Reversible and irreversible β -relaxations in metallic glasses

The localized \ensuremath{\beta}-relaxation process is critical for understanding the complex dynamics and controlling the properties of glasses. However, the \ensuremath{\beta}-relaxation in most metallic glasses only appears in a form of excess wing or shoulder in dynamic mechanical spectra while the underlying mechanism of the \ensuremath{\beta}-relaxation remains elusive. In the present work, the \ensuremath{\beta}-relaxation of metallic glasses is systematically studied by calorimetry where the glass-transition temperature (${T}_{\mathrm{g}}$) is resolved. The key finding is that the long-time sub-${T}_{\mathrm{g}}$ annealing induces an endothermic peak upon heating prior to ${T}_{\mathrm{g}}$ with an activation energy of $\ensuremath{\sim}26R{T}_{\mathrm{g}}$. By using an annealing-scanning-annealing thermal protocol, we show that this distinct endothermic sub-${T}_{\mathrm{g}}$ peak is a reversible \ensuremath{\beta}-relaxation, indicating that the \ensuremath{\beta}-relaxation has both reversible and irreversible parts, which can be refined by the combination of calorimetry and the designed thermal protocol. The results might deepen our understanding of relaxation and the aging of metallic glasses.