Thermoelectric materials convert heat into electricity and vice versa, offering potential for waste heat recovery and solid-state cooling. The efficiency of thermoelectric materials is quantified by the dimensionless figure of merit ZT, which depends on the Seebeck coefficient, electrical conductivity, thermal conductivity, and absolute temperature. Reducing lattice thermal conductivity without significantly degrading electronic properties is a key strategy for improving ZT. Phonon-engineered nanocomposites, particularly those with nanoscale precipitates embedded in a matrix, have emerged as a promising approach to achieve this by manipulating phonon transport through boundary scattering and interface engineering.

The thermal conductivity of a material is governed by both electronic and lattice contributions. In semiconductors and semimetals, the lattice component often dominates, making phonon scattering a critical lever for thermal management. Nanocomposites introduce a high density of interfaces that scatter phonons, reducing their mean free path and suppressing lattice thermal conductivity. The effectiveness of this scattering depends on the size, distribution, and nature of the nanoscale precipitates, as well as the properties of the matrix-precipitate interfaces.

Phonon scattering at interfaces can be categorized into coherent and incoherent processes. Coherent interfaces maintain crystallographic continuity between the matrix and precipitates, leading to phonon wave interference effects. In such cases, the acoustic mismatch between the two phases is small, and phonons may experience wave-like refraction or reflection. Coherent interfaces are common in epitaxially grown nanocomposites, where the lattice mismatch is minimal. The scattering behavior here is influenced by the contrast in phonon velocities and elastic properties between the matrix and precipitates. Theoretical models suggest that coherent interfaces are most effective at scattering mid- to high-frequency phonons, which have wavelengths comparable to the precipitate spacing.

Incoherent interfaces, on the other hand, exhibit significant structural or chemical discontinuity, leading to diffuse phonon scattering. These interfaces are typical in nanocomposites with large lattice mismatches or amorphous regions at boundaries. Incoherent scattering is more effective across a broader range of phonon frequencies, including low-frequency phonons that typically contribute significantly to thermal conductivity. The presence of disordered or defective regions at these interfaces further enhances phonon scattering by introducing additional mechanisms such as point defect scattering and strain field interactions.

The size and spacing of nanoscale precipitates play a crucial role in determining the dominant phonon scattering regime. When the precipitate size is smaller than the average phonon mean free path, boundary scattering becomes significant. For most thermoelectric materials, the mean free path of heat-carrying phonons ranges from a few nanometers to hundreds of nanometers. Precipitates with diameters in the 1-50 nm range are particularly effective at scattering mid-frequency phonons, while larger precipitates may only affect low-frequency phonons. The optimal size distribution often involves a combination of small and large precipitates to target a wide spectrum of phonon frequencies.

Modeling phonon transport in nanocomposites requires advanced computational techniques due to the complexity of the scattering processes. Molecular dynamics simulations have been used to study phonon interactions with interfaces at the atomic scale, revealing that interfacial roughness and chemical mixing can drastically alter thermal resistance. Boltzmann transport equation approaches, incorporating frequency-dependent relaxation times, provide insights into how different phonon modes contribute to thermal conductivity reduction. First-principles calculations further aid in predicting the phonon dispersion relations and scattering rates in both the matrix and precipitate phases.

Experimental studies on lead chalcogenide-based nanocomposites have demonstrated the effectiveness of nanoscale precipitates in reducing lattice thermal conductivity. For instance, PbTe with embedded SrTe or NaSbTe2 precipitates exhibits thermal conductivity reductions of up to 50% compared to bulk PbTe, leading to ZT values exceeding 2.0. Similar improvements have been observed in SiGe alloys with nanoscale Si or Ge inclusions, where interface scattering suppresses phonon propagation while maintaining reasonable electrical conductivity. These results highlight the importance of selecting precipitate materials with appropriate acoustic impedance mismatches relative to the matrix.

Beyond thermal conductivity reduction, the electronic properties of nanocomposites must be carefully optimized to avoid detrimental effects on the power factor. The presence of precipitates can influence carrier mobility through interface scattering, but if the precipitate-matrix band alignment is favorable, energy filtering effects may enhance the Seebeck coefficient. For example, in some semiconductor nanocomposites, potential barriers at interfaces selectively scatter low-energy carriers, increasing the average energy per charge carrier and thus the Seebeck coefficient. This effect can partially offset the reduction in electrical conductivity caused by carrier scattering.

Recent advances in processing techniques have enabled precise control over precipitate size, distribution, and interface quality. Bottom-up approaches such as colloidal synthesis followed by consolidation allow for tailored nanocomposite architectures with minimal interfacial defects. Top-down methods, including phase separation during solidification or annealing, offer scalability for industrial applications but require careful optimization to avoid excessive coarsening of precipitates. The choice of synthesis route depends on the desired balance between interface engineering and production feasibility.

Future research directions include exploring new material combinations with extreme phonon scattering contrasts, such as soft matrix materials with hard precipitates or vice versa. Additionally, hierarchical nanostructures incorporating multiple length scales of porosity and precipitation could further suppress thermal conductivity by targeting phonons across a wider range of mean free paths. Advances in characterization techniques, such as in situ TEM thermal measurements, will provide deeper insights into the nanoscale mechanisms governing phonon transport in these complex materials.

In summary, phonon-engineered nanocomposites represent a powerful strategy for enhancing thermoelectric performance through targeted manipulation of phonon transport. By carefully designing the size, distribution, and interface properties of nanoscale precipitates, significant reductions in lattice thermal conductivity can be achieved while preserving or even improving electronic properties. Continued progress in both theoretical understanding and experimental synthesis will further unlock the potential of these materials for practical thermoelectric applications.