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

Abstract

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 (i n؉ ) 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. Kp(La) is parameterized via an exchange reaction involving CaAl 2 Si 2 O 8 and the La-feldspar component La 0.5 Na 0.5 Al 2 Si 2 O 8 . 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 p s 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 (NaAlSi 3 O 8 ) and anorthite (CaAl 2 Si 2 O 8 ), 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 ( 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 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.

Trace element partitioning between plagioclase and melt: An investigation of the impact of experimental and analytical procedures

“…All of our new D Pb are similar to the experimental values of Tepley et al . [] and Dohmen and Blundy []. However, they are substantially lower than the values of Aigner‐Torres et al .…”

“…Pb was analyzed for in the piston cylinder experiments, but was found to be below detection limits. This may be due to leakage or to alloying of Pb with the capsule [ Dohmen and Blundy , ] as noted above.…”

“…The pattern of decrease in REE compatibility in plagioclase with increasing atomic number and increasing anorthite content has been well established [ Drake and Weill , ]. Those initial observations have been confirmed by subsequent research [ Tepley et al ., ; Green , ; McKay et al ., , Simon et al ., , Blundy , , Aigner‐Torres et al ., ; Dohmen and Blundy , ]. Examining our new data within the context of the published data demonstrates that the composite dataset exhibits those same characteristics (Figures and ), but exhibit extensive scatter, including reported values >1 for Ce.…”

“…For example, calculated REE trends will exhibit anomalies that are artifacts of the model calibration, not related to the actual behavior of the elements. The approach of tying predictive models to a specific unifying theme (elastic strain in the case of Dohmen and Blundy []) can minimize the effects of anomalously high or low experimentally determined literature values used to calibrate the model. The impact of the approach can be seen in the predicted versus measured correlations [ Dohmen and Blundy , , Figure ].…”

“…; Bindeman and Davis ; Bedard ; Aigner‐Torres et al . ; Tepley et al ., ; Dohmen and Blundy , ]. However, there has not been a review of how we conduct or report trace element experimental data for over 20 years [ McKay , ; Green , ].…”