A material model for the evolution of size and composition of olivine grains in a magma mush zone as a consequence of mechano-chemical effects of diffusion

Diffusion chronometry is used to understand various geological processes that occur in Magma reservoirs [1] and during solid state transformations. However, recrystallization restricts the timescales which can be accessed by diffusion chronometry. Recrystallization as a consequence of chemical dissolution-precipitation reactions or mechanical deformation are well known aspects of rock evolution. However, recrystallization due to a coupling of chemical and mechanical forces has not been studied yet in detail, although it is known from both natural settings [2] as well as experiments [3]. We have developed a thermodynamic multiphysics model to address this problem. We define an overall free energy function of a system that contains the standard chemical terms (enthalpy, entropy, volume) as well as the effects of mechanical stress (elastic as well as plastic). This function is minimized to study the evolution of a system, in particular with reference to evolution of the radius of a grain. It is found that the balance of chemical and mechanical forces may lead to continual growth of a mineral grain, or lead to the disappearance of a grain by shrinking (and growth of a new grain), depending on the values of different parameters. The behavior of the system is shown to be governed by four non-dimensional parameters, and the behavior of any given system may be predicted when a set of relevant material parameters are known.

In this presentation we build on the model introduced by Haddenhorst et al. [4] to describe the evolution of olivine crystals surrounded by a melt. We can use the model to calculate the lifespan of an olivine grain, the maximum size of a crystal and the time taken to reach that size as a function of pressure, temperature and a set of material parameters. Illustrative examples for magma mush zones will be shown.

References:
[1]: Chakraborty, S., & Dohmen, R. (2022). Diffusion chronometry of volcanic rocks: looking backward and forward. Bulletin of Volcanology, 84 (6), 57. Retrieved from https://doi.org/10.1007/s00445-022-01565-5
[2]: Bestmann, M., Pennacchioni, G., Grasemann, B., Huet, B., Jones, M. W. M., & Kewish, C. M. (2021). Influence of deformation and fluids on ti exchange in natural quartz. Journal of Geophysical Research: Solid Earth, 126 (12), e2021JB022548. Retrieved from https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2021JB022548
[3]: Nachlas, W., & Hirth, G. (2015). Experimental constraints on the role of dynamic recrystallization on resetting the ti-in-quartz thermobarometer. Journal of Geophysical Research: Solid Earth, 120 (12), 8120–8137.
[4]: Haddenhorst, H. H., Chakraborty, S., & Hackl, K. (2023). A model for the evolution size and composition of olivine crystals. Proceedings in Applied Mathematics and Mechanics, 00, e202300081. https://doi.org/10.1002/pamm.202300081