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• Birefringent crystals are a critical type of optoelectronic materials that are used to regulate and detect the polarization state of light in optical devices. It is widely used in laser polarization technology, optical isolators, optical communications, phase compensators, etc. [1-6]. Over the past few years, several birefringent crystals have been commercially used, including YVO₄ (0.204@532 nm) [7], TiO₂ (0.256@546 nm) [8], CaCO₃ (0.172@532 nm) [9], LiNbO₃ (0.074@546 nm) [10], and α-BaB₂O₄ (0.122@546 nm) [11]. However, these crystals have significant disadvantages, such as the defects and impurities in CaCO₃ and TiO₂ crystals. The high production costs for YVO₄, LiNbO₃, and α-BaB₂O₄. Thus, new birefringent crystals with the advantages of high birefringence, large transmittance range, and good physical and chemical stability are urgently desired.

  Chalcogenides are widely used as optical function materials since they have a wide infrared (IR) transmittance range covering the important atmospheric windows (3−5 and 8−12 µm) [12-17]. However, very few reports of chalcogenide birefringent crystals can be commercially applied. The main question is that the measured birefringence value difficultly reaches the level of oxide crystals. Meanwhile, the strong absorption in the IR waveband limited the application of oxide crystals. Therefore, looking for a new chalcogenide with large birefringence is a current research focus. It has widely been received that the birefringence value is related to the structural anisotropy of the crystal. Large structure anisotropy is the benefit of obtaining the large birefringence [18-20]. At present, the improvement of birefringence can be achieved by introducing highly anisotropic functional motifs, such as the planar triangle arrangement of [BS₃] and [B₃S₆] units in the thioborate system, the Pb²⁺, Sn²⁺, and Sb³⁺ with stereochemical active lone pair, the transition metal d⁰ cations V⁵⁺, Ti⁴⁺, and Nb⁵⁺ with octahedron coordination [21-23]. These motifs could play a critical role in the birefringence. For example, the NaBaBS₃ with the π-conjugated [BS₃] planar unit features a birefringence of 0.177 at 550 nm [24]. The β-BaGa₂Se₄ with strong structure anisotropy of one dimensional (1D) [GaSe₂]_∞ chain exhibits a large experimental birefringence of 0.18 at 550 nm [25]. The band gap (E_g) is also an important parameter for an optical material, which determines the transmittance cutoff edge in the application. Meanwhile, the thiophosphate with strong electronegativity in the P−S bond could benefit from obtaining the large E_g. In addition, designing compounds with few components is beneficial to the growth of single crystals. Therefore, based on the thiophosphate system, introducing the anisotropic structure units is a feasible way to obtain optical material with large birefringence.

  This work introduced the highly electronegativity P⁵⁺ and 6s² lone-pair electrons of Pb²⁺ into the Pb−P−S system [26-28]. A new lead-based thiophosphate phase of β-Pb₃P₂S₈, was obtained by the high-temperature solid-state spontaneous crystallization method. The β-Pb₃P₂S₈ crystallizes in the orthorhombic space group, while the other phase of known α-Pb₃P₂S₈ belongs to the cubic crystal system [29]. As we know, the cubic system is optically isotropic. Therefore, the birefringence of α-Pb₃P₂S₈ is zero. Meanwhile, the consistent arranged [PbS_n] polyhedral layers in β-Pb₃P₂S₈ could effectively increase the structural anisotropy, while the arrangement mode in α-Pb₃P₂S₈ is irregular. The orthorhombic phase of β-Pb₃P₂S₈ realizes the decrease of symmetry, which can be a candidate as the birefringence crystal. Due to the introduction of high electronegativity P⁵⁺, the β-Pb₃P₂S₈ possesses a moderate E_g (2.37 eV) in the thiophosphate-based compounds optical crystal system. The IR spectrum and thermogravimetric analysis measurements indicate that β-Pb₃P₂S₈ has a wide transmittance range and excellent thermal stability. In addition, the birefringence measurement was performed by a polarizing microscope. This crystal has an exceptional birefringence effect of 0.26@550 nm, which is the largest value for experiment-reported chalcogenides and larger than that of commercialized birefringent crystals. Furthermore, the theoretical calculation of birefringence (0.23@550 nm) is close to the experimental value, demonstrating the accuracy of the test. The exceptional birefringence effect can be attributed to the collaborative contribution between lone-pair electrons of Pb²⁺ and parallelly arranged polyhedral layers in β-Pb₃P₂S₈.

  The β-Pb₃P₂S₈ crystallizes in the orthorhombic centrosymmetry Pbcn space group with unit cell parameters of a = 12.8708(8) Å, b = 9.6073(6) Å, c = 10.2685(7) Å, V = 1269.74(14) ų, and Z = 4. There are two crystallography unique Pb atoms (Wyckoff sites: 8d and 4c), one P atom (Wyckoff site: 8d), and four S atoms (Wyckoff site: 8d) in an asymmetric unit. The detailed crystal refinement data for β-Pb₃P₂S₈ is shown in Table 1. The bond valance calculations (Pb: 1.760−1.797; P: 5.301; S: 1.524−2.053) indicate that Pb, P, and S atoms are in valence states of +2, +5, and −2 (Table S1 in Supporting information), which confirms that the reasonable structure solution. The bond lengths of Pb−S range from 2.846(3) Å to 3.231(3) Å (Table S3 in Supporting information), which is consistent with some known Pb-based sulfides, such as PbGa₄S₇ (Pb−S: 2.742(3)−3.533(3) Å) [30], Pb₄Ga₄GeS₁₂ (Pb−S: 2.827(5)−3.375(4) Å) [31] and PbU₂S₅ (Pb−S: 2.786(16)−3.103(16) Å) [32]. The bond lengths of P−S are range from 2.014(5) Å to 2.068(4) Å (Table S3), which is consistent with the CuHgPS₄ (P−S: 2.056(3)−2.061(3) Å) [33], Eu₂P₂S₆ (P−S: 1.979(6)−2.061(6) Å) [26], and Hg₃P₂S₈ (P−S: 2.036(5)−2.080(5) Å) [34]. In order to better describe the structural characteristics, we only considered Pb−S bonds with lengths less than 3.11 Å as [PbS_n] polyhedrons. As shown in Fig. 1a and Fig. S1 (Supporting information), the crystal structure of β-Pb₃P₂S₈ is composed of [Pb(1)S₅] tetragonal pyramid, [Pb(2)S₄] distorted tetrahedron, and [PS₄] tetrahedron. The [PS₄] tetrahedra are arranged in reverse parallel pairs in the ac plane while not connected with each other (red-shaded area). The [PS₄] tetrahedra are edge-shared and vertex-shared with [Pb(1)S₅] tetragonal pyramids and [Pb(2)S₄] tetrahedra (Fig. S12a in Supporting information), forming the 3D structure (Fig. 1c), eventually.

  Table 1

  

  Table 1.  Crystal information and structure refinement data for β-Pb₃P₂S₈.

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  Figure 1

  

  Figure 1.  Crystal structures of β-Pb₃P₂S₈ and α-Pb₃P₂S₈: (a) The arrangement of [PS₄] tetrahedra and Pb atoms in β-Pb₃P₂S₈ along the a-axis. (b) The whole structure framework diagram of α-Pb₃P₂S₈ along the a-axis. (c) The whole structure framework diagram of β-Pb₃P₂S₈ along the a-axis. (d) The [Pb₃S₄]_∞ polyhedral layer in β-Pb₃P₂S₈.

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  As displayed in Fig. 1b and Fig. S1, the α-Pb₃P₂S₈ is composed of [PS₄] and [Pb(1)S₄] tetrahedra. The [PS₄] tetrahedra are edge-shared with [Pb(1)S₄] tetrahedra forming the 3D structure (Fig. S12b in Supporting information). At the same time, the inconsistent arrangement of basic build units (BBUs) is not conducive to improving the structural anisotropy. And α-Pb₃P₂S₈ belongs to the cubic system, which has no optical anisotropy. However, in the structure of β-Pb₃P₂S₈, the BBUs rank more regularly along the b-axis direction. As shown in Fig. 1d, the [Pb(1)S₅] tetragonal pyramids are vertex-shared with [Pb(2)S₄] tetrahedra forming the [Pb₃S₄]_∞ polyhedral layer in ac plane. Eventually, the alternately arranged [Pb₃S₄]_∞ polyhedral layers and [PS₄] tetrahedra improve the optical anisotropy in β-Pb₃P₂S₈ (Fig. 1c).

  The polycrystalline of β-Pb₃P₂S₈ was synthesized through the high-temperature solid-state spontaneous crystallization method with additional Cu. However, Cu does not participate in the synthesis of the Pb−P−S system and produces the by-product of Cu₃PS₄. The Cu may act as a cocatalyst in the synthesis process. A similar situation was also reported in Cs₅Ga₉S₁₆, RbGa₅S₈, CsGa₅S₈, and CsLiGa₆S₁₀ with the additional elements added before the synthesis [35-37]. In addition, the synthesis process of known α-Pb₃P₂S₈ was grown by the two-step vapor transport reaction in a gradient furnace with I₂ transport agent [29]. The synthesis method is completely different for them. The β-Pb₃P₂S₈ phase was tested by powder X-ray diffraction (XRD) measurement (Fig. S2 in Supporting information), in which the experimental XRD curve matched well with the simulated XRD curve of β-Pb₃P₂S₈ phase calculated from the Crystallographic Information File (CIF). The diffraction peaks do not match the simulated α-Pb₃P₂S₈ phase, indicating the successfully synthesized new β-Pb₃P₂S₈ phase. In addition, the phase purity was measured by the refined powder XRD for β-Pb₃P₂S₈ (Fig. S3 in Supporting information). The energy-dispersive spectrum (EDS) result is shown in Fig. S4 (Supporting information). The Pb, P, and S elements were detected and distributed uniformly on a single crystal surface. The ratio of elements is 2.95:2:7.85, close to the chemical formula of β-Pb₃P₂S₈. In addition, the Raman spectrum of β-Pb₃P₂S₈ is presented in Fig. S5 (Supporting information), in which the peaks at 379 cm⁻¹ and 561 cm⁻¹ belong to the vibration modes of the P−S bond, the absorption peaks at 195 cm⁻¹ and 248 cm⁻¹ could be assigned to the Pb−S bond vibration.

  The thermogravimetric (TG) analysis of β-Pb₃P₂S₈ was measured from 300 K to 1273 K under the N₂ atmosphere. As shown in Fig. S6 (Supporting information), the β-Pb₃P₂S₈ is stabilized to 990 K and has begun to decompose. The differential thermal analysis (DTA) curve shows an endothermic peak at 1099 K, indicating the phase decomposition behavior of β-Pb₃P₂S₈. In order to measure the phase stability of β-Pb₃P₂S₈ with temperature change, the differential scanning calorimetry (DSC) and temperature-dependent XRD measurements were executed. As shown in Fig. S7 (Supporting information), the heating and cooling DSC curves show no endothermic or exothermic peak from 300 K to 773 K, indicating the non-phase transition behavior for β-Pb₃P₂S₈. Meanwhile, the temperature-dependent XRD measurement in Fig. S8 (Supporting information) shows that the β-Pb₃P₂S₈ has the same diffraction peaks from 300 K to 723 K, also indicating the irreversible phase transition between the α- and β-Pb₃P₂S₈. The UV–vis-NIR diffuse reflection spectrum for β-Pb₃P₂S₈ was collected by the polycrystalline powder displayed in Fig. 2a. The reflection spectrum indicates that β-Pb₃P₂S₈ has moderate visible light transmittance (including 550 nm). The experimental E_g result is approximately 2.37 eV in accordance with the orange color of the crystal, converted by the Kubelka-Munk function. Compared with the E_g in the lead-based chalcogenides optical crystal system (Table S5 in Supporting information), the β-Pb₃P₂S₈ has a large E_g and attains the requirement for optical material. The IR spectrum is shown in Fig. 2b with no obvious absorption peak between 2.5−15 µm, which indicates that β-Pb₃P₂S₈ has high IR transmittance and covers the two critical atmospheric windows of 3−5 and 8−12 µm. However, the IR transmittance spectra for the pressed pellet of "KBr + powder" samples are always wider than the single crystals [38]. The larger and higher quality of β-Pb₃P₂S₈ single crystals need to be synthesized to obtain the accurate transmittance spectrum.

  Figure 2

  

  Figure 2.  (a) The experimental E_g from UV–vis-near infrared diffuse reflection spectrum of β-Pb₃P₂S₈ and (b) IR spectrum measurement of β-Pb₃P₂S₈.

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  The birefringence of β-Pb₃P₂S₈ was measured by the polarizing microscope. One smooth plate single crystal was selected for testing. As shown in Fig. S10 (Supporting information), the β-Pb₃P₂S₈ achieves complete extinction under the orthogonal polarized light. The optical path difference (R) was tested to be 2.471 µm with a thickness (T) of 9.33 µm. The measured crystal face is (001), which was determined by the single crystal diffractometer (Fig. S9 in Supporting information). According to the birefringence calculated formula of R = |N_e − N_o| × T = Δn × T [39], the experimental birefringence value of β-Pb₃P₂S₈ is calculated to be 0.26. Because the measured crystal face may not be the most anisotropic in the structure, the actual birefringence of β-Pb₃P₂S₈ is larger than or equal to 0.26@550 nm. Interestingly, it surpasses the commercialized birefringence materials at present, such as CaCO₃ (0.172@532 nm) [9], YVO₄ (0.204@532 nm) [7], α-BaB₂O₄ (0.122@532 nm) [11], and TiO₂ (0.256@546 nm) [8]. Meanwhile, compared with the reported experimental birefringence of the chalcogenides system (Fig. 3) [24,25,40-45], the β-Pb₃P₂S₈ possesses the highest birefringence in the chalcogenides under 550 nm. It demonstrates the huge potential for application as a newly birefringence crystal.

  Figure 3

  

  Figure 3.  Compared with the reported experimental birefringence values in the chalcogenides at 550 nm.

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  In order to further comprehend the origin of the optical properties in the structure, the first-principles calculations based on the density function theory (DFT) method were performed in the Cambridge Sequential Total Energy Package (CASTEP). As shown in Fig. 4a, the electronic band structural calculation result indicates that β-Pb₃P₂S₈ is an indirect band gap compound of 2.1 eV with valence band maximum (VBM) and conduction band minimum (CBM) situated at G and Z points, respectively. The calculated result shows the difference from the experimental value of 2.37 eV, caused by the discontinuity of exchange-correlation energy [46]. In addition, the calculated birefringence in Fig. 4b shows that β-Pb₃P₂S₈ has a large value of 0.23@550 nm, consistent with the experimental result. The calculated total density of states (DOS) and partial density of states (PDOS) are shown in Fig. S14 (Supporting information). The VBM is mainly dominated by S-3p orbital, Pb-6s orbital, and Pb-6p orbital. In comparison, the major contribution of the CBM is from the S-3p orbital and the Pb-6p orbital, with little from the P-3p orbital. Therefore, the Pb-6p orbital and S-3p orbital concentrated on the VBM and CBM stands for the strong hybridization between [PbS_n] polyhedrons, indicating that the optical properties of β-Pb₃P₂S₈ are mainly determined by Pb−S bond. In addition, a method of Barder charge analysis was used to evaluate the concrete birefringence contributions of ions for β-Pb₃P₂S₈ [47]. As a result, the Pb²⁺ contributes 28.56% to birefringence, S²⁻ contributes 71.68% to birefringence, but P⁵⁺ produces the opposite contribution of −0.24% to birefringence. Thus, it shows that [PbS_n] polyhedron plays a vital role in the birefringence of β-Pb₃P₂S₈.

  Figure 4

  

  Figure 4.  (a) Calculated electronic band structure of β-Pb₃P₂S₈ and (b) the calculated refractive index curves of β-Pb₃P₂S₈.

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  In summary, a new thiophosphate phase of β-Pb₃P₂S₈ was synthesized by the high-temperature solid-state method to meet the requirement of birefringent crystals in the infrared band. The β-Pb₃P₂S₈ exhibits a large E_g ~2.37 eV in the lead-based chalcogenides system, a wide infrared transparent window (2.5−15 µm), and excellent thermal stability. In comparison, the arrangement of structural units in α-Pb₃P₂S₈ is irregular, deteriorating the structural anisotropy. On the contrary, the parallelly arranged [Pb₃S₄]_∞ polyhedral layers in β-Pb₃P₂S₈ improve structural anisotropy. The exceptional birefringence effect of β-Pb₃P₂S₈ is 0.26@550 nm, which is the highest value in reported chalcogenides. The result of the theoretical calculation is consistent with the experimental birefringence. The Barder charge analysis shows that Pb²⁺ and S²⁻ contribute mainly to birefringence, indicating the strong hybridization of [PbS_n] polyhedrons. More importantly, the strong anisotropy of polyhedron layered stack structure offers a new viewpoint to the design and synthesis of chalcogenides with exceptional birefringence effect.

  Declaration of competing interest

  The authors declare no competing financial interest.

  CRediT authorship contribution statement

  Weiping Guo: Writing – original draft, Methodology, Investigation, Data curation. Ying Zhu: Methodology, Investigation. Hong-Hua Cui: Investigation, Formal analysis, Conceptualization. Lingyun Li: Writing – review & editing, Supervision, Methodology, Investigation, Conceptualization. Yan Yu: Writing – review & editing, Resources, Funding acquisition, Conceptualization. Zhong-Zhen Luo: Writing – review & editing, Supervision, Resources, Methodology, Funding acquisition, Data curation, Conceptualization. Zhigang Zou: Resources, Project administration, Funding acquisition, Conceptualization.

  Acknowledgments

  This study was supported in part by the National Natural Science Foundation of China (No. 52102218), the National Key Research and Development Program of China (No. 2020YFA0710303), and the Fujian Science & Technology Innovation Laboratory for Optoelectronic Information of China (No. 2021ZZ127). The authors acknowledge the Minjiang Scholar Professorship (No. GXRC-21004) and the Natural Science Foundation of Fujian Province of China (No. 2021J01594). The authors thank Prof. Sangen Zhao at Fujian Institute of Research on the Structure of Matter for helping with the birefringence measurement.

  Supplementary materials

  Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.cclet.2024.110256.

  
  
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• 

  Figure 1  Crystal structures of β-Pb₃P₂S₈ and α-Pb₃P₂S₈: (a) The arrangement of [PS₄] tetrahedra and Pb atoms in β-Pb₃P₂S₈ along the a-axis. (b) The whole structure framework diagram of α-Pb₃P₂S₈ along the a-axis. (c) The whole structure framework diagram of β-Pb₃P₂S₈ along the a-axis. (d) The [Pb₃S₄]_∞ polyhedral layer in β-Pb₃P₂S₈.

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  Figure 2  (a) The experimental E_g from UV–vis-near infrared diffuse reflection spectrum of β-Pb₃P₂S₈ and (b) IR spectrum measurement of β-Pb₃P₂S₈.

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  Figure 3  Compared with the reported experimental birefringence values in the chalcogenides at 550 nm.

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  Figure 4  (a) Calculated electronic band structure of β-Pb₃P₂S₈ and (b) the calculated refractive index curves of β-Pb₃P₂S₈.

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  Table 1.  Crystal information and structure refinement data for β-Pb₃P₂S₈.

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