A-site cation manipulation of exemplary second harmonic generation response and optical anisotropy in rare-earth borates

Abstract

Ultraviolet nonlinear optical (UV NLO) materials have garnered significant interest for their prospective applications in advanced laser technologies. However, tailoring the desired structure in these materials remains a formidable challenge. Here, we propose a simple yet effective strategy for synthesizing rare-earth borates, K_xNa_3−xLa₂B₃O₉ (x = 2–3), by manipulating the A-site cations to induce structural evolution. Notably, K_xNa_3−xLa₂B₃O₉ undergoes a phase transition from the Pnc2 to the Amm2 space group by adjusting the K⁺ content to reach x = 2.6. Moreover, the target compounds exhibit strong phase-matching second harmonic generation (SHG) efficiencies, ranging from 1.3 to 3.3 times that of KDP (KH₂PO₄), and feature short UV cutoff edges of around 204–208 nm. Additionally, the correlation between microscopic polarizability, optical anisotropy, and the structural evolution of these materials was characterized through structural and theoretical analyses. These findings highlight the potential applications of K_xNa_3−xLa₂B₃O₉ as UV NLO materials and underscore the viability of manipulating A-site cations to fabricate NLO crystals with desirable properties.

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Introduction

Nonlinear optical (NLO) crystals have garnered considerable attention in scientific and industrial applications due to their ability to manipulate laser frequency and produce coherent light. In particular, ultraviolet (UV) NLO materials have emerged as crucial contenders for extending the wavelength range of solid-state lasers into the UV region, facilitated by a second harmonic generation (SHG) process.^1–3 These materials hold significant promise in various optoelectronic fields such as laser processing, short-wave communication, semiconductor lithography, biomedicine, and high-density storage.^4–7 Despite considerable efforts and advancements in exploring acentric materials, the practical realization of UV NLO crystals remains limited. Noteworthy examples include KH₂PO₄ (KDP), β-BaB₂O₄ (β-BBO), LiB₃O₅ (LBO), KBe₂BO₃F₂ (KBBF), and CsLiB₆O₁₀ (CLBO), among others.^8–12 In response to the development of laser technology, there is an increasing demand for novel NLO crystals capable of directly generating UV coherent light. However, the fabrication of NLO crystals faces challenges stemming from the inherent propensity of inorganic materials to exhibit undesired dipole–dipole interactions or spatial effects, tending to crystallize centrosymmetric structures.^13,14 Consequently, the development of innovative synthetic strategies to exploit NLO crystals with SHG-enhanced activity remains a significant challenge.

Borates, characterized by their versatile structural configurations and favorable UV transparency attributed to strong covalent B–O bonds, have emerged as a candidate system for exploring UV optical crystals.^15–19 To effectively innovate and construct novel NLO crystals, the introduction of highly polarizable chromophores into borates is an optional strategy to modify the structure and enhance the optical properties. Strategies such as incorporating second-order Jahn–Teller (SOJT) active cations (Zr⁴⁺, Nb⁵⁺, Ta⁴⁺, etc.), stereo-chemically active lone-pair cations (Te⁴⁺, Bi³⁺, etc.), or d¹⁰ transition metal cations (Zn²⁺, Cd²⁺, etc.) have been widely recognized in the quest for new optical materials.^20–22 Following these design strategies, numerous borates with acentric structures have been synthesized, including BaZr(BO₃)₂, CsNbB₂O₆, K₃M₃B₂O₁₂ (M = Nb, Ta), α-BiB₃O₆, CaBi₂B₂O₇, Cd₄BiO(BO₃)₃, Bi₃TeBO₉, Na₂ZnB₆O₁₁, Cs₃Zn₆B₉O₂₁, and CaZn₂(BO₃)₂.^2,23–31 However, the strategies for excavating UV NLO crystals are still limited due to challenges in accurately regulating the structure.

Recent studies have elucidated the indispensable role of alkali metal cations (A-site cations) in the exploration of novel NLO materials, due to the fact that alkali metal cations are devoid of d–d or f–f electron transitions, enabling the broadening of the bandgap and consequently achieving short absorption edges.³² Additionally, alkali metal cations with various ionic radii also have a significant impact on the spatial molecular arrangements and macroscopic symmetry. Notable examples include RbB₄O₆F (0.8 × KDP), CsB₄O₆F (1.9 × KDP), CsRbB₈O₁₂F₂ (1.1 × KDP), K₇SrY₂B₁₅O₃₀ (1.1 × KDP), Rb₇SrY₂(B₅O₁₀)₃ (0.9 × KDP), Na₃La₂(BO₃)₃ (2 × KDP), and KNa₂La₂(BO₃)₃ (2.6 × KDP),^33–38 exhibiting different NLO activities attributed to the presence of diverse A-site cations. A similar situation has also been observed in alkali metal borophosphate and phosphate UV NLO crystals, such as Rb₃B₁₁P₂O₂₃ (2.5× KDP), Cs₃B₁₁P₂O₂₃ (3 × KDP), α-KZnPO₄ (0.2 × KDP) and α-LiZnPO₄ (2.3 × KDP).^39–41 These investigations suggest that the optimization of local structures induced by A-site cations may enhance SHG performance. However, limited research has been conducted thus far on the evolution process of the structure and performance of distinct A-site cations in these NLO borate-based derivatives.

To tackle this challenge, we utilized rare earth borates as a foundation and introduced alkali metals with varying ionic radii to optimize the structural arrangement and optical properties by adjusting the composition of alkali metals. For instance, the substitution of Na⁺ and K⁺ cations is widely regarded as a viable approach due to the inherent flexibility in doping between these components.⁴² Additionally, the incorporation of rare earth cations, like Sc³⁺, Y³⁺, La³⁺, Gd³⁺ and Lu³⁺, not only contributes to excellent transparency in the UV region, but also offers various coordination types.⁴³ Notably, the La³⁺ cation with a sizable ionic radius tends to form flexible SHG-active chromophores, thereby generating favorable SHG effects.³⁸ Inspired by these ideas, our work focuses on rare earth borate-based materials and explores the underlying mechanism of the NLO effect and optical anisotropy by employing a facile strategy to manipulate the components of A-site alkali metal cations. The synthesis of rare-earth borates K_xNa_3−xLa₂B₃O₉ (x = 2–3) was achieved through structural evolutions attributed to A-site cation manipulations. As anticipated, these compounds displayed remarkable phase-matching SHG efficiencies ranging from 1.3 to 3.3 times that of KDP, while featuring short UV cutoff edges of approximately 204 nm. These findings highlight the potential of K_xNa_3−xLa₂B₃O₉ as favorable candidates for UV NLO applications and underscore the significance of regulating A-site alkali metal cations in the exploration of new NLO crystals.

Results and discussion

Synthesis and phase transformation

The preparation of the target compounds was performed through a modified solid-phase reaction. To monitor the influence of A-site cations on the crystal structure, a series of compounds with varying proportions of A-site cations, namely K₂, K_2.2, K_2.4, K_2.6, K_2.8, and K₃, were synthesized. The phase purity of the resulting products was verified using PXRD analysis. It is evident from Fig. 1a that the K₂ and K₃ compounds demonstrate distinct crystal structural characteristics. Specifically, the structural characteristics of K_2.8 and K₃ exhibited isomorphism, suggesting a consistent structural framework despite the varying proportions of K cations in the A-site. However, when the K⁺ cation proportion reached approximately K_2.6, structural features indicative of the K₂ compound were initially observed, implying the coexistence of two distinct polycrystalline phases. This observation confirms that the structural transition from K₃ to K₂ occurs at around the K_2.6 proportion. Furthermore, the PXRD peak patterns of K₂, K_2.2, and K_2.4 displayed a high degree of similarity, suggesting isomorphism between these compounds. These observations provide clear evidence of the critical impact of the A-site cation proportions on the structural regulation of these materials. Notably, as illustrated in Fig. 1b, an increase in the K proportion within the range of K₂–K_2.4 leads to a gradual shift of PXRD peaks towards lower angles, indicating larger lattice constants.⁴⁴ This trend is also observed when considering the proportion of K variation within the K_2.8–K₃ range. These findings strongly suggest that the proportion of K⁺ cations exerts a direct impact on the lattice constants of these compounds.

Fig. 1 (a) Experimental and calculated PXRD patterns for K₂, K_2.2, K_2.4, K_2.6, K_2.8, and K₃ polycrystals, respectively. (b) The enlarged PXRD curves observed in the 2θ range of 10–20°.

Thermal analyses

Thermal analyses were conducted to further investigate the structural transformations and evaluate the thermal stability of the title compounds. TG-DTA measurements revealed the remarkable thermal stability of the K₂, K_2.2, K_2.4, K_2.6, K_2.8, and K₃ compounds, as evidenced by sharp absorption peaks observed above 850 °C (Fig. 2a). Notably, the thermal stability of compounds within the K₂–K_2.6 range exhibited a decreasing trend with increasing proportions of K⁺ cations (Fig. 2b). In contrast, within the K_2.6–K₃ range, the compounds displayed an upward trend in thermal stability (Fig. 2g). Among the tested compound systems, it has been observed that the K_2.6 compound demonstrated the lowest thermal stability. When the K⁺ cation reaches a composition of 2.6, this behavior can potentially be attributed to the influence of mixed components present in the system that cannot be ignored, leading to a decrease in the melting point of the system. These findings further highlight the role of the K_2.6 compound, which possesses mixed-phase structures that align with the PXRD analyses.

Fig. 2 (a–f) TG-DTA curves for the K₂, K_2.2, K_2.4, K_2.6, K_2.8, and K₃ compounds, respectively. (g) Comparative results of thermal stabilities for the title compounds.

Crystal structures of K₂ and K₃

In light of the isomorphism observed among the K₂, K_2.2, and K_2.4 compounds, as well as the isomorphism between the K_2.8 and K₃ compounds, we have selected K₂ and K₃ as representative samples for conducting a thorough analysis of their respective crystal structures. The structural features of K₂ and K₃ were determined through the utilization of single-crystal XRD analysis (Tables S1–S5†). Our analysis revealed that K₂ adopts an asymmetric orthorhombic crystal structure, belonging to the space group Amm2 (no. 38), while K₃ exhibits a similar orthorhombic structure in the Pnc2 space group (no. 30), as summarized in Table S1.† In the crystal structure of K₂, the asymmetric unit consists of two distinct K, one Na, one La, two B, and four O atoms. Conversely, the asymmetric unit of K₃ contains three K, three La, four B, and eleven O atoms. As shown in Fig. 3a and b, the B atoms are coordinated by three O atoms, forming [BO₃] plane triangles, and the La atom is surrounded by nine O atoms, resulting in the formation of distorted [LaO₉] polyhedra. The B–O bond lengths in K₂ range from 1.360(2) to 1.379(12) Å, while the La–O bond lengths range from 2.466(12) to 2.687(5) Å. In K₃, the B–O bond lengths vary from 1.300(5) to 1.409(15) Å, whereas the La–O bond lengths range from 2.412(8) to 3.02(2) Å. In K₂, adjacent [LaO₉] polyhedra are connected to each other through oxygen edge-sharing, forming a pseudo-one-dimensional (1D) chain denoted as [La₂O₁₆]_∞. These 1D chains, along with [BO₃] units, further interconnect through oxygen corner-sharing to form pseudo-two-dimensional (2D) layers on the bc plane (Fig. 3c). These pseudo-2D layers are then bridged with [BO₃] units along the a-axis through oxygen corner-sharing, ultimately giving rise to a three-dimensional (3D) structural framework (Fig. 3d). In the case of K₃, three distorted [LaO₉] polyhedra associate to form distinct [La₃O₂₁] clusters via oxygen face-sharing. These clusters are further interconnected with [BO₃] units by sharing oxygen along the bc plane, as presented in Fig. 3e, with the K⁺ cations located in the channels (Fig. 3f).

Fig. 3 Structural characteristics of K₂ and K₃. (a and b) [BO₃] plane triangles, [LaO₉] polyhedra, and [La₂O₁₆]_∞ and [La₃O₂₁] clusters. (c) Pseudo-2D layers of K₂. (d) 3D structural framework of K₂. (e) Presentation of [La₃O₂₁]_∞ clusters connected with [BO₃] units in K₃ viewed from the bc plane. (f) 3D structural network of K₃ viewed along the c-axis.

To shed light on the structural evolution exhibited by the K₂ and K₃ compounds, our study focuses on a thorough analysis of the arrangement and interrelationships of fundamental [BO₃] units. Notably, while both K₂ and K₃ compounds feature isolated planar triangles formed by [BO₃] units, a notable disparity arises in the spatial arrangement of these triangles within their respective 3D frameworks. As shown in Fig. 4a–c, it is noteworthy that the two distinct [BO₃] plane triangles in K₂ exhibit a regular arrangement, manifesting a constant angle of 90 degrees between the planes they occupy. In contrast, the planes defined by the distinct [BO₃] units in K₃ feature varying angles, including 63.312, 89.061, and 69.942 degrees, which deviate significantly from the uniform 90 degree arrangement observed in K₂. The variations in the spatial angles between the [BO₃] building blocks in K₂ and K₃ have distinct implications for the anisotropic characteristics of their respective structures. These observations would contribute to a more comprehensive understanding of the potential structural and application-related implications associated with the different spatial arrangements of [BO₃] units in K₂ and K₃.

Fig. 4 Comparison of the arrangements of distinct [BO₃] units in the K₂ and K₃ compounds. (a–c) Arrangements and orientations of the isolated [BO₃] units in the K₂ compound. (d–f) Arrangements and orientations of the isolated [BO₃] units in the K₃ compound.

Spectroscopic properties

To investigate the optical properties of the title compounds, the UV-vis-NIR diffuse reflectance spectra of the title compounds were recorded under consistent conditions (Fig. 5). The obtained spectra revealed distinct UV transmittance cut-off edges for each compound: 208, 206, 206, 207, 208, and 204 nm for the K₂, K_2.2, K_2.4, K_2.6, K_2.8, and K₃ compounds, respectively. These favorable UV transmittance characteristics directly correspond to energy band gaps of 5.15, 5.24, 5.20, 5.19, 5.23, and 5.29 eV, respectively, as determined using the Kubelka–Munk formula.⁴⁵ Furthermore, we conducted a detailed analysis of the infrared (IR) spectra of the compounds, which revealed similar characteristics among them, as depicted in Fig. S1.† Taking the K₂ compound as an example, the absorption peaks observed at around 1392.73 and 1200.69 cm⁻¹ are attributed to the asymmetric stretching vibrations of the [BO₃] units, while the peak near 950.08 cm⁻¹ corresponds to the symmetric stretching vibrations. The peaks around 743.24 and 604.83 cm⁻¹ are caused by the bending vibrations of the [BO₃] units. The presence of these distinct vibration modes further confirms the existence of the [BO₃] unit within the compounds.^37,38,43b Notably, we observed a slight redshift phenomenon in the absorption peak positions of the IR spectrum with an increasing K to Na component ratio. This trend can primarily be attributed to the expansion of the alkali metal cation radius.⁴⁶ With a larger cation radius, the bond length between the cation and oxygen atom increases, resulting in a lower vibration frequency and a consequent redshift in the absorption peak position of the IR absorption spectrum. These findings provide valuable insights into the intrinsic relationship between structural changes and the optical properties exhibited by the investigated compounds.

Fig. 5 (a–f) UV-vis-NIR diffuse reflectance spectra for the K₂, K_2.2, K_2.4, K_2.6, K_2.8, and K₃ polycrystalline samples, respectively.

SHG characterization

The title compounds are considered to possess SHG responses because they crystallize in non-centrosymmetric space groups. Fig. 6a presents a plot illustrating the correlation between the particle size and the detected powder SHG signals. It is observed that the SHG response intensity of each compound increases with increasing particle size until it reaches its maximum value, suggesting phase-matching behavior in accordance with the rules proposed by Kurtz and Perry.⁴⁷

Fig. 6 (a) Phase-matched curves for KDP, K₂, K_2.2, K_2.4, K_2.6, K_2.8, and K₃ polycrystalline powders under 1064 nm laser irradiation. (b) Comparison of SHG intensity between the KDP reference and the title compounds. (c) Comparison of the reported SHG intensity of alkali/alkaline earth metal rare earth borates containing [BO₃] units.

Furthermore, the SHG intensities of K₂, K_2.2, K_2.4, K_2.6, K_2.8, and K₃ were determined to be 3.3, 3.1, 2.3, 2.0, 1.7, and 1.3 times that of the benchmark KDP, respectively, within a particle size range of 177 to 210 μm (Fig. 6b). The SHG responses are sufficiently large for UV NLO applications. Notably, the significant disparity in the SHG effect between K₂ and K₃ can primarily be attributed to the disordered arrangement of oxygen atoms in K₃, which gives rise to an inconsistent alignment of the [BO₃] triangular units, consequently resulting in a lower microscopic second-order hyper-polarizability compared to K₂.⁴⁸ Additionally, as the ratio of K to Na in these compounds gradually increases, the SHG response correspondingly decreases. This observation may be closely related to the unit cell volume of the crystal structure, where a larger unit cell volume tends to weaken the second-order polarizability. Fig. 6c and Table S6† provide a compilation of the reported SHG intensities of alkali and alkaline earth metal borate compounds containing [BO₃] triangular units from the literature.⁴⁹ Notably, K₂ exhibits a significant SHG response compared with other reported compounds, thereby bolstering its potential as a NLO crystal.

Birefringence characterization

The birefringence of K₂ and K₃ crystals was evaluated within the visible wavelength range using a polarizing microscope. Fig. 7a–d show the complete extinction of both K₂ and K₃ crystals under orthogonally polarized light. The measured crystal thicknesses (d) were found to be 29 μm and 16 μm, corresponding to the optical path differences (R) of 841 nm and 896 nm,⁵⁰ respectively. Consequently, the birefringence values of K₂ and K₃ crystals were determined to be 0.029 and 0.056, respectively, across the visible wavelength range. The theoretical birefringent values of the two crystals were also calculated, yielding values of 0.028 and 0.051 for K₂ and K₃ crystals (Fig. 7g and h), respectively, at a wavelength of 1 μm, which aligns with the experimental observations. Notably, the birefringence value of K₃ is significantly higher than that of K₂, nearly double that of K₂. This significant difference primarily stems from the angles between the [BO₃] planes in K₂ and K₃, as discussed in the “Crystal structure” section. Specifically, the spatial structure of K₂ consists of two distinct perpendicular [BO₃] units oriented at a 90 degree angle to each other, indicating relatively small structural anisotropy. In contrast, K₃ displays an arrangement in which the [BO₃] units form varying angles, including 63.312, 89.061, and 69.942 degrees, thereby deviating from perpendicularity. This distinct structural feature in K₃ results in relatively large structural anisotropy.²⁹

Fig. 7 (a–d) Original interference state and complete extinction of K₂ and K₃ crystals under cross-polarized light, respectively. (e and f) The thickness of the K₂ and K₃ crystals, respectively. (g and h) Theoretical dispersion curve of the refractive index for K₂ and K₃ crystals, respectively.

Structure–property correlations

To delve deeper into the electronic structures of K₂ and K₃ crystals and their inherent relationships with optical properties, this study employed DFT-based computational methods for theoretical research.⁵¹ Through first-principles calculations,⁵² we discovered that both K₂ and K₃ crystals are direct bandgap compounds, indicating that the lowest point of the conduction band and the highest point of the valence band overlap in momentum space (k-space). The calculated theoretical bandgap values for K₂ and K₃ crystals are 4.634 eV and 4.001 eV, respectively, as shown in Fig. 8a–c. The orbital contributions of each atom to the energy bands of K₂ and K₃ can be identified from the corresponding partial densities of states (PDOSs). As shown in Fig. 8b–d, below the Fermi level, the valence band maximum predominantly consists of B 2p and O 2p orbitals, while the conduction band minimum primarily originates from the La 5d orbitals in both K₂ and K₃ compounds. It is noteworthy that the electron states in K₂ predominantly occupied by K 3p orbitals range from −12 to −11 eV, whereas those in K₃, governed by K 3p orbitals, span from −13 to −11 eV. Given the close correlation between the optical properties and the optical transitions occurring between electronic states in proximity to the band gap, it can be deduced that the optical activities of the K₂ and K₃ crystals are primarily influenced by the [BO₃] units and [LaO₉] polyhedra.

Fig. 8 (a and b) The presentation of the band structure as well as the PDOS and TDOS for K₂, respectively. (c and d) The presentation of the band structure as well as the PDOS and TDOS for K₃, respectively.

Conclusions

In summary, a new family of alkaline-metal rare-earth borates, K_xNa_3−xLa₂B₃O₉ (x = 2–3), was synthesized through A-site cation control engineering. The investigation of these compounds via DTA-TG analyses and PXRD tests revealed a structural transition from the Pnc2 to the Amm2 space group. Notably, the structural phase of the K_xNa_3−xLa₂B₃O₉ compounds was found to be modulated by adjusting the A-site cation K⁺ content. Intriguingly, these materials display large SHG intensities, which are 1.3 to 3.3 times that of KDP with phase-matchable ability, along with short UV absorption edges at approximately 204–208 nm. Moreover, the K₂NaLa₂B₃O₉ and K₃La₂B₃O₉ crystals selected for analysis possess moderate birefringence values of 0.029 and 0.056, respectively, with the variation primarily attributed to differing orientations of the [BO₃] planes. These favorable findings make K₂NaLa₂B₃O₉ and K₃La₂B₃O₉ good potential candidates for UV NLO applications. The rational regulation of A-site cations underscores a versatile approach for the fabrication of novel NLO crystals with desired performance attributes.

Data availability

The data supporting this article have been included as part of the ESI.† Crystallographic data for 2374500 and 2374501 have been deposited at the CCDC.

Author contributions

Jie Song and Huijian Zhao: experiment, investigation, data curation, writing original draft. Conggang Li: conceptualization, funding acquisition, methodology, project administration, review & editing. Ning Ye, Zhanggui Hu and Yicheng Wu: resources, funding acquisition.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work was supported by the National Key R&D Program of China (2021YFA0717800), National Natural Science Foundation of China (No. 61835014 and 52002273), and State Key Laboratory of Crystal Materials, Shandong University (No. KF2303).

Notes and references

1. D. F. Eaton, Nonlinear Optical Materials, Science, 1991, 253, 281–287.
2. M. J. Xia, X. X. Jiang, Z. S. Lin and R. K. Lit, “All-Three-in-One”: A New Bismuth-Tellurium-Borate Bi₃TeBO₉ Exhibiting Strong Second Harmonic Generation Response, J. Am. Chem. Soc., 2016, 138, 14190–14193.
3. X. L. Chen, B. B. Zhang, F. F. Zhang, Y. Wang, M. Zhang, Z. H. Yang, K. R. Poeppelmeier and S. L. Pan, Designing an Excellent Deep-Ultraviolet Birefringent Material for Light Polarization, J. Am. Chem. Soc., 2018, 140, 16311–16319.
4. P. S. Halasyamani and J. M. Rondinelli, The must-have and nice-to-have experimental and computational requirements for functional frequency doubling deep-UV crystals, Nat. Commun., 2018, 9, 2972.
5. C. Wu, C. B. Jiang, G. F. Wei, X. X. Jiang, Z. J. Wang, Z. S. Lin, Z. P. Huang, M. G. Humphrey and C. Zhang, Toward Large Second-Harmonic Generation and Deep-UV Transparency in Strongly Electropositive Transition Metal Sulfates, J. Am. Chem. Soc., 2023, 145, 3040–3046.
6. G. H. Zou and K. M. Ok, Novel ultraviolet (UV) nonlinear optical (NLO) materials discovered by chemical substitution-oriented design, Chem. Sci., 2020, 11, 5404–5409.
7. C. Y. Pan, X. R. Yang, L. Xiong, Z. W. Lu, B. Y. Zhen, X. Sui, X. B. Deng, L. Chen and L. M. Wu, Solid-State Nonlinear Optical Switch with the Widest Switching Temperature Range Owing to Its Continuously Tunable Tc, J. Am. Chem. Soc., 2020, 142, 6423–6431.
8. N. Zaitseva, L. Carman and I. Smolsky, Habit control during rapid growth of KDP and DKDP crystals, J. Cryst. Growth, 2002, 241, 363–373.
9. K. Miyazaki, H. Sakai and T. Sato, Efficient deep-ultraviolet generation by frequency doubling in β-BaB₂O₄ crystals, Opt. Lett., 1986, 11, 363–373.
10. Q. Wang, F. Yang, X. Wang, J. Zhou, J. Ju, L. Huang, D. J. Gao, J. Bi and G. H. Zou, Deep-Ultraviolet Mixed-Alkali-Metal Borates with Induced Enlarged Birefringence Derived from the Structure Rearrangement of the LiB₃O₅, Inorg. Chem., 2019, 58, 5949–5955.
11. B. Wu, D. Tang, N. Ye and C. Chen, Linear and nonlinear optical properties of the KBe₂BO₃F₂ (KBBF) crystal, Opt. Mater., 1996, 5, 105–109.
12. Y. Mori, I. Kuroda, S. Nakajima, T. Sasaki and S. Nakai, New nonlinear optical crystal: Cesium lithium borate, Appl. Phys. Lett., 1995, 67, 1818–1820.
13. L. Kang and Z. S. Lin, Deep-ultraviolet nonlinear optical crystals: concept development and materials discovery, Light: Sci. Appl., 2022, 11, 201.
14. G. A. Valdivia-Berroeta, E. W. Jackson, K. C. Kenney, A. X. Wayment, I. C. Tangen, C. B. Bahr, S. J. Smith, D. J. Michaelis and J. A. Johnson, Designing Non-Centrosymmetric Molecular Crystals: Optimal Packing May Be Just One Carbon Away, Adv. Funct. Mater., 2020, 30, 1904786.
15. (a) M. Mutailipu, K. R. Poeppelmeier and S. L. Pan, Borates: A Rich Source for Optical Materials, Chem. Rev., 2021, 121, 1130–1202; (b) M. Mutailipu, M. Zhang, H. P. Wu, Z. H. Yang, Y. H. Shen, J. L. Sun and S. L. Pan, Ba₃Mg₃ (BO₃)₃F₃ polymorphs with reversible phase transition and high performances as ultraviolet nonlinear optical materials, Nat. Commun., 2018, 9, 3809; (c) X. Long, R. An, Y. Lv, X. Wu and M. Mutailipu, Tunable Optical Anisotropy in Rare-Earth Borates with Flexible [BO₃] Clusters, Chem.–Eur. J., 2024, 30, e202401488.
16. J. L. Song, C. L. Hu, X. Xu, F. Kong and J. G. Mao, A Facile Synthetic Route to a New SHG Material with Two Types of Parallel π-Conjugated Planar Triangular Units, Angew. Chem., Int. Ed., 2015, 54, 3679–3682.
17. H. Huppertz and B. von der Eltz, Multianvil high-pressure synthesis of Dy₄B₆O₁₅: the first oxoborate with edge-sharing BO₄ tetrahedra, J. Am. Chem. Soc., 2002, 124, 9376–9377.
18. G. Sohr, N. Ciaghi, M. Schauperl, K. Wurst, K. R. Liedl and H. Huppertz, High-Pressure Synthesis of Cd(NH₃)₂[B₃O₅(NH₃)]₂: Pioneering the Way to the Substance Class of Ammine Borates, Angew. Chem., Int. Ed., 2015, 54, 6360–6363.
19. F. Kong, S. P. Huang, Z. M. Sun, J. G. Mao and W. D. Cheng, Se₂(B₂O₇): a new type of second-order NLO material, J. Am. Chem. Soc., 2006, 128, 7750–7751.
20. (a) W. Q. Lu, Z. L. Gao, X. T. Liu, X. X. Tian, Q. Wu, C. G. Li, Y. X. Sun, Y. Liu and X. T. Tao, Rational Design of a LiNbO₃-like Nonlinear Optical Crystal, Li₂ZrTeO₆, with High Laser-Damage Threshold and Wide Mid-IR Transparency Window, J. Am. Chem. Soc., 2018, 140, 13089–13096; (b) C. F. Sun, C. L. Hu, X. Xu, J. B. Ling, T. Hu, F. Kong, X. F. Long and J. G. Mao, BaNbO(IO₃)₅: A New Polar Material with a Very Large SHG Response, J. Am. Chem. Soc., 2009, 131, 9486.
21. (a) 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; (b) C. G. Li, Z. L. Gao, P. Zhao, X. X. Tian, H. Y. Wang, Q. Wu, W. Q. Lu, Y. X. Sun, D. L. Cui and X. T. Tao, Crystallographic Investigations into the Polar Polymorphism of BaTeW₂O₉: Phase Transformation, Controlled Crystallization, and Linear and Nonlinear Optical Properties, Cryst. Growth Des., 2019, 19, 1767–1777.
22. Y. N. Chen, M. Zhang, M. Mutailipu, K. R. Poeppelmeier and S. L. Pan, Research and Development of Zincoborates: Crystal Growth, Structural Chemistry and Physicochemical Properties, Mol, 2019, 24, 2763.
23. (a) D. Schultze, K.-T. Wilke and C. Waligora, Zur Chemie in Schmelzlösungen. IV. Darstellung von kristallinen Boraten M²⁺M⁴⁺(BO₃)₂, Z. Anorg. Allg. Chem., 1971, 380, 37–40; (b) V. Hornebecq, P. Gravereau, J. P. Chaminade and E. Lebraud, BaZr(BO₃)₂: a non-centrosymmetric dolomite-type superstructure, Mater. Res. Bull., 2002, 37, 2165–2178.
24. A. Akella and D. A. Keszler, Crystal Chemistry of Noncentrosymmetric Alkali-Metal Nb and Ta Oxide Pyroborates, J. Solid State Chem., 1995, 120, 74–79.
25. J. Choisnet, D. Groult, B. Raveau and M. Gasperin, Nouvelles structures à tunnels de section pentagonale K₃Nb₃B₂O₁₂ et K₃Ta₃B₂O₁₂, Acta Crystallogr., 1977, 33, 1841–1845.
26. K. Zhang, X. Chen and X. Wang, Review of Study on Bismuth Triborate (BiB₃O₆) Crystal, J. Synth. Cryst., 2005, 34, 438.
27. J. Barbier and L. M. D. Cranswick, The non-centrosymmetric borate oxides, MBi₂B₂O₇ (M = Ca, Sr), J. Solid State Chem., 2006, 179, 3958–3964.
28. W. L. Zhang, W. D. Cheng, H. Zhang, L. Geng, C. S. Lin and Z. Z. He, A Strong Second-Harmonic Generation Material Cd₄BiO(BO₃)₃ Originating from 3-Chromophore Asymmetric Structures, J. Am. Chem. Soc., 2010, 132, 1508.
29. M. Mutailipu, F. M. Li, C. C. Jin, Z. H. Yang, K. R. Poeppelmeier and S. L. Pan, Strong Nonlinearity Induced by Coaxial Alignment of Polar Chain and Dense BO₃ Units in CaZn₂(BO₃)₂, Angew. Chem., Int. Ed., 2022, 61, e202202096.
30. Y. Q. Chen, J. K. Liang, Y. X. Gu, J. Luo, J. B. Li and G. H. Rao, Synthesis and crystal structure of a novel hexaborate, Na₂ZnB₆O₁₁, Powder Diffr., 2010, 25, 9–14.
31. H. W. Yu, H. P. Wu, S. L. Pan, Z. H. Yang, X. L. Hou, X. Su, Q. Jing, K. R. Poeppelmeier and J. M. Rondinelli, Cs₃Zn₆B₉O₂₁: A Chemically Benign Member of the KBBF Family Exhibiting the Largest Second Harmonic Generation Response, J. Am. Chem. Soc., 2014, 136, 1264–1267.
32. X. H. Meng, X. Y. Zhang, Q. X. Liu, Z. Y. Zhou, X. X. Jiang, Y. G. Wang, Z. S. Lin and M. J. Xia, Perfectly Encoding π-Conjugated Anions in the RE₅(C₃N₃O₃)(OH)₁₂ (RE = Y, Yb, Lu) Family with Strong Second Harmonic Generation Response and Balanced Birefringence, Angew. Chem., Int. Ed., 2023, 62, e202214848.
33. Z. H. Yang, A. Tudi, B. H. Lei and S. L. Pan, Enhanced nonlinear optical functionality in birefringence and refractive index dispersion of the deep-ultraviolet fluorooxoborates, Sci. China Mater., 2020, 63, 1480–1488.
34. Y. Wang, B. B. Zhang, Z. H. Yang and S. L. Pan, Cation-Tuned Synthesis of Fluorooxoborates: Towards Optimal Deep-Ultraviolet Nonlinear Optical Materials, Angew. Chem., Int. Ed., 2018, 57, 2150–2154.
35. M. Mutailipu, Z. Q. Xie, X. Su, M. Zhang, Y. Wang, Z. H. Yang, M. Janjua and S. L. Pan, Chemical Cosubstitution-Oriented Design of Rare-Earth Borates as Potential Ultraviolet Nonlinear Optical Materials, J. Am. Chem. Soc., 2017, 139, 18397–18405.
36. Y. F. Li, F. Liang, H. M. Song, W. Liu, Z. S. Lin, G. C. Zhang and Y. C. Wu, Rb₇SrY₂(B₅O₁₀)₃: A Rare-Earth Pentaborate with Moderate Second-Harmonic Response and Interesting Phase-Matching Behavior, Inorg. Chem., 2019, 58, 8943–8947.
37. G. C. Zhang, Y. C. Wu, P. Z. Fu, G. F. Wang, S. L. Pan and C. T. Chen, A new nonlinear optical berate crystal Na₃La₂(BO₃)₃, Chem. Lett., 2001, 30, 456–457.
38. J. Song, C. G. Li, J. M. Jiao, Y. H. She, W. L. Zhao, F. Liang, N. Ye, Z. G. Hu and Y. C. Wu, KNa₂La₂(BO₃)₃: a shortite-type lanthanide borate exhibiting strong nonlinear optical activity induced by isolated BO₃ triangles and distorted LaO₉ polyhedra, Inorg. Chem. Front., 2023, 10, 5488–5495.
39. H. N. Liu, H. P. Wu, Z. G. Hu, J. Y. Wang, Y. C. Wu, P. S. Halasyamani and H. W. Yu, Rb₃B₁₁P₂O₂₃: Materials Design of a New Chemically Benign Deep-Ultraviolet Nonlinear Optical Material, ACS Mater. Lett., 2023, 5, 155–161.
40. H. A. Liu, H. P. Wu, Z. G. Hu, J. Y. Wang, Y. C. Wu and H. W. Yu, Cs₃(BOP)₂(B₃O₇)₃: A Deep-Ultraviolet Nonlinear Optical Crystal Designed by Optimizing Matching of Cation and Anion Groups, J. Am. Chem. Soc., 2023, 145, 12691–12700.
41. X. M. He, L. Qi, W. Y. Zhang, R. X. Zhang, X. Y. Dong, J. H. Ma, M. Abudoureheman, Q. Jing and Z. H. Chen, Controlling the Nonlinear Optical Behavior and Structural Transformation with A-Site Cation in α-AZnPO₄ (A = Li, K), Small, 2023, 19, 2206991.
42. S. J. Han, Y. Wang, S. L. Pan, X. Y. Dong, H. P. Wu, J. Han, Y. Yang, H. W. Yu and C. Y. Bai, Noncentrosymmetric versus Centrosymmetric: Influence of the Na⁺ Substitution on Structural Transition and Second-Harmonic Generation Property, Cryst. Growth Des., 2014, 14, 1794–1801.
43. (a) Y. C. Wu, J. G. Liu, P. Z. Fu, J. X. Wang, H. Y. Zhou, G. F. Wang and C. T. Chen, A new lanthanum and calcium borate La₂CaB₁₀O₁₉, Chem. Mater., 2001, 13, 753–755; (b) R. Q. Liu, H. P. Wu, H. W. Yu, Z. G. Hu, J. Y. Wang and Y. C. Wu, K₅Mg₂La₃(BO₃)₆: An Efficient, Deep-Ultraviolet Nonlinear Optical Material, Chem. Mater., 2021, 33, 4240–4246; (c) Z. Q. Xie, M. Mutailipu, G. J. He, G. P. Han, Y. Wang, Z. H. Yang, M. Zhang and S. L. Pan, A Series of Rare-Earth Borates K₇MRE₂B₁₅O₃₀ (M = Zn, Cd, Pb; RE = Sc, Y, Gd, Lu) with Large Second Harmonic Generation Responses, Chem. Mater., 2018, 30, 2414–2423.
44. L. L. H awes, The determination of lattice constants using low angle diffraction lines, Acta Crystallogr., 1959, 12, 443–445.
45. P. Kubelka and F. Munk, An Article on Optics of Paint Layers, Zeitschrift für Technische Physik, 1931, 12, 593–601.
46. F. He, J. H. Zhuang, B. Lu, X. L. Liu, J. L. Zhang, F. N. Gu, M. H. Zhu, J. Xu, Z. Y. Zhong, G. W. Xu and F. B. Su, Ni-based catalysts derived from Ni-Zr-Al ternary hydrotalcites show outstanding catalytic properties for low-temperature CO₂ methanation, Appl. Catal., B, 2021, 293, 120218.
47. S. K. Kurtz and T. T. Perry, A Powder Technique for the Evaluation of Nonlinear Optical Materials, J. Appl. Phys., 1968, 39, 3798–3813.
48. X. Y. Li, Q. Wei, C. L. Hu, J. Pan, B. X. Li, Z. Z. Xue, X. Y. Li, J. H. Li, J. G. Mao and G. M. Wang, Achieving Large Second Harmonic Generation Effects via Optimal Planar Alignment of Triangular Units, Adv. Funct. Mater., 2023, 33, 2210718.
49. (a) G. C. Zhang, Y. C. Wu, Y. G. Li, F. Chang, S. L. Pan, P. Z. Fu and C. T. Chen, Flux growth and characterization of a new oxyborate crystal Na₃La₉O₃(BO₃)₈, J. Cryst. Growth, 2005, 275, E1997–E2001; (b) M. E. Gao, H. P. Wu, H. W. Yu, Z. G. Hu, J. Y. Wang and Y. C. Wu, BaYOBO₃: a deep-ultraviolet rare-earth oxy-borate with a large second harmonic generation response, Sci. China: Chem., 2021, 64, 1184–1191; (c) F. X. Shan, L. Kang, G. C. Zhang, J. Y. Yao, Z. S. Lin, M. J. Xia, X. Y. Zhang, Y. Fu and Y. C. Wu, Na₃Y₃(BO₃)₄: a new noncentrosymmetric borate with an open-framework structure, Dalton Trans., 2016, 45, 7205–7208; (d) F. X. Shan, M. J. Xia, G. C. Zhang, J. Y. Yao, X. Y. Zhang, T. X. Xu and Y. C. Wu, Growth, structure, and optical properties of a self-activated crystal: Na₃Nd₉O₃(BO₃)₈, Solid State Sci., 2015, 41, 31–35; (e) R. A. Kumar, M. Arivanandhan and Y. Hayakawa, Recent advances in rare earth-based borate single crystals: potential materials for nonlinear optical and laser applications, Prog. Cryst. Growth Charact. Mater., 2013, 59, 113–132; (f) M. Iwai, T. Kobayashi, H. Furuya, Y. Mori and T. Sasaki, Crystal Growth and Optical Characterization of Rare-Earth (Re) Calcium Oxyborate ReCaO(BO)(Re = Y or Gd) as New Nonlinear Optical Material, Jpn. J. Appl. Phys., 1997, 36, L276–L279; (g) Y. Q. Liu, F. P. Yu, Z. P. Wang, S. Hou, L. Yang, X. G. Xu and X. Zhao, Bulk growth and nonlinear optical properties of thulium calcium oxyborate single crystals, Crystengcomm, 2014, 16, 7141–7148.
50. W. Q. Huang, X. Zhang, Y. Q. Li, Y. Zhou, X. Chen, X. Q. Li, F. F. Wu, M. C. Hong, J. H. Luo and S. G. Zhao, A Hybrid Halide Perovskite Birefringent Crystal, Angew. Chem., Int. Ed., 2022, 61, e202202746.
51. R. W. Godby, M. Schlüter and L. J. Sham, Self-energy operators and exchange-correlation potentials in semiconductors, Phys. Rev. B: Condens. Matter Mater. Phys., 1988, 37, 10159–10175.
52. S. J. Clark, M. D. Segall, C. J. Pickard, P. J. Hasnip, M. J. Probert, K. Refson and M. C. Payne, First principles methods using CASTEP, Z. Kristallogr., 2005, 220, 567–570.

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Footnotes

† Electronic supplementary information (ESI) available: Experimental section, CIF file, crystallographic data, IR spectra, and SHG comparison for K₂ and K₃. CCDC 2374500 and 2374501 for K₂ and K₃. For ESI and crystallographic data in CIF or other electronic format see DOI: https://doi.org/10.1039/d4sc05081a

‡ Song J. and Zhao H. contributed equally to this work.

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