A Simple Thermodynamic Model for Grain Interfaces: Some Insights on Nucleation, Rock Textures, and Metamorphic Differentiation

  • James B. ThompsonJr.
Part of the NATO ASI Series book series (ASIC, volume 218)


By assuming that all grain interfaces may be approximated by a mosaic of planar elements, it is possible to obtain certain relationships that should, within the validity of the model, characterize an equilibrium texture. These include “Wulff’s Law” for the equilibrium form of a crystal in a fluid, and also a rule of indentation that has features in common with Becke’s concept of a “crystalloblastic series.” The model also leads to simple expressions relating the critical size of new crystal nuclei to the activation energy for nucleation.

Disequilibrium textural features are of special interest because each carries with it a historical message. Disequilibrium textures may also provide the driving forces for the material transfers that lead to certain types of metamorphic differentiation. Metamorphic differentiation, however, may also arise through the selectively localized nucleation of new porphyroblasts or may be modified by kinematic effects.


Surface Element Critical Radius Homogeneous Part Equilibrium Form Unit Quantity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Adamson, A. W. (1976) Physical Chemistry of Surfaces, 3rd ed., John Wiley & Sons, New York, 648 p.Google Scholar
  2. Becke, F. (1913) ‘Über Mineralbestand und Struktur der Kristallinen.’ Schiefer. Denkschr. Akad. Wiss. Wien, 75, 1–53.Google Scholar
  3. Bennema, P. (1973) ‘Generalized Herring treatment of the equilibrium form’ In, P. Hartman, ed., Crystal Growth: An Introduction, North Holland, Amsterdam, 342–357.Google Scholar
  4. Curie, Pierre (1885) ‘Sur la formation des cristaux et sur les constant capillaires de leurs differentes faces.’ Bull, de la Soc. Mineral, de France, 8, 145–150.Google Scholar
  5. DeVore, G. W. (1959) ‘Role of minimum interfacial free energy in determining the macroscopic features of mineral assemblages. I. The Model.’ Jour. Geol., 67, 211–227.CrossRefGoogle Scholar
  6. Dinghas, Alexander (1944) ‘Über einen geometrischen Satz von Wulff fur die Gleichgewichtsformen von Kristallen.’ Zeitschr. f. Kristallog., 105, 304–314.Google Scholar
  7. Frondel, Clifford (1934) ‘Selective incrustation of crystal forms,’ Am. Mineral., 19, 316–329.Google Scholar
  8. Frondel, Clifford (1940) ‘Oriented inclusions of staurolite, zircon and garnet in muscovite, skating crystals and their significance.’ Am. Mineral., 25, 64–87.Google Scholar
  9. Gibbs, J. W. (1875–1878, 1928) ‘On the equilibrium of heterogeneous substances.’ In: Collected Works of J. Willard Gibbs, Ph.D., LL.D., Vol. I: Thermodynamics. Yale University Press, 1928, 55–353.Google Scholar
  10. Gomer, Robert and Smith, C. S. (1953) Structure and Properties of Solid Surfaces, University of Chicago Press, 491 p.Google Scholar
  11. Guggenheim, E. P. and Adam, N. K. (1938) ‘The thermodynamics of adsorption at the surface of solutions.’ Proc. Roy. Soc. London, A139, 218–236.Google Scholar
  12. Herring, Conyers (1953) ‘The use of chemical macroscopic concepts in surface energy problems.’ In: Robert Gomer and C. S. Smith, eds., Structure and Properties of Solid Surfaces, University of Chicago Press, 5–81.Google Scholar
  13. Hilton, Harold (1903) Mathematical Crystallography, Oxford University Press, 262 p.Google Scholar
  14. Hoffman, D. W. and Cahn, J.W. (1972) ‘A vector thermodynamic for anisotropic surfaces. I. Fundamentals and application to plane surface junctions.’ Surface Science, 31, 368–388.CrossRefGoogle Scholar
  15. Johnson, E. A. (1965) ‘Generalization of the Gibbs-Thomson Equation.’ Surface Science, 3, 429–444.CrossRefGoogle Scholar
  16. Kingery, W. A. (1974) ‘Plausible concepts necessary and sufficient for interpretation of ceramic grain-boundary phenomena.’ Jour. Am. Ceram. Soc, 57, 1–8, 74–83.CrossRefGoogle Scholar
  17. Kretz, R. (1966) ‘Interpretation of the shape of mineral grains in metamorphic rocks.’ Jour. Petrol, 7, 68–94.Google Scholar
  18. Liebmann, Heinrich (1913) ‘Der Curie-Wulff’sche Satz über Combinations-Formen von Krystallen.’ Zeitschr. f Kristallog., 53, 171–177.Google Scholar
  19. Ostwald, W. (1900) ‘Über die vermeintliche Isomerie des roten und gelben Quecksilberoxyds und die Oberflachenspannung fester Korper.’ Zeitschr. f Phys. Chem., 34, 495–504.Google Scholar
  20. Roedder, Edwin (1984) ‘Fluid inclusions’. In: P. H. Ribbe, series ed., Min. Soc. Am., Rev. in Mineral., 12, 644 p.Google Scholar
  21. Smith, C. S. (1948) ‘Grains, phases and interfaces: An interpretation of micro structure.’ Trans. Am. Inst. Min. Metall. Engrs., 175, 515–575.Google Scholar
  22. Smith, C. S. (1953) ‘Microstructure.’ Trans. Am. Inst. Min. Metall. Engrs., 175, 15–51.Google Scholar
  23. Smith, C. S. (1964) ‘Some elementary principles of polycrystalline microstructure.’ Metal Rev., 4, 33.Google Scholar
  24. Spry, Alan (1969) Metamorphic Textures. Pergamon Press, Oxford, 350 p.Google Scholar
  25. Stanton, R. L. (1964) ‘Mineral interfaces in stratiform ores.’ Trans. Inst. Min. Metall, London, 74, 45–79.Google Scholar
  26. Stranski, I. N. (1943) ‘Über die Thomson Gibbsche Gleichung und über die sogennante Theorie der Verwachsungskonglomerate.’ Zeitschr. f. Kristallog., 105, 91–123.Google Scholar
  27. Verhoogen, J. (1948) ‘Geological significance of surface tension.’ Jour. Geol, 56, 211–217.CrossRefGoogle Scholar
  28. Vernon, R. (1968) ‘Intergranular microstructure of high-grade metamorphic rocks at Broken Hill, Australia.’ Jour. Petrol, 9, 1–22.Google Scholar
  29. von Laue, M. (1943) ‘Der Wulffsche Satz für die Gleichgewichts Formen von Kristallen.’ Zeitschr. f. Kristallog., 105, 124–133.Google Scholar
  30. Wulff, Georg (1901) ‘Zur Frage der Geschwindigkeit des Wachsthums und der Auflosung der Krystallflächen.’ Zeitschr. f. Kristallog., 34, 449–530.Google Scholar

Copyright information

© D. Reidel Publishing Company 1987

Authors and Affiliations

  • James B. ThompsonJr.
    • 1
  1. 1.Department of Earth and Planetary SciencesHarvard UniversityCambridgeUSA

Personalised recommendations