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Half-Heusler alloys have been the focus of recent experimental research as emerging thermoelectric materials. Particular attention has been focused on the MNiSn (M = Ti, Zr, and Hf) alloys with substitutions made to reduce the lattice thermal conductivity and enhance the electrical transport properties. The effect of these substitutions on the relaxation time of phonon scattering in the material, and the impact on the lattice thermal conductivity, was investigated with a focus on modeling the experimental data. A modified Callaway model was used to describe experimental data, which were then compared to theoretical results predicted using phonon scattering by mass fluctuation and strain field models. The correlation between the coefficients obtained with experimental fits and theoretical models shows a predictable and systematic relationship between alloy composition and the thermal conductivity. In addition, the role of the normal (N) phonon-phonon scattering process is investigated following a recent theoretical study that indicated that the effect of N-process was underestimated in original Callaway's model. A comparison of the lattice thermal conductivity behavior using the phonon relaxation times in the original Callaway's model and the newly suggested theoretical model by Allen for the normal process is presented and discussed.

The differential effective medium method (DEM) is presented from a physical viewpoint and employed to calculate the lattice thermal conductivity of nano-bulk composites comprising of core-shell particles. Extended from the average-T-matrix single-particle approximation, DEM incorporates multiparticle effect essential for the study of core-shell nanocomposites (CSN).Interparticle boundary scattering in addition to intraparticle boundary scattering in CSN is found to add to the reduction of thermal conductivity of nanocomposites. Thus, CSN hold the promise of improving the thermoelectric dimensionless figure of merit ZT above that of monolithic nanobulk phases. Si and SiGe based CSN serve as illustrative examples.

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To further reduce the lattice thermal conductivity of thermoelectric materials, the technique of embedding nano-inclusions into bulk matrix materials, in addition to point defect scattering via alloying, was widely applied. Differential Effective Medium (DEM) method was employed to calculate two-phase heterogeneous systems. However, in most effective medium treatment, the interface scattering of matrix phonons by embedded nanoparticle was underestimated by adopting particle's projected area as scattering cross-section. Herein, modified cross-section calculations, as well as grain sizes dispersions, are applied in DEM, with the calculations then validated by comparing with Monte-Carlo simulations and existing experimental data. Predictions of lattice thermal conductivity reduction on in-situ formed Full Heusler (FH)/Half Heusler (HH) nano/matrix system are discussed