Unraveling Temperature-Induced Vacancy Clustering in Tungsten: From Direct Microscopy to Atomistic Insights via Data-Driven Bayesian Sampling

Abstract

The evolution of the microstructure of materials is primarily governed by defect-mediated diffusion. Here, we examine the intriguing role played by vacancies in tungsten, a strategic metal for high-temperature fusion-energy systems. We address the existing apparent contradictions between experimental observations indicating the presence of voids and theoretical predictions of vacancy self-repulsion by employing both experimental and theoretical methods. We have designed a transmission-electron-microscopy experiment and developed a theoretical data-driven approach using the Bayesian adaptive biasing force method to investigate the finite-temperature properties of mono- and di-vacancies and characterize their relative stability via their formation free energies. Our investigation reveals that di-vacancies are energetically unfavorable at low temperatures but stabilize entropically as the temperature increases. This result is entirely consistent with experimental observations of the clustering of quenched-in vacancies in tungsten during reannealing treatments at intermediate temperatures. This work provides critical insights into the temperature-dependent stability of defects, bridging the gap between theoretical predictions and experimental observations, with significant implications for the design and optimization of high-temperature materials for fusion.