From BaAlBO₃F₂ to BaAlB₃O₆F₂ and BaAl₂(B₃O₆)₂F₂: the enhancement of birefringence and band gap by extending the π-conjugated system combined with [Al–O/F] functional groups

Abstract

The investigation of birefringent materials is predominantly focused on π-conjugated systems; however, a large band gap or deep ultraviolet (DUV) transmittance cannot be guaranteed. In this work, we propose an extended π-conjugated strategy to increase the birefringence while keeping the large band gap. In the scheme, two new fluoroaluminoborates, BaAlB₃O₆F₂ and BaAl₂(B₃O₆)₂F₂, are synthesized by combining the [BO₃] group with the [AlO₄F₂] group and the [B₃O₆] group with the [AlO₃F] group through a rational structural design. The experimental results indicate that both BaAlB₃O₆F₂ and BaAl₂(B₃O₆)₂F₂ exhibit shorter UV cutoff wavelengths (<200 nm) and larger birefringence (Δn > 0.07@546 nm). Notably, this is a new finding in the Ba–Al–B–O–F system since the discovery of the well-known nonlinear optical crystal BaAlBO₃F₂. In comparison with BaAlBO₃F₂, BaAlB₃O₆F₂ and BaAl₂(B₃O₆)₂F₂ exhibit a markedly elevated birefringence (0.0418 vs. 0.087/0.105 at 546 nm). Furthermore, BaAl₂(B₃O₆)₂F₂ exhibits the largest band gap (7.87 eV) of all known F-containing aluminoborates. This work not only identifies two potential DUV birefringent materials, but also proposes a novel design approach for reconciling the conflicting properties between birefringence and bandgap.

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Introduction

Birefringent crystals are of significant importance in the field of optical applications. They are key materials for the production of prisms, polarizers, lenses, precision optics, and electronic laser components.^1–6 Currently, some birefringent materials such as MgF₂,⁷ CaCO₃,⁸ α-BaB₂O₄,⁹ YVO₄,¹⁰ LiNbO₃,¹¹ and quartz crystals¹⁰ are well developed and commercially available. However, the respective defects of these materials restrict their potential applications in the DUV (wavelengths less than 200 nm) range. For instance, MgF₂ and quartz crystals can be applied to DUV while their birefringence is relatively low. Conversely, CaCO₃, LiNbO₃ and YVO₄ exhibit high birefringence and are easily processed, but their operational wavelength is limited to the visible and near-infrared region. α-BaB₂O₄ possesses the requisite properties for DUV birefringent materials. However, its UV cut-off edge is only up to 189 nm, and crystal growth is challenging due to phase transition. Two essential prerequisites for the development of DUV birefringent materials are an adequate band gap and a sufficient birefringence.¹² However, it is a difficult problem to balance these two conflicting properties. Consequently, it remains imperative to identify DUV birefringent materials with optimized optical properties.

To search new DUV birefringent materials, the rational selection of functional groups in the structure of crystalline materials is a key factor.^13–16 For example, in the borate structure, the large electronegativity difference between B and O atoms gives it a wide transmittance. Meanwhile, the [BO₃] and [B₃O₆] groups have large optical anisotropy, which is conducive to the formation of large birefringence.^17–19 Therefore, the borate system represents an excellent source for the exploration of DUV birefringent crystals.^20–27 It is known that π-conjugated units such as [BO₃],²⁸ [B₃O₆],²⁹ [CO₃],³⁰ [NO₃]³¹ and [C₃N₃O₃]³² can produce enough optical anisotropy, resulting in large birefringence. However, the so-called dangling bonds of these π-conjugated units reduce the band gap, which limits their DUV transmittance window. To solve the problem, the π-conjugated units must connect with other functional groups by covalence bonds in order to remove the dangling bonds. Recently, Chen et al. proposed a confined π-conjugated strategy, in which π-conjugated groups should be connected by non-π-conjugated groups to weaken the interaction of π-conjugated groups.³³ In addition, in order to increase birefringence, the π-conjugated units should be arranged in a suitable way in the crystal structure.³⁴ In addition, it is reported that the introduction of secondary building units such as [BO₄],²² [BO₃F],²² [BeO₄],³⁵ and [PO₄],³⁶ can help the rational arrangement of the π-conjugated units. However, in previous efforts, it was difficult to increase the band gap and birefringence simultaneously.

In this work, we propose a strategy to enhance the contradictory properties of DUV birefringent materials by combining an extended π-conjugated unit with newly developed [Al–O/F] functional units. It is known that the [B₃O₆] unit has a larger π-conjugated system compared to [BO₃], which is beneficial to produce large birefringence. When a large electronegativity F atom is further introduced, Al atoms can be combined with O/F atoms to form complex and diverse [Al–O/F] functional groups.³⁷ The [Al–O/F] group has three advantages: (1) replacing O with a more electronegative F can increase the band gap and optical anisotropy compared to aluminoborate; (2) the rich coordination environment in [Al–O/F] groups provides more structural possibilities; and (3) compared with other fluoroborates, fluoroaluminoborates generally have better thermal stability, and it is easier to obtain large crystals in open systems.³⁸ Thus, fluoroaluminoborates containing both π-conjugated units and [Al–O/F] functional groups could be a new source for DUV birefringent materials.

To verify the above idea, BaAlBO₃F₂,³⁹ a famous nonlinear optical crystal with a small birefringence, was selected as a prototype. Before this work, BaAlBO₃F₂ was the only known compound in the Ba–Al–B–O–F system, with a band gap of 7.52 eV and a frequency doubling response of 2 times KDP. However, its birefringence is only 0.042@546 nm, and DUV phase matching cannot be realized. Therefore, this system has potential and requires further exploration. Two new alkali-earth fluoroaluminoborates BaAlB₃O₆F₂ and BaAl₂(B₃O₆)₂F₂ were discovered through the comprehensive exploration of Ba–Al–B–O–F. From BaAlBO₃F₂ to BaAlB₃O₆F₂ and BaAl₂(B₃O₆)₂F₂, it was demonstrated that a large band gap and birefringence can be simultaneously achieved by the rational combination of extended π-conjugated [B₃O₆] and [AlO₃F] groups. In addition, the single crystal structure and thermal and optical properties of the two materials were characterized and analyzed.

Experimental section

Reagents

BaF₂, Al₂O₃, H₃BO₃ (analytically pure, Aladdin Chemical Industry Co., Ltd) and AlF₃ (99%, Rhawn Chemical Industry Co., Ltd) were used without further processing.

Synthesis

The synthesis of BaAlB₃O₆F₂ and BaAl₂(B₃O₆)₂F₂ was carried out using the high-temperature solution method, yielding single crystals of the compounds. For BaAlB₃O₆F₂, the starting materials were BaF₂ (0.7013 g, 4 mmol), Al₂O₃ (0.2039 g, 4 mmol), and H₃BO₃ (1.1129 g, 18 mmol), which were mixed and ground before being placed in an alumina crucible. The temperature increased to 770 °C over a period of 8 h, was maintained at this temperature for 12 h, and cooled to room temperature at a rate of 105 °C h⁻¹. For BaAl₂(B₃O₆)₂F₂, BaF₂ (1.038 g, 6 mmol), AlF₃ (0.497 g, 6 mmol), and H₃BO₃ (1.465 g, 24 mmol) were mixed and ground, heated to 850 °C in 8 h, held for 6 h and cooled to 650 °C at 2 °C per hour before finally being cooled to room temperature. Small, colourless crystals of BaAlB₃O₆F₂ and BaAl₂(B₃O₆)₂F₂ were obtained from the products for structural determination.

The polycrystalline crystal of BaAlB₃O₆F₂ was obtained using the same conditions as used for the single crystal synthesis. The products were further washed with hot water to remove excess boric acid before the test. Polycrystalline samples of BaAl₂(B₃O₆)₂F₂ were prepared by the conventional solid-state method using stoichiometric ratios of raw materials. The mixed sample was subjected to a 2 h preheat at 510 °C, followed by 4 h calcination at 830 °C, and finally cooled to room temperature. It is noted that the synthesis of BaAl₂(B₃O₆)₂F₂ is sensitive to temperature and holding time. An inappropriate calcination temperature or longer holding time will decrease the purity and crystallinity.

Single-crystal structure determination

Single-crystal data for BaAlB₃O₆F₂ and BaAl₂(B₃O₆)₂F₂ were collected on a Bruker D8 VENTURE diffractometer equipped with a Mo IμS 3.0 microfocus X-ray source (λ = 0.71073 Å). Integration and absorption correction of the single-crystal data were performed using the SAINT program and processed using Olex2.⁴⁰ The structure was solved using the intrinsic phase method and refined using least squares techniques. The structure was checked for possible higher symmetry using PLATON.⁴¹ The crystal data and detailed refinement information are given in Table S1.† The atom positions, isotropic displacement parameters, and bond valence sums of each atom are presented in Tables S2 and S3† for BaAlB₃O₆F₂ and BaAl₂(B₃O₆)₂F₂, respectively. Selected bond distances and angles are summarized in Tables S4–S7.†

Powder XRD

Powder XRD was performed on a Haoyuan DX-27 mini X-ray diffractometer with Cu Kα radiation (λ = 1.54056 Å) at room temperature. The scanning was done with the 2θ angles in the interval 5–70°, a scan step width of 0.02°, and a fixed counting time of 2 s.

Thermal analysis

The thermal gravimetric (TG) analysis and differential scanning calorimetry (DSC) of BaAlB₃O₆F₂ and BaAl₂(B₃O₆)₂F₂ were performed with a HENVEN HCT-2 instrument under flowing air. The sample was placed in an Al₂O₃ crucible and heated from 30 to 1100 °C with a heating rate of 10 °C min⁻¹.

Infrared spectroscopy

The IR spectra of BaAlB₃O₆F₂ and BaAl₂(B₃O₆)₂F₂ were recorded on a Shimadzu IR Affinity-1 Fourier transform infrared spectrometer in the range of 400–4000 cm⁻¹. The sample was mixed with KBr and ground well.

UV–vis–NIR diffuse reflectance spectrum

The diffuse reflectance spectrum was measured at room temperature with a Shimadzu UV-2600i UV spectrophotometer in the 200–1100 nm wavelength range.

Birefringence measurements

The birefringence was assessed with a polarizing microscope (NIKON Eclipse Ci-POL) equipped with a quartz wedge compensator under a light source of 546 nm. According to the equation, R (retardation) = Δn × d, the birefringence was calculated, where R, Δn, and d represent the optical path difference, birefringence, and thickness of the crystal, respectively. The thickness of the crystalline sample was measured on a single-crystal XRD diffractometer.

Theoretical calculations

The electronic structures and optical properties for BaAlB₃O₆F₂ and BaAl₂(B₃O₆)₂F₂ were calculated using the CASTEP package.⁴² The generalized gradient approximation (GGA) with the Perdew–Burke–Ernzerhof (PBE) functional was selected as the exchange–correlation potential.⁴³ The norm-conserving pseudopotentials (NCP) were adopted.⁴⁴ The cutoff energy was set as 850 eV for both compounds. The dense k-points in the Brillouin zone were set as 2 × 1 × 2 and 2 × 2 × 1 for BaAlB₃O₆F₂ and BaAl₂(B₃O₆)₂F₂, respectively. The configurations for diverse electron orbitals were Ba: 5s²5p⁶6s², Al: 3s²3p¹, B: 2s²2p¹, O: 2s²2p⁴, and F: 2s²2p⁵, respectively. The GGA method usually underestimates the band gaps of crystals; therefore, the HSE06 method was also adopted to evaluate the band gap.⁴⁵

Results and discussion

Crystal structure

BaAlB₃O₆F₂ crystallized in monoclinic space group P2₁/c with the cell parameters a = 7.1245(6) Å, b = 12.708(1) Å, c = 7.6246(7) Å, and β = 112.189(3) Å (Table S1†). In this structure, one Ba atom, one Al atom, three B atoms, six O atoms, and two F atoms are combined to form an asymmetric unit. One Ba atom is coordinated with six O atoms and four F atoms to form [BaO₆F₄] polyhedron (Fig. 1a). The B atom is connected with three O atoms to form [BO₃] groups, and these [BO₃] groups are connected to each other to form a one-dimensional [BO₃]_∞ chain structure (Fig. 1d). The independent Al atom forms a trans-[AlO₄F₂] octahedron with four O atoms and two F atoms. The F atoms are located at opposite positions of the octahedron with the Al–O bond lengths ranging from 1.8458 to 1.8995 Å and the Al–F bond lengths ranging from 1.8088 to 1.8130 Å. The two trans-[AlO₄F₂] octahedra are connected to form the [Al₂O₆F₄] group by sharing two O atoms (Fig. 1b), and the [BaO₆F₄] polyhedra are connected to each other through an O and an F in [AlO₄F₂] to form a layered structure (Fig. 1c). Such cationic layers are connected to each other through a [BO₃]_∞ chain to form a three-dimensional frame (Fig. 1e). The bond valence sum (BVS) was calculated for all atoms of BaAlB₃O₆F₂ (Table S2†). The calculated results are consistent with their valences, which also proves the rationality of the structural model.

Fig. 1 (a) The coordination environment of the Ba atom. (b) The [Al₂O₆F₄] group formed by the connection of two [AlO₄F₂] octahedra. (c) The layered structure formed by the connection of the [BaO₆F₄] polyhedron and [AlO₄F₂] group in the c direction. (d) [BO₃] are connected to each other to form an infinite chain. (e) The 3D framework structure of BaAlB₃O₆F₂.

BaAl₂(B₃O₆)₂F₂ crystallized in trigonal space group R3̄c with cell parameters a = 7.0654(18) Å, b = 7.0654(18) Å, c = 37.529(13) Å (Table S1†). In the asymmetric unit, the unique Ba atom coordinates with 12 O atoms and 2 F atoms to form the [BaO₁₂F₂] polyhedron (Fig. 2a). The B atoms combine with three O atoms to form a plane [BO₃] triangle. The Al atoms combine with three O atoms and one F atom to form the distorted [AlO₃F] tetrahedron with an Al–O bond length of 1.743 Å and an Al–F bond length of 1.664 Å. Three [BO₃] and one [AlO₃F] units are connected by shared O atoms to form [AlB₃O₆F] basic building blocks (Fig. 2b), which are connected to each other forming a two-dimensional [AlB₃O₆F] infinite layer. The [AlB₃O₆F] layers are further connected via [BaO₁₂F₂] polyhedra to form a 3D framework structure (Fig. 2c), and Ba atoms are filled between the [AlB₃O₆F] layers. The BVS calculation results of BaAl₂(B₃O₆)₂F₂ also validate the structural correctness.

Fig. 2 (a) The coordination environment of the Ba atom. (b) The basic building block of [AlB₃O₆F] formed by the connection of [B₃O₆] and [AlO₃F] groups. Crystal structures of (c) BaAl₂(B₃O₆)₂F₂, (d) KBe₂BO₃F₂, and (e) BaAlBO₃F₂ in the a direction.

The crystal structure of BaAlB₃O₆F₂ exhibits a unique structure type similar to that of SrAlB₃O₆F₂,⁴⁶ while the structure of BaAl₂(B₃O₆)₂F₂ is very close to those of KBe₂BO₃F₂ and BaAlBO₃F₂. Fig. 2d and e show the 3D framework structure of KBe₂BO₃F₂ and BaAlBO₃F₂ in the a direction, respectively. It can be seen that BaAl₂(B₃O₆)₂F₂, KBe₂BO₃F₂ and BaAlBO₃F₂ show similar layered structural features. In KBe₂BO₃F₂,⁴⁷ [BeO₃F] and [BO₃] are connected to form a layered structure, and K atoms are filled between the layers. BaAl₂(B₃O₆)₂F₂ has changed its original structure by replacing [BeO₃F] with [AlO₃F] and [BO₃] with [B₃O₆], and K cations are substituted by Ba cations.

In addition, the [Al–O/F] functional units are [AlO₃F₂], [AlO₄F₂], [AlO₃F], in which the central Al atoms adopts sp³d, sp³d², and sp³ hybridization, for BaAlBO₃F₂, BaAlB₃O₆F₂, and BaAl₂(B₃O₆)₂F₂, respectively. Fig. S1† shows the different arrangements of [Al–O/F] groups in BaAlBO₃F₂, BaAlB₃O₆F₂, and BaAl₂(B₃O₆)₂F₂. The layered structure in BaAlBO₃F₂ is composed of the connection of [AlO₃F₂] to the [BO₃] group. Different from BaAlBO₃F₂, the layered structure in BaAlB₃O₆F₂ is composed of the connection of the [BO₃] chain to [AlO₄F₂]. The layered structure in BaAl₂(B₃O₆)₂F₂ is composed of [AlO₃F] connected to the [B₃O₆] group, which greatly increases its optical anisotropy, resulting in a large birefringence.

PXRD and thermal properties

The synthesis of polycrystalline samples of BaAlB₃O₆F₂ is not straightforward, while BaAl₂(B₃O₆)₂F₂ can be obtained easily. Initially, according to the stoichiometric ratio of BaAlB₃O₆F₂, only the known compound BaAlBO₃F₂ can be obtained. Then, on the basis of the stoichiometric ratio, 50% additional boric acid can be added to obtain the pure phase of BaAlB₃O₆F₂. However, if the pure phase of BaAlBO₃F₂ is synthesized, it is not possible to transform it to BaAlB₃O₆F₂ by adding the same amount of boron oxide, even under different calcination conditions. It is speculated that BaAlBO₃F₂ is a very stable compound, and no other reaction can occur if it is generated. BaAlB₃O₆F₂ can only be formed by the initial addition of excess boron oxide as a flux. Phase analysis of the prepared BaAlB₃O₆F₂ and BaAl₂(B₃O₆)₂F₂ was carried out. As shown in Fig. S2,† the experimental patterns of BaAlB₃O₆F₂ and BaAl₂(B₃O₆)₂F₂ are in good agreement with their simulated XRD patterns. The thermal analysis of BaAlB₃O₆F₂ and BaAl₂(B₃O₆)₂F₂ demonstrated that both of them have high thermal stability, with a maximum weight loss of 3% before 950 °C (Fig. S3†). Their thermogravimetric results revealed endothermic peaks at 880 and 810 °C, respectively. The pure phases of BaAlB₃O₆F₂ and BaAl₂(B₃O₆)₂F₂ were melted and cooled to room temperature slowly. It was found that they formed an amorphous phase after melting although the thermogravimetric curves showed no weight loss. Because of the high viscosity of boron-rich melt, it is necessary to introduce additional flux to perform crystal growth.

Spectrum analysis

The infrared spectra of BaAlB₃O₆F₂ and BaAl₂(B₃O₆)₂F₂ are presented in Fig. S4a and S4b,† respectively. For BaAlB₃O₆F₂, the strong absorption band between 1470 and 1150 cm⁻¹ can be attributed to the asymmetric stretching of the [BO₃] group, while the peaks near 958 and 924 cm⁻¹ can be attributed to the symmetric stretching of [BO₃]. The peaks at 756 and 700 cm⁻¹ belong to the bending vibration of [BO₃], and the peaks between 600 and 400 cm⁻¹ are mainly caused by the stretching bending vibration of [AlO₄F₂]. For BaAl₂(B₃O₆)₂F₂, the peaks at 1300 cm⁻¹ and 1400 cm⁻¹ are due to the asymmetric stretching of the [BO₃] group, while the peaks at 1010 cm⁻¹ and 1090 cm⁻¹ are mainly related to the symmetric stretching vibration of the [BO₃] group. The peaks at 835 cm⁻¹ and 727 cm⁻¹ correspond to the out-of-plane bending of the [BO₃] group, and the peaks at 696 cm⁻¹ and 469 cm⁻¹ may correspond to the stretch-bending vibration of the [AlO₃F] group. The test results clearly demonstrate that BaAlB₃O₆F₂ and BaAl₂(B₃O₆)₂F₂ have completely different fundamental building units, which is consistent with the single crystal XRD structure analysis.

The UV–vis–NIR spectra of BaAlB₃O₆F₂ and BaAl₂(B₃O₆)₂F₂ demonstrate that both of them do not exhibit any absorption peak before 200 nm. This observation indicates that the UV cut off edge of BaAlB₃O₆F₂ and BaAl₂(B₃O₆)₂F₂ is less than 200 nm (Fig. 3). The reasons for the large band gap of BaAlB₃O₆F₂ and BaAl₂(B₃O₆)₂F₂ can be attributed to the following factors: (1) the valence electrons of Ba²⁺ do not contain d–d and f–f transitions; (2) the introduction of fluorine widens the band gap; and (3) the absence of dangling bonds in the [BO₃] and [B₃O₆] groups further increases the band gap.

Fig. 3 UV–vis–NIR diffuse reflectance spectra of (a) BaAlB₃O₆F₂ and (b) BaAl₂(B₃O₆)₂F₂.

Birefringence measurements

Due to the [BO₃] ring structure of BaAlB₃O₆F₂ and the [B₃O₆] ring structure of BaAl₂(B₃O₆)₂F₂, both materials are predicted to have large birefringence. The birefringence of BaAlB₃O₆F₂ and BaAl₂(B₃O₆)₂F₂ was measured using a Nikon polarizing microscope under cross-polarized light. Their crystal picture and the image after extinction are shown in Fig. 4. The experimental results show that the crystal interference color of BaAlB₃O₆F₂ observed under polarized light is fifth-order yellow. According to the Michel–Levy interference color diagram, its optical path difference is 2.53 μm and the crystal thickness (d) is 29 μm (Fig. S5a†). Therefore, according to the relationship Δn = R/d, the measured birefringence is 0.087 at 546 nm. The interference color of BaAl₂(B₃O₆)₂F₂ measured by the same steps is sixth grade yellow, its optical path difference is 3.01 μm and the crystal thickness is 29 μm (Fig. S5b†). Therefore, it has a birefringence of 0.105. Compared with BaAlBO₃F₂, the birefringence of the two materials is significantly improved. In order to predict their optical anisotropy, we also use the DFT method to calculate their birefringence. The birefringence values of BaAlB₃O₆F₂ and BaAl₂(B₃O₆)₂F₂ at 546 nm are 0.073 and 0.097, respectively, which are in good agreement with the measured birefringence. The birefringent properties of BaAlB₃O₆F₂ and BaAl₂(B₃O₆)₂F₂ are comparable to those of some recently published UV birefringent materials, such as Ba_3.75MgB₇O₁₄F_2.5 (Δn = 0.081@546 nm),⁴⁸ RbSb₂(C₂O₄)F₅ (Δn = 0.09@546 nm),⁴⁹ Rb[B₃O₃F₂(OH)₂] (Δn = 0.09@546 nm),⁵⁰ Ba₂K_1.6Na_0.4Sc₂(BO₃)₄ (Δn = 0.11@550 nm),⁵¹ (NH₄)[C(NH₂)₃][B₃O₃F₄(OH)] (Δn = 0.101@1064 nm)⁵² and RbBaScB₆O₁₂ (Δn = 0.139@550 nm).⁵³

Fig. 4 Photos of the original (a) BaAlB₃O₆F₂ crystal and (d) BaAl₂(B₃O₆)₂F₂ crystal. Photos of (b) the BaAlB₃O₆F₂ crystal and (e) the BaAl₂(B₃O₆)₂F₂ crystal after extinction. The calculated refractive indices of (c) BaAlB₃O₆F₂ and (f) BaAl₂(B₃O₆)₂F₂.

BaAlB₃O₆F₂ possesses a [BO₃]_∞ chain structure, which has a denser [BO₃] arrangement in comparison with BaAlBO₃F_2. By calculating the density per unit volume of [BO₃] in BaAlBO₃F₂(0.0155), BaAlB₃O₆F₂(0.0188) and BaAl₂(B₃O₆)₂F₂(0.027), it is obvious that a higher [BO₃] density is beneficial to increase optical anisotropy, i.e., birefringence. In addition to the density of the [BO₃] groups, the arrangement of the [BO₃] groups also has an effect on the birefringence. Therefore, the dihedral angles between adjacent [BO₃] groups in BaAlB₃O₆F₂ and BaAl₂(B₃O₆)₂F₂ were calculated. The dihedral angles between adjacent [BO₃] groups in BaAlB₃O₆F₂ are 12.454°, 18.069°, and 38.536°, respectively, demonstrating that the [BO₃] groups are not perfectly aligned, while the dihedral angle is almost zero in BaAl₂(B₃O₆)₂F₂. Compared to BaAlBO₃F₂, BaAl₂(B₃O₆)₂F₂ has an extended π-conjugated [B₃O₆] ring, and it contains [AlO₃F] (point group, C_3v) units in contrast to highly symmetrical [AlO₃F₂] (point group, D_3h) units in BaAlBO₃F₂. For BaAl₂(B₃O₆)₂F₂, the introduction of the [B₃O₆] ring and its layered structure further increases the birefringence property, while covalently bonded [AlO₃F] units help remove the dangling bonds of [B–O] groups, which inherit the advantages of the large band gap feature of KBe₂BO₃F₂ and BaAlBO₃F₂.

Theoretical calculations

In order to clarify the relationship between the optical properties and electronic structures, the band structure, density of state and partial density of state (PDOS) of BaAlB₃O₆F₂ were calculated using first principles. Considering that GGA underestimates the bandgap of the compound in standard DFT calculations due to the discontinuity of the exchange associated energy, we further corrected the band gaps using the HSE06 method. The results indicate that BaAlB₃O₆F₂ and BaAl₂(B₃O₆)₂F₂ have wide band gaps of 7.53 and 7.87 eV (Fig. S6†), respectively, and both of them show an indirect band gap feature. The corresponding UV cutoff edges are 165 and 157.5 nm for BaAlB₃O₆F₂ and BaAl₂(B₃O₆)₂F₂, respectively. The calculated results are in good agreement with the experimental ones (UV cut off edges < 200 nm). Table S8† shows the bandgap, birefringence and [Al–O/F] arrangement of the currently reported F-containing aluminoborates. Fig. 5 presents a plot of band gap and birefringence values of some F-containing aluminoborates. Notably, BaAl₂(B₃O₆)₂F₂ has the largest band gap (7.87 eV) and a large birefringence (Δn = 0.105 at 546 nm) among all known F-containing aluminoborates (including aluminoborate fluorides and fluoroaluminoborates). This demonstrates that BaAlB₃O₆F₂ and BaAl₂(B₃O₆)₂F₂ are potential DUV birefringent materials.

Fig. 5 Comparison of the bandgap and birefringence of F-containing aluminoborates.

The PDOS diagram of BaAlB₃O₆F₂ is similar to that of BaAl₂(B₃O₆)₂F₂ (Fig. 6). For both compounds, the top of the valence bands is mainly composed of O 2p and F 2p orbitals. The bottom of the conduction bands is mainly composed of Ba 5d, Al 3s3p, and B 2s2p orbitals. The difference is that the contribution of the B 2s2p orbitals in BaAl₂(B₃O₆)₂F₂ to the valence bands is greater than that in BaAlB₃O₆F₂. The high densities and overlaps of Al 3s3p, B 2s2p, O 2p, and F 2p near Fermi level orbitals indicate that the [B–O] and [Al–O/F] groups mainly determine the optical properties of BaAlB₃O₆F₂ and BaAl₂(B₃O₆)₂F₂.

Fig. 6 Calculated total and partial densities of states of (a) BaAlB₃O₆F₂ and (b) BaAl₂(B₃O₆)₂F₂.

Conclusions

In summary, our work provides two new barium fluoroaluminoborates, BaAlB₃O₆F₂ and BaAl₂(B₃O₆)₂F₂, as potential DUV birefringent materials. The two crystals were synthesized in an open system through reasonable structural design. It presents a systematic work on the Ba–Al–B–O–F system many years after the discovery of BaAlBO₃F₂, which also enriches the fluoroaluminoborate family. Compared with the compound BaAlBO₃F₂, the birefringence of the two materials is significantly improved; the birefringence values of BaAlB₃O₆F₂ (Δn = 0.087@546 nm) and BaAl₂(B₃O₆)₂F₂ (Δn = 0.105@546 nm) are 2 and 2.5 times that of BaAlBO₃F₂, respectively. In particular, BaAl₂(B₃O₆)₂F₂ have [AlO₃F] and [B₃O₆] rings, which further improve the birefringenc performance on the basis of inheriting the advantages of the large band gap and large birefringence of KBe₂BO₃F₂. In addition, among all known F-containing aluminum borates, BaAl₂(B₃O₆)₂F₂ exhibits the largest band gap (7.87 eV) among all known F-containing aluminoborates. The first principles calculations demonstrate that the [AlO₃F] tetrahedron and the [B₃O₆] ring make a major contribution to the optical properties of BaAl₂(B₃O₆)₂F₂. We reveal that extending π-conjugated units combined with [Al–O/F] functional units can help in the design of DUV birefringent materials. This finding also provides new possibilities for searching DUV birefringent materials in fluoroaluminoborates.

Author contributions

The manuscript was written through the contributions of all authors: conceptualization, Y.W.; methodology, C.C.; software, C.C. and B.Z.; validation, Y.W.; formal analysis, C.C. and Y.B.; investigation, C.C, Y.W.; data curation, C.C and D.D.; writing (original draft preparation), C.C.; writing (review and editing), Y.W.; visualization, C.C.; supervision, Y.W.; project administration, Y.W.; funding acquisition, Y.W., B.Z. All authors have given approval to the final version of the manuscript.

Data availability

• The data supporting this article have been included as part of the ESI.†

• Crystallographic data for BaAlB₃O₆F₂ and BaAl₂(B₃O₆)₂F₂ has been deposited at the CCDC under 2356772 and 2356774† and can be obtained from https://www.ccdc.cam.ac.uk/.

Conflicts of interest

The authors declare no competing financial interest.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 21975062 and 52072109), the Natural Science Foundation of Hebei Province (E2023201017 and B2023201108), and the Excellent Youth Research Innovation Team of Hebei University (QNTD202403).

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Footnote

† Electronic supplementary information (ESI) available. CCDC 2356772 and 2356774. For ESI and crystallographic data in CIF or other electronic format see DOI: https://doi.org/10.1039/d4qi01530d

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