Reaction of zoning of garnet
Compositional zoning of garnet in metamorphic or igneous rocks preserves evidence of the equilibration history of the sample and can be interpreted in terms of a growth-fractionation, diffusion-exchange, or diffusion-reaction model. Diffusion zoning is usually assumed to result from exchange reactions between garnet and other phases as the partitioning coefficient varies in response to changing environmental conditions, primarily temperature. However, in many natural environments where garnet grew originally in divariant equilibrium with other phases, changing conditions can promote continuous or “divariant” reactions and consequent compositional shifts of phases that can be much greater in some systems showing these reactions than those related to the small changes of partitioning. Diffusional zoning related to overstepping of these continuous reactions must be related to incongruent reaction and necessitates formulation of a kinetic diffusion-reaction model involving moving phase boundaries as well as solid-state diffusion.
Three samples containing zoned garnets from the metamorphic aureole around the Ronda ultramafic intrusion in southern Spain are used to illustrate two possible models of diffusion-reaction processes. The examples are particularly informative because the reactions are demonstrably irreversible and evidence of the reaction system is preserved. Partitioning data indicates that compositions of product phases are not in equilibrium with the original garnet and do not vary with extent of reaction; therefore, exchange reactions with garnet were not possible and garnet changed composition only by incongruent reaction. After a small amount of reaction, Mg/Fe of the rim composition approaches a value apparently in equilibrium with product phases, but the garnets are zoned inward to the original garnet composition preserved in the interior. Grossularite content is approximately constant and spessartite content variable but small, thus, the rim composition of pyrope or almandine is assumed to be fixed by the external reaction process and is taken as a boundary condition in the following models.
The zoning profile of pyrope or almandine component between the fixed rim and core compositions (assumed to extend to ∞) is described in semiinfinite, half-space models appropriate for large garnets with narrow rims. The first model corresponds to a reaction system in which all garnet compositions are metastable (case 1) and zoning depends on the independent variables of the diffusion constant, velocity of the interface between garnet and matrix, and time. The second model, corresponding to systems in which the initial garnet composition is metastable but an equilibrium composition is stable (case 2), depends on the independent variables diffusion constant, time, and a function of reaction compositions. In case 1 the consumption velocity is assumed constant and a steady state zoning profile is reached at large time, whereas, in case 2, the velocity decreases with the concentration gradient and steady state is not possible.
The models were tested using a reaction time estimated from cooling models of the aureole, mass of garnet consumed, determined petrographically, and phase compositions. The two cases are somewhat independent in that different parameters are independent variables. The estimate of the diffusion constant of 10−18±2 cm2/sec (assumed to be a mutual or binary coefficient for almandine and pyrope) is considered reasonable for the temperature range of reaction (probably 600–900° C), and the two models are consistent considering the probable error and possible real temperature differences.
It is obvious that details of the metamorphic reaction system must be known to successfully apply diffusion models. Kinetic models, involving consumption or growth of the phase as well as diffusion are probably necessary when dealing with natural rocks. Several possible and interesting complications, such as cross coupling between components, can be investigated if more data were available. Experimental determination of diffusion constants allow natural reaction rates to be estimated by this method. Diffusion zoning is an important consideration that could increase the efficiency of experimentation with chemically recalcitrant phases.
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