  Melting is well understood in terms of the Lindemann criterion, essentially
stating that crystalline materials melt when the thermal vibrations of their
atoms become such vigorous that they shake themselves free of the binding
forces. However, how about another common type of solids: glasses, where the
nature of the solid-liquid crossover is highly controversial? The Lindemann
criterion implies that the thermal expansion coefficients alpha of crystals are
inversely proportional to their melting temperatures. Here we find that,
unexpectedly, alpha of glasses decreases much stronger with increasing
glass-transition temperature Tg marking the liquid-solid crossover in this
material class. However, scaling alpha by the fragility m, a measure of
particle cooperativity, restores the proportionality, i.e., alpha/m ~ 1/Tg.
Obviously, for a glass to become liquid, it is not sufficient to simply
overcome the interparticle binding energies. Instead, more energy has to be
invested to break up the typical cooperative particle network which is
considered a hallmark feature of glassy materials. Surprisingly, alpha of the
liquid phase reveals similar anomalous behaviour and is universally enhanced by
a constant factor of ~3. The found universalities allow estimating
glass-transition temperatures from thermal expansion and vice versa.
