Modeling the Gallium-Aluminum Wetting Transition via Topological Data Analysis of Interfacial Network Collapse

Historically, the mechanics of Liquid Metal Embrittlement (LME) have been bifurcated between thermodynamic wetting models and dislocation-mediated stress concentration mechanisms. While these frameworks successfully capture macroscopic wetting criteria and localized plastic deformation, they exhibit a fundamental limitation: they treat the grain boundary as a uniform, continuous continuum. Consequently, they struggle to resolve the principal paradox of LME; namely, how liquid metal species such as gallium can induce catastrophic, brittle-like degradation across a rigid polycrystalline interface within seconds under macroscopically zero external stress. Our computational framework demonstrates that resolving this paradox requires abandoning continuum approximations in favor of discrete network topology. By representing the grain boundary as a weighted simplicial complex K, we shift the analytical focus from continuum stress tensors to the multiscale evolution of atomic coordination geometry.