Deformation-induced phase transitions: testing host-inclusion systems through 2D chemico-mechanical numerical models

Developing coupled models of deformation and metamorphism is a key challenge in geodynamics, as these two processes are known to be closely intertwined. Here, we aim to contribute to this challenge by describing fundamental characteristics of deformation-induced phase transition models, such as the evolution of the pressure field and the time scale of the phase transition. We present an isothermal, compressible, Newtonian viscous numerical model for inclusion-host systems submitted to pure shear boundary conditions and use the quartz-coesite (SiO₂) phase transition as an example. We derive the pressure-density relation via PerpleX (Connolly, 2005) using the (Holland and Powell, 1998) database. The simple geometry, involving an inclusion weaker than the matrix, enables direct comparisons of our results to the analytical solution of the incompressible case, as well as with numerical solutions for incompressible and compressible (but without phase transition) cases. We then tested the effects of key parameters (viscosity, applied background strain rate, and density difference between reactant and product) on the evolution of the model.

The applied background strain rate induces dynamic pressure variations around the weak inclusion, triggering the phase transition initiation in the matrix at zones of overpressure. The developing pressure field follows the prediction of the incompressible analytical solution, with a systematic shift (i.e. a pressure deficit where the phase transition occurs) controlled by physical properties (strain rate, viscosity). Pressure increases in small increments while the phase transition is taking place and increases rapidly to its steady state value once the transition is completed. Density is updated based on pressure via linear interpolation between the end-member quartz and coesite densities. The combination of this density update and elastic compressibility introduces an “internal” phase transition timescale in the model (where no kinetic law is prescribed): the faster the pressure increases, the less time the phase transition takes. This timescale strongly depends on the physical properties of the model, which is crucial to consider when dealing with compressible geodynamic models as well as when comparing results to natural cases. Results may also be used to interpret laboratory experiments and field observations and lay the basis for further comparisons of model timescales and real-world transformation kinetics.

Acknowledgements

B.K. was supported by the EKÖP-25 University Research Scholarship Program of the Ministry for Culture and Innovation from the source of the National Research, Development and Innovation Fund.

K.P. was supported by the National Research, Development and Innovation Fund, Hungary (PD143377) and the János Bolyai Research Scholarship of the Hungarian Academy of Sciences.

Connolly, J. A. D., 2005, Computation of phase equilibria by linear programming: A tool for geodynamic modeling and its application to subduction zone decarbonation: Earth and Planetary Science Letters, 236, 1-2, 524-541, DOI: 10.1016/j.epsl.2005.04.033.

Holland, T. J. B., and Powell, R., 1998, An internally consistent thermodynamic data set for phases of petrological interest: Journal of Metamorphic Geology, 16, 3, 309-343, DOI: 10.1111/j.1525-1314.1998.00140.x.