A KINETIC PHASE DIAGRAM FOR CLASSIFICATION OF ELEMENT / ISOTOPE EXCHANGE REACTIONS - DIFFUSION- OR INTERFACE- CONTROL?

Conventionally, diffusion models have addressed the exchange of species (elements / isotopes) between a mineral and a reservoir with which it is in contact (e.g. an adjacent mineral or fluid). These are the basis of common formulations for calculating closure temperatures, cooling rates etc. In such models it is arbitrarily assumed that the reactions are not interface controlled - equilibrium partitioning is achieved instantaneously at the interface. Often, however, two mineral grains exchanging a species are not in physical contact with each other i.e. they communicate via the mediation of a fluid or by transport through the intergranular region. We have developed an analytical model to describe the behavior of such systems. A rich variety of behaviors emerges as a function of three dimensionless parameters that characterize the system. The conventional behavior are shown to be special cases of our general model for limited ranges of values of the three characteristic parameters. These parameters depend on independently measurable physical quantities such as diffusion rates in solids and fluid, reaction rates at interfaces, porosity and solubility of the species in the fluid etc. Knowing these properties, it is possible for the first time to predict the mechanism of reaction and course of evolution of a given system. The analysis reveals that diffusion- and interface-control are not the only two possibilities; instead, a kinetic phase diagram can be generated where domains for different kinds of behavior are demarcated as a function of these parameters. There are six regimes: (a) interface control (b) solid diffusion control (c) fluid diffusion control and the fields separating these end member types where mixed behavior is observed. Experimental results and observations in natural rocks are consistent with predictions. While common assumptions (e.g. rim-rim geothermometry) are shown to be valid most of the time, there are surprising exceptions. These allow us to explain some anomalous observations and alert us to potential problems in interpreting compositional zoning in minerals. Such cases will be discussed.