Modelling garnet-fluid partitioning in H₂O-bearing systems: a preliminary statistical attempt to extend the crystal lattice-strain theory to hydrous systems

Accurate geochemical models of magmatic processes require an understanding of crystal-melt partitioning of trace elements. Many major igneous processes at different tectonic environments in Earth occur in the presence of garnet as a residual phase. Since the pioneering crystal lattice-strain model, several attempts have been made to quantify garnet-melt partitioning coefficients over a wide range of conditions. However, high pressure high-temperature experimental data demonstrate distinct differences in partitioning determined at anhydrous conditions and partitioning determined in the presence of H₂O. In this study, we present for the first time a constraint on the partitioning of REE, Y, and Sc between garnet and hydrous fluids as a function of the water content in the fluid phase. We analysed published hydrous experimental partitioning data using different statistical methods and modelled key parameters in the crystal lattice strain model (r_0,D₀, and E). We show a robust correlation between r₀, temperature and garnet-fluid partitioning of Mg. We further show that D₀ can be predicted using the garnet-fluid partitioning of Fe and that E can be predicted using various parameters describing the fluid phase. We validate and illustrate the ability to predict partitioning of REE in H₂O-bearing systems using major element analysis of garnet and fluid only. Consequently, our statistical model paves the way to integrate thermodynamic models based on major element chemical equilibria with trace element studies on hydrous magmatic systems, allowing a description of the transfer of key trace elements in more realistic conditions.