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Electron density difference maps and the corresponding F c , calculated using the VASP code. Red and blue spheres represent the guest atoms at nonequivalent sites. Gray spheres represent Si atoms. (a)–(c) Charge redistribution with the introduction of guest atoms in Ba 8 Si 46 , K 8 Si 46 and Ne 8 Si 46 , where the blue region is electron decreased and the yellow region is electron increased. (d),(e) Difference in spatial charge density (electron-decreased region) between positively charged (+8 and +16) and neutral systems. (f) A comparison with the calculated F c .
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We report that anomalous low-energy excitation (ALE) peaks in the heat capacity emerging from single-crystal cage materials can be successfully rationalized in terms of a single unified exponential line for a variety of type-I clathrates by employing a parameter associated with the freedom of space and the modified radii of guest atoms estimated by...
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... 5(a)-5(c), and the F c estimated for the 6d parallel modes are shown in Fig. 5(f). These calculations provide important information regarding how the ionic states of divalent (Ba 2+ ), monovalent (K + ), and zero-valent (Ne 0 ) guest atoms affect the interaction strength. At first glance, an electron is transferred from the guest atoms to the host cage frameworks as can be visualized in Figs. 5(a)-5(c) by blue ...
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... 6d parallel modes are shown in Fig. 5(f). These calculations provide important information regarding how the ionic states of divalent (Ba 2+ ), monovalent (K + ), and zero-valent (Ne 0 ) guest atoms affect the interaction strength. At first glance, an electron is transferred from the guest atoms to the host cage frameworks as can be visualized in Figs. 5(a)-5(c) by blue (electron-decreased) and yellow (electron-increased) regions. For instance, one electron or two electrons are transferred from K or Ba to the Si 46 cage network in the case of Ba 8 Si 46 and K 8 Si 46 , respectively, while negligible electron transfer was detected for Ne 8 Si 46 . Meanwhile, the calculated F c 's, which ...
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... are transferred from K or Ba to the Si 46 cage network in the case of Ba 8 Si 46 and K 8 Si 46 , respectively, while negligible electron transfer was detected for Ne 8 Si 46 . Meanwhile, the calculated F c 's, which are quantitatively in good agreement with the values used in Fig. 3, become smaller from Ba to K and to Ne, as can be seen in Fig. 5(f). One may imagine that the guest valences may have some influence on the guest-host interactions; however, this conclusion is not correct as we shall see in the following ...
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... LUMO+i (r)| 2 (i = 0 to 3 for −8e and i = 0 to 7 for −16e; (r) is a kohn-Sham orbital; LUMO denotes lowest unoccupied molecular orbital) of the neutral Ba 8 Si 46 . Strikingly, the frequencies of the guest vibrations have a negligible dependence on these hypothetical charge variations, as shown in Fig. 5(f). These calculations clearly demonstrate that the Coulombic ionic interactions do not make a significant contribution to the excitation peaks. Therefore the different F c 's shown in Fig. 5(f) should be ascribed to the free space of the guest atoms associated with van der Waals radii rather than their charge valences. For further ...
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... neutral Ba 8 Si 46 . Strikingly, the frequencies of the guest vibrations have a negligible dependence on these hypothetical charge variations, as shown in Fig. 5(f). These calculations clearly demonstrate that the Coulombic ionic interactions do not make a significant contribution to the excitation peaks. Therefore the different F c 's shown in Fig. 5(f) should be ascribed to the free space of the guest atoms associated with van der Waals radii rather than their charge valences. For further understanding, we calculated the F c when the lattice of Ba 8 Si 46 is hypothetically contracted up to 0.94a, where a is the cell parameter. Importantly, the F c evaluated by first-principles ...
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... The current understanding of type-I clathrate A 8 Ga 16 Ge 30 , which is based mainly on thermal and electrical properties, can be summarized in three points: (1) the low value of k L in Ba 8 Ga 16 Ge 30 (BGG) is attributed to the Umklapp scattering of the low-energy acoustic phonons by means of weakly dispersive rattling phonons [12,24]; (2) the k L of p-type BGG shows a glasslike temperature dependence with a plateau around 10e30 K, whereas that of n-type BGG exhibits a crystalline k L , indicating the different dynamical behaviours of the guest Ba atom and the Ga atom [16,25,26]; (3) the interaction between the guest atom and the host cage is electrostatic due to the electron charge transfer from the rattling atom to the Ga/Ge framework. If the electrons are highly delocalized, one might treat the cage as having a uniform negative charge [27,28]. ...
Intermetallic clathrates are materials characterized by a large cage structure where guest atoms can move anharmonically, providing these materials exotic thermoelectric properties. Unfortunately, the dynamical and atomic nature of the rattling phonons, and their interactions with the electronic structure, are not fully understood. Here, we report that a germanium isotope effect can trigger an inherent guest rattling and cage distortion in clathrate Ba8Ga16Ge30 (BGG). Raman-scattering spectroscopy and advanced electron microscopy demonstrate that the atomic germanium isotope effect induces an off-centre rattling at the 6d sites as well as a tetrakaidecahedron deformation which is anisotropic for n-type BGG but isotropic for p-type BGG. The present findings indicate that the large n-type germanium isotope effect arises from the strong electron-phonon coupling, which opens up a novel avenue for manipulating dynamical motions of phonons via atomic isotope engineering.
... In our previous work, 18 we addressed a van der Waalstype interaction between a filler and its surrounding cage framework as the origin of the rattling ALE modes by focusing only on the 6d parallel modes in type-I clathrates. ...
... We have exemplified the situation in the heat capacity analyses for K 8 Ga 8 Sn 38 , where the number of ALE modes obtained from data fitting exceeds what we expect from the number of guest atoms, showing clearly the contributions from van Hove singularities. 18 In order to obtain a correct value for ω E , temperature dependent ADP of a guest atom is useful. 4 Therefore, the ω E 's in the present analyses are mainly derived from ADP data from literatures (Refs. ...
... To interpret the guest vibration modes, we introduce a modified Morse potential as we did previously. 18,45 As shown in Fig. 1, the potential of a guest atom inside a cage can be simplified by pair-wise potentials and expressed by, ...
Rattling motion of fillers in cage materials has been of great interest for their import roles in superconductivity and thermoelectric applications. The standing waves of the rattling oscillations are normally lower in energy than the propagating waves of the acoustic phonons, thus exert large influences on the configuration of phonon dispersions as well as the associated thermal and electrical properties. Although it has been extensively studied, the origin of the low energy soft modes is still not clear. In the present paper, we show that van der Waals-type interactions are predominant between fillers and their surrounding cage frameworks, which explains the origin of the low energy modes in cage materials as a universal rule. Mass, free space and chemical environment of guest atoms are shown to be the most important factors to determine the three dimensional van der Waals-type interactions. The present work is mainly focused on type-I clathrates, skutterudites and pyrochlores.
Different fluxes, Ga, Bi, In, Sb, and Sn, have been used to grow clathrate Ba8Cu5.3Ge40.7 (BCG) single crystals using a flux method, and BCG single crystals have been successfully synthesized by Bi-, In- and Sn-flux. The grown crystals were characterized by single crystal and power X-ray diffraction as well as energy dispersive X-ray spectroscopy measurements. The solubility of flux inside the crystals was determined and the actual chemical composition was decided to be: Ba8Cu5.1Ge40.5 (BCG-Bi), Ba8Cu4.6In1.4Ge40.0 (BCG-In) and Ba8Cu5.1Ge40.2Sn0.7 (BCG-Sn) for the compounds grown from Bi-, In- and Sn-flux, respectively. A high electron mobility (μ), 44.8 cm² V⁻¹ s⁻¹ at 300 K, is observed for BCG-In, which is almost 5 times higher than the reported data at a similar carrier concentration. Therefore, enhanced thermoelectric power factors and ZT values are obtained. The relationship between the structure and electrical/thermoelectric properties is discussed. The high μ is most probably due to the relatively ordered cage framework structure in BCG-In, because the 6c site is fully occupied by Cu and In, and the other two sites are uniformly occupied by Ge.
We investigate the role of the quartic anharmonicity in lattice dynamics and thermal transport of type-I clathrate Ba$_{8}$Ga$_{16}$Ge$_{30}$ based on \textit{ab initio} self-consistent phonon calculations. We show that the strong quartic anharmonicity of rattling guest atoms causes the hardening of vibrational frequencies of low-lying optical modes and thereby affects calculated lattice thermal conductivities $\kappa_{L}$ significantly, resulting in an improved agreement with experimental results including the deviation from $\kappa_{L}\propto T^{-1}$ at high temperature. Moreover, our static simulations with various different cell volumes shows a transition from crystal-like to \textit{glasslike} $\kappa_{L}$ around 20 K. Our analyses suggest that the resonance dip of $\kappa_{L}$ observed in clathrates with large guest-free-spaces is attributed mainly to the strong Umklapp scattering of acoustic modes along with the presence of higher-frequency dispersive optical modes.
We report thermoelectric (TE) properties of topological surface Dirac states (TSDS) in three-dimensional topological insulators (3D-TIs) purely isolated from the bulk by employing single crystal Bi$_{2-x}$Sb$_x$Te$_{3-y}$Se$_y$ films epitaxially grown in the ultrathin limit. Two intrinsic nontrivial topological surface states, a metallic TSDS (m-TSDS) and a gap-opened semiconducting topological state (g-TSDS), are successfully observed by electrical transport, and important TE parameters (electrical conductivity (${\sigma}$), thermal conductivity (${\kappa}$), and thermopower ($S$)) are accurately determined. Pure m-TSDS gives $S$=-44 {\mu}VK$^{-1}$, which is an order of magnitude higher than those of the conventional metals and the value is enhanced to -212 {\mu}VK$^{-1}$ for g-TSDS. It is clearly shown that the semi-classical Boltzmann transport equation (SBTE) in the framework of constant relaxation time (${\tau}$) most frequently used for conventional analysis cannot be valid in 3D-TIs and strong energy dependent relaxation time ${\tau}(E)$ beyond the Born approximation is essential for making intrinsic interpretations. Although ${\sigma}$ is protected on the m-TSDS, ${\kappa}$ is greatly influenced by the disorder on the topological surface, giving a dissimilar effect between topologically protected electronic conduction and phonon transport.
Single crystals of type I clathrate \(\hbox {K}_{8}\hbox {Zn}_4\hbox {Sn}_{42}\) and \(\hbox {K}_8\hbox {In}_8\hbox {Sn}_{38}\) were grown by the flux method. The structure properties of both clathrates were investigated by single-crystal x-ray diffraction. Both clathrates crystallize in space group \(Pm\bar{3}n\), and no phase transition was observed in the investigated temperature range (100 K–450 K). The Debye temperature, the Einstein temperature, and the static disorder parameters of each clathrate were derived. The spread of the Einstein temperatures for \(\hbox {K}_8\hbox {In}_8\hbox {Sn}_{38}\), \(\hbox {K}_{8}\hbox {Zn}_4\hbox {Sn}_{42}\), and \(\hbox {K}_8\hbox {In}_8\hbox {Sn}_{38}\) suggest that the charge distribution on the cage framework is crucial to the energy of rattling mode in the tetrakaidecahedron of the type-I clathrate.
