Phonons in a medium with correlated substitutional disorder: A one-dimensional study

1D lattice dynamics are considered for a pseudo-binary atomic chain in order to investigate the effects of thermodynamical clustering due to non-ideality of the solid solution A_xB_1-xC on the phonon density of states (DOS). Using an exact dimensional distribution function for impurity clusters, phonon spectra are calculated numerically for 1D models of (Cd,Hg)Te and (Al,Ga)As of different compositions and temperatures of alloy preparation. The phonon DOS is also obtained analytically near the limits of the frequency range, and in the vicinity of the local mode. It is shown that clustering strongly suppresses the local mode. Moreover, for the decaying alloy where impurity clusters can be quite long, the DOS looks like a superposition of the phonon DOSs of pure materials, and positions of the maxima of the alloy DOS with respect to those in pure materials are sensitive to the degree of clustering.