Atomistic simulations reveal that secondary relaxations in metallic glasses originate from string-like atomic motions.

Melting is well understood in terms of the Lindemann criterion, which essentially states that crystalline materials melt when the thermal vibrations of their atoms become so vigorous that they shake themselves free of the binding forces. This picture does not necessarily have to hold for glasses, where the nature of the solid–liquid cross-over is highly debated. The Lindemann criterion implies that the thermal expansion coefficients of crystals are inversely proportional to their melting temperatures. Here we find that, in contrast, the thermal expansion coefficient of glasses decreases more strongly with increasing glass temperature, which marks the liquid–solid cross-over in this material class. However, this proportionality returns when the thermal expansion coefficient is scaled by the fragility, a measure of particle cooperativity. Therefore, for a glass to become liquid, it is not sufficient to simply overcome the interparticle binding energies. Instead, more energy must be invested to break up the typical cooperative particle network that is common to glassy materials. The thermal expansion coefficient of the liquid phase reveals similar anomalous behaviour and is universally enhanced by a constant factor of approximately 3. These universalities allow the estimation of glass temperatures from thermal expansion and vice versa.

Secondary (also known as Johari-Goldstein or β-) relaxations are an intrinsic feature of supercooled liquids and glasses. They are important in many respects but the underlying mechanisms are not well understood. A long-standing puzzle is why some glasses show β-relaxations as pronounced peaks, whereas others as unobvious excess wings. Here we demonstrate that these different behaviours are related to the fluctuations of chemical interactions by using prototypical systems of metallic glasses. A general rule is summarized: pronounced β-relaxations are associated with systems where all the atomic pairs have large similar negative values of enthalpy of mixing, whereas positive or significant fluctuations in enthalpy of mixing suppress β-relaxations. The emerging physical picture is that strong and comparable interactions among all the constituting atoms maintain string-like atomic configurations for the excitations of β-events and can be considered as the formation of molecule-like metallic glasses.

In a model metallic glass, we study the relaxation dynamics in both the linear and the nonlinear response regimes by numerical simulations of dynamical mechanical spectroscopy and analyze the atomic displacement statistics. We find that the primary ($\alpha$) relaxation always takes place when the most probable atomic displacement reaches a critical fraction ($\sim 20\%$) of the average interatomic distance, irrespective of whether the relaxation is induced by temperature (linear response) or by mechanical strain (nonlinear response). Such a unified scenario, analogous to the well-known Lindemann criterion for crystal melting, provides insight into the structural origin of the strain-induced glass-liquid transition.