Rigid-band model
model used by condensed matter physicists to describe the behavior of metal alloys
The Rigid-Band Model (or RBM) is one of the models used to describe the behavior of metal alloys. In some cases the model is even used for non-metal alloys such as Si alloys. According to the RBM the shape of the constant energy surfaces (hence the Fermi surface as well) and curve of density of states of the alloy are the same as those of the solvent metal under the following conditions:
The excess charge of the solute atoms localizes around them.
The mean free path of the electrons is much greater than the lattice spacing of the alloy.
The electron states of interest in the pure solvent are all in one energy band, which is greatly separated in energy from the other bands.
The only effect of the addition of the solute, given that its valence is greater than that of the solvent, is the addition of electrons to the valence band. This results to swelling the Fermi surface and filling the density of states curve to a higher energy.
Theory
In a pure metal, because of the periodicity of the lattice, the features of its electronic structure are well known. The single-particle states can be described in terms of Bloch states, the energy structure is characterized by Brillouin zone boundaries, energy gaps and energy bands. In reality though no metal is perfectly pure.
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