Another version of a ``one-phase'' theory of bulk melting suggested by Born [9] in 1937. His theory is based on the fact
that a liquid differs from a crystal in having zero resistance to the shear stress. The distances between
the atoms are increased due to thermal expansion, hence the restoring forces between the atoms are reduced,
and therefore the shear elastic moduli decrease with rising temperature. The softening of the shear moduli
leads to a mechanical instability
of the solid structure and finally to a collapse of the crystal lattice at some temperature.
The general conditions for stability of a crystal lattice were derived by Born. He
analyzed the free energy of a solid with a cubic crystalline lattice. For a lattice to be stable, the free
energy must be represented by a positive defined quadratic form, and this is fulfilled if the following
inequalities for the shear elastic coefficients
are satisfied:

(2.4) |

(2.5) |

(2.6) |

(2.7) |

(2.8) |

(2.9) |

The applicability of the Born criterion at zero and non-zero external stress could be directly tested in computer simulations. Bulk melting (the surface of the solid is eliminated by means of periodic boundary conditions) of copper under condition of zero external stress was studied in molecular dynamics (MD) simulations [15]. It was found that the shear modulus vanishes at some temperature , but this temperature is large than thermodynamic melting temperature , i.e , measured experimentally. Thus the elastic coefficients remain finite at . The conclusion was drawn that mechanical bulk melting, proposed by Born, is valid only for a perfect infinite crystal, but a real crystal with boundaries and defects undergoes thermodynamic melting at , before it reaches the mechanical melting point.

The Born criterion was modified by Tallon to reach better agreement with experiment [16]. Tallon measured the shear moduli of various substances (metallic, organic, molecular and ionic crystals) as a function of molar volume. He confirmed that the shear moduli do not vanish at the melting point, though the volume of the melt at the melting point can be predicted by a continuous extrapolation one of shear modulus to the zero value at zero external stress. (See Fig. 1.5)

Tallon suggested that the shear modulus decreases with an increase of the volume of the solid and one of the shear moduli vanishes as a critical volume is reached. At that point each atom can access the entire substance volume due to the enhanced diffusion. The entropy of the system increases and the Gibbs free energy is lowered. At the system transforms discontinuously from the solid to the liquid state. In another words, the Born scenario would work if the crystal could be superheated until it will reach the molar volume of the liquid! Unfortunately another mechanism of melting is triggered at the surface of the real solid at temperature which lower than the melting temperature predicted by the Born model, preventing from us to observe mechanical collapse of the crystal lattice.