Sr₃Zr₂Cu₄Q₉ (Q = S and Se): two novel layered quaternary mixed transition metal chalcogenides

Abstract

Depending on their bandgaps, mixed metal layered chalcogenides are potential candidates for thermoelectric and photovoltaic applications. Herein, we reported the exploratory synthesis of Sr–Zr–Cu–Q (Q = S/Se) systems, resulting in the identification of two novel quaternary chalcogenides: Sr₃Zr₂Cu₄S₉ and Sr₃Zr₂Cu₄Se₉. These isoelectronic compounds (Sr₃Zr₂Cu₄Q₉) crystallized in two different structural types. The Sr₃Zr₂Cu₄S₉ structure (space group: P1̄) adopted the Ba₃Zr₂Cu₄S₉ structure type with eighteen unique atomic sites: 3 × Sr, 2 × Zr, 4 × Cu, and 9 × S. In contrast, the Sr₃Zr₂Cu₄Se₉ structure (P1̄) represented a unique structure type with nineteen unique atomic positions including one additional Cu site compared to the Sr₃Zr₂Cu₄S₉ structure. The sulfide structure was stoichiometric, whereas the selenide structure was found to be non-stoichiometric with three partially occupied Cu positions. The Sr₃Zr₂Cu₄Q₉ structures consisted of layers with the Sr²⁺ cations occupying the interstitial spaces. In both structures, the Zr atoms occupied distorted octahedral positions. A striking difference between the two structures resulted from the distinct bonding interactions between the Cu and Q atoms. The optical bandgap of polycrystalline Sr₃Zr₂Cu₄S₉ was 1.7(1) eV. Interestingly, resistivity measurements of polycrystalline Sr₃Zr₂Cu₄Se₉ revealed metallic/degenerate semiconducting behavior at low temperatures. The photovoltaic performance of semiconducting Sr₃Zr₂Cu₄S₉ demonstrated ∼24% increment in power conversion efficiency when incorporated into a TiO₂/CdS photoanode due to its narrower bandgap, which increased the light-harvesting ability of the cell. We also explored the theoretical electronic structures, COHP, and Bader charges of the Sr₃Zr₂Cu₄Q₉ structures using DFT calculations.

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1. Introduction

Inorganic multinary chalcogenide compounds, featuring two or more types of metals/metalloids and chalcogen elements (Q), such as sulfur, selenium, and tellurium, represent a fascinating class of materials. Their tunable compositions and structural flexibility enable the tailoring of physical properties for a wide range of technological applications. Therefore, chalcogenides have emerged as potential materials for a variety of applications, such as high-temperature superconductivity,^1,2 photovoltaics,^3,4 catalysis,^5,6 thermoelectric properties,^7,8 and non-linear optics.^9–12 Unlike binary counterparts, multinary chalcogenides allow the incorporation of multiple metals and chalcogen atoms, opening a vast design space to tailor their properties. This flexibility allows for fine-tuning of the energy difference between the electron-filled and empty states, thereby influencing their electrical and thermal conductivity, light absorption, and emission. Many chalcogenides are also well known for their sensitivity to light and other stimuli, making them ideal candidates for use in advanced sensors and imaging technologies.^13–16

Copper-containing chalcogenides, especially sulfides and selenides, are emerging materials for photovoltaic and thermoelectric (TE) applications due to their non-toxicity and earth abundance.^4,17–20 The high mobility of Cu¹⁺ ions in these multinary chalcogenide structures is well known in compounds such as Cu_2−xSe,²¹ Cu₇PSe₆,²² CuCrSe₂,²³ and AgCuSe.²⁴ However, some of these structures are unstable at higher temperatures due to the migration of Cu ions within their crystal lattices (e.g., Cu_2−xSe).^25,26 Unlike copper oxides, the Cu atoms in chalcogenides exist in the monovalent state and are mostly four-coordinated with a tetrahedral coordination geometry. Notable examples of such compounds include BaCu_6−xSeTe₆,²⁷ BaLnCuS₃ (Ln = Pr, Sm, Dy, Ho, Yb),^28,29 and Cu₄SnS₄.³⁰ In these structures, alkali (A) and alkaline-earth (Ak) metals function as electron donors and exhibit higher coordination numbers than the transition metals. The A¹⁺ or Ak²⁺ ions in these compounds can be replaced with lower or higher valent chemical dopants to control the number of charge carriers. Also, many of these multinary chalcogenides offer low intrinsic thermal conductivity values due to their complex structures and chemical bonding. Therefore, the Cu-containing multinary chalcogenides with narrow bandgaps are actively pursued for their potential thermoelectric applications. Examples of such compounds are ACuZrQ₃³¹ and BaSc_1−xGd_xCuTe₃.³²

Moreover, the tunable bandgaps of the Cu/Ag-containing chalcogenides also make them potential candidates for solar cells, light-emitting diodes (LEDs), and photocatalysis applications. As discussed earlier, thanks to the high mobility of copper or silver atoms in these semiconducting chalcogenides, additional electronic levels close to the valence band are present in these compounds, making them efficient in electron transfer rather than hole recombination on sunlight absorption.^33,34 BaCu₂SnS_4−xSe_x,³⁵ CuGaSe₂,³⁶ CuSbS₂,³⁷ BaCeCuS₃,³⁸ Cu₂ZnSnQ₄ (Q = S, Se),³⁹ and CuIn_xGa_1−x(S_xSe_1−x)₂ ⁴⁰ are a few examples of such chalcogenide materials with excellent photovoltaic power conversion efficiencies. CuSbS₂ ³⁷ is one of the chalcogenides actively explored for photovoltaics and thermoelectric applications.

Therefore, many research groups worldwide have been actively synthesizing new Cu/Ag-containing multinary chalcogenides with semiconducting properties to identify new potential materials for solar cells and TE applications. We have produced several novel complex metal chalcogenides in our quest to develop new semiconducting compounds for TE and solar cell applications; these include 12-BaBi₂S₄,⁴¹ Ba₈Zr₂Se₁₁(Se₂),⁴² and BaCeCuS₃.³⁸ In this work, we report the synthesis of two novel compounds, namely, Sr₃Zr₂Cu₄S₉ and Sr₃Zr₂Cu₄Se₉, with layered structures. Sr₃Zr₂Cu₄S₉ is the first quaternary phase in the Sr–Zr–Cu–S system, while Sr₃Zr₂Cu₄Se₉ is the second member of the Sr–Zr–Cu–Se system for which only the quaternary phase, Sr_0.5CuZrSe₃,⁴³ is reported. Sr₃Zr₂Cu₄Se₉ represents a new structure type. We have studied the structural aspects and physical properties of Sr₃Zr₂Cu₄Q₉ compounds. Thermoelectric properties of Sr₃Zr₂Cu₄Se₉, a semimetal/degenerate semiconductor, are explored in detail. The Sr₃Zr₂Cu₄S₉ sulfide, a semiconductor with an optical bandgap of 1.7(1) eV, is explored for photovoltaic applications. Incorporating the quaternary title sulfide phase in a TiO₂/CdS photoanode shows a 24% increment in the power conversion efficiency of the fabricated solar cell. The electronic band structures of the Sr₃Zr₂Cu₄Q₉ phases are studied using the DFT method.

2. Experimental section

2.1 Chemicals used and synthetic methodologies

Sr₃Zr₂Cu₄S₉ and Sr₃Zr₂Cu₄Se₉ phases were synthesized using S/Se powder, Cu powder, Zr rod, and Sr granules. All these elements were procured from Sigma Aldrich with purities ≥99.5%. The Sr granules were cut into smaller pieces, and the zirconium rod was filed into powder for the reactions. Unless stated otherwise, all the chemicals are handled inside a glove box filled with argon gas.

We used the SnO₂ : F (FTO) coated glass substrates (Pilkington) with a sheet resistance of ∼25 Ω cm⁻² to fabricate solar cells for photovoltaic studies. Other chemicals (reagent grade) used for preparing the solar cells and photovoltaic measurements are the following: TiO₂ P25 powder, fumed silica and Ni-foam were procured from Evonik, Cabosil, and Gelon, respectively, and cadmium acetate, sodium sulfide, titanium tetrachloride, methanol, toluene, Triton X-100, acetylacetone, multi-walled carbon nanotubes (MWCNTs), polyvinylidene fluoride (PVdF), carbon black (CB), and N-methyl-2-pyrrolidone (NMP) were purchased from Merck and used directly.

2.1.1 Syntheses of Sr₃Zr₂Cu₄Q₉ (Q = S and Se) crystals. The elements (Sr, Zr, Cu, and Q) were reacted at high temperatures to prepare Sr₃Zr₂Cu₄Q₉ crystals. The elements, strontium (53.21 mg, 0.61 mmol), zirconium (36.93 mg, 0.40 mmol), copper (51.45 mg, 0.81 mmol), and sulfur (58.41 mg, 1.82 mmol) were poured in a fused silica tube, which was subsequently flame-sealed under a vacuum (ca. 10⁻⁴ Torr). The inner surface of the fused silica container (8 mm outer diameter) was carbonized before its use as the reaction vessel. A box furnace was used to heat the sealed reaction mixture.

Similarly, a vacuum-sealed tube containing the elements strontium (37.28 mg, 0.43 mmol), zirconium (25.88 mg, 0.28 mmol), copper (36.05 mg, 0.57 mmol), and selenium (100.79 mg, 1.28 mmol) was also heated in the furnace to prepare single crystals of Sr₃Zr₂Cu₄Se₉.

The tubes were heated in the furnace using the temperature profile described in section S1 of the ESI.† After completion of the reactions, dark reddish and black-colored melted lumps were found for the reactions targeting the sulfide and selenide, respectively. These lumps were further fractured, and a few crystals were chosen for their semiquantitative elemental energy-dispersive X-ray spectroscopic (EDX) analyses using a field-emission scanning electron microscope (FE-SEM) (Model: JSM 7610F) and an X-ray spectrometer (octane elite, EDAX Inc., USA).

Most of the red-colored crystals selected from the sulfide reaction product showed Sr : Zr : Cu : S ≈ 3 : 2 : 4 : 9, consistent with the loaded Sr₃Zr₂Cu₄S₉ composition (Fig. 1a). A few crystals turned out to be binary SrS (1 : 1). The crystals of Sr₃Zr₂Cu₄Se₉ were black in color, and their average composition was also consistent with the loaded ratio of Sr : Zr : Cu : Se ≈ 3 : 2 : 4 : 9 (Fig. 1a inset).

Fig. 1 (a) The EDX spectrum of a typical Sr₃Zr₂Cu₄S₉ crystal. The inset shows the EDX spectrum of a Sr₃Zr₂Cu₄Se₉ crystal. (b) The Le Bail refinement plots of the powder X-ray diffraction (PXRD) patterns of Sr₃Zr₂Cu₄S₉ and Sr₃Zr₂Cu₄Se₉.

A few of these EDX-analyzed red and black-colored crystals were further used for structural characterization at room temperature (RT) using the single-crystal X-ray diffraction (SCXRD) method.

2.1.2 Syntheses of polycrystalline Sr₃Zr₂Cu₄Q₉ (Q = S, Se) samples. We have employed two methods, namely, the solid-state reaction and CS₂ methods, which are described below, to synthesize the polycrystalline Sr₃Zr₂Cu₄Q₉ (Q = S, Se) phases.
Solid state method. Phase pure bulk polycrystalline Sr₃Zr₂Cu₄Q₉ (Q = S, Se) phases were prepared by first heating the respective elements using the temperature profile discussed in section S1 of the ESI† and then reheating the homogenized products in the form of compressed pellets inside the vacuum-sealed fused silica tubes in two steps.

The elements, strontium (266.03 mg, 3.04 mmol), zirconium (184.65 mg, 2.02 mmol), copper (257.25 mg, 4.05 mmol), and sulfur (292.07 mg, 9.11 mmol), were sealed in a fused silica tube under vacuum and heated inside the furnace to synthesize polycrystalline Sr₃Zr₂Cu₄S₉.

Similarly, a vacuum-sealed fused silica tube containing strontium (186.41 mg, 2.13 mmol), zirconium (129.38 mg, 1.41 mmol), copper (180.26 mg, 2.84 mmol), and selenium (503.95 mg, 6.38 mmol) was heated in the furnace to prepare the polycrystalline Sr₃Zr₂Cu₄Se₉ using the heating profile discussed in section S1 of the ESI.†

The products of the reactions were homogenized into fine powders and were compressed individually into cylindrical-shaped thin pellets. These pellets were again encapsulated inside evacuated fused silica tubes and annealed at 1023 K for two days. This step is required to make high-quality polycrystalline Sr₃Zr₂Cu₄Q₉ (Q = S, Se) samples. The heat-treated pellets were ground again, and the products were characterized using the PXRD studies.

We also attempted to synthesize polycrystalline Sr₃Zr₂Cu₄S₉ by heating stoichiometric amounts of metal oxides/carbonates under N₂ and CS₂ atmosphere at 1073 K for 9 h. The details of this CS₂ method are given in section S2 of the ESI.† The ease of making bulk samples and the scalability of the method without the need for expensive fused silica tubes were the motivations behind attempting the CS₂ method. However, we failed to synthesize the phase pure material via the CS₂ method. Further optimization of the reaction temperature and time is required to find suitable reaction conditions to synthesize the Sr₃Zr₂Cu₄S₉ phase in the future.

The PXRD data sets of the powdered samples mentioned above were collected with the help of a PANalytical X'pert pro-X-ray diffractometer (Cu-Kα, λ = 1.5406 Å) at RT. The TOPAS V6 software program was used to refine the unit cell parameters of the polycrystalline samples, Sr₃Zr₂Cu₄Q₉, using the Le Bail refinement method (Fig. 1b).⁴⁴

2.2 Single-crystal X-ray diffraction studies

Two SCXRD datasets for the Sr₃Zr₂Cu₄S₉ and Sr₃Zr₂Cu₄Se₉ crystals at RT under a normal atmosphere were recorded using a Bruker D8 Venture diffractometer. We used EDX-characterized crystals for the SCXRD studies. The diffractometer was fitted with a Photon III mixed-mode X-ray detector. Graphite was utilized to monochromatize the X-ray radiations from a Mo-Kα radiation source (λ = 0.71073 Å). The intensity data for the Sr₃Zr₂Cu₄Q₉ (Q = S, Se) crystals were collected using a series of ω and φ scans with 0.5° frame width and 2 s per frame of the exposure time with the help of the APEX3 software.⁴⁵

The crystal structures for the Sr₃Zr₂Cu₄Q₉ compounds were determined and refined in the centrosymmetric triclinic space group P1̄ with the help of the SHELXTL⁴⁶ program suite. For the sulfide structure, all the atomic positions were easily assigned to respective elements, which resulted in the formula Sr₃Zr₂Cu₄S₉. However, the reliability factor values were poor: R(F) = 8.87%, R_w(F_o²) = 26.72%, and the maximum positive residual electron density was 13.3 e⁻ Å⁻³. Later, the CELLNOW⁴⁵ program was used to check the presence of any twinning in the dataset, which identified two twin domains for the crystal. Also, absorption correction was done afterward using the TWINABS.⁴⁷ The second twin domain was found to be rotated from the first domain with an angle of about 180° along the [1 0 1] direction. After these steps, the refinement parameters were significantly improved with final R(F) = 4.74% and R_w(F_o²) = 12.38%. The Sr₃Zr₂Cu₄S₉ structure is stoichiometric and isostructural to the Ba₃Zr₂Cu₄S₉⁴⁸ (space group: P1̄) structure. The final structure solution identified a total of 18 independent sites, out of which three sites were identified as Sr, two as Zr, four sites as Cu, and the remaining nine as S sites. The STRUCTURE TIDY⁴⁹ program was used to standardize the atomic positions of the Sr₃Zr₂Cu₄Q₉ structure.

We also found multiple twin domains for the Sr₃Zr₂Cu₄Se₉ dataset using the CELLNOW⁴⁵ program. Similar to the sulfide structure, for this structure as well, the two domains are related with a rotation angle of about 180° with the [1 0 1] direction as the rotation axis. The APEX3⁴⁵ was used to integrate the SCRXD dataset using two twin domains in the triclinic setting. The TWINABS⁴⁷ was used for the X-ray absorption corrections of the observed reflections. The final structure solution of the Sr₃Zr₂Cu₄Se₉ with the P1̄ space group was comprised of nineteen crystallographically independent sites. The structure was refined considering 100% occupancy for all the atoms. The reliability parameters R(F) and R_w(F_o²) were 6.68% and 17.56%, respectively. The anisotropic displacement parameters (ADPs) of the Cu atoms were abnormally large, indicating some vacancies at these sites. Subsequently, the fractional occupancy factor (SOF) values of these sites were allowed to be refined freely, resulting in an improvement of the reliability parameters: R(F) = 5.34% and R_w(F_o²) = 11.82%. The freely refined SOF values of the Cu1, Cu3, and Cu4 atomic sites are 0.598, 0.856, and 0.533. The final refined formula, Sr₃Zr₂Cu_3.99(1)Se₉, is close to the electrically neutral composition, Sr₃Zr₂Cu₄Se₉. Thus, we refer to the chemical formula of the selenide as Sr₃Zr₂Cu₄Se₉ in this study.

We finally validated the symmetry of the Sr₃Zr₂Cu₄S₉ and Sr₃Zr₂Cu₄Se₉ structures using the ADDSYM program of the PLATON⁵⁰ software. Further crystallographic details are given in Tables 1, 2 and Tables S1, S2, S3, and S4 in the ESI.†

Table 1 Crystallographic data and structure refinement details for Sr₃Zr₂Cu₄S₉ and Sr₃Zr₂Cu₄Se₉^a

a λ = 0.71073 Å, T = 298(2) K. b R(F) = ∑||Fo| − |Fc||/∑|Fo| for Fo^2 > 2σ(Fo^2). c R w(Fo^2) = {∑[w(Fo^2 − Fc^2)^2]/∑wFo^4}^1/2. For Fo^2 < 0, w = 1/[σ^2(Fo^2) + (mP)^2 + nP]; where P = (Fo^2 + 2Fc^2)/3. For the sulfide structure, m = 0.0574 and n = 6.3137, and for the selenide structure, m = 0 and n = 27.2292.
	Sr3Zr2Cu4S9	Sr3Zr2Cu4Se9
Space group	P1̄
a (Å)	6.6907(13)	6.9779(14)
b (Å)	10.312(2)	10.685(2)
c (Å)	11.929(2)	12.302(3)
α (°)	109.49(3)	109.18(3)
β (°)	104.54(3)	105.38(3)
γ (°)	96.73(3)	96.56(3)
V (Å^3)	732.6(3)	814.6(3)
Z	2
ρ (g cm^−3)	4.479	5.745
μ (mm^−1)	19.12	36.13
R(F)^b	0.047	0.053
R w(Fo^2)^c	0.124	0.118

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Table 2 Important bond distances (in Å) of the Sr₃Zr₂Cu₄Q₉ structures

	Sr3Zr2Cu4S9	Sr3Zr2Cu4Se9
Zr–Q (Å)	2.490(2)–2.694(2)	2.6342(19)–2.8083(18)
Tetrahedral Cu–Q (Å)	2.309(2)–2.372(2)	2.386(4)–2.682(5)
Trigonal Cu–Q (Å)	2.234(2)–2.312(2)	—
Sr–Q (Å)	2.924(3)–3.628(2)	3.0655(19)–3.4277(19)

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2.3 Solid-state ultraviolet-visible (UV-vis)-near-infrared (NIR) spectroscopy

Diffuse reflectance datasets of the polycrystalline Sr₃Zr₂Cu₄S₉ and Sr₃Zr₂Cu₄Se₉ samples were recorded at RT using a spectrophotometer JASCO V-770. A dry sample of BaSO₄ was used for calibration. The Kubelka–Munk equation⁵¹ was utilized to obtain absorption data from the reflectance data.

2.4 Thermal conductivity (κ_tot) measurements

Sr₃Zr₂Cu₄S₉ and Sr₃Zr₂Cu₄Se₉ powders were first pressed into thin cylindrical pellets (dia. 8 mm) and then sintered at 973 K (for 24 h) using the sealed tube method. A hydraulic press was used to compact the powders into hard pellets under ca. 8 tons of pressure. The density (d) values of the resulting compact pellets of Sr₃Zr₂Cu₄S₉ and Sr₃Zr₂Cu₄Se₉ were determined using the Archimedes method.⁵² The experimental density values were about 92% of the theoretical density.

The thermal diffusivity (D) values of Sr₃Zr₂Cu₄S₉ and Sr₃Zr₂Cu₄Se₉ were measured using a LINSEIS XFA 500 instrument. The details of the measurements are given elsewhere.⁴¹ The Dulong–Petit law⁵³ was employed to estimate the heat capacity (C_p) values of the Sr₃Zr₂Cu₄S₉ and Sr₃Zr₂Cu₄Se₉ samples. Finally, the total thermal conductivity (κ_tot = D × d × C_p) values were calculated. The final κ_tot value has an uncertainty of around ±10%.

2.5 Transport property measurements for Sr₃Zr₂Cu₄S₉ and Sr₃Zr₂Cu₄Se₉

The sintered rectangular parallelepiped-shaped Sr₃Zr₂Cu₄S₉ and Sr₃Zr₂Cu₄Se₉ pellets were obtained using the method described in section 2.4. The electrical resistivity (ρ) values of the Sr₃Zr₂Cu₄Q₉ (Q = S, Se) pellets were measured at low temperatures using the standard four-contact method. The pellets were cooled using a Janis SHI-950 closed-cycle cryostat, and the four contacts on each of the pellets were made using the Cu-probes (0.05 mm diameter) and Ag-paint. A nanovoltmeter (Keithley, Model: 2182A) and a current source (Keithley, Model: 6221) were used for the study.

The Sr₃Zr₂Cu₄Se₉ pellet was further used for the simultaneous determination of electrical resistivity and Seebeck coefficient (S) values at higher temperatures (323 K–573 K) with the help of a ULVAC-RIKO ZEM-3 equipment under a low-pressure He-atmosphere. No hysteresis between the heating and cooling cycles of the measured data was observed.

2.6. Photovoltaic study of Sr₃Zr₂Cu₄S₉

A photoanode, FTO/TiO₂/CdS, was prepared using the method described elsewhere.³⁸ The powdered Sr₃Zr₂Cu₄S₉ was dispersed in toluene at 1 mg mL⁻¹ concentration by ultrasonication for 2 h and then drop-casted over the FTO/TiO₂/CdS electrode and dried under vacuum for two days to obtain a FTO/TiO₂/CdS/Sr₃Zr₂Cu₄S₉ photoanode.

A counter electrode (CE) was fabricated by coating MWCNTs over a Ni foam substrate. CB, PVdF, and MWCNTs were mixed in a 1 : 1 : 8 weight ratio, ground well, and converted into a slurry using NMP. The slurry was coated on the Ni-foam and dried. A polysulfide gel was prepared by adding 5 wt% of fumed silica in an aqueous suspension of (1 M Na₂S + 1 M S) under constant stirring until it became a uniform gel.

Finally, we made the solar cells, FTO/TiO₂/CdS/S²⁻, S/MWCNTs/Ni-foam and FTO/TiO₂/CdS/Sr₃Zr₂Cu₄S₉/S²⁻, and S/MWCNTs/Ni-foam, by sandwiching the polysulfide gel in between the photoanodes and the CE using binder clips. These solar cells were subjected to I–V measurements with the help of a Newport Oriel 3A solar simulator coupled with a Keithley 2420 source meter. A 450 W Xenon arc lamp was used as the light source with a light intensity of 100 mW cm⁻² and Air Mass (AM) 1.5G illumination; the spatial uniformity of irradiance was determined by calibrating with a 2 cm × 2 cm Si reference cell and confirmed using a Newport power meter.

2.7 Theoretical and computational methodologies

We employed density functional (DFT) calculations⁵⁴ to investigate the electronic structures and estimate the structural parameters of relaxed Sr₃Zr₂Cu₄S₉ and Sr₃Zr₂Cu₄Se₉ unit cells. The Kohn–Sham equations within the DFT framework are solved using the plane wave basis expansion with the help of the VASP package.⁵⁵ Further details of the theoretical calculations are given in the ESI (see Section S3).† We used the Sr₃Zr₂Cu₄Se₉ unit cell with half-occupied (50%) Cu1 and Cu4 atomic sites for the calculations.

3. Results and discussion

3.1 Syntheses

The Sr₃Zr₂Cu₄S₉ and Sr₃Zr₂Cu₄Se₉ crystals were prepared by the reaction of elements at high temperatures (T_max = 1223 K) and slow cooling of the reaction mixtures to RT. The Sr₃Zr₂Cu₄S₉ crystals were red in contrast to the black-colored crystals of the Sr₃Zr₂Cu₄Se₉ phase.

Furthermore, we used two methods to prepare bulk polycrystalline samples of Sr₃Zr₂Cu₄S₉: (a) the direct reaction of elements at high temperatures and (b) the CS₂ method. The CS₂ method failed to produce the targeted Sr₃Zr₂Cu₄S₉ phase. Instead, the cubic SrS phase (space group: Fm3̄m)⁵⁶ was formed as the major phase according to the PXRD analysis (see Fig. S1 of the ESI†). Presumably, the phases containing Zr and Cu are amorphous in the powdered sample obtained by the CS₂ reaction. On the other hand, the high-temperature reaction of elements with one intermittent grinding and reheating produced a monophasic Sr₃Zr₂Cu₄S₉ sample. The polycrystalline Sr₃Zr₂Cu₄Se₉ sample was prepared using heating conditions similar to those employed for the sulfide sample.

The PXRD patterns of the Sr₃Zr₂Cu₄Q₉ (Q = S, Se) phases are shown in Fig. 1b. The refined unit cell parameters of Sr₃Zr₂Cu₄S₉ and Sr₃Zr₂Cu₄Se₉, calculated from the PXRD data using the Le Bail refinement method, are a = 6.695(2) Å, b = 10.322(1) Å, c = 11.941(2) Å, α = 109.60(1)°, β = 104.54(1)°, γ = 96.67(1)°, and a = 6.986(2) Å, b = 10.695(2) Å, c = 12.272(1) Å, α = 109.33(1)°, β = 105.35(1)°, γ = 96.57(1)°, respectively. The cell parameters of Sr₃Zr₂Cu₄Q₉ (Q = S, Se) obtained from the powder and single crystal XRD studies are in good agreement.

3.2 Crystal structure description

The quaternary sulfide Sr₃Zr₂Cu₄S₉ is the first quaternary compound found in the Sr–Zr–Cu–S system, whereas Sr₃Zr₂Cu₄Se₉ is the second member of the Sr–Zr–Cu–Se system for which a Sr-deficient phase Sr_0.5ZrCuSe₃ ⁴³ is known in the literature.

The single-crystal XRD study showed that, at RT, Sr₃Zr₂Cu₄S₉ crystallizes in the triclinic Ba₃Zr₂Cu₄S₉ ⁴⁸ structure. As expected, the unit cell volume of the centrosymmetric triclinic Sr₃Zr₂Cu₄S₉ structure (space group: P1̄) with the refined cell parameters a = 6.6907(13) Å, b = 10.312(2) Å, c = 11.929(2) Å, α = 109.49(3)°, β = 104.54(3)°, and γ = 96.73(3)°, is smaller than the Ba₃Zr₂Cu₄S₉ cell. These experimental lattice parameters augur well with those obtained from theoretical calculations (see section 3.7). The asymmetric unit of the Sr₃Zr₂Cu₄S₉ structure contains nine sulfur and nine metal sites (3 × Sr sites, 2 × Zr sites, and 4 × Cu sites). As seen in Fig. 2a, the layers of the Sr₃Zr₂Cu₄S₉ structure are separated by the Sr²⁺ cations. The anionic layer features distorted ZrS₆ octahedra, CuS₄ tetrahedra (Cu2 and Cu4), and trigonal planar CuS₃ units (Cu1 and Cu3), which serve as the main motifs of the structure.

Fig. 2 The unit cells of (a) Sr₃Zr₂Cu₄S₉ and (b) Sr₃Zr₂Cu₄Se₉ crystal structures along the b-axis.

The Sr₃Zr₂Cu₄Se₉ structure is isoelectronic to the related sulfide. Interestingly, its structure is different from the Sr₃Zr₂Cu₄S₉ structure. The selenide adopts the original structure type with triclinic symmetry (space group: P1̄). The refined cell constants of the Sr₃Zr₂Cu₄Se₉ structure are a = 6.9779(14) Å, b = 10.685(2) Å, c = 12.302(3) Å, α = 109.18(3)°, β = 105.38(3)°, and γ = 96.56(3)°. In contrast to the sulfide structure, the Sr₃Zr₂Cu₄Se₉ phase is non-stoichiometric with partially vacant Cu sites. Sr₃Zr₂Cu₄Se₉ is best described as the pseudo-2D structure, like the sulfide structure, as shown in Fig. 2b.

The selenide structure comprises nineteen independent atoms (3 × Sr, 2 × Zr sites, 5 × Cu sites, and 9 × Se sites), i.e., one additional Cu site in reference to the sulfide structure. The three Cu sites, Cu1, Cu3, and Cu4, have free SOF values of 0.598(8), 0.856(7), and 0.532(8), respectively, in the Sr₃Zr₂Cu₄Se₉ structure. The composition of the infinite layers present in the selenide structure is identical to the sulfide structure, i.e., and their negative charges are counterbalanced by the Sr²⁺ ions. The Zr and Cu atoms in the selenide structure are octahedrally and tetrahedrally coordinated with the Se atoms, respectively. The short Cu1⋯Cu1 and Cu4⋯Cu4 distances (<2.2 Å) in the Sr₃Zr₂Cu₄Se₉ structure are the result of their occupancy disorder and imply that these Cu atoms do not coexist simultaneously close to each other in the structure.

Next, we compare the layers of the Sr₃Zr₂Cu₄S₉ and Sr₃Zr₂Cu₄Se₉ structures in Fig. 3.

Fig. 3 (a) The chains that are bridged by the Cu1 and Cu3 atoms in the Sr₃Zr₂Cu₄S₉ and (b) chains of the Sr₃Zr₂Cu₄Se₉ that are bridged by the Cu1, Cu3, and Cu4 atoms to form infinite layers of .

The layers of both the structures have edge and vertex-sharing ZrQ₆ octahedra (see Fig. 3). The oppositely oriented Cu2S₄ and Cu4S₄ tetrahedra share edges and vertices with the ZrS₆ octahedra to form chains of (see Fig. 3a). Similarly, the connectivity of ZrSe₆ octahedra, Cu2Se₄, and Cu5Se₄ tetrahedra in the Sr₃Zr₂Cu₄Se₉ structure creates chains (see Fig. 3b). Finally, the layers in both structures are formed by filling of Cu atoms in the structures, which hold together the chains, as shown in Fig. 3. The main difference between the layers of the title structures is the bonding environments of the additional Cu atoms, Cu1 and Cu3, of the sulfide structure and Cu1, Cu3, and Cu4 atoms in the selenide structure. The Cu atoms (Cu1 and Cu3) in the sulfide structure are only three-coordinated in contrast to the four-coordinated (tetrahedral) Cu atoms of the selenide structure.

The important interatomic distances of the Sr₃Zr₂Cu₄Q₉ structures are provided in Table 2. The Zr–S distances of Sr₃Zr₂Cu₄S₉ (see Table 2) match well with the corresponding distance of the Ba₃Zr₂Cu₄S₉ (2.525(1) Å–2.704(1) Å)⁴⁸ structure. The Cu–S distances of the CuS₃ unit (2.234(2) Å–2.312(2) Å) are shorter than the tetrahedral CuS₄ units (2.309(2) Å–2.372(2) Å) in the title sulfide structure. These distances compare well with those found in Ba₃Zr₂Cu₄S₉ (2.241(2) Å–2.364(2) Å)⁴⁸ and the BaCeCuS₃ (2.351(1) Å–2.461(2) Å)³⁸ structures.

The Cu–Se (2.386(4) Å–2.682(5) Å) distances of Sr₃Zr₂Cu₄Se₉ are consistent with those found in the BaCu₂Se₂ (2.456(1) Å to 2.618(3) Å)⁵⁷ and BaNdCuSe₃ (2.460(4) Å to 2.567(3) Å)⁵⁸ structures. The Zr–Se bond distances of ZrSe₆ octahedra vary from 2.6342(19) Å to 2.8083(18) Å in the Sr₃Zr₂Cu₄Se₉ structure. These distances are in good agreement with those reported for the Ba_0.5ZrCuSe₃ (2.661(7) Å to 2.707(5) Å)⁴³ and Ba₈Zr₂Se₁₁(Se₂) (2.6337(7) Å to 2.7940(7) Å)⁴² structures.

Another interesting feature of Sr₃Zr₂Cu₄Q₉ (Q = S, Se) is the Cu⋯Cu interactions, which are intermediate to the single Cu–Cu bond (∼2.556 Å)⁵⁹ and the van der Waals distance of 2.80 Å (ref. 60) between two Cu atoms. These interactions are shown in Fig. 4 for the Sr₃Zr₂Cu₄Q₉ (Q = S, Se) structures. The Cu⋯Cu interactions are shorter in the Sr₃Zr₂Cu₄Se₉ structure (2.621(5) Å to 2.711(4) Å) than in the Sr₃Zr₂Cu₄S₉ structure (2.753(3) Å to 2.845(3) Å). Similar Cu⋯Cu interactions are also known for the Cu₅FeS₄ (2.587 Å–2.989 Å),⁶¹ K₂Cu₃AlS₄ (2.734(3) Å–2.736(3) Å),⁶² and Cu₃SbSe₃ (2.665(2) Å)⁶³ structures. The chalcogen atoms of Sr₃Zr₂Cu₄Q₉ structures make distorted bicapped trigonal prism-like geometries around the Sr atoms, as shown in Fig. S2 in the ESI.†

Fig. 4 A fragment of the layers showing the short Cu⋯Cu interactions in (a) Sr₃Zr₂Cu₄S₉ and (b) Sr₃Zr₂Cu₄Se₉ structures.

To the best of our knowledge, only monovalent copper species are known for the chalcogenide structures. Also, the Sr₃Zr₂Cu₄Q₉ structures are traditional chalcogenides (not polychalcogenides) with more stable Q²⁻ species. Therefore, these two structures can be charge balanced with the Sr²⁺, Zr⁴⁺, Cu¹⁺, and Q²⁻ species, i.e., the charge partitioned formula of the title phases is (Sr²⁺)₃(Zr⁴⁺)₂(Cu¹⁺)₄(Q²⁻)₉.

3.3 Structural relationship between Ak₃Zr₂Cu₄S₉ (Ak = Ba and Sr), Sr₃Zr₂Cu₄Se₉, and Sr_0.5ZrCuSe₃ structures

We next correlate the structural aspects of the three structure types: Ak₃Zr₂Cu₄S₉ (Ak = Ba and Sr),⁴⁸ Sr₃Zr₂Cu₄Se₉, and Sr_0.5ZrCuSe₃ ⁴³ structures. A common feature of these structure types is the presence of anionic layers built up of the transition metals and Q (S/Se) atoms. These anionic frameworks are counterbalanced and separated by the Ak²⁺ cations (Ak = Ba and Sr) (see Fig. 5). Among these structures, Sr_0.5ZrCuSe₃ ⁴³ is stabilized with the highest symmetry (space group: Cmcm) and is isotypic with the KCuZrS₃ (Cmcm)⁶⁴ structure type. In the literature, a large number of quaternary chalcogenides are known to adopt the KCuZrS₃ ⁶⁴ type structure.

Fig. 5 Unit cells of the (a) Ak₃Zr₂Cu₄S₉ (Ak = Ba, Sr) (P1̄) and (b) Sr_0.5ZrCuSe₃ (Cmcm) structures.

The Sr₃Zr₂Cu₄Se₉ (P1̄) type is closely related to Sr_0.5ZrCuSe₃ ⁴³ in terms of the coordination environments of the transition metals, i.e., Zr and Cu atoms, which occupy distorted octahedral and tetrahedral sites, respectively. The CuS₃ units with a triangular planar geometry make the triclinic Ak₃Zr₂Cu₄S₉ (Ak = Ba and Sr) structure type (P1̄)⁴⁸ unique to the other two structure types. No short Cu⋯Cu interactions exist in the Sr_0.5ZrCuSe₃⁴³ structure. In contrast, the Ak₃Zr₂Cu₄S₉ (Ak = Ba and Sr) and Sr₃Zr₂Cu₄Se₉ structure types feature a variety of short Cu⋯Cu interactions.

Although the Ak₃Zr₂Cu₄S₉ (Ak = Ba, Sr) and Sr₃Zr₂Cu₄Se₉ structures are isoelectronic and layered, the intralayer connections are entirely different in these two structure types, as described above (see Fig. 3). While the stoichiometric sulfur compound has two Cu sites as the bridging elements, the non-stoichiometric selenide compound has three Cu atoms to link the chains, as shown in Fig. 3 and 4. Thus, the flexibility of copper atoms to stabilize different polyhedra in the title sulfide structure can be considered as the main contrasting feature between the Ak₃Zr₂Cu₄S₉ and Sr₃Zr₂Cu₄Se₉ types.

3.4 Optical bandgap and electrical resistivity

We used the polycrystalline samples of Sr₃Zr₂Cu₄Q₉ (Q = S, Se) for physical property measurements. The Tauc plot of the Sr₃Zr₂Cu₄S₉ powder shows a sharp drop in absorption coefficient (α) value below 2 eV, as shown in Fig. 6a.

Fig. 6 (a) Tauc plots of the finely ground polycrystalline Sr₃Zr₂Cu₄S₉ and Sr₃Zr₂Cu₄Se₉ samples. (b) The electrical resistivity plot of the Sr₃Zr₂Cu₄Se₉ compound below RT.

A direct bandgap energy value of 1.7(1) eV is calculated for the Sr₃Zr₂Cu₄S₉ phase from the Tauc plot, which agrees with the reddish-brown color of the powder. The theoretical bandgap of 1.78 eV for the Sr₃Zr₂Cu₄S₉ structure is in good agreement with the experimental value (see section 3.7 for details). On the other hand, Sr₃Zr₂Cu₄Se₉, which is black in color, does not show any sharp transition in the Tauc plot, indicating that this selenide has a narrow bandgap energy (E_g < 0.6 eV), or it is a metal/semimetal.

The sulfide sample, Sr₃Zr₂Cu₄S₉, is electrically insulating, having resistance values of the order of MΩ at RT in contrast to the Sr₃Zr₂Cu₄Se₉, which has electrical resistivity (ρ) values of about 80 mΩ cm (at RT). The ρ-value further drops to ∼20 mΩ cm on cooling the Sr₃Zr₂Cu₄Se₉ sample to 3 K, as shown in Fig. 6b. A kink in the resistivity plot was observed at ∼225 K, and this effect was reproducible. The origin of the kink observed in the resistivity plot is not clear. The resistivity values of Sr₃Zr₂Cu₄Se₉ are several orders higher than coinage metals like Cu (1.7 × 10⁻³ mΩ cm at RT) and Ag (1.6 × 10⁻³ mΩ cm at RT). Thus, Sr₃Zr₂Cu₄Se₉ can be described as a poor metal or a degenerate semiconductor. The detailed theoretical electronic structure of Sr₃Zr₂Cu₄Se₉ is discussed in section 3.7.

3.5 High-temperature transport studies: thermal conductivity (κ_tot), Seebeck coefficient (S), and electrical resistivity (ρ)

Both Sr₃Zr₂Cu₄S₉ and Sr₃Zr₂Cu₄Se₉ are relatively good heat conductors in comparison to related layered quaternary structures such as the RbZrCuTe₃ (0.49 W mK⁻¹ at 323 K to 0.35 W mK⁻¹ at 575 K)³¹ and BaCeCuS₃ (0.62 W mK⁻¹ at 323 K to 0.32 W mK⁻¹ at 773 K).³⁸ The Sr₃Zr₂Cu₄Se₉ compound shows a κ_tot of 3.5 W mK⁻¹ at 323 K, which is almost twice the value observed for Sr₃Zr₂Cu₄S₉ (1.82 W mK⁻¹ at 323 K). As expected, the κ_tot values gradually decreased as the samples were heated from 323 K to higher temperatures (573 K). The κ_tot value drops to 2.5 W mK⁻¹ and 1.4 W mK⁻¹ for Sr₃Zr₂Cu₄Se₉ and Sr₃Zr₂Cu₄S₉, respectively, at 573 K (Fig. 7a).

Fig. 7 (a) Temperature-dependent thermal conductivity plots of Sr₃Zr₂Cu₄Q₉ (Q = S, Se) compounds. (b) Electrical resistivity and (c) Seebeck coefficient as a function of temperature for the Sr₃Zr₂Cu₄Se₉ compound.

The κ_tot value for each sample is the sum of the electronic (κ_ele) and lattice thermal conductivities (κ_lat) of the crystals. Since Sr₃Zr₂Cu₄Se₉ is metallic, in contrast to the insulating Sr₃Zr₂Cu₄S₉, the free charge carriers in the former compound contribute to the total thermal conductivity. On the contrary, the κ_ele value of the insulating Sr₃Zr₂Cu₄S₉ is negligible in comparison to the κ_lat values. We calculated the κ_ele value of Sr₃Zr₂Cu₄Se₉ using the Wiedemann–Franz model⁶⁵ (refer to the caption of Fig. S3 in the ESI†) to compare the κ_lat values of the two compounds. The κ_lat value is also higher for Sr₃Zr₂Cu₄Se₉ (3.08 W mK⁻¹ to 2.1 W mK⁻¹ in the range of 323 K to 573 K) than for the isoelectronic sulfide (see Fig. 7a). The higher thermal conductivity values for Sr₃Zr₂Cu₄Q₉ (Q = S, Se) make them unsuitable for thermoelectric applications.

Next, we discuss the trends of the Seebeck coefficient and resistivity data obtained for Sr₃Zr₂Cu₄Se₉ as a function of temperature. The electrical resistivity plot shown in Fig. 7b is consistent with metal-like behavior with a gradual increase in ρ-values on increasing the sample's temperature. The ρ-value of Sr₃Zr₂Cu₄Se₉ elevated from 190 mΩ cm at 323 K to 320 mΩ cm at 573 K. The p-type nature of Sr₃Zr₂Cu₄Se₉ is confirmed by the positive sign of the S-values, as shown in Fig. 7c. As expected, the S-value increases at higher temperatures as the sample becomes more electrically resistive. Unfortunately, the low S values (12.51 μV K⁻¹ at 323 K to 24.60 μV K⁻¹ at 573 K) combined with the relatively higher thermal conductivity values of the Sr₃Zr₂Cu₄Se₉ sample make it unsuitable for thermoelectric applications.

The maximum thermoelectric figure of merit, zT, is almost zero (16.5 × 10⁻⁷), as can be seen from the zT plot in Fig. S3 in the ESI.† Further improvement of the zT value by optimization of the charge carrier concentration seems unlikely due to the poor S-value of Sr₃Zr₂Cu₄Se₉.

3.6 Photovoltaic studies of the Sr₃Zr₂Cu₄S₉ polycrystalline compound

The current density (J)–voltage (V) measurements of the solar cells were performed under one sun illumination. The J–V plot of the solar cell, FTO/TiO₂/CdS/S²⁻, S/MWCNTs/Ni-foam, presented in Fig. 8, shows the open circuit voltage (V_OC) = 723 mV, short circuit current density (J_SC) = 13.00 mA cm⁻², fill factor (FF) = 58.83%, and the power conversion efficiency (PCE or η) = 5.59%.

Fig. 8 The J–V characteristics of the solar cells based on different photoanodes, S²⁻, S gel electrolyte, and MWCNTs/Ni-foam as CE under 1 sun (AM 1.5G, 100 m cm⁻²).

The J–V plot of the FTO/TiO₂/CdS/Sr₃Zr₂Cu₄S₉/S²⁻, S/MWCNTs/Ni-foam shows: V_OC = 868 mV, J_SC = 13.28 mA cm⁻², FF = 60.11%, and the efficiency = 6.93%, as seen in Table 3. From the Tauc plot, shown in Fig. 6a, the bandgap of Sr₃Zr₂Cu₄S₉ was estimated to be 1.7 eV, which is much lower than the bandgaps of TiO₂ (3.2 eV) and CdS (2.3 eV) used in our solar cell. By the inclusion of Sr₃Zr₂Cu₄S₉ in the photoanode, the overall efficiency was increased by ∼24% because Sr₃Zr₂Cu₄S₉, a narrow band gap semiconductor, serves as a co-sensitizer. This implies that in the co-sensitized cell, upon illumination, in addition to the CdS, the Sr₃Zr₂Cu₄S₉ phase also undergoes an electron–hole separation. Hence, in the co-sensitized cell, additional charge carriers are available for circulation, improving the V_OC as well as the J_SC, thus increasing the efficiency of the cell. Furthermore, co-sensitization also reduces back electron transfer to the electrolyte during cell operation, which maximizes charge separation and enhances efficiency.

Table 3 Parameters of the solar cells containing 1 M polysulfide gel electrolyte and MWCNTs/Ni-foam as CE, under 1 sun illumination (AM 1.5G, 100 mW cm⁻²) and with an exposed cell area of ∼0.1 cm²

Photoanode	VOC (mV)	JSC (mA cm^−2)	FF (%)	PCE (%)
FTO/TiO2/CdS	723	13.00	58.83	5.59
FTO/TiO2/CdS/Sr3Zr2Cu4S9	868	13.28	60.11	6.93

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3.7 Band structures of Sr₃Zr₂Cu₄S₉ and Sr₃Zr₂Cu₄Se₉

We estimated the structural parameters of the optimized unit cells and explored the electronic structures of Sr₃Zr₂Cu₄S₉ and Sr₃Zr₂Cu₄Se₉. The results are tabulated in Table 4 and are found to be aligned with the experimental values. As can be seen, the GGA (LDA) schemes slightly overestimate (underestimate) the cell parameters as expected. In general, the GGA (LDA) XC schemes slightly overestimate (underestimate) the cell parameters, respectively, for most of the material systems.⁶⁶ The GGA bandgap energy for Sr₃Zr₂Cu₄S₉ is computed to be 1.37 eV. As expected, the computed GGA bandgap value for the sulfide is lower as compared to the experimental value of ∼1.7 eV since the GGA (LDA) schemes are known to underestimate the bandgaps as much as by ∼50%. The bandgap of 1.78 eV for Sr₃Zr₂Cu₄S₉ computed using the GGA-1/2 scheme is in better agreement with the experimental value. The GGA-1/2 scheme is expected to provide better bandgap estimates since it partially corrects the self-interaction error in local and semi-local XC functionals for extended systems.

Table 4 The computed lattice parameters and bandgap (eV) values of Sr₃Zr₂Cu₄S₉ and Sr₃Zr₂Cu₄Se₉

			a (Å)	b (Å)	c (Å)	α	β	γ	E g (eV)
	Cal.	GGA	6.719	10.321	11.937	109.41	104.79	96.80	1.37
Sr3Zr2Cu4S9		LDA	6.539	9.953	11.713	109.97	104.21	96.99	1.29
		GGA-1/2	—	—	—	—	—	—	1.78
	Exp.		6.662	10.232	11.939	109.69	104.84	96.39	1.7(1)
	Cal.	GGA	7.044	10.697	12.333	109.31	105.68	96.50	1.17
Sr3Zr2Cu4Se9		LDA	6.830	10.402	12.006	109.33	105.60	96.56	1.09
		GGA-1/2	—	—	—	—	—	—	1.56
	Exp		6.9779	10.685	12.302	109.18	105.38	96.56	0

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The GGA and GGA-1/2 computed bandgap values of Sr₃Zr₂Cu₄Se₉ are 1.17 eV and 1.56 eV, respectively. These computed bandgap energies disagree with the experimental result that suggests Sr₃Zr₂Cu₄Se₉ is metallic/degenerate semiconducting in nature. This disagreement may be partially attributed to the slightly different occupancy values of Cu1, Cu3, and Cu4 sites in the unit cell used to model the Sr₃Zr₂Cu₄Se₉ structure as compared to the experimental unit cell content obtained from the SCXRD study. In our theoretical model, the Cu1 and Cu4 sites are half occupied (50%), whereas the Cu3 site is fully occupied (100%). However, in the experimental unit cell, the Cu1, Cu3, and Cu4 sites have occupancies of 59.8%, 85.8%, and 53.3%, respectively.

Fig. 9 shows the density of states (DOS) and the band structure plots for Sr₃Zr₂Cu₄S₉. The energies in the DOS plot are scaled in such a way that the valence band maximum (VBM) lies at 0 (see Fig. 9a). As can be seen, the top of the valence band (VB) (∼−5.5 eV < E < 0) is primarily comprised of Cu-3d, Zr-4d, and S-3p states. The VB at ∼−12 eV is mainly contributed by the S-3s localized states, with some minor contributions from the Sr-4s states. The conduction band (CB) close to the Fermi energy (∼1.1 eV < E < 2.2 eV) is primarily made up of the antibonding Zr-4d states. The contributions to the CB in the higher energy range (2.9 eV < E < 4.5 eV) are from the Zr-4d and Sr-4d states. The band structure of Sr₃Zr₂Cu₄S₉, as shown in Fig. 9b, indicates that the bandgap is indirect. However, the difference between the indirect and direct bandgap is minute (∼0.07 eV). The DOS and band structure plots for Sr₃Zr₂Cu₄Se₉ are found to be qualitatively similar to that for Sr₃Zr₂Cu₄S₉, as shown in Fig. S4 of the ESI.†

Fig. 9 (a) The total and projected density of states (DOS) and (b) the band structure plot along high symmetry directions in the Brillouin zone for Sr₃Zr₂Cu₄S₉. The high symmetry k-points are Y ≡ (0, ½, 0), Γ ≡ (0, 0, 0), X ≡ (½, 0, 0), C ≡ (½, ½, 0), and Z ≡ (0, 0, ½).

The projected crystal orbital Hamilton populations (COHP)⁶⁷ are computed for the title structures to estimate the bonding type between the constituent atoms and their strength. Fig. 10 shows the −COHP (E) and integrated-COHP plots for Sr₃Zr₂Cu₄S₉. The −ICOHP values suggest that the bond strength between atom pairs varies in the order Zr–S > Cu–S > Cu–Zr > Sr–S. The COHP and ICOHP plots for Sr₃Zr₂Cu₄Se₉ are presented in Fig. S5 in ESI† and indicate a similar order for bonding strengths.

Fig. 10 (a) The crystal orbital Hamilton populations (COHP) and (b) the integrated COHP (ICOHP) values for the bonding atoms in Sr₃Zr₂Cu₄S₉.

We next discuss the computed Bader charges (Q_B) of the atoms in the Sr₃Zr₂Cu₄Q₉ structures. In general, the magnitudes of the Bader charges are smaller than the formal oxidation states of atoms since the latter values are calculated by considering the full charge transfer from metals (cations) to non-metals (anions), i.e., considering the crystalline inorganic solids as perfect ionic compounds. The Q_B values provide estimates of the relative charge transfer between atom pairs and the degree of ionic/covalent character of the bonds.⁶⁸ For Sr₃Zr₂Cu₄S₉, these charges are +1.54, +2.02, +0.39, and −1.16 for Sr, Zr, Cu, and S ions, respectively. Likewise, in Sr₃Zr₂Cu₄Se₉, Q_B values of +1.49, +1.87, +0.35, and −1.10 were found for the Sr, Zr, Cu, and Se ions, respectively. Indeed, the magnitudes of the computed Q_B values are smaller than the formal oxidation states +II, +IV, +I, and −II for the Sr, Zr, Cu, and S (Se) ions. The deviation of Q_B values of the atoms, especially Zr, Cu, and S, in the Sr₃Zr₂Cu₄Q₉ structures from their formal oxidation numbers indicate the partial covalent character of the metal–chalcogen bonds due to the overlapping of orbitals, as discussed earlier.

4. Conclusions

The single crystals and polycrystals of two new quaternary mixed metal chalcogenides, Sr₃Zr₂Cu₄S₉ and Sr₃Zr₂Cu₄Se₉, were successfully prepared by reacting elemental reactants at high temperatures under vacuum. The SCXRD studies of the prepared quaternary crystals are carried out at RT, revealing that Sr₃Zr₂Cu₄Se₉ adopts a new structure type. The selenide phase is non-stoichiometric due to Cu-deficiency in the structure. On the contrary, the isoelectronic sulfide, Sr₃Zr₂Cu₄S₉, is stoichiometric and crystallizes in the Ba₃Zr₂Cu₄S₉ structure type. The triclinic structures (space group: P1̄) of both Sr₃Zr₂Cu₄Q₉ phases are pseudo-two-dimensional, containing layers of . The two structures differ in the coordination geometries of their Cu atoms. For the sulfur analog, there are tetrahedral CuS₄ units and trigonal CuS₃ units, and for the selenide structure, only tetrahedrally coordinated Cu atoms are present in the structure. The optical absorption study of the red-colored Sr₃Zr₂Cu₄S₉ sample yields a direct bandgap of 1.7(1) eV. The resistivity study of the selenide, Sr₃Zr₂Cu₄Se₉, shows a temperature dependence typical for a semimetal/degenerate semiconductor. Also, the p-type nature of the Sr₃Zr₂Cu₄Se₉ sample is established from the Seebeck study. The photovoltaic behavior of the Sr₃Zr₂Cu₄S₉ powder was studied by using it as a co-sensitizer in a CdS-based solar cell, which increased the overall efficiency by ∼24%. The DFT studies were used to calculate the electronic structures of Sr₃Zr₂Cu₄Q₉. The theoretical analysis of the band structure of the Sr₃Zr₂Cu₄S₉ phase shows the direct bandgap nature of the sulfide and it is consistent with the experimental studies. The COHP, ICOHP, and Bader charge calculation studies suggest the bonding interactions between Zr/Cu and S atoms are stronger than the Sr–S interactions.

Data availability

Electronic supplementary information (ESI) is available, providing additional crystallographic details of the Sr₃Zr₂Cu₄S₉ and Sr₃Zr₂Cu₄Se₉ structures. The CIF files for these structures have been deposited with the joint CCDC/FIZ Karlsruhe deposition service under CSD numbers 2390675 and 2390676, respectively.†

Conflicts of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this article.

Acknowledgements

JP thanks DST-SERB, the Government of India (GOI) for the financial support under the core research grant (Grant Number: CRG/2021/0003641), and IIT Hyderabad for research facilities. SB and SY thank MOE and GOI for the Prime Minister Research Fellowship (PMRF). AKR thanks DST, India, for the INSPIRE fellowship, and Swati thanks CSIR for the Senior Research Fellowship. The authors are thankful to DST-FIST(SR/FST/PSI-215/2016) for computational resources. The authors also acknowledge Dr Surya Jammalamadaka from the Department of Physics at IIT Hyderabad for his help with electrical resistivity data collection.

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Footnote

† Electronic supplementary information (ESI) available: Additional crystallographic details of the Sr₃Zr₂Cu₄S₉ and Sr₃Zr₂Cu₄Se₉ structures. CCDC 2390675 and 2390676. For ESI and crystallographic data in CIF or other electronic format see DOI: https://doi.org/10.1039/d4dt02928c

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