Dendritic Growth Patterns in Rocks: Inverting the Driving and Triggering Mechanisms

Mineral precipitation can form complex patterns under non-equilibrium conditions, in which two representative patterns are rhythmic Liesegang stripes and fractal dendrites. Interestingly, both patterns occur in the same rock formations, including various dendritic morphologies found in different rocks, such as limestone and sandstone. However, the underlying mechanism for selecting the vastly different mineral precipitation patterns remains unclear. We use a phase-field model to reveal the mechanisms driving pattern selection in mineral precipitation. Simulations allow us to explore the effects of diffusion parameters on determining the dendritic morphologies. We also propose a general criterion to distinguish the resulting dendrites in simulations and field observations based on a qualitative visual distinction into three categories and a quantitative fractal dimension (FD) phase diagram. Using this model, we reproduce the classified dendrites in the field and invert for the key parameters that reflect the intrinsic material properties and geological environments. This study provides a quantitative tool for identifying the morphology selection mechanism with potential applications to geological field studies, exploration for resource evaluation, and other potential industrial applications. Dendrites are branched, tree-like structures that are found in various natural and biological systems. In the context of mineral precipitation or crystal growth, dendrites refer to the branching patterns formed by the deposition of minerals or crystals in a non-equilibrium environment. Other patterns frequently found in these reactive systems are concentric ring-like or striped patterns called Liesegang patterns. Although these patterns occur in the same rock formations, the mechanism for selecting different mineral precipitation patterns is not well understood. Here we use a phase-field model to explore how different diffusion parameters affect the selection of dendritic morphologies. We propose a criterion to distinguish different dendrites in simulations and field observations based on a qualitative visual distinction (needle-like, tree-like and seaweed-like) and a quantitative fractal dimension phase diagram. The model can be deployed to invert for the intrinsic rock properties as well as the geological environments these dendrites grow in. The numerical scheme is robust and efficient, allowing easy implementation of add-on features in the future for potential applications across scientific and engineering disciplines. Fractal dendritic morphology diagram reproduces natural dendrite patternsCompared to Liesegang patterns, dendrites require higher fluid diffusivity and tend to grow along interfacesInversion of phase-field diffusivity and self-diffusion coefficient of solute is possible from photographic images of dendritic patterns