Intrinsic rattler-induced low thermal conductivity in Zintl type TlInTe 2

Transcription

1 Supporting Information Intrinsic rattler-induced low thermal conductivity in Zintl type TlInTe 2 Manoj K. Jana 1, Koushik Pal 2, Avinash Warankar 3, Pankaj Mandal 3, Umesh V. Waghmare 2 and Kanishka Biswas 1, * 1 New Chemistry Unit and 2 Theoretical 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. * kanishka@jncasr.ac.in S1

2 Methods Synthesis. Polycrystalline ingots of TlInTe 2 were prepared by melting stoichiometric quantities of high-purity Tl, In and Te (total weight of 6 g) in sealed carbon-coated quartz ampoules, evacuated at high vacuum of 10-5 torr. The contents were heated up to 1123 K in 7 hr, soaked at this temperature for 10 hr and cooled to room temperature in 15 hr. Powder X-ray diffraction (PXRD). PXRD patterns for all the samples were recorded on Bruker D8 diffractometer using Cu Kα (λ= Å) radiation. Structure refinement was carried out using GSAS crystallographic analysis program. 1 Rapid induction hot-pressing. Finely powdered samples were loaded into cylindrical graphite dies (10 mm inner diameter), ramped up to 723 K in 150 sec under Ar atmosphere in an induction-furnace, pressed at ca. 47 MPa for five minutes and subsequently cooled to room temperature. The as-obtained cylinder (ca. 9 mm x 10 mm) and disc (ca. 10 mm x 2.5 mm) shaped samples were used for electrical and thermal transport measurements respectively. The density of the pellets, measured using Archimedes method, is more than 98 % of the theoretical density of 7.3 g/cm -3. Electrical and thermal transport. Electrical conductivity (σ) and Seebeck coefficient (S) were simultaneously measured along the hot-pressing direction under He-atmosphere from 300 K up to 673 K using ULVAC-RIKO ZEM-3 instrument. Rectangular bar shaped samples (ca mm 3 ) cut from cylindrical samples were used for the electrical measurements (Figure S6).The thermal diffusivity, D, was measured between 300 K and 673 K using laser flash diffusivity technique in Netzsch LFA-457 instrument. The thermal diffusivity was measured along the same direction as that for electrical transport measurement i.e, along the hot-pressing direction. Disc-shaped pellets with ca. 10 mm x 2.5 mm dimensions were used for thermal transport measurement. Total thermal conductivity (κ tot ) was estimated using the relation, κ tot =DxC p xρ, where ρ is the density of the sample and C p is the specific heat capacity measured with respect to pyroceram reference-standard in Netzsch LFA-457 instrument (Figure S6). Lattice thermal conductivity (κ Lat ) is extracted by subtracting electronic thermal conductivity ( κ el ) from total thermal conductivity. κ el is calculated using the Wiedemann Franz law, κ el = LσT, where σ is the electrical conductivity and L is the temperature dependent Lorentz number. L is estimated from reduced chemical potential and temperature dependent Seebeck coefficient using single parabolic band model described elsewhere. 2 Due to very low σ, κ Lat κ tot for TlInTe 2. S2

3 Computational details. Our first-principles calculations are based on density functional theory (DFT) using Quantum espresso (QE) code. 3 It uses plane wave basis to represent wavefunctions and charge density and pseudopotentials to capture the effect of potential arising from the nucleus and core electrons of an atom. We used norm-conserving pseudopotentials in our calculations. We treated the exchange and correlation energy of the electrons with a generalized gradient approximated (GGA) 4 functional as parametrized by Perdew, Burke and Ernzerhof. 5 The expansion of electronic wave function and charge density in plane wave basis was truncated with cut-off energies of 60 Ry and 240 Ry respectively. Brillouin Zone (BZ) integrations were sampled on a uniform mesh of k-points. The discontinuity in the occupations number of electronic states near the gap was smeared with Fermi-Dirac distribution functions with a broadening of k B T = Ry. Fully optimized lattice constants of TlInTe 2 agree quite well with that of its experimental values (see below). We have determined the electronic structure and lattice dynamical properties at the optimized crystal structure of TlInTe 2. We have used QE implementation of density functional perturbation theory (DFPT) 6 to obtain phonon dispersion of TlInTe 2. In this, the interatomic force constant matrices were first obtained on a mesh of q-points in the BZ, and were Fourier interpolated at an arbitrary q-vector. Grüneisen parameter (γ) measures the degree of anharmonicity of phonons in a material. We have estimatedγ i of each of the phonon modes using finite difference formula (γ i dω = V/ω i i ) and taking phonon dispersion calculated dv at two volumes (V 0 and 0.96V 0, V 0 being the equilibrium volume at 0 GPa). The average Grüneisen parameter is estimated to be 1.8 using the calculated sound velocities in table S2 and equations described in the supporting information of reference S7. Terahertz time domain spectroscopy. In order to probe low-energy optical phonons, Terahertz (THz)-Time Domain Spectroscopy (TDS) was carried out on TlInTe 2 sample (a disc of ~7 mm diameter and 480 µm thickness) at room temperature. TDS is a non-contact way of measuring material dielectric response. 8 Our THz time domain spectrometer is based on an amplified ultrafast laser system, consisting of a Ti:Sapphire oscillator (Spectra Physics Tsunami ) and regenerative amplifier (Spectra Physics Spitfire Pro). The amplifier output has peak wavelength at 800 nm, pulse duration of 50 fs, 1 KHz repetition rate, and 4 W of total power. We use half of the laser power for generation and coherent detection of THz radiation using air photonics. 9 The schematic of the setup is shown in Figure S3 in SI and the details are described elsewhere. 10 The entire THz path is enclosed and continuously purged with dry nitrogen to avoid THz absorption by water vapour. All THz data were collected at room S3

4 temperature. Because of very high absorption coefficient of the sample at the concerned spectral range ( THz), THz-TDS in transmission mode shows very little THz transmission through the sample. Hence, we have collected the THz-TDS in reflection geometry with an incidence angle of 45º. Time domain THz electric field reflected from a reference (E Si (t)) and the sample (E sam (t)) were collected. High resistivity Silicon wafer was used as reference. The ratio of the Fourier transforms of the time domain sample and reference signals is related to the refractive indices of the sample and reference according to the following Fresnel equation for reflection: 11 2 nsam cosθ n air n2 sam n 2 air sin 2 θ R ω = E sam(ω) E ref (ω) = n2 sam cosθ+n air n2 sam n 2 air sin 2 θ n 2 si cosθ nair n 2 si nair 2 sin 2 θ n 2 si cosθ+nair n 2 si nair 2 sin 2 θ Complex refractive index (n sam = n + ik ) of the sample was calculated numerically. Refractive indices of silicon (n si =3.45) and air (n air = 1) are almost constant over entire range of detected THz frequencies. Real part (n) of complex refractive index is actual refractive index of sample while the imaginary part, extinction coefficient (k), is related to absorption coefficient (α) as: α = 2ωk/c, where ω is angular frequency and c is the speed of light. Since the absorption by the sample is very high above 5 THz even in reflection mode, the optical parameters (n and ) obtained may not be reliable beyond this frequency range. S4

5 Table S1. Structural parameters of Rietveld refinement. Space group: I4/mcm; a=b= (27); c= (28); unit cell volume=516.94(5) Atom Wyck. x/a y/b z/c U iso In 4b Te 8h U 11 U 22 U 33 Tl 4a Reduced χ 2 =5.6; R p = ; wr p = Table S2. Calculated Phonon sound velocities in the vicinity of Brillouin zone centre (v TA1, v TA2, v LA ), and cut-off frequencies for longitudinal (LA) and transverse acoustic phonon branches (TA1, TA2) along the Γ-X, Γ -Z and Γ-M directions in the Brillouin zone. The cut-off frequency (ω max ) is the highest acoustic frequency along a given direction and i is the polarization index (i.e. LA or TA1 or TA2). Direction v LA v TA1 v TA2 ω max ω max ω max (m/s) (m/s) (m/s) (cm -1 ) (cm -1 ) (cm -1 ) LA TA1 TA2 Γ-X Γ-M Γ-Z Average S5

6 Table S3. Fitting parameters for modelling C p /T vs. T 2 plot given in Figure 3b in main text. Parameter γ /10-3 J mol -1 K ± β /10-4 J mol -1 K ± Θ E1 /K ± (~ 0.52 THz) Θ E2 /K Θ E3 /K ± (~ 0.92 THz) ± (~ 1.66 THz) Θ D (K) 250 R χ S6

7 Table S4. Calculated phonon frequencies of zone centre optical phonons in TlInTe 2 S. No Mode Frequency in cm -1 1 A 2u A 2g E g E u E g A 2g E u B 1g B 2g B 1u A 1g E g A 2u E u B 2g S7

8 (a) (b) (c) y z x (d) Figure S1 a) Electronic structure of TlInTe 2 revealing a direct band gap of ca. 0.5 ev at the Z-point and an indirect band gap of ca ev between the valence band maximum (VBM) and conduction band minimum (CBM) appearing at M point and along X-P lines respectively in the Brillouin zone shown in (b). Electronic structure was calculated at the experimental lattice constant of primitive unit cell shown in (c). Red, grey and blue spheres denote In, Tl and Te atoms respectively. d) Total and atom-projected electronic density of states (DOS) of TlInTe 2. Electronic DOS shows the contribution of Tl-6s orbital to the valence band near the Fermi level (E=0 ev). S8

9 Γ-X X-M M-Γ z y x Figure S2 Eigen-displacements associated with the anharmonic flat phonon branch along Γ- X-M- Γ line in reciprocal space, showing dominant vibrations of Tl + cations parallel to z-axis (c-axis of tetragonal unit cell). Yellow, violet and orange spheres denote Tl, In and Te atoms respectively. S9

10 Figure S3. Schematic of THz-spectrometer S10

11 (a) (b) Figure S4: a) Time domain and corresponding b) frequency domain amplitude spectra in reflection geometry with an incidence angle of 45º. High resistivity silicon has been used as reference. (c) S11

12 2.5 (a) (b) (S/cm) S ( V/K) S 2 ( W/cm.K 2 ) (c) T(K) zt T(K) (e) (d) T(K) (f) T (K) D (mm 2 /s) C p (J/g/K) Dulong Petit value T (K) T(K) Figure S5. High-temperature electrical and thermal properties. a) electical conductivity (σ), b) Seebeck coefficient (S), c) power factor (σs 2 ) and d) thermoelectric figure of merit (zt), e) Diffusivity (D) and f) specific heat capacity (C p ) of TlInTe 2 measured parallel to pressingdirection. S12

13 // (W/m.K) T(K) Figure S6. Thermal conductivity of TlInTe 2, measured parallel (//) and perpendicular ( ) to the pressing-direction. S13

14 (a) (b) (c) Figure S7 Eigen-displacements associated with the lowest three optical modes at the Brillouin zone centre all of which show dominant vibrations of Tl + cations parallel to z-axis (c-axis of tetragonal unit cell). Yellow, violet and orange spheres denote Tl, In and Te atoms respectively. Equation S1: Calculation of κ min of TlInTe 2 κ min of TlInTe 2 is estimated using Cahill's model which assumes a random walk of energy between localized oscillators of varying sizes and frequencies 12 : κ min = π k b n a 2 3 v i T θ i 2 0 θ i T x 3 e x e x 1 2 dx i where the summation is taken over three acoustic modes (one longitudinal (LA) and two transverse (TA) modes), k b is the Boltzmann constant, n a is the number density of atoms (~ 3.1 x cm -3 for TlInTe 2 ), θ i is the cut-off frequency for each polarization branch (in the units of K), v i is the sound velocity of each polarization branch and i is the polarization index (TA 1, TA 2 and LA). κ min of TlInTe 2 is estimated to be about 0.28 W/mK by using calculated values of v i and θ i (see Table S2, SI). S14

15 References (S1) Toby, B. J. Appl. Cryst. 2001, 34, 210. (S2) a) Zevalkink, A.; Toberer, E. S.; Zeier, W. G.; Flage-Larsen, E.; Snyder, G. J. Energy Environ. Sci. 2011, 4, 510; b) 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. (S3) Giannozzi, P.; Baroni, S.; Nicola Bonini; Matteo Calandra; Roberto Car; Cavazzoni, C.; Davide Ceresol; Guido L Chiarotti; Matteo Cococcioni; Ismaila Dabo; Andrea Dal Corso; Stefano de Gironcoli; Stefano Fabris; Guido Fratesi; Ralph Gebauer; Uwe Gerstmann; Christos Gougoussis; Anton Kokalj; Michele Lazzeri; Layla Martin-Samos; Nicola Marzari; Francesco Mauri; Riccardo Mazzarello; Stefano Paolini; Alfredo Pasquarello; Lorenzo Paulatto; Carlo Sbraccia; Sandro Scandolo; Gabriele Sclauzero; Ari P Seitsonen; Alexander Smogunov; Umari, P.; Wentzcovitch, R. M. J. Phys.: Condens. Matter 2009, 21, (S4) Hua, X.; Chen, X.; Goddard, W. A. Phys. Rev. B 1997, 55, (S5) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1996, 77, (S6) Baroni, S.; de Gironcoli, S.; Dal Corso, A.; Giannozzi, P. Rev. Mod. Phys. 2001, 73, 515. (S7) Ying, P.; Li, X.; Wang, Y.; Yang, J.; Fu, C.; Zhang, W.; Zhao, X.; Zhu, T. Adv. Funct. Mater. 2017, 27, (S8) a) Beard, M. C.; Turner, G. M.; Schmuttenmaer, C. A. J. Phys. Chem. B 2002, 106, 7146;b) Jepsen, P. U.; Cooke, D. G.; Koch, M. Laser & Photon. Rev. 2011, 5, 124. (S9) a) Baxter, J. B.; Guglietta, G. W. Anal. Chem.2011, 83, 4342;b) Clough, B.; Dai, J.; Zhang, X.-C. Mater. Today 2012, 15, 50. (S10) Yettapu, G. R.; Talukdar, D.; Sarkar, S.; Swarnkar, A.; Nag, A.; Ghosh, P.; Mandal, P. Nano Lett. 2016, 16, (S11) a) Jepsen, P. U.; Jensen, J. K.; Møller, U. Opt. Express 2008, 16, 9318;b) Jepsen, P. U.; Møller, U.; Merbold, H. Opt. Express 2007, 15, (S12) Cahill, D. G.; Watson, S. K.; Pohl, R. O. Phys. Rev. B 1992, 46, S15