Lattice strain model for rare earth element partitioning between apatite and silicate melt: effect of apatite/melt composition and temperature with implications for lunar basalts

We present new parameterized lattice strain models to predict the apatite/silicate melt partition coefficients of the rare earth elements (REE) in natural magmatic systems as a function of temperature and melt composition with high accuracy and precision. We collected published experimental REE partition coefficients for apatite coexisting with melt ranging from picrobasaltic to rhyolitic and phonolitic composition. Resulting dataset was analysed using the lattice strain model to assess the data quality. The three lattice strain parameters (D₀, r₀, and E) were subjected to a multivariate nonlinear least-squares analysis as a function of intensive variables, and we attempted to develop two independent models, on the basis of melt and apatite composition. In melt composition-based model, it was found that the D₀ parameter increases with increasing melt polymerization, which can be expressed by the newly proposed simplified melt polymerization index P.I. = ( \(\:{X}_{{\text{S}\text{i}\text{O}}_{2}}\) +2 \(\:{X}_{{\text{A}\text{l}}_{2}{\text{O}}_{3}}\) + \(\:{X}_{{\text{T}\text{i}\text{O}}_{2}}\) +2 \(\:{X}_{{\text{P}}_{2}{\text{O}}_{5}}\) )/( \(\:{X}_{\text{M}\text{g}\text{O}}\) + \(\:{X}_{\text{F}\text{e}\text{O}}\) + \(\:{X}_{\text{C}\text{a}\text{O}}\) +2 \(\:{X}_{\text{a}\text{l}\text{k}}\) ), where individual \(\:{X}_{i}\) variables represent the molar fractions of the oxides in the melt. By disentangling the effect of each component of the P.I., it was found that the CaO content of the melt is the oxide that affects more the D₀ parameter. Thus, the D₀ parameter is expressed as a power law function of melt CaO content. Through extensive search of the parameter space, the E and r₀ variables were found to correlate strongly with linear combination of melt CaO, P₂O₅ and of reciprocal temperature, 1/T. Based on the apatite composition, we could not find any dependence of the partitioning parameters on compositional variables that would outperform solely a reciprocal temperature-based fit. The new parameterization was applied to predict REE partition coefficients in lunar basalts and suggests that lunar apatite could only equilibrate with evolved melt at late stages of fractional crystallisation.