Hg₂(HTe₂O₅)(PO₄): a novel phosphate crystal with enhanced birefringence enabled by the synergistic modification of multiple functional groups

Abstract

Birefringent crystals are crucial for the miniaturization of optical devices. Phosphate crystals, characterized by their highly symmetrical tetrahedral structures, exhibit excellent stability and wide optical bandgaps. However, their intrinsic symmetry typically results in low birefringence, with most phosphate compounds having birefringence values below 0.1. Efforts to enhance birefringence by introducing highly anisotropic ions and groups have been impeded by the tetrahedral coordination of phosphate, which often leads to the cancellation of anisotropic effects. To address this challenge, we propose an approach that leverages the synergistic modification of multiple functional groups to disrupt the anisotropic cancellation in phosphate crystals and significantly enhance their birefringence. Specifically, we incorporate Te(IV), which features stereo-chemically active lone pairs, and Hg(II), known for its high polarizability and deformability, into the phosphate system. We synthesized a novel phosphate compound, Hg₂(HTe₂O₅)(PO₄), which exhibits a calculated birefringence of 0.162 at 546 nm and a measured birefringence of 0.168 at 546 nm. This value is comparable to that of the commercial birefringent material CaCO₃ (Δn = 0.172@546 nm) and surpasses most previously reported phosphate materials. Additionally, Hg₂(HTe₂O₅)(PO₄) demonstrates a wide bandgap and excellent stability. Using the PAWED method, we determined that the significant birefringence of Hg₂(HTe₂O₅)(PO₄) is primarily due to the combined contributions of the HgO₇ polyhedra (19.86%), PO₄ tetrahedra (29.17%), and Te₂O₅ groups (47.40%). Our work demonstrates that the synergistic modification of multiple functional groups is an effective strategy for enhancing the birefringence of tetrahedral compounds, providing a new pathway for the development of high-performance birefringent materials.

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Introduction

Tetrahedral phosphate crystals have received significant attention in the design of optical functional crystals due to their excellent thermal stability and short ultraviolet cutoff edges.^1–4 Among them, typical compounds such as KH₂PO₄ (KDP) and KTiOPO₄ (KTP) have been successfully commercialized as nonlinear optical crystals.⁵ However, the highly symmetrical tetrahedral configuration of phosphate crystals generally results in low birefringence, which poses a considerable barrier to the miniaturization of optical devices.^6–11 Therefore, enhancing the birefringence of phosphate materials has become an urgent and critical issue.

To enhance the birefringence of phosphates, researchers have made efforts in several aspects: (i) combining with π-conjugated groups,^12–14 such as K₂PbB₅P₃O₁₇ (0.045@1064 nm),¹⁵ Cs₃[(BOP)₂(B₃O₇)₃] (0.075@532 nm),¹⁶ K₃B₄PO₁₀ (0.0445@532 nm)¹⁷ and (NH₄)₃B₁₁PO₁₉F₃ (0.045@1064 nm);¹⁸ (ii) introducing d¹⁰ transition metals with high polarizability,^19,20 such as Na(C₂H₁₀N₂)₂[Zn₃(PO₄)₂(H_0.5PO₄)]₂ (0.060@546 nm),²¹ (NH₄)₃(H₃O)Zn₄(PO₄)₄ (0.032@1064 nm),²² and LiHgPO₄ (0.068@1064 nm);²³ (iii) incorporating lone-pair cations,^24–28 for example, (NH₄)₃[Sn₂(PO₄)₂]Cl (0.065@1064 nm),²⁹ Cs₂Sb₃O(PO₄)₃ (0.034@1064 nm),³⁰ [Sn₃OF]PO₄ (0.104@546 nm),³¹ SrSn(PO₄)PO₂(OH)₂ (0.080@1064 nm),³² Sn₂PO₄I (0.664@546 nm),³³ Ba₂TeP₂O₉ (0.126@1064 nm),³⁴ Rb₂SbFP₂O₇ (0.15@546 nm)³⁵ and α-NaSb₃P₂O₁₀ (0.121@1064 nm);³⁶ (iv) adding d⁰ transition metal cations,^37,38 like [C(NH₂)₃]₁₀(MoO₃)₁₀(PO₄)₂(HPO₄)₂·5H₂O (0.158@550 nm),³⁹ LiTiOPO₄ (0.17@1064 nm)⁴⁰ and K₂MgMoP₂O₁₀ (0.187@546 nm).⁴¹ Although the introduction of these highly anisotropic ions and groups has to some extent improved the birefringence of phosphates, the highly symmetrical tetrahedral configuration inevitably leads to the cancellation of polarization anisotropy, resulting in most compounds having birefringence values below 0.1.

To address this challenge, we propose a strategy of synergistic modification using multiple functional groups to enhance the birefringence of phosphates. First, different functional groups exhibit varying degrees of polarization anisotropy, which can prevent the complete cancellation of polarization anisotropy when coordinated with phosphate groups. Moreover, the interactions between different functional groups can avoid their coordination with phosphate in a regular tetrahedral form. Therefore, we attempt to introduce multiple functional groups to improve the birefringence of phosphates.

The d¹⁰ transition metal Hg features diverse coordination configurations, high polarizability, and deformability, all of which positively contribute to birefringence.^42–44 Meanwhile, Te(IV) with lone-pair electrons also possesses strong anisotropy, which is beneficial for enhancing the birefringence of compounds.^45–48 More importantly, our previous work in Hg-based and Te-based birefringent materials has yielded fruitful results, successfully pushing the birefringence of sulfates to 0.542 at 546 nm.⁴⁹ To obtain phosphate materials with large birefringence, we attempt to combine the above two groups with phosphates. We have conducted research in the Hg–Te–P–O system and successfully synthesized Hg₂(HTe₂O₅)(PO₄). This compound exhibits a large birefringence of 0.162 at 546 nm, a wide bandgap of 3.58 eV, and excellent stability. This paper will introduce its synthesis, structure, optical properties, and theoretical calculations.

Results and discussion

Compound Hg₂(HTe₂O₅)(PO₄) was successfully synthesized via a conventional hydrothermal method using TeO₂, HgO, and H₃PO₃ as starting materials at 230 °C, yielding a product with a 36% yield. Detailed synthetic procedures can be found in the “Synthesis” section of the ESI.† The purity of the Hg₂(HTe₂O₅)(PO₄) was confirmed by powder X-ray diffraction (XRD), as shown in Fig. S1.† Detailed crystallographic information is provided in Table S1 of the ESI.†

Hg₂(HTe₂O₅)(PO₄) crystallizes in the triclinic space group P1̄ with the following unit cell parameters: a = 5.8856(3) Å, b = 7.2589(3) Å, c = 10.1972(4) Å, α = 81.006(3)°, β = 74.483(3)°, γ = 82.959(4)°, and V = 413.12(3) ų. The asymmetric unit consists of two Hg atoms, two Te atoms, one P atom, one H atom, and nine O atoms, comprising a total of fifteen atoms, all of which are located in general positions. In this structure, each P atom is tetrahedrally coordinated to four O atoms, with P–O bond lengths ranging from 1.539(6) to 1.560(6) Å. The Te atoms are coordinated to three O atoms in a trigonal pyramidal geometry, with Te–O bond lengths ranging from 1.870(6) to 1.999(5) Å. The Hg atoms are coordinated to seven O atoms, forming a HgO₇ polyhedron, with Hg–O bond lengths ranging from 2.108(6) to 2.805(5) Å. Bond valence calculations reveal that the bond valences of Hg, Te, and P are 2.047–2.139, 3.461–3.536, and 4.696, respectively, indicating oxidation states of +2, +4, and +5. The lower oxidation state of Te may be attributed to the neglect of Te–O bonds longer than 2.0 Å. If these bonds are considered, the oxidation states of Te(1) and Te(2) can be increased to 4.176 and 3.802, respectively.

Hg₂(HTe₂O₅)(PO₄) exhibits a three-dimensional (3D) structure composed of two-dimensional (2D) mercury tellurite layers bridged by phosphate tetrahedra (Fig. 1). Within this structure, two Hg(1)O₇ polyhedra share oxygen atoms to form Hg(1)₂O₁₂ dimers, which are further interconnected with two Hg(2)O₇ polyhedra to create a mercuric oxide six-membered ring as the fundamental building unit (Fig. 1a). These six-membered rings extend to form a 2D mercury oxide layer (Fig. 1d). The Te₂O₅ units are connected to this layer through oxygen atoms O(1), O(2), O(3), O(4) and O(5), thereby constructing the mercury tellurite layers (Fig. 1c). The phosphate tetrahedra bridge these layers by linking four oxygen atoms to two Hg(1) and two Hg(2) atoms (Fig. 1b), ultimately forming the 3D network structure of the compound (Fig. 1e).

Fig. 1 Mercuric oxide six-membered ring (a), the coordination environments of PO₄ group (b), the coordination environments of Te₂O₅ group (c), two-dimensional layer structure of mercury oxide (d) and three-dimensional structure of Hg₂(HTe₂O₅)(PO₄) (e).

Thermogravimetric analysis (TGA) of Hg₂(HTe₂O₅)(PO₄) was investigated under a N₂ atmosphere over a temperature range of 20 to 1200 °C (Fig. S2†). The compound was found to be stable up to 300 °C. Upon heating to 1200 °C, the compound exhibited a weight loss equivalent to the release of 0.5 molecules of H₂O, 2 molecules of Hg, and 1 molecule of TeO₂. The experimental weight loss was 87.9%, which is in good agreement with the calculated theoretical value of 87.6%. Additionally, the compound was exposed to air for up to six months and remained stable throughout the exposure period, indicating its robustness under atmospheric conditions.

The infrared spectrum (IR) Hg₂(HTe₂O₅)(PO₄) was performed using KBr as a background at room temperature (Fig. S3†). The results revealed distinct absorption peaks at 3459 cm⁻¹, 1651 cm⁻¹ and 1602 cm⁻¹, which are attributed to the vibrational absorption of O–H bonds. Additionally, absorption peaks at 990 cm⁻¹, 1083 cm⁻¹, and 1352 cm⁻¹ correspond to the asymmetric and symmetric stretching vibrations of P–O bonds. Peaks in the range of 777–860 cm⁻¹ and 535 cm⁻¹ are associated with the symmetric stretching and bending vibrations of P–O bonds. The absorption peaks for Te–O bonds appear in the ranges of 459–535 cm⁻¹ and 615–674 cm⁻¹. These observed peaks are consistent with those reported in the literature. Compared with the IR spectrum of the compound Hg^I₂Hg^II(Te₂O₄)₂(HPO₄)₂, Hg₂(HTe₂O₅)(PO₄) does not show the characteristic P–H peaks around 2350 cm⁻¹, which further confirms the correctness of the hydrogen addition in our structural analysis.⁵⁰ Additionally, the assignments of these absorption peaks are consistent with those reported in the literature.^51–54

The UV–Vis–NIR spectrum of Hg₂(HTe₂O₅)(PO₄) was measured in the range of 2000 to 200 nm (Fig. 2). The results show that the UV cutoff edge of this compound is at 282 nm, corresponding to an experimental band gap of 3.58 eV. This band gap is comparable to or even larger than those of previously reported Hg-based compounds, such as Hg₂(SeO₃)(TeO₃) (3.5 eV),⁵⁵ Hg₃Se(SeO₃)(SO₄) (3.5 eV),⁴² Rb₂Hg₂(SeO₃) (3.6 eV),⁵⁶ Hg₃(Te₃O₈)(SO₄) (3.36 eV)⁵⁷ and Hg₂Ga(SeO₃)₂F (2.8 eV).⁵⁸

Fig. 2 The UV–Vis–NIR diffuse reflectance spectra of Hg₂(HTe₂O₅)(PO₄).

In Fig. S4,† the birefringence of Hg₂(HTe₂O₅)(PO₄) was measured at 546 nm using a polarizing microscope. Hg₂(HTe₂O₅)(PO₄) exhibited complete extinction under positive polarization. The optical path difference was observed to be 0.954 μm for a crystal thickness of 5.67 μm. By employing the formula R = Δn × T (where R represents the optical path difference, Δn is the birefringence, and T is the thickness),⁵⁹ the experimental birefringence of Hg₂(HTe₂O₅)(PO₄) at 546 nm was determined to be 0.168.

To gain a deeper understanding of the relationship between the structure and optical properties, we employed density functional theory (DFT) to investigate the electronic structure and linear optical properties of Hg₂(HTe₂O₅)(PO₄). The calculations reveal that Hg₂(HTe₂O₅)(PO₄) is an indirect bandgap material with a theoretical bandgap of 2.755 eV (Fig. S5†). Due to the limitations of the GGA-PBE functional, the theoretical bandgap is underestimated.^60–62 To reduce the computational error, we subsequently applied a scissor operator of 0.825 eV in our calculations. The total and partial density of states (DOS) diagrams show that the valence band maximum of Hg₂(HTe₂O₅)(PO₄) is primarily composed of O-2p orbitals, while the conduction band minimum is mainly contributed by Te-5p and Hg-6s orbitals. Therefore, the bandgap of this compound is predominantly determined by the O, Te, and Hg atoms (Fig. 3).

Fig. 3 The total and partial density of states for Hg₂(HTe₂O₅)(PO₄).

The linear optical response properties of Hg₂(HTe₂O₅)(PO₄) were calculated based on the complex dielectric function ε(ω) = ε₁(ω) + iε₂(ω) (Fig. 4).⁶³ This compound is a biaxial crystal and exhibits different refractive indices along the x, y, and z axes. The calculations show that the birefringence of this compound is 0.162 at 546 nm and 0.147 at 1064 nm, which is close to the measured birefringence of 0.168 at 546 nm. Through the synergistic modification of multiple functional groups, we successfully increased the birefringence of the phosphate material to above 0.1, reaching a level comparable to that of the commercial birefringent crystal CaCO₃ (0.172@546 nm).⁶⁴ The birefringence of this compound is significantly higher than that of some previously reported phosphate birefringent materials, such as LiHgPO₄ (0.068@1064 nm)²³ and SnHPO₄ (0.078@550 nm).⁶⁵ Excitingly, the birefringence of Hg₂(HTe₂O₅)(PO₄) even surpasses that of some lone-pair systems, such as Hg₂(SeO₃)(TeO₃) (0.097@546 nm),⁵⁵ Cs₂Hg₃(SeO₃)₄ (0.043@546 nm),⁵⁶ Sb₄O₅I₂ (0.084@1064 nm),⁶⁶ Rb₃Sb₂OCl₇ (0.098@1064 nm)⁶⁷ and AgAl(Te₄O₁₀) (0.092@1064 nm).⁶⁸

Fig. 4 The calculated refractive indices and birefringence values of Hg₂(HTe₂O₅)(PO₄).

To further elucidate the origin of the large birefringence in Hg₂(HTe₂O₅)(PO₄), we conducted an analysis using the Polarizability Anisotropy Weighted Electron Density (PAWED) method (Fig. 5).⁶⁹ Our findings indicate that the significant birefringence of Hg₂(HTe₂O₅)(PO₄) is primarily attributed to the synergistic contributions from the HgO₇ polyhedra, Te₂O₅ groups, and PO₄ tetrahedra. Specifically, the contributions from these structural units are 19.86%, 47.40%, and 29.17%, respectively. This suggests that the HgO₇ polyhedra, Te₂O₅ groups, and PO₄ tetrahedra play a dominant role in the birefringence, with the Te₂O₅ groups contributing the most.

Fig. 5 PAWED plots in the VB and CB for Hg₂(HTe₂O₅)(PO₄).

Conclusions

In summary, we have successfully synthesized the phosphate tellurite compound Hg₂(HTe₂O₅)(PO₄) via a hydrothermal reaction, based on the strategy of synergistic modification by multiple functional groups. This compound features a novel 3D structure composed of 2D mercury tellurite layers bridged by phosphate tetrahedra. Excitingly, Hg₂(HTe₂O₅)(PO₄) exhibits good optical properties. It has a large birefringence of 0.162 at 546 nm and 0.147 at 1064 nm, a band gap of 3.58 eV, and thermal stability up to 300 °C. Additionally, it remains stable when exposed to air for up to six months. These characteristics make Hg₂(HTe₂O₅)(PO₄) a promising candidate as a birefringent material. PAWED calculations have revealed that the large birefringence is a result of the synergistic effects between the HgO₇ unit (19.86%), PO₄ group (29.17%) and Te₂O₅ unit (47.40%). Our work not only introduces a new phosphate birefringent material but also provides a novel approach to enhance the birefringence of tetrahedral compounds. This method of synergistic modification by multiple functional groups may inspire the development of other high-performance birefringent materials.

Author contributions

Peng-Fei Li: investigation, formal analysis, writing – original draft. Chun-Li Hu: formal analysis, theoretical calculations. Bo Zhang: investigation. Jiang-Gao Mao: supervision, resources, funding acquisition. Fang Kong: conceptualization, project administration, writing – review & editing. All authors have given approval to the final version of the manuscript.

Data availability

The data that support the findings of this study are available in the ESI† of this article.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No.: 22475215 and 22031009), the Natural Science Foundation of Fujian Province (Grant No.: 2023J01216, 2024J010039) and the Self-deployment Project Research Program of Haixi Institutes, Chinese Academy of Sciences (No. CXZX-2022-GH06). We are grateful for the birefringence measurements provided by Dr Hongyuan Sha at FJIRSM.

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39. Y. Zhang, M. H. Lv, S. F. Li, H. Huang, B. Zhang and D. Yan, [C(NH₂)₃]₁₀(MoO₃)₁₀(PO₄)₂(HPO₄)₂·5H₂O: Synergy effect of multiple functional units results in significant birefringence, J. Solid State Chem., 2024, 337, 124823.
40. K. Hou, C. Liu, Q. Feng, Y. Yang and B. Zhang, Enhanced Birefringence in Phosphates via “Two Steps in One”: d0 Transition Metal Regulation and Fluorination Synergistic Strategy, J. Phys. Chem. C, 2024, 128, 7352–7358.
41. Z. Gao, Q. Feng, J. Lu and H. Du, K₂MgMoP₂O₁₀ and K₃Mg₂MoP₃O₁₄: two new molybdophosphates exhibiting different optical anisotropy induced by variable dimensionality of the anion framework, Dalton Trans., 2024, 53, 10686–10692.
42. P. F. Li, C. L. Hu, B. X. Li, J. G. Mao and F. Kong, Hg₃Se(SeO₃)(SO₄): A Mixed-Valent Selenium Compound with Mid-Infrared Transmittance Obtained by In Situ Reaction, Inorg. Chem., 2024, 63, 4011–4016.
43. M. S. Zhang, W. D. Yao, S. M. Pei, B. W. Liu, X. M. Jiang and G. C. Guo, HgBr₂: An Easily Growing Wide-Spectrum Birefringent Crystal, Chem. Sci., 2024, 15, 6891–6896.
44. X. H. Dong, L. Huang, H. M. Zeng, Z. E. Lin, K. M. Ok and G. H. Zou, High-Performance Sulfate Optical Materials Exhibiting Giant Second Harmonic Generation and Large Birefringence, Angew. Chem., Int. Ed., 2022, 61, e202116790.
45. R. L. Tang, Y. L. Lv, L. Ma, B. W. Miao, W. L. Liu and S. P. Guo, “All-Four-in-One”: A Novel Mercury Tellurite-Nitrate Hg₃(TeO₃)(Te₃O₇)(NO₃)₂ Exhibiting Exceptional Optical Anisotropy, Chem. Sci., 2025, 16, 4749–4754.
46. T. Wu, X. Jiang, K. Duanmu, C. Wu, Z. Lin, Z. Huang, M. G. Humphrey and C. Zhang, Giant Optical Anisotropy in a Covalent Molybdenum Tellurite via Oxyanion Polymerization, Adv. Sci., 2024, 23, 2306670.
47. Y. Ding, M. Zhu, J. Wang, B. Li, H. Qi, L. Liu and Y. Chu, Pb₂TeV₂O₁₀: A Lead Vanadate Tellurate with Wide Mid-IR Transparency and Large Birefringence Induced by Multiple Birefringence-Active Groups, Inorg. Chem., 2024, 63, 20003–20013.
48. T. Zhang, J. Jiao, W. Zhao, F. Wang, F. Liang, N. Ye, Z. Hu, Y. Wu and C. Li, Rational Design of a Niobium Tellurite Crystal Nb₂Te₃O₁₁ Exhibiting Good Overall Infrared NLO Performance by Structural Genetic Engineering, Inorg. Chem., 2023, 62, 17522–17529.
49. P. F. Li, C. L. Hu, Y. F. Li, J. G. Mao and F. Kong, Hg₄(Te₂O₅)(SO₄): A Giant Birefringent Sulfate Crystal Triggered by a Highly Selective Cation, J. Am. Chem. Soc., 2024, 146, 7868–7874.
50. P. F. Li, C. L. Hu, J. G. Mao and F. Kong, A Giant Optically Anisotropic Phosphate Driven by Mixed Valence Mercury Units, Laser Photonics Rev., 2025, 19, 2401488.
51. L. Ma, Y. L. Lv, X. F. Ao, W. Liu, S. P. Guo and R. L. Tang, Centric Sc(HPO₃)(H₂PO₃)(H₂O) and Acentric Sc(H₂PO₃)₃: Two Ultraviolet Scandium Phosphite Optical Crystals, Inorg. Chem., 2024, 63, 7118–7122.
52. Y. She, J. Jiao, Z. Wang, J. Chai, S. Jie, N. Ye, Z. Hu, Y. Wu and C. Li, LiVTeO₅: a mid-infrared nonlinear optical vanadium tellurate crystal exhibiting enhanced second harmonic generation activities and notable birefringence, Inorg. Chem. Front., 2023, 10, 6557–6565.
53. Q. Wu, J. Zhou, X. Liu, X. Jiang, Q. Zhang, Z. Lin and M. Xia, Ca₃(TeO₃)₂(MO₄) (M = Mo, W): Mid-Infrared Nonlinear Optical Tellurates with Ultrawide Transparency Ranges and Superhigh Laser-Induced Damage Thresholds, Inorg. Chem., 2021, 60, 18512–18520.
54. P. F. Li, C. L. Hu, B. X. Li, J. G. Mao and F. Kong, From CdPb₈(SeO₃)₄Br₁₀ to Pb₃(TeO₃)Br₄: The first tellurite bromide exhibiting SHG response and mid-IR transparency, Inorg. Chem. Front., 2023, 10, 7343–7350.
55. P. F. Li, C. L. Hu, J. G. Mao and F. Kong, Hg₂(SeO₃)(TeO₃): A novel tellurite-selenite birefringent crystal achieved by assembling multiple functional groups, J. Mater. Chem. C, 2025, 13, 4374–4378.
56. J. Ren, H. Cui, L. Cheng, Y. Zhou, X. Dong, D. Gao, L. Huang, L. Cao and N. Ye, A₂Hg_x(SeO₃)_y (A = K, Rb, Cs): Three Alkali Metal Mercury Selenites Featuring Unique 1D [HgO_m(SeO₃)_n]_∞ Chains, Inorg. Chem., 2023, 62, 21173–21180.
57. P. F. Li, C. L. Hu, Y. P. Gong, F. Kong and J. G. Mao, Hg₃(Te₃O₈)(SO₄): a new sulfate tellurite with a novel structure and large birefringence explored from d¹⁰ metal compounds, Chem. Commun., 2021, 57, 7039–7042.
58. P. F. Li, C. L. Hu, B. Zhang, J. G. Mao and F. Kong, From HgGa₂(SeO₃)₄ to Hg₂Ga(SeO₃)₂F: the first Hg^I-based selenite birefringent crystal triggered by linear groups and fluoride ions, Chin. Chem. Lett., 2024, 110588,  DOI:10.1016/j.cclet.2024.110588.
59. H. Sha, D. Yang, Y. Shang, Z. Wang, R. Su, C. He, X. Yang and X. Long, Trithionic guanidine: A novel semi-organic short-wave ultraviolet nonlinear optical sulfate with dimeric heteroleptic tetrahedra, Chin. Chem. Lett., 2024, 109730,  DOI:10.1016/j.cclet.2024.109730.
60. P. F. Li, C. L. Hu, F. Kong and J. G. Mao, The First UV Nonlinear Optical Selenite Material: Fluorination Control in CaYF(SeO₃)₂ and Y₃F(SeO₃)₄, Angew. Chem., Int. Ed., 2023, 62, e202301420.
61. B. Zhang, S. Zhou, B. X. Li, X. Wu, H. Lin and Q. L. Zhu, Exploring New Horizons in Mid-to-Far Infrared Nonlinear Optical Crystals: The Significant Potential of Trigonal Pyramidal [TeS₃]²⁻ Functional Units, Chem. Sci., 2025, 16, 3218–3227.
62. M. Y. Ran, S. H. Zhou, B. X. Li, X. T. Wu, H. Lin and Q. L. Zhu, Balanced IR Nonlinear Optical Performance Achieved by Cation–Anion Module Cosubstitution in V-Based Salt-Inclusion Oxychalcogenides, Chem. Mater., 2024, 36, 11996–12005.
63. P. F. Li, C. L. Hu, J. G. Mao and F. Kong, A UV non-hydrogen pure selenite nonlinear optical material for achieving balanced properties through framework-optimized structural transformation, Mater. Horiz., 2024, 11, 1704–1709.
64. G. Ghosh, Dispersion-equation coefficients for the refractive index and birefringence of calcite and quartz crystals, Opt. Commun., 1999, 163, 95–102.
65. X. Shi, X. Liu, C. Nie, Y. Zhang, D. Zhong, B. Teng, Z. Lin, Y. Huang and S. Sun, SnHPO₄: A Layered Tin(II) Phosphate with Enhanced Birefringence, Inorg. Chem., 2025, 64, 2127–2132.
66. J. Guo, X. Zhan, J. Lan, X. Liu, S. Zhao, X. Xu, L.-M. Wu and L. Chen, Sb₄O₅I₂: Enhancing Birefringence through Optimization of Sb/I Ratio for Alignment of Stereochemically Active Lone Pairs, Inorg. Chem., 2024, 63, 2217–2223.
67. X. Y. Li, X. Y. Cheng, C. L. Hu, B. X. Li, Z. Y. Zhou, J. H. Zhang, S. Q. Deng, J. G. Mao and F. Kong, From Holodirected to Hemidirected Coordination Activated by Oxygenation Strategy: A Facile Route to Long Wave Infrared Birefringent Crystal, Angew. Chem., Int. Ed., 2025, e202501481,  DOI:10.1002/anie.202501481.
68. P. F. Li, C. L. Hu, F. Kong and J. G. Mao, AAl(Te₄O₁₀) (A = Na, Ag) and K₂Ga₂(HTe₆O₁₆)(HTeO₃): Three Aluminum/Gallium Tellurites with Large Birefringence and Wide Band Gap, Inorg. Chem., 2023, 62, 8494–8499.
69. Q. Q. Chen, C. L. Hu, M. Z. Zhang and J. G. Mao, (C₅H_6.16N₂Cl_0.84)(IO₂Cl₂): A Birefringent Crystal Featuring Unprecedented (IO₂Cl₂)⁻ Anions and π-Conjugated Organic Cations, Chem. Sci., 2023, 14, 14302–14307.

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Footnote

† Electronic supplementary information (ESI) available: Experimental section, computational method, crystal data, important bond distances and bond valences, PXRD patterns, TGA curves, IR spectrum, experimental birefringence and band structures. CCDC 2430737. For ESI and crystallographic data in CIF or other electronic format see DOI: https://doi.org/10.1039/d5qi00757g

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