Complex coordinated functional groups: A great genes for nonlinear optical materials

Complex coordinated functional groups: A great genes for nonlinear optical materials

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Weikang Wang^a, Dajiang Mei^a^,^c^,^*, Shaoguo Wen^a, Jian Wang^b, Yuandong Wu^a

Chinese Chemical Letters | 2022, 33(5) : 2301 - 2315

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Chinese Chemical Letters | 2022, 33(5): 2301-2315

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Complex coordinated functional groups: A great genes for nonlinear optical materials

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Weikang Wang^a, Dajiang Mei^a^,^c^,^*, Shaoguo Wen^a, Jian Wang^b, Yuandong Wu^a

Affiliations

^aCollege of Chemistry and Chemical Engineering, Shanghai University of Engineering Science, Shanghai 201620, China

^bDepartment of Chemistry and Biochemistry, Wichita State University, Wichita, KS 67260, United States

^cState Key Laboratory of Structural Chemistry, Fujian Institute of Research on the Structure of Matter, Chinese Academy of Sciences, Fuzhou 350002, China

Published: 2022-05-15 doi: 10.1016/j.cclet.2021.11.089

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Abstract

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Complex coordinated functional groups [MA_xB_y] (M = Central coordination element; A, B = P, O, S, Se, F, Cl, Br or I) are composed of different types of anions A, B jointly linked to the same central cation M, which are in high potential to tune the physical properties of materials, e.g., second-order susceptibility, energy gaps and birefringence. Recently, Compound containing complex coordinated functional groups have attracted great attention in the nonlinear optical (NLO) field and a large number of this type crystals exhibit promising NLO performance. However, the inherent relationship between ionic group structure and optical properties of complex coordinated NLO materials have not been systematically studied. This article systematically summarizes complex coordinated NLO materials in recent five years from the perspective of the internal relationship between crystal structure and optical properties. In addition, we propose the ideal combination and arrangement modes for structural building units, and also reveal the influence of complex coordinated functional groups [MA_xB_y] toward the NLO response, optical band gap and phase matching ability of complex coordinated NLO materials.

Key words

Complex coordinated / Nonlinear optical / Second harmonic generation / Optical band gap / Structure-performance relationship

Cite this Article

Weikang Wang, Dajiang Mei, Shaoguo Wen, Jian Wang, Yuandong Wu. Complex coordinated functional groups: A great genes for nonlinear optical materials[J]. Chinese Chemical Letters, 2022 , 33 (5) : 2301 -2315 . DOI: 10.1016/j.cclet.2021.11.089

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1 Introduction

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Nonlinear optical (NLO) crystals can generate tunable laser beams from deep ultraviolet (DUV, wavelength less than 200 nm) to mid IR (MIR, wavelength between 3 µm and 30 µm) via frequency conversion technology, thus plays an important role in optoelectronic and laser technology [1-14]. Researchers have been dedicated to explore NLO crystals with good performance since Franken et al. discovered second harmonic generation phenomenon in quartz crystal in 1961 [15]. In the past few decades, many NLO crystals with comprehensively excellent properties have emerged, such as β-BaB₂O₄ (β-BBO) [16], LiB₃O₅ (LBO) [17], LiNbO₃ (LN) [18], KH₂PO₄ (KDP) [19] and KTiOPO₄ (KTP) [20]. With the extensive application of laser from the 21^st century, the demand for DUV and MIR laser keeps increasing [21-25]. However, the commercialized crystals in the DUV and MIR region cannot meet the practical needs due to the lack of comprehensive performances [26-29]. The prerequisites of the ideal NLO crystal in these two important wavelength regions are large second harmonic generation (SHG) coefficient d_ij, suitable birefringence value Δn and wide optical band gap E_g [30, 31]. Large SHG coefficient d_ij corresponds to high frequency conversion efficiency, and suitable birefringence value Δn can ensure the phase matching output [32-34]. Wide optical band gap E_g corresponds to short ultraviolet cut-off edge and large laser damage threshold [35].

According to the anion group and functional moieties theory, the optical properties of the compounds are mainly affected by the anion functional groups in the structure [36-38]. Keeping a good balance among d_ij, Δn and E_g is not easy for NLO crystals with only one anionic functional group [39]. Rational combination of various anionic functional groups is critical to obtain the ideal NLO crystals. In the last few years, different research groups have systematically summarized the NLO materials with mixed anion. For example, De Yoreo et al. comprehensively reviewed the crystal chemistry and optical properties of metal halide borate NLO materials, according to the arrangement of anionic groups (0D clusters, 1D chain, 2D layer, 3D network) [19]. Pan et al. specifically analyzed the crystal chemistry and optical properties of the mixed anion NLO materials [39]. Li et al. summarized different types of IR mixed anion NLO inorganic compounds from the perspective of structure-property relationship [40].

Inorganic salts containing two or more anions or anionic groups are normally defined as mixed anion compounds. For example, two type ions Cl^- and S^2- exist in the structure of salt sulfide halide compounds [K₃Cl][Ga₃PS₈] [41]. There are two single anion functional groups [IO₃] and [NO₃] in iodate nitrates Sc(IO₃)₂(NO₃) [42]. It should be noted that the compounds above are composed of different types of anions or anionic groups. Different from the traditional mixed anion compounds, the different anions A and B of [MA_xB_y] groups in complex coordinated crystals jointly link to the same central atom M [43]. Complex coordinated functional groups exhibit superior propertiesthan the single-anion group from the following aspects: (1) The structure of mixed anion group [MA_xB_y] has a stronger distortion and polarity, which is conducive to a strong SHG effect. (2) Due to different size and electronic properties of A and B anions, the mixed anion group [MA_xB_y] has stronger anisotropy and large birefringence values, which is conducive to the appropriate phase matching ability. (3) In the DUV nonlinear optics field, the compounds containing mixed anion group produced by the introduction of halogen element with strong electronegativity, e.g., F and oxygen in [B/PO₄] have a wider DUV transparent region and also strong SHG effects and a suitable birefringence value. (4) In the field of IR NLO region, the compounds containing [MO_xS_y] gene containing O and S can have large band gap and strong NLO effect [43–46]. The mixed anion functional group [MA_xB_y] has been proven to be superior NLO active units, and the compounds containing this group are more likely to keep a good balance among three key property parameters (d_ij, Δn and E_g) [27, 40]. For example, the well-performed DUV NLO crystal KBe₂BO₃F₂(KBBF) contains the mixed anion group [BeO₃F] [47, 48]. Moreover, the strongly polarized mixed anion group [SbOS₄] has been recognized as the origin of the strong SHG effect in the new MIR NLO crystal Sr₆Cd₂Sb₆O₇S₁₀ [46]. Since 2017, complex coordinated NLO materials have attracted great attention in the NLO field. Different research groups have designed and synthesized a large number of NLO optical crystals with mixed anion groups, which have potential to become candidates for the next generation of DUV and MIR NLO crystals. For example, AB₄O₆F (A = Rb, Cs, K, Na, NH₄) series [42, 49–51], A(B₅O₇)F₃ (A = Sr, Ca, Pb) series [52–54], Ba₃Mg₃(BO₃)₃F₃ [55], CsAlB₃O₆F [56], γ-Be₂BO₃F [57], C(NH₂)₃SO₃F [58], Ba₂NaP₂O₇Cl [59], CsSiP₂O₇F [60], NaNH₄PO₃F·H₂O [61], have short ultraviolet cut-off edges and strong SHG effect, thus are regarded as potential source of DUV NLO crystals. K₅(W₃O₉F₄)(IO₃) [62], BiIO₃F [63], (NH₄)Bi₂(IO₃)₂F₅ [64], CsVO₂F(IO₃) [65], K₂Bi₂(SeO₃)₃F₂ [66], Pb₂GaF₂(SeO₃)₂Cl [67], Pb₁₃O₆Cl₉Br₅ [68] and M^II₃PnI₃ (M^II = Zn, Cd; Pn = P, As) [69], etc., have a wide MIR transparent area, which can achieve a good balance between a wide E_g and a large d_ij, regarded as a potential candidate of MIR NLO crystals. The difference between traditional complex coordinated compounds and those with complex coordinated groups as structural building units (SBUs) are still not clear, especially systematic summary of how complex coordinated functional groups [MA_xB_y] influence on the optical properties of NLO crystal materials.

This article focuses on complex coordinated NLO materials in recent five years. The preparation methods, crystal structure, and optical properties of this type NLO crystals are comprehensively reviewed. The regulation law of multiple critical properties (SHG effect, phasemaching capability and band gap) by the permutation pattern of the complex coordinated functional group [MA_xB_y] was highlighted. Via the structure-performance analysis of the NLO complex coordinated materials, the ideal combination and arrangement modes of the anion group of UV/DUV and MIR NLO complex coordinated crystals are proposed, respectively. We hope that this article can help future research minimize time-consuming "trial and error" and provide some insights on the design and synthesis of next-generation complex coordinated NLO crystals.

2 IR complex coordinated NLO materials

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In the field of infrared (IR) nonlinear optics, the common single-anion NLO active units (NAUs) consist of tri-coordinated and tetra-coordinated groups. Tri-coordinated groups play a key role in NLO response, and exhibit large microscopic SHG effects and good optical anisotropy [70-72]. Tetrahedron-based sulfides have been widely used in the research on IR NLO crystals due to their spacious IR transparent region and good balance between E_g and d_ij [73]. In the last few years, a number of research groups have combined these single-anion units with mixed anion groups to design and synthesize a series of new IR NLO materials. In this part, some representative complex coordinated compounds are presented and the relationship between crystal structure and optical properties of this type compounds are summarized in detail (Table 1). According to the types of anions, the IR NLO crystals containing single anions and mixed anions as SBUs can be divided into: (1) [MA_xB_y] and [IO₃] as SBUs; (2) [MA_xB_y] and [Se/TeO₃] as SBUs; (3) [MA_xB_y] and [MS₄] as SBUs. In addition, another type IR complex coordinated NLO materials contain only mixed-anion [MA_xB_y]. In the field of IR nonlinear optics, this type of compound mainly includes the following three groups: (1) PbO-PbCl₂-PbBr₂, PbO-PbCl₂-PbI₂ series of IR NLO crystals containing O-Pb-X complex coordinated groups; (2) M^II₃PnI₃ containing [MPn₃I] mixed anion (M^II = Zn, Cd; Pn = P, As) series pnictides; (3) oxychalcogenides.

2.1 [MA_xB_y] and [IO₃] as NLO active units

The iodates with the lone pair electron benefit the formation of the NCS structure required by the compound for the SHG response. [IO₃] group has received extensive attention in NLO region due to their wide IR transparent region [74]. Recently, Mao, Ye, Poeppelmeier and other research groups combined the [IO₃] group with the mixed anion group [MA_xB_y] to design and synthesize a series of IR NLO crystals with excellent performance, such as Ba₂[GaF₄(IO₃)₂](IO₃) [75], (NH₄)Bi₂(IO₃)₂F₅ [64], Ba₂[VO₂F₂(IO₃)₂]IO₃ [76]. This section summarizes this type of NLO crystal from the perspective of the structure-performance relationship and anionic group structure dimensions from 0D to 3D.

2.1.1 0D cluster formed by [MA_xB_y] and [IO₃] anionic groups

Ba₂[GaF₄(IO₃)₂](IO₃) polymorphs are representative compounds of this type iodates. Mao et al. obtained colorless and transparent α-Ba₂[GaF₄(IO₃)₂](IO₃) and β-Ba₂[GaF₄(IO₃)₂](IO₃) [75] on the basis of Ba₂[VO₂F₂(IO₃)₂](IO₃) [76] by chemical substitution. They have a similar crystal structure. Taking α-Ba₂[GaF₄(IO₃)₂](IO₃) as an example, its structure is composed of one mix-anion [GaF₄O₂] group and two [IO₃]^- groups to form OD isolation molecular structure (Fig. 1a). Ba²⁺ is trapped in molecular voids to maintain charge balance. Both of them exhibit wide transparent areas of 0.26–12.5 µm and 0.28–12.9 µm, respectively. The powder test shows that both of them have phase matching ability and strong SHG response of 6 times that of KDP (d₃₆ = 0.38 pm/V) under 1064 nm laser irradiation. Optical experiments revealed that they have a large E_g: 4.61 and 4.35 eV. The theoretical analysis of partial densities of states (PDOS) shows that the valence bands (VBs) maximum is occupied by O 2p orbitals, while the conduction bands (CBs) minimum is contributed by O 2p and I 5p orbitals, which indicates that its optical properties are mainly dominated by [IO₃] groups. The 2p orbital of F is above top of the VBs, which indicates that the mix-anion [GaF₄O₂] group contribute the large energy band gap.

2.1.2 1D chain formed by [MA_xB_y] and [IO₃] anionic groups

α, β-Ba₂[VO₂F₂(IO₃)₂]IO₃: Poeppelmeier et al. synthesized β-Ba[VFO₂(IO₃)₂], α, β-Ba₂[VO₂F₂(IO₃)₂]IO₃ series [76] fluoroiodate compounds by hydrothermal method. β-Ba[VFO₂(IO₃)₂] has a 0D isolated molecular structure which composed of [VO₄F] mixed-anion polyhedra and two [IO₃] units (Fig. 1c). α, β-Ba₂ [VO₂F₂(IO₃)₂]IO₃ polymorphs have similar crystal structure. Both of their crystal structures are composed of [VO₄F₂] polyhedra and two [IO₃] units to form a 1D chain, and Ba²⁺ are incorporated between the chains. However, in the α phase of polymorphic Ba₂[VO₂F₂(IO₃)₂]IO₃, the order of [VO₄F] mixed-anion polyhedra and [IO₃] units are better than that of β phase (Fig. 1b). Optical experiments show that they have a wide transparent region (~0.5–10.5 µm) in the IR band. Polymorphic Ba₂[VO₂F₂(IO₃)₂]IO₃ have type I phase matching ability, and can maintain a good balance between the wide E_g (> 2.5 eV) and strong SHG effect (~ 9 × KDP).

K₅(W₃O₉F₄)(IO₃): Wu et al. obtained the colorless and transparent K₅(W₃O₉F₄)(IO₃) crystal by hydrothermal method [62]. As shown in Fig. 1d, in the crystal structure of K₅(W₃O₉F₄)(IO₃), [WO₅F] and [WO₄F₂] mixed-anion tetrahedrons form [W₃O₁₂F₄]_∞ 1D chain through common vertex connection and [IO₃] groups are isolated and scattered in the chain. Optical experiments show that the transparent region of K₅(W₃O₉F₄)(IO₃) is 0.32–10.5 µm, and the indirect band gap is 3.83 eV. K₅(W₃O₉F₄)(IO₃) had phase matching (PM) ability, and the SHG response was 11 × KDP and 0.5 × AgGaS₂ (AGS) (d₃₆ = 23.6 ± 2.4 pm/V) under 1064 nm and 2100 nm laser irradiation, respectively. DFT calculations show that VBs maximum and CBs minimum of K₅(W₃O₉F₄)(IO₃) are mainly determined by I 5p, W 5d, O 2p, and F 2p orbitals, which means that the optical properties of this compound are determined by mixed-anion group [WO₃F] and single anion groups [WO₄], [IO₃].

Sn(IO₃)₂F₂: Luo et al. obtained a colorless and transparent fluorocompound iodate Sn(IO₃)₂F₂ by heating and cooling in a sealed high-pressure reactor fitted with the gold liner [77]. As shown in Fig. 1e, the 1D chain structure of Sn(IO₃)₂F₂ is connected by two [IO₃] groups and a low symmetry mixed-anion [SnO₄F₂] polyhedral. Optical experiments show that Sn(IO₃)₂F₂ has a wide IR band transparent region and an E_g of 4.08 eV. In addition, the SHG powder test show that Sn(IO₃)₂F₂ exhibited type-I PM behavior, and the SHG response was 3 × KDP@1064 nm. DFT calculation shows that the introduction of highly polar halogen F based mixed-anion group in iodate is not only beneficial to SHG response, but also beneficial to increase the optical band gap.

2.1.3 2D layered formed by [MA_xB_y] and [IO₃] anionic groups

(NH₄)Bi₂(IO₃)₂F₅ is representative compound of this type iodates. In 2019, Fan et al. prepared the first ammonium containing multianion fluoride iodate (NH₄)Bi₂(IO₃)₂F₅ by hydrothermal method with KBi₂(IO₃)₂F₅ as template [64]. As shown in the Fig. 1f, mixed-anion groups [Bi(1)O₂F₅] and [Bi(2)O₄F₄] form a 2D layered structure through co-edge connection and co-vertex connection with [IO₃] group. It is worth noting that the NH₄⁺ and F distributed between layers form N-H-F hydrogen bonds, which can strengthen the interaction between layers. Optical experimental results show that (NH₄)Bi₂(IO₃)₂F₅ has a wide E_g (3.88 eV) and a high transparency in the range of 2.5–6.8 µm. Kurtz powder test show that it had type-I PM ability, and SHG response was 9.2 × KDP@1064 nm. DFT calculations show that the VBs maximum and CBs minimum of (NH₄)Bi₂(IO₃)₂F₅ are mainly determined by the atomic orbitals of Bi, I, O and F atoms which indicates that optical properties of (NH₄)Bi₂(IO₃)₂F₅ are dominated by the [Bi(1)O₂F₅], [Bi(2)O₄F₄] and [IO₃] groups.

2.1.4 3D framework formed by [MA_xB_y] and [IO₃] anionic groups

BiIO₃F, Bi₃OF₃(IO₃)₄: Mao and Pan et al. designed and synthesized Bi-based fluorinated iodate BiIO₃F, Bi₃OF₃(IO₃)₄ by hydrothermal method [63, 78]. As shown in Fig. 1g, the crystal structure of BiIO₃F is built by [BiO₄F₄] polyhedrons and interconnection of [IO₃] groups to build a 3D framework structure. The network tunnel structure of Bi₃OF₃(IO₃)₄ is composed of [BiO₇F₂] polyhedrons connected with [IO₃] groups, and part of [IO₃] groups are scattered in the tunnel holes (Fig. 1h). The experimental results show that BiIO₃F and Bi₃OF₃(IO₃)₄ both have wide MIR transparent regions, with E_g of 3.97 eV and 3.70 eV, respectively. Kurtz powder test showed that they all had PM ability, and SHG strength was 11.5 and 6.0 × KDP@1064 nm, respectively.

Ce(IO₃)₂F₂·H₂O: Abudouwufu et al. synthesized Ce(IO₃)₂F₂·H₂O by hydrothermal method [79]. As shown in Fig. 1i, its 3D framework structure formed by mixed-anionic [CeO₅F₄] groups and [IO₃] groups. In addition, two H atoms are connected with O atoms to form an H₂O unit interwoven with the tunnel holes. The experimental results show that the E_g of Ce(IO₃)₂F₂·H₂O is 2.6 eV, and SHG response is 3 × KDP@1064 nm with PM behavior. Theoretical analysis shows that VBs maximum of Ce(IO₃)₂F₂·H₂O is composed of I and O atomic orbitals, and the CBs minimum is composed of atomic orbitals of Ce. Therefore, its optical properties are mainly determined by the mixed-anionic [CeO₅F₄] groups and [IO₃] groups.

Y(IO₃)₂F, Cd(IO₃)F: Cao et al. synthesized rare earth fluorocompound iodate Y(IO₃)₂F and transition metal fluorocompound iodate Cd(IO₃)F by hydrothermal method [80, 81]. As shown in the Fig. 1j, the crystal structure of Y(IO₃)₂F is connected by complex coordinated group [YO₆F₂] polyhedrons through co-edge to form a curved 1D chain, which is further connected by [IO₃] group and finally forms a 3D skeleton structure. The 3D skeleton structure of Cd(IO₃)F is composed of the mixed anion group [CdO₅F₂] polyhedrons and [IO₃] groups (Fig. 1k). Optical experiments show that Y(IO₃)₂F and Cd(IO₃)F have wide transparent region in the IR band, with E_g of 3.91 eV and 4.22 eV, respectively. Kurtz powder test show that they all had type I PM ability, and d_ij was 2 and 6.2 × KDP@1064 nm, respectively.

CsVO₂F(IO₃): Chen et al. synthesized the mixed-anion fluoroiodate C_SVO₂F(IO₃) by hydrothermal method [65]. C_SVO₂F(IO₃) is the first alkali metal vanadifluoroioioate compound with 3D anion skeleton. It is formed by the interconnection of [IO₃] and [VO₅F] polyhedral groups (Fig. 1l). C_SVO₂F(IO₃) has a wide MIR transparent region (0.5–10.5 µm) and E_g is 2.39 eV. Kurtz powder test show that it has type I PM behavior, and SHG response is 1.1 × KTP (d₃₃ = 17.4 pm/V). DFT calculations show that the VBs maximum and the CBs minimum of C_SVO₂F(IO₃) are mainly occupied by V, F and O atomic orbitals, which reveals that the optical properties of C_SVO₂F(IO₃) are determined by the [IO₃] and [VO₅F] polyhedral groups.

2.2 [MA_xB_y] and [Se/TeO₃] as NLO active units

In addition to iodate, selenite and tellurite containing three coordinated [SeO₃] and [TeO₃] groups have also received more and more attention in the nonlinear optics field [67]. Similar to [IO₃] groups, the combination of planar π-conjugated groups [SeO₃] and [TeO₃] with complex coordinated groups [MA_xB_y] favors to the generation of IR NLO crystals with excellent comprehensive performance. Recently, Mao, Ye, OK and other research groups have found a series of IR NLO materials of this type, such as Ba(MoO₂F)₂(QO₃)₂(Q = Se, Te) [82], K₂Bi₂(SeO₃)₃F₂ [66], Bi₃(SeO₃)₃(Se₂O₅)F [83]. In this part, based on the anionic crystal structure dimension from 1D to 3D, this type of NLO crystals were comprehensively summarized from the perspective of structure-property relationship.

2.2.1 1D chain formed by [MA_xB_y] and [SeO₃] anionic groups

Lin and You et al. synthesized isomorphically Pb₂GaF₂(SeO₃)₂X (X = Cl, Br) by hydrothermal method [67, 84]. They have similar crystal structure. Taking Pb₂GaF₂(SeO₃)₂Cl as an example, its crystal structure is connected by [GaO₃F₃] polyhedron and [SeO₃] group to form a 1D chain structure, and each Cl atom connects two Pb atoms along the ab direction (Fig. 2a). The results of optical experiment show that both of them have wide MIR transparent region, and the E_g are 4.32 eV and 3.73 eV for Pb₂GaF₂(SeO₃)₂Cl and Pb₂GaF₂(SeO₃)₂Br, respectively. Under 1064 nm laser irradiation, their SHG response is 4.5 × KDP, and they have type I PM capability. Theoretical analysis shows that [GaO₃F₃] and [SeO₃] units play a major role in their large d_ij.

2.2.2 2D layered formed by [MA_xB_y] and [Se/TeO₃] anionic groups

Ba(MoO₂F)₂(QO₃)₂ (Q = Se, Te): Liang et al. synthesized the colorless and transparent alkaline earth metal fluoroselenite and fluorotellurite compounds Ba(MoO₂F)₂(QO₃)₂ (Q = Se, Te) by hydrothermal method [82]. They belong to NCS orthogonal space group Aba2 (No. 41). They have similar crystal structures. Taking Ba(MoO₂F)₂(SeO₃)₂ as an example, there are two NAUs of mixed anion [MoO₅F] and [SeO₃] in the structure. They form a 2D layer by sharing vertexs, and Ba²⁺ is scattered between the layers (Fig. 2b). It is worth noting that the SHG intensity (7.8 × KDP@1064 nm) of Ba(MoO₂F)₂(TeO₃)₂ with PM ability is significantly greater than that of Ba(MoO₂F)₂(SeO₃)₂ (2.8 × KDP@1064 nm). This indicates that the SHG activity of [TeO₃] group is stronger than that of [SeO₃] group. Their E_g are 2.96 eV and 3.23 eV, respectively. DFT calculations show that the VBs maximum of Ba(MoO₂F)₂(TeO₃)₂ is mainly occupied by atomic orbitals of O 2p and F 2p, while CBs minimum is mainly occupied by atomic orbitals of O 2p, Te 5p and Mo 4d, which indicates that its optical properties are mainly determined by [MoO₅F] and [TeO₃] groups.

RbGa₃F₆(SeO₃)₂: Wu et al. designed and synthesized the alkali metal fluoride selenite compounds RbGa₃F₆(SeO₃)₂ by hydrothermal method [85]. In the crystal structure of RbGa₃F₆(SeO₃)₂, [SeO₃] groups connect the mixed-anion groups [GaO₂F₄] (Fig. 2c). Optical experiments show that RbGa₃F₆(SeO₃)₂ have a wide transparent region in IR wavelengths. Kurtz powder test showed that RbGa₃F₆(SeO₃)₂ have type I phase matching ability, and SHG strength was 5.6 × KDP@1064 nm and E_g is 3.57 eV. According to the calculated PDOS diagram, the VBs maximum and CBs minimum are mainly occupied by the atomic orbitals of Ga, F, Se and O atoms, which indicates that the optical properties of RbGa₃F₆(SeO₃)₂ are mainly determined by the [SeO₃] and [GaO₂F₄] units.

2.2.3 3D framework formed by [MA_xB_y] and [SeO₃] anionic groups

Lu₃F(SeO₃)₄: Wu et al. synthesized the colorless and transparent rare earth metal fluoroselenite compound Lu₃F(SeO₃)₄ by hydrothermal method [86]. The 3D frame structure of Lu₃F(SeO₃)₄ is formed by twisted [LuO₇F] polyhedron and planar p-conjugated [SeO₃] groups (Fig. 3a). Lu₃F(SeO₃)₄ has a wide transparent region in IR wavelengths and E_g is 3.57 eV. Kurtz powder test show that Lu₃F(SeO₃)₄ exhibits PM behavior, and the SHG strength of Lu₃F(SeO₃)₄ is 2.5 × KDP@1064 nm. DFT calculation revealed that the optical properties of Lu₃F(SeO₃)₄ are mainly determined by [LuO₇F] and [SeO₃] groups.

K₂Bi₂(SeO₃)₃F₂, Bi₃(SeO₃)₃(Se₂O₅)F: Shi et al. synthesized a colorless and transparent Bi-based alkali metal selenite K₂Bi₂(SeO₃)₃F₂ by hydrothermal method [66]. In the crystal structure of K₂Bi₂(SeO₃)₃F₂, Bi(1) atoms connect six O atoms and two F atoms to form a [BiO₆F₂] group, and Bi(2) atoms link to five O atoms and two F atoms to form [BiO₅F₂] group. [BiO₆F₂] group and [BiO₅F₂] group share one O and one F atom to form a 1D chain structure, and [IO₃] connects these 1D chains to finally form a 3D framework structure (Fig. 3b). The transparent region of the growing block K₂Bi₂(SeO₃)₃F₂ crystal covers the important band 3–5 µm in the IR region. K₂Bi₂(SeO₃)₃F₂ with phase matching ability can maintain a balance between the wide E_g (3.72 eV) and the strong SHG response (15 × KDP @1064 nm). DFT calculation indicated that the optical properties are mainly determined by [BiO_xF_y] and [SeO₃] groups.

Chung et al. synthesized colorless and transparent Bi-based selenite fluoride Bi₃(SeO₃)₃(Se₂O₅)F by hydrothermal method [83]. There are three active NLO groups [BiO₇], [BiO₆F] and [SeO₃] in the crystal structure, in which [BiO₇] and [BiO₆F] polyhedra form a 2D layer through co-edge connection, and [SeO₃] further connects the 2D layer to form a 3D frame structure (Fig. 3c). The optical results show that Bi₃(SeO₃)₃(Se₂O₅)F has a wide IR transparent window. Furthermore, Bi₃(SeO₃)₃(Se₂O₅)F exhibits wide band gap (3.80 eV) and strong SHG response (8.0 × KDP@1064 nm) with type-I PM behavior. Theoretical analysis shows that the strongly twisted mixed-anion [BiO₆F] polyhedron play an important role in its good comprehensive performance.

Pb₂Cd(SeO₃)₂Cl₂, Pb₃(SeO₃)Br₄: Chen and Ma et al. synthesized lead halogen selenite Pb₂Cd(SeO₃)₂Cl₂ and Pb₃(SeO₃)Br₄ by hydrothermal method [87, 88]. As shown in Fig. 3d, the crystal structure of Pb₂Cd(SeO₃)₂Cl₂ is composed of [CdO₆Br], [PbO_xBr_y] and [SeO₃] groups. They interpenetrate and connect to form a 3D framework structure. The crystal structure of Pb₃(SeO₃)Br₄ has three kinds of NAUs, e.g., [PbBr₅O₂], [PbBr₄O₃] and [SeO₃], in which [PbBr₅O₂] and [PbBr₄O₃] form 3D tunnel structure by sharing Br atoms (Fig. 3e). Under 1064 nm laser irradiation, Pb₂Cd(SeO₃)₂Cl₂ and Pb₃(SeO₃)Br₄ with type I phase matching ability exhibit 1.8 and 1.0 times SHG effects that of KDP, respectively. Their E_g are 4.10 eV for Pb₂Cd(SeO₃)₂Cl₂ and 3.35 eV for Pb₃(SeO₃)Br₄, respectively. DFT calculations suggest the VBs maximum and CBs minimum of Pb₂Cd(SeO₃)₂Cl₂ mainly occupy by Pb, Se, Cl, O atomic orbitals, which suggests that its optical properties are mainly depends on [PbO_xBr_y] and [SeO₃] groups. The VBs maximum and CBs minimum of Pb₃(SeO₃)Br₄ mainly occupy by the orbitals all constituent atoms, suggesting that its optical properties are mainly determinated by [PbBr₅O₂], [PbBr₄O₃] and [SeO₃] groups.

In summary, most of the IR NLO crystals composed of the complex coordinated group [MA_xB_y] and tri-coordinated group [Se/TeO₃] have a 3D framework structure. Similar to iodates, they all have good optical anisotropy and all have phase matching capabilities. According to theoretical analysis, the introduction of highly electronegative halogens, such as F, Cl, Br, is in favor of enhancing the E_g of iodate. Most compounds with complex coordinated groups [MA_xB_y] and [Se/TeO₃] SBUs have ideal optical band gaps (larger than 3.5 eV). It is worth noting that the compounds with [BiO_xF_y] and [SeO₃] as SBUs have good overall performance (good phase matching ability, large optical band gap, strong SHG effect).

2.3 [MA_xB_y] and [MS₄] as NLO active units

Compared with oxygen-based tri-coordinated groups, few IR NLO compounds are composed of mixed anions [MA_xB_y] and [MS₄] as SBUs. Recently, Wang et al. designed and synthesized two compounds Sr₆Cd₂Sb₆O₇S₁₀ [46] and Sr₅Ga₈O₃S₁₄ [89] by combining the complex coordinated group [MO_xS_y] with the tetra-coordinated group [MS₄]. Herein, these two compounds are selected as representatives to discuss the influence of SBUs functional groups on optical properties of this type compound.

Sr₆Cd₂Sb₆O₇S₁₀: Wang et al. obtained the red Sr₆Cd₂Sb₆O₇S₁₀ crystal by solid-phase synthesis [46]. As shown in Fig. 4a, its 2D layered structure is formed by the mixed-anion SBUs [SbOS₄], the single anion poly-coordinated group [SbS₅] and the tetra-coordinated group [CdS₄] connected to each other on the bc plane. The powder frequency doubling test shows that Sr₆Cd₂Sb₆O₇S₁₀ has phase matching ability. When the particle size is 150–210 µm, the SHG effect is 4.0 × AGS in 2090 nm. The bandgap of Sr₆Cd₂Sb₆O₇S₁₀ is 1.89 eV. Atomistic first principles calculations show that the 5S^2- electron [SbO_xS_5-x]^7- (x = 0, 1) groups make a major contribution to its strong SHG effect. In addition, further theoretical analysis shows that the mixed-anionic group [SbOS₄] has a greater contribution to the d_ij than the single-anionic unit [SbS₅].

Sr₅Ga₈O₃S₁₄: Wang et al. obtained colorless and transparent melilite-derived oxysulfide Sr₅Ga₈O₃S₁₄ crystals by solid-phase synthesis [89]. As shown in Fig. 4b, the crystal structure consists of a mixed polyanion group [GaOS₃] tetrahedron and [GaS₄] tetrahedron group connected to form a 3D framework structure, with Sr²⁺ scattered in the tunnel holes. Optical research shows that Sr₅Ga₈O₃S₁₄ with NPM behavior exhibits a large E_g (3.9 eV) and a strong SHG effect (0.8 × AGS @2090 nm). It has a wide IR transparent area of 0.3–13.4 µm. Theoretical calculations show that the mixed polyanionic group [GaOS₃] tetrahedron and [GaS₄] tetrahedron group play the main contribution to the SHG effect of Sr₅Ga₈O₃S₁₄.

To sum up, the reasonable combination of complex coordinated groups [MA_xB_y] and other single anionic groups, such as [IO₃], [SeO₃], [TeO₃], [MS₄], is a very effective strategy to design and synthesize great-performance IR NLO crystals. At present, this type of NLO material, complex coordinated groups [MA_xB_y] and tri-coordinated groups [IO₃], [SeO₃], [TeO₃] as building units, has been widely explored. They all have good phase matching capabilities, and most of them have a wide optical band gap. The key issue is how to effectively improve the NLO effect. Interestingly, [MO_xF_y] (M = V, Mo, W, Bi, etc.) composed of mixed anion groups centered on transition metal or metal with lone pair electrons not only provide strong SHG contribution, but also help guide tri-coordinated groups [IO₃], [SeO₃], [TeO₃] to arrange orderly. Therefore, most compounds with this group have excellent comprehensive properties, such as K₅(W₃O₉F₄)(IO₃), BiIO₃F, Ba₂[VO₂F₂(IO₃)₂]IO₃, (NH₄)Bi₂(IO₃)₂F₅, CsVO₂F(IO₃), Ba(MoO₂F)₂(TeO₃)₂, K₂Bi₂(SeO₃)₃F₂ and Bi₃(SeO₃)₃(Se₂O₅)F. All of compounds above can keep a good balance between strong SHG reponse with phase matching ability and wide E_g. The combination of complex coordinated group [MA_xB_y] and tetra-coordinated group [MS₄] has the potential to design NLO crystals with strong SHG effect. For example, Sr₆Cd₂Sb₆O₇S₁₀ has an extremely strong SHG intensity of 4 times that of AGS.

2.4 Halides-based pnictides

Chen et al. solved the shortcomings of the band gap of phosphorus compounds by introducing strong electronegative heavy halogen "I" into phosphorus compounds [69]. They obtain four kinds of iodinated phosphorus NLO crystals by heterovalent anion substitution strategy, namely M^II₃PnI₃ (M^II = Zn, Cd; Pn = P, As). It has a defective diamond-like structure, and the mixed anion [M^IIPnI₃] tetrahedral groups arrange toward the same direction. Taking ZnPI₃ as an example, as shown in Fig. 5a, its structure stacked by [ZnPI₃] tetrahedrons along [111] direction by sharing vertexes. The optical experiment results show that their E_g are 2.85 eV and 2.38 eV, respectively. Their SHG effect are 2.7 and 4.3 × AGS, respectively, without PM capability. Taking CdPI₃ as an example, as shown in figure, its structure stacked by [CdPI₃] tetrahedrons along [001] direction by sharing vertexes (Fig. 5b). The optical experiment results show that their E_g are 2.44 eV and 2.05 eV, respectively. Their SHG effect are 2.7 and 4.3 × AGS, respectively, with type-I PM behavior.

2.5 Oxychalcogenides

Compared with traditional oxides and chalcogenides, oxychalcogenides have received few attentions in NLO region. In recent years, oxychalcogenides has attracted people's attention. Different research groups have designed and synthesized several IR NLO crystals with mixed anions [MO_xQ_y] (Q = S, Se) as SBUs [90-92]. Herein, the crystal structure and optical properties of this type compounds are analyzed in details.

AEGeOSe₂ (AE = Ba, Sr): Liu et al. synthesized oxychalcogenides BaGeOSe₂ and SrGeOSe₂ by solid-phase method [44, 45]. They have similar crystal structures. As shown in Fig. 6a, their crystal structures are composed of mixed-anion groups [GeO₂Se₂] connected by common edges to form a 1D chain structure, with Ba²⁺ and Sr²⁺ scattered among the chains. The optical band gap of BaGeOSe₂ and SrGeOSe₂ are 3.20 eV and 3.14 eV, respectively. Under 1400 and 2050 nm laser irradiation, both of them exhibit type-I PM behavior and SHG signal output intensity are 1.1 and 1.3 times that of benchmark AGS. Theoretical analysis shows that complex coordinated groups [GeO₂Se₂] make major contributions to their strong SHG effect.

SrZn₂S₂O: Loye et al. obtained NCS polar oxysulfide SrZn₂S₂O by solid-phase synthesis. As shown in Fig. 6b, its 2D layered structure consists of complex coordinated tetrahedral groups [ZnS₃O] connected to each other along the ac plane. The powder frequency doubling absorption spectrum curve shows that SrZn₂S₂O has a large E_g of 3.86 eV. DFT calculations show that the VBs maximum of SrZn₂S₂O is mainly occupied by atomic orbitals of O 2p and S 3p, while the CBs minimum are mainly occupied by atomic orbitals of Zn 4s and Zn 4p, which indicates that its optical properties are mainly determined by mixed-anion [ZnS₃O] groups.

Sr₃Ge₂O₄Se₃: Xing et al. obtained colorless and transparent Sr₃Ge₂O₄Se₃ crystals through solid-phase synthesis [93]. As shown in Fig. 6c, the crystal structure of Sr₃Ge₂O₄Se₃ contains [GeOSe₃] mixed anion group and [GeO₄] tetra-coordinated group, which are connected to form a unique dumbbell-like dimer [Ge₂O₄Se₃]^6-. The energy band gap of Sr₃Ge₂O₄Se₃ is 2.96 eV. Under 1064 nm laser irradiation, Sr₃Ge₂O₄Se₃ exhibits phase matching behavior, and the NLO response is 0.8 times that of AGS. DFT calculation indicates that the VBs maximum of Sr₃Ge₂O₄Se₃ are mainly determined by the atomic orbits of O 2p and Se 4s, and the CBs minimum are predominantly composed of Ge 4s and 4p orbits. It is worth noting that the mixed anion group [GeOSe₃] 's contribution to SHG effect is significantly stronger than that of the single anionic group [GeO₄].

In conclusion, the comprehensive performance of IR NLO crystals with complex coordinated groups as SBUs exhibit superior performance to that of traditional single-anionic compounds. In comparison to traditional phosphides, M^II₃PnI₃ halides-based pnictides inherit the large effect of phosphides, and also have an increased optical band gap. The oxychalcogenides series also exhibit superior optical properties to conventional oxides and chalcogenides.

3 UV/DUV complex coordinated NLO materials

Less

In the field of UV and DUV nonlinear optics, common single-anion NAUs are composed of oxygen-based tri-coordinated groups and tetra-coordinated groups, e.g., [BO₃], [NO₃], [CO₃], [PO₄], [SO₄] [20, 90-96]. In the last few years, a large number of UV/DUV NLO crystals with good performance have been designed and synthesized by different research groups in combination of the above groups with the mixed anion groups [MA_xB_y]. Pan, Ye, Halasyamani and other teams applied KBBF as a template to design and synthesize many DUV NLO crystals with excellent performance. Many of these compounds not only have better comprehensive properties than KBBF, but also are expected to overcome the limitations of the layered growth habit. In addition, Mao, Ye, Zou and Halasyamani have synthesized a series of novel UV and DUV NLO materials by combining tri-coordinated ([NO₃], [CO₃]) and tetra-coordinated groups ([PO₄], [SO₄]) with mixed-anion group [MO_xF_y]. According to the types and structural characteristics of the anions, the crystals can be divided into: (1) KBBF-derived crystals; (2) nitrate and carbonate; (3) phosphates; (4) sulfate. This part specifically summarizes UV/DUV complex coordinated NLO materials in recent five years on the relationship between crystal structure and optical properties (Table 2) in combination to theoretical analysis results.

3.1 KBBF-derived crystals

KBBF has been regarded as the benchmark in this field as one of the most commercialized DUV NLO materials [47, 48]. The discussion on the structure-property analysis of KBBF crystals has been reported in other literatures will not be summarized here. This part focuses on the analysis of a series of new DUV NLO materials derived from KBBF template and taking representative compounds as an example. Figs. 7–10 show their crystal structure. Performance enhancement method originated from ntrinsic property is analyzed by relationship between their crystal structure and optical properties of KBBF. Depending on the type of compound, it is divided into six sections according to the type of compounds.

3.1.1 AB₄O₆F (A = Rb, Cs, K, Na, NH₄) family

Wang and their team designed and synthesized a series of colorless and transparent KBBF-derived fluorooxoborate, including CsB₄O₆F, RbB₄O₆F, CsKB₈O₁₂F₂, NaB₄O₆F, NH₄B₄O₆F [32, 49–51]. These crystals were prepared by solid phase reaction method. CsKB₈O₁₂F₂ and NaB₄O₆F belong to NCS space groups P32₁ and C2, respectively. The crystal structure of these compounds is similar to KBBF, in which the cation K⁺ is replaced by Cs⁺, Rb⁺, Cs⁺ and K⁺ mixed cations, Na⁺ and NH₄⁺, respectively. As shown in Fig. 7, the interlayer spacing of CsB₄O₆F, CsKB₈O₁₂F₂ and NH₄B₄O₆F is significantly smaller than that of KBBF (6.25 Å), indicating that their interlayer forces are stronger than KBBF's. In addition, the substitution of [BO₃F] for [BeO₃F] can eliminate the toxicity of Be element. Optical experiments show that they all have a wide transparent region in the UV/DUV band, and these compounds have short ultraviolet cut-off edge: CsB₄O₆F (155 nm), RbB₄O₆F (< 200 nm), CsKB₈O₁₂F₂ (< 200 nm), NaB₄O₆F (< 180 nm), NH₄B₄O₆F (156 nm). In addition, all of these compounds have phase matching capability. As shown in Table 2, the SHG effect of CsB₄O₆F, CsKB₈O₁₂F₂ and NH₄B₄O₆F is stronger than that of KBBF (1.2 × KDP@1064 nm) under the irradiation of 1064 nm laser. More importantly, the theoretical analysis shows that their shortest second harmonic phasematching wavelength are less than 200 nm. All these properties indicate that these crystals are promising to be the next generation DUV materials. DFT calculation shows that the optical properties of AB₄O₆F (A = Rb, Cs, K, Na, NH₄) family are mainly determined by the anion layer [B₄O₆F]^-_∞.

3.1.2 M(B₅O₇)F₃ (M = Sr, Ca, Pb)

Pan's team designed and synthesized KBBF-type SrB₅O₇F₃ and CaB₅O₇F₃ crystals [52, 54]. SrB₅O₇F₃ and CaB₅O₇F₃ have a 2D layered structure. The structural units [B₅O₇F₃] are composed of three [BO₃F] units and two [BO₃] units. These [B₅O₇F₃] units form 2D layer in the ac plane by co-apex connection (Fig. 8a). The NLO response of SrB₅O₇F₃ and CaB₅O₇F₃ are 1.6 and 2.0 × KDP@ 1064 nm, respectively. Their ultraviolet cut-off edges are less than 180 nm. In addition, theoretical calculations show that their shortest second harmonic phasematching wavelengths are 180 nm and 183 nm, respectively. All these properties indicate that SrB₅O₇F₃ and CaB₅O₇F₃ have the potential to be the next generation DUV materials. According to DFT calculation, the VBs maximum of CaB₅O₇F₃ is mainly determined by O 2p and F 2p atomic orbitals, while CBs minimum is mainly determined by Ca 3p and B 2p atomic orbitals. Therefore, the optical properties of CaB₅O₇F₃ are determined by the Ca²⁺ and [B₅O₇F₃] units. This is different from AB₄O₆F (A = Rb, Cs, K, Na, NH₄) family compounds.

Pan et al. designed and synthesized a Pb-based PbB₅O₇F₃ crystal that is isomorphic to SrB₅O₇F₃ [53]. Its anionic layered framework is similar to SrB₅O₇F₃, and stereochemically active lone-pair (SCALP) cations are connected by Pb-F bonds to form a 3D framework structure (Fig. 8b). The distance between adjacent layers (4.38 Å) is significantly smaller than that of KBBF (6.25 Å). PbB₅O₇F₃ has a strong SHG effect (6.0 × KDP@1064 nm), showing a PM capability. In addition, the ultraviolet cut-off edge of PbB₅O₇F₃ is less than 225 nm, which is significantly less than other Pb-based NLO compounds. According to theoretical calculations, the VBs maximum of PbB₅O₇F₃ are predominately determined by O 2p, F 2p, B 2p and Pb 6s, p orbitals. The CBs minimum is mainly determined by O 2p, B 2p, Pb 6s, p atomic orbitals. Obviously, due to the influence of Pb, the band gap of PbB₅O₇F₃ is smaller than that of Sr-based compounds. Further theoretical analysis shows that due to the high electronegativity of F and the O-B-F bands, the band gap of PbB₅O₇F₃ is larger than other Pb-containing compounds. The SHG-density method proves that the strong SHG response of PbB₅O₇F₃ is mainly derived from the cooperation of [BO₃], [BO₃F], [PbO₆F₃] groups.

3.1.3 Ba₃Mg₃(BO₃)₃F₃, CsAlB₃O₆F

Mutailipu et al. designed and synthesized polymorphs Ba₃Mg₃(BO₃)₃F₃ by solid-phase synthesis method using SBBO as a template [55]. α- and β-Ba₃Mg₃(BO₃)₃F₃ have similar 2D layered structure. Their crystal structures are connected by [BO₃] groups and [MgO₄F₂] polyhedrons to form 2D layers in bc and ab planes, respectively, and further connected by Mg-F bond to form 3D framework structure (Fig. 9a). It is worth noting that α-Ba₃Mg₃(BO₃)₃F₃ has grown high-quality large-size (16 × 14 × 8 mm³) crystals. Optical experiment tests show that phasematching α-Ba₃Mg₃(BO₃)₃F₃ has a strong SHG response (1.8 × KDP@1064 nm) and a short ultraviolet cut-off edge (184 nm). All these properties indicate that α-Ba₃Mg₃(BO₃)₃F₃ is a potential DUV material.

Liu et al. designed and synthesized KBBF-type CsAlB₃O₆F crystal through flux method [56]. CsAlB₃O₆F also has a KBBF-type 2D layered structure. Cs⁺ is replaced by K⁺, and [BeO₃F] is replaced by [AlO₃F]. [AlO₃F] and [BO₃] groups are connected in the bc plane to form a 2D layer, and Cs⁺ is located in the 18 membered ring tunnel which composed of [AlO₃F] and [BO₃] units (Fig. 9b). Notably, the interlaminar distance of CsAlB₃O₆F (4.03 Å) is significantly smaller than that of KBBF (6.25 Å), indicating that the interlaminar force of CsAlB₃O₆F is stronger than that of KBBF. Consequently, the growth characteristic of CsAlB₃O₆F would be better than that of KBBF. Optical experiments show that phasematching CsAlB₃O₆F has a strong SHG response (2.0 × KDP@1064 nm) and a short ultraviolet cut-off edge (< 190 nm). In addition, theoretical calculation shows that the shortest second harmonic phasematching wavelength is 182 nm. All these properties indicate that CsAlB₃O₆F is a potential DUV material. According to calculation of density of states, the VBs maximum of CsAlB₃O₆F is mainly occupied by O 2p and F 2p orbitals, while the CBs minimum is mainly occupied by atomic orbitals of Ca 3p and B 2p.

3.1.4 LaB₄O₆(OH)₂Cl

Guo et al. designed and synthesized colorless transparent KBBF type LaB₄O₆(OH)₂Cl crystal by hydrothermal method [97]. The crystal structure of LaB₄O₆(OH)₂Cl is composed of 18-membered ring [B₄O₈(OH)₂] structural motifs which formed by two [BO₃(OH)] tetrahedrons and three [BO₃] groups. These structural motifs are connected to each other to form a 2D layer (Fig. 9c). Optical experiments show that phasematching LaB₄O₆(OH)₂Cl has a strong frequency doubling effect (2.3 × KDP@1064 nm) and short UV cutoff edge (< 180 nm). It can be seen from DFT calculation that the VBs maximum of LaB₄O₆(OH)₂Cl are mainly determined by the atomic orbits of O 2p and Cl 3p, and the CBs minimum are predominantly composed of La 5p and B 2p orbits.

3.1.5 Pb₂BO₃I

Halasyamani and his team designed and synthesized Pb-based KBBF-type Pb₂BO₃I crystal by hydrothermal method [98]. The 3D framework crystal structure of Pb₂BO₃I is formed by [PbO₃I₂] and [BO₃] groups in ab plane. Compared with KBBF, the [PbO₃I₂] groups in Pb₂BO₃I replaces [BeO₃F] groups, and the K-F bond is replaced by Pb-I bond (Fig. 9d). The calculation results show that the interlayer force of Pb₂BO₃I is stronger than that of KBBF. It should be noted that Pb₂BO₃I has the strongest SHG efficiency (10.0 × KDP@1064 nm) of KBBF family NLO compounds. It shows type-I phase matching ability. Th optical experiment test proves that the ultraviolet cut-off edge of Pb₂BO₃I is 330 nm. Pb₂BO₃I has the potential to become the ultraviolet NLO materials.

3.1.6 NH₄Be₂BO₃F₂, γ-Be₂BO₃F, C(NH₂)₃SO₃F

Ye et al. designed and synthesized colorless and transparent KBBF-type NH₄Be₂BO₃F₂ and γ-Be₂BO₃F crystals by high temperature hydrothermal method [57]. NH₄Be₂BO₃F₂ and γ-Be₂BO₃F have similar structure with KBBF, but their interlayer force is stronger than KBBF. Especially for γ-Be₂BO₃F, the cation at A site is directly removed from its crystal structure, and the layers are directly connected by Be-F-Be bonds, which eliminates the disadvantage of KBBF layer-by-layer growth habit (Figs. 10c and d). Under 1064 nm laser irradiation, phase matching NH₄Be₂BO₃F₂ and γ-Be₂BO₃F have strong SHG response (1.2 and 2.3 × KDP, respectively. The ultraviolet cut-off edges of these two compounds are less than 190 nm. DFT calculation shows that their shortest second harmonic phase matching wavelengths are 173.9 nm and 146 nm, respectively. All these optical properties indicate that they have potential to become DUV NLO materials.

Recently, Ye et al. have grown colorless plate-like KBBF type C(NH₂)₃SO₃F crystal in solution [77]. [SO₃] units replace [BO₃] units, and [SO₃F] units replace [BeO₃F] units from KBBF to C(NH₂)₃SO₃F. The difference is that the [BeO₃F] tetrahedrons in KBBF are arranged in opposite intervals, while the [SO₃F] groups in C(NH₂)₃SO₃F are arranged in the same direction (Fig. 10b), which is in favor of the superposition of d_ij. C(NH₂)₃SO₃F exhibits strong SHG response (5 × KDP) and moderate birefringence (0.133). The ultraviolet cut-off edge of C(NH₂)₃SO₃F is 200 nm. Theoretical calculation shows that its shortest second harmonic phase matching wavelength is less than 200 nm.

In general, it is a very effective method to design DUV NLO materials using KBBF as a template. Many crystals in this part inherit the excellent properties of KBBF and overcome some intrinsic performance limitations. In the AB₄O₆F (A = Rb, Cs, Na, NH₄), A(B₅O₇)F₃ (A = Sr, Ca, Pb) series compounds, K⁺ is replaced by other alkali metal/alkaline earth metal cations or NH₄⁺, and mixed anion SBUs [BeO₃F] are replaced by [BO₃F]. These compounds exhibit a good balance among short ultraviolet cut-off edge, strong SHG response and suitable phase matching ability. In addition, the substitution of the non-toxic element B with Be and much stronger interlayer forces make these compounds more applicable in practical use. γ-Be₂BO₃F and C(NH₂)₃SO₃F are potential candidate as DUV NLO materials with strong interlayer forces and excellent comprehensive properties. Pb(B₅O₇)F₃ and Pb₂BO₃I showed strong SHG response with 6.0 and 10.0 × KDP, respectively.

3.2 Nitrate and carbonate

In this part, the NLO crystals containing tri-coordinated groups [NO₃], [CO₃] and complex coordinated groups [MA_xB_y] are analyzed. The four compounds Pb₂(NO₃)₂(H₂O)F₂ [99], Rb₃SbF₃(NO₃)₃ [100], KMgCO₃F [101] and NaZnCO₃F [102] emerged in recent years are represented.

3.2.1 Pb₂(NO₃)₂(H₂O)F₂

Ye and his team designed and synthesized the first fluoronitrate crystal of Pb₂(NO₃)₂(H₂O)F₂ by hydrothermal method [103]. The 3D framework crystal structure of Pb₂(NO₃)₂(H₂O)F₂ consists of mixed-anion [PbO₉F₂] and [NO₃] groups (Fig. 11a). Optical experimental tests show that phasematching Pb₂(NO₃)₂(H₂O)F₂ has a very strong frequency doubling effect (12.0 × KDP@1064 nm) and a short ultraviolet cut-off edge (300 nm). The DFT calculation shows that the VBs maximum and CBs minimum of Pb₂(NO₃)₂(H₂O)F₂ are predominately determined by the atomic orbitals of O, N, Pb and F. Therefore, the linear and NLO properties of Pb₂(NO₃)₂(H₂O)F₂ are mainly affected by the [NO₃] groups, the Pb-O and Pb-F bonds.

3.2.2 Rb₃SbF₃(NO₃)₃

Wang et al. designed and synthesized Sb-based Rb₃SbF₃(NO₃)₃ crystal [100]. Rb₃SbF₃(NO₃)₃ has a 0D isolated molecular structure, which consists of two [SbO₃F₃] polyhedrons and three [NO₃] groups with holes hosting Rb⁺ cations (Fig. 11b). The NLO response of Rb₃SbF₃(NO₃)₃ is 2.2 × KDP@1064 nm, and it shows PM behavior. The bandgap of Rb₃SbF₃(NO₃)₃ is 3.75 eV (corresponding to 331 nm of ultraviolet cut-off edge). Rb₃SbF₃(NO₃)₃ has the potential to become the next generation UV NLO material. DFT calculation shows that the VBs maximum and CBs minimum of Rb₃SbF₃(NO₃)₃ are determined by the atomic orbitals of O, N, Sb and F, thus its optical properties are mainly affected by [NO₃] and [SbO₃F₃] groups.

3.2.3 KMgCO₃F, NaZnCO₃F

Halasyamani and Tran et al. designed and synthesized alkali metal fluorocarbonates KMgCO₃F [101] and NaZnCO₃F [102], respectively. They have a similar crystal structure. The crystal structure of KMgCO₃F is composed of mixed anion [MgO₃F₂] group and [CO₃] group to form a 3D framework structure (Fig. 11c). The optical experiment test shows that both KMgCO₃F and NaZnCO₃F have phase matching ability and show a strong frequency doubling effect (3.0, 2.75 × KDP@1064 nm). In addition, they have short ultraviolet cut-off edges (< 180 nm, 230 nm). All these properties indicate that KMgCO₃F and NaZnCO₃F have the potential to become NLO materials for the next generation of UV applications.

In a word, compounds obtained by the combination of tri-coordinated groups [NO₃], [CO₃] and complex coordinated groups [MA_xB_y] are critical for UV NLO materials exploration. All crystals of this type have good phase matching capability. Pb₂(NO₃)₂(H₂O)F₂ had the largest SHG effect, which was 12 × KDP. In addition, Rb₃SbF₃(NO₃)₃, KMgCO₃F and NaZnCO₃F can keep a balance between the strong SHG response and the short ultraviolet cut-off edge, and they are potential candidates for UV NLO crystals.

3.3 Phosphates

This part mainly studies the new type of NLO crystals containing p-block coordination tetrahedral group [PO₄] and mixed anion group [MA_xB_y]. These compounds can be divided into the following three parts according to the combined tetrahedral units, such as [PO₄], [P₂O₇]. The comprehensive performance, including optical band gap, SHG effect and phase matching ability, are evaluated in combination with crystal structure and complex coordinated groups arrangement ([MA_xB_y] and [PO₄] groups).

3.3.1 BaZn(PO₄)F, RbBPO₄F, (NH₄)₂BPO₄F₂

Tang et al. synthesized the fluorophosphate BaZn(PO₄)F crystal by hydrothermal method [103]. The crystal structure of BaZn(PO₄)F consists of the interconnection of [PO₄] groups and [ZnO₄F] mixed-anion polyhedrons to form a 3D framework structure (Fig. 12a). Optical experiments show that the ultraviolet cut-off edge of BaZn(PO₄)F is less than 190 nm, and the d_ij is 0.26 × KDP, showing type-I PM capability. DFT calculation indicates that the VBs maximum and CBs minimum of BaZn(PO₄)F are mainly determined by the atomic orbitals of Zn, P, O and F, which indicates that the effect of alkaline earth metal element Ba on its optical properties is negligible.

Subsequently, Wu et al. synthesized fluoroborophosphates RbBPO₄F and (NH₄)₂BPO₄F₂ crystals by hydrothermal method [104]. In the crystal structure of RbBPO₄F, the mixed-anion [BO₃F] and [PO₄] groups are connected to each other to form a 3D tunnel structure. The alkali metal Rb⁺ is located in the tunnel (Fig. 12b). As shown in Fig. 12c, the 1D chain structure of (NH₄)₂BPO₄F₂ is composed of [PO₄] tetrahedrons and complex coordinated [BO₂F₂] groups. Optical experimental tests show that the ultraviolet cut-off edges of RbBPO₄F and (NH₄)₂BPO₄F₂ are both less than 200 nm, and their SHG effects are 0.4, 0.8 × KDP@1064 nm, respectively. RbBPO₄F exhibits non-phasematching behavior due to its cubic structure, while (NH₄)₂BPO₄F exhibits type-I phase matching ability. Theoretical calculations reveal that the NLO response of these two compounds mainly comes from the [PO₄]⁺ groups.

3.3.2 Ba₂NaP₂O₇Cl, CsSiP₂O₇F, K₂Sb(P₂O₇)F

Chen et al. synthesized colorless and transparent fresnoite-like structure Ba₂NaP₂O₇Cl crystal by a high temperature solid-state reaction technology [59]. Ba₂NaP₂O₇Cl is a 3D tunnel structure formed by the connection of [P₂O₇] dimer groups and [NaO₄Cl₂] polyhedra, and Ba²⁺ is located in the center of the pore (Fig. 13a). Ba₂NaP₂O₇Cl can maintain a good balance among short ultraviolet cut-off edge (< 176 nm), strong SHG response (0.9 × KDP@1064 nm), and sufficient birefringence value (0.017). All these properties indicate that Ba₂NaP₂O₇Cl has the potential to be DUV NLO materials.

Ding et al. synthesized CsSiP₂O₇F crystal by high temperature solid-state reaction technology [60]. As shown in Fig. 13b, the 3D frame structure of CsSiP₂O₇F is composed of the [P₂O₇] dimer unit and [SiO₅F] polyhedrons, and Cs⁺ are scattered in the tunnel holes. CsSiP₂O₇F can also maintain a good balance between short cut-off edge (< 190 nm), strong SHG effect (0.7 × KDP@1064 nm), and good phase matching ability. DFT calculation shows that the VBs maximum of CsSiP₂O₇F is mainly occupied by the atomic orbitals of Cs, P and Si, and the CBs minimum is occupied by the atomic orbitals of O and F, which indicates that all atoms have an effect on the linear optical properties. The SHG-density method proves that the anions [P₂O₇] dimer units and [SiO₅F] groups make major contributions to whole SHG effect.

Deng et al. synthesized colorless and transparent K₂Sb(P₂O₇)F crystal by means of solvent-free synthesis technology [105]. K₂Sb(P₂O₇)F has a 2D layered structure, which is built by [P₂O₇] dimer and [SbO₄F] polyhedra along the ab plane (Fig. 13c). Optical experiments show that K₂Sb(P₂O₇)F has a strong frequency doubling effect (4 × KDP@1064 nm), showing the PM behavior. The ultraviolet cut-off edge of K₂Sb(P₂O₇)F is 261 nm. DFT calculations show that VBs maximum of K₂Sb(P₂O₇)F is mainly occupied by atomic orbitals of F, P and O, and the CBs minimum is mainly occupied by atomic orbitals of Sb and F, which indicates that the effect of alkali metal K on its optical properties is minimal.

3.3.3 Na₃Sc₂(PO₄)₂F₃

Xu et al. synthesized rare earth fluorophosphate Na₃Sc₂(PO₄)₂F₃ under hydrothermal conditions [106]. The 3D framework structure of Na₃Sc₂(PO₄)₂F₃ is composed of [PO₄] tetrahedrons and [ScO₄F₂] mixed-anion polyhedrons. Na⁺ is scattered in the tunnel holes (Fig. 14). The SHG response of Na₃Sc₂(PO₄)₂F₃ is 0.26 × KDP under 1064 nm laser irradiation, and it has type-I phase matching ability. Na₃Sc₂(PO₄)₂F₃ exhibits short cutoff edge of 255 nm and a large birefringence value (0.0978). All these properties indicate that Na₃Sc₂(PO₄)₂F₃ has the potential to be a UV NLO material.

To summarize, compounds containing mixed anion groups [MA_xB_y] and [PO₄] are important candidates for UV/DUV NLO materials. This type of compound has strong optical anisotropy and exhibits good phase matching ability. It is worth noting that when the mixed anion groups [MA_xB_y] and [PO₄] are arranged in 2D layers, it is easier to maintain a balance between strong SHG response and the short ultraviolet cut-off edge. For example, Ba₂NaP₂O₇Cl, CsSiP₂O₇F, K₂Sb(P₂O₇)F all show excellent comprehensive performance.

3.4 Sulfate

In addition to phosphates containing [PO₄] tetrahedrons, metal sulfates are also well-known UV/DUV NLO materials. In this part, CsSbF₂SO₄ [107], NH₄SbF₂SO₄ [108] and RbSbSO₄Cl₂ [109] are taken as representative compounds to analyze the influence of the binding and arrangement manner of [SO₄] tetra-coordination groups and mixed-anion group [MA_xB_y] on optical band gap, SHG effect and phase matching ability.

3.4.1 CsSbF₂SO₄, NH₄SbF₂SO₄

Dong et al. designed and synthesized CsSbF₂SO₄ [107] by electrothermal synthesis. The 1D chain structure of CsSbF₂SO₄ is composed of twisted [SbO₂F₂] groups and [SO₄] tetrahedral groups. Cs⁺ is distributed among the chains (Fig. 15a). The ultraviolet cut-off edge of CsSbF₂SO₄ is 240 nm. Under 1064 nm laser irradiation, it exhibits strong frequency doubling effect (3 × KDP) with phase matching behavior. The theoretical calculation indicates that the NLO response of CsSbF₂SO₄ mainly comes from the highly distorted [SbO₂F₂] units, while the [SO₄] group is beneficial to the parallel arrangement of [SbO₂F₂] units.

Jantz et al. designed and synthesized NCS ammonia fluorine chalcogenide salt NH₄SbF₂SO₄ [108]. The 1D chain structure of NH₄SbF₂SO₄ is formed by connecting twisted [SbO₂F₂] groups and [SO₄] tetrahedral groups, with NH₄⁺ distributed between the chains (Fig. 15b). The optical experiment test shows that the ultraviolet cut-off edge of NH₄SbF₂SO₄ is 266 nm. It has PM capability, and the SHG effect is about 0.7 × KDP.

3.4.2 RbSbSO₄Cl₂

He et al. synthesized RbSbSO₄Cl₂ by hydrothermal method [109]. RbSbSO₄Cl₂ has a 1D chain structure, which is composed of twisted [SbO₃Cl₂] polyhedrons and [SO₄] units, while Rb⁺ is scattered among the chains (Fig. 15c). The ultraviolet cut-off edge of RbSbSO₄Cl₂ is 347 nm. Under 1064 nm laser irradiation, the frequency doubling effect is 2.7 × KDP with type-I PM capability. RbSbSO₄Cl₂ has the potential to become UV NLO materials. Theoretical calculations show that the VBs maximum and CBs minimum of RbSbSO₄Cl₂ are determined by the atomic orbitals of Rb, O, Sb, S and Cl. Therefore, the optical properties of RbSbSO₄Cl₂ mainly depend on [RbO₅Cl₄], [SbO₃Cl₂], [SO₄] groups.

3.5 Complex coordinated group [BO₃F] as NLO active units

Sn[B₂O₃F₂]: HöPPE and his team synthesized colorless massive Sn[B₂O₃F₂] crystals [109]. The power X-ray diffraction test shows that Sn[B₂O₃F₂] crystallizes in space group P31m (No. 157). The crystal structure of Sn[B₂O₃F₂] is composed of two-dimensional layers connected by the [BO₃F] cells along the ab plane, and Sn²⁺ is distributed among the layers to maintain the charge balance (Fig. 16a). The UV cutoff edge of Sn[B₂O₃F₂] is 243 nm. Under 1054 nm laser irradiation, its SHG effect is even stronger that of KDP, and it has phase matching ability. Sn[B₂O₃F₂] has the potential to become the next generation of UV NLO materials. Theoretical calculations show that the VBs maximum and CBs minimum of Sn[B₂O₃F₂] are mainly determined by the atomic orbitals of Rb, O, Sb, S and Cl. Its optical properties mainly depend on [RbO₅Cl₄], [SbO₃Cl₂] and [SO₄] groups.

3.6 Mixed-anion group [TeO₂F₂] as NLO active units

BaF₂TeF₂(OH)₂: In 2020, He et al. designed and synthesized colorless and transparent BaF₂TeF₂(OH)₂ crystal by hydrothermal method [110]. Power X-ray diffraction results show that BaF₂TeF₂(OH)₂ belongs to NCS space group Pmn2₁ (No. 31). BaF₂TeF₂(OH)₂ has a typical aurivillius structure. The [TeF₂(OH)₂] groups are connected with each other in the ac plane to form a two-dimensional layer, and the [BaF₄] tetrahedrons are also connected by common edge to form 2D layers. The crystal structure of BaF₂TeF₂(OH)₂ is composed of the two layers which are mutually spaced along the b-axis (Fig. 16b). The UV cut-off edge of BaF₂TeF₂(OH)₂ is 205 nm. Under 1064 nm laser irradiation, it shows strong SHG effect (3 × KDP) and good phase matching ability. All these properties indicate that BaF₂TeF₂(OH)₂ has the potential to become the next generation of UV NLO materials.

3.7 Mixed-anion group [PO₃F] as NLO active units

NaNH₄PO₃F·H₂O: Lu et al. designed and synthesized colorless and transparent NaNH₄PO₃F·H₂O crystal [61]. Power x-ray diffraction results show that NaNH₄PO₃F·H₂O belongs to monoclinic space group Pc (No. 7). The crystal structure of NaNH₄PO₃F·H₂O is composed of [PO₃F] groups, which are connected with [NH₄] and H₂O molecules through hydrogen bonds, and finally form a two-dimensional layered structure, with Na⁺ scattered among the layers (Fig. 16c). NaNH₄PO₃F·H₂O exhibits a strong SHG effect of 1.1 times that of KDP under 1064 nm laser irradiation. Theoretical calculation shows that its shortest second harmonic phase matching wavelength is 194 nm. There is no doubt that NaNH₄PO₃F·H₂O has the potential to apply in the next generation of DUV NLO materials.

4 Summary and outlook

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To sum up, complex coordinated functional groups [MA_xB_y] are excellent NLO active units, and compounds containing this group are more likely to guarantee excellent comprehensive performance. This group is combined with traditional NLO active group ([MQ₄] (M = metal cationic, Q = S, Se, Te, P), [IO₃], [SeO₃], [TeO₃], [CO₃], [NO₃], [SO₄], [PO₄], B-O groups, etc.) is an important direction to explore new high-performance nonlinear optical materials. In this paper, a comprehensive review of NLO crystal materials with mixed anion functional groups [MA_xB_y] as the basic structural unit is made based on theoretical analysis results, anion combination methods, and available experimental performance test results. Through systematic summary, it can be concluded that: (1) The combination of complex coordinated groups [MA_xB_y] and [C(1)O₃] (C(1) = I, Se, Te) oxygen-containing groups is conducive to the synthesis of large band gap mid-IR NLO crystals with good phase matching ability. In order to solve the shortcoming of small NLO effect of this kind of compound, it is necessary to introduce d⁰-transition metal element, e.g., W⁶⁺, V⁵⁺, or metal element containing stereochemically active lone pairs, which is easy to produce strong distorted multi-coordination groups e.g., Bi and Pb. (2) The combination of the complex coordinated groups [MA_xB_y] and [MQ₄] (Q = S, P) tetra-coordinated units to form a 3D frame structure is conducive to the synthesis of ideal MIR NLO crystals with phase matching ability, large band gap and strong SHG effect. (3) The comprehensive performance of IR NLO crystals with complex coordinated groups [MA_xB_y] as SBUs is improved compared with that of traditional single anionic compounds. (4) When the mixed anion functional groups [MO_xF_4-x] and [C(2)O₃] (C(2) = B, N, C) tri-coordinated oxygen-containing groups are arranged in a KBBF-like structure model (three coordination groups and four coordination groups containing halogen F are connected to form a 2D layer), it is beneficial to the formation of excellent deep ultraviolet NLO crystals (short ultraviolet cut-off edge, strong SHG effect, small second harmonic phasematching wavelength). (5) When the complex coordinated functional groups [MA_xB_y] and [C(3)O₄] (C(3) = P, S) tetra-coordination groups are arranged in 2D layers, and there are scattered alkali/alkaline earth metal cations in the structure, it is more likely to achieve a balance between short cut-off edge and strong SHG effect. (6) UV/DUV NLO crystals composed of a 2D layered arrangement of complex coordinated groups [MA_xB_y] exhibit excellent comprehensive properties. It is believed that the combination mode of the anion NLO active units and the regulation of the arrangement rules on the optical properties above will be of guiding significance for the future design of MIR/DUV NLO materials.

For the future design and synthesis of complex coordinated NLO crystals, we should focus on the following aspects: (1) For the field of IR nonlinear optics, the research of tetra-coordinated compounds is relatively less, and we should pay more attention to the diamond-like compounds composed of [MA_xB_4-x] (A, B is one of the elements of P, O, S, Se, F, Cl, Br, I) with four coordination groups arranged in parallel. (2) For the field of UV/deep UV nonlinear optics, more alternative structural templates similar to KBBF should be explored. In addition, at present, there are only a few compounds in type IV NLO materials with only [MA_xB_4-x] as SBUs, which has a lot of exploration potential in the future. (3) The practical application of NLO materials needs large single crystals with good quality, so the best growth conditions of NLO crystals with mixed anion group [MA_xB_y] as SBUs should be explored in the future. (4) The design and synthesis of [MA_xB_4-x] as SBUs NLO crystal is a time-consuming and laborious work. In order to improve the efficiency, it is necessary to combine theoretical analysis with experimental exploration.

Declaration of competing interest

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The authors declare no conflict of interest.

Acknowledgment

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This work was supported by National Natural Science Foundation of China (No. 51972208).

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doi: 10.1016/j.cclet.2021.11.089

Receive Date：2021-09-13
Online Date：2025-12-19
Published：2022-05-15

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Received：2021-09-13
Revised：2021-10-21
Accepted：2021-11-29

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^aCollege of Chemistry and Chemical Engineering, Shanghai University of Engineering Science, Shanghai 201620, China

^bDepartment of Chemistry and Biochemistry, Wichita State University, Wichita, KS 67260, United States

^cState Key Laboratory of Structural Chemistry, Fujian Institute of Research on the Structure of Matter, Chinese Academy of Sciences, Fuzhou 350002, China

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表12种不同金属材料的力学参数

科 Family	属数 Number of genus	种数 Number of species	占总种数比例 Percentage of total species (%)	属 Genus	种数 Number of species	占总种数比例 Percentage of total species (%)
鹅膏菌科Amanitaceae	2	11	5.26	鹅膏菌属 Amanita	10	4.78
小菇科 Mycenaceae	2	12	5.74	丝盖伞属 Inocybe	5	2.39
多孔菌科 Polyporaceae	8	14	6.70	蜡蘑属 Laccaria	5	2.39
红菇科 Russulaceae	3	23	11.00	小皮伞属 Marasmius	6	2.87
				小菇属 Mycena	11	5.26
				光柄菇属 Pluteus	5	2.39
				红菇属 Russula	17	8.13
				栓菌属 Trametes	5	2.39

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Fig. 1 Crystal structure of NLO materials with [MA_xB_y] and [IO₃] as NLO active units.

Fig. 2 Crystal structure and NLO performance of (a) Pb₂GaF₂(SeO₃)₂Cl, (b) Ba(MoO₂F)₂(TeO₃)₂ and (c) RbGa₃F₆(SeO₃)₂.

Fig. 3 Crystal structure and NLO performance of 5 representative 3D framework selenities.

Fig. 4 Crystal structure and NLO performance of Sr₆Cd₂Sb₆O₇S₁₀ and Sr₅Ga₈O3S₁₄.

Fig. 5 Crystal structure of ZnPI₃ and CdPI₃.

Fig. 6 Crystal structure and NLO performance of (a) AEGeOSe₂(AE = Ba, Sr), (b) SrZn₂S₂O and (c) Sr₃Ge₂O₄Se₃.

Fig. 7 Crystal structure of AB₄O₆F (A = Rb, Cs, K, Na, NH₄) series compounds.

Fig. 8 Crystal structure and NLO performance of SrB₅O₇F₃ and PbB₅O₇F₃.

Fig. 9 Crystal structures and NLO performance of α-Ba₃Mg₃(BO₃)₃F₃, CsAlB₃O₆F, LaB₄O₆(OH)₂Cl and Pb₂BO₃I.

Fig. 10 Crystal structure of NH₄Be₂BO₃F₂, γ-Be₂BO₃F and C(NH₂)₃SO₃F.

Fig. 11 Crystal structures and NLO performance of (a) Pb₂(NO₃)₂(H₂O)F₂, (b) Rb₃SbF₃(NO₃)₃ and (c) KMgCO₃F.

Fig. 12 Crystal structures and NLO performance of (a) BaZn(PO₄)F, (b) RbBPO₄F and (c) (NH₄)₂BPO₄F₂.

Fig. 13 Crystal structures and NLO performance of (a) Ba₂NaP₂O₇Cl, (b) CsSiP₂O₇F and (c) K₂Sb(P₂O₇)F.

Fig. 14 Crystal structure and NLO performance of Na₃Sc₂(PO₄)₂F₃.

Fig. 15 Crystal structures and NLO performance of CsSbF₂SO₄, NH₄SbF₂SO₄ and RbSbSO₄Cl₂.

Fig. 16 Crystal structures and NLO performance of Sn[B₂O₃F₂], NaNH₄PO₃F·H₂O and BaF₂TeF₂(OH)₂.

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