Two-Dimensional CsAg5Te3-xSx Semiconductors: Multi-Anion

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Two-Dimensional CsAgTe S Semiconductors: Multi-Anion Chalcogenides with Dynamic Disorder and Ultralow Thermal Conductivity James M Hodges, Yi Xia, Christos D. Malliakas, Grant C. B. Alexander, Maria K. Y. Chan, and Mercouri G. Kanatzidis Chem. Mater., Just Accepted Manuscript • DOI: 10.1021/acs.chemmater.8b03306 • Publication Date (Web): 12 Sep 2018 Downloaded from http://pubs.acs.org on September 13, 2018

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Chemistry of Materials

Two-Dimensional CsAg5Te3-xSx Semiconductors: Multi-Anion Chalcogenides with Dynamic Disorder and Ultralow Thermal Conductivity James M. Hodgesa, Yi Xiab, Christos D. Malliakasa, Grant C. B. Alexandera, Maria K. Y. Chanb, and Mercouri G. Kanatzidisa,d a

Department of Chemistry, Northwestern University, Evanston, Illinois 60208, USA. Center for Nanoscale Materials, Argonne National Laboratory, Argonne, Illinois 60439, USA. c Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, USA. d Materials Science Division, Argonne National Laboratory, Illinois 60439, USA. b

ABSTRACT: Metal chalcogenides underpin a wide variety of energy-related applications and are ideal systems for probing lattice dynamics and fundamental transport phenomena. Here, we describe the synthesis and transport properties of CsAg5TeS2 and its solid solution CsAg5Te3-xSx (x = 1-2), new semiconductors with tunable bandgaps ranging from 0.17 to 0.30 eV. CsAg5TeS2 has a fully ordered two-dimensional structure that includes a group of Ag atoms in a heteroleptic, tetrahedral coordination geometry (AgTe2S2). Single crystal X-ray diffraction indicates that the compounds crystallize in the tetragonal space group P4/mmm, while pair-distribution function (PDF) analysis reveals off-centering at the heteroleptic Ag sites, signifying a lower symmetry I4/mcm space group. The underlying disorder acts as a phonon-blocking mechanism that helps facilitate ultralow lattice thermal conductivity below 0.40 W⋅m-1⋅K-1 at ~300 K and highlights the importance of local disorder in thermal transport. Density functional theory (DFT) provides additional insight into the electronic and thermal properties of the materials, which are good candidates for p-type thermoelectrics.

INTRODUCTION The chemical bonds in metal chalcogenides are less ionic than those found in the corresponding oxides and halides, which affords them with smaller bandgaps and greater carrier mobility.1,2 These physicochemical attributes, along with their high air and moisture stability, make the chalcogenides useful materials in an array of energy-related applications. For example, PbTe and Bi2Te3 are the best systems for thermoelectric power generation due to their small bandgaps and polar covalent bonds, which facilitate high carrier mobility and low thermal conductivity.3–5

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Although simple binaries are the most studied, ternary and quaternary systems offer greater structural diversity and in many cases, more sophisticated functionality.

In the last two decades, there have been an impressive number of new ternary and quaternary chalcogenides reported, which is due to advances in solid-state synthesis.6 In particular, complex chalcogenides that incorporate alkali metals exhibit remarkable structural diversity and span a broad range of physicochemical properties. The complex crystal chemistry and large unit cells in these compounds affords them with intrinsically low lattice thermal conductivity (κlatt), making them especially attractive materials for thermoelectric applications.7–10 Recently, several ternary chalcogenides have emerged as high-performance thermoelectric materials, many of which include silver as a primary metal.11–13 Silver atoms form soft covalent bonds with chalcogen anions and can adopt a variety of asymmetric coordination geometries. The anharmonic bonding in these systems suppress phonon velocities while also yielding low-lying optical modes that can scatter acoustic phonons.11 Accordingly, some of the lowest κlatt values are found in ternary silver-chalcogenide systems.14,15

Recently, Lin et al. reported the thermoelectric properties of CsAg5Te3, a narrow-gap semiconductor with a complex three-dimensional structure (Figure 1), which exhibits a figure-ofmerit ZT of 1.5 at 730 K.16 The high performance was attributed to ultralow κlatt below 0.2 W⋅m1

⋅K-1 in the 300 to 750 K temperature range, the lowest values reported for a state-of-the-art

thermoelectric material. It was shown that the low κlatt was related to the complex crystal structure and asymmetric bonding in CsAg5Te3. Specifically, a subset of Ag atoms with long AgTe bond distances were found to vibrate in a “concerted rattling” mechanism, creating lowfrequency optical modes that interact with heat-carrying acoustic phonons. This powerful new phonon-scattering mechanism placed CsAg5Te3 as a promising new thermoelectric material and demonstrated its utility as a model system for understanding ultralow thermal conductivity.

Building on this result, we attempted to further probe the properties of CsAg5Te3 by alloying sulfur onto the tellurium sites. Unexpectedly, we find that when tellurium is partially replaced with sulfur, a new ordered quaternary compound is formed, which adopts a layered structure not found in the known single-anion CsAg5Q3 (Q = Se, Te) analogues.


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In this contribution, we describe the synthesis, crystal structure, and transport properties of CsAg5TeS2 (Figure 1) and its solid solution CsAg5Te3-xSx (x = 1-2). Single crystal diffraction indicates that these materials crystallize in a two-dimensional structure composed of alternating layers of Cs+ and [Ag5TeS2]- with the P4/mmm space group (a = 4.3160(3) Å, c = 11.2486(8) Å at room temperature). CsAg5TeS2 is fully ordered with Ag atoms in both square planar (AgTe4) and heteroleptic tetrahedral geometries (AgTe2S2). The compounds have optical bandgaps ranging from 0.17 eV to 0.30 eV and exhibit ultralow thermal conductivity below 0.40 W⋅m-1⋅K1

over the temperature range of 300 to 800 K. Pair distribution function (PDF) analysis in

conjunction with density functional theory (DFT) calculations indicate that the heteroleptic Ag atoms are positionally off-centered about their ideal lattice positions, which helps to facilitate glass-like phonon transport. The atomic displacement parameters (ADP) for the off-centered Ag atom increases faster with temperature than the other atoms in the unit cell between 100 and 300 K, providing evidence for dynamic disorder. We believe that this mechanism, which is different from “concerted rattling”, is an important design feature for suppressing phonon transport in thermoelectric materials.

EXPERIMENTAL SECTION Materials. All chemicals were used as received: Cesium metal (Cs; 99.8%) was purchased from Alfa Aesar. Sulfur flakes (S; 99.99%) and silver metal (Ag; 99.99%) were purchased from Sigma Aldrich. Tellurium shot (Te; 99.999%) and selenium shot (Se; 99.999%) were purchased from American Elements. The Cs2S precursor was obtained by reacting stoichiometric amounts of elemental cesium and sulfur in liquid ammonia, which has been described in detail elsewhere.17

Synthesis. CsAg5Te3-xSx (x = 1, 1.5, 2) samples were obtained by loading the appropriate amount of Cs2S, Ag, Te, and S into a 13 mm carbon-coated fused silica tube, which was flame sealed at a pressure of ~ 3×10-3 torr. The reaction tubes were placed into a tube furnace and heated to 723 K in 5 h and held at this temperature for 10 h to allow the S to melt. The samples were then heated to 1073 K in 5 h and then soaked at this temperature for 4 h, followed by slow cooling in the furnace. The resulting ingots contained single crystals larger than 1 mm that were used for single crystal diffraction.


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Powder X-ray Diffraction. The phase purity of the synthesized samples was determined by powder X-ray diffraction (pXRD). Data was collected using a Rigaku Miniflex powder X-ray diffractometer with Cu Kα radiation (λ = 1.5406 Å) with a 30 kV voltage and 15 mA current. Simulated pXRD patterns and visualization of the crystal structures was done with the Vesta software.18

Temperature-Dependent Powder X-ray Diffraction. A STOE-STADIMP high-resolution diffractometer equipped with an oven attachment was used to obtain temperature-dependent powder X-ray diffraction data. The CsAg5TeS2 ingot was ground into a fine powder and passed through a 53 µm sieve, and then diluted in 3:1 mass ratio with carbon powder (99.9%, Sigma Aldrich). The powder was packed into a 0.5 mm fused-silica capillary and flame sealed at ~ 3×10-3 torr. The line focused Cu X-ray tube was operated at 40 kV and 40 mA and the sample was spun during collection.

Scanning Electron Microscopy. Scanning electron microscopy (SEM) and energy-dispersive X-ray spectroscopy (SEM-EDS) were performed on a Hitachi S-3400 scanning electron microscope equipped with a PGT energy-dispersive X-ray analysis instrument. EDS was performed at 25 kV, 70 mA probe current and a 60 s acquisition time.

Fourier-Transform Infrared Spectroscopy. The optical bandgap of the CsAg5Te3-xSx (x = 1, 1.5, 2) samples was determined using Fourier-Transform Infrared Spectroscopy (FTIR). The data was collected using a Nicolet 6700 IR spectrometer under a flow of nitrogen. The collected reflectance data was converted to absorbance using the Kebulka-Munk equation (f(R) = (1R2)/2R = α/S, where R is the absolute reflectance, α is the absorption coefficient and S is the scattering coefficient).19

Differential Thermal Analysis. Differential thermal analysis (DTA) was performed using a Netzsch STA 449 F3 Jupiter simultaneous thermal analysis (STA) instrument. Samples were loaded into a carbon-coated fused silica ampule and flame-sealed at pressure of ~3×10-3 torr.


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Each sample was heated to 1073 K at a rate of 10 K/min and then cooled to 300 K at K/min, and this cycle was repeated one time.

Single Crystal Diffraction. Single crystal X-ray diffraction data for CsAgTeS2 (100 K and 300 K) was collected on a Bruker KAPPA APEX Diffractometer with a Mo Kα microsource and MX optics. The structure was solved by the direct method and refined on F2 using the SHELX14 program suite.20 All atoms were refined anisotropically. Data collection for CsAg5Te2S was performed on a STOE IPDS II diffractometer using Mo Kα radiation (λ = 0.71073 Å) operating at 50 kV and 40 mA at 293 K. Integration and numerical absorption corrections were performed on each structure using X-AREA, X-RED, and X-SHAPE.21 The structure was solved by the direct method and refined on F2 using the SHELX14 program suite.

Densification. The CsAgTeS2 ingot was ground into a fine powder using an agate mortar and pestle and then placed into a 12.7 mm diameter graphite die and densified by spark plasma sintering (SPS, SPS-211LX, Fuji Electronic Industrial Co., Ltd.) at 673 K for 10 min under an axial compressive pressure of 40 MPa while under dynamic vacuum. The density of the samples was determined using their physical dimensions and masses, and was found to be ~95% of the theoretical value. Electrical Properties. The temperature-dependent electrical conductivity (σ) and Seebeck coefficient (S) of the SPS-processed CsAgTeS2 pellet (~10×5×2 mm) was measured simultaneously using an ULVAC Riko ZEM-2 instrument under a low-pressure helium atmosphere. The bars were coated with BN to prevent outgassing, except at the points of the electrical contacts.

Thermal Conductivity. The temperature-dependent diffusivity (D) of the SPS-processed CsAgTeS2 pellet (~6×6×2 mm) was measured using a Netzsch LFA457 instrument, and analyzed using the Cowan model with pulse correction. The cut bars were coated with graphite to minimize radiative heat loss, and total thermal conductivity was calculated using the equation κtot = D×Cp×d, where d is density and Cp is heat capacity, which was estimated using the DulongPetit relationship, Cp = 3R/M, where R is the gas constant and M is the average molar mass. The


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lattice thermal conductivity (κlatt) was calculated by subtracting the electronic thermal conductivity (κelec) from κtot using the Wiedemann-Franz law, κelec=L⋅σ⋅T, where L is the Sommerfeld Lorentz number (2.45⋅10-8 Ω⋅W⋅K-2). The uncertainty in κtot is estimated to be 10%, which is a widely accepted value for this measurement.

Pair Distribution Function Analysis. The synchrotron X-ray total scattering measurements were performed on the 11-1D-B beam line at the Advanced Photon Source located at Argonne National Laboratory. The samples were prepared by transferring the CsAg5TeS2 powder into Kapton capillaries that were sealed with epoxy. From the coherent part Icoh(Q) of the measured total diffracted intensity of the material, we find the total scattering structure function, S(Q)22

I coh (Q) − ∑ c f (Q) i i S (Q) = 2 ∑ ci fi (Q)

2 +1

where the coherent intensity is corrected for background and other experimental effects and normalized by the flux and number of atoms in the sample. Here, ci and fi are the atomic concentration and X-ray atomic form factor, respectively, for the atomic species of type i. The momentum transfer, Q, is given by23 Q = 4π sin ϑ λ .

By Fourier transforming the expression Q[S(Q)-1] we have24

Q max G(r ) = (2 π ) ∫ Q[ S (Q) − 1] sin(Q ⋅ r )dQ Q=0 where G(r) is the atomic pair distribution function which is also defined as25

G(r) = 4π ⋅ r[ρ(r) − ρ ] 0 where ρ0 is the average atomic number density, ρ(r) is the atomic pair-density, and r is a radial distance. The function G(r) gives information about the number of atoms in a spherical shell of unit thickness at a distance r from a reference atom. Finally, the experimental G(r) can be compared and refined against a theoretical G(r) from a structural model given by26


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1 G(r ) + 4π ⋅ r ⋅ ρ = ∑∑ 0 r

ν µ

f (0) f (0)

ν

f (0) 2

µ

δ (r − r ) νµ .

Band Structure Calculations. The Vienna Ab initio Simulation Package (VASP) was used to perform density-functional-theory (DFT) calculations.27,28 The projector-augmented wave (PAW) method29,30 was used. For crystal structure relaxation, the revised Perdew-BurkeErnzerhof for solids (PBEsol)31 generalized gradient approximation (GGA)32 was used for the exchange-correlation (xc) functional.33 DFT calculation of the primitive cell for CsAg5TeS2 was performed using a 6×6×6 Γ-centered k-point mesh and a kinetic energy cutoff of 500 eV. The force and energy convergence thresholds were set to be 10-3 eV/Å and 10-8 eV, respectively. Since semi-local DFT functionals are well known to underestimate band gaps, we utilized the screened HSE0634 hybrid functional to compute the band structure along high symmetry lines of the Brillouin zone.

Phonon Dispersions. For lattice dynamics and thermal transport properties calculations, 2×2×2 supercell structures were constructed, which were sampled with 3×3×3 Γ-centered k-point mesh, to extract 2nd- and 3rd -order interatomic force constants (IFCs) for CsAg5SeS2. No explicit distance cutoff is imposed for 2nd-order IFCs by taking into account the cumulative IFCs,35 while the diameter cutoff of 3rd-order interactions was limited to 5.0 Å. In order to eliminate the imaginary phonon modes obtained from harmonic approximation at 0 K, structural stability at room temperature was further explored using an anharmonic phonon renormalization scheme we recently developed,36 which is based on extracting temperature-dependent IFCs through iteratively refining vibrational free energy. Both 2nd- and 3rd-order IFCs were simultaneously extracted using a recently developed direct method named compressive sensing lattice dynamics (CSLD).37 With obtained effective harmonic and anharmonic IFCs, phonon lifetimes were evaluated using Fermi’s golden rule by treating 3rd-order IFCs as perturbation to renormalized phonons,38 and linearized Boltzmann transport equation (BTE) was solved in an iterative manner to account for the non-equilibrium phonon distributions.39–41 The ShengBTE package,42 which was modified to accommodate CSLD, was used to perform all lattice dynamics calculations including the iterative solution of lattice thermal conductivity using a 12×12×12 q-point mesh.


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RESULTS AND DISCUSSION Synthesis and Characterization. Polycrystalline CsAg5Te3-xSx (x = 1, 1.5, 2) samples were synthesized by reacting the appropriate amount of Cs2S, Ag, Te, and S at 1073 K for 4h. The assynthesized ingots are observed to have a dark color with a slight purple luster as shown in the inset of Figure 2a. The ingots yielded crystals exceeding 1 mm in length that were suitable for single crystal diffraction, and the CsAg5TeS2 and CsAg5Te2S samples were found to adopt the same structure with the P4/mmm space group (Table S1). The pXRD patterns for the samples are shown in Figure 2a, along with the simulated pattern for CsAg5TeS2 obtained from single crystal analysis. Each sample exhibits all of the expected Bragg reflections and no observable impurities. The peaks in the pXRD shift to lower angles with increasing Te content, signifying an increase in unit cell volume (Figure 2b), which is consistent with solid-solution behavior. In order to determine the morphology and chemical homogeneity of CsAg5TeS2, SEM and SEMEDS was performed and the results are shown in Figure 3a. The SEM image shows a representative crystal that has dense flat surfaces, which are indicative of a layered material. The corresponding SEM-EDS maps for Cs, Ag, Te, and S show good chemical homogeneity, and the quantitative elemental analysis is consistent with the targeted composition. Diffuse reflectance spectra were obtained using FTIR and then converted to absorption using the Kebulka-Munk equation, and the absorption spectra for each sample shows a sharp optical transition (Figure 3b). To determine the bandgaps of the compounds, we plotted [(α/S)⋅hν]1/2 against photon energy (eV), where the x-intercept of the extrapolated linear region yielded the bandgap energy (Figure S1). This is equivalent to the Tauc plot analysis for an indirect electronic transition,43 which is predicted from the band structure calculations shown below. The measured bandgaps range from 0.17 to 0.30 eV, which is smaller than the 0.67 eV gap reported for CsAg5Te3. This is somewhat unexpected, since a low-dimensional sulfur-containing compound would typically have a larger bandgap then a three-dimensional telluride. We attribute this to the structural and bonding variances in the two compounds (see discussion below).

DTA was used to probe the thermal properties of CsAg5TeS2 and CsAg5Te2S, and the data are shown in Figure S2. Upon heating, CsAg5TeS2 shows a minor endothermic peak at 860 K and a


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more prominent (melting) peak at 893 K, with corresponding exothermic peaks at 886 K and 860 K upon cooling, respectively. Similarly, CsAg5Te2S shows an endothermic peak at 874 K and 905 K, along with exothermic peaks at 901 K and 874 K upon cooling. In order to determine if the minor peaks are due to a phase change, temperature-dependent pXRD was performed on CsAg5TeS2 using a diffractometer equipped with a capillary holder and heating stage (Figure S3). We observe no additional Bragg reflections in the pXRD pattern between 860 and the 890 K. Accordingly, we attribute the first endothermic peaks in the DTA curves to incongruent melting events that yield two slightly different compositions of the same phase, which are too close in composition to be distinguished by pXRD.

Crystal Structure. CsAg5TeS2 crystallizes in a two-dimensional structure with the P4/mmm space group, where a = 4.3160(3) Å, c = 11.2486(8) Å, V = 209.54(3) Å3, and has a calculated density of d = 6.847 g⋅cm-3. The structure is composed of alternating layers of Cs+ cations and [Ag5TeS2]- anionic slabs as shown in Figure 4a, and is structurally similar to RbAg5Se3 (P4/nbm). The anionic [Ag5TeS2] layer has two unique Ag sites, where Ag1 is found at the center of the layer and coordinated to Te in a square planar geometry with a bond distance of 3.0519(2) Å. The Ag1-Te square planar net is viewed along the c-axis in Figure 4b. On either side of the square planar net is a layer of Ag2 atoms, followed by a layer of S atoms that terminate the slab. The Ag2 atoms are coordinated to two Te and two S atoms in a heteroleptic, tetrahedral geometry with bond distances of 3.0885(4) Å and 2.5587(9) Å, respectively. Figure 4c shows a row of heteroleptic AgTe2S2 polyhedra, and to best of our knowledge, this is the only example of this structural motif. Although the Ag atoms in this compound are formally Ag(I), there are Ag1Ag2 distances of 3.0885(4) Å that are similar to the Ag2-Te bond lengths. We note that close Ag-Ag interactions are not uncommon in silver chalcogenides, and indeed, there are shorter AgAg distances in Ag2Te (2.84 Å) than in metallic Ag (2.89 Å).44 In CsAg5TeS2, the two different chalcogen atoms occupy distinct sites in the structure with no intermixing. The Te atoms are bound to four Ag1 atoms and eight Ag2 atoms in a cuboctahedral coordination geometry, while the S atoms are bound to four Ag1 atoms and four Cs atoms in a square antiprismatic arrangement. The Cs atoms sit between the layers and are bound to eight S atoms (four from each adjacent layer) with bond lengths of 3.6709(9) Å and has a cubic


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geometry. CsAg5Te2S adopts the same structure and P4/mmm space group, with a = 4.4637(6) Å, c = 11.335(2) Å, V = 225.86(8) Å3, and a calculated density of d = 7.097 g/cm3. The additional Te atoms in this compound mix with the S atoms at the edge of the slab (Figure S4).

Pair Distribution Function Analysis. In order to better understand the local structure of CsAg5TeS2, we performed PDF analysis. PDF is a powerful technique for probing atomic-scale disorder that cannot be detected using traditional diffraction methods.45–47 Unlike other crystallographic methods, PDF is a total scattering technique, which means both Bragg and diffuse scattering are included in the analysis. PDF studies both the long-range periodic structure (Bragg reflections) and the local structure imperfections (diffuse component of the diffraction pattern). The experimental PDF data for CsAg5TeS2, along with the pattern simulated from the ideal P4/mmm structure, is shown in Figure 5a. The primary bonds in the P4/mmm structure range from 2.6 Å to 3.1 Å, and accordingly, the major peak at ~ 3.0 Å is attributed to these primary interactions. The medium and long range ordering from 2.0 Å to 10 Å is in good agreement with the obtained single crystal model, and yields a reasonable goodness-of-fit (Rw) of approximately 20%. However, at shorter distance (~2.5 Å), we observe a shoulder on the left side of the main peak at ~3 Å, which is unaccounted for in the crystallographic model (Figure 5a inset). The good fit in the long range and the poor fit in the short range suggest that there is a local distortion present in the structure.47 We extracted quantitative information about the distortion by fitting the PDF data between 2.0 Å and 4.0 Å using a crystallographic model with a lower symmetry, I4/mcm space group. Figure 5b shows that the simulated pattern from the modified crystallographic model fits the shoulder at 2.5 Å in the experimental data. Figure S5 compares the structures determined by single crystal diffraction (P4/mmm) and PDF analysis (I4/mcm). The key difference is the heteroleptic Ag2 atom, which shifts away from the ideal tetrahedral position towards a distorted trigonal geometry in the I4/mcm structure. The distortion yields a Ag1-S bond distance of ~2.54 Å that is shorter than the corresponding distance in the P4/mmm structure, and accordingly, we attribute the shoulder at ~2.5 Å to this interaction.

Figure S5 indicates that Ag2 is disordered between two symmetrically equivalent positions at either side of the ideal tetrahedral site, which can be either static (random, non-correlated) or dynamic. In order to understand the nature of the disorder at the Ag2 site, we examined the


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atomic displacement parameters (ADP) from the single crystal diffraction experiments conducted at 100 and 300 K. The temperature-dependence of the ADP can provide insight into this type of disorder. Specifically, dynamically disordered atoms are expected to exhibit ADP that increase faster with temperature than other atoms in the structure.48,49 Figure 6 shows the isotropic ADP for each atom at both 100 K and 300 K along with a linear interpolation. Clearly, the rate of increase in the ADP for the Ag2 atom is considerably larger than that of Cs, Ag1, Te, or S, providing evidence for dynamic disorder. The anisotropic ADP for Ag2 in the direction of the distortion (U11) is also shown, and exhibits a dramatic increase between 100 and 300 K. Figure 6b shows a depiction of the potential energy surface for the dynamically disordered Ag2 atoms.

Electronic and Thermal Transport. In order to measure the electronic and thermal transport properties of CsAg5TeS2, the as-synthesized ingot was pulverized and pressed into a dense pellet using an SPS instrument (see experimental section). The pressed samples have a dark metallic luster (Figure 7a inset) and have a density of 6.503 g⋅cm-3 (~95 % of theoretical density). The corresponding pXRD (Figure S6) shows significantly less preferred orientation than in the assynthesized ingot, but the samples still exhibit slight transport anisotropy. Accordingly, measurements were taken both parallel (//) and perpendicular (⊥) to the SPS pressing direction. Figure 7a shows the electrical conductivity as a function of temperature, which gradually increases from ~5 to ~15 S⋅cm-1 in the temperature range of 300 to 800 K for both samples, indicating semiconductor behavior. The Seebeck coefficients are positive and range from 340 to 190 µV⋅K-1 in the perpendicular direction and 310 to 140 µV⋅K-1 in the parallel direction between 300 and 800 K (Figure S7a), and the anisotropy is attributed to the complex band structure, which is described below. The positive values indicate that the samples have p-type carriers that are likely due to Ag vacancies. Temperature-dependent thermal conductivity was measured using the laser-flash diffusivity method (see Figure S7b for thermal diffusivity data) and is shown in Figure S7c. In the direction perpendicular to the SPS pressure, the thermal conductivity decreases from 0.41 to 0.38 W⋅m-1⋅K-1 between 300 and 800 K, while in the parallel direction it decreases from 0.33 to 0.28 W⋅m-1⋅K-1. The corresponding κlatt values were calculated by subtracting the electronic component of the thermal conductivity (κelec) determined from the Wiedemann-Franz law (see experimental section) and are shown in Figure 7b. The κlatt values decrease from 0.40 to 0.36 W⋅m-1⋅K-1 between 300 to 800 K in the direction perpendicular


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to the SPS pressing direction, and decrease from 0.32 to 0.25 in the parallel direction. These are among the lowest values reported for a metal chalcogenide system, although slightly higher than reported for CsAg5Te3.2,16,50 Computed Electronic Structure and Phonon Properties. Using the I4/mcm space group, we computed the electronic band structure and partial density of states (pDOS) for CsAg5TeS2 as shown in Figure 8a and S8, respectively. Although CsAg5TeS2 is experimentally determined to be a semiconductor with a bandgap of ~0.30 eV, the calculated band structure shows the conduction band minimum falling below the Fermi level, erroneously suggesting semi-metal behavior. We attribute this discrepancy to the observed disorder and the sensitivity of bandgap opening to subtle lattice distortions. In spite of this, the calculation offers useful information regarding the location of the band edges within the Brillouin zone. The conduction band minimum (CBM) is found to be a highly dispersed band found at the Γ-point, while the valence band maximum (VBM) is composed of two bands, one along X-Y line and the other at the Ppoint, indicating an indirect bandgap. This is an intriguing feature, since narrow-gap semiconductors with multiple bands at or near the Fermi level can have enhanced Seebeck coefficients and high thermoelectric performance,10,51,52 making CsAg5TeS2 a good candidate for further p-type thermoelectric studies. The pDOS in Figure S8 shows that the VBM is primarily populated by Ag, S, and to a lesser extent Te, while the CBM is primarily populated by Ag. Figure S8 also shows the individual contribution from each unique Ag atom, indicating that the square planar Ag1 atoms make a larger contribution to the VBM and CBM than Ag2. Accordingly, we attribute the smaller bandgap in CsAg5TeS2 (0.30 eV) relative to CsAg5Te3 (0.67 eV) to the square planar Ag atoms, which are rarely observed in solid-state compounds.53

To gain a deeper understanding of the lattice dynamics and structural stability of CsAg5TeS2, we used DFT to calculate its phonon band structure. We first calculated phonon dispersions for CsAg5TeS2 in the P4/mmm space group from single-crystal diffraction (Figure S9), which display negative (imaginary) phonon modes at multiple points in the Brillouin zone. Moreover, these imaginary phonon modes remain even after considering finite temperature effect through anharmonic phonon renormalization. The presence of imaginary phonons indicates a lattice instability associated with a phase transition to a lower symmetry structure.54,55 Critically, we


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find that the phonon dispersions for CsAg5TeS2 are stabilized at and above 300 K, and do not exhibit imaginary modes with the I4/mcm space group (Figure 8b), corroborating the PDF analysis.

The simulated phonon dispersions for CsAg5TeS2 with the lower symmetry I4/mcm space group is shown in Figure 8b. In the Brillouin zone, the Γ-X(Y) direction corresponds to the a(b) axis, while the Γ-Z direction corresponds to the c axis. The acoustic modes (red lines) along the Γ-Z direction are observed to be softer (slower phonon velocities and lower Debye temperature) than along the Γ-(X)Y direction, which is consistent with the anisotropic crystal structure. We observe massive low-lying optical modes below 5 meV that have multiple anticrossing points with longitudinal acoustic modes along the Γ-Z, Γ-(X)Y, and Γ-Σ directions, as indicated by the blue arrows in Figure 8b. The atom-projected phonon density of states (DOS) indicate that the acoustic and low-lying optical phonon modes are dominated by Ag atoms, and the anticrossing points signify rattling-like vibrations similar to CsAg5Te3 that suppress thermal transport. We ascribe the rattling-like localized vibrations to the Ag atoms in the heteroleptic coordination geometry. These rattler-like phonon modes not only suppress acoustic modes but also act as extra phonon scattering channels,56 and accordingly, low lattice thermal conductivity is expected.

To quantitatively predict the lattice thermal conductivity using theory, we estimated moderesolved phonon lifetimes by computing phonon scattering rates from three-phonon interactions using second-order perturbation theory.57 The resulting calculated thermal conductivity as a function of temperature is shown in Figure 9, along with the experimentally measured κlatt values. These values are averaged over three principal axes in order to better compare with experimental measurements on polycrystalline samples. Interestingly, although the predicted values are below 1.0 W⋅m-1⋅K-1 at 300 K, the experimental values are still lower, with improved agreement at high temperature. The large discrepancy in κlatt at low temperature cannot be entirely due to grain boundary scattering, since this effect is weak in materials with intrinsically low κlatt, where heat-carrying phonons have mean free paths that are smaller than the size of the grains.58,59 We note that the theoretical calculation does not take into account phonon scattering due to dynamic disorder, an omission which may be responsible for the overestimation of lattice thermal conductivity. We hypothesize that at relatively low temperatures the underlying atomic


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disorder plays a significant role in reducing lattice thermal conductivity, while at high temperatures, where atoms occupy a higher symmetry position,55 intrinsic phonon-phonon scattering dominates.

CONCLUSIONS The structural complexity in ternary and quaternary chalcogenides affords them with enhanced functionality that make them especially useful thermoelectric materials. These systems often exhibit subtle lattice distortions that can strongly influence their properties but are difficult to detect using traditional diffraction methods. Accordingly, they provide an important platform for studying the effect that local disorder has on lattice dynamics and semiconductor transport properties. Here, we describe the multi-chalcogen narrow-gap semiconductors CsAg5TeS2 and its solid solution CsAg5Te3-xSx (x = 1-2), which have ultralow thermal conductivity below 0.35 W⋅m-1⋅K-1 at 300 K. Although the single chalcogen analogues CsAg5Q3 (Q = Se, Te) adopt a three-dimensional phase, these multi-anion compounds have a two-dimensional structure with unusual crystal chemistry, including Ag atoms in a heteroleptic bonding geometry. Single crystal diffraction suggests that the materials adopt a tetragonal P4/mmm space group, but DFT calculations show that this structure is dynamically unstable. Using PDF, we show that the heteroleptic Ag atoms are positionally disordered about their ideal lattice positions, yielding a lower I4/mcm symmetry. The DFT-calculated lattice thermal conductivity, which does not take into account atomic disorder, is significantly higher than the experimentally measure values. This suggests that the underlying disorder plays an important role in the observed ultralow thermal conductivity, highlighting the importance that subtle lattice distortions can have on the transport properties of narrow-gap semiconductors.

ACKNOWLEDGEMENTS This work was supported by the Midwest Integrated Center for Computational Materials (MICCoM) as part of the Computational Materials Sciences Program funded by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division (No. 5J-30161-0010A). Use of the Center for Nanoscale Materials, an Office of Science user facility, was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DE-AC02-06CH11357. This


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research used resources of the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. Use was made of the IMSERC X-ray Facility at Northwestern University, which has received support from the Soft and Hybrid Nanotechnology Experimental (SHyNE) Resource (NSF ECCS-1542205); the State of Illinois and International Institute for Nanotechnology (IIN).

SUPPORTING INFORMATION X-ray crystallographic data for CsAg5TeS2 (100 K and 300 K) and CsAg5Te2S in CIF format, as well as crystal data and structure refinement, displacement parameters, anisotropic displacement parameters, bond lengths, and bond angles; Tauc plots; DTA; Temperature-dependent pXRD for CsAg5TeS2; Crystal structure of CsAg5Te2S; Comparison of CsAg5TeS2 structure with P4/mmm and I4/mcm space group; pXRD for SPS-pressed CsAg5TeS2 pellet; Temperature-dependent Seebeck coefficient, thermal diffusivity, and total thermal conductivity for CsAg5TeS2; DFTcalculated phonon dispersions for CsAg5TeS2 with P4/mmm space group; Electronic pDOS for CsAg5TeS2.

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Figure 1. Crystal structure of CsAg5Te3 (P42/mnm) and CsAg5TeS2 (P4/mmm).

Figure 2. (a) Powder XRD data for CsAg5Te3-xSx (x = 1, 1.5, 2) along with simulated diffraction pattern for CsAg5TeS2 from single crystal analysis (Table S1). (b) Monotonic shift in the (003) reflection to lower angles with increasing Te content indicates solid-solution behavior.


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Figure 3. (a) Representative SEM image of CsAg5TeS2 showing flat surface indicates a layered structure-type. The corresponding SEM-EDS elemental maps show good chemical homogeneity and the normalized atomic % is consistent with the target composition. (b) Absorption spectra for CsAg5Te3-xSx (x = 1, 1.5, 2) showing a blueshift in bandgap with increasing sulfur content.


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Figure 4. (a) Crystal structure of CsAg5TeS2 (P4/mmm) viewed along the a-axis showing alternating layers of Cs and [Ag5TeS2] slabs. (b) Square planar Ag1-Te net viewed along the caxis and (c) a selection of Ag2 atoms in a heteroleptic, tetrahedral bonding geometry.


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Figure 5. (a) Experimental PDF plot for CsAg5TeS2 along with simulated pattern from P4/mmm space group. The inset shows and expanded view of the short-range interaction at ~2.5 Å that is unaccounted for in the P4/mmm model. (b) The simulated pattern from the lower symmetry I4/mcm space group matches well with experimental pattern. The inset shows the symmetry breaking off-centering of the heteroleptic Ag2 atom, which is exaggerated for clarity.

Figure 6. (a) Isotropic (Ueq) atomic displacement parameters (ADP) for each atom at 100 K and 300 K from single crystal diffraction. The ADP for Ag2 (blue line) increases at a faster rate than the other atoms in the structure, suggesting dynamic disorder. The anisotropic U11 ADP for Ag2 (dotted line) corresponds to the direction of the distortion and shows the greatest rate of increase. (b) Depiction of the potential energy surface for Ag2 atom, showing dynamic disorder between the symmetry equivalent positions on either side of the ideal tetrahedral site.


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Figure 7. (a) Temperature-dependent electrical conductivity and (b) lattice thermal conductivity for CsAg5TeS2, which was measured in both the parallel (//; black) and perpendicular (⊥; red) directions relative the SPS pressing direction. The inset in (a) shows the densified CsAg5TeS2 pellet along with cut and polished bars for transport measurements, and the observed anisotropy is attributed to preferred orientation of the two-dimensional crystals within the pellet.

Figure 8. (a) Electronic band structure for CsAg5TeS2 (I4/mcm) showing that the VBM is composed of two bands, one along X-Y line and the other at the P-point. The plot shows the conduction band falling below the Fermi level, which is an erroneous artifact from the DFT calculation. (b) Phonon dispersions for CsAg5TeS2 (I4/mcm), which show acoustic phonons in red and optical phonons in grey, along with the corresponding phonon DOS. Low-frequency optical modes are shown create anticrossing rattling modes at multiple points in Brillouin zone, indicating suppressed thermal transport.


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Figure 9. Experimental and DFT-calculated lattice thermal conductivity for CsAg5TeS2 (I4/mcm) as a function of temperature. The DFT values (dashed blue line) represent the average κlatt over the three crystallographic axes for better comparison with the polycrystalline sample, which was measured in the parallel (//; black) and perpendicular (⊥; red) directions relative the SPS pressing direction.


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Table of Contents Graphic.


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Two-Dimensional CsAg5Te3-xSx Semiconductors: Multi-Anion

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