  In this paper we shall discuss the effect of disorder induced configuration
fluctuations on single particle and two-particle phonon Green functions in
substitutional random binary alloys. The randomness of the system will be dealt
within the augmented space theorem, introduced by one of us [J. Phys. C : Solid
State Phys. 6, L205(1973)]. This will be combined with a generalized
Edwards-Langer diagrammatic technique to extract various useful results in the
form of mathematical expressions. The purpose of present manuscript will be to
describe the scattering diagrams in full detail. This will form the basis of
the calculational algorithms which we had used in an earlier paper on NiPd and
NiPt alloys [J. Phys.: Condens. Matter 18, 4589-4608 (2006)]. We shall show the
structure of all possible scattering diagrams up to the 4-th order and
subsequently illustrate how to obtain Dyson's equation from a re-summation of
the diagrammatic series. We shall also study how disorder scattering affects
two-particle Green functions associated with thermal response. We shall show
that disorder scattering renormalizes both the phonon propagators as well as
the heat currents. These renormalized heat currents will be shown to be related
to the self-energy of the propagators. We shall also study a different class of
scattering diagrams which are not related to the self-energy but rather to the
vertex corrections.
