The factors that affect the thermal conductivity of semiconductors is a topic of great scientific interest, especially in relation to thermoelectrics. Key developments have been the concept of the phonon-glass-electron-crystal (PGEC) and the related idea of rattling to achieve this. We use first principles phonon and thermal conductivity calculations in order to explore the concept of rattling for stoichiometric ordered half-Heusler compounds. These compounds can be regarded as filled zinc blende materials, and the filling atom could be viewed as a rattler if it is weakly bound. We use two simple metrics, one related to the frequency and the other to bond frustration and anharmonicity. We find that both measures correlate with thermal conductivity. This suggests that both may be useful in screening materials for low thermal conductivity.
Recent discoveries of materials with ultra-low thermal conductivity open a pathway to significant developments in the field of thermoelectricity. Here, we conduct a comparative study of three chemically similar antimonides to establish the root causes of their extraordinarily low thermal conductivity ($0.4-0.6$ Wm$^{-1}$K$^{-1}$ at 525 K). The materials of interest are: the unconventional type-XI clathrate K$_{58}$Zn$_{122}$Sb$_{207}$, the tunnel compound K$_{6.9}$Zn$_{21}$Sb$_{16}$, and the type-I clathrate K$_8$Zn$_{15.5}$Cu$_{2.5}$Sb$_{28}$ discovered herein. Calculations of the phonon disp…
A series of infrared-active optical phonons have been detected in type-I clathrate Ba$_8$Ga$_{16}$Ge$_{30}$ by terahertz time-domain spectroscopy. The conductivity spectra with the lowest-lying peaks at 1.15 and 1.80 THz are identified with so-called rattling phonons, i.e., optical modes of the guest ion Ba$^{2+}(2)$ with $T_{1u}$ symmetry in the oversized tetrakaidecahedral cage. The temperature dependence of the spectra from these modes are totally consistent with calculations based on a one-dimensional anharmonic potential model that, with decreasing temperature, the shape becomes asymmetri…
A solid with larger sound speeds exhibits higher lattice thermal conductivity (k_{lat}). Diamond is a prominent instance where its mean sound speed is 14400 m s-1 and k_{lat} is 2300 W m-1 K-1. Here, we report an extreme exception that CuP2 has quite large mean sound speeds of 4155 m s-1, comparable to GaAs, but the single crystals show a very low lattice thermal conductivity of about 4 W m-1 K-1 at room temperature, one order of magnitude smaller than GaAs. To understand such a puzzling thermal transport behavior, we have thoroughly investigated the atomic structure and lattice dynamics by co…
We have investigated optical conductivity spectra of $n$- and $p$-type Ba$_8$Ga $_{16}$Sn$_{30}$ ($α$-BGS) with type-VIII clathrate structure, at temperatures from 296\,K down to 6\,K with a terahertz time-domain spectrometer (0.2\,-\,2.5\,THz). The continuous spectra contributed from charge carriers are dispersive in this frequency range and also temperature- and carrier type-dependent. The Drude-Smith model taking multiple-scatterings of charge carriers into account well reproduces those data. The relaxation rate of the $n$-type carriers decreases more sharply than that in the $p$-type mater…
Semiconducting half- and, to a lesser extent, full-Heusler compounds are promising thermoelectric materials due to their compelling electronic properties with large power factors. However, intrinsically high thermal conductivity resulting in a limited thermoelectric efficiency has so far impeded their widespread use in practical applications. Here, we report the computational discovery of a class of hitherto unknown stable semiconducting full-Heusler compounds with ten valence electrons ($X_2YZ$, $X$=Ca, Sr, and Ba; $Y$= Au and Hg; $Z$=Sn, Pb, As, Sb, and Bi) through high-throughput $ab-initio…
We have performed ab initio molecular dynamics (MD) simulations to study the alkali-metal dynamics in the Al-doped (KAl0.33W1.67O6 and RbAl0.33W1.67O6) and undoped (KW2O6 and RbW2O6) defect pyrochlore tungstates. The K atoms exhibit novel rattling dynamics in both the doped and undoped tungstates while the Rb atoms do not. The KAl0.33W1.67O6 experimental thermal conductivity curve shows an unusual depression between ~ 50 K and ~ 250 K, coinciding with two crossovers in the K dynamics: the first at ~ 50 K, from oscillatory to diffusive, and the second at ~ 250 K, from diffusive back to oscillat…
The spin Hall conductivity (SHC) and anomalous Hall conductivity (AHC) in more than 120 full Heusler compounds are calculated using density functional theory in a high-throughtput way. The electronic structures are mapped to the Wannier basis and the linear response theory is used to get the conductivity. Our results show that the mechanism under the SHC or AHC cannot be simply related to the valence electron numbers or atomic weights, is related to the very details of the electronic structure, which can only be obtained by calculations. A high throughput calculation is efficient to screen out…
Half-Heusler compounds usually exhibit relatively higher lattice thermal conductivity that is undesirable for thermoelectric applications. Here we demonstrate by first-principles calculations and Boltzmann transport theory that the BiBaK system is an exception, which has rather low thermal conductivity as evidenced by very small phonon group velocity and relaxation time. Detailed analysis indicates that the heavy Bi and Ba atoms form a cage-like structure, inside which the light K atom rattles with larger atomic displacement parameters. In combination with its good electronic transport propert…
The half-Heusler compound has drawn attention in a variety of fields as a candidate material for thermoelectric energy conversion and spintronics technology. This is because it has various electronic structures, such as semi-metals, semiconductors, and a topological insulator. When the half-Heusler compound is incorporated into the device, the control of high lattice thermal conductivity owing to high crystal symmetry is a challenge for the thermal manager of the device. The calculation for the prediction of lattice thermal conductivity, which is an important physical parameter for controlling…
The thermoelectric properties of half-Heusler alloy TiNiSn have been studied for decade, however, theoretical report on its thermal conductivity is still little known, because it is difficult to estimate effectively the lattice thermal conductivity. In this work, we use the ShengBTE code developed recently to examine the lattice thermal conductivity of TiNiSn. The calculated lattice thermal conductivity at room temperature is 7.6 W/mK, which is close to the experimental value of 8 W/mK. We also find that the total and lattice thermal conductivities dependent temperature are in good agreement w…
The quest to improve the thermoelectric figure of merit has mainly followed the roadmap of lowering the thermal conductivity while keeping unaltered the power factor of the material. Ideally an electron-crystal phonon-glass system is desired. In this work, we report an extraordinary reduction of the cross-plane thermal conductivity in crystalline (TiNiSn):(HfNiSn) half-Heusler superlattices. We create SLs with thermal conductivities below the effective amorphous limit, which is kept in a large temperature range (120-300 K). We measured thermal conductivity at room temperature values as low as …
Since their discovery around a century ago, the structure and chemistry of the multi-functional half-Heusler semiconductors have been studied extensively as three component systems. The elemental groups constituting these ternary compounds with the nominal formula XYZ are well established. From the very same set of well-known elements we explore a phase space of quaternary double ($X'X''Y_2Z_2$, $X_2Y'Y''Z_2$, and $X_2Y_2Z'Z''$), triple ($X_2'X''Y_3Z_3$) and quadruple ($X_3'X''Y_4Z_4$) half-Heusler compositions which 10 times larger in size. Using a reliable, first-principles thermodynamics me…
With a terahertz time-domain spectrometer (0.3 - 3.0 THz) we have measured the optical conductivity of the type-I clathrate Ba$_8$Ga$_{16}$Sn$_{30}$ at temperatures from 300 K down to 7 K. Independent six spectra superimposed on the Drude conductivity are identified to infrared active vibrational modes of guest Ba ions and the cages. While the spectra of five higher-frequency modes depend hardly on temperature, the lowest-lying spectrum with a peak at 0.72 THz due to the Ba(2) ion's off-centering vibration in the oversized cage changes with temperature characteristically. With lowering tempera…
The anomalous transport properties of Heusler compounds become a hotspot of research in recent years due to their unique band structure and possible application in spintronics. In this paper, we report the anomalous Hall effect in polycrystalline NiCoMnGa quaternary Heusler compound by experimental means and theoretical calculations. The experimental anomalous Hall conductivity (AHC) was found at about 256 S/cm at 10K with an intrinsic contribution of ~ 121 S/cm. The analysis of Hall data reveals the presence of both extrinsic and intrinsic contributions in AHE. Our theoretical calculations sh…
The microscopic physics behind the lattice thermal conductivity of NiTiSn is investigated using first-principles-based anharmonic lattice dynamics. The calcu lated lattice thermal conductivity of bulk materials (5.3 W/m.K) is in good agreement with the experimental value at the optimal working temper ature (700 K), but is overestimated below this temperature. The calculated values can be strongly affected by the size of the crystalline grains. We show tha t the lattice thermal conductivity is dominated by the acoustic (transverse and mostly longitudinal) modes with no contribution from the opt…
Crystalline compounds exhibiting low-frequency rattling phonons constitute an important class of high-performance thermoelectrics owning to their intrinsically very low lattice thermal conductivity ($κ_{l}$). Theoretical approach that is capable of revealing the physical origin and accurately predicting $κ_{l}$ is of particular interest, which, however, still remains an outstanding challenge. In this study, we perform a case study of lattice dynamics and thermal transport properties of Ag$_{6}$Ge$_{10}$P$_{12}$, which has recently been identified as a high-performance thermoelectric phosphide …
Low lattice thermal conductivity is essential for high thermoelectric performance of a material. Lattice thermal conductivity is often computed using density functional theory (DFT), typically at a high computational cost. Training machine learning models to predict lattice thermal conductivity could offer an effective procedure to identify low lattice thermal conductivity compounds. However, in doing so, we must face the fact that such compounds can be quite rare and distinct from those in a typical training set. This distinctness can be problematic as standard machine learning methods are in…
High lattice thermal conductivity in half-Heusler alloys has been the major bottleneck in thermoelectric applications. Disordered half-Heusler alloys could be a plausible alternative to this predicament. In this paper, utilizing first-principles simulations, we have demonstrated the low lattice thermal conductivity in two such phases, NbFe$_{0.5}$Ni$_{0.5}$Sn and TaFe$_{0.5}$Ni$_{0.5}$Sn, in comparison to well-known half-Heusler alloy TiCoSb. We trace the low thermal conductivity to their short phonon lifetime, originating from the interaction among acoustic and low-lying optical phonons. We r…
Science-driven design of future thermoelectric materials requires a deep understanding of the fundamental relationships between microstructure and transport properties. Grain boundaries in polycrystalline materials influence the thermoelectric performance through the scattering of phonons or the trapping of electrons due to space-charge effects. Yet, the current lack of careful investigations on grain boundary-associated features hinders further optimization of properties. Here, we study n-type NbCo1-xPtxSn half-Heusler alloys, which were synthesized by ball milling and spark plasma sintering …
One of the key requirements for good thermoelectric materials is a low lattice thermal conductivity. Here we present a combined neutron scattering and theoretical investigation of the lattice dynamics in the type I clathrate system Ba-Ge-Ni, which fulfills this requirement. We observe a strong hybridization between phonons of the Ba guest atoms and acoustic phonons of the Ge-Ni host structure over a wide region of the Brillouin zone which is in contrast with the frequently adopted picture of isolated Ba atoms in Ge-Ni host cages. It occurs without a strong decrease of the acoustic phonon lifet…
Thermoelectric figures of merit, ZT > 0.5, have been obtained in arc-melted TiNiSn-based ingots. This promising conversion efficiency is due to a low lattice thermal conductivity, which is attributed to excess nickel in the half-Heusler structure.
Ternary intermetallic half-Heusler (HH) compounds (XYZ) with 18 valence electron count viz. ZrCoSb, ZrNiSn, and ZrPdSn, have revealed promising thermoelectric properties. Exemplarily, it has been experimentally observed that a slight change in the content of Y-site atoms (by ~3-12.5% i.e., m =0.03, 0.125 in ZrY(1+m)Z) leads to drastic lowering in the lattice thermal conductivity (kL) by more than 65-80% in many of these compounds. The present work aims at exploring the possibility of maximizing the electronic transport scenario after achieving the low kL limit in these compounds. By taking int…
The lattice thermal conductivity (κω) is a key property for many potential applications of compounds. Discovery of materials with very low or high κω remains an experimental challenge due to high costs and time-consuming synthesis procedures. High-throughput computational pre-screening is a valuable approach for significantly reducing the set of candidate compounds. In this article, we introduce efficient methods for reliably estimating the bulk κω for a large number of compounds. The algorithms are based on a combination of machine-learning algorithms, physical insights, and automatic ab-init…
Half Heusler (HH) alloys with 18 valence electron count have attracted significant interest in the area of research related to thermoelectrics. Understanding the novel transport properties exhibited by these systems with semiconducting ground state is an important focus area in this field. Large thermal conductivity shown by most of the HH alloy possesses a major hurdle in improving the figure of merit (ZT). Additionally, understanding the mechanism of thermal conduction in heavy constituents HH alloys is an interesting aspect. Here, we have investigated the high temperature thermoelectric pro…
Thermoelectric application of half-Heusler compounds suffers from their fairly high thermal conductivities. Insight into how effective various scattering mechanisms are in reducing the thermal conductivity of fabricated XNiSn compounds (X = Hf, Zr, Ti, and mixtures thereof) is therefore crucial. Here, we show that such insight can be obtained through a concerted theory-experiment comparison of how the lattice thermal conductivity kLat(T) depends on temperature and crystallite size. Comparing theory and experiment for a range of Hf0.5Zr0.5NiSn and ZrNiSn samples reported in the literature and i…
We address the electron transport characteristics in bulk half-Heusler alloys with their compositions tuned to the borderline between topologically nontrivial semi-metallic and trivial semiconducting phases. The precise first-principles calculations based on the coherent potential approximation (CPA) reveal that all the studied systems exhibit sets of dispersionless impurity-like resonant levels, with one of them being located right at the Dirac point. By means of the Kubo formalism we reveal that the residual conductivity of these alloys is strongly suppressed by impurity scattering, whereas …
Low and Anisotropic Thermal Conductivity in Mixed-Valent Sn$_2$S$_3$
Beijing Institute of Technology（北京理工大学）；College of Materials Science and Engineering, Fuzhou University（福州大学材料科学与工程学院）；Beijing Institute of Technology, Zhuhai（北京理工大学珠海学院）
We investigate electronic structures and thermoelectric properties of recent synthetic half-Heusler $\mathrm{ZrNiPb}$ by using generalized gradient approximation (GGA) and GGA plus spin-orbit coupling (GGA+SOC). Calculated results show that $\mathrm{ZrNiPb}$ is a indirect-gap semiconductor. Within the constant scattering time approximation, semi-classic transport coefficients are performed through solving Boltzmann transport equations. It is found that the SOC has more obvious influence on power factor in p-type doping than in n-type doping, leading to a detrimental effect in p-type doping. Th…
We explore the structural, electronic, mechanical and thermoelectric properties of a new half Heusler compound, HfPtPb which is all metallic heavy element and has been recently been proposed to be stable [Nature Chem 7 (2015) 308]. In the present work, we employ density functional theory and semiclassical Boltzmann transport equations with constant relaxation time approximation. The mechanical properties such as Shear modulus, Young modulus, elastic constants, Poisson ratio, and shear anisotropy factor are investigated. The elastic and phonon properties reveal that this compound is mechanicall…
We report on the high-temperature (350 K <T< 1000 K) thermoelectric properties of the ternary compounds LuNiSb (cubic) and LuNiSn (orthorhombic) and a composite material (LuNiSb)$_{0.5}$(LuNiSn)$_{0.5}$. The electrical conductivity in LuNiSn is metallic, while it is semiconducting-like in LuNiSb. The Seebeck coefficient reaches -5.5 $μ$V/K at 700 K for the former compound and 66 $μ$V/K at 607 K for the latter one. The composite sample (LuNiSb)$_{0.5}$(LuNiSn)$_{0.5}$ constructed from orthorhombic matrix with cubic inclusions combines the electrical conductivity of LuNiSn with the thermoelectri…
Materials design based on first-principles electronic calculations has proven a fruitful strategy to identify new thermoelectric materials with a favorable figure of merit. Recent electronic structure calculations predict that in cobalt-based half-Heusler systems a power factor higher than in CoTiSb can be achieved upon p-type doping of CoVSn, CoNbSn, CoTaSn, CoMoIn, and CoWIn. Here, using a first-principles approach and semi-classical Boltzmann transport theory, we investigate the electrical and thermal transport properties of these materials. The calculated thermal conductivity at room tempe…
Cocktail effect and robust Berry curvature driven anomalous Hall conductivity in the entropy-stabilized Heusler alloy Co$_2$(Ti$_{0.25}$V$_{0.25}$Cr$_{0.25}$Fe$_{0.25}$)Al
Thapar Institute of Engineering and Technology（塔帕尔工程与技术学院）；Bennett University（贝内特大学）；Jaypee Institute of Information Technology (JIIT)（贾伊皮信息技术学院）
The electronic and transport properties of the half-Heusler compound LaPtSb are investigated by performing first-principles calculations combined with semi-classical Boltzmann theory and deformation potential theory. Compared with many typical half-Heusler compounds, the LaPtSb exhibits obviously larger power factor at room temperature, especially for the n-type system. Together with the very low lattice thermal conductivity, the thermoelectric figure of merit (ZT) of LaPtSb can be optimized to a record high value of 2.2 by fine tuning the carrier concentration.
Defective half-Heusler systems X(1-x)YZ with large amounts of intrinsic vacancies, such as Nb(1-x)CoSb, Ti(1-x)NiSb and V(1-x)CoSb, are a group of promising thermoelectric materials. Even with high vacancy concentrations they maintain the average half-Heusler crystal structure. These systems show high electrical conductivity but low thermal conductivity arising from an ordered YZ lattice, which conducts electrons, while the large amounts of vacancies on the X sublattice effectively scatters phonons. Using electron scattering it was recently observed that in addition to Bragg diffraction from t…
We investigated six heavy element bismuth-based 18-VEC half-Heusler alloys CoTiBi, CoZrBi, CoHfBi, FeVBi, FeNbBi, and FeTaBi by first principles approach, in search of better thermoelectric prospects. The motivation is driven by expected lower thermal conductivity and the recent discovery of CoZrBi-based materials. Significantly, our calculated power factor values of all the systems show an increment of $\sim$40\% in comparison to the reported \textit{p}-type CoTiSb. We propose that doping at Bi-site, on account of electronic features, will be helpful in achieving the proposed power factor val…
Half-Heusler (HH) compounds have shown high Figure of merits up to 1.5. The key to these high thermoelectric efficiencies is an intrinsic phase separation, which occurs in multicomponent Half-Heusler compounds and leads to an significantly reduction of the thermal conductivity. For commercial applications, compatible n- and p-type materials are essential and their thermal stability under operating conditions, e.g. for an automotive up to 873 K, needs to be guaranteed. For the first time, the long-term stability of n- and p-type HH materials is proved. We investigated HH materials based on the …
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 dispers…
Full Heusler compounds with Cobalt as a primary element show anomalous transport properties owing to the Weyl fermions and broken time-reversal symmetry. We present here the study of anomalous Hall effect (AHE) in Co2FeGe Heusler compound. The experiment reveals anomalous Hall conductivity (AHC) 100 S/cm at room temperature with an intrinsic contribution of 78 S/cm . The analysis of anomalous Hall resistivity suggests the scattering independent intrinsic mechanism dominates the overall behaviour of anomalous Hall resistivity. The first principles calculation reveals that the Berry curvature or…
A half-Heusler material FeNb$_{0.8}$Ti$_{0.2}$Sb has been identified as a promising thermoelectric material due to its excellent thermoelectric performance at high temperatures. The origins of the efficient thermoelectric performance are investigated through a series of low-temperature (2 - 400 K) measurements. The high data coherence of the low and high temperatures is observed. An optimal and nearly temperature-independent carrier concentration is identified, which is ideal for the power factor. The obtained single type of hole carrier is also beneficial to the large Seebeck coefficient. The…
Accelerating Discovery of Vacancy Ordered 18-Valence Electron Half-Heusler Compounds: A Synergistic Approach of Machine Learning and Density Functional Theory
Improvements in the thermoelectric properties of Half-Heusler materials have been achieved by means of a micrometer-scale phase separation that increases the phonon scattering and reduces the lattice thermal conductivity. A detailed study of the p-type Half-Heusler compounds Ti(1-x)Hf(x)CoSb0.85Sn0.15 using high-resolution synchrotron powder X-ray diffraction and element mapping electron microscopy evidences the outstanding thermoelectric properties of this system. A combination of intrinsic phase separation and adjustment of the carrier concentration via Sn substitution is used to realize a r…
Magnetic lanthanide half-Heuslers ($R$PtBi; $R$ being the lanthanide) represent an attractive subgroup of the Heusler family and have been identified as ideal candidates for time reversal symmetry breaking topological Weyl semimetals. In this paper, we present the detailed analysis of the magnetotransport properties of frustrated antiferromagnet TbPtBi. This material shows large, non-saturating magnetoresistance (MR) with unusual magnetic field dependence. The MR of TbPtBi is significantly anisotropic with respect to the magnetic field, applied along different crystallographic directions and i…
First principles study of thermoelectric properties of $\text{Nb}_2\text{Co}_2\text{InSb}$ and $\text{Nb}_2\text{Co}_2\text{GaSb}$ double half-Heuslers
We investigate the role of rattling guest atoms on the lattice thermal-conductivity of a type-I clathrate Ba$_{8}$Ga$_{16}$Ge$_{30}$ by first-principles lattice dynamics. Comparing phonon properties of filled and empty clathrates, we show that rattlers cause 10-fold reductions in the relaxation time of phonons by increasing the phonon-phonon scattering probability. Contrary to the resonant scattering scenario, the reduction in the relaxation time occurs in a wide frequency range, which is crucial for explaining unusually low thermal-conductivities of clathrates. We also find that the impact of…
A compound with metallic electrical conductivity usually has a considerable total thermal conductivity because both electrons and photons contribute to thermal transport. Here, we show an exceptional example of iridium oxide, Bi3Ir3O11, that concurrently displays metallic electrical conductivity and ultralow thermal conductivity approaching 0.61 W m-1 K-1 at 300 K. The compound crystallizes into a cubic structural framework with space group Pn-3. The edge- and corner-sharing IrO6 octahedra with a mixed Ir4.33+ charge state favor metallic electrical transport. Bi3Ir3O11 exhibits an extremely lo…
Room temperature intrinsic anomalous Hall effect in disordered half-metallic ferromagnetic quaternary Heusler alloy CoRuFeSi
National Institute of Technology Andhra Pradesh（安得拉邦国立技术学院）；Indian Institute of Technology Hyderabad（海德拉巴印度理工学院）；Institute of Low Temperature and Structure Research, Polish Academy of Sciences（波兰科学院低温结构研究所）；Indian Institute of Technology Kanpur（坎普尔印度理工学院）；UGC-DAE Consortium for Scientific Research, Kolkata Centre（UGC-DAE科学研究中心加尔各答中心）
It has been demonstrated that InSb nanoinclusions, which are formed in situ, can simultaneously improve all three individual thermoelectric properties of the n-type half Heusler compound (Ti,Zr,Hf)(Co,Ni)Sb [Xie et al., Acta Mater. 58, 4795 (2010)]. In the work presented herein, we have adopted the same approach to the p-type half Heusler compound Ti(Co,Fe)Sb. The results of resistivity, Seebeck coefficient, thermal conductivity, and Hall coefficient measurements indicate that the combined high mobility electron injection, low energy electron filtering, and boundary scattering, again, lead to …
In spite of their relatively high lattice thermal conductivity $κ_{\ell}$, the XNiSn (X=Ti, Zr or Hf) half-Heusler compounds are good thermoelectric materials. Previous studies have shown that $κ_{\ell}$ can be reduced by sublattice-alloying on the X-site. To cast light on how the alloy composition affects $κ_\ell$, we study this system using the phonon Boltzmann-transport equation within the relaxation time approximation in conjunction with density functional theory.The effect of alloying through mass-disorder scattering is explored using the virtual crystal approximation to screen the entire…
Half-Heusler phases (space group F43m, C1b) have recently captured much attention as promising thermoelectric materials for heat-to-electric power conversion in the mid-to-high temperature range. The most studied ones are the RNiSn-type half-Heusler compounds, where R represents refractory metals Hf, Zr, and Ti. These compounds have shown a high-power factor and high-power density, as well as good material stability and scalability. Due to their high thermal conductivity, however, the dimensionless figure of merit (zT) of these materials has stagnated near 1 for a long time. Since 2013, the ve…
The optical conductivity spectra of the rattling phonons in the clathrate Ba$_8$Ga$_{16}$Ge$_{30}$ are investigated in detail by use of the terahertz time-domain spectroscopy. The experiment has revealed that the lowest-lying vibrational mode of a Ba(2)$^{2+}$ ion consists of a sharp Lorentzian peak at 1.2 THz superimposed on a broad tail weighted in the lower frequency regime around 1.0 THz. With decreasing temperature, an unexpected linewidth broadening of the phonon peak is observed, together with monotonic softening of the phonon peak and the enhancement of the tail structure. These observ…
