Solute partitioning under continuous cooling conditions as a cooling rate indicator

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Abstract
A mathematical model is developed to describe the concentration profiles as a function of time of a solute dissolved in two coexisting finite phases under continuous cooling conditions. A temperature‐dependent partitioning of the solute between the two phases is included. The model relates to the use of experimentally determined solute profiles to infer the rates at which various rocks cooled. The model employs finite difference equations and the Thomas tridiagonal method to solve the appropriate differential equations describing the solute partitioning. To illustrate the application of the model, the partitioning of zirconia between coexisting ilmenite and ulvöspinel is considered. It is shown that cooling rates can be calculated not only from solute concentration profiles within the grains but also from the ratio of the solute concentrations at a given distance on both sides of the interface or from the ratio of the average solute concentrations in the two phases. The cooling rates of a suite of Apollo 15 Elbow Crater gabbros are calculated from measured ratios of concentrations at 10 μm from the interfaces between the phases. A comparison is made of calculated concentration ratios 10 μm from the interface and cooling rates for equilibrium versus uniform initial concentrations. It is shown that the Elbow Crater gabbros could not have had a uniform concentration profiles at the previously suggested initial temperature of 1350 K. Also considered are the effects of the initial temperature, the grain sizes, and the diffusion coefficients of Zr in the phases on the calculated cooling rates. Finally, suggestions are made for other systems where the present model can be applied to estimate the thermal histories of rocks.

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