The phonon frequency line widths related to the phonon relaxation times is evaluated for impurity, anharmonic and interference scattering processes using double time temperature dependent Green's function method. The effects of force constant changes at impurity site and interference mode (new vibrational mode) on lattice thermal conductivity are the new features of the work. A few comments are made on the additivity of inverse relaxation times. The theory have been utilized to analyse the lattice thermal conductivity of ten synthetic aluminum garnets containing trivalent rare earth ions using Callaway's formula. The calculations show excellent agreements between theory and experiments.