“…For example, vacancy engineering is one of the core issues in the design and application of energy materials, such as oxygen vacancies in photocatalytic materials 7 and hydrogen storage materials, 8 vacancy creation in water electrolysis catalysts, 9 and cation vacancies in energy-related 2D nanosheets. 10 Since Frenkel 11 in 1926 and Wagner and Schottky 12 in 1930 independently proposed the mechanisms of vacancy formation, significant progress has been made in various areas related to vacancies. However, there are still many important scientific issues that urgently need to be re-examined, such as the most fundamental equilibrium concentration of vacancies and their equilibration pathway, 3,13–15 the exact interaction between vacancies and their sources and sinks, 16–19 and the ultra-high vacancy concentration in nanomaterials and its impact on other properties.…”