A Multi-Component Entropy Method for Modeling Phase Transitions in a Heterogeneous Mantle

Accurately incorporating realistic phase transitions in geodynamic models is crucial but challenging. Phase transitions strongly influence mantle convection, as their effects on buoyancy can hinder or accelerate slabs and plumes. In a heterogeneous mantle, different mineral assemblages undergo phase transitions at different depths, leading to lateral buoyancy variations that can cause specific compositions to stagnate or accumulate within characteristic depth ranges. However, complex phase relations, abrupt changes in material properties, and the release or absorption of latent heat pose significant challenges for modeling phase transitions. Dannberg et al. (2022) addressed these challenges by solving the energy equation in terms of entropy rather than temperature, allowing it to capture realistic phase changes in geodynamic models. However, this method was limited to chemically homogeneous systems.

Building on our earlier work, we now present a new multi-component formulation that extends the entropy method to systems with compositional heterogeneities. Our formulation assumes thermal equilibrium below the scales resolved by our mesh, i.e., all components share a single temperature at each point represented in the model. Pressure changes during advection produce an isentropic temperature change. As different chemical components may have different isentropic temperature gradients, which would imply different temperatures for each component at the same location, our multicomponent formulation involves a thermal equilibration step. Using a series of benchmarks and test cases, we show that our implementation in the geodynamic modeling software ASPECT satisfies the conservation of total energy and captures phase transitions self-consistently, regardless of their sharpness, during advection of chemical heterogeneities.

We show the applicability of our new formulation in a series of global convection models. We compare: (1) a single-component pyrolite model, and (2) a two-component mechanical mixture of basalt and harzburgite with the same pyrolitic bulk composition. Our results reveal that small differences in the ringwoodite to bridgmanite + ferropericlase transition between these assemblages with the same composition can significantly affect slab and plume stagnation. Our results highlight the importance of accurately capturing the full effects of phase transitions in a chemically heterogeneous mantle, and our approach enables new investigations into how planetary mantles evolve.

 

References: Dannberg, J., Gassmöller, R., Li, R., Lithgow-Bertelloni, C., & Stixrude, L. (2022). An entropy method for geodynamic modelling of phase transitions: capturing sharp and broad transitions in a multiphase assemblage. Geophysical Journal International, 231(3), 1833-1849.