A transferable framework for structure-energy mapping of nanovoid-solute complexes: Tungsten alloys as a model system

Understanding the structures and energetics of nanovoid-solute complexes is essential for elucidating the coupled evolution of defects in metals. Yet their vast and complex configurational space poses a major challenge to conventional approaches. Using W-Re as a representative system, we demonstrate that solute segregation at nanovoid surfaces can be decomposed into direct nanovoid-solute interactions and nanovoid-mediated solute-solute interactions. Both are governed by local coordination motifs, with identical motifs giving nearly identical energetics. Based on first-principles data, we trained machine-learning models to map diverse local motifs to their energetics, enabling the energetics of any nanovoid-solute complex to be reconstructed from a finite set of constituent local motifs. We further developed a size-dependent configurational-search framework to efficiently identify thermodynamically stable structures, using exhaustive enumeration, simulated annealing, and greedy addition for small, medium-sized, and large complexes, respectively. This framework enabled the construction of a large database, revealed the staircase-like segregation behavior of Re, and derived a simple criterion based on Re surface coverage for rapid energy prediction across a wide size range. It also links Re segregation to vacancy-mediated nanovoid evolution and provides benchmarks for existing models and empirical potentials. Extensions to Os and Ta support the generality of the local-motif concept, and the predicted segregation behavior of solutes at nanovoids agrees with a range of experimental observations. This work establishes a physically transparent, accurate, and transferable framework for studying nanovoid-solute co-evolution in metals and provides reliable energetic inputs for multiscale simulations.