The search for materials with extreme thermal properties continues because of their importance for thermal management applications. Materials with low κ are used in data storage devices, thermal barrier coatings, and thermoelectrics, whereas high-κ materials are useful for thermal energy transmission and heat dissipation. Energy costs, carbon emissions from fossil fuels, and energy wasted as heat in the world’s energy economy (>60%) drive tremendous interest in advanced processes and materials for thermal energy transmission, storage, and conversion.
Toward these goals, discovery of higher-efficiency thermoelectric materials (TEs) for use in waste heat recovery is highly desirable. The efficiency of TEs for thermal-to-electric energy conversion is characterized by the figure of merit; , where σ is electrical conductivity, S is the Seebeck coefficient, and κ is thermal conductivity. Numerous schemes for improving the power factor () and minimizing κ have been devised to achieve enhanced ZT. However, the complex interplay of σ, S, and κ remains a challenging bottleneck toward further advances. Disordered and amorphous materials typically exhibit ultralow κ values owing to lack of lattice periodicity, but these also give low σ. Therefore, theoretical and experimental efforts targeting quality crystalline materials with very low κ and large power factors have been a strong driver in thermoelectric research.
A number of materials, mostly with complex structure, have been proposed for thermoelectric applications, including half-Heuslers, skutterudites, and clathrates where anharmonic rattling modes give strong intrinsic phonon resistance and suppressed κ. The lowest reported room temperature κ value among bulk crystalline TEs is 0.47 W/m-K in SnSe. Thermal conductivity values similar to this are rare in crystalline materials, although lower values are typical in highly disordered or amorphous materials where the phonon picture is not applicable.
Disordered transport regimes are not yet fully understood, although great strides have been taken, experimentally and theoretically, to gain insights into these. Most relevant to this work, Cahill, Watson, and Pohl put forth a κ model (CWP formula) to describe a lower bound to κ based on random hops of “instantaneously” localized (not to be confused with Anderson localization) vibrational thermal energy among uncorrelated oscillators in glassy and amorphous materials. This was first proposed by Einstein to explain the measured κ of KCl and failed dramatically as phonons carry the majority of heat in that material. In disordered materials, κ monotonically increases with temperature (T) before saturating above the Debye temperature, thus having an effective minimum κ nearly independent of T for a broad range of T.
In contrast, phonon κ in crystalline materials typically increases with T from T = 0 following a Debye T3behavior, peaks at intermediate T, often dictated by isotope or defect scattering, and then exhibits a near 1/T behavior with increasing T above the Debye temperature owing to intrinsic umklapp scattering. For complex crystalline materials whose phonon mean free paths (λ) are strongly suppressed, approaching lengths on the order of interatomic spacings [Ioffe-Regel limit similar to those in disordered materials, the CWP formula is often invoked.
A full report on this subject investigated the mechanisms behind the very low κ of a cubic Tl3VSe4 crystal (Fig. 1) using combined measurements and a Peierls-Boltzmann transport (PBT) methodology coupled with interatomic forces from density functional theory. Tl3VSe4 generally has typical phonon behavior from 5 K < T < 300 K. The team calculated intrinsic phonon-phonon interactions, and extrinsic phonon scattering, from natural isotope variations and from crystallite boundaries with the length (0.2 μm) empirically determined from the measured κ at 6 K. Researchers found that the extrinsic scattering has little impact on the overall κ for T > 50 K as the intrinsic phonon scattering resistance is very strong. For lower temperatures, where extrinsic scattering is more important, our calculated and measured κ are in good agreement.