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We have used an atomistic {\it ab initio} approach with no adjustableparameters to compute the lattice thermal conductivity of Si$_{0.5}$Ge$_{0.5}$with a low concentration of embedded Si or Ge nanoparticles of diameters up to4.4 nm. Through exact Green's function calculation of the nanoparticlescattering rates, we find that embedding Ge nanoparticles in$\text{Si}_{0.5}\text{Ge}_{0.5}$ provides 20% lower thermal conductivities thanembedding Si nanoparticles. This contrasts with the Born approximation whichpredicts an equal amount of reduction for the two cases, irrespective of thesign of the mass difference. Despite these differences, we find that the Bornapproximation still performs remarkably well, and it permits investigation oflarger nanoparticle sizes, up to 60 nm in diameter, not feasible with the exactapproach.

The role of lighter and heavier embedded nanoparticles on the thermal conductivity of SiGe alloys