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.

The noncrystalline glassy state of matter plays a role in virtually all fields of materials science and offers complementary properties to those of the crystalline counterpart. The caveat of the glassy state is that it is out of equilibrium and therefore exhibits physical aging, i.e., material properties change over time. For half a century, the physical aging of glasses has been known to be described well by the material-time concept, although the existence of a material time has never been directly validated. We do this here by successfully predicting the aging of the molecular glass 4-vinyl-1,3-dioxolan-2-one from its linear relaxation behavior. This establishes the defining property of the material time. Via the fluctuation-dissipation theorem, our results imply that physical aging can be predicted from thermal-equilibrium fluctuation data, which is confirmed by computer simulations of a binary liquid mixture.

Glassy solids evolve towards lower-energy structural states by physical aging. This can be characterized by structural relaxation times, the assessment of which is essential for understanding the glass’ time-dependent property changes. Conducted over short times, a continuous increase of relaxation times with time is seen, suggesting a time-dependent dissipative transport mechanism. By focusing on micro-structural rearrangements at the atomic-scale, we demonstrate the emergence of sub-diffusive anomalous transport and therefore temporal fractional diffusion in a metallic glass, which we track via coherent x-ray scattering conducted over more than 300,000 s. At the longest probed decorrelation times, a transition from classical stretched exponential to a power-law behavior occurs, which in concert with atomistic simulations reveals collective and intermittent atomic motion. Our observations give a physical basis for classical stretched exponential relaxation behavior, uncover a new power-law governed collective transport regime for metallic glasses at long and practically relevant time-scales, and demonstrate a rich and highly non-monotonous aging response in a glassy solid, thereby challenging the common framework of homogeneous aging and atomic scale diffusion.

Observing frequency invariant aging dynamics suggests that the homogeneous process of rate exchange rather than heterogeneous relaxation governs structural recovery.