Heteroanion-introduction-driven birefringence enhancement in oxychalcogenide Ba₃M^IIGe₃O₂S₈ (M^II = Mn, Cd)

Abstract

Birefringent crystals play a crucial role in regulating the polarization of light and are widely used in optoelectronic fields. However, the effective design of novel infrared (IR) birefringent crystals with large birefringence (Δn) still face significant challenges. In this study, we present the rational design and successful synthesis of two novel quinary oxychalcogenides with the formula Ba₃M^IIGe₃O₂S₈ (M^II = Mn, Cd), employing a heteroanion-introduction strategy via high-temperature solid-state reactions. Ba₃M^IIGe₃O₂S₈ (M^II = Mn, Cd) crystallized in the monoclinic space group P2₁/n (no. 14) and the structures comprised one-dimensional (1D) [M^IIGe₃S₈O₂]⁶⁻ chains arranged in an antiparallel manner and separated by Ba²⁺ cations. The coexistence of multiple heteroanionic ligands ([M^IIOS₅] octahedra, [GeOS₃], and [GeO₂S₂] tetrahedra) in one material was surprisingly discovered for the first time in the realm of oxychalcogenides. It was revealed that the heteroanion-introduction strategy not only leads to a reduction in the structural dimensionality but also enhances the optical anisotropy significantly. Notably, Ba₃M^IIGe₃O₂S₈ (M^II = Mn, Cd) demonstrated large Δn values of 0.11 and 0.14, which represent a remarkable improvement compared to the three-dimensional (3D) parent AE₃M^IIM^IV₂Q₈ system (Δn = 0). Furthermore, theoretical calculations suggest that the significant Δn of Ba₃M^IIGe₃O₂S₈ (M^II = Mn, Cd) resulted primarily from the combination of polarizabilities from the various heteroanionic groups. Overall, these results highlight the potential of the heteroanion-introduction strategy for designing novel IR birefringent materials for optoelectronic applications.

---

1. Introduction

Birefringent crystals play a crucial role in high-performance optics, especially in polarization apparatus, phase-matching elements, and laser processing.¹ Currently, the majority of the commercially available birefringent crystals are inorganic oxides, such as YVO₄,² CaCO₃,³ and α-BaB₂O₄.⁴ However, these materials have their limitations. For instance, they suffer from detrimental metal–oxygen (M–O) bond absorptions, which restrict their usage in the infrared (IR) region. Conversely, the current commercially available birefringent crystals are suitable for the ultraviolet and visible region, and few birefringent crystals has been explored for the IR region. In addition, the excellent birefringence (Δn) of crystals enables the downsizing of crystal optical devices.⁵ Consequently, there is an increasing demand for high-performance IR birefringent crystals in both the scientific research and technological development fields.

The analysis of the structure–property relationships of birefringent crystals revealed a positive correlation between the Δn and anisotropy.⁶ In other words, a larger anisotropy corresponds to a greater Δn. Effective structural design strategies can be employed to modulate the Δn, such as introducing π-conjugated units,⁷ stereochemically active lone pairs (SCALPs),⁸ and functional building units (FBUs) with large polarizability anisotropy.⁹ Recently, the heteroanion-introduction strategy has been proved to be an effective and direct approach for boosting the Δn, such as Rb₂VO(O₂)₂F (Δn = 0.189 @ 546 nm),¹⁰ Sn₂BO₃I (Δn = 0.393 @ 546 nm), Sn₂PO₄I (Δn = 0.664 @ 546 nm),¹¹ RbTeMo₂O₈F (Δn = 0.263 @ 546 nm),¹² and K₂Sb(P₂O₇)F (Δn = 0.157 @ 546 nm).¹³ Oxychalcogenides with rich structures, varying from isolated zero-dimensional (0D) to dense three-dimensional (3D) frameworks, are an exciting class of heteroanionic system that have attracted significant attention in recent years owing to their high Δn, which can obtained by partial anion substitution from the parent structure.¹⁴ Some examples include Ba₃Ge₂O₄Te₃ (0.14 @ 2090 nm, maternal structure: Ba₂ZnGe₂O₇),¹⁵ SrGeOSe₂ (0.16 @ 2050 nm, maternal structure: SrGeO₃),¹⁶ Sr₂CdGe₂OS₆ (0.193 @ 2050 nm, maternal structure: Sr₂CdGe₂O₇),¹⁷ Nd₃[Ga₃O₃S₃][Ge₂O₇] (0.091 @ 2050 nm, maternal structure: Cs₃[Sb₃O₆][Ge₂O₇]),¹⁸ and Sr₂ZnSn₂OS₆ (0.12 @ 2050 nm, maternal structure: Sr₂ZnSi₂O₇).¹⁹ The parent structures mentioned above are all oxides. However, no examples have been reported using chalcogenides as parent structures to generate new oxychalcogenides by introducing oxygen atoms.

The quaternary AE₃M^IIM^IV₂Q₈ (AE = Sr, Ba; M^II = divalent transition metals; M^IV = Ge, Sn; Q = chalcogen) family is a complex system that distinguishes itself as an intriguing nonlinear optical (NLO) system owing to its structural flexibility at every crystallographic site.²⁰ However, its crystallization in the cubic space group results in the Δn values of 0, rendering it incapable of achieving phase-matching in NLO applications. Inspired by the previous strategy of introducing heteroanions, we successfully obtained two new oxychalcogenides, i.e. Ba₃M^IIGe₃O₂S₈ (M^II = Mn, Cd). In this study, the syntheses, structures, optical properties, and birefringent characteristics of the title compounds are described. Furthermore, theoretical calculations were conducted to achieve a better understanding of the structure–activity relationships.

2. Results and discussion

In the structure of AE₃M^IIM^IV₂Q₈, the [M^IVQ₄] tetrahedron links 3 [M^IIQ₄] tetrahedra while [M^IIQ₄] links 4 [M^IVQ₄] tetrahedra to build up a 3D framework. Inside this framework, charge-balanced AE²⁺ cations are located in the cavity (Fig. 1a and c). Unfortunately, the dense 3D structure, which crystallizes in the cubic system (space group I4̄3d (no. 220)), has an inappropriate anisotropy, resulting in a Δn value of 0 for AE₃M^IIM^IV₂Q₈, and thereby rendering phase-matching impossible. It is widely recognized that the anisotropic polarization of a structure significantly impacts its Δn. Hence, the search for low-dimensional structures exhibiting significant anisotropy is considered one of the most effective means to obtain materials with a large Δn.²¹

Fig. 1 Structural evolution from 3D AE₃M^IIM^IV₂Q₈ to 1D Ba₃M^IIGe₃O₂S₈: (a and b) ball-and-stick models viewed from the ac-plane; (c and d) schematic diagram of equivalent models; (e) projection of the 1D [MGe₃O₂S₈]⁶⁻ chain along the bc-plane; (f) coordination environment of [GeOS₃], [GeO₂S₂], and [M^IIOS₅] (M^II = Mn, Cd) FBUs with the atom numbers marked.

The oxychalcogenides Ba₃M^IIGe₃O₂S₈ (M^II = Mn, Cd) represent a novel type of quinary compound discovered in AE/M^II/M^IV/Q/O systems. These compounds crystallize in the centrosymmetric monoclinic space group P2₁/n (no. 14); their detailed crystallographic information is shown in Table 1. The asymmetric unit consists of three independent Ba sites, one independent M^II site, three independent Ge sites, two independent O sites, and eight independent S sites. All the independent atom sites are located in the Wyckoff position 4e. The basic structure of Ba₃M^IIGe₃O₂S₈ can be seen as composed of 1D [M^IIGe₃O₂S₈]⁶⁻ infinite chains, while AE²⁺ cations fill the space to balance the charge (refer to Fig. 1b and d). The coordination environments of Ge and M^II atoms are shown in Fig. 1f, and the key bond distances and angles are given in Table S1.† Ge1 and Ge3 atoms are linked to 1 O atom and 3 S atoms, forming heteroanionic [GeOS₃] FBUs with Ge–S bond lengths in the regular range of 2.174–2.205 Å and Ge–O bond distances of 1.806–1.838 Å. The Ge2 atom, on the other hand, is linked to 2 O atoms and 2 S atoms, forming heteroanionic [GeO₂S₂] FBUs with Ge–S bond lengths in the range of 2.137–2.178 Å and Ge–O bond lengths in the range of 1.779–1.787 Å. The M^II atom is coordinated with 1 O and 5 S atoms to form a highly distorted [M^IIOS₅] octahedron, with M^II–S and M^II–O bond lengths falling within the normal ranges.²² Two [GeOS₃] FBUs and one [GeO₂S₂] FBU form a [Ge₃O₂S₈] cluster through bridging O atoms. These clusters are then interconnected with octahedral [M^IIOS₅] FBUs, resulting in the formation of 1D [M^IIGe₃O₂S₈]⁶⁻ infinite chains through face-sharing (Fig. 1e). The Ba atoms also have different coordination behaviors. For instance, Ba1 and Ba3 atoms are surrounded by 8 S atoms, forming a [BaS₈] bicapped trigonal prism. On the other hand, the Ba2 atom is surrounded by 1 O atom and 7 S atoms, resulting in a more twisted [BaOS₇] bicapped trigonal prism (Fig. S1 and S2†).

Table 1 Crystal data and structural refinement details for Ba₃M^IIGe₃O₂S₈ (M^II = Mn, Cd)

a R 1 = ∑||Fo| − |Fc||/∑|Fo|, wR2 = [∑w(Fo^2 − Fc^2)^2/∑w(Fo^2)^2]^1/2.
Empirical formula	Ba3CdGe3O2S8	Ba3MnGe3O2S8
CCDC	2234469	2234468
Formula weight	1030.67	973.21
Temperature (K)	293(2)	293(2)
Crystal system	Monoclinic	Monoclinic
Crystal color	Light yellow	Light yellow
Size (mm^3)	0.08 × 0.10 × 0.10	0.07 × 0.10 × 0.11
Space group	P21/n (no. 14)	P21/n (no. 14)
a (Å)	8.8294(10)	8.8298(7)
b (Å)	11.9334(13)	11.8254(11)
c (Å)	15.2993(17)	15.2442(11)
β (°)	90.839(2)	90.548(7)
V (Å^3)	1611.8(3)	1591.7(2)
Z	4	4
D c (g cm^−3)	4.247	4.061
μ (mm^−1)	15.037	14.684
GOOF on F^2	1.139	1.119
R 1, wR2 (I > 2σ(I))^a	0.0265, 0.0720	0.0456, 0.1248
R 1, wR2 (all data)	0.0290, 0.0725	0.0483, 0.1233
Largest diff. peak and hole (e Å^−3)	1.512, −1.727	2.520, −1.257

---

The detailed structural evolution from 3D AE₃M^IIM^IV₂Q₈ to 1D Ba₃M^IIGe₃O₂S₈ is depicted in Fig. 1. The introduction of O atoms, which have a different electronegativity (χ_O = 3.44 vs. χ_S = 2.58), can be viewed as acting like structural scissors to break the dense high-dimensional framework structure, resulting in the formation of a loosely connected low-dimensional chain structure. Consequently, a significantly anisotropic structure was obtained. This could be further confirmed by the experimental results and theoretical research on birefringence discussed in the following section.

Furthermore, through comparing and analyzing the reported oxychalcogenides, we discovered that Ba₃M^IIGe₃O₂S₈ (M^II = Mn, Cd) demonstrated structural novelty in three distinct aspects. First, the heteroanionic [GeO_xQ_4−x] FBUs can only exist in a singular form in oxychalcogenides,^23–28 such as [GeOTe₃], [GeO₂S₂], and [GeO₃Se], identified in AE₃Ge₂O₄Te₃,^15,23 AEGeOS₂,²⁵ and Sr₃Ge₂O₄Se₃,²⁷ respectively. However, the title compounds simultaneously contained two [GeO_xS_4−x] FBUs, namely, [GeOS₃] and [GeO₂S₂]. Second, it has been reported that there are relatively few oxychalcogenides with transition-metal-based [TMO_xQ_y] FBUs,²⁹ but some examples include [ZnO₂S₂] in BaZnOS,³⁰ [ZnOS₃] in SrZn₂S₂O,³¹ [CoO₂S₂] in BaCoOS,³² and [CoOS₃] in CaCoOS.³³ Notably, in contrast to the previously reported four-coordinated [TMO_xQ_y], two new heteroanionic FBUs, [MnOS₅] and [CdOS₅], were successfully observed in Ba₃M^IIGe₃O₂S₈ (M^II = Mn, Cd) for the first time, which enhances the diversity of oxychalcogenides. Third, compounds with two or more heteroanionic FBUs are currently very rare, with the few examples limited to Ba₆V₄O₅S₁₁ ([VOS₃] + [VO₂S₂])³⁴ and (Ba₁₉Cl₄)(Ga₆Si₁₂O₄₂S₈) ([GaOS₃] + [GaO₂S₂]).³⁵ The coexistence of multiple heteroanionic FBUs (octahedral [M^IIOS₅], tetrahedral [GeOS₃] and [GeO₂S₂]) in the title compounds was surprisingly discovered for the first time in the realm of oxychalcogenides.

The compounds Ba₃M^IIGe₃O₂S₈ (M^II = Mn, Cd) were synthesized using a traditional high-temperature solid-state method. Single crystals with a millimeter-size were carefully selected for characterization and measurement (Fig. 2). The elemental analysis of Ba₃M^IIGe₃O₂S₈ (M^II = Mn, Cd) confirmed the symmetrical distribution through EDX mapping, and the Ba : M^II : Ge : O : S ratio was found to be highly consistent with the results obtained from single-crystal XRD (Fig. S3 and S4†). The purity phase of Ba₃M^IIGe₃O₂S₈ (M^II = Mn, Cd) was examined by powder XRD measurements (see Fig. 2a and b). The experimental results matched well with the simulated patterns derived from the single-crystal XRD measurements. The UV–Vis–NIR diffuse reflectance spectrum revealed optical energy gap (E_g) values of 3.82 and 3.39 eV for Ba₃CdGe₃O₂S₈ and Ba₃MnGe₃O₂S₈ (Fig. 2c and d), respectively, using the Kubelka–Munk function.³⁶ These values are higher compared to other reported TM-based oxychalcogenides, such as Sr₆Cd₂Sb₆O₇S₁₀ (1.89 eV),³⁷ Sm₃NbS₃O₄ (2.68 eV),³⁸ and [Sr₃VO₄][InSe₃] (2.62 eV).³⁹ Additionally, Ba₃M^IIGe₃S₈O₂ (M^II = Mn, Cd) exhibited high thermal stability up to 1100 K under a N₂ atmosphere based on the thermal analysis (Fig. S5†). There were no melting or phase transition behaviors observed in the corresponding DSC curves, which was consistent with the powder XRD results (Fig. S6†). Furthermore, Ba₃CdGe₃O₂S₈ (M^II = Mn, Cd) demonstrated a broad IR transmission cut-off region from 2.5 to 13.3 μm (Fig. S7†), indicating their potential as IR birefringent candidates.

Fig. 2 Characterization of Ba₃M^IIGe₃O₂S₈ (M^II = Mn, Cd): experimental and simulated powder XRD patterns for the as-synthesized (a) Ba₃CdGe₃S₈O₂ and (b) Ba₃MnGe₃S₈O₂; optical E_g for (c) Ba₃CdGe₃S₈O₂ and (d) Ba₃MnGe₃S₈O₂ (inset: optical images of the target single crystals).

Inspired by oxychalcogenides that exhibit an appropriate Δn value,⁴⁰ the Δn of Ba₃CdGe₃O₂S₈ (M^II = Mn, Cd) was also measured using a ZEISS Axio A1 cross-polarizing microscope. The retardations (R values) and crystal thicknesses (T values) were tested as 1.073 μm and 9.8 μm for Ba₃MnGe₃O₂S₈, and 0.85 μm and 5.9 μm for Ba₃CdGe₃O₂S₈ respectively. Notably, the measured Δn values for Ba₃MnGe₃O₂S₈ and Ba₃CdGe₃O₂S₈ were found to be 0.11 and 0.14, respectively, using the formula Δn = R/T (Fig. 3).⁴¹ These values are larger than those of commercial materials like MgF₂ (0.012 @ 632 nm)⁴² and LiNbO₃ (0.08 @ 632 nm),⁴³ as well as many recently reported chalcogenides, such as [Ba₄(S₂)][ZnGa₄S₁₀] (0.053 @ 1064 nm),⁴⁴ LiBaSbS₃ (0.045 at 532 nm),⁴⁵ and K₂Na₂Sn₃S₈ (0.070 at 546 nm).⁴⁶ This indicates that the target compounds have potential as birefringent materials. Moreover, it is noteworthy that compared to the 3D AE₃M^IIM^IV₂Q₈ with a Δn value of 0, the 1D Ba₃M^IIGe₃O₂S₈ (M^II = Mn, Cd) oxychalcogenides displayed appropriate Δn values. These findings indicate that the heteroanion-introduction strategy is effective in increasing optical anisotropy and boosting Δn in the oxychalcogenide family.

Fig. 3 (a and b) Ba₃MnGe₃O₂S₈ and (c and d) Ba₃CdGe₃O₂S₈ crystals for birefringence determination and the interference colors observed before and after complete extinction.

For a more comprehensive understanding of the electronic structures and optical performances of Ba₃M^IIGe₃O₂S₈ (M^II = Mn, Cd), detailed theoretical calculations were conducted using the DFT method. As depicted in Fig. S8† and Fig. 4a, Ba₃MnGe₃O₂S₈ and Ba₃CdGe₃O₂S₈ exhibited direct band gaps, with calculated E_g values of 1.53 and 2.47 eV, respectively. These values were notably different from the tested values obtained from the UV–vis–NIR spectra (3.39 and 3.82 eV). This discrepancy may be attributed to the limited accuracy of the conventional DFT functional in describing band gaps.⁴⁷ A detailed Brillouin zone plot with high symmetry points is provided in Fig. S9.† Since the Ba₃MnGe₃O₂S₈ and Ba₃CdGe₃O₂S₈ compounds demonstrated similarities in the partial density of states (PDOS) curves (Fig. 4b and S8†), Ba₃CdGe₃O₂S₈ was chosen as the representative compound for further elucidation. In the PDOS graphs, the valence band maximum (VBM) was defined by the S-3p and O-2p nonbonding states, while the conduction band minimum (CBM) was dominated by the unoccupied Cd-4s, Ge-3s, and Ba-4p orbitals. Thus, the E_g of Ba₃CdGe₃O₂S₈ was primarily determined by the heteroanionic [GeOS₃], [GeOS₃] and [CdOS₅] FBUs, namely, 1D [CdGe₃O₂S₈]⁶⁻ chains.

Fig. 4 Theoretical calculated results of Ba₃CdGe₃O₂S₈: (a) electronic band structure; (b) PDOS curve.

Besides, based on DFT calculations, the Δn of Ba₃M^IIGe₃O₂S₈ (M^II = Mn, Cd) was also calculated (Fig. 5a and S10†). The results reveal that the calculated Δn of Ba₃CdGe₃O₂S₈ was 0.15 @ 2050 nm. Additionally, when combined with the analysis by the partial charge density graphs in the VBM and CBM ranges (Fig. 5b), it was evident that the heteroanionic FBUs play a significant role in achieving a large Δn. This implies that the introduction of heteroanions into the structure is favorable to the structural anisotropy.

Fig. 5 (a) Calculated refractive index dispersion curves and birefringence of Ba₃CdGe₃O₂S₈; (b) distribution of the partial charge density maps in the VBM and CBM parts. Black atoms: Ba; pink atoms: Cd; blue atoms: Ge; yellow atoms: S; red atoms: O.

3. Conclusions

With the aim of obtaining new IR birefringent materials in the AE–TM–M^IV–O–Q system, two novel oxychalcogenides Ba₃M^IIGe₃O₂S₈ (M^II = Mn or Cd) were successfully synthesized by employing a heteroanion-introduction strategy of replacing part of the Q atoms from the parent AE₃M^IIM^IV₂Q₈. This is the first case that contains multiple heteroanionic ligands in oxychalcogenides, and the 1D anionic [M^IIGe₃O₂S₈]⁶⁻ chain is exclusively constructed by three heteroanionic units, that is, octahedral [M^IIOS₅], and tetrahedral [GeOS₃] and [GeO₂S₂]. Both compounds exhibited a large E_g (3.39 and 3.82 eV), a broad IR transparency region (2.5–13.3 μm), and good thermal stability (approximately 1100 K). Specifically, Ba₃M^IIGe₃O₂S₈ (M^II = Mn or Cd) demonstrated a large Δn (0.11 and 0.14 @ 549 nm), implying its potential application as an IR birefringent candidate. Analysis of their structure–property relationships displayed that the 1D chains in a reversed arrangement is favorable for generating a large Δn. Overall, this study represents significant progress in the field of IR birefringent materials and presents a new paradigm for developing crystal structures with enhanced Δn that are suitable for optoelectronic applications.

Author contributions

Sheng-Hua Zhou: investigation, methodology, validation, writing – original draft. Mao-Yin Ran: investigation, formal analysis, writing – original draft. Wen-Bo Wei: formal analysis, validation. A-Yang Wang: formal analysis, validation. Xin-Tao Wu: conceptualization, writing – review & editing. Hua Lin: supervision, conceptualization, writing – review & editing. Qi-Long Zhu: supervision, writing – review & editing.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This research was supported by the National Natural Science Foundation of China (21771179), Fujian Science & Technology Innovation Laboratory for Optoelectronic Information of China (2021ZR118), and the Natural Science Foundation of Fujian Province (2022L3092 and 2023H0041).

References

1. (a) Z. Xie, L. Sun, G. Han and Z. Gu, Optical Switching of a Birefringent Photonic Crystal, Adv. Mater., 2008, 20, 3601–3604; (b) N. Berti, S. Coen, M. Erkintalo and J. Fatome, Extreme waveform compression with a nonlinear temporal focusing mirror, Nat. Photonics, 2022, 16, 822–827; (c) Y. Zhou, X. Zhang, M. Hong, J. Luo and S. Zhao, Achieving effective balance between bandgap and birefringence by confining π-conjugation in an optically anisotropic crystal, Sci. Bull., 2022, 67, 2276–2279; (d) M. Mutailipu, J. Han, Z. Li, F. M. Li, J. J. Li, F. F. Zhang, X. F. Long, Z. H. Yang and S. L. Pan, Achieving the full-wavelength phase-matching for efficient nonlinear optical frequency conversion in C(NH₂)₃BF₄, Nat. Photonics, 2023, 17, 694–701; (e) F. Zhang, X. Chen, M. Zhang, W. Jin, S. Han, Z. Yang and S. Pan, An excellent deep-ultraviolet birefringent material based on [BO₂]_∞ infinite chains, Light: Sci. Appl., 2022, 11, 252; (f) X. Dong, L. Huang, H. Zeng, Z. Lin, K. M. Ok and G. Zou, High-Performance Sulfate Optical Materials Exhibiting Giant Second Harmonic Generation and Large Birefringence, Angew. Chem., Int. Ed., 2022, 61, e202116790; (g) 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.
2. H. Luo, T. Tkaczyk, E. Dereniak and K. Oka, High birefringence of the yttrium vanadate crystal in the middle wavelength infrared, Opt. Lett., 2006, 31, 616–618.
3. G. Ghosh, Dispersion-equation coefficients for the refractive index and birefringence of calcite and quartz crystals, Opt. Commun., 1999, 163, 95–102.
4. G. Zhou, J. Xu, X. Chen, H. Zhong and F. Gan, Growth and spectrum of a novel birefringent α-BaB₂O₄ crystal, J. Cryst. Growth, 1998, 191, 517–519.
5. S. Niu, J. Graham, H. Zhao, Y. Zhou, O. Thomas, H. Huaixun, S. Jad, M. Krishnamurthy, U. Brittany and J. Wu, Giant optical anisotropy in a quasi-one-dimensional crystal, Nat. Photonics, 2018, 12, 392–396.
6. (a) A. Tudi, S. Han, Z. Yang and S. Pan, Potential optical functional crystals with large birefringence: Recent advances and future prospects, Coord. Chem. Rev., 2022, 459, 214380; (b) Q. Shi, L. Dong and Y. Wang, Evaluating refractive index and birefringence of nonlinear optical crystals: Classical methods and new developments, Chin. J. Struct. Chem., 2023, 42, 100017; (c) Y. Long, X. Dong, L. Huang, H. Zeng, Z. Lin, L. Zhou and G. Zou, BaSb(H₂PO₂)₃Cl₂: An Excellent UV Nonlinear Optical Hypophosphite Exhibiting Strong Second-Harmonic Generation Response, Mater. Today Phys., 2022, 28, 100876; (d) P.-F. Li, J.-G. Mao and F. Kong, A survey of stereoactive oxysalts for linear and nonlinear optical applications, Mater. Today Phys., 2023, 37, 101197; (e) P.-F. Li, Y.-P. Gong, C.-L. Hu, B. Zhang, J.-G. Mao and F. Kong, Four UV Transparent Linear and Nonlinear Optical Materials Explored from Pure Selenite Compounds, Adv. Opt. Mater., 2023, 11, 2301426.
7. (a) X. Y. Zhang, X. G. Du, J. H. Wang, F. Y. Wang, F. Liang, Z. G. Hu, Z. S. Lin and Y. C. Wu, K₃C₆N₇O₃·2H₂O: A Multifunctional Nonlinear Optical Cyamelurate Crystal with Colossal π-Conjugated Orbitals, ACS Appl. Mater. Interfaces, 2022, 14, 53074–53080; (b) Y. Li, X. Zhang, J. Zheng, Y. Zhou, W. Huang, Y. Song, H. Wang, X. Song, J. Luo and S. Zhao, A Hydrogen Bonded Supramolecular Framework Birefringent Crystal, Angew. Chem., Int. Ed., 2023, 62, e202304498.
8. (a) H. Lin, Y. Y. Li, M. Y. Li, Z. J. Ma, L. M. Wu, X. T. Wu and Q. L. Zhu, Centric-to-acentric structure transformation induced by a stereochemically active lone pair: a new insight for design of IR nonlinear optical materials, J. Mater. Chem. C, 2019, 7, 4638–4643; (b) M.-M. Chen, Z. Ma, B.-X. Li, W.-B. Wei, X.-T. Wu, H. Lin and Q.-L. Zhu, M₂As₂Q₅ (M = Ba, Pb; Q = S, Se): A source of infrared nonlinear optical materials with excellent overall performance activated by multiple discrete arsenate anions, J. Mater. Chem. C, 2021, 9, 1156–1163; (c) M. M. Chen, S. H. Zhou, W. B. Wei, B. X. Li, M. Y. Ran, X. T. Wu, H. Lin and Q. L. Zhu, RbBiP₂S₆: A Promising IR Nonlinear Optical Material with a Giant Second-Harmonic Generation Response Designed by Aliovalent Substitution, ACS Mater. Lett., 2022, 4, 1264–1269; (d) S. Han, A. Tudi, W. Zhang, X. Hou, Z. Yang and S. Pan, Recent Development of Sn(II), Sb(III)-based Birefringent Material: Crystal Chemistry and Investigation of Birefringence, Angew. Chem., Int. Ed., 2023, 62, e202302025; (e) C. Liu, S.-H. Zhou, C. Zhang, Y.-Y. Shen, X.-Y. Liu, H. Lin and Y. Liu, CsCu₃SbS₄: rational design of a two-dimensional layered material with giant birefringence derived from Cu₃SbS₄, Inorg. Chem. Front., 2022, 9, 478–484; (f) C. Zhang, M.-Y. Ran, X. Chen, S.-H. Zhou, H. Lin and Y. Liu, Stereochemically active lone-pair-driven giant enhancement of birefringence from three-dimensional CsZn₄Ga₅Se₁₂ to two-dimensional CsZnAsSe₃, Inorg. Chem. Front., 2023, 10, 3367–3374.
9. (a) M. Y. Li, B. X. Li, H. Lin, Z. J. Ma, L. M. Wu, X. T. Wu and Q. L. Zhu, Sn₂Ga₂S₅: A Polar Semiconductor with Exceptional Infrared Nonlinear Optical Properties Originating from the Combined Effect of Mixed Asymmetric Building Motifs, Chem. Mater., 2019, 31, 6268–6275; (b) M. Y. Li, Z. J. Ma, B. X. Li, X. T. Wu, H. Lin and Q. L. Zhu, HgCuPS₄: An Exceptional Infrared Nonlinear Optical Material with Defect Diamond-like Structure, Chem. Mater., 2020, 32, 4331–4339; (c) J. Zhou, L. Wang, Y. Chu, H. Wang, S. Pan and J. Li, Na₃SiS₃F: A Wide Bandgap Fluorothiosilicate with Unique SiS₃F Unit and High Laser-Induced Damage Threshold, Adv. Opt. Mater., 2023, 11, 2300736.
10. S. Liu, X. Liu, S. Zhao, Y. Liu, L. Li, Q. Ding, Y. Li, Z. Lin, J. Luo and M. Hong, An Exceptional Peroxide Birefringent Material Resulting from d-π Interactions, Angew. Chem., Int. Ed., 2020, 59, 9414–9417.
11. J. Guo, A. Tudi, S. Han, Z. Yang and S. Pan, Sn₂PO₄I: an excellent birefringent material with giant optical anisotropy in non π-conjugated phosphate, Angew. Chem., Int. Ed., 2021, 60, 24901–24904.
12. Y. Hu, C. Wu, X. Jiang, Z. Wang, Z. Huang, Z. Lin, X. Long, M. G. Humphrey and C. Zhang, Giant Second-Harmonic Generation Response and Large Band Gap in the Partially Fluorinated Mid-Infrared Oxide RbTeMo₂O₈F, J. Am. Chem. Soc., 2021, 143, 12455–12459.
13. Y. Deng, L. Huang, X. Dong, L. Wang, K. M. Ok, H. Zeng, Z. Lin and G. Zou, K₂Sb(P₂O₇)F: Cairo pentagonal layer with bifunctional genes reveal optical performance, Angew. Chem., Int. Ed., 2020, 59, 21151–21156.
14. (a) H. Lin, W. B. Wei, H. Chen, X. T. Wu and Q. L. Zhu, Rational design of infrared nonlinear optical chalcogenides by chemical substitution, Coord. Chem. Rev., 2020, 406, 213150; (b) Y. F. Shi, W. Wei, X. T. Wu, H. Lin and Q. L. Zhu, Recent progress in oxychalcogenides as IR nonlinear optical materials, Dalton Trans., 2021, 50, 4112–4118; (c) M. Y. Ran, A. Y. Wang, W. B. Wei, X. T. Wu, H. Lin and Q. L. Zhu, Recent progress in the design of IR nonlinear optical materials by partial chemical substitution: structural evolution and performance optimization, Coord. Chem. Rev., 2023, 481, 215059; (d) H. D. Yang, M. Y. Ran, W. B. Wei, X. T. Wu, H. Lin and Q. L. Zhu, Recent advances in IR nonlinear optical chalcogenides with well-balanced comprehensive performance, Mater. Today Phys., 2023, 35, 101127.
15. M. Sun, X. Zhang, C. Li, W. Liu, Z. Lin and J. Yao, Highly polarized [GeOTe₃] motif-driven structural order promotion and an enhanced second harmonic generation response in the new nonlinear optical oxytelluride Ba₃Ge₂O₄Te₃, J. Mater. Chem. C, 2022, 10, 150–159.
16. M. Y. Ran, Z. J. Ma, H. Chen, B. X. Li, X. T. Wu, H. Lin and Q. L. Zhu, Partial Isovalent Anion Substitution to Access Remarkable Second-Harmonic Generation Response: A Generic and Effective Strategy for Design of Infrared Nonlinear Optical Materials, Chem. Mater., 2020, 32, 5890–5896.
17. (a) M. Y. Ran, S. H. Zhou, B. Li, W. Wei, X. T. Wu, H. Lin and Q. L. Zhu, Enhanced Second-Harmonic-Generation Efficiency and Birefringence in Melilite Oxychalcogenides Sr₂MGe₂OS₆ (M = Mn, Zn, and Cd), Chem. Mater., 2022, 34, 3853–3861; (b) R. Wang, F. Liang, X. Liu, Y. Xiao, Q. Liu, X. Zhang, L. M. Wu, L. Chen and F. Huang, Heteroanionic Melilite Oxysulfide: A Promising Infrared Nonlinear Optical Candidate with a Strong Second-Harmonic Generation Response, Sufficient Birefringence, and Wide Bandgap, ACS Appl. Mater. Interfaces, 2022, 14, 23645–23652.
18. M. Y. Ran, S. H. Zhou, W. Wei, B. Li, X. T. Wu, H. Lin and Q. L. Zhu, Rational Design of a Rare-Earth Oxychalcogenide Nd₃[Ga₃O₃S₃][Ge₂O₇] with Superior Infrared Nonlinear Optical Performance, Small, 2023, 19, 2300248.
19. Y. Cheng, H. Wu, H. Yu, Z. Hu, J. Wang and Y. Wu, Rational Design of a Promising Oxychalcogenide Infrared Nonlinear Optical Crystal, Chem. Sci., 2022, 13, 5305–5310.
20. (a) N. Zhen, K. Wu, Y. Wang, Q. Li, W. H. Gao, D. W. Hou, Z. H. Yang, H. D. Jiang, Y. J. Dong and S. L. Pan, BaCdSnS₄ and Ba₃CdSn₂S₈: syntheses, structures, and non-linear optical and photoluminescence properties, Dalton Trans., 2016, 45, 10681; (b) R. H. Duan, P. F. Liu, H. Lin, Y. J. Zheng, J. S. Yu, X. T. Wu, S. X. Huang-Fu and L. Chen, Ba₆Li₂CdSn₄S₁₆: lithium substitution simultaneously enhances band gap and SHG intensity, J. Mater. Chem. C, 2017, 5, 7067; (c) R.-H. Duan, R.-A. Li, P.-F. Liu, H. Lin, Y. Wang and L.-M. Wu, Modifying Disordered Sites with Rational Cations to Regulate Band-Gaps and Second Harmonic Generation Responses Markedly: Ba₆Li₂ZnSn₄S₁₆ vs Ba₆Ag₂ZnSn₄S₁₆ vs Ba₆Li_2.67Sn_4.33S₁₆, Cryst. Growth Des., 2018, 18, 5609; (d) Y. Yang, M. Song, J. Zhang, L. Gao, X. Wu and K. Wu, Coordinated regulation on critical physiochemical performances activated from mixed tetrahedral anionic ligands in new series of Sr₆A₄M₄S₁₆ (A = Ag, Cu; M = Ge, Sn) nonlinear optical materials, Dalton Trans., 2020, 49, 3388; (e) Y. K. Lian, R. A. Li, X. Liu, L. M. Wu and L. Chen, Sr₆(Li₂Cd)A₄S₁₆ (A = Ge, Sn): How to Go beyond the Band Gap Limitation via Site-Specific Modification, Cryst. Growth Des., 2020, 20, 8084; (f) G. Cicirello, K. Wu and J. Wang, Synthesis, crystal structure, linear and nonlinear optical properties of quaternary sulfides Ba₆(Cu₂X)Ge₄S₁₆ (X = Mg, Mn, Cd), J. Solid State Chem., 2021, 300, 122226; (g) H. Chen, M. Y. Ran, W. B. Wei, X. T. Wu, H. Lin and Q. L. Zhu, A comprehensive review on metal chalcogenides with three-dimensional frameworks for infrared nonlinear optical applications, Coord. Chem. Rev., 2022, 470, 214706.
21. (a) M. Zhou, C. Li, X. Li, J. Yao and Y. Wu, K₂Sn₂ZnSe₆, Na₂Ge₂ZnSe₆, and Na₂In₂GeSe₆: A New Series of Quaternary Selenides with Intriguing Structural Diversity and Nonlinear Optical Properties, Dalton Trans., 2016, 45, 7627–7633; (b) M. Y. Li, Y. X. Zhang, H. Lin, Z. J. Ma, X. T. Wu and Q. L. Zhu, Combined experimental and theoretical investigations of Ba₃GaS₄I: interesting structure transformation originated from the halogen substitution, Dalton Trans., 2019, 48, 17588–17593; (c) M. Y. Ran, Z. Ma, X. T. Wu, H. Lin and Q. L. Zhu, Ba₂Ge₂Te₅: a ternary NLO-active telluride with unusual one-dimensional helical chains and giant second-harmonic-generation tensors, Inorg. Chem. Front., 2021, 8, 4838–4845; (d) Q. Wu, C. Yang, X. Liu, J. Ma, F. Liang and Y. Du, Dimensionality reduction made high-performance mid-infrared nonlinear halide crystal, Mater. Today Phys., 2021, 21, 100569; (e) C. Zhang, S. H. Zhou, Y. Xiao, H. Lin and Y. Liu, Interesting dimensional transition through changing cations as the trigger in multinary thioarsenates displaying variable photocurrent response and optical anisotropy, Inorg. Chem. Front., 2022, 9, 5820–5827.
22. (a) H. Lin, L. J. Zhou and L. Chen, Sulfides with Strong Nonlinear Optical Activity and Thermochromism: ACd₄Ga₅S₁₂ (A = K, Rb, Cs), Chem. Mater., 2012, 24, 3406–3414; (b) H. Lin, L. Chen, L. J. Zhou and L. M. Wu, Functionalization Based on the Substitutional Flexibility: Strong Middle IR Nonlinear Optical Selenides AX^II₄X^III₅Se₁₂, J. Am. Chem. Soc., 2013, 135, 12914–12921; (c) Y. J. Zheng, Y. F. Shi, C. B. Tian, H. Lin, L. M. Wu, X. T. Wu and Q. L. Zhu, An Unprecedented Pentanary Chalcohalide with the Mn Atoms in Two Chemical Environments: Unique Bonding Characteristics and Magnetic Properties, Chem. Commun., 2019, 55, 79–82.
23. M. Sun, W. Xing, M. Lee and J. Yao, Bridging oxygen atoms in trigonal prism units driven strong second-harmonic-generation efficiency in Sr₃Ge₂O₄Te₃, Chem. Commun., 2022, 58, 11167–11170.
24. B. Liu, X. Jiang, G. Wang, H. Zeng, M. Zhang, S. Li, W. Guo and G. Guo, Oxychalcogenide BaGeOSe₂: Highly Distorted Mixed-Anion Building Units Leading to a Large Second-Harmonic Generation Response, Chem. Mater., 2015, 27, 8189–8192.
25. (a) X. Zhang, Y. Xiao, R. Wang, P. Fu, C. Zheng and F. Huang, Synthesis, crystal structures and optical properties of noncentrosymmetric oxysulfides AeGeS₂O (Ae = Sr, Ba), Dalton Trans., 2019, 48, 14662–14668; (b) H. D. Yang, S. H. Zhou, M. Y. Ran, X. T. Wu, H. Lin and Q. L. Zhu, Oxychalcogenides as Promising Ultraviolet Nonlinear Optical Candidates: Experimental and Theoretical Studies of AEGeOS₂ (AE = Sr and Ba), Inorg. Chem., 2022, 61, 15711–15720.
26. (a) N. Zhang, Q. Xu, Z. Shi, M. Yang and S. Guo, Characterizations and Nonlinear-Optical Properties of Pentanary Transition-Metal Oxysulfide Sr₂CoGe₂OS₆, Inorg. Chem., 2022, 61, 17002–17006; (b) H. D. Yang, S. H. Zhou, M. Y. Ran, X. T. Wu, H. Lin and Q. L. Zhu, Melilite oxychalcogenide Sr₂FeGe₂OS₆: a phase-matching IR nonlinear optical material realized by isomorphous substitution, Inorg. Chem. Front., 2023, 10, 2030.
27. W. Xing, P. Fang, N. Wang, Z. Li, Z. Lin, J. Yao, W. Yin and B. Kang, Two Mixed-Anion Units of [GeOSe₃] and [GeO₃S] Originating from Partial Isovalent Anion Substitution and Inducing Moderate Second Harmonic Generation Response and Large Birefringence, Inorg. Chem., 2020, 59, 16716–16724.
28. S. Cui, H. Wu, Z. Hu, J. Wang, Y. Wu and H. Yu, The Antiperovskite-Type Oxychalcogenides Ae₃Q[GeOQ₃] (Ae = Ba, Sr; Q = S, Se) with Large Second Harmonic Generation Responses and Wide Band Gaps, Adv. Sci., 2022, 10, 2204755.
29. (a) Y. Y. Li, W. J. Wang, H. Wang, H. Lin and L. M. Wu, Mixed-Anion Inorganic Compounds: A Favorable Candidate for Infrared Nonlinear Optical Materials, Cryst. Growth Des., 2019, 19, 4172–4192; (b) H. Chen, W. B. Wei, H. Lin and X. T. Wu, Transition-metal-based chalcogenides: A rich source of infrared nonlinear optical materials, Coord. Chem. Rev., 2021, 448, 214154; (c) J. J. Xu and K. Wu, Comprehensive review on multiple mixed-anion ligands, physicochemical performances and application prospects in metal oxysulfides, Coord. Chem. Rev., 2023, 486, 215139.
30. T. Sambrook, C. F. Smura, S. J. Clarke, K. M. Ok and P. S. Halasyaman, Vertex-Linked ZnO₂S₂ Tetrahedra in the Oxysulfide BaZnOS: a New Coordination Environment for Zinc in a Condensed Solid, Inorg. Chem., 2007, 46, 2571–2574.
31. Y. Tsujimoto, C. A. Juillerat, W. G. Hang, K. Fujii, M. Yashima, S. Halasyamani and H. Z. Loye, Function of Tetrahedral ZnS₃O Building Blocks in the Formation of SrZn₂S₂O: A Phase Matchable Polar Oxysulfide with a Large Second Harmonic Generation Response, Chem. Mater., 2018, 30, 6486–6493.
32. M. Valldor, U. Rößler, Y. Prots, C. Kuo, J. Chiang, Z. Hu, T. Pi, R. Kniep and L. Tjeng, Synthesis and characterization of Ba[CoSO]: magnetic complexity in the presence of chalcogen ordering, Chem. – Eur. J., 2015, 21, 10821–10828.
33. A. Reshak, Spin-polarized second harmonic generation from the antiferromagnetic CaCoSO single crystal, Sci. Rep., 2017, 7, 46415.
34. J. B. Litteer, J. C. Fettinger and B. W. Eichhorn, Ba₆V₄O₅S₁₁, Acta Crystallogr., Sect. C: Cryst. Struct. Commun., 1997, 53, 163–165.
35. Y. F. Shi, X. F. Li, Y. X. Zhang, H. Lin, Z. Ma, L. M. Wu, X. T. Wu and Q. L. Zhu, [(Ba₁₉Cl₄)(Ga₆Si₁₂O₄₂S₈)]: a Two-Dimensional Wide-Band-Gap Layered Oxysulfide with Mixed-Anion Chemical Bonding and Photocurrent Response, Inorg. Chem., 2019, 58, 6588–6592.
36. (a) P. Kubelka, Ein beitrag zur optik der farbanstriche, J. Tech. Phys., 1931, 12, 593; (b) M. A. Butler, Photoelectrolysis and physical properties of the semiconducting electrode WO₂, J. Appl. Phys., 1977, 48, 1914.
37. R. Wang, F. Liang, F. Wang, Y. Guo, X. Zhang, Y. Xiao, K. Bu, Z. Lin, J. Yao, T. Zhai and F. Huang, Sr₆Cd₂Sb₆O₇S₁₀: Strong SHG Response Activated by Highly Polarizable Sb/O/S Groups, Angew. Chem., Int. Ed., 2019, 58, 8078–8081.
38. X. Lian, Z. T. Lu, W. D. Yao, S. H. Yang, W. Liu, R. L. Tang and S. P. Guo, Structural Transformation and Second-Harmonic-Generation Activity in Rare-Earth and d0 Transition-Metal Oxysulfides RE₃NbS₃O₄ (RE = Ce, Sm, Gd, Dy), Inorg. Chem., 2021, 60, 10885.
39. R. Wang, F. Liang, X. Zhang, Y. Yang and F. Huang, Synthesis, structural evolution and optical properties of a new family of oxychalcogenides [Sr₃VO₄][MQ₃](M = Ga, In, Q = S, Se), Inorg. Chem. Front., 2022, 9, 4768–4775.
40. (a) Y. Shi, S. Zhou, P. Liu, X. Wu, H. Lin and Q. Zhu, Unique [Sb₆O₂S₁₃]¹²⁻ finite chain in oxychalcogenide Ba₆Sb₆O₂S₁₃ leading to ultra-low thermal conductivity and giant birefringence, Inorg. Chem. Front., 2023, 10, 4425–4434; (b) H. Liu, Z. Song, H. Wu, Z. Hu, J. Wang, Y. Wu and H. Yu, [Ba₂F₂][Ge₂O₃S₂]: An Unprecedented Heteroanionic Infrared Nonlinear Optical Material Containing Three Typical Anions, ACS Mater. Lett., 2022, 4, 1593–1598; (c) Y. Shi, Z. Ma, B. Li, X. Wu, H. Lin and Q. Zhu, Phase matching achieved by isomorphous substitution in IR nonlinear optical material Ba₂SnSSi₂O₇ with an undiscovered [SnO₄S] functional motif, Mater. Chem. Front., 2022, 6, 3054–3061.
41. Y. X. Chen, Z. X. Chen, Y. Zhou, Y. Q. Li, Y. C. Liu, Q. R. Ding, X. Chen, S. G. Zhao and J. H. Luo, An Antimony(III) Fluoride Oxalate With Large Birefringence, Chem. – Eur. J., 2021, 27, 4557–4560.
42. D. E. Zelmon, D. L. Small and D. Jundt, Infrared corrected Sellmeier coefficients for congruently grown lithium niobate and 5 mol% magnesium oxide-doped lithium niobate, J. Opt. Soc. Am. B, 1997, 14, 3319–3322.
43. M. J. Dodge, Refractive properties of magnesium fluoride, Appl. Opt., 1984, 23, 1980–1985.
44. K. Ding, H. Wu, Z. Hu, J. Wang, Y. Wu and H. Yu, [Ba₄(S₂)][ZnGa₄S₁₀]: Design of an Unprecedented Infrared Nonlinear Salt-Inclusion Chalcogenide with Disulfide-Bonds, Small, 2023, 19, 2302819.
45. A. Abudurusuli, K. Wu, A. Tudi, Z. Yang and S. Pan, ABaSbQ₃ (A = Li, Na; Q = S, Se): Diverse Arrangement Modes of Isolated SbQ₃ Ligands Regulating the Magnitudes of Birefringences, Chem. Commun., 2019, 55, 5143–5146.
46. X. Ji, H. Wu, B. Zhang, H. Yu, Z. Hu, J. Wang and Y. Wu, Intriguing Dimensional Transition Inducing Variable Birefringence in K₂Na₂Sn₃S₈ and Rb₃NaSn₃Se₈, Inorg. Chem., 2021, 60, 1055–1061.
47. P. E. Blochl, Projector augmented-wave method, Phys. Rev. B: Condens. Matter, 1994, 50, 17953–17979.

---

Footnotes

† Electronic supplementary information (ESI) available: Additional experimental and theory results, together with additional tables and figures. CCDC 2234468 and 2234469. For ESI and crystallographic data in CIF or other electronic format see DOI: https://doi.org/10.1039/d3qi01456h

‡ These authors contributed equally to this work.

---