A Cation-Driven Approach toward Deep-Ultraviolet Nonlinear Optical Materials

A Cation-Driven Approach toward Deep-Ultraviolet Nonlinear Optical Materials

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Cong Hu¹^,², Meng Cheng¹^,², Wenqi Jin¹^,², Jian Han¹^,², Zhihua Yang¹^,²^,^*, Shilie Pan¹^,²^,^*

Research. Vol 6 Article ID 0053

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Research. Vol 6 Article ID 0053

• Research Article •

A Cation-Driven Approach toward Deep-Ultraviolet Nonlinear Optical Materials

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Cong Hu¹^,², Meng Cheng¹^,², Wenqi Jin¹^,², Jian Han¹^,², Zhihua Yang¹^,²^,^*, Shilie Pan¹^,²^,^*

Affiliations

¹Research Center for Crystal Materials, CAS Key Laboratory of Functional Materials and Devices for Special Environments, Xinjiang Technical Institute of Physics & Chemistry, CAS, 40–1 South Beijing Road, Urumqi 830011, China.

²Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing 100049, China.

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^† These authors contributed equally to this work.

Published: 2023-03-20 doi: 10.34133/research.0053

Outline

Abstract

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The design of new materials with special performances is still a great challenge, especially for the deep-ultraviolet nonlinear optical materials in which it is difficult to balance large bandgaps and strong second harmonic generation responses due to their inverse relationship. Cation variation not only influences the whole structure frameworks but also directly participates in the formation of electronic structures, both of which could lead to the uncontrollability of the properties of the designed materials. Here, a novel approach, aiming at purposeful and foreseeable material designs, is proposed to characterize the role of cations. By the verification of several series of borates, the influences of cation variation on property changes are explored systematically. Accordingly, a feasible strategy of designing deep-ultraviolet nonlinear optical materials by substituting barium for lead has been concluded, which could obviously blue-shift the ultraviolet cutoff edge and maintain the relatively strong second harmonic generation response (more than 2 times of KH₂PO₄), achieving the property optimization, and especially works efficiently in fluorooxoborates. The property optimization design strategy and the cation characterization method are not only helpful in exploring nonlinear optical materials but also enlightening in material design and selection.

Cite this Article

Cong Hu, Meng Cheng, Wenqi Jin, Jian Han, Zhihua Yang, Shilie Pan. A Cation-Driven Approach toward Deep-Ultraviolet Nonlinear Optical Materials[J]. Research, 2023 , 6 (3) : 0053 - . DOI: 10.34133/research.0053

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Introduction

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Aiming at desirable performances, the material exploration assisted by quantum chemical calculation on computers has led to many new approaches, such as high-throughput screening and machine learning in data mining, or structure prediction by exploratory algorithms [1,2]. With the great demand in laser photolithography, micro-nano processing, optical communication, and medical treatment [3–10], a series of nonlinear optical (NLO) crystals have been discovered and commercialized successfully [11–17]. At present, deep-ultraviolet (DUV) NLO materials particularly attract many academic and commercial interests as the frequency conversion core to achieve coherent light with large photon flow and ultrahigh resolution and are expected to break the “200 nm wall”[18]. However, a large bandgap (E_g > 6.2 eV) is indispensable for DUV transparency, while E_g is inversely proportional to the second harmonic generation (SHG) response (d_ij) [19]. Therefore, how to satisfy the balance between the two critical performances (E_g and d_ij) is a key factor in the design of outstanding DUV NLO materials. KBe₂BO₃F₂ (KBBF) exhibits excellent properties as a promising DUV NLO crystal [20,21], but the toxicity and layer-growing habit seriously impede its application. Finding KBBF replacements and balancing E_g and d_ij in the DUV region are still urgent.

To guarantee appropriate E_g and d_ij of designed NLO materials, several advantageous NLO-active (the sources of NLO effects) anion units are introduced, such as conjugated π configurations [BO₃]³⁻, [B₃O₆]³⁻, distorted d⁰ or d¹⁰ transition-metal-centered (V⁵⁺, Cd²⁺) polyhedra, fluorooxoborate anionic units [BO_nF_4-n]⁽ⁿ⁺¹⁾⁻ (n = 1, 2, 3), and so on [22–25]. Actually, as parts of the whole electron structures, A-site metal cations could also directly influence the optical properties besides the size effects in crystal structures, but a special study of the role of cation variation is rare. Here, a convenient cation characterization approach, “Cation differentiation by electron spatial distribution” (CRESD), is proposed to distinguish the role of cations in optical properties, and an accompanying design strategy is concluded from cation variation to achieve property optimization, for example, balancing large E_g and large d_ij in the DUV region. We note that the property optimization strategy and cation characterization approach can be applied in the design of high-performance materials not only for the NLO functions but also for other objects, such as perovskite solar cells.

Results and Discussion

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Design strategy based on cations

Along with the increase of E_g, the SHG response of typical NLO materials [26–50] demonstrates an obvious downward trend as shown in Fig. 1 (more details are shown in Table S1 in the Supplementary Materials). It is noteworthy that the compounds with outstanding SHG response (compared to d₃₆ = 0.39 pm/V of KH₂PO₄ [KDP]) in different bandgap regions (or ultraviolet [UV] cutoff ranges) are highlighted in Fig. 1, especially, (I) 3 to 4 eV, Bi₃TeBO₉ (20.0 KDP) [51]; (II) 4 to 5 eV, CsPbCO₃F (13.4 KDP) [52] and BiB₂O₄F (12.0 KDP) [53]; (III) 5 to 6 eV, PbB₂O₃F₂ (13.0 KDP) [54]; (IV) 6 to 7 eV, β-BaB₂O₄ (BBO, 5.7 KDP) [55] and K₃B₆O₁₀Cl (KBOC, 4.0 KDP) [56]; and (V) > 7 eV, CsB₃O₅ (CBO, 2.7 KDP) [57], LiB₃O₅ (LBO, 2.7 KDP) [58], NH₄B₄O₆F (ABF, 3.0 KDP) [59], and KBBF (1.2 KDP) [21]. Among the above materials, four compounds exhibit a remarkably large SHG response, more than 10 times that of KDP, and half of the four ones contain lead atoms. However, commercialized applications of lead-containing NLO materials would face two shortcomings, narrow bandgaps, which is one of the main obstacles to the practical DUV applications, and the nonnegligible toxicity of lead cations. The unbalanced performances drive the combination properties of lead borates to be optimized.

To verify the feasibility of property optimization by the design strategy of cations, six lead borates with hierarchical SHG responses, from 3.5 to 13.4 KDP, are selected: Pb₂Ba₃(BO₃)₃Cl [31], Pb₃B₆O₁₁F₂ [35], Pb₂B₅O₉Cl [60], Pb₂BO₃Br [28], PbB₅O₇F₃ [61], and PbB₂O₃F₂ [54], which crystallize in the noncentrosymmetric space groups, C222₁ (No. 20), P2₁ (No. 4), Pnn2 (No. 34), P321 (No. 150), Cmc2₁ (No. 36), and P31m (No. 157), respectively. The isostructural barium borates of the first 3 have been reported previously, namely, Ba₅(BO₃)₃Cl [62], Ba₃B₆O₁₁F₂ [40], and Ba₂B₅O₉Cl [63]. It notes that between Pb₂Ba₃(BO₃)₃Cl and Ba₅(BO₃)₃Cl, the substitution from Pb²⁺ to Ba²⁺ only exists in the 8c cation Wyckoff positions, while Ba²⁺ in two 4b and one 4a positions are retained. In Pb₂Ba₃(BO₃)₃Cl/Ba₅(BO₃)₃Cl, the anionic framework is formed by noncondensed BO₃ units, while both Pb₂B₅O₉Cl/Ba₂B₅O₉Cl and Pb₃B₆O₁₁F₂/Ba₃B₆O₁₁F₂ possess a 3-dimensional B-O network consisting of BO₃ and BO₄ units (Fig. 2A to C). Theoretical structural models Ba₂BO₃Br, BaB₅O₇F₃, and BaB₂O₃F₂ (BaB₂O₃F₂-P31m, hereinafter referred to as BaB₂O₃F₂) are derived from Pb₂BO₃Br, PbB₅O₇F₃, and PbB₂O₃F₂ by cation substitutions, in which the anion frameworks are formed by a noncondensed BO₃ group, a [B₅O₇F₃]_∞ layer, and a [B₆O₉F₆]_∞ layer, respectively. It should be noticed that the connection of the halide atoms is also different, where F in the fluorooxoborate unit BO₃F connects both with the metal Ba and B atoms, while Br connects only to the metal Ba (Fig. 2D to F). The structural information of predicted Ba₂BO₃Br, BaB₅O₇F_3, and BaB₂O₃F₂ are shown in Tables S2–S4, and their crystallographic details (atomic coordinates, bond distances, angles, etc.) have been listed in Tables S5–S12.

In addition, recently, a noncentrosymmetric BaB₂O₃F₂ with lower symmetry, P2₁, was successfully synthesized by our group [64]. The relative total energy (Helmholtz free energy) calculated by DFT (density functional theory) between predicted BaB₂O₃F₂ (P31m) and experimental BaB₂O₃F₂ (P2₁) is less than 20 meV/atom (Fig. 3), and the formation enthalpy of BaB₂O₃F₂ (P31m) is 0.024 eV/atom, and there is no imaginary phonon mode in the phonon spectrum of BaB₂O₃F₂ (P31m) (Fig. S1), indicating the thermodynamical metastability and kinetical stability. Moreover, for comparison, the structure of PbB₂O₃F₂ (P2₁) is built by a cation substitution for experimental BaB₂O₃F₂ (P2₁), and the relative total energy between PbB₂O₃F₂ (P2₁) and experimental PbB₂O₃F₂ (P31m) is about 20 meV/atom, and the formation enthalpy of PbB₂O₃F₂ (P2₁) is −0.023 eV/atom, which shows the thermodynamical possibility of being synthesized. Here, the formation enthalpies of BaB₂O₃F₂ (P31m) and PbB₂O₃F₂ (P2₁) are calculated from the general experimental source, B₂O_3, and BaF₂/PbF₂.

CRESD method

To clarify the role of cations in property changes, the CRESD method is proposed to characterize the volumetric effects of various metal cations by the occupied volume of electrons, namely, electron spatial distribution (ESD). Taking the above isostructural substitutions of lead/barium borates as examples, the magnitudes of ESD between lead and barium atoms are compared on the basis of atom radius R(M), cation radius R(M²⁺), and cation volume V(M²⁺), where V(M²⁺) = (2 × R(M²⁺))³ (Table 1). Here, deviation γ is defined as (P₁ − P₂)/((P₁+P₂)/2) to evaluate the differentiation of P₁ and P₂, where parameter P could be the magnitudes of ESD based on atom/cation radius and cation volume, or any other parameters, such as crystal volume, in the following contents. The deviations γ of Pb²⁺/Ba²⁺ ESD based on R(M), R(M²⁺), and V(M²⁺) are 21.4%, 13.3%, and 39.5%, respectively. Considering the isostructural substitutions, the deviation γ of ESD between Pb²⁺ and Ba²⁺ should change slightly. ESD [R(M²⁺)] is better to characterize the cations but hard to sum arithmetically for composite cations. ESD [V(M²⁺)] can also be summed arithmetically, but its deviation γ is too large. More importantly, all of the above ESD values are incapable of ion groups, such as [NH₄]⁺, [CH₃NH₃]⁺, and so on. Consequently, ESD based on Bader volumes could overcome the above restrictions, where the electron density in the whole space is partitioned by DFT calculation [65,66], and hereinafter the ESD refers to the results on Bader volumes. Pb²⁺ and Ba²⁺ have similar values of ESD, and their deviations γ are 6.7%, 8.7%, and 9.0% in M₂Ba₃(BO₃)₃Cl, M₃B₆O₁₁F₂, and M₂B₅O₉Cl (M = Pb²⁺, Ba²⁺), all of which are lower than that of ESD [R(M²⁺)] (Table 2), indicating that the ESD changes slightly in isostructural substitution.

ESD can be not only applied in the comparison of experimental structures but also introduced to analyze the change regulations on structures and performances of theoretical structures, such as Ba₂BO₃Br and BaB₂O₃F₂ mentioned above. As the lattice parameters are relaxed in geometric structure optimization, the values of ESD have been calculated from both optimized and experimental (no-optimization) structures. The ESD and crystal volume in Pb₂BO₃Br are 27.7/28.3 and 143.6/149.0 Å³ without/with optimization, and their deviation γ is 2.2% and 3.7% (Table S2), indicating the feasibility of structure optimization. Interestingly, the ESD of Pb/Ba in Pb₂BO₃Br/Ba₂BO₃Br is 28.3/32.5 Å³, distinctly larger than those of the other 4 couples of lead/barium borates, ~22.0/24.0 Å³, and the deviation γ of cation ESD is 13.9%, the largest one among the 6 couples of lead/barium borates. The reason mainly comes from incompact structures. Pb₂BO₃Br/Ba₂BO₃Br belongs to rich metal borates with metal:boron = 2:1, resulting in the delocalization of electrons around metals, where the evidence is the larger deviation γ of crystal volumes between Pb₂BO₃Br and Ba₂BO₃Br, 18.6%. On the contrary, PbB₂O₃F₂/BaB₂O₃F₂ contains fewer metal atoms, metal:boron = 1:2, and the cation ESD is also relatively small, 22.0/22.3 Å³. The deviation γ of ESD is the smallest, 5.7%, and the deviation γ of crystal volumes is only 3.0% (Table S3).

Property optimization for balancing bandgaps and SHG responses

To assess the influence of cation variation on property change, the optical properties of the selected lead/barium borates are evaluated and analyzed in detail by DFT calculation. Based on generalized gradient approximation (GGA)-Perdew-Burke-Ernzerhof (PBE) functionals, the calculated bandgaps of these lead borates, Pb₂Ba₃(BO₃)₃Cl, Pb₃B₆O₁₁F_2, and Pb₂B₅O₉Cl, are 3.54, 3.81, and 3.36 eV, which are lower than their experimental or HSE06 values, 3.97 eV (312 nm), 5.17 eV (240 nm), and 4.41 eV (281 nm, HSE06), respectively. Here, the underestimation of bandgaps under GGA-PBE functional is derived from the inherent discontinuous exchange-correlation energy [67], and a scissors operator is adopted as the difference between the GGA bandgap and the experimental bandgap to eliminate this underestimation in the calculation of optical properties. In addition, a more expensive calculation, hybrid functional HSE06 [68], is used to achieve the value of bandgap more accurately for the lack of experimental bandgaps.

To verify the theoretic simulations, a couple of borates, M₂B₅O₉Cl (M = Pb, Ba), were synthesized in experiments, and the UV cutoff edge and SHG intensity were also measured (powder X-ray diffraction [XRD] patterns are shown in Fig. S2). As shown in Fig. 4, the UV absorbing cutoff of Pb₂B₅O₉Cl is 281 nm, which is consistent with our HSE06 calculation value of 281 nm. Ba₂B₅O₉Cl shows a UV cutoff edge of 189 nm, which is similar to 185 nm in the previous work [63].

By cation substitution in the three lead borate prototypes with moderate SHG responses, the bandgaps of barium borates have increased to 5.26 eV (236 nm, HSE06), 6.53 eV (190 nm, exp.), and 6.56 eV (189 nm, exp., this work) for Ba₅(BO₃)₃Cl, Ba₃B₆O₁₁F_2, and Ba₂B₅O₉Cl, which exhibit 76, 50, and 92 nm blue-shift from the isostructural lead borates. Correspondingly, the SHG responses have changed to 0.5, 3.0, and 0.7 KDP for Ba₅(BO₃)₃Cl, Ba₃B₆O₁₁F₂, and Ba₂B₅O₉Cl from 3.2, 4.0, and 1.2 KDP of Pb₂Ba₃(BO₃)₃Cl, Pb₃B₆O₁₁F₂, and Pb₂B₅O₉Cl. The experimental SHG intensities of M₂B₅O₉Cl (M = Pb, Ba) are shown in the insets of Fig. 4. It is noted that both Ba₃B₆O₁₁F₂ and Ba₂B₅O₉Cl have obtained DUV cutoff edges (<200 nm), but only borate fluoride Ba₃B₆O₁₁F₂ maintained relatively strong SHG responses (> 2 KDP). For the last three prototypes, borate halide Pb₂BO₃Br and fluorooxoborates PbB₅O₇F₃ and PbB₂O₃F₂ exhibit remarkably strong SHG responses, 9.5, 6.0, and 13.0 KDP, but their bandgaps are different, 3.33 eV (372 nm), 5.51 (225 nm), and 5.64 eV (220 nm), respectively. After cation substitutions, the combination property of the former changes slightly, 3.87 eV (320 nm) and 7.8 KDP for Ba₂BO₃Br. Contrarily, BaB₅O₇F₃ and BaB₂O₃F₂ show a great change in their prototype, 7.92 eV (157 nm) with 2.5 KDP, and 8.24 eV (150 nm) with 4.8 KDP. Furthermore, to analyze the source of the variation in bandgaps among the above metal borates, the total and partial density of states are shown in Figs. S3 to S8. Compared to the partial density of states among these metal borates, it is found that the conduction band minima are mainly composed of Pb-p or Ba-d and a little of B-p orbitals, while the valence band maxima mainly contain O-p, a little of halogen p orbitals, along with slight Pb/Sn-s orbitals for the stereochemically active lone pairs. According to the revised lone pair model [69], the interaction between Pb and O drives from the mixture of empty Pb p and a filled antibonding state between Pb-s and O-p states in PbO, and the lone pair stereochemical activity of Pb cations greatly influences the reduction of bandgaps in series of metal borates [70]. Therefore, the cation substitution from Pb to Ba could avoid the stereochemical activity of the lone pairs to achieve a relatively large bandgap, a similar effect that introducing the F atom could eliminate the dangling bonds of BO₃ groups in a series of fluorooxoborates [25,47,50,59]. As far as the purpose of property optimization, doubtless, the cation substitution in the fluorooxoborates BaB₅O₇F₃ and BaB₂O₃F₂ is more successful.

Figure 5 shows the changes for bandgap (E_g) and SHG response in the cation substitution from lead to barium. The whole region is divided into 4 sections: I, E_g < 6.2 eV, SHG < 2 KDP; II, E_g ≥ 6.2 eV, SHG < 2 KDP; III, E_g < 6.2 eV, SHG ≥ 2 KDP; IV, E_g ≥ 6.2 eV, SHG ≥ 2 KDP, where 6.2 eV and 2 KDP are DUV and relatively strong SHG response bounds, respectively. Here, before the cation substitution, 5 lead borates in 6 are all located at Section III, indicating strong SHG responses but not DUV cutoff edges. After the cation substitution, these 5 barium borates scatter into 3 sections, 1 (Ba₂BO₃Br) still in Section III, 1 (Ba₅(BO₃)₃Cl) in Section I, and 3 in Section IV (Ba₃B₆O₁₁F₂, BaB₅O₇F₃, and BaB₂O₃F₂). Although Ba₂B₅O₉Cl shows a DUV bandgap, its SHG response is relatively small for the reason that the SHG intensity of its prototype is not strong. It is found that these lead borates could keep strong SHG responses (≥2 KDP) after cation substitution except Pb₂Ba₃(BO₃)₃Cl and Pb₂B₅O₉Cl, whose SHG response is the smallest among the 6 lead borates. What is more important, the bandgaps of all the lead borates have visibly widened, and especially four of them have exceeded the DUV limit (6.2 eV, 200 nm) after cation substitution. Therefore, the cation substitution from lead to barium could optimize the combination properties.

Considering the importance of SHG response for NLO materials, exploring the role of cation variation on SHG response is vital to deepen the understanding of the structure–property relationship. The real-space atom-cutting technique is an efficient postprocessing tool to evaluate the contribution of microscopic structural groups to optical properties, such as the SHG coefficient. Table 3 shows the results of the calculated SHG coefficients before (original) and after (e.g., cut Pb) cutting the metal cations, and the “SHG reducing” is expressed as “SHG (reducing) = 1 − SHG (cut)/SHG (original)”, which is related to the contribution of metal cations to SHG coefficients. Various nonzero components of SHG coefficients are related to the different symmetries of the point groups (relatively small values, < 0.1 pm/V, are not listed here), and the final SHG response is characterized by the largest SHG coefficient in the effective SHG formula. The results indicate that in Ba₃B₆O₁₁F₂ and Ba₂B₅O₉Cl, lead and barium cations contribute equally to the SHG coefficient. In M(BO₃)₃Cl (M = Pb₂Ba₃, Ba₅), the Wyckoff site cations cause various contributions to the SHG coefficient d₁₄. Namely, in Pb₂Ba₃(BO₃)₃Cl, two 8c Pb contribute the most of d₁₄, 29% in 33%, and two 4b Ba and one 4a Ba contribute the relatively small parts, 7% and 0.3% in 33%, respectively. In Ba₅(BO₃)₃Cl, two 8c Ba contribute almost all of the d₁₄, but 4a Ba makes a remarkably negative contribution, −30%, which leads to an obvious decrease of the SHG response from Pb₂Ba₃(BO₃)₃Cl to Ba₅(BO₃)₃Cl. For MB₅O₇F₃ (M = Pb, Ba), the metal cations contribute about 10% to 15%, and the relatively small contribution mainly derives from the ratio of metal cations to B-O/B-O-F anion groups is only 1:5.

Furthermore, in M₂BO₃Br₂ and MB₂O₃F₂ (M = Pb, Ba), the cations exert a remarkable contribution to the SHG responses. In addition, in the SHG density map (Fig. S9), there are plenty of unoccupied states contributing to the VE and virtual-hole (VH) process and occupied states contributing to the VH process around Pb and Ba. In MB₂O₃F₂ (M = Pb, Sn, Ba), Sn shows a vitally negative contribution for d₃₃ (−130%), which is the reason that the SHG response of SnB₂O₃F₂ is much lower than that of isostructural PbB₂O₃F₂, in accordance with the results from another group [54], while Sn and Pb play similar contributions to d₂₂, 73% to 72%.

On the other hand, to explore the trends of property changing from PbB₂O₃F₂ to BaB₂O₃F₂, two virtual middle structures, Pb_0.75Ba_0.25B₂O₃F₂ (Pb_0.75Ba_0.25) and Pb_0.25Ba_0.75B₂O₃F₂ (Pb_0.25Ba_0.75) are introduced. As shown in Fig. 6A, along with the bandgap increasing, the |d₃₃| and |d₂₂| decrease, as the negative relationship between bandgap and SHG response. Here, we add a trend line with the formula d = a / E_g⁵, where d and E_g are SHG coefficient and HSE06 bandgap values, and the constant a is calculated by the value of d and E_g. Of course, this formula only considers the bandgap effect and ignore the momentum matrix elements [71], so it is a very rough approximation to estimate the trends of SHG coefficients along with bandgaps semiquantitatively. Furthermore, as shown in Table S13, a single Pb atom makes much more contributions to d₂₂ than Ba (22% to 4% in Pb_0.75Ba_0.25 and 33% to 7% in Pb_0.25Ba_0.75), while Pb and Ba show similar contributions to d₃₃ (12% to 9% in Pb_0.75Ba_0.25 and 13% to 13% in Pb_0.25Ba_0.75). Interestingly, the contributions of a single Ba atom develop both in d₂₂ and d₃₃ as the proportion of Ba content increases. Therefore, the SHG coefficient trends of PbB₂O₃F₂, Pb_0.75Ba_0.25, and Pb_0.25Ba_0.75 do not vary so much, while the SHG coefficients of BaB₂O₃F₂ are much larger than the expected value according to the trend lines.

From Fig. S10, the location of Pb-6p in conduction band minimum is nearer to the Fermi surface than that of Ba-5d for the stereochemical activity of the lone pairs. Meanwhile, the SnB₂O₃F₂ obtains a smaller bandgap than PbB₂O₃F₂ for stronger stereochemical activity. Table 3 also shows that Ba²⁺ contributes the main part of d₃₃ in BaB₂O₃F₂, so the BaB₂O₃F₂ could maintain a large SHG coefficient when obtaining a large bandgap. Furthermore, we also calculate the ESD value of Pb_0.75Ba_0.25 and Pb_0.25Ba_0.75 and compared them with PbB₂O₃F₂ and BaB₂O₃F₂. Then, Fig. 6B shows SHG response decreasing along with the increase of ESD in MB₂O₃F₂ (M = Pb, Ba). It is important to note that the above conclusion has only been obtained in the case of cation substitution between Pb and Ba in MB₂O₃F₂ structures.

Conclusion

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Through the investigation of a series of barium borates, Ba₅(BO₃)₃Cl, Ba₃B₆O₁₁F₂, Ba₂B₅O₉Cl, Ba₂BO₃Br, BaB₅O₇F₃, and BaB₂O₃F₂, along with their prototypes of cation substitutions lead borates, we found that ESD is very useful to describe the electron occupied space, and the magnitudes of ESD are similar in the isostructural substitutions. As the aim of chemical substitutions is to develop performances, three cases, one borate fluoride, and two fluorooxoborates, in 6 cation substitutions from lead to barium have achieved the property optimization, enlarging bandgaps to enter the DUV region (6.2 eV, 200 nm) from outside DUV as the absence of lone pair in metal cations, and maintaining relatively strong SHG responses (> 2 KDP) for the reason that metal cations show less contribution to SHG responses than the anion frames. The cation substitution between Pb and Ba in MB₂O₃F₂ structures shows the negative relation between ESDs and SHG responses, which indicates the direction of searching for the NLO material with larger SHG responses. In conclusion, by analyzing the cation variations, a cation substitution approach toward DUV NLO materials has been proposed, and two predicted fluorooxoborates BaB₅O₇F₃ and BaB₂O₃F₂ have achieved the balance between large bandgaps and strong responses.

Experimental and Computational Methods

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Experiment details

Solid-state synthesis

Polycrystalline samples of Ba₂B₅O₉Cl and Pb₂B₅O₉Cl were prepared by using standard high-temperature solid-state techniques. For Pb₂B₅O₉Cl, a stoichiometric mixture of PbCl₂ and H₃BO₃ was heated at 473 K for 10 h, cooled and ground, and then heated again at 873 K for 48 h. For Ba₂B₅O₉Cl, a stoichiometric mixture of BaCl₂·2H₂O, BaCO₃, Ba(OH)₂, and H₃BO₃ was heated at 573 K for 10 h, cooled and ground, and then heated again at 1153 K for 48 h. The starting materials of PbCl₂, BaCl₂·2H₂O, BaCO₃, and H₃BO₃ were gathered from commercial sources without any purification.

Powder X-ray diffraction

XRD patterns of Ba₂B₅O₉Cl and Pb₂B₅O₉Cl were obtained on an automated Bruker D2 X-ray diffractometer equipped with a diffracted beam monochromator set for Cu-Kα radiation (λ = 1.5418 Å) at room temperature in the angular range of 2θ = 10° to 70° with a scan step of 0.01° and a fixed counting time of 0.1 s/step.

UV-visible-near-infrared diffuse reflectance spectrum

The diffuse reflectance spectrum was measured by a Shimadzu SolidSpec-3700DUV spectrophotometer at room temperature from 175 to 2600 nm.

Second-order NLO measurements

Powder SHG effects were measured by using the Kurtz-Perry method with a Q-switched Nd: YVO₄ solid-state laser at 1064 nm [72]. Polycrystalline samples of Ba₂B₅O₉Cl and Pb₂B₅O₉Cl were ground and sieved into the following particle size ranges: 38 to 55, 55 to 88, 88 to 105, 105 to 150, 150 to 200 μm. To make relevant comparisons with known SHG materials, the crystalline KDP sample was also ground and sieved into the same particle size ranges.

Computation details

Electronic structure calculation

In this paper, the CASTEP package, a plane wave pseudo-potential method [73], was used for the DFT calculation of electronic structure properties. With the GGA-PBE functionals were chosen as the exchange-correlation functionals [74]. Norm-conserving pseudopotential [75] was used with the element valance states, Ba 5s²5p⁶6s², Pb 5s²5p⁶5d¹⁰6s²6p², B 2s²2p¹, O 2s²2p⁴, F 2s²2p⁵, Cl 3s²3p⁵, and Br 4s²4p⁵. The cutoff energies of M₂Ba₃(BO₃)₃Cl, M₃B₆O₁₁F₂, M₂B₅O₉Cl, M₂BO₃Br, MB₅O₇F₃ and MB₂O₃F₂ (M = Ba²⁺, Pb²⁺) were all no more than 940 eV and the Monkhorst-Pack k-point grids were 3 × 3 × 3, 4 × 3 × 3, 6 × 1 × 4, 4 × 4 × 2, 4 × 4 × 3, and 5 × 5 × 4, respectively.

SHG coefficient calculation

When the phase-matching condition is met, the SHG conversion efficiency of an NLO material is significantly determined by the SHG coefficients [76]. Also, the SHG coefficient components are relevant to second-order nonlinear susceptibilities, d = χ/2. Through the result of the band structure from the CASTEP package, the second-order nonlinear susceptibilities at the limit of zero frequency, χ_ijk⁽²⁾(0), can be expressed as the sum of the contribution of the virtual-electron processes and the VH processes [19,71].

χ ijk 2 = χ ijk 2 VE + χ ijk 2 VH

χ ijk 2 VE = e 3 2 ℏ m 3 ∑ vc c ′ ∫ d 3 k ⃑ 4 π 3 P ijk Im p vc i p c c ′ j p c ′ v k 1 ω cv 3 ω v c ′ 2 + 2 ω vc 4 ω c ′ v

χ ijk 2 VH = e 3 2 ℏ m 3 ∑ v v ′ c ∫ d 3 k ⃑ 4 π 3 P ijk Im p v v ′ i p v ′ c j p cv k 1 ω cv 3 ω v ′ c 2 + 2 ω vc 4 ω c v ′

Here, i, j, and k are Cartesian components, v (v') and c (c') are valence and conduction bands, and P(ijk) represents full permutation.

Associated Content

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Supplementary Materials

Phonon spectra, powder XRD patterns, total and partial density of states, SHG density, comparison of typical NLO materials in bandgap and SHG response, structure information of predicted structures, and real-space atom-cutting results of SHG coefficients are shown in the Supplementary Materials.

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doi: 10.34133/research.0053

Receive Date：2022-11-20
Online Date：2026-10-27
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Accepted：2023-01-02

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²Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing 100049, China.

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^* Address correspondence to: zhyang@ms.xjb.ac.cn (Z.Y.)

slpan@ms.xjb.ac.cn (S.P.)

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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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Table 1. Comparison between lead and barium elements of ESD based on atom radius R(M), valence state radius R(M²⁺), and ionic volume V(M²⁺).

	ESD[R(M)] (Å)	ESD[R(M²⁺)] (Å)	ESD[V(M²⁺)] ^b (Å³)
Pb	1.75	1.19	13.5
Ba	2.17	1.36	20.1
Deviation γ ^a	21.4%	13.3%	39.5%

^aDeviation γ, for example, is defined as

γ = P Ba − P Pb P Ba + P Pb / 2

, where P is the magnitude of ESD based on radius R or volume V. Electron spatial distribution (ESD). ^bESD based on ionic volume is calculated by ESD[V(M²⁺)] = (2 × R(M²⁺))³

Table 2. Comparison between lead and barium compounds of cation ESD based on Bader volumes.

Compound A	ESD (Å³)	Compound B	ESD (Å³)	Deviation γ
Pb₂Ba₃(BO₃)₃Cl	23.1 (Pb1)	Ba₅(BO₃)₃Cl	24.7 (Ba1)	6.7%

Pb₃B₆O₁₁F₂	22.6 (Pb1)	Ba₃B₆O₁₁F₂	24.2 (Ba1)	6.8%
	22.0 (Pb2)		24.0 (Ba2)	8.7%
	21.3 (Pb3)		23.7 (Ba3)	10.7%
			Average	8.7%

Pb₂B₅O₉Cl	22.7 (Pb1)	Ba₂B₅O₉Cl	24.2 (Ba1)	6.4%
	22.0 (Pb2)		24.7 (Ba2)	11.6%
			Average	9.0%

Pb₂BO₃Br	28.3 (Pb1)	Ba₂BO₃Br	32.5 (Ba1)	13.9%

PbB₅O₇F₃	21.5 (Pb1)	BaB₅O₇F₃	24.2 (Ba1)	11.8%

PbB₂O₃F₂	22.0 (Pb1)	BaB₂O₃F₂	23.3 (Ba1)	5.7%

Table 3. Real-space atom-cutting results of SHG coefficients.

Compound		SHG Coefficient (pm/V)	SHG Reducing^a	Compound		SHG Coefficient (pm/V)	SHG Reducing
Pb₂Ba₃(BO₃)₃Cl	Original	2.102 (d₁₄)		Ba₅(BO₃)₃Cl	Original	−0.481 (d₁₄)
	Cut PbBa	1.410 (d₁₄)	33%		Cut Ba	−0.426 (d₁₄)	11%
	Cut Pb (8c)	1.501 (d₁₄)	29%		Cut Ba (8c)	−0.273 (d₁₄)	43%
	Cut Ba (4b)	1.965 (d₁₄)	7%		Cut Ba (4b)	−0.485 (d₁₄)	−0.8%
	Cut Ba (4a)	2.095 (d₁₄)	0.3%		Cut Ba (4a)	−0.627 (d₁₄)	−30%
Pb₃B₆O₁₁F₂	Original	0.688 (d₁₄) 2.057 (d₁₆) −0.903 (d₂₂)		Ba₃B₆O₁₁F₂	Original	−0.469 (d₁₄) −1.104 (d₁₆) 1.109 (d₂₂)
	Cut Pb	0.588 (d₁₄) 1.150 (d₁₆) −0.835 (d₂₂)	14% 44% 8%		Cut Ba	−0.416 (d₁₄) −0.680 (d₁₆) 0.995 (d₂₂)	11% 38% 10%
Pb₂B₅O₉Cl	Original	−2.525 (d₁₅) −0.811 (d₂₄) 1.094 (d₃₃)		Ba₂B₅O₉Cl	Original	−0.742 (d₁₅) −0.473 (d₂₄) 0.766 (d₃₃)
	Cut Pb	−1.067 (d₁₅) −0.688 (d₂₄) 0.783 (d₃₃)	58% 15% 28%		Cut Ba	−0.356 (d₁₅) −0.409 (d₂₄) 0.515 (d₃₃)	52% 13% 33%
Pb₂BO₃Br	Original	6.182 (d₁₁)		Ba₂BO₃Br	Original	3.039 (d₁₁)
	Cut Pb	1.708 (d₁₁)	72%		Cut Ba	0.759 (d₁₁)	75%
PbB₅O₇F₃	Original	2.640 (d₁₅) −1.341 (d₂₄) −1.534 (d₃₃)		BaB₅O₇F₃	Original	1.010 (d₁₅) −0.430 (d₂₄) −0.747 (d₃₃)
	Cut Pb	2.273 (d₁₅) −1.146 (d₂₄) −1.288 (d₃₃)	14% 15% 16%		Cut Ba	0.918 (d₁₅) −0.375 (d₂₄) −0.674 (d₃₃)	9% 13% 10%
PbB₂O₃F₂	Original	−2.800 (d₂₂) −4.952 (d₃₃)		BaB₂O₃F₂	Original	−0.809 (d₂₂) −1.881 (d₃₃)
	Cut Pb	−0.780 (d₂₂) −2.776 (d₃₃)	72% 44%		Cut Ba	−0.530 (d₂₂) −0.732 (d₃₃)	34% 61%
SnB₂O₃F₂	Original	0.938 (d₂₂) −0.849 (d₃₃)
	Cut Sn	0.254 (d₂₂) −1.956 (d₃₃)	73% −130%

^aSHG reducing is calculated by formula: SHG(reducing) = 1 − SHG(cut)/SHG(original)

Fig. 1. Comparison of typical NLO materials on bandgap and SHG response. Nonlinear optical (NLO); second harmonic generation (SHG). Several famous NLO crystals and promising materials with outstanding SHG responses are highlighted in the different bandgap regions: (I) 3 to 4 eV, Bi₃TeBO₉ (20.0 KDP); (II) 4 to 5 eV, CsPbCO₃F (13.4 KDP) and BiB₂O₄F (12.0 KDP); (III) 5 to 6 eV, PbB₂O₃F₂ (13.0 KDP); (IV) 6 to 7 eV, BBO (5.7 KDP) and K₃B₆O₁₀Cl (4.0 KDP); (V) >7 eV, CBO (2.7 KDP), LBO (2.7 KDP), ABF (3.0 KDP), and KBBF (1.2 KDP).

Fig. 2. Crystal structures of barium borates after cation substitutions, Ba₅(BO₃)₃Cl (A), Ba₃B₆O₁₁F₂ (B), Ba₂B₅O₉Cl (C), Ba₂BO₃Br (D), BaB₅O₇F₃ (E), and BaB₂O₃F₂ (P31m) (F).

Fig. 3. Relative total energy between theoretical (red) and experimental (blue) structures in PbB₂O₃F₂, BaB₂O₃F₂, and Ba₂BO₃Br.

Fig. 4. Ultraviolet−visible−near infrared diffuse reflectance spectrum of Pb₂B₅O₉Cl (A) and Ba₂B₅O₉Cl (B). The insets are SHG intensity oscilloscope traces.

Fig. 5. Property changes from lead borates to barium borates. Changes in optical properties (SHG response and bandgap), and the classifications of four value sections based on the DUV (200 nm) and relatively strong SHG response (2 KDP) bounds in the cation substitution from lead to barium. Deep-ultraviolet (DUV); second harmonic generation (SHG).

Fig. 6. SHG response decreases along with the increase of (A) bandgap and (B) electron spatial distribution (ESD) in MB₂O₃F₂ (M = Pb, Pb_0.75Ba_0.25, Pb_0.25Ba_0.75, Ba).

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