Non-Equilibrium Thermodynamic Modeling of Mantle Melting and Phase Transformation

One of the most powerful approaches that scientists have for understanding chemical systems, both natural and synthetic, is equilibrium thermodynamics. This approach allows us to predict, in detail, the state that systems will settle into if given enough time to react completely. Implementing such tools in geodynamic models thus provides a self-consistent framework by which the thermochemical evolution of the mantle and its constituent processes can be modeled. However, equilibrium thermodynamics has a number of major limitations. Firstly, free energy minimization is an expensive calculation. The typical workaround is to generate petrological tables in bulk composition space, but this is a problematic constraint when chemical fractionation processes occur (e.g., melting). Secondly, because kinetics and microstructural state are ignored, the rates of change between equilibrium states cannot be accounted for. It is already generally appreciated that metastable states can be important in some geodynamic systems, such as olivine-group phase transformations in subducting slabs. However, kinetics may also be critical in other settings as well, such as transformations in oceanic and continental lithospheric mantle, and in the course of decompression melting. Moreover, although the kinetics of change has long been studied in experimental settings, computational tools for the study of non-equilibrium phenomena are generally simplified. We will describe our efforts to develop a new numerical framework for modeling non-equilibrium thermodynamic phenomena at the grain scale. Such processes include grain coarsening, phase transformation, major and trace element diffusion, reactions, and melting of minerals and rocks. We use phase field and statistical thermodynamics methods to jointly model the underlying interfacial and diffusional phenomena in a multi-phase multi-component thermodynamic system. We will describe the fundamental characteristics of such models and provide examples for relevant mantle systems.