Session P17: Focus Session: Thermoelectrics - TE and Thermal Conductivity

Skutterudite Thermoelectric Generator for Electrical Power Generation from Automotive Waste Heat

Filled skutterudites are state-of-the- art thermoelectric (TE) materials for electrical power generation from waste heat. They have suitable intrinsic transport properties as measured by the thermoelectric figure of merit ZT = S$^{2}\sigma {\rm T}$/$\kappa $ (S = Seebeck coefficient, $\sigma $ = electrical conductivity, T = temperature, and $\kappa $ = thermal conductivity) and good mechanical strength for operation at vehicle exhaust gas temperatures of $>$550\r{ }C. We have demonstrated TE electrical power generation on a production test vehicle equipped with a fully functional prototype TE generator (TEG). It was assembled with TE modules fabricated from filled skutterudites synthesized at GM. Our results and analysis show that improvement in total power generated can be achieved by enhanced thermal and electrical interfaces and contacts. A substantial T decrease along the exhaust gas flow results in a large variation of voltage, current, and power output for each TE module depending on its position in the module array. Total TEG output power depends directly on the position-dependent T profile via the temperature dependence of both ZT and Carnot efficiency. Total TEG power output also depends on how the modules are connected in parallel or series combinations because mismatch in output voltage and/or internal resistance among the modules degrades the performance of the entire array. Uniform T profiles and consistent TE module internal resistances improve overall TEG performance.   

Theoretical Study of the Properties of the Type II Clathrates A$_{x}$Si$_{136}$ and A$_{x}$Ge$_{136}$ (A = Na, K)

Type II clathrate semiconductors have cage-like lattices where atoms are tetrahedrally coordinated and sp$^{3}$ bonded. An observed property of these materials is the variation of unit cell volume as different types of alkali metal atoms are placed in the clathrate cages. Experiments\footnote{M. Beekman, et al, \textit{Inorganic Chem} \underline {49}, 5338 (2010)} on Na$_{x}$Si$_{136}$ reveal that, starting with Si$_{136}$, as x increases (0 $<$ x $<$ 8), the cell volume contracts; where (8 $<$ x $<$ 24), the cell volume expands. This variation with x has been explained\footnote{Ibid.} as due to preferential incorporation of Na into the Si$_{28}$ cages for x $<$ 8, followed by incorporation into the Si$_{20}$ cages for 8 $<$ x (when all Si$_{28}$ cages are full). With this motivation, we have used density functional theory to explore the possibility Type II Si and Ge clathrates with alkali atom guests other than Na may exhibit a similar variation in cell volume with guest inclusion. We present results for the electronic and vibrational properties of the Na$_{x}$Si$_{136}$, Na$_{x}$Ge$_{136}$, K$_{x}$Si$_{136}$, and K$_{x}$Ge$_{136}$ clathrates. These results are compared with experiment and the properties of the materials are compared and contrasted.   

Enhanced Thermoelectric Property of Single Phase MnSi1.75 through Non-equilibrium Synthesis Method

We report thermoelectric properties of the single phase MnSi1.75 using a one-step non-equilibrium synthesis method. Extremely high quenching speed of melt spinning prevents the formation of the second phase MnSi, which is usually found in this class of materials made by using the conventional solid state reaction methods. We found that the phase-pure MnSi1.75 samples exhibit much higher electrical conductivity, as compared with the conventionally prepared samples. Thermal conductivity is measured and analyzed by introducing the Debye model. It is found that the reduced grain sizes after melt spinning play an important role on decreasing lattice thermal conductivity. The combination of enhanced electrical conductivity and reduced lattice thermal conductivity results in large increase of the thermoelectric figure of merit zT at room temperature.   

Investigation of phonon mass-difference scattering model by molecular dynamics

While nanostructuring has been shown to be a promising approach to effectively reduce lattice thermal conductivity and enhance efficiency of thermoelectrics, alloying still remains to be a key process that determines the base material performance. Therefore, understanding lattice thermal conductivity of alloyed crystals, particularly from the viewpoint of mode-dependent phonon transport, holds importance. In this work, we have investigated phonon scattering rates in alloy crystals by focusing on the mass-difference scattering. The phonon mass-difference scattering rates were obtained through spectral analysis of phase-space molecular trajectories computed by molecular dynamics simulations. Obtained results for simple Lennard-Jones crystals show that the mass-difference scattering rates of long-wavelength phonons follow the frequency dependence of Rayleigh scattering regardless of isotope mass and concentration. Meanwhile we obtained the large deviation from scattering models based on the mass perturbation theory. We will report and discuss details of frequency-dependence of mass-difference scattering rates to~clarify validity and limit of the models.~Furthermore, the analysis will be extended to thermoelectric materials, such as lead telluride. This work is supported by Global COE Program, Global Center of Excellence for Mechanical System Innovation.   

Stronger phonon scattering by larger differences in atomic mass and size in p-type half-Heuslers Hf$_{1-x}$Ti$_{x}$CoSb$_{0.8}$Sn$_{0.2}$

High lattice thermal conductivity has been the bottleneck for further improvement of thermoelectric figure-of-merit (ZT) of half-Heuslers (HHs) Hf$_{1-x}$Zr$_{x}$CoSb$_{0.8}$Sn$_{0.2}$. Theoretically the high lattice thermal conductivity can be reduced by exploring larger differences in atomic mass and size in the crystal structure. In this paper, we experimentally demonstrated that lower than ever reported thermal conductivity in p-type HHs can indeed be achieved when Ti is used to replace Zr, i.e., Hf$_{1-x}$Ti$_{x}$CoSb$_{0.8}$Sn$_{0.2}$, due to larger differences in atomic mass and size between Hf and Ti than Hf and Zr. The highest peak ZT of about 1.1 in the system Hf$_{1-x}$Ti$_{x}$CoSb$_{0.8}$Sn$_{0.2}$ (x=0.1, 0.2, 0.3, and 0.5) was achieved with x=0.2 at 800 $^{o}$C.   

Neutron Scattering Study of the Temperature-Dependent Phonon Spectra of AgSbTe$_{2}$

The thermoelectric material AgSbTe$_{2}$ has attracted much attention due to its simple rocksalt structure, high thermoelectric figure-of-merit, and its extremely low thermal conductivity in bulk samples. Previous theoretical studies have suggested that phonons can be scattered by anharmonicity (phonon-phonon coupling) and nano-defects in AgSbTe$_{2}$. However, systematic measurements of phonons in this compound have not been available. We report our results of detailed time-of-flight neutron scattering measurements, as a function of temperature, and departure from stoichiometry. The temperature dependence of the phonon density-of-states is discussed, and compared with the reported thermal conductivity in this system.   

Inelastic Neutron Study of Phonon Lifetime Effects in Thermoelectric Bi$_2$(Se,Te)$_3$ Alloys

One important avenue of optimizing the thermoelectric figure of merit, ZT, is to reduce the thermal conductivity of phonons while preserving the electrical conductivity. Mass disorder caused by alloying provides an avenue of enhancing phonon scattering. In this work, the phonon spectra of different alloys of Bi$_2$(Se,Te)$_3$ are measured using inelastic neutron measurements. The temperature and composition dependence provide information on phonon softening and enhanced phonon scattering of acoustic phonon modes. Measurements on single crystals also reveal the dependence on the polarization of the modes. An additional low energy dispersing mode has been observed.   

Anomalous Lattice Dynamics in PbTe and Its Implications to Low Intrinsic Lattice Thermal Conductivity

Recent experiments on PbTe-based high performance thermoelectric materials raise fundamental questions about the nature of low intrinsic lattice thermal conductivity and underlying lattice dynamics. We show by first-principles calculations that the reported results can be attributed to abnormally large-amplitude thermal vibrations that stem from a delicate competition of dual ionicity and covalency, which puts PbTe near ferroelectric instability. It produces anomalous properties such as partially localized low-frequency phonon modes, a soft transverse optical phonon mode, and a positive temperature coefficient for the band gap. These results account for experimental findings and resolve the underlying atomistic mechanisms. The relation between these anomalies and the low intrinsic lattice thermal conductivity will be discussed.   

Phonon Anharmonicity in PbTe Thermoelectrics

Achieving high thermoelectric conversion efficiency requires limiting the thermal conductivity, through the disruption of phonon propagation. A detailed understanding of phonon dispersions and linewidths is thus critical to develop accurate microscopic theories of thermal conductivity, and design efficient thermoelectric materials. We investigate the phonon dispersions and linewidths in the thermoelectric material PbTe with inelastic neutron scattering experiments. Our measurements indicate that the soft transverse optic mode in PbTe is strongly anharmonic, which could cause a lowering of thermal conductivity by scattering the heat-conducting acoustic modes [1]. We also present results on the effect of alloying. \\[4pt] [1] O. Delaire et al., Nature Materials 10, 614 (2011).   

Anharmonic vibrational effects of thermoelectric Cu-Sb-Se ternary semiconductors: Density-functional theory studies

Strong anharmonicity can lead to intrinsically minimal thermal conductivity even in defect-free single crystals. In an effort to understand this behavior, we have investigated two Cu-Sb-Se ternary semiconductors, Cu$_3$SbSe$_4$ and Cu$_3$SbSe$_3$, by both experimental measurements and density functional theory (DFT) calculations. The experimental lattice thermal conductivity measurements show that while Cu$_3$SbSe$_4$ exhibits classical behavior, the lattice thermal conductivity in Cu$_3$SbSe$_3$ is anomalously low and nearly temperature independent. The vibrational properties of these two semiconductors are calculated by DFT phonon calculations within the quasi-harmonic approximation. The average of the Gr\"{u}neisen parameters of the acoustic mode in Cu$_3$SbSe$_3$ is larger than that of Cu$_3$SbSe$_4$, which theoretically confirms that Cu$_3$SbSe$_3$ has a stronger lattice anharmonicity than Cu$_3$SbSe$_4$. Using our DFT-determined longitudinal and transverse Gr\"{u}neisen parameters, Debye temperatures, and phonon velocities, we calculate the lattice the lattice thermal conductivity using the Debye-Callaway model (without the use of any adjustable parameters). The calculated thermal conductivity is in good agreement with the experimental measurements.   

First-principles calculation of anharmonicity induced phonon lifetimes in FeSi

FeSi has attracted a lot of interest as a promising thermoelectric material for refrigeration applications. We present a first principle calculation of phonon lifetimes of FeSi based on our newly developed computational technique which combines first-principles density functional theory (DFT) and quantum scattering theory. Phonon lifetimes are calculated within the Fermi's golden rule using third order lattice anharmonicity tensors and vibrational phonon frequencies as inputs. Second order force constant matrices and third order lattice anharmonicity tensors are extracted using a real space supercell technique within the local density approximation (LDA). We compare our calculated phonon spectrum and lifetimes with recent neutron scattering measurements of phonon dispersions and linewidths. Finally we use the calculated phonon lifetimes to estimate the thermal conductivity of FeSi using kinetic transport theory.   

Resistivity and Specific Heat under Localized Anharmonic Motion in Type-I Ba$_{8}$Ga$_{16}$Sn$_{30}$ Clathrate

Anharmonic guest atom oscillation has direct connection to the thermal transport and thermoelectric behavior of type-I Ba$_{8}$Ga$_{16}$Sn$_{30}$ clathrates. This behavior can be observed through several physical properties, with for example the heat capacity providing a measure of the overall excitation level structure. In addition the nuclear magnetic resonance (NMR) relaxation behavior provides a sensitive probe for the oscillator dynamics, as we have recently reported. Localized anharmonic excitations also influence the low-temperature resistivity, as we show in this paper. By combining heat capacity and transport measurements we address the distribution of local-oscillators in this material, as well as the shape of the confining potential for Ba ions in the cages. Analyzed along with NMR relaxation measurements for the same sample, a two phonon Raman process is used to extract information about the excitation energies, which along with a quantum computational solver we have used to address the potential structure. We also compare to the soft-potential model and other models used for this system. The results indicate that a single confining potential cannot describe the system properly, whereas a distribution of local oscillators provides a more reasonable fit to the data.   

The Debye-Waller factor and its application to anharmonic vibrations

The Debye-Waller factor relates the intensities of the Bragg peaks to the mean square displacements of the atoms. In the structural refinement of diffraction data it is standard practice to use the harmonic expression for Debye-Waller factor. For most materials and conditions the phonons are only mildly anharmonic, thus the harmonic assumption is a good one. For some materials and conditions, however, the phonons can be strongly anharmonic, and thus the harmonic assumption is physically unrealistic. As examples we cite the rattling atoms in clathrates and skutterudites, and atoms participating in displacive phase transitions. In the present study we investigate the error associated with using the harmonic Debye--Waller factor to analyze anharmonic vibrations. We find that even for strongly anharmonic potentials, such as a double well, the mean square displacements deduced using the harmonic approximation are at most 15$\%$ larger than those deduced using a full anharmonic analysis. Furthermore, the quasi-harmonic and anharmonic values have nearly the same temperature dependences. We conclude that the error introduced by using the harmonic approximation is comparable to or smaller than the usual errors associated with measurement and refinement of diffraction patterns.   

Minimum thermal conductivity in superlattices: A first-principles formalism

In certain superlattice systems such as silicon-germanium superlattices a minimum in thermal conductivity with increase in period thickness has been observed. This minimum has been reported at a relatively short superlattice period of a few nanometers and cannot be explained by existing formalisms. An accurate prediction of this minimum thermal conductivity holds importance for thermoelectrics where low thermal conductivity is desired. We develop a first-principles formalism based on use of harmonic and anharmonic force-constants derived from density-functional perturbation theory and single-mode relaxation time approximation to predict the thermal conductivity of superlattices. The phonon relaxation times are computed based on scattering due to both anharmonicity and interface roughness. We show that the formalism leads to an excellent agreement between predicted and measured values and also explains the observed minimum in thermal conductivity.   

Thermal transport across perovskite superlattices

Understanding thermal transport across interfaces is useful for designing materials for thermal management, thermoelectricity etc. Despite years of investigation, there are several open questions on the nature of thermal transport across solid-solid interfaces. The ability to control materials synthesis down to a monolayer has enabled study of interface phonon scattering in systems such as superlattices, heterostructures etc. We chose perovskite oxides, which are excellent thermoelectric materials, as model systems to study interfacial thermal transport. Superlattices of SrTiO$_3$, CaTiO$_3$ and CaMnO$_3$, with period thicknesses ranging from 1-176 monolayers were grown using pulsed laser deposition, monitored by in-situ RHEED. We measured temperature dependent (100 - 400 K) cross plane thermal conductivity of these superlattices using the time domain thermoreflectance (TDTR). The lowest thermal conductivity measured is below the alloy limit at room temperature. The period thickness dependent thermal conductivity shows signs of zone folding for short period superlattices.