A general framework for decoding grain growth kinetics from grain size distributions

The mean-field theories for grain growth, such as Hillert's model, have long faced challenges in predicting experimental and simulated grain size distributions (GSDs). The root cause lies in the inadequate description of the underlying growth rate function. Here, I establish a general analytical framework that inverts this problem: it directly extracts the grain growth rate function from an experimentally observed or simulated GSD. I demonstrate the framework's utility by re-analyzing simulation and experimental data, thereby identifying the dominant coarsening mechanism without direct kinetic measurements. The close agreement between the extracted and measured kinetics validates the framework's effectiveness in revealing the true growth kinetics. This work represents a paradigm shift from assuming growth laws to directly decoding them from microstructures, which can be used to analyze the reasonableness of some theories on grain growth kinetics.