Retrokinetics of crystallization

During crystallization, crystals nucleate and grow within materials, often impinging and interacting in a stochastic manner. This complexity has long hindered accurate reconstructions of a material’s crystallization history. By considering a representative material region with a finite crystal population, we derive equations that accurately predict crystal size and free surface evolution throughout the crystallization process. These equations, paired with a numerical solver, enable reconstructing nucleation events and crystallinity progression using the crystal size distribution and growth rates. We demonstrate this method by pinpointing the nucleation and crystallinity timelines of simulated, manufactured, and ancient geological materials, entirely without real-time observation. Our model offers unprecedented insights into extreme crystallization environments that are difficult to mimic, such as volcanic magma chambers, and supports the design of advanced materials.