Linking structure and process in dendritic growth using persistent homology with energy analysis

We present a material analysis method that links structure and process in dendritic growth using explainable machine learning approaches. We employed persistent homology (PH) to quantitatively characterize the morphology of dendritic microstructures. By using interpretable machine learning with energy analysis, we established a robust relationship between structural features and Gibbs free energy. Through a detailed analysis of how Gibbs free energy evolves with morphological changes in dendrites, we uncovered specific conditions that influence the branching of dendritic structures. Moreover, energy gradient analysis based on morphological feature provides a deeper understanding of the branching mechanisms and offers a pathway to optimize thin-film growth processes. Integrating topology and free energy enables the optimization of a range of materials from fundamental research to practical applications. We introduce a novel method that bridges structure and process in dendritic growth by integrating persistent homology with energy analysis. Our framework quantitatively maps dendritic morphology to Gibbs free energy variations, revealing energy gradients that drive branching behavior. This approach provides new insights into crystal growth and offers a powerful, data-driven pathway for optimizing thin-film fabrication.