Theory of Melting, Dislocation Model. I

A theory of melting is developed based on the dislocation model, in which liquid is regarded as a crystal saturated with dislocations. It is shown that introduction of dislocations is accompanied with lattice dilatation due to lattice anharmonicity. The dilatation makes the dislocation energy per unit length a decreasing function of the dislocation density, which is a necessary condition for first order transition. The vibration frequencies of segments of dislocation networks are estimated from excess specific heat of amorphous solid, and the contribution of the dislocation vibration to fusion entropy is shown to be important. Some empirical relationships are found to be compatible with the dislocation model.