Among the theoretical criteria for melting, the Lindemann and Born criteria are those most frequently used as a basis to analyse the melting conditions.
The Lindemann criterion states that melting occurs because of "vibrational instability", e.g. crystals melt; when the average amplitude of thermal vibrations of atoms is relatively high compared with interatomic distances, e.g. > > δR, where δu is the atomic displacement, the Lindemann parameter δ ≈ 0.20...0.25 and R is one-half of the inter-atomic distance. The "Lindemann melting criterion" is supported by experimental data both for crystalline materials and for glass-liquid transitions in amorphous materials.
The Born criterion is based on a rigidity catastrophe caused by the vanishing elastic shear modulus, i.e. when the crystal no longer has sufficient rigidity to mechanically withstand the load, it becomes liquid.