Electron theory of melting in close-packed metals

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.