On the coherency-controlled growth habit of precipitates in minerals

Minimization of interfacial energy is the dominant factor governing the equilibrium habit, i.e. orientation and morphology, of a precipitate in the parent crystal. Existing models of optimum interphase boundaries have established criteria that minimize the lattice misfit and/or the strain energy by the comparison of the interplanar spacings of the two interpenetrating lattices. Based on a detailed analytical transmission electron microscopy (TEM) study of two precipitate–matrix systems with different degrees of structural similarity in oxygen sublattices, i.e. hematite in rutile and magnetite in clinopyroxene from metamorphic rocks, it is reported that the optimum interphase boundary and the equilibrium habit of a precipitate in these structurally complex systems can be defined from the special geometry characteristics of diffraction patterns along specific zone axes. Analysis of the TEM results shows that a precipitate in a parent crystal, either with or without a similar oxygen framework, always poses a specific crystallographic relationship with the differences in the g vector pairs (Δg), i.e. misfits of diffraction-spot pairs, of two structures aligned in the same direction, and that the precipitate exhibits a growth habit plane normal to Δg. This new insight into the interfacial energetics, rather than kinetically or topologically controlled mineral growth, can be understood by the coherency of lattice planes in the interphase boundaries and rationalized by the normal-to-Δg principle originally developed for structural transformations in alloys with simple close-packed structures. The normal-to-Δg principle is formulated to calculate the optimum interphase boundaries in the present systems, feldspars and clinopyroxenes of broad geological/mineralogical interest, and gives results comparable to other models yet in a more straightforward manner. This alternative approach can be readily applied in interphase boundary modelling of minerals and sheds light on the growth habit as a potential geothermobarometer of metamorphic rocks.