Modeling differentiation in igneous systems: On the importance of considering temperature & composition dependent partition coefficients

Studying processes involved in magma accumulation and transfer is one of the keys to understand the architecture and evolution of volcanic plumbing systems. One of the main processes, magma differentiation, governs the thermal evolution and chemical composition of the melt-crystal assemblage (magma or mush depending on the relative proportions), and therefore exerts a first order control over its physical properties (density, viscosity), and thus on eruption dynamics. Various approaches have been implemented to model differentiation in an attempt to benchmark all the involved variables like initial and mineral composition, temperature, pressure, and oxygen fugacity (C₀, X, T, P, f_O2). Those are among others mass balance calculations considering partition coefficients (D) values, experimental studies, thermodynamic models or a combination of those. In any of those cases, the evolution of trace elements is governed by the value of the D that is known to be dependent on (P, T, X, f_O2). However, most of the present day studies still use fixed values of D to provide first order estimates.

Here, we present an approach combining thermodynamic modeling (relying on Rhyolite-MELTS), that integrates X-T-P-f_O2-dependent D for Rare Earth Elements (REE). We applied this new approach to a MORB system, with olivine, clinopyroxene and plagioclase as main mineral phases, and compared results to more classical approaches. D are derived from the models of Sun & Liang (2012, 2013, 2014) and Sun et al. (2017). The resulting model highlights that T & X effects on the D values can add or counterbalance each other depending on the mineral considered. In any cases our results highlight the gain of using thermodynamic models along with both T- & X-dependent D values to properly model the evolution of igneous systems. Relying on our results we were also able to provide D for any mineral composition crystallized from this MORB system. Results presented on the figure bellow brings to light the error we may introduce when considering a fixed value of D (example of D_La in plagioclase, reference value taken from Bédard, 2001).