  We present here a formulation for the calculation of the configuration
averaged lattice thermal conductivity in random alloys. Our formulation is
based on the augmented-space theorem, introduced by one of us, combined with a
generalized diagrammatic technique. The diagrammatic approach simplifies the
problem of including effects of disorder corrections to a great extent. The
approach allows us to obtain an expression for the effective heat current in
case of disordered alloys, which in turn is used in a Kubo-Greenwood type
formula for the thermal conductivity. We show that disorder scattering
renormalizes the phonon propagators as well as the heat currents. The
corrections to the current terms have been shown to be related to the
self-energy of the propagators. We also study the effect of vertex corrections
in a simplified ladder diagram approximation. A mode dependent diffusivity
$D_{\gamma}$ and then a total thermal diffusivity averaged over different modes
are defined. Schemes for implementing the said formalism are discussed. A few
initial numerical results on the frequency and temperature dependence of
lattice thermal conductivity are presented for NiPd alloy and are also compared
with experiment. We also display numerical results on the frequency dependence
of thermal diffusivity averaged over modes.
