Long range order, short range order and energy gaps

The theory of multiple scattering by clusters of atoms is employed to analyse the electronic density of states in crystalline and amorphous materials. A study is made of different sizes of clusters, geometries, types of atoms and boundary conditions including the case when the use of periodic boundary conditions simplifies the problem by imposing 'translational symmetry' as in a superlattice of similar clusters. The results suggest that some combinations of scattering potentials in systems with appropriate short range order can be a sufficient condition for the existence of an energy gap in the electronic density of states above the muffin tin zero.