Studying diffusion of hydrogen in nominally anhydrous minerals (NAMs), like clinopyroxene, at low temperatures is a challenging task due to experimental and analytical difficulties. We applied a combination of hydrogen implantation to produce concentration gradients in natural diopside crystals with Nuclear Resonance Reaction Analysis (NRRA) measurements of nanoscale diffusion profiles. Thereby, we were able to conduct experiments at temperatures between 195 – 400 °C. Obtained diffusion rates show a consistent Arrhenius relation Ｄн = 5.47 (± 13.98) ·10⁻⁸ · exp (-115.64 (±11.5) kJ mol⁻¹/RT) m²s⁻¹. Notably, our results lie well within the range of extrapolations from high temperature experiments (≥ 600 °C) of previous studies. This implies that fast diffusion of hydrogen (compared to other elements) extends to low temperatures. We used these results in a non-isothermal diffusion model that simulates the ascent of crystals (0.5, 1.0, and 2.0 mm) along two representative geotherms (oceanic and continental) from 600 to 100 °C, to assess potential re-equilibration of H contents in clinopyroxene at low temperatures. Our model highlights the need to carefully consider boundary conditions, which are a function of P-T-𝘧O₂, that control the concentration gradient at the crystal’s rim. The results from this model allow an assessment when re-equilibration in dependence of crystal size and cooling rate must be considered. Fast ascent (e.g., kimberlitic melt) preserves initial hydrogen contents even in 0.5 mm size clinopyroxene crystals. However, dwelling at low temperatures (e.g., 300 °C) for several thousands of years (e.g., serpentinization) leads to extensive re-equilibration in 2 mm crystals.

The tool of phase-field modeling for the prediction of chemical as well as microstructural evolution during crystallization from a melt in a mineralogical system has been developed in this work. We provide a compact theoretical background and introduce new aspects such as the treatment of anisotropic surface energies that are essential for modeling mineralogical systems. These are then applied to two simple model systems - the binary olivine-melt and plagioclase-melt systems - to illustrate the application of the developed tools. In one case crystallization is modeled at a constant temperature and undercooling while in the other the process of crystallization is tracked for a constant cooling rate. These two examples serve to illustrate the capabilities of the modeling tool. The results are analyzed in terms of crystal size distributions (CSD) and with a view toward applications in diffusion chronometry; future possibilities are discussed. The modeling results demonstrate that growth at constant rates may be expected only for limited extents of crystallization, that breaks in slopes of CSD-plots should be common, and that the lifetime of a given crystal of a phase is different from the lifetime of a phase in a magmatic system. The last aspect imposes an inherent limit to timescales that may be accessed by diffusion chronometry. Most significantly, this tool provides a bridge between CSD analysis and diffusion chronometry - two common tools that are used to study timescales of magmatic processes.