Summary and conclusions

Amorphous and liquid metals provide experimental evidence [4] that stable ion configurations require strong influence of the electrons at the Fermi level. In the present paper strong electronic influence is ascribed to highly constructive electronic interference which is analyzed in the single-scattering approximations. Two aspects of electronic interference are seen in this paper. First, a condition is searched which ensures that all scattered waves add up to a strong field without restricting the phase of this resulting scattered field. We obtain the relation $k_F=\frac{6}{5} \pi N_0^{-1/3}$ between the Fermi wave number and the atom number density which provides the critical number $\overline{Z} \approx 1.81$ of nearly free electrons per atom in agreement with experiments [4] [7].

A second aspect, namely the importance of the phase difference between the scattered field and the primary field, becomes obvious if the consequences are investigated which arise from constructive electronic interference. In this respect and in view of the Nagel-Tauc concept we deal with the environment contribution to the local electronic density of states of an atomic sphere. This contribution is due to the interference of a wave which emerges from this atomic sphere with a wave which is scattered back from its environment. We ask which sequence of the reflecting neighbour shells provides the reflected wave at $E_F$ in opposite phase to the emerging wave. This must generate a minimum of the total density of electron states at $E_F$ and thus stability of the system.

We show that different partial components of the electronic density of states impose not necessarily the same trend on the shell sequence. The case of hcp zinc reveals clearly the competition of two different trends. We show that only the asymptotic shell sequence is necessarily uniformly spaced with the Friedel wave length. The shells close to the central atom, however, may deviate from the extrapolated asymptotic sequence due to the higher electronic angular momenta involved. We emphasize that the radial distribution of atoms in metallic materials reveals the importance of scattering paths cycles which involve only one scattering event. Generally, scattering-path statistics may be a key to the extraction of physically important trends in topologically disordered systems.

Acknowledgements

This work has been supported by the Deutsche Forschungsgemeinschaft (DFG-contract number So 288/1-1).