Fig. 1. The effect of random and correlated disorder on electronic and phonon bands.

a Ordered A₂B structure with A halfway between B atoms on a square lattice. b A random configuration of A site distortions. c Two-in-two-out rule for correlated distortions. d Correlated disorder with perpendicular strong bonds. e–h The corresponding diffuse scattering patterns. The square lattice of black dots are Bragg peaks, which are several orders of magnitude stronger than diffuse scattering. i–l Electronic bands for these systems along special directions, with Γ = (0, 0), X = (${}^1/{}_2$, 0) and M = (${}^1/{}_2{,}^1/{}_2$). The energy scale is arbitrary and the zero point does not imply the Fermi level. m–p Phonon bands.