
  45. Jurewicz, S. R., and A.J.G. Jurewicz, Distribution of apparent angles on random sections with emphasis on dihedral angle measurements, J. Geophys. Res., 91, 9277–9282, 1986.CrossRefGoogle Scholar
  46. Jurewicz, S. R., and J.H. Jones, Preliminary results of sulfide melt/silicate wetting experiments in a partially melted ordinary chondrite, Lunar Planet. Sci., XXV, 653–654, 1995a.Google Scholar
  47. Jurewicz, S. R., and J.H. Jones, Preliminary results of olivine-metal wetting experiments and the direct measurement of metal phase interConnectivity, Lunar Planet. Sci., XXVI, 709–710, 1995b.Google Scholar
  48. Jurewicz, S. R., and E.B. Watson, Distribution of partial melt in a felsic system: the importance of surface energy, Contrib. Mineral. Petrol., 85, 25–29, 1984.CrossRefGoogle Scholar
  49. Jurewicz, S. R., and E.B. Watson, The distribution of partial melt in a granitic system: the application of liquid phase sintering theory, Geochim. Cosmochim. Acta, 49, 1109–1121, 1985.CrossRefGoogle Scholar
  50. Keene, B. J., Surface tension of slag systems, in: Slag Atlas, edited by Verein Deutscher EisenHüttenleute, pp. 403–462, 2nd edition, 1995a.Google Scholar
  51. Keene, B. J., Interfacial tension between ferrous melts and molten slags, in: Slag Atlas, edited by Verein Deutscher EisenHüttenleute, pp. 463–511, 2nd edition, 1995b.Google Scholar
  52. Kern, R., The equilibrium form of a crystal, in: Morphology of crystals, edited by I. Sunagawa, pp. 77–206, Terra Scientific Publishing Co., Tokyo, 1987.Google Scholar
  53. Kohlstedt, D. L., Structure, rheology and permeability of partially molten rocks at low melt fractions, in: Mantle flow and melt generation at mid-ocean ridges, Geophys. Monograph 71, edited by J. Phipps Morgan, D.K. Blackman, and J.M. Sinton, pp.103–121, AGU, Washington, 1992.CrossRefGoogle Scholar
  54. Laplace, P. S., Mécanique céleste, suppl. 10e livre, 1806.Google Scholar
  55. Laporte, D., Wetting behaviour of partial melts during crustal anatexis: the distribution of hydrous silicic melts in polycrystalline aggregates of quartz, Contrib. Mineral Petrol, 116, 486–499, 1994.CrossRefGoogle Scholar
  56. Laporte, D., and E.B. Watson, Direct observation of near-equilibrium pore geometry in synthetic quartzites at 600°–800°C and 2–10.5 Kbar, J. Geology, 99, 873–878, 1991.CrossRefGoogle Scholar
  57. Laporte, D., and A. Provost, The equilibrium crystal shape of silicates: implications for the grain-scale distribution of partial melts, EOS Trans. Am. Geophys. Union, 75, 364, 1994.Google Scholar
  58. Laporte, D., and A. Provost, The equilibrium geometry of a fluid phase in a two-dimensional polycrystalline aggregate with anisotropic surface energies, J. Geophys. Res. (subm.)Google Scholar
  59. Laporte, D., and D. Vielzeuf, Wetting behaviour of partial melts during crustal anatexis: the distribution of hydrous silicic melts in polycrystalline aggregates of quartz, EOS Trans. Am. Geophys. Union, 75, 364, 1994.Google Scholar
  60. Laporte, D., and E.B. Watson, Experimental and theoretical constraints on melt distribution in crustal sources: the effect of crystalline anisotropy on melt interconnectivity, Chem. Geol, 124, 161–184, 1995.CrossRefGoogle Scholar
  61. Laporte, D., C. Rapaille, and A. Provost, Wetting angles, equilibrium melt geometry, and the permeability threshold of partially molten crustal protoliths, in: Granite: from segregation of melt to emplacement fabrics, edited by J.-L. Bouchez, D.H. Hutton and W.E. Stephens, pp. 31–54, Kluwer, Amsterdam, 1997.Google Scholar
  62. Longhi, J., and S.R. Jurewicz, Plagioclase-melt wetting angles and textures: implications for anorthosites, Lunar Planet. Sci., XXVI, 859–860, 1995.Google Scholar
  63. Lupulescu, A., and E.B. Watson, Granitic melt connectivity at low-melt fraction in a mafic crustal protolith, EOS Trans. Am. Geophys. Union, 75, 585–586, 1994.Google Scholar
  64. Lupulescu, A., and E.B. Watson, Tonalitic melt connectivity at low-melt fraction in a mafic crustal protolith at 10 kb and 800 °C, EOS Trans. Am. Geophys. Union, 76, 299–300, 1995.CrossRefGoogle Scholar
  65. Maaløe, S., Principles of igneous petrology, 374 pp., Springer-Verlag, Berlin, 1985.CrossRefGoogle Scholar
  66. Maury, R. C, and H. Bizouard, Melting of acid xenoliths into a basanite: an approach to the possible mechanisms of crustal contamination, Contrib. Mineral. Petro.l, 48, 275–286, 1974.CrossRefGoogle Scholar
  67. McKenzie, D., The generation and compaction of partially molten rock, J. Petrol., 25, 713–765, 1984.Google Scholar
  68. McKenzie, D., The extraction of magma from the crust and mantle, Earth Planet. Sci. Lett., 74, 81–91, 1985.CrossRefGoogle Scholar
  69. McKenzie, D., Some remarks on the movement of small melt fractions in the mantle, Earth Planet. Sci. Lett., 95, 53–72, 1989.CrossRefGoogle Scholar
  70. Mehnert, K. R., W. Busch, and G. Schneider, Initial melting at grain boundaries of quartz and feldspar in gneisses and granulites, N. Jahr. Mineral. Monatsh., 4, 165–183, 1973.Google Scholar
  71. Minarik, W. G., and E.B. Watson, Interconnectivity of carbonate melt at low melt fraction, Earth Planet. Sci. Lett., 133, 423–437, 1995.CrossRefGoogle Scholar
  72. Minarik, W. G., F.J. Ryerson, and E.B. Watson,. Textural entrapment of core-forming melts, Science, 272, 530–533, 1996.CrossRefGoogle Scholar
  73. Murr, L. E., Interfacial phenomena in metals and alloys, Addison-Wesley, London, 1975.Google Scholar
  74. Parks, G. A., Surface and interfacial free energies of quartz, J. Geophys. Res., 89, 3997–4008, 1984.CrossRefGoogle Scholar
  75. Provost, P., and J.-P. Provost, Thermodynamique physique et chimique, 314 pp., CEDIC/Fernand Nathan, Paris, 1984.Google Scholar
  76. Raia, F., and F.J. Spera, Simulations of crustal anatexis: implications for the growth and differentiation of continental crust, J. Geophys. Res., 102, 22629–22648, 1997.CrossRefGoogle Scholar
  77. Riegger, O. K., and L.H. van Vlack, Dihedral angle measurement, AIME Trans., 218, 933–935, 1960.Google Scholar
  78. Rignault, E., Modélisation de la géométrie d’équilibre d’une phase fluide dans un agrégat polycristallin. Implications pour le transport des fluides géologiques, PhD thesis, Blaise Pascal University, Clermont-Ferrand, France, 1998.Google Scholar
  79. Riley, G. N., Jr., and D.L. Kohlstedt, Kinetics of melt migration in upper mantle-type rocks, Earth Planet. Sci. Lett., 105, 500–521, 1991.CrossRefGoogle Scholar
  80. Rubie, D.C., and A.J. Brearley, A model for rates of disequilibrium melting during metamorphism, in: High Temperature Metamorphism and Crustal Anatexis, edited by J.R. Ashworth and M. Brown, London, Unwin Hyman, 1991.Google Scholar
  81. Rutter, E. H., The influence of deformation on the extraction of crustal melts: a considerationof the role of melt-assisted granular flow, in: Deformation-enhanced fluid transport in the Earth’s crust and mantle, edited by M.B. Holness, pp. 82–110, Chapman & Hall, London, 1997Google Scholar
  82. Scott, D.R., and D.J. Stevenson, Magma ascent by porous flow, J. Geophys. Res., 91, 9283–9296, 1986.CrossRefGoogle Scholar
  83. Shannon, M. C. and C.B. Agee, High pressure constraints on percolative core formation, Geophys. Res. Lett., 23, 2717–2720, 1996.CrossRefGoogle Scholar
  84. Smith, C. S., Some elementary principles of polycrystalline microstructure, Metall. Rev., 9, 1–48, 1964.CrossRefGoogle Scholar
  85. Stevenson, D. L., 1990. Fluid dynamics of core formation, in: Origin of the Earth, edited by H.E. Newsom and J.H. Jones, pp. 231–249, Oxford Univ. Press, Oxford, 1990.Google Scholar
  86. Stickeis, C. A., and E.E. Hucke, Measurement of dihedral angles, Trans. Am. Inst. Min. Metall. Pet. Eng., 230, 795–801, 1964.Google Scholar
  87. Sutton, A. P., and R.W. Balluffi, Interfaces in crystalline materials, Monographs in the Physics and Chemistry of Materials, no. 51, 852 pp., Clarendon Press, Oxford, 1995.Google Scholar
  88. Swain, M. V., and B.K. Atkinson, Fracture surface energy of olivine, Pageoph., 116, 866–872, 1978.CrossRefGoogle Scholar
  89. Takahashi, E., Melting of a Yamato L3 chondrite (Y-74191) up to 30 kbar, in: Proceedings of the 8 th Symposium on Antarctic Meteorites (Mem. Nat. Inst. Polar Res. Spec. Issue Jpn), vol. 30, pp. 168–180, 1983.Google Scholar
  90. Takahashi, E., Melting of a dry peridotite KLB-1 up to 14 GPa: Implications on the origin of peridotitic upper mantle, J. Geophys. Res., 91, 9367–9382, 1986.CrossRefGoogle Scholar
  91. Taniguchi, H., Surface tensions of melts in the system CaMgSi2O6-CaAl2Si2O8 and its structural significance, Contrib. Mineral. Petrol., 100, 484–489, 1988.CrossRefGoogle Scholar
  92. Taylor, G. J., Core formation in asteroids, J. Geophys. Res., 97, 14717–14726, 1992.CrossRefGoogle Scholar
  93. Toramaru, A., and N. Fujii, Connectivity of melt phase in a partially molten peridotite, J. Geophys. Res., 91, 9239–9259, 1986CrossRefGoogle Scholar
  94. Turcotte, D. L., and G. Schubert, Geodynamics, John Wiley, New York, 1982.Google Scholar
  95. Vicenzi, E.P., R.P. Rapp, and E.B. Watson, Crystal/melt wetting characteristics in partially-molten amphibolite, EOS Trans. Am. Geophys. Union, 69, 482, 1988.Google Scholar
  96. von Bargen, N., and H.S. Waff, Permeabilities, interfacial areas and curvatures of partially molten systems: results of numerical computations of equilibrium microstructures, J. Geophys. Res., 91, 9261–9276, 1986.CrossRefGoogle Scholar
  97. von Bargen, N., and H.S. Waff, Wetting of enstatite by basaltic melt at 1350°C and 1.0- to 2.5-GPa pressure, J. Geophys. Res., 93, 1153–1158, 1988.CrossRefGoogle Scholar
  98. Waff, H. S., and J.R. Bulau, Equilibrium fluid distribution in an ultramafic partial melt under hydrostatic conditions, J. Geophys. Res., 84, 6109–6114, 1979.CrossRefGoogle Scholar
  99. Waff, H. S., and J.R. Bulau, Experimental determination of near-equilibrium textures in partially molten silicates at high pressures, in: High pressure research in geophysics, Adv. Earth Planet. Sci. 12., edited by S. Akimoto S. and M.H. Manghnani, pp. 229–236, Centre for Academic Publication, Tokyo, 1982.CrossRefGoogle Scholar
  100. Waff, H. S., and U.H. Faul, Effects of crystalline anisotropy on fluid distribution in ultramafic partial melts, J. Geophys. Res., 97, 9003–9014, 1992.CrossRefGoogle Scholar
  101. Walker, D., and C.B. Agee, Ureilite compaction, Meteoritics, 23, 81–91, 1988.Google Scholar
  102. Walker, D., S. Jurewicz, and E.B. Watson, Adcumulus dunite growth in a laboratory thermal gradient, Contrib. Mineral Petrol., 99, 306–319, 1988.CrossRefGoogle Scholar
  103. Wanamaker, B. J., and D.L. Kohlstedt, The effect of melt composition on the wetting angle between silicate melts and olivine, Phys. Chem. Minerals, 18, 26–36, 1991.CrossRefGoogle Scholar
  104. Watson, E.B., Diffusion in fluid-bearing and slightly melted rocks: experimental and numerical approaches illustrated by iron transport in dunite, Contrib. Mineral. Petrol., 107, 411–434, 1991.CrossRefGoogle Scholar
  105. Watson, E.B., and J.M. Brenan, Fluids in the lithosphere, 1. Experimentally determined wetting characteristics of CO2−H2O fluids and their implications for fluid transport, host-rock physical properties and fluid inclusion formation, Earth Planet. Sci. Lett., 85, 497–515,1987.CrossRefGoogle Scholar
  106. Watson, E. B., J.M. Brenan, and D.R. Baker, Distribution of fluids in the continental mantle, in: Continental Mantle, edited by M. A. Menzies, pp. 111–125, Clarendon, Oxford, 1990.Google Scholar
  107. Wolf, M.B. and P.J. Wyllie, Dehydration-melting of solid amphibolite at 10 kbar: textural development, liquid interconnectivity and application to the segregation of magmas, Mineral Petrol., 44, 151–179, 1991.CrossRefGoogle Scholar
  108. Wortis, M., Equilibrium crystal shapes and interfacial phase transitions, in: Chemistry and physics of solid surfaces VIII, edited by R. Vanselow and R.F. Howe, pp. 367–405, Springer Verlag, Berlin, 1988.Google Scholar
  109. Wray, P.J., The geometry of two-phase aggregates in which the shape of the second phase is determined by its dihedral angle, Acta Metall., 24, 125–135, 1976.CrossRefGoogle Scholar

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© Springer Science+Business Media Dordrecht 2000

Authors and Affiliations

  • Didier Laporte
    • 1
  • Ariel Provost
    • 1
  1. 1.Laboratoire “Magmas et Volcans”OPGC, CNRS & Université Blaise PascalClermont-Ferrand CedexFrance

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