Relationship between grain/interphase boundary energies and phase diagrams

We have examined the relationship between the type of phase diagram and relative grain boundary to interphase boundary energy in order to answer a long-term unsolved question: Why do crystals prefer different neighbors? For minerals as well as metals and ceramics, dihedral angles formed at triple grain junctions involving two different crystalline phases (A and B) are commonly <120° . Based on the interface tension balance equation 2cos(θ /2) = γ _gb/γ _int (Eq. 1) -- where \theta is dihedral angle and γ is either grain or interphase boundary energy -- a value of θ <120° indicates that the interphase boundary energy is lower than of the grain boundary energy. Grain boundary energies of metals correlate linearly with latent heat of fusion and/or melting temperature. Systems composed of two crystalline phases often have a eutectic point at a lower temperature than the melting points of pure phases; accordingly, the latent heat of fusion is lower for the two-phase system than for the individual component phases. Therefore, we predict that the interphase boundary energy is lower than that of the grain boundaries in the case of a eutectic system; however, the opposite holds for monotectic systems. We examined grain boundary versus phase boundary energies for binary systems in which one phase is Ag and the other is Fe, Co, Ni, Cu, Ge, or Si. The systems formed from Ag and any of the former three elements are monotectics, while the systems composed of Ag and any of the latter three elements are eutectics. To obtain binary polycrystalline materials, we sintered the powders of 5-10 μ m of Ag plus either Fe, Co, Ni or Cu at vacuum conditions. We also made amorphous ribbons of Ag-Si and Ag-Ge by the rapid rolling technique, which we then annealed for 10-15 h to cause crystallization and grain growth. After surface etching, we measured dihedral angles with a field emission SEM. Also, we used dihedral angle data for synthetic and natural mineral assemblages of quartz-feldspar and olivine-orthopyroxene. In terms of Eq. (1), the interphase boundary energy is lower than grain boundary energies in all of the eutectic systems. In contrast, the interphase boundary energy (γ _AB) is higher than at least one grain boundary energies (γ _AA and/or γ _BB) in all of the monotectic systems. Based on published molecular dynamic simulations, high-resolution microscopy observations, and grain boundary segregation analyses, a general high-angle grain boundary assumes a melt-like structure with a width of 1-3 atomic layers; this region cannot be defined as a thin boundary phase. Extending this concept, we can predict the type of phase diagram for any multi-phase system simply by measuring the dihedral angle. If a system changes from eutectic to monotectic or vice versa by adding trace elements such as water, this transition will be evident from the dihedral angle.