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Intrinsic rattler-induced low thermal conductivity in Zintl type TlInTe2 Manoj K. Jana, Koushik Pal, Avinash Warankar, Pankaj Mandal, Umesh V. Waghmare, and Kanishka Biswas J. Am. Chem. Soc., Just Accepted Manuscript • DOI: 10.1021/jacs.7b01434 • Publication Date (Web): 06 Mar 2017 Downloaded from http://pubs.acs.org on March 6, 2017
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Intrinsic rattler-induced low thermal conductivity in Zintl type TlInTe2 Manoj K. Jana1, Koushik Pal2, Avinash Warankar3, Pankaj Mandal3, Umesh V. Waghmare2 and Kanishka Biswas1* 1
New Chemistry Unit and 2Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research (JNCASR), Bangalore, India. 3 Department of Chemistry, Indian Institute of Science Education and Research (IISER), Pune, India. Supporting Information Placeholder ABSTRACT: Understanding the nature of chemical bonding and lattice dynamics together with their influence on phonon-transport is essential to explore and design crystalline solids with ultralow thermal conductivity for various applications including thermoelectrics. TlInTe2 with interlocked rigid and weakly bound substructures, exhibits lattice thermal conductivity as low as ca. 0.5 W/mK near room temperature, owing to rattling dynamics of weakly bound Tl cations. Large displacements of Tl cations along the c-axis, driven by electrostatic repulsion between localized electron clouds on Tl and Te ions, are akin to those of rattling guests in caged-systems. Heat capacity of TlInTe2 exhibits a broad peak at low-temperatures due to contribution from Tlinduced low-frequency Einstein modes as also evidenced from THz time domain spectroscopy. First-principles calculations reveal a strong coupling between large-amplitude coherent optic vibrations of Tl-rattlers along the c-axis, with acoustic phonons which likely causes the low lattice thermal conductivity in TlInTe2. Crystalline solids exhibiting ultralow thermal conductivity are centric to the development of thermoelectrics, refractories and thermal barrier coatings for efficient energy-management. Thermal transport is indeed reckoned to be a limiting factor for realizing efficient thermoelectric (TE) materials.1 Extrinsic strategies such as alloying and nanostructuring 2 have been proven effective to suppress the lattice thermal conductivity (κLat ) but may also deteriorate electrical mobility. Solids with intrinsically low κLat are, therefore, practically attractive being capable of offering nearly independent control over electrical transport. Investigations on minimal κLat in certain TE solids have unveiled non-traditional phonon-scattering mechanisms viz. resonant phonon-scattering in filled-skutterudites3 and clathrates4 with randomly rattling guest-fillers, and thermal damping due to liquidlike atomic dynamics in Cu3SbSe35 and Cu2Se6. A common characteristic of the above materials is the crystallographic heterogeneity with coexisting rigid and fluctuating sublattices. Intrinsically low κLat in rock-salt I-V-VI chalcogenides7-9 and PbCuSbS310 was ascribed to the strong lattice-anharmonicity induced by electrostatic repulsions due to cationic ns2 lone pair electrons. Other intrinsic phenomena leading to low κLat include resonant bonding,11 rattling-modes,12 multicentre bonding13,14 and layered structure with significant anharmonicity.15 A microscopic understanding of the underlying correlation amongst structure, chemical bonding and lattice dynamics together with their impact on phonon transport is not only of fundamental interest but also
indispensable to explore and design new materials with ultralow thermal conductivity. Herein, we report an ultra-low κLat (< 0.5 W/mK) in Zintl type TIInTe2 in the 300-673 K range, which remains close to its theoretical minimum limit, κmin .We have investigated the aspects of structure and lattice dynamics responsible for the low κLat in TlInTe2 through low-temperature heat capacity and THz time domain spectroscopy, combined with first-principles calculations. TlInTe2 exhibits rattling dynamics of Tl+ cations inside the cagelike Thompson cubes formed by surrounding Te atoms. The ensuing low-frequency optical phonons scatter the acoustic phonons, thereby causing low κLat in TlInTe2. The latter represents a class of solids with relatively simple unit cells yet exhibiting low κLat due to hierarchical bonds and electrostatic repulsion between localized electron clouds on Tl and Te ions. TlInTe2 has a tetragonal crystal structure with I/4mcm space group as verified by Rietveld refinement of the powder X-ray diffraction data (Figure 1a and Table S1, SI). It constitutes anionic (InTe2)n-n chains alternating with chains of Tl+ cations (Figure 1b).16 Each In makes four covalent (sp3) bonds with four Te atoms forming tetrahedrons; the latter share their horizontal edges to form anionic chains along the crystallographic c-axis. The covalent bond distance between In and Te is about 2.81 Å being close to the sum of covalent radii of In (1.44 Å) and Te (1.35 Å). Each Tl is surrounded by eight Te atoms (of the anionic substructure) in a distorted square antiprismatic arrangement forming skewed cages referred to as Thompson cubes. The latter share squarefaces along the c-axis forming cationic chains (Figures 1b and 2c). The Tl-Te distance of 3.59 Å is close to the sum of ionic radii of Tl+ (1.59 Å) and Te2- (2.21 Å). TlInTe2 is structurally analogous to 1D Zintl compounds such as Ca3AlSb3, Ca5Al2Sb6 and Sr3GaSb3 constituting 1D anionic chains.17 The latter exhibit low κLat owing to complex unit cells (26-56 atoms per unit cell). Zintl-type structures with cationic and anionic substructures are adopted by electron-deficient compounds which cannot form all two-center-two-electron (2c-2e) covalent bonds. Electrons are transferred from the more electropositive cations to the anionic substructure where they are used to form 2c-2e covalent bonds.18 TlInTe2 adopts a Zintl-like structure as the sp3 hybridized In has only three valence electrons and hence, cannot form four 2c-2e bonds with Te atoms. Based on Zintl-Klemm rules of valence-counting,19 the more electropositive Tl atom in TlInTe2 donates one valence electron to the anionic chain and leaves behind its 6s2 lone pair to attain a formal valence of +1. Treating In as a part of anionic substructure, In being bonded to four Te atoms has a formal valence of -1, whereas Te
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being shared between two tetrahedra has a formal valence of 0. Accordingly, TlInTe2 is a valence compound described as Tl+In1 Te20 and exhibits semiconducting properties in agreement with our calculated electronic structure (see Figure S1a, SI). It is noted that TlInTe2, with only 16 atoms per unit cell, is simple relative to the aforementioned 1D Zintl compounds yet exhibits low κLat (~ 0.5 W/m.K at 300 K) owing to distinct lattice dynamics thereof.
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Figure 2. Plots of (a) total charge density and (b) electron localization function (ELF); c) ADPs of all the atoms plotted as 80 % probability ellipsoids. Yellow, violet and orange atoms denote Tl, In and Te atoms respectively; d) potential energy vs. displacements along crystallographic x- and z- directions of tetragonal unit cell. with its large ADP, and induces low-energy optical modes which scatter the heat-carrying acoustic phonons. It is important to note that the large anisotropic ADP of Tl+ cation is in contrast with small (< 0.015 Å2) and isotropic ADPs associated with the cations in other 1D Zintl compounds such as Ca3AlSb3 Ca5Al2Sb6 and Sr3GaSb3.21 The electrostatic repulsion between the localized electrons (lone pair) of Tl and the surrounding Te-ions plausibly drives large displacements of Tl and hence, large ADP along the c-axis. This also avoids dimerization of Tl+ and collective motion of Tl+ ions belonging to Tl-chain along c-axis.
Figure 1. a) Rietveld refinement of powder XRD pattern of TlInTe2 and b) crystal structure of TlInTe2 viewed down z-axis. Yellow, violet and orange atoms denote Tl, In and Te atoms respectively.
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As TlInTe2 consists of rigid and weakly bound substructures, we expect the chemical bonding in TlInTe2 to be different from solids with crystallographic homogeneity. We have examined the bonding environments in TlInTe2 with the aid of real-space descriptors such as charge density and electron localization function (ELF) calculated using the DFT. The calculated total charge density of TlInTe2 reveals overlapping charge densities of In and Te atoms within the InTe4 tetrahedra signifying a strong covalent bonding between them (Figure 2a). On the other hand, the more electropositive Tl is surrounded by non-overlapping, nearly spherical charge density due to 6s2 electron lone pair of Tl (Figure 2a) implying the interaction between Tl and the surrounding Te atoms to be electrostatic in nature. ELF estimates the degree of electron localization in a solid taking into account the local influence of the Pauli repulsion. As seen from the ELF map shown in Figure 2b, spherical electron localization around Tl is associated with its 6s2 lone pair, whereas a lobe-shaped asymmetrically distributed electron cloud around Te arises from the 5s2 lone pair of Te, partially hybridized as permitted by its site symmetry. The atomic displacement parameter (ADP) measures the meansquare displacement of an atom about its equilibrium position in a crystal. ADPs were obtained from the atom-refinement of powder XRD pattern (see Table S1, SI). In and Te atoms are associated with isotropic ADPs whereas Tl is associated with a large anisotropic ADP (U3'3' ~ 0.07 Å2 at 300 K) with its maximum displacement being along the c-axis (Figure 2c and Table S1, SI). Large ADP implies a weak bonding and is characteristic of rattlers, for instance, in filled-skutterudites.3,20 Tl can, therefore, be regarded as a rattler in TlInTe2 with the surrounding Thompson cage of Te-atoms resembling the over-sized cages in filledskutterudites and clathrates. Given the large ADP of Tl, phonon scattering mechanism beyond traditional scattering processes is expected to operate causing the low κLat observed in TlInTe2. To get an insight into atomic-level dynamics, we have calculated the potential energy curves by off-centering the atoms relative to their static equilibrium positions along the x- and zdirections. It is clear from figure 2d that In and Te atoms are confined in steep potential wells whereas Tl atom is located in a flat potential well suggesting that Tl atoms would easily rattle within hallow Thompson cages with large amplitudes, especially along the z-axis (c-axis). The flat potential well of Tl is consistent
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Figure 3. a) κLat of TlInTe2 measured between 300 and 673 K. The dashed line is the theoretical κmin of TlInTe2; b) Cp/T vs. T2 plot in 2-30 K range. The red solid line is calculated using combined Debye-Einstein model. The individual contributions from electronic (γ), Debye (β) and the three Einstein terms (E1, E2, E3) are also plotted. Cp/T3 vs. T plot in the inset shows a broad peak that can be fitted only with combined Debye-Einstein model and not the Debye model alone (green line). Figure 3a shows the temperature-dependent κLat of hot-pressed TlInTe2 in the 300-673 K range. It varies slightly from about 0.46 W/mK at 300 K to 0.31 W/mK at 673 K. The dotted line corresponds to the theoretical minimum (κmin ) of TlInTe2 estimated using Cahill's model (Equation S1, SI) which assumes a random walk of energy between localized oscillators of varying sizes and frequencies.22 κmin of TlInTe2 is estimated to be about 0.28 W/mK by using calculated values of sound velocities and mode Debye temperatures (see Table S2, SI). It is interesting to note that κLat of TlInTe2 is close to the estimated κmin throughout the temperature range investigated.
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For clathrates and filled-skutterudites where a set of weakly bound atoms rattle within oversized cages (in contrast to Tl-chains here), the rattling atoms are treated as independent harmonic oscillators (or Einstein oscillators) and the remaining lattice is treated within Debye model.4 Thermodynamic properties such as specific heat capacity (Cp) of the above compounds have been successfully interpreted considering Einstein modes in a Debye host.4 Figure 3b shows the low-temperature Cp of TlInTe2 in the range of 2-30 K. The plot of Cp/T vs. T2 can be well fitted by using the combined Debye-Einstein model23: 𝐶𝑝 𝑇
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In the above Eq., the first term denotes the electronic contribution and the second term, to the Debye lattice contribution with β = C.(12π4NAkB/5).(ΘD)-3 , where NA, kB and ΘD are Avogadro number, Boltzmann constant and characteristic Debye temperature respectively. The parameter C is given as C = 1 − 𝑛 𝐴𝑛 / 3𝑁𝑅, where N is the number of atoms per formula unit and R is the gas constant (8.314 J / mol. K). The third term represents the contribution from Einstein oscillator modes where An is the prefactor of the nth Einstein oscillator mode. The various fitting parameters are listed in Table S3, SI. A minimum of three Einstein modes are required to adequately model the temperaturedependence of Cp, whose characteristic temperatures were estimated though fitting to be ΘE1 = 24.8 ± 3.9 K, ΘE2 = 44.5 ± 4.1 K, and ΘE3 = 79.8 ± 5.1 K. The estimated Debye temperature (ΘD) of TlInTe2 is 250 K. At low temperatures, Cp exhibits a broad peak in the 5-15 K range as seen clearly in the Cp/T3 vs. T plot (inset of Figure 3b); the broad peak can be fitted only by using combined Debye-Einstein model as Debye model (green line) alone cannot suffice to reproduce the observed Cp data asserting the contribution from Einstein oscillators. This broad peak resembles the Boson-like hump observed in the low-T Cp of disordered glasses while in clathrates and skutterudites, it was ascribed to the excess phonon density of states (DOS) resulting from guest-induced lowlying optical modes.4 In TlInTe2, an excess contribution to Cp at low temperatures arises due to low-energy optical modes originating from weakly bound Tl-rattlers, which manifest as the Einstein oscillators. These low-lying optical modes couple with heatcarrying acoustic modes decreasing the group velocities of the latter and thereby suppressing κLat . The calculated phonon dispersion (figure 4a) exhibits several low-frequency phonon modes starting from ca. 12.4 cm-1 at the Γpoint and dispersing to higher frequencies along high-symmetry directions in the Brillouin zone. The calculated phononfrequencies at the Γ-point are listed in Table S4 in SI. A striking feature of phonon dispersion plot is the presence of a nondispersive branch along Γ-X-M-Γ path. The corresponding eigendisplacements viewed at the Γ, X and M points essentially constitute large-amplitude coherent vibration of Tl atoms along the caxis (see Figure S2, SI). Beyond the Γ-point, optic-acoustic coupling is discernible from the avoided-crossing feature of the phonon dispersion (inset of Figure 4a). The cut-off frequencies of acoustic phonons lie below 45 cm-1 and the average sound velocities are quite low (Table S2, SI). Atom-projected phonon DOS in Figure 4b shows that the dominant contribution in the low-energy region (< 50 cm-1) comes from Tl atom further indicating that the lowenergy phonons are mainly dictated by Tl-vibrations. The lowest optical phonon at 12.4 cm-1 is in reasonable agreement with the lowest Einstein mode (ΘE1 = 24.8 K) obtained from the fittinganalysis of the low-T Cp. It is also lower than the lowest optical phonon in low-κ α-MgAgSb (κLat =0.6 W m−1K−1 at 300 K).14 In α-MgAgSb, the low-frequency optical phonons arise from weak multicenter bonding interactions and reduce the κLat through re-
sonant phonon scattering. Similar low-frequency optic modes have been shown to cause low κLat in filled-skutterudites, clathrates and Cu-based chalcogenides.23,24 In TlInTe2, the lowfrequency optical modes arise from rattling Tl atoms and couple with heat-carrying acoustic phonons through symmetry-allowed interactions as clearly evident from the avoided-crossing in the phonon dispersion. Secondly, the flat non-dispersive nature of optical branch suggests that the coupling exists at all wavelengths of optic mode (inset of Fig. 4a). It is thus clear from the low-T Cp and first-principles analysis, that Tl-induced low-energy optical modes play an important role in causing low κLat . (a)
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Figure 4. a) Calculated phonon dispersion of TlInTe2. Inset shows the avoided-crossing between green and red branches near the Γpoint due to optical-acoustic coupling, b) phonon DOS showing the dominant contribution of Tl atom in the low-frequency region, c) dispersion of mode Grüneisen parameter along various k-points for the lowest flat branch, d) absorption coefficient of TlInTe2 as a function of THz frequency at room temperature. Grüneisen parameter (γ) quantifies the strength of anharmonicity in a solid. We have determined the k-dispersion of mode Grüneisen parameters (𝛾𝑖 ) at two different volumes in a finitedifference method. The aforementioned flat phonon branch shows anomalously high 𝛾𝑖 of ∼ 60 along M-Γ path (Figure 4c); the high 𝛾𝑖 may arise due to a) flat potential well of Tl (low phonon frequency) and b) dependence of restoring force on volume via electrostatic repulsion between Tl and the surrounding Te ions. At high-temperatures where the Umklapp phonon scattering is dominant, κLat decays as 𝛾𝑖2 .7 Therefore, such a high value of 𝛾𝑖 indeed reflects strong anharmonicity and phonon-phonon interactions in TlInTe29 and also confirms the dominant role of localized and low-frequency rattling mode of Tl cations in the reduction of κLat in TlInTe2. To experimentally verify the presence of low-frequency optical modes, we have carried out Terahertz time-domain spectroscopy (THz-TDS) (see methods, and Figures S3 and S4, SI).25 Figure 4d shows the plot of absorption coefficient as a function of THz frequency, obtained at 300 K. There are three distinct peaks below 1.5 THz in the THz absorption plot at about 0.5, 0.9 and 1.2 THz which are in reasonable agreement with the three aforementioned Einstein modes and the calculated low-energy optical phonons (see Table S4, SI). In summary, TlInTe2 manifests hierarchical chemical bonding with a rigid covalent framework interlocked with weakly bound ionic substructure comprising of Tl+ cations. The latter act as intrinsic rattlers akin to guest-rattlers in filled-skutterudites. The large displacement of Tl atom along the c-axis is driven by electrostatic repulsion between localized electron clouds around Tl
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and surrounding Te atoms. Both low-T Cp and THz-TDS reveal the low-energy optical phonons resulting from weakly bound Tlrattlers. First-principles calculations reveal strong optical-acoustic coupling which results in anharmonic damped vibration of Tlcations along the c-axis. Strong optical-acoustic coupling together with the low sound velocities and cut-off frequencies leads to κLat as low as ca. 0.5 W/mK at 300 K. We propose that large ADPs associated with a specific set of atoms (i.e. hierarchical bonding) besides rightly oriented electron lone pairs should serve as indicators of low thermal conductivity, and guide in exploring new materials for TE applications. ASSOCIATED CONTENT
Supporting Information Methods, THz-TD spectra, Cp-fitting parameters, TE properties, calculated sound velocities, gamma-point phonon frequencies and Eigen displacements. AUTHOR INFORMATION
Corresponding Author *
[email protected] Notes The authors declare no competing financial interests. ACKNOWLEDGMENT KB thanks SERB (EMR/2016/000651), Sheik Saqr Lab and JNCASR for funding. MKJ thanks CSIR for fellowship. PM thanks SERB (EMR/2016/003734). UVW thanks DST for JCB National fellowship. We thank P. S. Anil Kumar (IISc) for low T heat capacity measurement. We thank Prof. C. N. R. Rao for the encouragement. REFERENCES (1) Sootsman, J. R.; Chung, D. Y.; Kanatzidis, M. G. Angew. Chem. Int. Ed. 2009, 48, 8616. (2) a) Biswas, K.; He, J.; Blum, I. D.; Wu, C.-I.; Hogan, T. P.; Seidman, D. N.; Dravid, V. P.; Kanatzidis, M. G. Nature 2012, 489, 414;b) Poudel, B.; Hao, Q.; Ma, Y.; Lan, Y.; Minnich, A.; Yu, B.; Yan, X.; Wang, D.; Muto, A.; Vashaee, D.; Chen, X.; Liu, J.; Dresselhaus, M. S.; Chen, G.; Ren, Z. Science 2008, 320, 634. (3) Shi, X.; Yang, J.; Salvador, J. R.; Chi, M.; Cho, J. Y.; Wang, H.; Bai, S.; Yang, J.; Zhang, W.; Chen, L. J. Am. Chem. Soc. 2011, 133, 7837. (4) Takabatake, T.; Suekuni, K.; Nakayama, T.; Kaneshita, E. Rev. Mod. Phys. 2014, 86, 669. (5) Qiu, W.; Xi, L.; Wei, P.; Ke, X.; Yang, J.; Zhang, W. Proc. Natl. Acad. Sci. 2014, 111, 15031. (6) Liu, H.; Shi, X.; Xu, F.; Zhang, L.; Zhang, W.; Chen, L.; Li, Q.; Uher, C.; Day, T.; Snyder, G. J. Nat Mater 2012, 11, 422.
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