Revealing Atomistic Ion Migration Pathways of Orientation-Dependent Long-Range Cu⁺ Ion Migration in β-Cu₂Se

Understanding the long-range migration behavior of Cu⁺ ions is essential for stabilizing β-Cu₂Se-based thermoelectrics at intermediate temperatures. A pivotal remaining issue is that the correlation between long-range migration and short-range hopping of Cu⁺ ions has not yet been established. In this study, we conduct in situ Cs-TEM and first-principles calculations to investigate the long-range migration of Cu⁺ ions in β-Cu₂Se. The results show Cu⁺ ions preferentially migrate along the ⟨111⟩ directions with lower energy barriers and higher precipitation rates compared to the ⟨001⟩ directions. Such orientation-dependent long-range migration behavior is governed by the short-range hopping dynamics of Cu⁺ ions. Along ⟨111⟩, the octahedral sites bridge the hopping of Cu⁺ ions between tetrahedral sites, leading to a reduced energy barrier as low as 0.19 eV, which promotes the long-range migration of Cu⁺ ions along the ⟨111⟩ direction. These insights highlight the significance of understanding lattice dynamics in regulating ion migration behavior or stabilizing ionic materials.