ACuZrQ <sub>3</sub> (A = Rb, Cs; Q = S, Se, Te): Direct Bandgap Semiconductors and Metals with Ultralow Thermal Conductivity

■ EXPERIMENTAL METHODS

Reagents. Cs (99.5%, Alfa Aesar), Rb (99.5% Alfa Aesar), S (99.99%, 5N Plus Inc.), Se (99.99%, American Elements), Te (99.999% American Elements), CuS (99.99%, Sigma-Aldrich), Zr (99.95% Alfa Aesar), CsCl (99.9%, Alfa Aesar), and RbCl (99.9%, Alfa Aesar) were used as purchased without additional purification. Cu (99.7%, MilliporeSigma) powder was activated by washing with 10 wt % HCl followed by a deionized water rinse and dried with isopropanol in a vacuum filter and stored in a glovebox.

Synthesis of A x Q y . Amounts of ∼15 g batches of A x Q y (A = Rb, Cs; Q = S, Se, Te) were prepared from stoichiometric reactions of the two respective elements in liquid ammonia NH 3 as described previously. 12,13 A typical synthesis is as follows: Cs or Rb metal was slightly heated (∼30 or ∼40 °C, respectively) and pipetted into a 250 mL three-neck round-bottom flask with a glass stir bar and a Teflon valve in a nitrogen glovebox. The airtight flask was then transferred out of the box to a Schlenk line. The line was then purged with nitrogen, and then 150 mL of ammonia gas was condensed into the flask at -77 °C with a dry ice/acetone bath and allowed to dissolve the alkali metal which formed a dark blue solution for about 1 h. The chalcogen was added to the mixture and stirred for several hours. The ammonia was then allowed to evaporate under a nitrogen flow by allowing the dry ice/acetone bath to warm up to room temperature. The air-sensitive material was then dried via vacuum overnight and stored in a glovebox. Rb 2 S and Cs 2 S were white/pale yellow. Rb 2 Se was white/pale orange. Rb 2 Te 2 and Cs 2 Te 2 appeared black (probably because of the presence of longer Te x 2-, x > 2, impurities). Cs 2 S 4 was orange.

Synthesis of RbCuZrQ 3 . RbCuZrQ 3 crystals suitable for single crystal X-ray diffraction were synthesized by using a combination of Rb 2 Q x (Q = S, Se and x = 1; Q = Te and x = 2), Cu or CuS, Zr, and either S, Se, or Te in a stoichiometric ratio. This mixture was then combined with RbCl in either a 1:7 ratio when Q = S or a 1:10 ratio when Q = Se or Te. For RbCuZrS 3 the reagents Rb 2 S (0.120 g, 0.591 mmol), CuS (0.113 g, 1.18 mmol), Zr (0.108 g, 1.18 mmol), S (0.057 g, 1.8 mmol), and RbCl (1.002 g, 8.286 mmol) were combined in a 1:2:2:3:14 ratio of Rb 2 S:CuS:Zr:S:RbCl. For RbCuZrSe 3 the reagents Rb 2 Se (0.104 g, 0.416 mmol), Cu (0.053 g, 0.83 mmol), Zr (0.076 g, 0.83 mmol), Se (0.164 g, 2.08 mmol), and RbCl (1.004 g, 8.303 mmol) were combined in a 1:2:2:5:20 ratio of Rb 2 Se:Cu:Zr:Se:RbCl. For RbCuZrTe 3 the reagents Rb 2 Te 2 (0.163 g, 0.383 mmol), Cu (0.049 g, 0.77 mmol), Zr (0.070 g, 0.77 mmol), Te (0.195 g, 1.53 mmol), and RbCl (0.924 g, 7.64 mmol) were combined in a 1:2:2:4:20 molar ratio of Rb 2 Te 2 :Cu:Zr:Te:RbCl. The mixture was prepared in a nitrogen glovebox and was homogenized with a mortar and pestle. Fused silica tubes with outer diameter (OD) 13 mm and inner diameter (ID) 11 mm lined with aluminum foil to prevent powder from sticking to the sides were charged with the respective mixture. The tube was then transferred to a vacuum line, evacuated to 2.9 × 10 -3 mbar, and then flame-sealed with a torch. The sealed tube was then placed inside a ceramic mullite tube inside of a programmable one-zone tube furnace packed with insulation wool. The tube was positioned such that the top of the tube was in the hot center of the tube furnace while the end with the reagents was adjacent to the thermocouple closer to the bottom of the furnace to suppress volatilization. The furnace was heated to 800 °C in 15 h and held at this temperature for 24 h. For RbCuZrTe 3 the furnace was turned off and allowed to cool to room temperature. For RbCuZrS 3 and RbCuZrSe 3 the furnace was cooled at 4 °C/h to 600 °C, and then the furnace was turned off and allowed to cool to room temperature. RbCuZrQ 3 (Q = S, Se, Te) in the form of black platelet crystals were mechanically separated for single-crystal X-ray diffraction.

Synthesis of CsCuZrS 3 . CsCuZrS 3 was synthesized by using a CsCl flux to produce pure bulk material. CsCuZrS 3 was synthesized by using Cs 2 S 4 (0.205 g, 0.520 mmol), CuS (0.100 g, 1.05 mmol), Zr (0.095 g, 1.04 mmol), and CsCl (1.000 g, 5.940 mmol) combined in a 1:2:2:5.657 molar ratio of Cs 2 S 4 :CuS:Zr:CsCl. The mixture was prepared in a nitrogen glovebox and was homogenized with a mortar and pestle. A fused silica tube with an OD of 13 mm and an ID of 11 mm lined with aluminum foil to prevent powder from sticking to the sides was charged with the mixture. The tube was then transferred to a vacuum line, evacuated to 2.9 × 10 -3 mbar, and then flame-sealed with a torch. The sealed tube was then placed inside a mullite tube in a programmable one-zone tube furnace which was then packed with insulation wool. To suppress any volatilization during the reaction, the tube was positioned such that the end with the reagents was adjacent to the thermocouple and the top of the tube was just below the center of the tube furnace, which is the hottest region of the furnace. The furnace was heated to 700 °C at a rate of 20 °C/h, dwelled for 24 h, and then the furnace was turned off and allowed to cool to room temperature. The tube was opened in a fume hood, and the material was ground and homogenized. The homogeneous mixture was then charged into a new fused silica tube with the same dimensions and flame-sealed under vacuum in the same manner. The tube was then placed into the same furnace in an identical manner. The furnace was then heated to 300 °C at a rate of 20 °C/h. The heating rate was then increased to 100 °C/h until it reached a temperature of 1000 °C and then dwelled for 6 h. The furnace was then turned off and allowed to cool to room temperature. Black platelet crystals, clear crystals, and red irregularly shaped crystals were observed. The product was then washed sequentially with deionized water, methanol, and dimethylformamide, removing the clear and red crystals. The remaining black platelets were then dried by a rinse of methanol followed by nitrogen gas until the methanol had evaporated. Pictures of the crystals are presented in the Supporting Information (Figure S14).

Synthesis of ACuZrTe 3 . A 5.5 g ingot of CsCuZrTe 3 was synthesized by stoichiometric combination by using Cs 2 Te 2 (2.137 g, 4.102 mmol), Cu (0.521 g, 8.20 mmol), Zr (0.748 g, 8.20 mmol), and Te (2.093 g, 16.41 mmol) combined in a 1:2:2:4 molar ratio of Cs 2 Te 2 :Cu:Zr:Te. A 5.5 g ingot of RbCuZrTe 3 was synthesized by stoichiometric combination by using Rb 2 Te 2 (1.881 g, 4.414 mmol), Cu (0.561 g, 8.83 mmol), Zr (0.805 g, 8.83 mmol), and Te (2.253 g, 17.66 mmol) combined in a 1:2:2:4 molar ratio of Rb 2 Te 2 :Cu:Zr:Te. The mixtures were prepared in a nitrogen glovebox and were homogenized with a mortar and pestle. Fused silica tubes with an OD of 10 mm and an ID of 8 mm lined with aluminum foil to prevent powder from sticking to the sides were charged with the mixture. The tube was then transferred to a vacuum line, evacuated to 2.9 × 10 -3 mbar, and then flame-sealed with a torch with an internal length of 20 cm. The sealed tube was then placed inside a mullite tube in a programmable one-zone tube furnace which was then packed with insulation wool. To suppress volatilization during the reaction, the tube was positioned such that the end with the reagents was adjacent to the thermocouple and the top of the tube was just below the center of the tube furnace, which is the hottest region of the furnace. The furnace was heated to 1000 °C at a rate of 100 °C/h, dwelled for 12 h, and then water quenched. The tubes were opened in a fume hood, and black ingots with metallic luster were obtained.

Single-Crystal X-ray Diffraction. Intensity data of suitable platelet-shaped single crystals were mounted on a glass fiber with super glue and diffracted on either a STOE IPDS 2, STOE IPDS 2T, or STOE StadiVari diffractometer at 293 K. The STOE IPDS 2 and STOE IPDS 2T diffractometers were equipped with Mo Kα (λ = 0.71073 Å) sealed X-ray source with X-ray fiber optics and an image plate detector. The STOE StadiVari diffractometer was equipped with an AXO Auxilia Microfocus Ag Kα (λ = 0.56083 Å) sealed X-ray source and a Dectris Pilatus3 R CdTe 300K Hybrid Photon Counting detector. Data reduction was performed with the STOE X-Area ver.

1.90 software package. A numerical absorption correction was applied by using STOE X-Red ver. 1.65.2 and STOE X-Shape ver. 2.21 followed by scaling and outlier rejection with STOE LANA ver. 1.83.8. 14 The structure was solved with the ShelXT intrinsic phasing solution method 15 and was refined with ShelXL full-matrix leastsquares minimization on the F 2 method. 16 Olex2 17 was used as the graphical interface. Select crystallographic information can be found in Tables 1 and2 with complete crystallographic information found in Tables S1-S34.

Electronic Structure and Phonon Dispersion Calculations. We performed first-principles calculations based on density functional theory (DFT) 18,19 using the Vienna Ab initio Simulation Package (VASP) 20,21 along with potentials of the elements derived by using the projector augmented-wave (PAW) 22 method. We used the following PAW potentials for Rb (4s 2 4p 6 5s 1 ), Cs (5s 2 5p 6 6s 1 ), Cu (3d 10 4s 1 ), Zr (4s 2 4p 6 4d 2 5s 2 ), S (3s 2 3p 4 ), Se (4s 2 4p 4 ), and Te (5s 2 5p 4 ) in our calculations. The Perdew-Burke-Ernzerhof (or PBEsol) 23 exchange-correlation energy functional for solids was employed in all calculations. We used 8000 k-points per reciprocal atom (KPPRA) for optimization of the unit cells. The plane wave basis set with cutoff energy of 520 eV was adopted. The crystal structures were fully relaxed until the total energy converged to 10 -8 eV, and the force on each atom is less than 0.001 eV/Å. The optimized lattice constants of CsCuZrS R all = 0.1214 R all = 0.0767 R all = 0.0788 R all = 0.0280 wR all = 0.2592 wR all = 0.1337 wR all = 0.2111 wR all = 0.0766

group (No. 62) and contains 24 atoms in the primitive unit cell whereas the rest of the quaternary compounds have the Cmcm space group (No. 63) and contain 12 atoms in their primitive unit cell. For the convenience of the calculations, we rearranged the lattice vectors of RbCuZrTe 3 and CsCuZrTe 3 such that a < b < c without changing the symmetries of their lattices. The spin-orbit coupling was included while calculating the electronic band structures of the compounds. We performed phonon calculations using the PHONOPY package 24 that utilized a finite displacement supercell method for the calculation of forces and construction of the second-order interatomic force constant matrices from the force-displacement data. For the sulfide and selenide compounds having Cmcm symmetry we used ([2, 0, 0], [0, 2, 0], [0, 0, 1]) supercell transformation matrix to generate the displaced supercells. Each supercell of the compounds having Cmcm space group contains 48 atoms, and we used a 5 × 5 × 7 k-point mesh for the calculation of forces on the atoms. On the other hand, we used

) supercell transformation matrices respectively for RbCuZrTe 3 and CsCuZrTe 3 to generate relatively isotropic supercells. Each supercell of RbCuZrTe 3 has 72 atoms, and we used a 4 × 4 × 4 k-point mesh to calculate the forces on the atoms. For CsCuZrTe 3 , each supercell contains 144 atoms, and a 2 × 2 × 2 k-point mesh was used for force calculations. We performed the crystal orbital Hamilton population (COHP) analysis using the LOBSTER code, 25,26 which can identify the nature of interactions (i.e., bonding, nonbonding and antibonding states) between the atoms. The COHP analysis does not include spin-orbit coupling. Thermoelectric Property Measurements. The RbCuZrTe 3 crystals were crushed and hand-ground into a fine powder and sintered via the spark plasma sintering (SPS) apparatus at 623 K under a pressure of 40 MPa in a vacuum for 5 min to obtain a densified bulk sample (φ 12.7 × 3.5 mm 2 , density = 5.0588 g cm -3 ). The SPSed sample was then cut and polished into a 3 × 3 × 10 mm 3 rectangular bar for electronic transport properties measurement and a 6 × 6 × 1.5 mm 3 piece for thermal conductivity measurement. The high-temperature electrical conductivity (σ) and the Seebeck coefficient (S) were simultaneously measured by using a four-probe setup in a commercial apparatus (ZEM-3, Ulvac Riko, Inc.) under a He atmosphere from 300 to 575 K. The sample was measured under two heating processes and one cooling process (labeled as heat 1, heat 2, and cool 1; see the Supporting Information); the transport properties are very similar for both the heating and cooling cycles, indicating the sample is thermostable. The thermal conductivity was calculated by using the thermal diffusivity (D), heat capacity (C p ), and sample density (ρ) according to the relationship κ = DC p ρ. The thermal diffusivity was measured in an Ar atmosphere by the laser flash diffusivity method (LFA 457; Netzsch). The heat capacity was calculated by the Dulong-Petit law, and the sample density was determined by measuring the mass and dimensions of the sample. We estimated the lattice thermal conductivity simply by subtracting the electronic thermal conductivity from the measured total thermal conductivity: κ L = κ totalκ ele = κ total -LσT, where κ L , κ total , and κ ele are the lattice thermal conductivity, total thermal conductivity, and electronic thermal conductivity, respectively. The latter can be estimated by the Wiedemann-Franz relation κ ele = LσT, where σ is the electrical conductivity and L is the Lorenz number.

■ RESULTS AND DISCUSSION

Synthesis and Crystal Growth. For the synthesis of ACuZrS 3 (A = Rb, Cs) careful consideration of the starting materials is needed to avoid undesired exothermic reactions before the reagents can be sealed under vacuum. Using activated copper powder and sulfur can cause a reaction upon grinding in a mortar and pestle, resulting in sulfur loss due to volatilization. 27 This can be avoided by using a copper sulfide binary as a starting material or by sealing and heating an unmixed Cu and S in a known stoichiometry and then grinding and homogenizing the reaction product. Such a mixture can then be treated as a Cu and S source with known stoichiometry without volatilizing sulfur and losing stoichiometric control. Moreover, synthetic attempts using Cs 2 S or Rb 2 S and S as starting materials (mainly when also using activated Cu, but not exclusively) resulted in exothermic reactions occurring either while evacuating the tube of air or during the silica flame-sealing step. A picture of this is shown in Figure S1. Cooling the silica tubes containing the starting materials with liquid nitrogen just after beginning to evacuate them and after some of the air has left the tube allows for most of the moisture in the air to leave and subsequently reduced the reactivity of the starting materials enough to avoid this exothermic event. In the case when activated Cu, S, and Cs 2 S were used and successfully sealed, an exothermic event inside the sealed tube upon initial heating in the furnace that dispersed the starting material throughout the inside of the reaction tube upon heating would still occur, preventing a homogeneous reaction mixture with stoichiometric control at the bottom of the tube. Ultimately, the use of Cs 2 S 4 and CuS for preparing CsCuZrS 3 was found to be the optimal to avoid these challenges. The use of Rb 2 S and CuS was sufficient for preparing RbCuZrS 3 when care was taken during preparation.

Single crystals were grown and mechanically separated for structure determination using either RbCl or CsCl as a salt flux for RbCuZrQ 3 or CsCuZrS 3 , respectively, with the following reaction as an example: Rb 2 Se + 2Cu + 2Zr + 5Se + 20RbCl → 2RbCuZrSe 3 + 20RbCl. In the case of ACuZrS 3 reactions, red side products were observed. For the Cs/S reaction, this red side product was identified as the new phase β-CsCuS 4 which crystallized in irregular shapes. β-CsCuS 4 is found to be soluble in water and in N,N-dimethylformamide (DMF). A bright blue color is observed when dissolved in DMF, characteristic of a solubilized polysulfide. 28 β-CsCuS 4 is a salt containing Cs + cations and [CuS 4 ] -polymeric anionics, which includes S 4 2ligands bonding to copper atoms, so the solubility of this phase in polar solvents and the blue polysulfide color in DMF is expected and reasonable. A picture of the blue DMF solution can be found in Figure S2. In the case of the Rb-containing reaction targeting RbCuZrS 3 , a suitable crystal could not be selected, so the side product could not be identified. The same blue color was still found in DMF, indicating the presence of a polysulfide which suggests likely a similar RbCuS 4 or RbCuS 6 polysulfide phase. In the RbCuZrTe 3 /RbCl salt flux reaction, the side product Rb 2 Cu 5 Te 5 was identified as black platelets that had a triangular shape instead of the more typical rectangular shape observed for RbCuZrTe 3 crystals. Washing the product from this reaction with DMF did not result in any color changes to the DMF. Optimized synthesis conditions for either pure bulk material or large crystals that were washed and mechanically separated were ultimately achieved for all five of the ACuZrQ3 materials reported here without using ACl (A = Rb, Cs) salt fluxes. This is detailed in the Experimental Methods section or the additional experimental details in the Supporting Information.

Attempts to scale up the bulk synthesis of RbCuZrSe 3 and ACuZrTe 3 (A = Rb, Cs) through a stoichiometric combination of A 2 Q x , Cu, Zr, and Q to 4 g or more presented challenges and required careful consideration due to tube failure. An ∼1 g reaction run in fused silica tubes sealed to be 10 cm long (or 12 cm for RbCuZrSe 3 ) with an inner diameter of 8 mm and outer diameter of 10 mm placed vertically in the tube furnace typically resulted in some black material dispersed throughout the tube including at the top. A picture of this for RbCuZrSe 3 is shown in Figure S3. Scaled-up reactions to 4 g resulted in the tubes breaking only at the top end with the rest of the silica tube intact (see photo in Figure S4). This indicates that the reactions are sufficiently exothermic upon heating to disperse or expand the material throughout the tube with enough force to break off the top of it when insufficient headspace in the tube is provided. In the case of ACuZrTe 3 (A = Rb, Cs), this was addressed by doubling the length of the tube to 20 cm long, which reproducibly survived for 5.5 g reactions. A 4 g reaction targeting RbCuZrSe 3 with a 15 cm long tube failed, and no successful scaled-up reaction conditions have been tested.

On the basis of experience in preparing these alkali metal containing chalcogenides, we can come to some useful guidelines for the preparation of these materials as well as other alkali metal containing chalcogenides that demonstrate substantial exothermic behavior. In general, the exothermic nature and the synthetic challenges associated with this follow the trend we would expect based on oxidizing power of the chalcogen where S > Se > Te. Liquid nitrogen cooling (after the evacuation process has started) lowers the reactivity of the starting materials and avoids reactions during the flame-sealing process, as observed for the sulfides. Reaction sizes below 1 g during exploratory stages or attempts to obtain suitable single crystals for structure determination reduce the chance of tubes breaking. Scaled-up reactions require larger tubes with additional head space to allow dispersed material to move without breaking the tube. For a specific system, the identification of plausible reaction steps that could be responsible for the exotherm can enable the choice of starting materials that avoid or minimize this effect. A x Q y is prepared via the liquid ammonia reaction method 12,13 to prevent the exothermic reaction of an alkali metal with chalcogen, while the reaction of A x Q y + Q can be performed on the gram scale without strong exothermic events. Use of sulfur-rich A x Q y and CuS avoids any exotherm associated with the reduction of sulfur. The large exotherm occurring during the preparation of the ACuZrS 3 phases is likely due to a threecomponent reaction since the reaction of sulfur with either copper or zirconium is not sufficiently exothermic. The formation of S 4 2-anions from the reaction of A 2 S + 3S in the presence of Cu could form the 1D polymeric [CuS 4 ] - chains of side product β-CsCuS 4 which would be highly exothermic. Using Cs 2 S 4 where the S 4 2-anions are already formed with CuS or ternary phase starting materials to prepare quaternary phases can reduce the magnitude of the exotherm making the formation of these phases more manageable.

Crystal Structure. The new compounds RbCuZrS 3 , RbCuZrSe 3 , and CsCuZrS 3 are isostructural and adopt the KCuZrSe 3 structure type 9 with the space group Cmcm shown in Figure 1. This structure comprises [CuZrQ 3 ] -layers built from CuQ 4 tetrahedra and ZrQ 6 octahedra, which alternate with layers of alkali metal cations that serve to both fill the voids between [CuZrQ 3 ] -layers and charge-balance the structure. Each alkali metal atom forms undistorted eightcoordinate AQ 8 polyhedra. The [CuZrQ 3 ] -layers are composed of parallel infinite columns of CuQ 4 tetrahedra and ZrQ 6 octahedra that extend along the a-axis direction. The columns alternate along the c-axis direction (CuQ 4 -ZrQ 6 -CuQ 4 -ZrQ 6 ). Each ZrQ 6 octahedron is edge-sharing with four adjacent CuQ 4 tetrahedra (two on each side) extending in the c direction and is also edge-sharing with the two adjacent ZrQ 6 octahedra forming a column extending in the a-axis direction.

The CuQ 4 tetrahedra are similarly edge-sharing with four adjacent ZrQ 6 octahedra extending in the c direction but are corner-sharing with the two adjoining CuQ 4 to form a column that extends along the a-axis direction as seen in Figure 1.

The CuQ 4 tetrahedra in this structure are relatively undistorted and exhibit a narrow range of bond lengths that is typical for the respective chalcogen. The ranges of Cu-S bond lengths in RbCuZrS For RbCuZrTe 3 and CsCuZrTe 3 the lower symmetry space group resulted in models such that the crystallographic directions did not end up identical with those crystallizing in the Cmcm KCuZrSe 3 structure type 9 but can be mapped for ease of comparison. The stacking direction and longest axis in KCuZrSe 3 is the b direction, while for RbCuZrTe 3 and CsCuZrTe 3 it is the c direction. The shortest axis and the direction that the metal polyhedra alternate along is the c direction in KCuZrSe 3 while for RbCuZrTe 3 and CsCuZrTe 3 that is the a-axis direction. This leaves the a-axis direction in KCuZrSe 3 which corresponds to the b-axis direction for RbCuZrTe The occurrence of Zr distortions in [CuZrQ 3 ] -layers in ACuZrQ 3 (A = Rb, Cs; Q = S, Se, Te) materials is clearly influenced by the nature of both the chalcogenide and alkali metal. Distortions occur only for larger chalcogenides. One possibility is that the ZrQ 6 octahedral cage that the Zr 4+ sits in is an adequate size for the smaller chalcogenides. Once the chalcogen is sufficiently large, the octahedral cage is too big for the Zr 4+ to occupy the center. The Zr 4+ then must distort toward one side of the octahedral cage to address this instability. The off-centering distortion results in additional orbital mixing with the now closer anions, resulting in stronger bonds, which is greater than the lengthening/weakening of corresponding bonds on the opposite side, thereby stabilizing the off-centering. Therefore, this is a second-order Jahn-Teller distortion and consistent with the increased bonding interactions observed below the Fermi level for RbCuZrTe 3 and CsCuZrTe 3 shown in the COHP curves discussed later. This is also consistent with how second-order Jahn-Teller distortions stabilize distortions. Considering the influence of the alkali metal, we see that the magnitude of the off-centering is more prominent in the case of the smaller alkali metal Rb than for Cs at 293 K. Substituting to a smaller alkali metal atom can be thought of as increasing the chemical pressure squeezing the layers closer together. With the larger amount of chemical pressure in RbCuZrTe 3 , the [CuZrQ 3 ] -slab gets squished by the electrostatic repulsion of the adjacent slabs. This secondary effect results in the ZrQ 6 octahedra distorting by getting squished along the stacking direction and the Zr 4+ atoms shifting to one side in the plane of the [CuZrQ 3 ] -slab to alleviate this pressure. This is further supported by the observation that cooling RbCuZrTe 3 from 293 to 100 K simultaneously results in thermal contraction of the unit cell bringing the slabs closer together, combined with the magnitude of the zirconium off-centering increasing by 47.4% from 0.0829(14) to 0.1222(17) Å. When this driving force is further increased in the case of the sodium analogue NaCuZrTe 3 , the [CuZrQ 3 ] slab that forms has ultimately rearranged to the alternating column sequence of (Zr-Zr-Cu-Cu) as described above while still exhibiting some Zr distortions.

β-CsCuS 4 was identified as a side product when making CsCuZrS 3 and is found to crystallize in the β-KCuS 4 structure type 30 with the space group P1̅ shown in Figure 4A,B 31 The chemical composition for all materials reported here was confirmed by using energy dispersive spectroscopy (EDS) in a scanning electron microscope (SEM) shown in Figures S5-S8.

Differential Thermal Analysis and Variable Temperature PXRD. The thermal behavior of the five ACuZrQ 3 materials was investigated by using differential thermal analysis (DTA) data combined with powder X-ray diffraction (PXRD) before and after the DTA. This is shown in Figure 5 for CsCuZrS 3 and CsCuZrTe 3 and in Figures S9-S13 for the RbCuZrQ 3 (Q = S, Se, Te). CsCuZrS 3 in Figure 5A shows multiple reproducible thermal events during both heating and cooling cycles, with the diffraction pattern practically unchanged after the DTA, as seen in Figure 5B. During both heating cycles, there are endothermic events that occur at 455 and 580 °C, and during both cooling cycles there are exothermic events that occur at 905, 616, and 464 °C. Moreover, there is an anomalous broad exothermic event observed during only the first heating cycle that starts 750 °C.

To probe the nature of these thermal events, we performed variable temperature PXRD on already synthesized CsCuZrS 3 from 20 to 930 °C as shown in Figure 6. Upon heating at 275 °C, a set of new Bragg reflections can be seen coming in simultaneously, which persist until 575 °C when they all disappear simultaneously. The appearance of these new reflections is coupled with a decrease in intensity for the Bragg reflections corresponding to CsCuZrS 3 . The new Bragg reflections that come in at 275 °C and disappear at 575 °C are assigned to the phase CsCuS 6 . The last heating scan where the CsCuZrS 3 reflections are observed is at 900 °C, and they all disappeared by the next scan at 910 °C, which persists to the maximum temperature of 930 °C. Upon cooling, the CsCuZrS 3 reflections reappear in the 900 °C scan and continue to grow in intensity and experience thermal contraction during the rest of the cooling. Additionally, we see the reflections for CsCuS 6 reappear on cooling at 525 °C, persisting to room temperature through the end of the experiment. Some residual red material was observed visually at the end of the experiment, consistent with the color of CsCuS 6 . On the basis of this experiment, we assign the melting point of 910 °C and the crystallization point for CsCuZrS 3 as 905 °C. Additionally, CsCuZrS 3 seems to undergo partial decomposition during heating, where the additional thermal events observed in the DTA are explained by the behavior of the secondary phase CsCuS 6 . The lack of CsCuS 6 at the end of the DTA experiment observable in the PXRD pattern is likely due to a smaller proportion of the material having decomposed because of the much faster cooling rate in the DTA experiment. This observation of CsCuS 6 as the decomposition product instead of β-CsCuS 4 was surprising as only β-CsCuS 4 was observed as a side product from the initial synthesis. This indicates that β-CsCuS 4 is not a decomposition product but a side product likely involved in the reaction pathway that formed CsCuZrS 3 that did not fully react. RbCuZrS 3 did not show any reproducible thermal events in the DTA in Figure S9 but does produce trace orange/red material found on the bottom of the post-DTA material as shown in Figure S9C. Additionally, a minor impurity Bragg reflection found at 9.3°2θ, which is located at a lower Bragg angle than the first RbCuZrS 3 reflection at 12.1°2θ, is observed in the post-DTA PXRD powder pattern. This indicates that RbCuZrS 3 also undergoes partial decomposition either during heating or cooling, resulting in a phase that is likely a RbCuS 4 or RbCuS 6 phase. The DTA of RbCuZrSe 3 shown in Figure S10 shows an endothermic event at 850 °C on the first heating cycle but then on the second heating cycle exhibits a very broad exothermic event from 690 to 907 °C. It did not reveal any thermal events on cooling. The PXRD before and after the DTA analysis shows that the material is unchanged after the DTA, and the images shown in Figure S10C show that the ground powder loaded into the ampoule has formed crystals. This suggests the material was annealed and formed crystals without melting as there is no observable exothermic event to assign as a crystallization point from having reached a melting point. The cause of the broad exothermic feature during the second heating cycle is unknown.

The DTA of RbCuZrTe 3 shows reproducible endothermic events during both heating cycles at 340 °C and a very weak event at 893 °C and shows exothermic events upon cooling at 878 and 330 °C (Figure S11A). The PXRD shown in Figure S11B shows that the pattern is mostly unchanged with a small additional shoulder on the higher Bragg angle side of the first reflection. The material looks like a solidified ingot at the end of the process. On the basis of this, RbCuZrTe 3 seems to melt congruently with a melting point of 893 °C. The origin of the 340 °C/330 °C event in the heating/cooling cycles may be due to a trace impurity or partial decomposition event that requires additional variable temperature PXRD experiments to study further.

The DTA of CsCuZrTe 3 has additional thermal events than RbCuZrTe 3 as in Figure 5C. Upon heating, we observed reproducible endothermic thermal events during both heating cycles at 300, 348, and 412 °C and an extremely weak event at 788 °C. Upon cooling, there are reproducible exothermic thermal events during both cooling cycles at 785, 381, 325, and 275 °C. The 785 °C events are assigned as the melting and crystallization events. The nature of the lowtemperature events, however, is unclear and requires variable temperature PXRD studies to probe. The PXRD of the post DTA sample shown in Figure 5D indicates that the material has partially decomposed with additional diffraction peaks present, which could not be identified. They could be from a Cs/Cu/Te phase similar to the new Rb 2 Cu 5 Te 5 compound reported here.

Optical and Electronic Properties. The optical absorption properties of RbCuZrQ 3 (Q = S, Se, Te), CsCuZrS 3 , and CsCuZrTe 3 were investigated by using UV-vis diffuse reflectance spectroscopy and photoemission yield spectroscopy in air (PYSA) measurements shown in Figure 7. The UV-vis data were used to determine the bandgap by extrapolating the linear onset of the absorption edges. For RbCuZrS 3 the bandgap was found to be 1.44 (5) eV (861 nm), while for CsCuZrS 3 it was 1.42( 5) eV (873 nm). These values are within the error of the measurement of each other, which is reasonable since substitution of alkali metal would not be expected to substantively change the energy of the orbitals that comprise the valence or conduction band edges. For RbCuZrSe 3 the bandgap was found to be 0.95 (5) eV (1305 nm). This value is reasonable compared to the sulfide analogue since isostructural substitution for a heavier chalcogen is expected to narrow the bandgap. This is because the smaller electronegativity difference between the metals and the Se combined with the more extended Se orbitals compared with those of S have greater orbital overlap resulting in broader electronic bands that narrow the bandgap. UV-vis diffuse reflectance and IR spectroscopy of CsCuZrTe 3 did not indicate an optical bandgap between 0.09 eV (13800 nm) and 3.50 eV (354 nm).

The PYSA measurements were performed to find the work functions that were determined by extrapolating the linear onset of the data. 32,33 For semiconductors, the work function is equal to the energy of the valence band maximum (VBM) with respect to the energy of a free electron. Considering the bandgap in combination with the work function allows for determining the energy level of the conduction band minimum (CBM) with respect to the energy of a free electron. For RbCuZrS 3 the work function was found to be 4.89 (5) eV while for CsCuZrS 3 it is 4.80(5) eV. These results, taken together with the bandgap values for RbCuZrS 3 , yield a VBM of 4.89 (5) eV and a CBM of 3.45 (7) eV while for CsCuZrS 3 yield a VBM of 4.80 (5) eV and a CBM of 3.38 (7) eV. These values are within error of each other, which is reasonable for the same reason described for the bandgaps. For RbCuZrSe 3 the work function was found to be 4.67 (5) eV. This value taken together with the bandgap results in a VBM of 4.67 (5) eV and a CBM of 3.72 (7) eV. The shallower VBM and deeper CBM of RbCuZrSe 3 compared with RbCuZrS 3 are consistent with the explanation provided for the narrower bandgap. For RbCuZrTe 3 and CsCuZrTe 3 the work functions were 4.64(5) and 4.79(5) eV, respectively.

Electronic Structure Calculations. The electronic band structure, the partial density of states (PDOS), and crystal orbital Hamilton population (COHP) plots for for RbCuZrS 3 and RbCuZrTe 3 are shown in Figure 8. For RbCuZrSe 3 , CsCuZrS 3 , and CsCuZrTe 3 they are shown in Figures S15,S16, and S17, respectively. Considering RbCuZrS 3 , RbCuZrSe 3 , and CsCuZrS 3 first, their electronic band structures reveal direct bandgaps at the Γ point calculated to be 0.533, 0.122, and 0.57 eV, respectively. These values are underestimated compared to the experimentally observed bandgaps, a well-known DFT limitation. 34 The electronic structure reveals linearly dispersive bands at the VBM along the Γ-X and Γ-Z directions, while the VBM is almost dispersionless along the Γ-Y direction for all three materials. Considering the representative RbCuZrS 3 , the calculated hole effective masses are -0.316 m 0 along Γ-X and -0.706 m 0 along Γ-Z compared with -5.345 m 0 along Γ-Y, where m 0 is the free electron mass. The dispersion in the CBM is consistent between RbCuZrS 3 and RbCuZrSe 3 but differs from CsCuZrS 3 . All three materials have a linearly dispersive band along the Γ-X direction. RbCuZrS 3 and RbCuZrSe 3 are least dispersive along the Γ-Z direction with the Γ-Y direction in the middle while for CsCuZrS 3 the Γ-Y direction is the least dispersive and the Γ-Z direction is in the middle.

For RbCuZrS 3 , the calculated electron effective masses are 0.407 m 0 along Γ-X and 3.552 m 0 along Γ-Z compared with 1.550 m 0 for the Γ-Y direction. For CsCuZrS 3 the calculated electron effective masses are 0.387 m 0 along Γ-X, 1.949 m 0 3. The relatively low carrier effective masses in the VBM and CBM along the Γ-X direction, which corresponds to the a crystallographic direction that the columns of metal polyhedra propagate along, are conducive for high carrier mobilities. On the other hand, the much heavier masses along the Γ-Y and Γ-Z directions, which are the b and c crystallographic directions, respectively, should result in low mobilities in these directions.

To understand the orbital contributions to the band structure, we have calculated the PDOS (Figure 8B), which shows that valence bands primarily consist of the 3p orbitals of S that strongly hybridize with 3d orbitals of Cu. In contrast, the conduction band mainly results from the empty 4d orbitals of Zr. To gain further insights into the nature of the chemical bonding, we performed COHP analysis 25,26 which partitions the energy of the band structure into pairs of orbital or atomic interactions. The COHP analysis reveals that p-d interactions between S and Cu below the Fermi level are antibonding in nature and dominate the valence band down to -2.5 eV. These filled antibonding states weaken the bond strength in the material and lead to soft phonon frequencies�a requisite for low lattice thermal conductivity.

To this end, we calculated the phonon dispersions shown in Figure 9A for RbCuZrS 3 and in Figures S18 andS19 for RbCuZrSe 3 and CsCuZrS 3 , respectively. All the phonon modes for these materials are positive, signifying their dynamical stability. Interestingly, the phonon dispersion for these materials exhibits nearly dispersionless low-energy phonon branches along the entire Brillouin zone (except near the Γpoint). The analysis of atom-resolved phonon density (Figure 9B) of states shows that the dispersionless phonon branches mainly arise from the alkali metal vibrational modes, which give rise to two sharp peaks (at 50 and 74 cm -1 ) for RbCuZrS 3 and for CsCuZrS 3 (at 38 and 62 cm -1 ). These phonon branches signify the rattling-like vibrations of the Rb and Cs atoms in layers of the crystal structure. Because rattler cations are shown to scatter phonons effectively, these materials are expected to exhibit low lattice thermal conductivities. The calculated electronic structures for RbCuZrTe 3 and CsCuZrTe 3 differ from the sulfide and selenide analogues in that they predict these tellurides are metals instead of semiconductors as shown in Figures 8D andS20, respectively. This prediction is supported by the lack of an observable optical bandgap and the fact that measured temperaturedependent conductivity for the potassium analogue KCuZrTe 3 was found to be a metal. 9 The PDOS shown in Figure 8E and the COHP plots in Figure 8F show that below the Fermi level mainly consist of antibonding p-d hybridized states between Cu and Te and above the Fermi level is primarily composed of Zr 4d states. Noteworthy, however, is the presence of substantive amounts of bonding interactions between empty Zr 4d states and the filled Te 5p between the Fermi level and -2 eV below the Fermi level shown in Figure 8F for RbCuZrTe 3 and in Figure S17 for CsCuZrTe 3 . The degree of bonding interactions between Zr 4d states and Te 5p is notably greater than what is seen for the sulfide (Figures 8C andS16C) and selenide (Figure S15C) analogues in the top 2 eV of the valence band. Additionally, the amount of bonding interactions in RbCuZrTe 3 is much greater than what is observed in the band structure of RbCuZrTe 3 , taking a theoretical KCuZrSe 3 structure type with Zr centered in its octahedral environment with the Cmcm space group with undistorted Zr environments shown in Figure S24C. Interestingly, the phonon dispersion for RbCuZrTe 3 taking the theoretical KCuZrSe 3 structure type with the Cmcm space group exhibits negative phonon modes shown in Figure S25 not observed for the experimental structure phonon dispersion shown in Figure 9C,D. The most negative phonon mode for the theoretical RbCuZrTe 3 structure at the Γ-point corresponds to a vibration mode that includes Zr moving off the center of the Zr octahedra.

Taking all of the above together, we can surmise that the long-range ordered off-centering of the Zr atoms in RbCuZrTe 3 and CsCuZrTe 3 is the result of the Zr atoms moving off-centering toward an axial Te in the octahedra Zr environment. This increases the orbital overlap and bonding interaction of Zr 4d states with the closer axial Te 5p state, which manifests in the COHP plot and provides the energetic driving force. As mentioned above, this type of distortion can be understood as a second-order Jahn-Teller distortion. [35][36][37][38][39] Resistivity and Thermoelectric Properties. The room temperature electrical resistivity was measured by using single crystals of CsCuZrS 3 and RbCuZrSe 3 as shown in Figures S22 andS23, respectively. Both materials exhibited ohmic behavior with no hysteresis for two cycles when enclosed in a light-tight box and upon exposure to ambient room light. CsCuZrS 3 and RbCuZrSe 3 samples were both fairly conductive with CsCuZrS 3 having a resistivity of 1 × 10 2 Ω•cm while RbCuZrSe 3 has a resistivity of 1 × 10 1 Ω•cm, suggesting they are extrinsically doped. The temperature-dependent electrical conductivity (σ), Seebeck (S), and thermal conductivity (κ) were measured for RbCuZrTe 3 and are shown in Figure 10. The sample shows a decent room temperature electrical conductivity of about 80 S cm -1 , decreasing with rising temperature. The electrical conductivity behavior indicates that the sample is a metal which is consistent with the calculated electronic band structure prediction that the material is a metal and the lack of an observable optical bandgap. The positive Seebeck coefficient indicates the sample is a p-type material. The temperaturedependent Seebeck coefficient follows the usual inverse relationship with respect to the temperature dependence of electrical conductivity, which increases from 75 μV K -1 at room temperature to 115 μV K -1 at 593 K as shown in Figure 10A.

The temperature-dependent total thermal conductivity for RbCuZrTe 3 is shown in Figure 10B. The total thermal conductivity is extremely low at 0.49 W m -1 K -1 at room temperature and drops to 0.34 W m -1 K -1 at 575 K. The lattice thermal conductivity, which is 0.44 W m -1 K -1 at room temperature and decreases to 0.29 W m -1 K -1 at 575 K, is shown in Figure S27E. This ultralow thermal conductivity should be attributed to the strong phonon-phonon scattering, caused by the rattling-like vibrations of the Rb and the Zr distortion. This ultralow thermal conductivity is consistent with the recent thermal conductivity predictions for this class of materials by Pal et al. 8 CsCuZrS 3 was predicted at 300 K to have in-plane thermal conductivity of 1.0 W m -1 K -1 and outof-plane thermal conductivity of 3.0 W m -1 K -1 , and we expect the Te analogue to have lower thermal conductivity than the sulfide. 8 This low thermal conductivity suggests that materials with this structure type have potential as thermoelectric materials. The selection of a composition with a narrow bandgap such as a potential Se-Te solid solution combined with doping to optimize the carrier concentration has promise for a material that retains the desirable very low thermal conductivity make it promising future thermoelectric investigations. 40 Heat Capacity. The heat capacity of RbCuZrTe 3 and CsCuZrTe 3 was measured between 3.8 and 275 K to investigate for evidence of a low-temperature phase transition as shown in Figure S28. Both materials did not show any discontinuities over this temperature range, indicating that there are no first-order phase transitions. At sufficiently low temperatures the heat capacity can be expressed as C p = γT + βT 3 , where γ parametrizes the electronic contributions to the specific heat and β determines the lattice contribution. 41 In the low-temperature region the relationship of C p /T vs T 2 should become linear where β is approximated as the slope and γ is approximated as the y-intercept. 42 The Debye temperature θ D is the characteristic temperature of the largest lattice vibrations of a material which is approximated from β as described in the Supporting Information. For CsCuZrTe 3 the relationship of C p /T vs T 2 is linear for T between 3.8 and 4.4 K while for RbCuZrTe 3 it is linear for T between 3.8 and 4.1 K. For CsCuZrTe 3 , these parameters were determined to be θ D ≈ 170(5) K, γ ≈ 84.6(8) mJ mol -1 K -2 , and β ≈ 2.47(37) mJ mol -1 K -4 . For RbCuZrTe 3 , θ D ≈ 150(5) K, γ ≈ 9.24(98) mJ mol -1 K -2 , and β ≈ 3.67(62) mJ mol -1 K -4 . The γ value is proportional to the density of states at the Fermi surface so the positive values for RbCuZrTe 3 and CsCuZrTe 3 are additional evidence of the metallic nature of the materials. The γ values are of a similar order of magnitude to each other as well as other metallic materials such as Al 43 which has a γ ≈ 1.35 mJ mol -1 K -2 or YbSb 2 44 which has a γ ≈ 3.18 mJ mol -1 K -2 . The θ D values for RbCuZrTe 3 and CsCuZrTe 3 are somewhat lower than the reported values for other low thermal conductivity thermoelectric materials such NaSn 5 SbTe 7 45 with a θ D ≈ 164 K and BiAgOSe 46 with a θ D ≈ 191 K and are also lower than both YbSb 2 44 (θ D ≈ 186 K) and Al 43 (θ D ≈ 427.7 K). Future measurements to temperatures below 3.8 K which we were unable to obtain due to instrumental limitations at this time would allow for a larger linear region enabling a more accurate determination of these values.

■ CONCLUDING REMARKS RbCuZrS 3 , RbCuZrSe 3 , and CsCuZrS 3 crystallize in the KCuZrSe 3 structure type with the space group Cmcm while RbCuZrTe 3 and CsCuZrTe 3 crystallize in the lower symmetry space group Pnma due to second-order Jahn-Teller distortion of the d 0 Zr in an ordered off-centering. The distortion is larger for the Rb analogue than the Cs analogue and increases for RbCuZrTe 3 upon cooling. DFT calculations predict direct gap semiconductors for the sulfide and selenide compositions, while ACuZrTe 3 are correctly predicted to be metals. The bandgaps and work functions are 1.44 (5) eV and 4.89(5) eV for RbCuZrS 3 and 0.95(5) eV and 4.67 (5) eV for RbCuZrSe 3 , while no optical bandgap was observed for RbCuZrTe 3 with a work function of 4.64 (5) eV. Variable temperature conductivity of RbCuZrTe 3 found metallic behavior. Heat capacity measurements also suggest RbCuZrTe 3 and CsCuZrTe 3 to be metals with Debye temperatures of 150 and 170 K, respectively. Phonon dispersion calculations at 0 K find lowlying vibrational modes of the alkali metal ions for all the quaternary phases reported here indicative of rattling behavior. RbCuZrTe 3 exhibits very low thermal conductivity below 0.5 W m -1 K -1 at room temperature.

From the point of view of physical property characteristics, we expect these materials to be similar to the recently reported A 2 Cu 2 nLn 4 Q 7+n (A = Cs, Rb; Ln = La-Nd, Sm, Gd-Yb; Q = S, Se) homologous series. 46 ■ ASSOCIATED CONTENT * sı Supporting Information

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.chemmater.2c02104.

Additional experimental details, full crystallographic tables, SEM and EDS, differential thermal analysis, powder X-ray diffraction, electronic band structure with DOS and COHP, phonon dispersion with DOS, thermoelectric properties, resistivity measurements, pictures, heat capacity, and Debye temperature (PDF)