In order to address the growth of crystals in veins, a multiphase-field model is used to capture the dynamics of crystals precipitating from a super-saturated solution. To gain a detailed understanding of the polycrystal growth phenomena in veins, we investigate the influence of various boundary conditions on crystal growth. In particular, we analyze the formation of vein microstructures resulting from the free growth of crystals as well as crack-sealing processes. We define the crystal symmetry by considering the anisotropy in surface energy to simulate crystals with flat facets and sharp corners. The resulting growth competition of crystals with different orientations is studied to deduce a consistent orientation selection rule in the free-growth regime. Using cracksealing simulations, we correlate the grain boundary tracking behavior depending on the relative rate of crack opening, opening trajectory, initial grain size and wall roughness. Further, we illustrate how these parameters induce the microstructural transition between blocky (crystals growing anisotropically) to fibrous morphology (isotropic) and formation of grain boundaries. The phase-field simulations of crystals in the free-growth regime (in 2D and 3D) indicate that the growth or consumption of a crystal is dependent on the orientation difference with neighboring crystals. The crack-sealing simulation results (in 2D and 3D) reveal that crystals grow isotropically and grain boundaries track the opening trajectory if the wall roughness is high, opening increments are small and crystals touch the wall before the next crack increment starts. Further, we find that within the complete crackseal regime, anisotropy in surface energy results in the formation of curved/oscillating grain boundaries (instead of straight) when the crack opening velocity is increased and wall roughness is not sufficiently high. Additionally, the overall capability of phase-field method to simulate large-scale polycrystal growth in veins (in 3D) is demonstrated enumerating the main advantages of adopting the novel approach.

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Bitaxial crack sealing by epitaxial crystal growth is the most common vein‐forming process in Earth's crust, but the details of the microstructural processes in these are not well understood. Here we model the evolution of bitaxial crack‐seal quartz veins in two and three dimensions, using the phase‐field method. Our numerical simulations show the influence of different parameters, such as the obliquity of crack opening and crack location, grain size, and orientations on the evolving vein microstructure. We examine the underlying growth competition observed during epitaxial growth of quartz. Results show many similarities with natural microstructures such as stretched crystals and compare well with the previous numerical findings. As the ratio of crack aperture and matrix grain size for the present studies is chosen to be sufficiently large for growth competition to occur before complete sealing, it leads to the formation of crystal fragments along the crack‐opening trajectory. We explain how such fragment trails act as potential indicators of the opening of crack‐seal veins, if they are confirmed to be common in natural microstructures. Finally, we highlight the importance of accounting for the third dimension in the numerical simulations by analyzing the evolution of fluid connectivity in 2‐D and 3‐D during the sealing process.