Role of Minimum Interfacial Free Energy in Determining the Macroscopic Features of Mineral Assemblages. I. the Model

The interfacial or grain boundary free-energy contribution to mineral interrelationships is largely ignored in the petrologic literature. Although only a small part of the total energy of the system, the interf acial free energy could play a dominant role during nucleation, crystal growth, exsolution, replacement, and diffusion transfer-processes that largely involve surface phenomena. By effectively determining the saturation point of the disperse phase, the nucleation sites, nucleation frequency, grain form, extent of individual grain growth, and, for certain systems, modal composition for the mineral assemblage could be determined by the minimum interfacial free energy of the system. Because of a continuously changing environment about a grain during its growth (caused by any grain boundary strain or orientation and/or compositional differences of the adjacent grains or phases), the average interfacial free energy associated with the grain and its associated grains must continuously increase, so that a continuous increase in the effective concentration of the disperse phase is required to support further growth, especially in systems of heterogeneous nucleation. In certain systems this increase in interfacial free energy could result in a maximum grain association limit for the growing grain if the concentration required for its further growth is higher than required to precipitate the material as a separate group of grains, such as in veins of the phase. Relative grain sizes, grain distributions, extent of various grain associations, and nature of grain contacts are interpreted as an expression of a minimum interfacial free energy of the mineral assemblage. A mechanism by which the influence of the interfacial free energy on the crystallization of a grain assemblage could be made significant is discussed in terms of a nucleation-crystal-growth model.