Electron theory of melting in close-packed metals

Abstract

A derivation of the Lindemann melting-point formula is given, for close-packed metals, by combining first-order electron theory with the Bragg-Williams theory of an order-disorder transition. The Lindemann constant cannot be predicted precisely from the theory, but it is shown that it can be estimated to better than order-of-magnitude accuracy. It is also shown that, in this linear theory, the long wavelength limit of the structure factor S(K) just above the melting point should be approximately constant. The value should be less than or of the order of 1/30. This is in fair accord with the available data. Finally, the concept of an `ideal' liquid metal is introduced, and a precise formulation of the Hamiltonian is given for this case.