Interpretation of X-ray Diffraction from Liquid Alkali Metals

Abstract

It is known that, near freezing, the peaks in the liquid structure factors of Na and K reflect the ordering of a body-centred cubic lattice. Therefore, we have considered the modifications introduced into the electron distribution of a body-centred cubic, nearly-free electron, metal by destruction of the long-range order. Use of the Wannier representation, as has been pointed out by Matthai et al., leads naturally in a metal to bond charges at the centres of near-neighbour, next-near neighbour, etc., bonds. Because of the absence of long-range order in the nuclei of liquid Na and K, it is argued that only near-neighbour and perhaps next-near neighbour bond charges remain meaningful. Thus, whereas in crystalline Na and K, the totality of the bond charge distributions, including however many longer and longer bonds, adds up to an almost constant electron density of the valence electrons, in the liquid the local angularity of the electron density is significant. We find then that a model which can explain the observed reflections, which are characteristic of a face-centred-cubic lattice, can be built up by:

a) Using local sp³ type bonding charges, with Pauling resonance invoked between occupied and unoccupied bonds and

b) Assuming, once local electron coordination characteristic of such bonds is formed, Wigner-type lattice ordering can propagate the face-centred lattice over distances of 30 to 40 Å.

The differences to be expected between nearly-free electron metals and tight-binding metals in the liquid state are finally stressed.