  We apply a new Kubo-Greenwood type formula combined with a generalized
Feynman diagram- matic technique to report a first principles calculation of
the thermal transport properties of disordered Fe_{1-x}Cr_{x} alloys. The
diagrammatic approach simplifies the inclusion of disorder-induced scattering
effects on the two particle correlation functions and hence renormalizes the
heat current operator to calculate configuration averaged lattice thermal
conductivity and diffusivity. The thermal conductivity K(T) in the present case
shows an approximate quadratic T-dependence in the low temperature regime (T <
20 K), which subsequently rises smoothly to a T-independent saturated value at
high T . A numerical estimate of mobility edge from the thermal diffusivity
data yields the fraction of localized states. It is concluded that the complex
disorder scattering processes, in force-constant dominated disorder alloys such
as Fe-Cr, tend to localize the vibrational modes quite significantly.
