states are no longer eigenstates and their energy becomes complex The imaginary part Γk shows that the Bloch state in the alloy is no longer an eigenstate but scatters into other states with a lifetime of the order of (2Γk)−1. However, if , where Δ is the width of the band, then the Bloch states are approximately eigenstates and they can be used to calculate the properties of the alloys. In this case we can ignore Γk . The change in the energy of a Bloch state with alloying is then When the perturbation is fairly localized about the solute site (which is one of the conditions of the RBM), ΔEk depends only on ek and not on k and thus . Therefore, the plot of versus k for the alloy will have the same shape of constant energy surfaces as for the plot of versus k for the pure solvent. A given energy surface of the alloy will naturally correspond to a different energy value from that of the same shaped surface of the pure solvent, but the shapes will remain exactly the same. Density of states According to the Rigid Band Model is constant (for a given energy level) and the density of states of the alloy has the shame shape as that of the pure solvent, displaced by . When the concentration of the solute a is small, is also small and the density of states of the alloy at constant a is where is the density of states of the pure solvent. In the case when is constant we get meaning that the shape of the density of states will be the same, only displaced by . References Electronic band structures