A predictive thermodynamic model for element partitioning between plagioclase and melt as a function of pressure, temperature and composition

One-atmosphere experiments in the system diopside-albite-anorthite (Di-Ab-An) have been used to explore the controls on plagioclase-melt partitioning of trace elements (Li, K, Rb, Cs, Mg, Zn, Sr, Ba, La, Sm, Y). By performing experiments along isotherms it was possible to isolate compositional controls from those of temperature. The lattice strain model accounts for variations in partition coefficients (K_p(i)) for isovalent series of cations (iⁿ⁺) and the experimental data are used to optimize the lattice strain parameters so that partition coefficients for n = 1 to 3 can be derived from K_p(Na), K_p(Ca), and K_p(La), respectively, at the conditions of interest. The optimized lattice strain parameters have magnitudes and compositional and thermal dependences that are consistent with elastic data for plagioclases. K_p(La) is parameterized via an exchange reaction involving CaAl₂Si₂O₈ and the La-feldspar component. La_0.5Na_0.5Al₂Si₂O₈. The free energy change of this reaction is small, but well constrained by the data, such that for a given P-T-X K_p(La) can be derived from a combination of K_p(Na) and K_p(Ca). In the case where K_p(Na) and K_p(Ca) are independently constrained, the models reproduce the experimental values of 749 K_ps for Li, Mg, K, Rb, Sr, Y, Cs, Ba, and REE (obtained from 91 individual experiments varying over five orders of magnitude) within a factor of 1.5 for 53 percent of the data and a factor of 2 for 74 percent of the data. The isothermal experimental data reveal that additional compositional effects, arising from non-ideal mixing in plagioclase and in melt, also influence K_p(i). A thermodynamic model based on the free energy of fusion of albite (NaAlSi₃O₈) and anorthite (CaAl₂Si₂O₈), and taking into account plagioclase and melt non-ideality in Di-Ab-An, is developed to express K_p(Na), K_p(Ca) as functions of pressure (P), temperature (T) and composition (X). The thermodynamic models are extended to a wider compositional range by means of an empirical parameterization of 919 K_p(Na) and 920 K_p(Ca) from a database of 991 published experiments. These models are able to reproduce 919 measured partitioning values for Li, Na, Mg, Ca, K, Rb, Sr, Y, Cs, Ba, and REE (from 91 experiments) with 47 percent of the model values within a factor of 1.5 of the measured values and 69 percent within a factor of 2 for any P-T-X condition. The models can also be used to constrain the dependence of the chemical potential of trace cations in plagioclase solid solutions (μ_i ^pl) for use in diffusion chronometry where the fully equilibrated trace element concentration profile must be known in order to calculate timescales. It is shown that μ_i ^pl is not adequately described by existing empirical models used to predict K_p as a function of anorthite because of the conflating effects of T and X in the polythermal experimental datasets from which those models were derived.