%0 Journal Article
%A Dohmen, Ralf
%A Blundy, Jon
%T A predictive thermodynamic model for element partitioning between plagioclase and melt as a function of pressure, temperature and composition
%D 2014
%R 10.2475/09.2014.04
%J American Journal of Science
%P 1319-1372
%V 314
%N 9
%X 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 (Kp(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 Kp(Na), Kp(Ca), and Kp(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. Kp(La) is parameterized via an exchange reaction involving CaAl2Si2O8 and the La-feldspar component La0.5Na0.5Al2Si2O8. The free energy change of this reaction is small, but well constrained by the data, such that for a given P-T-X Kp(La) can be derived from a combination of Kp(Na) and Kp(Ca). In the case where Kp(Na) and Kp(Ca) are independently constrained, the models reproduce the experimental values of 749 Kps 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 Kp(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 Kp(Na), Kp(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 Kp(Na) and 920 Kp(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 (μipl) 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 μipl is not adequately described by existing empirical models used to predict Kp 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.
%U https://www.ajsonline.org/content/ajs/314/9/1319.full.pdf