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A Discussion on natural strain and geological structure - Diffusion in metamorphic tectonites: lattice-fixed reference frames

The nature of volume diffusion during metamorphism may be studied by examining compositional zoning in metamorphic minerals. Garnets with sharp optical zones and internal fabrics related to deformation are of special interest, because they provide a link between partitioning by growth and by diffusion. Diffusion in the almandine-rich garnets of pelitic schists involves, at the very least, the migration of four ionic components (Fe2+, Mn2+, Mg2+ and Ca2+). Because of the possible occurrence of uphill diffusion and other phenomena we do not intuitively associate with diffusion, the search for evidence of volume diffusion must be preceded by a careful theoretical and experimental examination of diffusion in multicomponent minerals. The theoretical and experimental investigation of diffusion in silicates may be simplified by: (1) the choice of ions as components in the flux equations; (2) the construction of lattice-fixed reference frames to reduce the number of flux equations and diffusion coefficients. Flux equations are developed specifically for diffusion via ionized vacancies, but they may be easily modified to treat diffusion via neutral vacancies or by one to one exchange of ions. Methods are presented for solving the flux equations under the constraint that the crystal remain electrically neutral during diffusion. The transition-state theory of Lane & Kirkaldy (1964), which allows the calculation of the matrix of chemical diffusion coefficients from the mobility of individual ions, is adapted to the particular lattice-fixed frames developed here.