Coupling of caged dynamics to the Johari-Goldstein β-relaxation and α-relaxation in metallic glasses

Caged dynamics is the process that precedes the Johari-Goldstein (JG) β-relaxation and the structural α-relaxation. It is exclusively observed in the glassy state in experiments carried out at sufficiently high frequency or short time such that even the JGβ relaxation is too slow to be observed. Remarkably and generally observed in many molecular and polymeric glass-formers, the caged dynamics changes its temperature dependence on crossing two temperatures. The lower one had been identified with the JGβ glass transition temperature T_gβ determined by either adiabatic calorimetry and positronium annihilation lifetime spectroscopy or by the relaxation time τ_β(T) reaching 10² or 10³ s. The higher one is the nominal glass transition temperature T_gα. This ubiquitous property of caged dynamics originates from its coupling to the JGβ relaxation and the α-relaxation as predicted by the Coupling Model. This fundamentally important property has never been found completely in metallic glasses by conventional mechanical modulus measurements because the probe frequencies are too low. There are two exceptions where the mechanical modulus of metallic glasses was measured at much higher frequencies, and the data should reveal the changes of the caged dynamics at T_gβ and T_gα, as found before in molecular and polymeric glasses. However, the property was not revealed from the experimental data in these two works and subsequently by others. This is due to the concept of caged dynamics and its coupling to JGβ and α relaxations are uncommon in metallic glasses research. In this paper, we revisit these two critical experimental data to identify the caged dynamics and show the changes of its temperature dependence on crossing T_gβ and T_gα. Thus, like molecular and polymeric glasses, caged dynamics in metallic glasses is also coupled to the JGβ and the α relaxations.