In this work, we demonstrate the correspondence between first principle
calculations and experimental measurements of size effects on thermal transport
in SiGe alloys. Transient thermal grating (TTG) is used to measure the
effective thermal conductivity. The virtual crystal approximation under the
density functional theory (DFT) framework combined with impurity scattering is
used to determine the phonon properties for the exact alloy composition of the
measured samples. With these properties, classical size effects are calculated
for the experimental geometry of reflection mode TTG using the
recently-developed variational solution to the phonon Boltzmann transport
equation (BTE), which is verified against established Monte Carlo simulations.
We find agreement between theoretical predictions and experimental measurements
in the reduction of thermal conductivity (as much as ∼ 25\% of the bulk
value) across grating periods spanning one order of magnitude. This work
provides a framework for the tabletop study of size effects on thermal
transport