DOUBLE FIT: Optimization procedure applied to lattice strain model

Modeling trace element partition coefficients using the lattice strain model is a powerful tool for understanding the effects of P-T conditions and mineral and melt compositions on partition coefficients, thus significantly advancing the geochemical studies of trace element distributions in nature. In this model, partition coefficients describe the strain caused by a volume change upon cation substitution in the crystal lattice. In some mantle minerals, divalent, trivalent, and tetravalent trace element cations are mainly substituted in one specific site. Lattice strain model parameters, for instance in olivine and plagioclase, are thus fit for one crystal site. However, trace element cations can be substituted in two sites in the cases of pyroxenes, garnets, amphiboles, micas, or epidote-group minerals. To thoroughly study element partitioning in those minerals, one must consider the lattice strain parameters of the two sites. In this paper, we present a user-friendly executable program, working on PC, Linux, and Macintosh, to fit a lattice strain model by an error-weighted differential-evolution-constrained algorithm (Stom, It, and Price, K. 1997. Differential evolution - A simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11, 341-359). This optimization procedure is called DOUBLE FIT and is available for download on http://celiadalou. wixsite.com/website/double-fit-program . DOUBLE FIT generates single or double parabolas fitting experimentally determined trace element partition coefficients using a very limited amount of data (at minimum six experimental data points) and accounting for data uncertainties. It is the fastest calculation available to obtain the best-fit lattice strain parameters while accounting for the elastic response of two different sites to trace element substitution in various minerals.