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 this 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.

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.