Minimization of interfacial energy is the dominant factor controlling the shape and orientation of crystalline precipitates and replacement products in minerals. The dimensional misfit of strain–free lattices at a phase boundary is directly related to interfacial energy and its minimization provides a convenient criterion for calculating interface orientation. The contribution of anisotropic elasticity is relatively insignificant except when the lattice misfit is essentially isotropic.

The existing lattice–misfit theory of Robinson and coworkers for two-dimensional lattices and its application to chain-silicate mineral systems is reviewed, and extended to both coincident and optimal phase boundaries. By recognizing that coincident and optimal phase boundaries have indices (hkl) common to both lattices, a generalized lattice–misfit theory for three-dimensional lattices is developed and applied to feldspar mineral systems. For optimal boundaries, structural continuity across an interface may be improved by local coherency stresses and dislocations. Discrepancies with observed orientations arise from topological constraints and the decrease in specific surface area with coarsening.

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