A criterion for the glass–liquid transition

•At the softening temperature there is a sharp delocalization of atoms.•Glass softening is due to the emergence of vibrational instability of atoms.•Glass softening is related with the melting of short-range order of the structure.•Process of glass softening has a criterion similar to Lindemann melting rule.

Criterion for softening of glassy solids, analogous to the Lindemann criterion of melting, is proposed. At glass softening the temperature ratio of root mean square atom displacement to mean interatomic distance is practically of constant value for different glasses. It is assumed that, when the root mean square amplitude of the thermal vibrations of an atom reaches a certain fraction of an interatomic distance, the excited atom loses its stability and the glass–liquid transition begins. The softening process in glasses as in crystals is due to the emergence of vibrational instability of atoms located in the lattice sites.