  We report the development and application of a new method for carrying out
computational investigations of the effects of mass and force-constant (FC)
disorder on phonon spectra. The method is based on the recently developed
typical medium dynamical cluster approach (TMDCA), which is a Green's function
approach. Excellent quantitative agreement with previous exact diagonalization
results establishes the veracity of the method. Application of the method to a
model system of binary mass and FC-disordered system leads to several findings.
A narrow resonance, significantly below the van Hove singularity, that has been
termed as the boson peak, is seen to emerge for low soft particle
concentrations. We show, using the typical phonon spectrum, that the states
constituting the boson peak cross over from being completely localized to being
extended as a function of increasing soft particle concentration. In general,
an interplay of mass and FC disorder is found to be cooperative in nature,
enhancing phonon localization over all frequencies. However, for certain range
of frequencies, and depending on material parameters, FC disorder can
delocalize the states that were localized by mass disorder, and vice-versa.
Modeling vacancies as weakly bonded sites with vanishing mass, we find that
vacancies, even at very low concentrations, are extremely effective in
localizing phonons. Thus, inducing vacancies is proposed as a promising route
for efficient thermoelectrics. Finally, we use model parameters corresponding
to the alloy system, Ni1-xPtx, and show that mass disorder alone is
insufficient to explain the pseudogap in the phonon spectrum; the concomitant
presence of FC disorder is necessary.
