Abderahmane Marouf
email: amarouf@unistra.fr

Nikolaos Simiriotis
email: nikolaos.simiriotis@imft.fr

J B Tô

Y Bmegaptche

Yannick Hoarau
email: hoarau@unistra.fr

Marianna Braza
email: marianna.braza@imft.fr

Reynolds A Marouf

DDES and OES Simulations of a Morphing Airbus A320 Wing and Flap in Different Scales at High Reynolds

Keywords: morphing, flap, wing, frequency, vibration, hybrid models

établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Many studies in recent years have aimed at improving the aerodynamic performance of a wide range of aircraft (military, transport, commercial and general aircraft). As such, a large part of contribution in the literature is focused on the improvement of aerodynamic performance in the cruise, take-off and landing configurations by increasing lift and decreasing drag. The new family of airfoils, known as supercritical has demonstrated an improvement in the aerodynamic characteristics compared to the earlier airfoils. This study introduces a new technology based on wing and flap deformation using electroactive morphing in the context of the H2020 Smart Morphing and Sensing a European project for Aeronautical Configurations www.smartwing.org/SMS/EU. Numerical simulations with hybrid turbulence models have been used in this study. Smart materials installed in the wing or the flap help to increase the aerodynamic performances and to decrease the aerodynamic noise in the wake. Several tests and simulations have been carried out to show the optimal vibration and the slight deformation of the trailing edge region. In the experimental set-up the actuation with a slight deformation is achieved through Micro-Fiber Composite (MFC) piezo-patches and the camber control is achieved by the Shape Memory Alloys (SMA) operating at low frequencies (order of 1 Hz), whereas the trailing-edge vibrations are of higher order (100-500 Hz). The combination of both actuations with the MFC and SMA, results in the hybrid morphing (G. Jodin et al 2017 [START_REF] Jodin | Dynamics of hybrid morphing wing with active open loop vibrating trailing edge by time-resolved PIV and force measures[END_REF]).

Numerical configuration and turbulence modeling 2.1 Flow configuration

The simulation of the A320 wing, concerns firstly the RS prototype (c=0.7 m) which was previously studied experimentally in our research group [1] [2]. This work was in the clean configuration and validated numerically by N. Simiriotis et al [START_REF] Simiriotis | Electroactive morphing on a supercritical wing targeting improved aerodynamic performance and flow control in high Reynolds numbers[END_REF] by means of computations for a high angle of attack at 10° and a freestream Mach number of 0.06 which corresponds to a chord-based Reynolds number of approximately 1 × 10 6 . In addition, deformable grid methods were used by means of a compressible Navier-Stokes code adopting the Organised Eddy Simulation model. Secondly the study illustrates the LS (c=2.72 m) with a two-element wingflap in the take-off position of the A320 operating at a Mach number of 0.032 and chord-based Reynolds of 2.25 × 10 6 . The attack angle is taken as 8° and compared to numerical and experimental results (W. LU et al [START_REF] Weishuang | Aerodynamic optimization and mechanism design of flexible variable camber trailing-edge flap[END_REF]).

Numerical parameters

The NSMB code (Y. Hoarau [START_REF] Hoarau | Recent Developments of the Navier Stokes Multi Block (NSMB) CFD solver[END_REF]) is used to perform fluid dynamics simulation. The code solves unsteady and steady compressible Navier Stokes equations using the finite volume method, a structured grid is used to simulate the flow around single and two-element wing-flap. This includes a variety of efficient high-order numerical schemes and turbulence modelling closures in the context of URANS, LES and hybrid turbulence modelling. This code includes efficient fluid-structure coupling for moving and deformable structures. In the present study, the fourthorder central scheme and second order dual-time stepping for the temporal discretisation are selected. Preconditioning artificial compressibility was used to simulate the flow in a subsonic speed range for both reduced and large-scale configurations. A physical time step of 10 µs was validated for 3D simulation after a detailed investigation, a typical number 100 of inner iterations was mandatory for the process of convergence for each outer time step.

Boundary and initial conditions

No-slip conditions are employed on the wing wall and the presence of the wind tunnel walls are taken into account in the RS configuration. After several tests, the results obtained with a slip boundary condition for the upper and lower walls gave a better approximation to the experimental results than no-slip conditions and to avoid refinement near to the walls. On the other hand, far-field conditions are selected for the LS configuration with the characteristic variables extrapolated in time due to the complexity of the wind tunnel. Total pressure P0 and total temperature T0 are taken as standard conditions, as well as the upstream Reynolds numbers of 1 × 10 6 and 2.25 × 10 6 and Mach numbers of 0.062 and 0.032 respectively. The measurement of the upstream turbulence intensity in the wind tunnels of IMFT is 0.01 %. The initial solution is taken as a steady-state generated field in each case.

Turbulence modelling :

The following URANS and hybrid turbulence modelling models are chosen. Twoequation OES-k -ε [START_REF] Bourguet | Anisotropic Organised Eddy Simulation for the prediction of non-equilibrium turbulent flows around bodies[END_REF] for the RS configuration, this model has the ability of the splitting the spectrum of energy based on organized coherent character. The coherent structures are resolved, and the random chaotic structures are modelled. In addition, hybrid DDES-k -ω SST and DDES-k -ε OES [START_REF] Spalart | Detached-Eddy Simulation[END_REF][9] models were used for the LS configuration. The activation of the ambient terms was necessary to prevent the free decay of the transported turbulence variables. The turbulent lenghscale l replaces the wall distance in the selected DDES models, this variable appears in the function fd through the near-wall parameter and it is defined as :

𝑙 = 𝑑 -𝑓 𝑑 max (0, 𝑑 -𝐶 𝐷𝐸𝑆 Δ 𝑚𝑎𝑥 ) (1)
Where 𝐶 𝐷𝐸𝑆 is a constant and Δ 𝑚𝑎𝑥 is based on the largest dimension of the local grid cell.

The Figure .1 represents the 𝑓 𝑑 and the non-dimensional streamwise velocity near wall regions, 6 positions are selected (near to leading edge, medium and trailing edge) of the upper surfaces in the wing and the flap. The switch from RANS to LES in all the cases is rapid and the 𝑓 𝑑 slope in the switching area is close to 0 (horizontal line). The flow is separated at the end of the wing (x/c=0.59) and the flap (x/c=0.9, x/c=0.98) and the thickness of the RANS layers are almost the same 10 -3 to 1.5. 10 -3 𝑧/𝐶, but the switch to LES happens inside the boundary layer compared to the other positions where no separation occurs. The delaying function fd tends to 0 in the RANS regions and 1 in LES regions (where rd << 1)

𝑓 𝑑 = 1 -tanh[(8𝑟 𝑑 ) 3 ] 𝑟 𝑑 = 𝜈 𝑡 +𝑣 𝑆 𝑑 𝑘 2 𝑑 2 𝑆 𝑑 = √ 𝜕𝑢 𝑖 𝜕𝑥 𝑗 . 𝜕𝑢 𝑖 𝜕𝑥 𝑗 (2)
As can be seen in Eq. ( 2), the turbulence length scale in DDES is also function of the local state of the flow by means of the eddy viscosity and the deformation tensor.

Grid generation and deformation

Multiblock structured grids were generated to simulate the flow around the RS and LS configurations as presented in the Figure . 2. The RS grid contains 20 million cells with a minimum local cell size less than 1 mm is defined near to the trailingedge of the wing to capture the flow detachment. A spanwise of 0.8C (80 cells in the span direction), which is sufficient for the OES model, the mesh was created similar to the IMFT wind tunnel with 11C for the total domain from the inlet to the outlet and the wing is placed in the middle. In the other hand, the LS grid has 30 million cells with a spanwise of 0.11C (40 cells in the span direction), in addition a far-field boundary conditions were selected with 20C. The Arbitrary Lagrangian Eulerian (ALE) [START_REF] Donea | An arbitrary lagrangian-eulerian finite element method for transient dynamic fluid-structure interactions[END_REF] is used in order to solve dynamic problems involving large and small deformations. This method is applied for the trailing edge of the wing in the RS configuration and in the flap for the LS configuration, the deformation is imposed each time step following a sinusoidal movement highlighted in the Figure .  3. The inner iterations help the convergence of the solution and this needs to be readapted for high frequency deformation to achieve a high accuracy. The vibration of the trailing-edge is controlled by means of the actuation frequency, the amplitude and the x displacement. These parameters are defined by the user as input to calculate the real displacement of each cell in every time step and compute the grid deformation. In the RS prototype the wing's trailing-edge is selected in the morphing configuration and in the LS prototype the flap's trailingedge will be morphed. An imposed small deformation of 0.35mm and high frequency of 300 Hz were selected as optimal configuration for the dynamic morphing based on our previous studies. A preconditioning method was tested based on the artificial compressibility in our compressible solver NSMB in the implicit dual time stepping method Lower Upper Symmetric Gauss Seidel (LU-SGS). This preconditioning gave approximate results to experimental data but a thinner wake deficit as presented in the Figure . 4. This is caused by the presence of the wind tunnel walls in the upper, lower and sided parts of the wing prototype, which were taken as slip conditions in numerical simulations. Another reason is the confinement of the wind tunnel, we think that the Reynolds number is slightly higher in the experimental than the numerical simulation. The suppression of the 3-dimensional instabilities in the spanwise direction is illustrated in the Figure . 5. The undulation that occurs as an inherent characteristic of the flow in the static case is obtained by the Organized Eddy Simulation model due to the non-linear interaction of turbulent structures at high Reynolds number. The evolution of the velocity magnitude appears clearly in the spanwise in Figure .  5 and displays an undulation with an irregular wavelength (chaotic flow) of von Kármán rows. Longitudinal vorticity 𝜔 𝑥 is clearly present in the spanwise direction for the static case. However, added to the wake flow some energy introduced by the vibration at the frequency 300 Hz and a slight deformation in the trailing edge, can suppress the three-dimensional undulation and transforms the wake flow into quasi two-dimensional. This helps to increase the lift with some percentage and decrease the pressure drag which is associated with the turbulence structures created in the wake flow at high Reynolds and angle of attack. Several simulations for a specific range of frequency and deformation have been tested to find the most appropriate configuration to show the good effects of the morphing wing. To illustrate the flow regions, Figure . 7 provides a view of the turbulence structures visualized by the iso-surfaces of the Q criterion colored by the velocity magnitude above the wing and in the wake by means of the SST-DDES and OES-DDES. The SST shows less solved turbulent structures compared to the OES which generates relatively large structures. This is caused by the modification of the constant Cmu for the OES model in the URANS region to predict the behaviour of the boundary layer detachment before switching to the LES Smagorinsky model better than the standard URANS models.

Results and discussion

Conclusion

High fidelity OES and hybrid RANS/LES models contributed to these relevant challenging test cases, providing results of single element in the clean RS configuration and two-element wing-flap in take-off LS configuration. In addition, an imposed deformation (with vibration) on the trailing edge to the single element RS wing using OES model in the clean RS configuration results in a completed elimination of the 3D effects in the spanwise direction of the wake, this can make the wake thinner. A decrease of the drag and an increase of the lift of some percentage have been noticed for low and high frequencies actuations in the morphing configuration. Thus, showing that the OES model does not require a refined mesh as hybrid models to capture 3 dimensional effects in the wake. In addition, the second part of the study hybrid models have been used and tested, the OES-DDES showed a better resolution of the turbulent structures compared to SST-DDES.

In perspectives of this study, the morphing (with vibration) cases under hybrid simulations as DDES for single and two element wing-flap in the future will be tested and this will probably illustrate more what will be modified in the smaller scales that are resolved in the wake.

Fig. 1 .

 1 Fig. 1. Presentation of the DDES-k -ω SST delaying function FD and the nondimensional streamwise velocity in six chosen positions over the wing and the flap.

Fig. 2 .

 2 Fig. 2. Slice of the different grids. (left) : Reduced Scale at the clean position.(right) : Large Scale at the take-off position.

Fig. 3 .

 3 Fig. 3. Presentation of the trailing-edge movement using the ALE method.

3. 1

 1 RS configurationThis part of the study focuses on the RS in clean configuration (c=0.7 m). Using the k-ε-OES, the resolved turbulence corresponds to an ensemble averaged flow evolution, representing the organized, coherent part of the flow. The homogeneous ambient terms are activated and described in Spalart and Rumsey (2007)[START_REF] Donea | An arbitrary lagrangian-eulerian finite element method for transient dynamic fluid-structure interactions[END_REF]. In addition, the Cmu=0.03 has shown an improvement in the boundary layer separation near the trailing edge compared to the Standard k-ε model Cmu=0.09.

Fig. 4 .

 4 Fig. 4. Comparison of experimental and numerical results. (left) : PIV results from IMFT by G. Jodin. (right) : 3D numerical results

Figure. 5

 5 Figure. 5 presents a first overview of the morphing (with vibration) by means of the ALE grid deformation in the 3D RS configuration compared with the static (no vibration)showing the iso-surfaces of the Q criterion at a fixed value of 1500 and colored by the vorticity magnitude. This highlights the morphing effects in the spanwise direction and the wake behavior.

Fig. 5 .

 5 Fig. 5. : Visualization of the iso-surfaces of Q criterion = 1000 colored by the velocity magnitude around the wing in clean configuration. Left : morphing case at 300 Hz (with vibration) and (right) : static case (no vibration).

3. 2

 2 LS configuration This part of the study concerns the highlift two-element airfoil at a large scale (c=2.72 m). The design of the DDES grid around the airfoil-flap requires a homogenous local grid cells with Δx ≈ Δy ≈ Δz following the recommendations of Spalart in the LES region. Two different hybrid models SST-DDES and OES-DDES have been chosen to simulate the flow around the LS wing-flap configuration Figure. 7. The classical Smagorinsky model for LES has been selected and the DES subgrid length-scale is taken as Δmax=max(Δx, Δy, Δz).

Fig. 6 .

 6 Fig. 6. Pressure coefficient of the wing-flap LS configuration for different grid Time step validation was carried out for 2D grids. Several tests with different values of Δ𝑡 = 10 -3 , 10 -4 and 10 -5 seconds were tested to find out the optimal time step. A 10 -5 seconds was sufficient and was adopted for the simulations. A typical number between 60 and 100 inner steps was sufficient for the convergence in each time step. The grid independency is presented in Figure.6. Comparing 2D normal, refined, Overset (Chimera) grids and the 3D grid tested with OES-DDES and SST-DDES, almost the same accuracy was shown with 2D results. Another comparison with W. Lu et al[START_REF] Simiriotis | Electroactive morphing on a supercritical wing targeting improved aerodynamic performance and flow control in high Reynolds numbers[END_REF] results of GA (w) 2 wing-flap and the A320 at the same flow configuration and speed in Figure.6 was tested. Numerical simulations show a good approximation to GA (w) 2 in CP distribution around the wing, but there is a small change in the upper surface of the wing due to the difference of shape. Notice that in GA (w) 2 flap is smaller than the A320 which explains the reason of the difference in the pressure distribution. Even though we still have a good agreement between both configurations.

Fig. 7 .

 7 Fig. 7. Presentation of the Q criterion = 1000, colored by the velocity magnitude, (left) : DDES-k -ω SST and (right) DDES-k -ε OES. 3 dimensional in the (x,y,z) on the top and a plane (x,z) taken from the middle down.


Subhendu Jana

Mohd Ishtiyak

Gopabandhu Panigrahi

Jai Prakash

Adel Mesbah

Saber Gueddida

Sébastien Lebègue

Christos D Malliakas

James A Ibers

Ternary Chalcogenides BaM x Te 2 (M = Cu, Ag): Syntheses, Modulated Crystal Structures, Optical Properties, and Electronic Calculations

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INTRODUCTION

The structural chemistry of multinary metal chalcogenides [chalcogens (Q = S, Se, and Te)] is richer and more complex than that of the metal oxides because the chalcogens have lower electronegativity than Oxygen. This leads to less ionic character of metal-chalcogen bonds, increased covalent character, and less repulsion between the anions. The combination of these factors results in the formation of a variety of Q-Q bonding in the metal chalcogenides. [START_REF] Cody | New one-dimensional ternary and quaternary cesium-metal-tellurium compounds[END_REF][START_REF] Mar | Metal-Metal vs Tellurium-Tellurium Bonding in WTe2 and Its Ternary Variants TaIrTe4 and NbIrTe4[END_REF][START_REF] Rouxel | Low-Dimensional Solids: An Interface between Molecular and Solid-State Chemistry? The Example of Chainlike Niobium and Tantalum Chalcogenides[END_REF] The chalcogens can form various species starting from a simple Q2 2-unit [e.g., Ba2Ag2Se2(Se2), [START_REF] Jana | Synthesis and Characterization of Ba2Ag2Se2(Se2)[END_REF] ZrTe3, [START_REF] Stöwe | Crystal Structure and Calculated Electronic Band Structure of ZrTe3[END_REF] and Rb2Te2 6 ] to complex nonlinear Qn 2-units [e.g., Te13 2-unit in Cs2Te13 7 ], and hypervalent (Qn) m-motifs (m, n > 2, Se3 4-in Ba2Ag4Se5, 8 Se5 4-in Nb2Se9, [START_REF] Meerschaut | The crystal structure of niobium selenide Nb2Se9 from twin-crystal data[END_REF] and Te5 4-in NaTe 10 ). Among the chalcogens, Te shows the most varied catenations. Te can form infinite chains (Ba3ScTe5, [START_REF] Ishtiyak | Modulated Linear Tellurium Chains in Ba3ScTe5: Synthesis, Crystal Structure, Optical and Resistivity Studies, and Electronic Structure[END_REF] Gd3Cu2Te7, [START_REF] Huang | Gd3Cu2Te7 and U2Cu0.78Te6: Two Examples of Linear Te Chains[END_REF] and LaCu0.40Te2 [START_REF] Huang | 0.40Te2[END_REF] ), square nets (EuCu0.66Te2, [START_REF] Patschke | Cu0.66EuTe2, KCu2EuTe4 and Na0.2Ag2.8EuTe4: compounds with modulated square Te nets[END_REF] Na0.2Ag2.8EuTe4, [START_REF] Patschke | Cu0.66EuTe2, KCu2EuTe4 and Na0.2Ag2.8EuTe4: compounds with modulated square Te nets[END_REF] KCu2EuTe4, [START_REF] Patschke | Cu0.66EuTe2, KCu2EuTe4 and Na0.2Ag2.8EuTe4: compounds with modulated square Te nets[END_REF] and K0.33Ba0.67AgTe2 [START_REF] Zhang | Distorted Square Nets of Tellurium in the Novel Quaternary Polytelluride K0.33Ba0.67AgTe2[END_REF] ), and neutral Te8 rings (e.g., Cs4Te28) [START_REF] Sheldrick | Synthesis and structure of Cs2Te13 and Cs4Te28, telluriumrich tellurides on the methanolothermal route to Cs3Te22[END_REF] .

In most of these structures, the charge balance of the compounds can be achieved by the Zintl-Klemm concept. [START_REF] Nesper | The Zintl-Klemm Concept -A Historical Survey[END_REF] However, charge-balancing in structures with infinite chalcogen chains and square nets is extremely difficult. Many of the initial reports of these structures showed equidistant Te atoms in these chains and square nets; theoretically these chains and nets are not stable and should be distorted. Hence, the crystal structures of many of these compounds (e.g. LnTe3, and Ln2Te5) [START_REF] Norling | The Crystal Structure of Neodymium Tritelluride[END_REF][START_REF] Ramsey | The Phase Equilibria and Crystal Chemistry of the Rare Earth-Group VI Systems. IV. Lanthanum-Tellurium[END_REF][START_REF] Wang | The Crystal Structure of Lanthanum Telluride and Tellurium-Deficient Neodymium Telluride[END_REF][START_REF] Lin | The Phase Equilibria and Crystal Chemistry of the Rare Earth Group VI Systems. III. Neodymium-Tellurium[END_REF][START_REF] Muravieva | Crystal Structure of LnTe3, Where Ln = La[END_REF] upon reinvestigation displayed weak superstructure reflections indicating that the Te chains and nets are in fact distorted. These structural distortions are believed to be responsible for their intriguing physical properties such as charge density waves (CDW) in the AMLnTe4 (A = K, Na; M = Cu, Ag; Ln = La, Ce) structures. [START_REF] Patschke | KCuCeTe4: A New Intergrowth Rare Earth Telluride with an Incommensurate Superstructure Associated with a Distorted Square Net of Tellurium[END_REF][START_REF] Patschke | Polytelluride compounds containing distorted nets of tellurium[END_REF] The average charges on these Te nets also vary depending on the structure type. For instance, the average charge on the Te atoms in the Te nets in quasi two-dimensional-structures of LnTe3 compounds is -0.5e -whereas it decreases -1e -in the Ln2Te3 structures. Thus, the physical properties of these square-net chalcogenides show a strong correlation with the charge on their Te atoms and the nature of the interactions between neighboring Te atoms. These different types of Q-Q interactions can stabilize new unprecedented and unexpected structures that we seek to discover by exploratory syntheses.

In the last few decades, we have focused on the exploratory syntheses of ternary and quaternary new transition metal/actinide chalcogenides and have reported a number of compounds that show a variety of new structure types with various chalcogen-chalcogen interactions. The flexibility of chalcogens to adopt various polyanionic units could not have been predicted have been but discovered depended on exploratory syntheses.

The chemistries of the actinides (An = Th, U, Np) are relatively unexplored. Consequently, actinide metal chalcogenides present an exciting area for exploratory chemistry. Generally such efforts fail; a few yield new compounds and surprising structures. Others yield new compounds that can only be prepared with the assistance of the actinides. Such is the case here where we present the syntheses, modulated crystal structures, Raman spectroscopy, optical properties, and electronic properties of two new compounds BaCuxTe2 and BaAgxTe2, which were discovered serendipitously while exploring the Ba-Th-Cu/Ag-Te systems. BaCuxTe2 could on be prepared with the assistance of Th. 232 Th is an α-emitting radioisotope and as such is considered to be a health risk. Experiments using radioisotopes require appropriate infrastructure and personnel trained in the handling of radioactive materials.

EXPERIMENTAL METHODS

Syntheses and Analyses. Caution!

The following starting materials were used as supplied: Ba rod (Alfa Aesar, 99+ %), Ag flakes (Sigma Aldrich, 99.9%), Cu powder (Sigma Aldrich, 99.9%), Th powder (MP Biomedicals, 99.1%), and Te ingot (Sigma Aldrich, 99.999%). These chemicals were handled inside an Arfilled glove box.

Synthesis of Single Crystals of BaCuxTe2. Black plate-shaped crystals of BaCuxTe2

were synthesized by standard solid-state methods. BaCuxTe2 crystals were first obtained serendipitously during an attempt to synthesize a new quaternary phase in the Ba-Th-Cu-Te system. First, Ba (35.5 mg, 0.259 mmol), Th (15 mg, 0.065 mmol), Cu (8.2 mg, 0.129 mmol), and Te (107.2 mg, 0.84 mmol) were loaded into a carbon-coated fused-silica tube (OD 6 mm) inside an Ar-filled glove box. The tube was then evacuated to ca. 10 -4 Torr before being sealed.

The tube was placed inside a programmable muffle furnace and heated to 1073 K in 36 h where it was kept for 15 h. The temperature of the furnace was then raised to 1173 K. The tube was kept for 198 h at 1173 K. Then it was cooled to 973 K in 96 h and then to 573 K in 100 h and then the furnace was turned off. The silica ampoule was opened under ambient condition and a black lump was found. The lump was gently broken into small pieces before being examined under a microscope. The product contained black plate-shaped crystals. The energy-dispersive X-ray (EDS) spectroscopy analysis of these crystals was carried out with the help of a Hitachi S3400 scanning electron microscope. Semi-quantitative EDS analysis of the crystals showed the presence of Ba, Cu, and Te and no trace of Th. The compositions of these crystals were close to BaCu0.7Te2 (Ba:Cu:Te  1:0.70:2). Other phases found were black plates of ThOTe, [START_REF] Beck | Die Verfeinerung der Kristallstruktur von ThOTe[END_REF] yellow BaTe, 25 and residual Te.

Synthesis of Single Crystals BaAgxTe2

. Black plate-shaped crystals of a new ternary compound BaAgxTe2 were obtained during the exploration of Ba-Th-Ag-Te quaternary system in a reaction of Ba (23.67 mg, 0.172 mmol), Th (10 mg, 0.043 mmol), Ag (9.30 mg, 0.086 mmol), and Te (76.99 mg, 0.603 mmol). These reactants were first loaded into a carbon-coated fused-silica tube inside an Ar-filled glove box. The tube was flame sealed under vacuum (ca. 10 -4 Torr) and then placed inside a computer-controlled muffle furnace. The heating profile of this reaction was the same as discussed above for the synthesis of BaCuxTe2 crystals. The reaction product of this reaction revealed the presence of black plates along with yellowish BaTe and unreacted Te. The EDS analysis of the plate-shaped crystals showed the presence of BaAgxTe2 (Ba:Ag:Te ≈ 1:0.8:2) along with ThOTe, [START_REF] Beck | Die Verfeinerung der Kristallstruktur von ThOTe[END_REF] BaTe, 25 and Te crystals.

Syntheses of Polycrystalline BaCuxTe2 (x = 1.0, 0.85, 0.70, 0.55, and 0.43) and BaAgxTe2 (x = 1.0, 0.9, and 0.8) Attempts to synthesize polycrystalline samples of nominal compositions and BaCuxTe2 (x = 1.0, 0.85, 0.70, 0.55, and 0.43) and BaAgxTe2 (x = 1.0, 0.9, and 0.8) were carried out by the reactions of elemental Ba, Cu or Ag, and Te using the sealed tube solid-state synthesis method, as described earlier. These reactions were loaded with a total mass of 0.5-0.6 g. The sealed silica tubes were first heated to 823 K in 20 h from 298 K. After 24 h at 823 K, the temperature was ramped up to 973 K with a heating rate of 20 K/h. After 48 h the furnace was switched off, and the reactions were cooled to 298 K. The products were opened under ambient conditions. All these reactions produced homogenous black lumps or ingots. The lumps were then homogenized into fine powders inside an Ar-filled glove box. The powders of the loaded reactions were then individually compressed into 4 mm circular pellets by using 15 MPa pressure. Each of these pellets was again sealed inside a carbon-coated fused-silica tube.

Each tube was heated to 773 K at 50 K/h. The temperature was kept constant at 773 K for 48 h. Finally, the furnace was switched off. The resulting pellets were ground into homogeneous powders inside an Ar-filled glove box for further characterization. Powder X-ray diffraction (PXRD) patterns of these products were used to assess their phase purity.

Crystal Structure Determinations. Single crystal X-ray diffraction data for BaCuxTe2 were collected at 293(2) K on a STOE IPDS II diffractometer equipped with graphite monochromatized Mo radiation (λ = 0.71073Å) and an Image Plate (IP) detector. The data were collected with an ω-scan technique from 0º-180º at an arbitrary φ-angle. Data reduction was performed with the X-AREA package. 26 An analytical absorption correction was performed (X-SHAPE2 within X-AREA). 26 Single crystal X-ray diffraction data from a BaAgxTe2 single crystal were collected at 100(2) K with the use of a Bruker APEX2 kappa diffractometer equipped with graphitemonochromatized Mo-Kα radiation (λ = 0.71073 Å). The data collection strategy was optimized with the use of the algorithm COSMO in the APEX2 package as a series of ω and φ scans. [START_REF]5-1 Data Collection and Processing Software[END_REF] Scans of 0.5º at 60 s/frame were used. The detector-to-crystal distance was 60 mm. The collection of intensity data as well as cell refinement and data reduction were carried out with the use of the program APEX3. [START_REF]5-1 Data Collection and Processing Software[END_REF] An analytical absorption correction was performed using JANA2006. [START_REF] Petříček | Crystallographic Computing System JANA2006: General Features[END_REF][START_REF] Oszlányi | Ab initio structure solution by charge flipping. II. use of weak reflections[END_REF][START_REF] Oszlányi | Ab initio structure solution by charge flipping[END_REF] Both structures are modulated. Atomic coordinates of the atoms in the subcells and initial values of their modulation functions were determined by the charge-flipping method. [START_REF] Oszlányi | Ab initio structure solution by charge flipping. II. use of weak reflections[END_REF][START_REF] Oszlányi | Ab initio structure solution by charge flipping[END_REF] The incommensurate superstructures were refined with JANA2006 software. [START_REF] Petříček | Crystallographic Computing System JANA2006: General Features[END_REF][START_REF] Oszlányi | Ab initio structure solution by charge flipping. II. use of weak reflections[END_REF][START_REF] Oszlányi | Ab initio structure solution by charge flipping[END_REF] The subcell of the BaCu0.43(3)Te2 compound was indexed with an orthogonal cell a = 4.6406(5) Å, b = 4.6596(5) Å, c = 10.362(1) Å, and the satellite reflections (supercell) were located at a diagonal incommensurate vector q = 0.3499(6)b*. None of the acceptable orthorhombic space groups gave a satisfactory refinement and structure was refined in the monoclinic superspace group P2(αβ1/2)0 (Table 1) with two Ba sites, two Cu sites, and four Te sites. Vacancies on the sites of Cu atoms were freely refined to the final stoichiometry BaCu0.43(3)Te2. Satellite reflections of one order were observed for BaCu0.43(3)Te2. Modulation waves of one order for positional and thermal displacement parameters were used for all Ba and Te atoms. There was no significant positional ordering of the Cu atoms; therefore, only the modulation terms of the occupancy parameters were refined. An inversion twin law [-1 0 0 0 -1 0 0 0 -1] was considered with a refined value of 0.6 (40)%.

The subcell of the BaAg0.77(1)Te2 compound was indexed with an orthogonal cell a = 4.6734(1) Å, b = 4.6468(1) Å, c = 11.1376(3) Å, and the satellite reflections (supercell) were located at an incommensurate vector q = 0.364(2)a*. The only orthorhombic space groups that gave good agreement indices for both the subcell and satellite reflections was P21212(α00)000 (Table 1). There are total of four independent crystallographic sites, one Ba site, one Ag site, and two Te sites, in the asymmetric unit. Vacancies on the sites of Ag were freely refined to the final stoichiometry BaAg0.77(1)Te2. Satellite reflections of one order were observed for BaAg0.77(1)Te2.

Modulation waves of one order for positional and thermal displacement parameters were used for all atoms. Only the symmetry allowed Fourier terms were refined. A twin law for racemic mixtures was used in the refinement. The electron density maps around the Cu2 atom of BaCu0.43(3)Te2 structure are shown in Supporting Information. The CRYSTALMAKER program was used to make all the drawings. Further details about the crystal structures are given in Table 1. Optical absorption studies on powdered samples of BaAg0.8Te2 were carried at 298(2) K using a JASCO V-770 UV/VIS/NIR spectrophotometer in diffuse reflectance mode. Dried BaSO4 powder was used as a standard reference. The reflectance data as a function of wavelength were recorded over a wavelength range from 2000 nm (0.62 eV) to 200 nm (6.2 eV). The reflectance data were converted to absorption data by using the Kubelka-Munk equation [START_REF] Kortüm | Reflectance Spectroscopy: Principles, Methods, Applications[END_REF] :

α/S = (1 -R) 2 /2R (1)
Here α, R, and S are the absorption coefficient, the reflectance, and the scattering coefficient, respectively. The bandgap was estimated by using the Tauc plot 33 :

(αhυ) n = A(hυ-Eg) (2)
Here α, h, and υ are absorption coefficient, Planck's constant, and frequency of light, respectively. Eg is the bandgap and A is a proportionality constant. The value of constant n determines the nature of bandgap. n = 2 and n = ½ values signify direct and indirect band gap, respectively.

Raman Spectroscopy. The Raman spectra of pelletized polycrystalline BaAg0.8Te2 were collected at 298(2) K using a Bruker SENTERRA II dispersive micro Raman spectrometer equipped with a confocal microscope. The spectra were recorded over a region of 50 to 3500 cm -1 with a resolution of 3.5 cm -1 . An excitation wavelength of 532 nm was used during the data collection. Raman spectra of individual pellets taken at different positions on the pellets showed no noticeable changes.

Electronic Structure Calculations. Because we cannot treat partial occupancies, we have considered the formulas BaCuTe2 and BaAgTe2 in order to obtain a qualitative understanding of the electronic structure of the compounds studied experimentally. The first principles calculations were carried out with the Vienna Ab Initio Simulation Package (VASP) [START_REF] Kresse | From ultrasoft pseudopotentials to the projector augmented-wave method[END_REF] code using the projector augmented wave method. [START_REF] Blöchl | Projector Augmented-wave method[END_REF][START_REF] Perdew | Generalized Gradient Approximation Made Simple[END_REF] For the exchange-correlation functional, we adopted the generalized gradient approximation with the Perdew, Burke, and Ernzerhof parametrization [START_REF] Heyd | Hybrid functionals based on a screened coulomb potential[END_REF][START_REF] Heyd | Hybrid functionals based on a screened coulomb potential[END_REF][START_REF] Paier | Screened hybrid density functionals applied to solids[END_REF] to relax the crystal structure and then the Heyd, Scuseria, and Ernzerhof functional to compute the density of states (DOS). [START_REF] Kohn | Self-consistent equations including exchange and correlation effects[END_REF][START_REF] Hohenberg | Inhomogeneous Electron Gas[END_REF] The integration over the Brillouin zone was sampled by 6 × 6 × 2 k-points for the two compounds. The kinetic energy cutoff for the expansion of the wave functions was set to the default value for both compounds.

RESULTS AND DISCUSSION

Syntheses. While exploring the Ba-Th-M-Te (M = Cu/Ag) system, we discovered black plate-shaped single crystals of BaCuxTe2 and BaAgxTe2 in the reactions of the elements at 1173 K. The yields of these two phases were around 30% based on M. The Th-free reaction for the BaAgxTe2 phase using the same reaction conditions did produce the desired BaAgxTe2 phase but the quality of the crystals was poor. In contrast, the BaCuxTe2 crystals could not be reproduced using the Th-free reaction of Ba, Cu, and Te. The crystals of BaMxTe2 were stable in air for at least one week. To study the stability of these phases, the syntheses of polycrystalline samples of BaCuxTe2 (x = 1.0, 0.85, 0.70, 0.55, and 0.43) and BaAgxTe2 (x = 1.0, 0.9, and 0. completely matches with a known phase Ba6.76Cu2.42Te14 (BaCu0.37Te2.07). [START_REF] Cui | Structures and Physical Properties of New Semiconducting Gold and Copper Polytellurides: Ba7Au2Te14 and Ba6.76Cu2.42Te14[END_REF] The PXRD pattern of the loaded composition BaCu0.43Te2 shows the formation of monophasic Ba6.76Cu2.42Te14 42 instead of the target BaCuxTe2 phase. The products of the BaCuxTe2 (x = 0.85, 0.70, 0.55) reactions also show the presence of the known ternary phase, Ba6.76Cu2.42Te14 (BaCu0.37Te2.07) [START_REF] Cui | Structures and Physical Properties of New Semiconducting Gold and Copper Polytellurides: Ba7Au2Te14 and Ba6.76Cu2.42Te14[END_REF] as a major phase along with small amounts of BaTe (See S. I.). Interestingly, the PXRD pattern for x = 1.0 composition did not show the presence of the known Ba6.76Cu2.42Te14 phase, but also could not be indexed completely based on the BaCu0.43(3)Te2 pattern simulated from the single-crystal X-ray structure determination. These observations suggest that BaCu0.43(3)Te2 is a kinetically stabilized phase that can only be synthesized by the Th-assisted reaction. No further attempts were made to synthesize BaCu0.43(3)Te2 phase by modifying the elemental ratios or heating profiles of Th-free reactions.

For BaAgxTe2 (x = 1.0, 0.9, and 0.8), most reflections matched the PXRD pattern calculated from the single-crystal data of BaAg0.77(1)Te2, but there were some unindexed reflections observed for the x = 1.0 and 0.9 phases. These unindexed reflections did not match known phases, including barium tellurides, silver tellurides, and BaAg2Te2 nor did we detect the presence of any unreacted reactants (Ba, Ag, and Te) in the PXRD patterns. The phase purity of x = 0.8 sample i.e. BaAg0.8Te2 is very close to the composition (BaAg0.77(1)Te2) obtained from the single crystal data (Figure 1). Hence, this polycrystalline sample with a loaded composition of BaAg0.8Te2, was used for further characterization and physical property measurements.

Crystal Structures of BaMxTe2 (M = Cu, Ag).

The superstructure of the BaCu0. KCuCeTe4 (2.667(4) Å), [START_REF] Patschke | KCuCeTe4: A New Intergrowth Rare Earth Telluride with an Incommensurate Superstructure Associated with a Distorted Square Net of Tellurium[END_REF] and NaCuZrTe3 (2.619(7) Å-2.695(7) Å). 45 Å-3.812(1) Å). [START_REF] Yang | Synthesis and Characterization of a Series of Quaternary Chalcogenides BaLnMQ3 (Ln = Rare Earth, M = Coinage Metal, Q = Se or Te)[END_REF] The average distances between Te1 and Te2 atoms in the square nets of Te atoms range from 3.293(5) Å to 3.298(5) Å. These distances are shorter than the van der Waals interactions of ~4.0 Å between two Te atoms and longer than a Te-Te single bond distance (~2.8 Å). A comparison of Te⋅⋅⋅Te interactions with related known compounds is presented in Table 3.

As discussed above, our attempts to synthesize polycrystalline BaCuxTe2 (x<1) led to formation of the known Ba6.76Cu2.42Te14 (or BaCu0.37Te2.07) compound as the major phase. The

The compound crystallizes in space group P63/mcm of the hexagonal system (see Figure S3 in S.I.). Its three-dimensional structure is composed of Ba cations that fill the channels made by

CuTe4 tetrahedral units and bent Te3 2-units. Unlike BaCu0.43(3)Te2 structure, Ba6.76Cu2.42Te14 contains conventional Te-Te bonding in the Te3 2-units, and hence charge balance for this compound is achieved as (Ba 2+ )6.76(Cu + )2.42(Te3 2-)3(Te 2-)5. The superstructure of BaAg0.77(1)Te2 was also found to be incommensurate, but different from that of BaCu0.43(3)Te2. It was solved in the orthorhombic P21212(α00)000 superspace group with cell dimensions of a = 4.6734(1) Å, b = 4.6468(1) Å, c = 11.1376(3) Å, and an incommensurate vector q = 0.364(2)a*. The asymmetric unit of the structure comprises a total of four independent crystallographic sites, one Ba, one Ag, and two Te sites.

The composition of this compound freely refined to the final stoichiometry BaAg0.77(1)Te2. The average atomic distances for BaAg0.77(1)Te2 are tabulated in Table 2. A view of the unit cell of the average subcell structure of BaAg0.77(1)Te2 is shown in Figure 2b. Each Ag atom in this structure is bonded to four Te1 atoms in a slightly distorted tetrahedral geometry similar to the Cu-coordination in the BaCu0.43(3)Te2 structure. These AgTe4 tetrahedra are fused together by sharing of all edges to form infinite two-dimensional layers of [Ag0.77(1)Te4/4] 1.23-.

The coordination number of Ba atoms in this structure is six and the geometry is trigonal prismatic (Figure 3b) in contrast to square-antiprismatic geometry of Ba in the BaCu0.

The average Ag1-Te1 distances of 2.865(2) Å to 2.879(3) Å in BaAg0.77 (1)Te2 are in good agreement with the Ag 1+ -Te distances in BaAg2Te2 (2.775(7) Å-2.938(8) Å), 48 K0.33Ba0.67AgTe2 (2.905(2) Å), [START_REF] Zhang | Distorted Square Nets of Tellurium in the Novel Quaternary Polytelluride K0.33Ba0.67AgTe2[END_REF] and Na0.2Ag2.8EuTe4 (2.829(6) Å-2.949(7) Å). [START_REF] Patschke | Cu0.66EuTe2, KCu2EuTe4 and Na0.2Ag2.8EuTe4: compounds with modulated square Te nets[END_REF] The average Ba-Te distances are in the range of 3.500 waves. [START_REF] Malliakas | A Double Charge Density Wave in the Single Tellurium Square Net in Cu0.63EuTe2?[END_REF][START_REF] Malliakas | Square Nets of Tellurium: Rare-Earth Dependent Variation in the Charge-Density Wave of RETe3 (RE = Rare-Earth Element)[END_REF][START_REF] Kim | Local Atomic Structure and Discommensurations in the Charge Density Wave of CeTe3[END_REF] There are also modulations in the Ag-Te and Ba-Te distances (Table 2). These 2.

Structural Relationships Among ThCr2Si2, 52 BaAgSe2, 4 BaMxTe2, and CaMnBi2. [START_REF] Brechtel | Zur Darstellung und Struktur von CaMnBi2[END_REF] The substructures of BaMxTe2 are related to the well-known structures of ThCr2Si2, BaAgSe2, and CaMnBi2. The unit cell structures of ThCr2Si2, BaAgSe2, and CaMnBi2 are shown in Figure 2. All the compounds but ThCr2Si2 have predominantly two-dimensional crystal structures. The Th atoms of ThCr2Si2 structure have bonding interactions with Si atoms. [START_REF] Shatruk | ThCr2Si2 structure type: The "perovskite" of intermetallics[END_REF] A common feature of these structure types is the presence of tetrahedral layers of transition-metal with chalcogen/pnictogen/tetrel. The compositions of these layers are [Cr2Si2] 4-, [AgSe4/4] 1-, [MxTe4/4] n-, and [MnBi4/4] 1-. The arrangement of atoms in these layers is of the anti-PbO type. [START_REF] Margadonna | Crystal structure of the new FeSe1-x superconductor[END_REF][START_REF] Guo | Superconductivity in the iron selenide KxFe2Se2 (0 ≤ x ≤ 1.0)[END_REF] The main difference among these structures is the composition of the chemical species If one assumes the full occupancy of the transition-metal site, then the chemical formula will be BaMTe2 with layers of [M 1+ Te 2-] 1-. Then the charged-balanced formula can be written as [(Ba 2+ )(M + Te 2-)(Te 1-)]. The transition-metal deficiency in our compounds should lower the average oxidation state of Te2 atoms of the square net to less than -1. This implies that the occupancy of M atom is equal to the negative charge on the Te2 atoms. This corresponds to -0.8 e -charge when the Ag occupancy is 80% i.e., [(Ba 2+ )(Ag 0.8+ Te 2-)(Te 0.8-)]. The structure of BaAg0.77(1)Te2 is similar to that of K0.33Ba0.67AgTe2 (space group: I4/mmm). [START_REF] Zhang | Distorted Square Nets of Tellurium in the Novel Quaternary Polytelluride K0.33Ba0.67AgTe2[END_REF] The main difference in these two structures is a vacancy at the Ag site of the two-dimensional layer in BaAg0.77(1)Te2 whereas in K0.33Ba0.67AgTe2 [START_REF] Zhang | Distorted Square Nets of Tellurium in the Novel Quaternary Polytelluride K0.33Ba0.67AgTe2[END_REF] The absorption edge study shows that BaAg0.8Te2 is a narrow band gap semiconductor with a direct bandgap of 1.0(2) eV, which agrees with the black color of the compound. The indirect bandgap of this compound is below 0.62 eV, which is beyond the limit of the instrument used in this study. Hence, the only direct bandgap is shown in Figure 4.

Raman Spectroscopy. A Raman spectrum of a pelletized polycrystalline sample of BaAg0.8Te2 was recorded at 298(2) K. The most intense bands around 83 cm -1 , 116 cm -1 , and 139 cm -1 (Figure 5) are Ag-Te stretching modes. These bands can be compared with the Ag-Te stretching modes of 80 cm -1 , 110 cm -1 , and 138 cm -1 in Ag2Te. [START_REF] Milenov | Preliminary studies of the Raman spectra of Ag2Te and Ag5Te3[END_REF] The bands at 667 cm -1 and 732 cm -1 are Ba-Te stretching modes, in good agreement with the Ba-Te stretching frequencies in BaIn2Te4

(667 cm -1 and 732 cm -1 ) [START_REF] Ishtiyak | Intrinsic extremely low thermal conductivity in BaIn2Te4: Synthesis, crystal structure, raman spectroscopy, optical, and thermoelectric properties[END_REF] and Ba3ScTe5 (671.5 cm -1 and 730 cm -1 ). 11 shows the presence of Ag-Te (83, 116, and 139 cm -1 ) and Ba-Te vibrations (667 cm -1 and 732 cm -1 ). A UV-vis-NIR spectroscopic study shows the compound to be a semiconductor with a direct band gap of 1.0(2) eV, consistent with its black color. DFT calculations give a pseudo bandgap with a weak value of the DOS at the Fermi level.

(NSF Grant ECCS-1542205), the State of Illinois, and the International Institute for Nanotechnology.

1 ]

 1 R indices [I>2σ(I)] Robs = 0.0679, wRobs = 0.1091 Robs = 0.0567, wRobs = 0.0824 R indices [all data] Rall = 0.1166, wRall = 0.1187 Rall = 0.1989, wRall = 0.1045 Final R main indices [I>2σ(I)] Robs = 0.0323, wRobs = 0.0636 Robs = 0.0440, wRobs = 0.0726 R main indices (all data) Rall = 0.0423, wRall = 0.0652 Rall = 0.0776, wRall = 0.0783 Final R 1 st order satellites [I>2σ(I)] Robs = 0.1788, wRobs = 0.2845 Robs = 0.1626, wRobs = 0.2648 R 1 st order satellites (all data) Rall = 0.2936, wRall = 0.3158 Rall = 0.5469, wRall = 0.4324 Extinction coefficient 12(15) 80(20) Twin law [-1 0 0 0 -1 0 0 0 -0.0(4) 0.5 Tmin and Tmax coefficients 0.3778 and 0.6923 0.2015 and 0.442 Largest diff. peak and hole 5.61 and -5.01 e•Å -3 10.67 and -11.64 e•Å -3 R = Σ||Fo|-|Fc|| / Σ|Fo|, wR = {Σ[w(|Fo| 2 -|Fc| 2 ) 2 ] / Σ[w(|Fo| 4 )]} 1/2 and w = 1/(σ 2 (I)+0.0004I 2 ) Powder X-ray Diffraction (PXRD) Study. The phase purities of the polycrystalline samples of BaCuxTe2 and BaAgxTe2 were analyzed by PXRD studies at 298(2) K using an X'Pert Pro-PAN analytical diffractometer. A Cu-Kα source of radiation (λ = 1.5406 Å) and an Xcelerator detector were used during the data collection. The operating current and voltage were 30 mA, and 40 kV, respectively. The reflection data were collected over a 2θ region of 10°-70° using a step size and scan time of 0.01° and 50 minutes, respectively. The simulated PXRD patterns were obtained from the single crystal data of BaMxTe2 using the deposited data and the Mercury program. 31 Solid-State Ultraviolet (UV)-Visible (VIS) Near-Infrared (NIR) Spectroscopy.

  8) were attempted by reactions of the elements using a two-step sealed tube method. The PXRD patterns of the final products of the BaCuxTe2 (x = 1.0 and 0.43) and BaAgxTe2 (x = 1.0, 0.9, and 0.8) reactions are shown in Figure 1. The PXRD patterns of BaCuxTe2 (x = 0.85, 0.70, and 0.55) are shown in the Supplementary Information.

Figure 1 :

 1 Figure 1: Powder X-ray diffraction patterns of (a) BaCuxTe2 (x = 1.0 and 0.43) along with the simulated PXRD pattern of BaCu0.43(3)Te2 structure and (b) BaAgxTe2 (x = 0, 0.9, and 0.8). The unindexed reflections for PXRD patterns of BaAgTe2 and BaAg0.9Te2 phases are shown by * and # symbols, respectively. The PXRD pattern of loaded composition BaCu0.43Te2completely matches with a known phase Ba6.76Cu2.42Te14 (BaCu0.37Te2.07).[START_REF] Cui | Structures and Physical Properties of New Semiconducting Gold and Copper Polytellurides: Ba7Au2Te14 and Ba6.76Cu2.42Te14[END_REF]

43 ( 3 )

 433 Te2 compound was solved in the monoclinic superspace group P2(αβ1/2)0 with cell constants of a = 4.6406(5) Å, b = 4.6596(5) Å, c = 10.362(1) Å, and a incommensurate vector q = 0.3499(6)b* + 1/2c*. The superstructure contains two Ba sites, two Cu sites, and four Te sites. The refinement of vacancies at the sites of Cu and the Te(1) atoms lead to the final stoichiometry of BaCu0.43(3)Te2. The average atomic distances for BaCu0.43(3)Te2 are given in Table 2 and the average subcell structure is shown in Figure 2(a).

Figure 2 :

 2 Figure 2: Average subcell structures of unit cells of (a) BaCu0.43(3)Te2 and (b) BaAg0.77(1)Te2, and views of the unit cells of (c) ThCr2Si2, (d) BaAgSe2, and (e) CaMnBi2 structures.

  3.61(2) × 2 3.58(2) × 2 3.64(2) × 2 3.563(2) × 2 3.444(4) × 2 3.684(4the superstructure of BaCu0.43(3)Te2 each of the Cu atoms is coordinated to four Te atoms (two Te3 and two Te4), forming a distorted CuTe4 tetrahedral unit. The CuTe4 tetrahedra are fused by the sharing of all edges. This results in the formation of infinite two-dimensional layers of [Cu0.43(3)Te4/4] 1.57-. These layers of [Cu0.43(3)Te4/4] 1.57-are extended along the bc plane. The arrangement of Cu and Te atoms in these layers can be classified as the anti-PbO type.[START_REF] Margadonna | Crystal structure of the new FeSe1-x superconductor[END_REF][START_REF] Guo | Superconductivity in the iron selenide KxFe2Se2 (0 ≤ x ≤ 1.0)[END_REF] These [Cu0.43(3)Te4/4] 1.57-layers are further separated by the layer of Ba1 and Ba2 atoms followed by a tellurium square net that is made up of Te1 and Te2 atoms (Figure2a). In the superstructure of BaCu0.43(3)Te2, the average Cu1-Te and Cu2-Te distances are 2.72(2) Å-2.73(2) Å and 2.72(2) Å-2.74(2) Å, respectively. These distances are consistent with the Cu-Te distances in the related structures such as Cu0.66EuTe2 (2.671(4) Å), 14 LaCu0.40Te2 (2.611(3) Å-2.781(4) Å),[START_REF] Huang | 0.40Te2[END_REF]

Figure 3 :

 3 Figure 3: Coordination environments of Ba atoms in the (a) BaCu0.43(3)Te2 and (b) BaAg0.77(1)Te2 substructures, respectively.

  (2) Å to 3.563(2) Å. The average distance between two neighboring Te2 atoms is 3.30(2) Å which is very close to the average Te•••Te interactions of 3.293(5) Å-3.298(5) Å in the BaCu0.43(3)Te2 structure. Both the BaCu0.43(3)Te2 and BaAg0.77(1)Te2 structures show modulation of theirTe square nets. The minimum, maximum, and average Te⋅⋅⋅Te interactions in BaAg0.77(1)Te2 are 3.03(1) Å, 3.58(1) Å, and 3.30(1) Å, which are significantly different from each other. This long-range modulation of Te square nets is akin to those compounds that show charge density wave (CDW)

  modulations in the Te square nets, Ag-Te distances, and Ba-Te distances contribute to the overall distortion in the BaAg0.77(1)Te2 structure. The modulation of BaCu0.43(3)Te2 structure is also mainly attributed to the modulation in the Te⋅⋅⋅Te interactions in the Te square nets, Cu-Te distances in [MxTe4/4] n-layers, and Ba-Te distances in BaTe8 square antiprism. The average, shortest, and maximum Te⋅⋅⋅Te interactions, Cu-Te, and Ba-Te distances are tabulated in Table

  that separate their layers and the number of layers per unit cell. The tetragonal ThCr2Si2 structure (space group I4/mmm) and monoclinic BaAgSe2 structure (space group P21/c) contain two layers per unit cell whereas the BaMxTe2 and CaMnBi2 structures contain only one layer per unit cell (Figure2). The [MxTe4/4] n-layers in the BaMxTe2 structure are separated by Ba cations and distorted square planes of Te atoms in contrast to the BaAgSe2 structure where Ba cations and Se2 2-dimers separate the [AgSe4/4] 1-layers. The [Cr2Si2] 4-layers in ThCr2Si2 are separated only by Th atoms. Both BaMxTe2 and BaAgSe2 can be considered as 122-type compounds if one ignores the M-vacancy, but still these structures are very different. The more pronounced catenation tendency Te > Se may be the reason for the stabilization of the BaMxTe2 structure with distorted Te squares instead of the monoclinic BaAgSe2 type structure.Assignment of Formal Oxidation States.As discussed earlier, the BaAg0.77(1)Te2 substructure consists of three layers ([Ag0.77(1)Te1], Ba1, and Te2 square net). Here, the oxidation states of Ag1, Ba1, and Te1 may be assigned as +1, +2, and -2, respectively. However, the assignment of an oxidation state for the Te2 atom involved in the formation of square nets is difficult and arbitrary owing to intermediate Te-Te interactions and silver deficiency. It is well established that the arrangement of Te in a perfect square net or linear chains with distances close to 2.8 Å (single Te-Te bond distance) will lead to Peierls distortion as these nets according to theoretical considerations are unstable.[START_REF] Peierls | More Surprises in Theoretical Physics[END_REF][START_REF] Papoian | Hypervalent Bonding in One, Two, and Three Dimensions: Extending the Zintl-Klemm Concept to Nonclassical Electron-Rich Networks[END_REF] These square nets can get stabilized if the charge on each Te is -2 (i.e., 8 electrons in the valence shell of the Te atom), which requires nonbonding interactions among neighboring Te atoms. If the effective charge on the Te atom is less negative then -2) it will lead to the stabilization of homoatomic bonding interactions between Te-Te atoms and the formation of polytelluride oligomers.[START_REF] Papoian | Hypervalent Bonding in One, Two, and Three Dimensions: Extending the Zintl-Klemm Concept to Nonclassical Electron-Rich Networks[END_REF] Electronic band structure calculations for a hypothetical ideal square net of Te atoms with oxidation state less negative then -2 should give a metal-like band structure where the Fermi energy (EF) levels crosses one or more bands.[START_REF] Zhang | Distorted Square Nets of Tellurium in the Novel Quaternary Polytelluride K0.33Ba0.67AgTe2[END_REF] But actually the distorted square nets of Te atoms with extended Te-Te interactions leads to the opening of a band gap, and semiconducting properties. Such distortion results in the formation of strong and weak Te-Te interactions where the effective charge on each Te atom in the distorted Te square nets depends on the extent of modulation/distortion, which is also controlled by the overall charge on the [MxTe] n-layers. Indeed, BaAgxTe2 single crystal data show satellite reflections indicative of a distorted modulated superstructure.

  the Ba and K cations that separate the twodimensional layers of [AgTe] are disordered at one crystallographic site. This leads to a formal charge of -0.67 for each of the Te atoms in the Te square net. The structure of BaCu0.43(3)Te2 has a vacancy at the transition metal site, is similar to the vacancy of Cu atoms in the two dimensional [CuxTe4/4] n-layer in EuCu0.66Te2 (space group: P4/mmm). In EuCu0.66Te2, the effective charge on each Te atom in the square net is -0.66. This type of vacancy in the transition metal site is common in antimonides having the formula of MxLaSb2 (M = Zn, Cu, and Mn; x = 0.52 -0.87).[START_REF] Cordier | Besetzungsvarianten der CaMnBi2-Struktur: Zur Kenntnis der Verbindungen LaZn0.52Sb2, LaCo0.68Sb2[END_REF] Optical Bandgap of BaAg0.8Te2.An absorption spectrum of a homogeneously ground polycrystalline sample of BaAg0.8Te2 was collected at 298(2) K over a wavelength region of 2000 nm to 200 nm.

Figure 4 :

 4 Figure 4: Tauc plot of solid-state UV-Vis-NIR spectrum of powdered polycrystalline BaAg0.8Te2.

Figure 5 :

 5 Figure 5: Raman spectrum of a powdered polycrystalline BaAg0.8Te2 sample.

Figure 6 :

 6 Figure 6: The calculated total (upper panel) and partial (lower panels) density of states (DOS) for (a) BaCuTe2 and (b) BaAgTe2.

Table 1 . Crystal Data and Structure Refinement for BaCu0.43(3)Te2 and BaAg0.77(1)Te2.

 1

	Empirical formula	BaCu0.43(3)Te2	BaAg0.77(1)Te2
	Formula weight	420.1	476
	Temperature (K)	293(2)	100(2)
	Wavelength	0.71073 Å	0.71073 Å
	Crystal system	monoclinic	orthorhombic
	Space group	P2(αβ1/2)0	P21212(α00)000
	Unit cell dimensions	a = 4.6406(5) Å	a = 4.67340(10) Å
		b = 4.6596(5) Å, β =	b = 4.64680(10) Å
		90.000(9)°	c = 11.1376(3) Å
		c = 10.3620(15) Å
	q-vector(1)	0a * + 0.3499(6)b * + 0.5c *	0.364(2)a *
	Volume	224.06(5) Å 3	241.868(10) Å 3
	Z	2	2
	Density (calculated)	6.23 g/cm 3	6.54 g/cm 3
	Absorption coefficient	23.4 mm -1	22.9 mm -1
	F(000)	345	393
	Crystal size	0.372 × 0.301 × 0.014 mm 3	0.09 × 0.07 × 0.04 mm 3
	θ range for data collection	4.75 to 38.15°	1.59 to 38.11°
	Index ranges	-8<=h<=8, -8<=k<=8, -	-8<=h<=8, -8<=k<=7, -
		18<=l<=18, -1<=m<=1	18<=l<=18, -1<=m<=1
	Reflections collected	23635 (7798 main + 15837	22714 (7558 main + 15156
		satellites)	satellites)
	Independent reflections	2446 (2421 main + 4865	3757 (1257 main + 2500
		satellites) [Rint = 0.1052]	satellites) [Rint = 0.1411]
	Completeness to θ = 38.15° 99%	98%
	Refinement method	Full-matrix least-squares on	Full-matrix least-squares on
		F 2	F 2
	Data / constrains / restraints	2446 / 5 / 0 / 87	3757 / 0 / 0 / 60
	/ parameters
	Goodness-of-fit on F 2	2.21	1.03
	Final

Table 2 . Average Interatomic Distances (in Å) in the Superstructure of BaMxTe2 (M = Cu,

 2

	Ag).
		M = Cu, x = 0.43(3)	M = Ag, x = 0.77(1)
	Average	Minimum	Maximum	Average	Minimum	Maximum
	M1-Te1 -	-	-	2.865(2) × 2	2.854(3) × 2	2.877(3) ×
				2.879(3) × 2	2.863(4) × 2	2.895(4) ×
	M1-Te3 2.73(2) × 2	2.71(2) × 2 2.75(2) × 2 -	-	-
	M1-Te4 2.72(2) × 2	2.70(2) × 2 2.74(2) × 2 -	-	-
	M2-Te3 2.74(2) × 2	2.72(2) × 2 2.75(2) × 2 -	-	-
	M2-Te4 2.72(2) × 2	2.70(2) × 2 2.74(2) × 2 -	-	-

Table 3 .

 3 Intermediate Te⋅⋅⋅Te Interactions in Some Related Layered Structures.

	Compound	Te⋅⋅⋅Te distance (Å)	Ref
	BaCu0.43(3)Te2	3.29(1)	This work
	BaAg0.77(1)Te2	3.30(1)	This work
	EuCu0.66Te2	3.168(1)	14
	KCu2EuTe4	3.1371(4)	14
	K0.33Ba0.67Te2	3.269(2)	15
	LaTe2	3.187(2)	19
	Na0.2Ag2.8EuTe4	3.1497(3)	14

ACKNOWLEDGMENTS J.P. thanks the Science and Engineering Research Board (SERB), Department of Science and Technology (DST), Government of India, for financial support under an Early Career Research award (Grant ECR/2017/000822) and IIT Hyderabad for seed grant and research facilities. S. J. and G. P. thank Ministry of Human Research Development and IIT Hyderabad for research fellowships. M.I. thanks DST India for research fellowship. Use was made of the Integrated Molecular Structure Education and Research Center X-ray Facility at Northwestern University, which has received support from the Soft and Hybrid Nanotechnology Experimental Resource

AUTHOR INFORMATION

Corresponding Author *E-mail: ibers@chem.northwestern.edu ORCID James A. Ibers: 0000-0002-5418-3645 Notes The authors declare no competing financial interest.

SUPPORTING INFORMATION

CCDC #1998322 and 1998323 contain supplementary crystallographic data for the superstructures. These data may be obtained free of charge by emailing data_request@ccdc.ccam.ac or www.ccdc.cam.ac.uk/data_request/cif or by contacting the Crystallographic Data Centre. 12 Union Road, Cambridge CB2 1EZ, UK; fax +44 1223 336033.

For the superstructure CCDC is unable to handle modulated structures but the raw fcf data are included with this submission. Supporting information includes details on reaction conditions, additional PXRD plots, atomic coordinates, interatomic distances and angles, and displacive details for BaCu0.43(3)Te2 and BaAg0.77(1)Te2 substructures.


Mohd Ishtiyak

Gopabandhu Panigrahi

Subhendu Jana

Jai Prakash

Adel Mesbah

Christos D Malliakas

Sébastien Lebègue

James A Ibers

Modulated Linear Tellurium Chains in Ba 3 ScTe 5 : Synthesis, Crystal Structure

Keywords:

come

INTRODUCTION

The study of structure-property relationships of transition metal chalcogenides is an active area in solid-state chemistry owing to a variety of applications to thermoelectric properties, magnetism, superconductivity, magnetoresistance, and charge density waves (CDW). [START_REF] Aydemir | YCuTe2: a member of a new class of the thermoelectric materials with CuTe4-based layered structure[END_REF][START_REF] Margadonna | Crystal structure of the new FeSe1-x superconductor[END_REF][START_REF] Park | K2Cu5Te5, a Novel Mixed-Valence Layered Compound with Metallic Properties[END_REF][START_REF] Lee | Band-Gap Tuning and Linear Magnetoresistance in the Silver Chalcogenides[END_REF][START_REF] Joshi | Short-range charge density wav order in 2H-TaS2[END_REF] The ternary and quaternary compounds such as Ba2MnQ3, [START_REF] Greaney | Studies on the Linear Chain Antiferromagnets: Ba2MnX3 (X = S, Se, Te) and Their Solid Solutions[END_REF] (BaF)2Fe2-xQ3, [START_REF] Sturza | Tuning the Magnetic Properties of New Layered Iron Chalcogenides (BaF)2Fe2-xQ3 (Q = S, Se) by Changing the Defect Concentration on the Iron Sublattice[END_REF] and AFeS2 (A = K and Rb) [START_REF] Bronger | The Antiferromagnetic Structures of KFeS2, RbFeS2, KFeSe2, and RbFeSe2 and the Correlation between Magnetic Moments and Crystal Field Calculations[END_REF] are examples that show interesting magnetic behavior. Furthermore, layered structures such as K2Cu5Te5, [START_REF] Park | K2Cu5Te5, a Novel Mixed-Valence Layered Compound with Metallic Properties[END_REF] MQ2 (M = V, Nb, and Ta; Q = S, Se, and Te), [START_REF] Chia | Electrocatalysis of layered Group 5 metallic transition metal dichalcogenides (MX2, M = V, Nb[END_REF] PtTe2 10 are metallic, and compounds like FeSe, 2 NbSe2, [START_REF] Pervin | Coexistence of superconductivity and ferromagnetism in defect-induced NbSe2 single crystals[END_REF] NbTe4, [START_REF] Yang | Pressure induced superconductivity bordering a charge-density-wave state in NbTe4 with strong spin-orbit coupling[END_REF] and MoTe2 13 are a few examples of superconducting chalcogenides. In the past few decades, metal chalcogenides with narrow band gaps and low thermal conductivities have been of interest for their promising thermoelectric properties. Examples include AkM2Te4 (Ak = Sr, Ba, M = Sc, Y), [START_REF] Assoud | Thermoelectric properties of the new tellurides SrSc2Te4 and BaSc2Te4 in comparison to BaY2Te4[END_REF] BaCu2-xAgxTe2, [START_REF] Yang | Realizing High Thermoelectric Performance in BaCu2-xAgxTe2 through Enhanced Carrier Effective Mass and Point-Defect Scattering[END_REF] Ba3Cu14-xTe12, [START_REF] Assoud | Thermoelectric Properties of the New Polytelluride Ba3Cu14-δTe12[END_REF] and YCuTe2. [START_REF] Aydemir | YCuTe2: a member of a new class of the thermoelectric materials with CuTe4-based layered structure[END_REF] The structural chemistry of metal chalcogenides is also very rich. Many of the metal chalcogenides are layered, but there are more complicated structures ranging from zerodimensional to three-dimensional. The chalcogen (Q = S, Se, and Te) atoms in these structures often show homoatomic bonding with a variety of Qn x-units, something not possible with oxides.

The tendency of chalcogens to form Q•••Q units is relatively more prominent for Te than for S or Se atoms. [START_REF] Ibers | Tellurium in a twist[END_REF] Thus, a large number of metal tellurides crystallize in the new structure types with intricate structures. The Te atoms in these metal tellurides form a wide range of polyanions (Qn x-) starting from the simplest Te2 2-units, [START_REF] Ibers | Tellurium in a twist[END_REF] oligomeric motifs Ten 2-, [START_REF] Graf | Solid State Polyselenides and Polytellurides: A Large Variety of Se-Se and Te-Te Interactions[END_REF] one-dimensional infinite chains of Te-Te-Te (e.g., LaCu0.40Te2, [START_REF] Huang | 0.40Te2[END_REF] GdCu0.33Te2, [START_REF] Huang | 0.40Te2[END_REF] and Gd3Cu2Te7 [START_REF] Huang | Gd3Cu2Te7 and U2Cu0.78Te6: Two Examples of Linear Te Chains[END_REF] ), and square nets of Te atoms in Cu0.66EuTe2, [START_REF] Patschke | Cu0.66EuTe2, KCu2EuTe4 and Na0.2Ag2.8EuTe4: compounds with modulated square Te nets[END_REF] KCu2EuTe4, 21 Na0.2Ag2.8EuTe4, [START_REF] Patschke | Cu0.66EuTe2, KCu2EuTe4 and Na0.2Ag2.8EuTe4: compounds with modulated square Te nets[END_REF] and K0.33Ba0.67AgTe2. [START_REF] Zhang | Distorted Square Nets of Tellurium in the Novel Quaternary Polytelluride K0.33Ba0.67AgTe2[END_REF] The compositions of such new tellurides are difficult to predict. Thus, exploratory solid statesynthesis is the most effective route to the discovery of new chalcogenides with interesting structures and properties.

The ternary Ak-Sc-Te system (Ak = Mg, Ca, Sr, and Ba) contains only two compounds, BaSc2Te4 and SrSc2Te4, that adopt the well-known CaFe2O4 structure type. [START_REF] Assoud | Thermoelectric properties of the new tellurides SrSc2Te4 and BaSc2Te4 in comparison to BaY2Te4[END_REF] In this report, we present the synthesis and crystal structure of the first polytelluride Ba3ScTe5 of the Ak-Sc-Te ternary system. Its structure is modulated. The subcell structure of this compound features linear infinite Te-Te-Te chains. We have also studied the physical properties of Ba3ScTe5, including optical bandgap and temperature-dependent resistivity studies along with its electronic structure.

EXPERIMENTAL METHODS

Syntheses. Caution! 238 U is an α-emitting radioisotope and as such is considered a health risk. Its use requires appropriate infrastructure and personnel trained in the handling of radioactive materials.

The following reactants were used as obtained: Ba (Johnson Matthey, 99.5 %), Te (Aldrich, 99.8 %), and Sc (Alfa Aesar, 99.9 %). Depleted U powder was obtained by hydridization and decomposition of turnings (IBI Labs) in a modification [START_REF] Bugaris | structures, and magnetic and optical properties of the compounds [Hg3Te2[END_REF] of a previous literature method. [START_REF] Haneveld | Some Ternary Uranium Chalcogenides[END_REF] "U-assisted" Synthesis of Crystals of Ba3ScTe5. The black irregular-shaped crystals of Ba3ScTe5 were first obtained from a reaction of Ba (34.6 mg, 0.252 mmol), U (10.0 mg, 0.042 mmol), Sc (3.8 mg, 0.084 mmol), and Te (85.8 mg, 0.672 mmol) during exploration of the quaternary Ba/Sc/U/Te system. The reactants were weighed inside an Ar-filled dry box. The reaction mixture was transferred into a carbon-coated fused-silica tube that was then evacuated and flame sealed under a vacuum (ca. 10 -4 Torr). The tube was placed in a programmable furnace for heat treatment. The temperature of the furnace was first ramped up to 1043 K in 24 h, and then the reaction was allowed to equilibrate at this temperature for 24 h before ramping up the temperature to 1173 K in 24 h. The temperature of the furnace was held constant at 1173 K for 199 h, and finally the reaction mixture was allowed to cool down to 373 K in 263 h. The composition of the products of the reaction was analyzed using the energy dispersive X-ray analysis (EDX) with the use of a Hitachi S3400 scanning electron microscope. The EDX study on black irregular shaped crystals showed the presence of Ba3ScTe5 (Ba:Sc:Te ≈ 3:1:5). The secondary phases present in the reaction product were black plate-shaped crystals of UOTe (U:Te ≈ 1:1), [START_REF] Murasik | Neutron Diffraction Measurements on Antiferromagnetic UOTe at 4.2 o K[END_REF] and yellow blocks of BaTe (Ba:Te ≈ 1:1). [START_REF]Crystal Structures[END_REF] Rational Synthesis of Crystals of Ba3ScTe5.The crystals of Ba3ScTe5 were successfully synthesized by loading the stoichiometric amounts of Ba (94.1 mg, 0.69 mmol), Sc (10.3 mg, 0.23 mmol), and Te (145.7 mg, 1.14 mmol) into a carbon-coated fused-silica 6 mm (inner diameter) tube inside an Ar filled glove box. The tube was sealed with a flame torch under vacuum (ca. 10 -4 Torr) and then it was placed vertically in an alumina crucible inside the computer-controlled chamber furnace. The following heating profile was used: The temperature was ramped up to 1223 K within 36 h and then the tube was annealed there for 96 h. After that, the reaction mixture was cooled to 772 K at the rate of 3.98 K/h and finally the furnace was turned off. After the completion of the reaction, a black solid lump was obtained. Black irregularshaped crystals of Ba3ScTe5 were found after breaking the black lump. Also present were BaTe crystals.

Synthesis of Polycrystalline Ba3ScTe5. The polycrystalline sample of Ba3ScTe5 was synthesized for physical property measurement by loading stoichiometric amounts of Ba (188.13 mg, 1.370 mmol), Sc (20.529 mg, 0.456 mmol), and Te (291.34 mg, 2.283 mmol) in a carboncoated fused-silica tube under an Ar atmosphere inside a glove box. The tube was evacuated (ca. 10 -4 Torr) and sealed. Then the tube was kept in a programmable muffle furnace and was heated to 1173 K in 36 hours. It was kept at 1173 K for four days and then the furnace was switched off.

Next the cooled product was ground into fine powder inside the Ar-filled glove box. From the PXRD study, the polycrystalline product was found to be almost single phase Ba3ScTe5 along with a minute amount of cubic BaTe.

Crystal Structure Determination. The single-crystal X-ray diffraction data on Ba3ScTe5 crystal that was obtained by the "U-assisted reaction" were collected at 100(2) K with the use of a Bruker APEX2 kappa diffractometer equipped with graphite-monochromized Mo-Kα radiation (λ = 0.71073 Å). The data collection strategy was optimized with the use of the algorithm COSMO in the APEX2 package as a series of ω and φ scans. 27 Scans of 0.3º at 20 s/frame were used. The detector to crystal distance was 50 mm. The collection of intensity data as well as cell refinement and data reduction were carried out with the use of the program APEX2. 27 Precession images of the data set showed additional satellite reflections indicative of a modulated structure. The substructure of Ba3ScTe5 was solved and refined in a straightforward manner in the hexagonal space group P63/mcm with the use of the SHELX-14 algorithms of the SHELXTL program package. [START_REF] Sheldrick | A short history of SHELX[END_REF]29 Face indexed absorption, incident beam, and decay corrections of the substructure were performed with the use of the program SADABS. 29 The thermal parameter of one of the crystallographically independent Te atom was found to be cigar-shaped.

The program STRUCTURE TIDY [START_REF] Gelato | STRUCTURE TIDY -a computer program to standardize crystal structure data[END_REF] in PLATON [START_REF] Spek | A Multipurpose Crystallographic Tool[END_REF] was used to standardize the atomic positions of the substructure. V (Å 3 ) 605.98 (7) ρ (g cm -3 ) 6.001 [START_REF] Margadonna | Crystal structure of the new FeSe1-x superconductor[END_REF] where q = 0.0059 for data collected at 100(2) K.

μ (mm -1 ) 21.89 R(F) b 0.029 Rw(Fo 2 ) c 0.067 a Space group is D 3 ,6h-P63/mcm, λ = 0.71073 Å, Z = 2. b R(F) = Σ ||Fo| -|Fc|| / Σ |Fo| for Fo 2 > 2σ(Fo 2 ). c Rw(Fo 2 ) = {Σ [w(Fo 2 -Fc 2 ) 2 ] /Σ wFo 4 } 1/2 . For Fo 2 < 0, w -1 = σ 2 (Fo 2 ); for Fo 2 ≥ 0, w -1 = σ 2 (Fo 2 ) + (qFo 2 )
Face-indexed absorption corrections for the incommensurate supercell were performed with the programs X-SHAPE2 [START_REF] Stoe | [END_REF] and JANA2006. [START_REF] Oszlányi | Ab initio structure solution by charge flipping[END_REF][START_REF] Oszlányi | Ab initio structure solution by charge flipping. II. Use of weak reflections[END_REF][START_REF] Petricek | Crystallographic Computing System JANA2006: General features[END_REF] Further details are given in Tables 1,2, and 3 and in the Supporting Information.

α/S = (1 -R) 2 /2R (1)
Here α, R, and S denote the absorption coefficient, reflectance coefficient, and scattering coefficient, respectively. The Tauc plot was used to estimate the band gap:

(αhν) n = A(hν -Eg) (2)
Here the symbols h, ν, n, A, and Eg stand for Planck's constant, frequency of light, a constant that decides the band gap nature, proportionality constant, and band gap, respectively.

The n = 2 value signifies a direct band gap and n = ½ signifies an indirect band gap.

Temperature-Dependent Resistivity Studies. The resistivity data as a function of temperature were collected on a polycrystalline compact pellet of Ba3ScTe5. The circular pellet with a thickness of ≈ 1.4 mm and a diameter of 8 mm was obtained by compacting the polycrystalline powder by applying a pressure of ≈ 10.3 MPa. The resulting compacted disk was further sintered at 923 K inside an evacuated carbon-coated fused-silica tube for ten hours. Fourprobe resistivity data were measured between 75 K and 300 K using equipment and procedures described previously. [START_REF] Jana | Synthesis and Characterization of Ba2Ag2Se2Se2[END_REF] Electronic Structure Calculations. The calculations were carried out with the VASP (Vienna ab Initio Simulation Package) [START_REF] Kresse | Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set[END_REF][START_REF] Kresse | From ultrasoft pseudopotentials to the projector augmented-wave method[END_REF] code that implements DFT (density functional theory) [START_REF] Kohn | Self-Consistent Equations Including Exchange and Correlation Effects[END_REF][START_REF] Hohenberg | Inhomogeneous Electron Gas[END_REF] within the projector augmented wave method. [START_REF] Blöchl | Projector augmented-wave method[END_REF] The DFT method has proven to be one of the most accurate methods for the computation of the electronic structure of solids. [START_REF] Reshak | Noncentrosymmetric Sulfide Oxide MZnSO (M = Ca or Sr) with Strongly Polar Structure as Novel Nonlinear Crystals[END_REF][START_REF] Huang | Visible-Light-Responsive Sillén-Structured Mixed-Cationic CdBiO2Br Nanosheets: Layer Structure Design Promoting Charge Separation and Oxygen Activation Reactions[END_REF][START_REF] Chen | Crystal Structure, and Optical Gap of Two-Dimensional Halide Solid Solutions CsPb2(Cl1-xBrx)5[END_REF] First, the crystal structure was relaxed using the Perdew, Burke, and Ernzerhof (PBE) functional, [START_REF] Perdew | Generalized Gradient Approximation Made Simple[END_REF] and then the density of states were obtained with the Heyd, Scuseria, and

RESULTS AND DISCUSSION

Syntheses. The black crystals of the ternary compound Ba3ScTe5 were first discovered serendipitously during the exploration of the quaternary Ba/U/Sc/Te system in a small yield of 20 wt% (based on Sc). Further, the synthesis of crystals of Ba3ScTe5 was reproduced using the stoichiometric reaction of the corresponding elements at 1223 K followed by slow-cooling to 298 K using the sealed-tube method. This reaction produced a better yield of Ba3ScTe5 crystals (ca. 80 wt.%). A similar reaction that was aimed for the synthesis of a bulk polycrystalline sample of Ba3ScTe5 was also carried out at 1173 K. The PXRD pattern of the reaction product showed almost a single phase of Ba3ScTe5 along with a very small amount of a secondary cubic BaTe phase (Figure 1). The reheating of the product at 1173 K as a compacted pellet did not improve the phase purity of the polycrystalline sample. We also attempted to make new ternary isostructural phases by replacing Ba with Pb and also replacing Ba with smaller alkaline-earth metals (Ca, Sr), but only binary phases resulted. Also, the replacement of Sc metal with Y metal (Ba3YTe5) afforded only binaries of the corresponding elements.

Structure of the Subcell of Ba3ScTe5. The subcell structure of Ba3ScTe5 (Figure 2) is related to the well-known Hf5Sn3Cu 50 structure type with the Ba atoms at Sn sites, Te atoms at Hf sites, and Sc atoms at Cu sites. Many intermetallic compounds with the Hf5Sn3Cu 50 type structure are known in the literature, but to the best of our knowledge this structure type is not known for any metal chalcogenides. Although, there are few reports on the synthesis of sulfur and selenium doping in binary compounds La5Ge3, La5Pb3, and Zr5Sb3 that adopt the Hf5Sn3Cu type structure but their crystal structures and amount of chalcogens doped in these compounds were not established, and only unit cell parameters of these chalcogen doped compounds were reported. [START_REF] Garcia | Chemistry in the Polar Intermetallic Host, Zr5Sb3. Fifteen Interstitial Compounds[END_REF][START_REF] Guloy | The Lanthanum-Germanium System. Nineteen Isostructural Interstitial Compounds of the La5Ge3 Host[END_REF][START_REF] Guloy | Exploration of the Interstitial Derivatives of La5Pb3 (Mn3Si3-Type)[END_REF] The crystal structure of subcell of Ba3ScTe5 comprises of two formula units in the hexagonal space group D 3 ,6h-P63/mcm with one crystallographic independent Sc site (site symmetry: -3.m), one Ba site (m2m), and two Te sites [Te1 (m2m) and Te2 (3.2)]. Crystal structure refinement details and metric data for the Ba3ScTe5 substructure are presented in Table 1 and3 Each ScTe6 octahedron is fused to two neighboring ScTe6 octahedra through sharing of two opposite triangular faces resulting in the formation of an infinite one-dimensional chain of 1 ,∞ [ScTe3 3-] along the [001]-direction (Figure 3a). In general, the face-sharing of polyhedral units is considered as least stable as compared with edge-and vertex-sharing of the polyhedra because the two metal atoms are closest in face-sharing. A survey of Sc chalcogenides using the ICSD web program [START_REF] Belsky | New developments in the Inorganic Crystal Structure Database (ICSD): accessibility in the support of materials research and design[END_REF] suggested only one example, RbSc5Te8, [START_REF] Babo | Synthesis and Crystal Structure of the Rubidium Scandium Telluride RbSc5Te8[END_REF] where both face-and edge-sharing of Scbased octahedra can be seen. However, the present ternary phase, Ba3ScTe5, is the first example of a Sc telluride where only face-shared ScTe6 octahedra are present. The six Te1 atoms form an almost perfect octahedral environment around Sc with the Sc-Te1 bond distances of 2.957(1) Å.

The Te-Sc-Te angles of these octahedra are also very close to the ideal octahedron with m-3m symmetry (Table 3). A comparison of Sc-Te distances in Ba3ScTe5 with the corresponding distances found in the related structures such as BaSc2Te4 (2.878(2)-2.958(1) Å), 14 SrSc2Te4

(2.892(1)-2.977(1) Å), 14 RbSc5Te8 (2.890(1)-2.926(1) Å), [START_REF] Babo | Synthesis and Crystal Structure of the Rubidium Scandium Telluride RbSc5Te8[END_REF] and TlScTe2 (2.9341(6) Å) [START_REF] Teske | Crystal Structure, Physical Properties and Electronic Band Structure of TlScQ2 (Q = S, Se and Te)[END_REF] reveals good agreement with the single Sc 3+ -Te bonding. [START_REF] Muravieva | Crystal structure of LnTe3, where Ln = La[END_REF] LnCuxTe2 (Ln = La, Nd, Sm, Gd, Dy), [START_REF] Huang | 0.40Te2[END_REF] Gd3Cu2Te7, 20 Ba2MAnTe7 (M = Ti, Cr, An = Th, U), [START_REF] Prakash | Three New Quaternary Actinide Chalcogenides Ba2TiUTe7, Ba2CrUTe7, and Ba2CrThTe7: Syntheses, Crystal Structures, Transport Properties, and Theoretical Studies[END_REF] KTh2Te6, 66 BaAnTe4 (An = Th and U), [START_REF] Prakash | Crystal Structures, Resistivity Stuides, and Electronic Properties of Three New Barium Actinide Tellurides: BaThTe4, BaUTe4, and BaUTe6[END_REF] and ATiU3Te9 (A = Rb and Cs). [START_REF] Ward | Synthesis and Characterization of Two Quaternary Uranium Tellurides, RbTiU3Te9 and CsTiU3Te9[END_REF] The assignments of +2 and +3 oxidation states to Ba and Sc atoms, respectively are clear in the Ba3ScTe5 substructure. However, the assignment of charges on Te atoms is challenging. As Optical Band Gap Study. The absorption spectrum (Figure 6) for a polycrystalline sample of Ba3ScTe5 was collected at 298(2) K. A broad absorption transition around 0.6(2) eV is apparent from Figure 6a. A direct bandgap of 1.1(2) eV was estimated from the analysis of the square of absorption data as a function of energy (Figure 6b). The value of indirect bandgap was found to be below the instrument limit (~0.8 eV). This experimental optical band gap, which is consistent with the black color of the compound, suggests that Ba3ScTe5 is a semiconductor.

Table 3. Selected Interatomic Lengths (Å) in the

Temperature-Dependent Resistivity Study. The resistivity of polycrystalline Ba3ScTe5 as a function of temperature shows an exponential drop in resistivity values with increasing temperature in the range 75 K to 300 K (Figure 7). CCDC #1951174 and 1950724 contain supplementary crystallographic data for the substructure and superstructure of Ba3ScTe5, respectively. These data may be obtained free of charge by emailing data_request@ccdc.ccam.acwww.ccdc.cam.ac.uk/data_request/cif, or by contacting the Crystallographic Data Centre. 12 Union Road, Cambridge CB2 1EZ, UK; fax +44 1223 336033.

Included with this submission are the cif and checkcif for the substructure. For the superstructure CCDC is unable to handle modulated structures but the raw fcf data are included with this submission.

For Table of Contents Only

Ba3ScTe5 was synthesized and its modulated crystal structure was solved in the hexagonal superspace group P-6(00γ)0 with a = 10.1188(3) Å and c = 6.8332(3) Å, and a modulation vector of q = 0.3718(2)c*. Its structure is made up of infinite chains of 1 ,∞[ScTe3 3-] that are separated by Ba 2+ cations and infinite linear chains of Te atoms that are distorted owing to the formation of long-and short-bonded pairs of Te atoms.

Table 2 . 3 R

 23 Crystallographic Data and Structure Refinement Details for the least-squares on F 2 Data / constrains / restrains / parameters 4804 / 2 / 0 / 87 Goodness-of-fit on F 2 0.88 Final R indices a [I>3σ(I)] Robs = 0.0292, wRobs = 0.0384 R indices [all data] Rall = 0.0801, wRall = 0.0447 Final R main indices [I>3σ(I)] Robs = 0.0251, wRobs = 0.0351 R main indices (all data) Rall = 0.0426, wRall = 0.0374 Final R 1 st order satellites [I > 3σ(I)] Robs = 0.0392, wRobs = 0.0667 R 1 st order satellites (all data) Rall = 0.1457,wRall = 0.0966 Extinction coefficient 820(30) Tmin and Tmax coefficients 0.5173 and 0.7419 Largest diff. peak and hole 4.79 and -5.38 e -Å -= Σ ||Fo|-|Fc|| / Σ |Fo|, wR = {Σ [w(|Fo| 2 -|Fc| 2 ) 2 ] / Σ [w(|Fo| 4 )]} 1/2 and w = 1/(σ 2 (I) + 0.000016I 2 ). Powder X-ray Diffraction Measurement (PXRD). PXRD studies at 298(2) K were used to confirm the phase purity of the polycrystalline samples. Cu-Kα radiation (λ = 1.5406 Å) was used in the diffractometer (Model: X'Pert Pro-PAN analytical) equipped with an Xcelerator detector. The finely ground polycrystalline sample was fixed at a flat sample stage. The X'Pert High Score software was used to collect the PXRD data in the 2θ range of 10-70° with step size and scan time of 0.01° and 50 min, respectively. The Match3! software suite (version 3.6.1) was used to analyze the PXRD patterns. Solid-State Ultra Violet-Visible Near Infrared Spectroscopy. A PerkinElmer UV/VIS/NIR spectrophotometer was used to study the optical band gap of polycrystallineBa3ScTe5 at 298(2) K in the diffuse reflectance mode over the wavelength range of 1500 nm to 200 nm. BaSO4 was dried overnight to remove undesired moisture and then was used as a standard reference. The absorption data were generated from the reflectance data using the Kubelka-Munk equation.[START_REF] Kortüm | Reflectance Spectroscopy: Principles, Methods, Applications[END_REF]

Ernzerhof 47 -

 47 [START_REF] Paier | Screened hybrid density functionals applied to solids[END_REF] (HSE) functional. To ensure the convergence of the calculations, a k-points grid of 8 × 8 × 6 was used for both HSE and PBE calculations. For the HSE calculation, the energy cutoff describing the plane-wave expansion in the wave function was set to the default value of 187.2 eV, while for the PBE relaxation of the structure it was set to 1000 eV. The DFT optimized lattice parameters a = b = 10.27 Å and c = 6.96 Å are in a reasonable agreement with the experimental values of the substructure (a = b = 10.1190(5) Å and c = 6.8336(3) Å).

Figure 1 :

 1 Figure 1: PXRD pattern of the polycrystalline Ba3ScTe5 compound. The symbol * indicates reflection from the secondary BaTe phase.

  , respectively. Sc atoms in this structure are coordinated to six Te atoms (6 × Te1) that are arranged in an octahedral fashion around the central metal atom.

Figure 2 :

 2 Figure 2: A general view of the structure of subcell of Ba3ScTe5 viewed approximately along the c-axis. Here and in succeeding figures Ba, Sc, and Te atoms are shown in blue, green, and orange, respectively.

  , the 1 ,∞[ScTe3 3-] chains are formed by sharing of triangular faces of ScTe6 octahedra (Figure3a). As a consequence of face-sharing, the Sc•••Sc distances are expected to be shorter than those in related structures that have edge-sharing or corner-sharing units of Sc octahedra. Indeed, the Sc•••Sc interactions of 3.4167(1) Å in Ba3ScTe5 are shorter when compared with TlScTe2 (4.2128(4) Å), 56 BaSc2Te4 (4.2692(1) Å),[START_REF] Assoud | Thermoelectric properties of the new tellurides SrSc2Te4 and BaSc2Te4 in comparison to BaY2Te4[END_REF] and CsCu2Sc3Te6 (4.0430(1) Å)[START_REF] Babo | CsCu2Sc3Te6 and CsCuY2Te4: Two new quaternary cesium copper rare-earth metal tellurides[END_REF] that have edge-shared ScTe6 octahedra. Only RbSc5Te8 shows a Sc•••Sc interaction of 3.6590(1) Å, which is closer to the corresponding interactions in Ba3ScTe5. There are few reports of Sc ternary compounds e.g., Sc6MTe2, [M = Cu (3.04(1) Å) and Ag (3.05(1) Å)],[START_REF] Chen | Structure, and Bonding of Sc6MTe2 (M = Ag, Cu, Cd): Hetrometal-Induced Polymerization of Metal chains in Sc2Te[END_REF] and Sc6PdTe2 (3.08(1) Å)[START_REF] Maggard | Insights into Metal Framework Constructions from the Syntheses of New Scandium-and Yttrium-Rich Telluride Compounds: Y5Ni2Te2 and Sc6PdTe2[END_REF] where a Sc-Sc metal bond is present. Barium atoms are surrounded by a total of nine Te atoms, five Te1 and four Te2 atoms, in a distorted tricapped trigonal prismatic geometry with Ba-Te distances of 3.405(1) Å to 3.724(1)Å (Figure3b).

Figure 3 :

 3 Figure 3: (a) A fragment of the ScTe6 chain and (b) the local coordination environment of Ba atom in the subcell structure of Ba3ScTe5.

Figure 4 :Figure 5 .

 45 Figure 4: A local view of infinite -Te-Te-Te-chains in (a) the subcell structure and (b) the modulated superstructure of Ba3ScTe5. The Te•••Te interactions are shown as black dashed lines and Te-Te bonds are shown as solid red lines. The Te-Te bonding threshold is 2.8-2.9 Å.

Figure 5 :

 5 Figure 5: Relations among the subcell structure of (a) Ba3ScTe5 with the (b) Hf5Sn3Cu 50 and (c) Mn5Si3 63 structures.

  discussed earlier, the Ba3ScTe5 substructure contains two types of Te atoms: Te1 atoms that are bonded with Sc atoms and Te2 atoms that are form the infinite Te•••Te•••Te chains with intermediate Te•••Te interactions. Hence, the charge on each Te1 atoms could be assigned as -2e -. This assignment results in an average nonintegral charge of -1.5 e -on each Te2 atom, i.e., the Te2 atoms are partially reduced in this Ba3ScTe5 substructure. The bond valence sum[START_REF] Brown | The Chemical Bond in Inorganic Chemistry, The Bond Valence Model[END_REF] calculations for Ba3ScTe5 substructure using Expo2014 software[START_REF] Altomare | a kit of tools for phasing crystal structures from powder data[END_REF] yields the following bond valances: 2.36 for Ba1, 2.55 for Sc, 2.17 for Te1, and 1.56 for Te2. The BVS calculation also indicates a partial reduction of Te2 atoms. The modulated structure of Ba3ScTe5 shows the splitting of these Te•••Te•••Te chains into Te2 n-dimers with Te-Te minimum and maximum distances of 2.8(1) and 3.9(1) Å, respectively. The modulated structure contains approximately one dimer per three Te atoms (Figure4b). There is no evidence of Te vacancies so that the dimerization model can account for the extra electron if all five Te atoms were isolated (Figure4b). This stabilization of the Ba3ScTe5 structure is not possible with Te2 2-dimers instead of distorted Te•••Te•••Te chains as it demands Ba in +1 state or Sc in +2 state. Hence, we conclude that the presence of these distorted chains of Te with an average charge of -1.5 e -per Te atom is responsible for stabilization of Ba3ScTe5 in the Hf5Sn3Cu structure type. Thus, based on the coordination environments and the distances between the homo/hetero atoms, charge balance in the valence-imprecise Ba3ScTe5 structure can be formulated as (Ba 2+ )3(Sc 3+ )(Te 2-)3(Te 1.5-)2. An average charge of -1.5 e -on the Te atoms of the infinite Te•••Te•••Te chains in BaAnTe4 is also known.[START_REF] Prakash | Crystal Structures, Resistivity Stuides, and Electronic Properties of Three New Barium Actinide Tellurides: BaThTe4, BaUTe4, and BaUTe6[END_REF] Such assignment of non-integer charge of Te atoms of Te•••Te•••Te chains is common and is reported for many of the tellurides including the Ba2MAnTe7 (M = Ti, Cr, An = Th, U)[START_REF] Prakash | Three New Quaternary Actinide Chalcogenides Ba2TiUTe7, Ba2CrUTe7, and Ba2CrThTe7: Syntheses, Crystal Structures, Transport Properties, and Theoretical Studies[END_REF] , CuxUTe3,[START_REF] Patschke | CuxUTe3: Stabilization of UTe3 in the ZrSe3 Structure Type via Copper Insertion. The Artifact of Te-Te Chains and Evidence for Distortions Due to Long Range Modulations[END_REF] and ATiU3Te9 structures.[START_REF] Ward | Synthesis and Characterization of Two Quaternary Uranium Tellurides, RbTiU3Te9 and CsTiU3Te9[END_REF]

Figure 6 :

 6 Figure 6: (a) Optical absorption spectrum and (b) solid-state UV/Vis direct bandgap Tauc plot for polycrystalline Ba3ScTe5.

Figure 7 :

 7 Figure 7: Temperature-dependent resistivity plot for polycrystalline Ba3ScTe5.

Figure 8 :

 8 Figure 8: Computed total (upper plot) and partial (lower plots) density of states (DOS) for the subcell structure of Ba3ScTe5. The DOS calculations were performed using the HSE functional.

Table 1 . Crystallographic Data and Structure Refinement Details for the Substructure of Ba3ScTe5.

 1

		Ba3ScTe5
	Temperature (K)	100(2)
	a (Å)	10.1190(5)
	c (Å)	6.8336(3)

ACKNOWLEDGMENTS J.P. thanks the Science and Engineering Research Board (SERB), Department of Science and Technology (DST), Government of India, for financial support under an Early Career Research award (Grant ECR/2017/000822) and IIT Hyderabad for seed grant and research facilities. M.I. thanks DST India for research fellowship. G. P. and S. J. thank Ministry of Human Research Development, IIT Hyderabad for research fellowships. Use was made of the Integrated Molecular Structure Education and Research Center X-ray Facility at Northwestern University, which has received support from the Soft and Hybrid Nanotechnology Experimental Resource (NSF Grant ECCS-1542205), the State of Illinois, and the International Institute for Nanotechnology. The authors also thank Dr. Surya Jammalamadaka and Dwipak P. Sahu from the Department of Physics, IIT Hyderabad, for their help in collecting temperature-dependent resistivity data and UV-vis-NIR study.

AUTHOR INFORMATION

Corresponding Author

*E-mail: ibers@chem.northwestern.edu 20 ORCID James A. Ibers: 0000-0002-5418-3645

The authors declare no competing financial interest.