Electronic Structure of Alloys

A theory of the electronic structure of alloys is presented which takes proper account of the symmetries present or absent in the alloy and does not rely on using Bloch's theorem either for the alloy or for the host metal. The band structure is worked out in an approximation which is exact for an ordered alloy and which gives a simple picture for a disordered substitutional alloy. Using this theory the band structure for the $d$ electrons of the transition metal alloys is qualitatively discussed. The rigid band model is shown to fail for alloy constituents having a large valency difference and it is shown that the theory of this paper agrees with the experimental results both for magnetic moments and specific heats in such cases. A simple physical interpretation of these results is given using arguments similar to those of the conventional tight binding approximation. It is suggested that the difference between NiAl and FeAl alloys might be due to the aluminum conduction band lying above the nickel $d$ band so that the latter fills, whereas the iron $d$ band does not lie below the aluminum conduction band. No reference is made to theories of ferromagnetism, though it is possible that the methods used in this paper could be used to obtain a great deal more information from alloys of the transition metals than is available at the moment.