In part (a) of the abstract, the decimal points should be subscript. / An algebraic procedure for considering the general n-tuple problem for a random defect lattice is developed in this thesis. When specialized to pairs {n=2) the deviations from randomicity have also been considered. The low concentration defect theory (n=l) is used to calculate: a) the frequencies and widths of phonons in disordered Cu₀.₉₇ Au₀.₃₃ b) the frequency shift of singular points in the defect-induced (Na⁺ , Sm⁺⁺) far infrared spectrum of RBr as a function of defect concentration c) the one phouon side bands of H₂, D₂, and N₂ in solid Ar. In order to take into account the "long range" behaviour of random substitutional defects, an effective lattice theory is formulated. This theory proves essential to the discussion of the Cu/Au dispersion curves and the one phonon side band of the vibrational spectrum of a H₂, (D₂) molecule in solid Ar. / Thesis / Doctor of Philosophy (PhD)