Ba₃Mg₃(BO₃)₃F₃ polymorphs with reversible phase transition and high performances as ultraviolet nonlinear optical materials

Abstract

Nonlinear optical (NLO) materials are the vital components of future photoelectric technologies as they can broaden the tunable wavelength range supplied by common laser sources. However, the necessary prerequisites for a practical NLO material are rather strict. Accordingly, considerable efforts have been focused on finding potential NLO materials. Here we report two asymmetric beryllium-free borates Pna2₁- and P$\bar 6$2m-Ba₃Mg₃(BO₃)₃F₃ featuring NLO-favorable ²_∞[Mg₃O₂F₃(BO₃)₂] layered structures. The reversible phase transition among two polymorphs was demonstrated by multiple experimental tests. The optical measurements reveal that Pna2₁-Ba₃Mg₃(BO₃)₃F₃ possesses the optical properties required for ultraviolet NLO applications. Remarkably, Pna2₁-Ba₃Mg₃(BO₃)₃F₃ has a large laser damage threshold, a deep-ultraviolet cutoff edge, a favorable anisotropic thermal expansion as well as the capacity of insolubility in water. These optical properties can be comparable or superior to that of commercial NLO material β-BaB₂O₄, which make Pna2₁-Ba₃Mg₃(BO₃)₃F₃ a promising ultraviolet NLO material.

Introduction

Nonlinear optical (NLO) materials applied from ultraviolet (UV) to infrared spectral ranges are the vital components of future photoelectric technologies^1,2,3,4. Accordingly, considerable and sustained efforts have been focused on designing and synthesizing new potential NLO materials^5,6,7,8,9. Generally speaking, a practical UV NLO material should simultaneously satisfy the following criteria: a noncentrosymmetric structure; a broad transparent spectral range down to the UV region (λ < 400 nm); a relatively large second-order nonlinear coefficient (d_ij > 0.39 pm/V); a moderate birefringence to satisfy the phase-matching condition, chemical stability (non-deliquescent), and resistance to laser (large laser damage threshold, large LDT); and ease of growth of large single crystals with high optical quality¹⁰. Targeting above conditions, until now, the borate system plays a dominant role in UV NLO materials because borates possess wide optical transparency windows, varied acentric structure types, high LDTs, and large polarizabilities^{11,12,13,14,15,16,17,18}. Therefore, a variety of commercial borate-based UV NLO materials have been widely investigated and developed. Among them, borates with planar [BO₃]³⁻ anionic groups have always been at the center of the search for NLO materials with large second-harmonic generation (SHG) response and birefringence, which mainly benefits from the π-conjugated molecular orbitals of [BO₃]³⁻ units^19,20,21,22. Based on this, several borates with [BO₃]³⁻ NLO-active units in coplanar and aligned configuration were continuously reported with good optical properties, including KBe₂BO₃F₂ (KBBF)¹⁹, BaAlBO₃F₂²⁰, NaSr₃Be₃B₃O₉F₄²¹, Li Sr(BO)²², etc.

For the sake of finding new novel UV or even deep-UV (λ < 200 nm) NLO crystals, an effective design tactic is to introduce fluorine into the structural framing of borate system based on the following considerations. First, the fluorine with the largest electronegativity (χ = 3.98) can widen the transparency area and make the cutoff edge of borates blue-shift into UV or even deep-UV spectral region^{19,20,21,23,24,25}. Second, substituting oxygen with fluorine in [BO₄]⁵⁻ maternal blocks to form [BO_xF_4−x]^(x+1)− (x = 0, 1, 2, 3) fundamental building blocks can make the anionic groups more flexible, and the negative effective charges at the terminal oxygen will be partly reduced, resulting in a suitable SHG coefficient and birefringence^26,27,28,29. Third, the introduction of fluoride-containing flux can effectively decrease the viscosity of the borate systems during the growth of single crystals, which is a desirable choose for growing the large single crystals^20,24,25,30.

For us, besides selecting the appropriate system (borate) and introducing anion (fluorine), how to effectively design UV NLO materials with presupposed structures and properties is also critically important. The following ideas were considered for designing the target molecules: first, in order to manipulate the B–O fundamental building blocks into isolated planar [BO₃]³⁻ configuration, we adjusted the ratio of cations and boron to >1.0 based on the rules proposed by Becker³¹. Second, we use the strategy of chemical cosubstitution to make structural modifications based on the classic NLO materials with the goal of obtaining new molecular structures contain NLO-favorable layered structures^32,33.

Motivated by these, considering that s-block elements Be and Mg, Sr and Ba appear tightly clustered in the periodic table with the similar electronic configurations, sharing many common physicochemical properties. Therefore, we attempted to substitute the Be and Sr atoms of Sr₂Be₂B₂O₇ (SBBO)¹ with Mg and Ba atoms through chemical cosubstitution idea to create new SBBO-like borates, which leads us to discover two new beryllium-free borates, Pna2₁- and P$\bar 6$2m-Ba₃Mg₃(BO₃)₃F₃ (Pna2₁- and P$\bar 6$2m-BMBF), featuring SBBO-like layered structures without structural instability. The ²_∞[Mg₃O₂F₃(BO₃)₂] layers in both of them not only preserve the NLO-favorable structural habits of SBBO, but also introduce the Mg–F bonds served between layers as bridges to enhance the interlayer interaction. Based on the top designing molecule structures, large-size single crystals of Pna2₁-BMBF were also grown through finding the suitable flux system. The optical measurements based on the crystal reveal that Pna2₁-BMBF possesses the NLO properties required for the UV NLO applications, which indicates that Pna2₁-BMBF is a potential UV NLO material.

Results

The reversible phase transition between two polymorphs

Single crystal X-ray diffraction reveals that two new borates crystallize into the asymmetric space group of Pna2₁ (No. 33) and P$\bar 6$2m (No. 189), respectively (Table 1 and Supplementary Table 1). Interestingly, the molecular formula of both phases was determined as Ba₃Mg₃(BO₃)₃F₃ through structure solutions, which have the same simplest molecular formula with BaMgBO₃F (monoclinic, Cc) reported by Li. et al.³⁴. And the relatively low temperature factors and residual factors verify the correctness of those two crystal models, which also indicates the existence of two polymorphs. Furthermore, the BMBF polymorphs and phase transitions are further confirmed by high-temperature in situ powder X-ray diffraction and thermal expansion coefficients experiment: based on the results of thermal gravimetric and differential scanning calorimetry analysis (Fig. 1a), we make circular heating and cooling the Pna2₁-BMBF samples in the region of 100–650 °C. When the temperature rises to 500 °C, the Pna2₁-BMBF phase start to transfer into P$\bar 6$2m-BMBF phase, and P$\bar 6$2m-BMBF is stable up to 650 °C. When the temperature begins to decrease, P$\bar 6$2m-BMBF phase can also transfer into Pna2₁-BMBF, indicating the reversibility of this phase transition behavior. More intuitively, the disappearance and appearance of X-ray diffraction peaks at about 2θ = 23.690, 26.994, and 27.686° in BMBF series can help us to judge this phase transition (Fig. 1b, c). The measured average thermal expansion coefficients based on the three as-polished (100), (010), and (001) wafers occur sudden change at about 450 °C, which is caused by the phase transitions of BMBF series (Fig. 1d).

Table 1 Crystallographic data for Pna2₁-and P$\bar 6$2m-Ba₃Mg₃(BO₃)₃F₃

Fig. 1

Basic physicochemical properties of Ba₃Mg₃(BO₃)₃F₃. a Thermal gravimetric and differential scanning calorimetry (DSC) curves. Endo means the endothermic direction. There are two remarkable endothermic peaks (741.8 and 1108.9 °C) on the heating curve and two exothermic peaks (634.1 and 1035.1 °C) on the cooling curve, respectively. b, c High-temperature in situ powder X-ray diffraction data circularly collected in the region of 100–650 °C. The experimental and caculated powder X-ray diffraction patterns of Pna2₁-Ba₃Mg₃(BO₃)₃F₃ (blue lines) and P$\bar 6$2m-Ba₃Mg₃(BO₃)₃F₃ (red lines). The enlarged version of c in the 2θ region from 22.3 to 28.2° is shown in b to better understand the phase transition behavior between two polymorphs. d Thermal expansion measurements tested by (100), (010), and (001) Pna2₁-Ba₃Mg₃(BO₃)₃F₃ crystal plates. dL and L₀ mean the change in crystal plates length and initial length of crystal plates, respectively. e Solubility experiments of Pna2₁-Ba₃Mg₃(BO₃)₃F₃, α- and β-BaB₂O₄

Crystal structures of Pna2₁- and P $\bar 6$2m-BMBF

The structural evolution among SBBO, Pna2₁-, and P$\bar 6$2m-BMBF are shown in Fig. 2, which verifies the validity of structure-oriented design strategy. As shown in Fig. 2a, b, e, BMBF series possess a similar layered crystal structures, their crystal structures are both composed of ²_∞[Mg₃O₂F₃(BO₃)₂] layers (Supplementary Figure 1) along the a-axis for Pna2₁-BMBF and c-axis for P$\bar 6$2m-BMBF, and those single layers are further connected by the Mg–F bonds to construct a three-dimensional framework with tunnels running along the c (or a)-axis. In the asymmetric unit of Pna2₁-BMBF, the Ba, Mg, B, and F atoms occupy three crystallographically unique positions, for the O atoms there are nine unique positions. While for P$\bar 6$2m-BMBF with higher symmetry, the Ba, Mg, B, O, and F atoms occupy one, one, two, two, and one unique positions (Supplementary Tables 2, 3, 5, and 6). In both BMBF polymorphs, the B atoms possess only one coordination type, the [BO₃]³⁻ triangles (Fig. 2c, d). The B–O bond distances and O–B–O bond angles locate in the range from 1.341 to 1.395 Å, 117.6 to 120.9 ° for Pna2₁-BMBF, and 1.349 to 1.381 Å, 117.0 to 122.8 ° for P$\bar 6$2m-BMBF, respectively (Supplementary Tables 4 and 7). The Mg atoms in both polymorphs are six-coordinated into the MgO₄F₂ octahedra with four O and two F atoms locating in the equatorial and axial positions, respectively. Three MgO₄F₂ units share three O atoms to generate a six-membered ring cluster Mg₃O₉F₆ (Supplementary Figure 2), then those clusters link together via the axial Mg–F bonds to build an isolated ³_∞[Mg₃O₉F₃] triangular prism (Supplementary Figure 3). Interestingly, two [BO₃]³⁻ units locate in and out of the six-membered ring Mg₃O₉F₆ to form polymer and further polymerize into ²_∞[Mg₃O₂F₃(BO₃)₂] infinite layers, and the connection is by bridging Mg–F bonds to form a three-dimensional multilayered structure. All the Ba atoms are coordinated into BaO_nF_m (m + n = 10 and 11) polyhedra, located between the adjacent ²_∞[Mg₃O₂F₃(BO₃)₂] layers, which is quite like the arrangement of the Sr atoms in SBBO¹.

Fig. 2

Crystal structural features of Pna2₁-Ba₃Mg₃(BO₃)₃F₃. a, b The structural evolution from Sr₂Be₂B₂O₇ to Pna2₁-Ba₃Mg₃(BO₃)₃F₃. c, d The orientation of [BO₃]³⁻ groups in Pna2₁- and P$\bar 6$2m-Ba₃Mg₃(BO₃)₃F₃, respectively. e The layered structure of derivative P$\bar 6$2m-Ba₃Mg₃(BO₃)₃F₃ derived by phase transition from Pna2₁-Ba₃Mg₃(BO₃)₃F₃

Structurally, the triangular [BO₃]³⁻ units in both Pna2₁- and P$\bar 6$2m-BMBF adopt nearly coplanar configuration. This is propitious to generate large SHG response and birefringence because of the strong anisotropy resulting from their different polarizabilities in different directions, which is similar to the NLO materials containing π-planar triangular [CO₃]^2−35,36. The F–Mg–F bonds act as bridge-linking role to connect the neighboring layers, which is similar to the [B₂O₅]⁴⁻ dimers in LiNa₅Be₁₂B₁₂O₃₃³⁷ and the [B₃O₆]³⁻ groups in Cs₃Zn₆B₉O₂₁^38,39. Further, the electrostatics force of the interaction between layers in Pna2₁- and P$\bar 6$2m-BMBF was evaluated and |F_Mg–F| is stronger than that of |F_K–F| in KBBF (Supplementary Table 8), indicating that the electrostatic interactions between Mg–F bonds in Pna2₁- and P$\bar 6$2m-BMBF provide better linkage of neighboring layers, which is favorable to improve the layering tendency and the same results can be concluded from the ease of the growth of block-like crystals of BMBF series than that of KBBF.

Crystal growth and optical quality of Pna2₁-BMBF

After various attempts, Pna2₁-BMBF crystal with dimensions up to 16 × 14 × 8 mm³ has been grown at the optimal conditions (Fig. 3a). Pna2₁-BMBF crystal has never cracked during cutting and polishing into (100), (010), and (001) wafers (Fig. 3b). The crystallization quality of the as-grown crystal was checked by the X-ray rocking curve. As shown in Fig. 3c, the full-width at half-maximum on (100) face of Pna2₁-BMBF crystal was measured to be 18″, indicating high crystalline quality. The conoscopic interference pattern (Fig. 3d) shows that the as-grown Pna2₁-BMBF crystal is biaxial, optical homogeneous, and does not have any strain inside. When taken together, Pna2₁-BMBF crystal shows high optical quality, and the optical measurements based on this crystal are reliable.

Fig. 3

The as-grown single crystal and optical quality experiments of Pna2₁-Ba₃Mg₃(BO₃)₃F₃. a Photograph of the as-grown crystal with dimensions up to 16 × 14 × 8 mm³ grown by the top-seeded solution growth method. b The cut and polished (100), (010), and (001) wafers with dimensions up to 4 × 4 × 1 mm³. The crystals were cut plane parallel and polished to optical quality using a Unipol-300 grinding/polishing machine. c The high-resolution X-ray diffraction rocking curve for (100) wafer. The full-width at half-maximum on (100) face of the Pna2₁-Ba₃Mg₃(BO₃)₃F₃ crystal is about 18″, indicating high crystalline quality. d The conoscopic interference pattern of Pna2₁-Ba₃Mg₃(BO₃)₃F₃ crystal. All the images and elements of them were created by ourselves

High performances as UV NLO materials

Pna2₁-BMBF was subjected to physicochemical property characterizations based on the single-crystal level.

Thermal expansion coefficients are vital parameters for crystal growth and application in devices. As can be seen in Fig. 1d, the average thermal expansion coefficients in the region from 100 to 450 °C are evaluated to be α_a = α(100) = 2.17 × 10⁻⁵ K⁻¹, α_b = α(010) = 1.63 × 10⁻⁵ K⁻¹, and α_c = α(001) = 1.53 × 10⁻⁵ K⁻¹, respectively. The value of α_a/α_c is about 1.43 for Pna2₁-BMBF crystal, which is smaller than that of β-BaB₂O₄ (β-BBO) (α_c/α_a = 9)⁴⁰. Therefore, Pna2₁-BMBF crystal exhibits a more favorable anisotropic thermal expansion, which will effectively protect the crystals from cracking caused by thermal expansion during crystal growth and optical devices fabrication.

To study the water solubility of Pna2₁-BMBF, we dipped the target Pna2₁-BMBF (0.113 g) crystal as well as the references α- and β-BBO crystals (0.159 and 0.105 g) into 20 mL de-ionized water at room temperature. As plotted in Fig. 1e, the weight of Pna2₁-BMBF did not change in the measured time ranges, while for α- and β-BBO crystals, they were dissolved in water in 90 h. These indicate that Pna2₁-BMBF is chemically stable and not soluble in the water.

We carried out the SHG measurements by the Kurtz–Perry method⁴¹ with incident lasers at λ = 1064 nm. Meanwhile, the well-known NLO material KH₂PO₄ (KDP) was used as the reference. The comparison of SHG signals produced by Pna2₁- and P$\bar 6$2m-BMBF polycrystalline samples in the same particle sizes ranging from 200 to 250 μm reveals that Pna2₁- and P$\bar 6$2m-BMBF exhibit suitable SHG responses of ∼1.8 and 2.0 × KDP, respectively. Such SHG responses are large enough for the applications of UV NLO materials and it is also comparable to those reported borates with deep-UV cutoff edges, such as KBBF (1.26 × KDP)¹⁹, LiNa₅Be₁₂B₁₂O₃₃³⁷ (1.4 × KDP), and Li₄Sr(BO₃)₂ (2 × KDP)²². According to the results, the SHG efficiency increases with the raising particle sizes, indicating that both BMBF polymorphs exhibit type I phase-matching behavior in 1064 nm incident lasers. In addition, the effective NLO coefficients (d_eff) of Pna2₁- and P$\bar 6$2m-BMBF crystal are estimated to be about 1.3 and 1.4 × KDP according to the square roots of the ratios of their corresponding SHG signal intensities. In order to verify the results, large sizes of single crystals should be grown and cut to evaluate the SHG coefficients based on the crystal level, which is discussed in detail in the following parts.

The as-grown crystals were cut and optically polished to 1 mm thickness for the spectrum measurement. As presented in Fig. 4b, the Pna2₁-BMBF crystal exhibits a broad transmission of 184–3780 nm, indicating that the application of Pna2₁-BMBF crystal can cover a spectral range from UV to near-infrared. Obviously, the UV cutoff edge of Pna2₁-BMBF is about 184 nm, which is 5 nm shorter than that of β-BBO (189 nm) in the same measured condition. And also the high transmittance of Pna2₁-BMBF in the UV spectral range makes it possible to be applied as a UV NLO material. The short cutoff edge is beneficial to obtain high LDT, therefore, LDT measurements were carried out using a pulsed nanosecond laser (1064 nm, 10 ns, and 10 Hz). A well-polished high-quality (001) wafer of Pna2₁-BMBF has a LDT of ∼6.2 GW/cm², which is comparable to β-BBO crystal (∼6.0 GW/cm²) at the same experimental conditions.

Fig. 4

Optical properties of Pna2₁-Ba₃Mg₃(BO₃)₃F₃. a Powder second-harmonic generation data for Ba₃Mg₃(BO₃)₃F₃ polymorphs at 1064 nm laser radiation. The well-known NLO material KH₂PO₄ (KDP) was used as the reference. The curves are drawn to guide the eyes, and are not fit to the data. The error bars from left to right correspond to sieved crystal particle size ranges: 20–38; 38–55; 55–88; 88–105; 105–150; 150–200; and 200–250 μm. b Transmission spectrum of Pna2₁-Ba₃Mg₃(BO₃)₃F₃ crystal. Transmittance curve (magenta line) between 180 and 2500 nm was collected by a Shimadzu Solid Spec-3700DUV Spectrophotometer. Transmittance curve (black line) between 2500 and 4000 nm was collected by a Shimadzu IRAffinity-1 spectrometer. Inset gives transmittance curves between 170 and 400 nm for Pna2₁-Ba₃Mg₃(BO₃)₃F₃ (red line) and β-BaB₂O₄ (blue line). The ultraviolet cutoff edge of Pna2₁-Ba₃Mg₃(BO₃)₃F₃ is about 184 nm, which is 5 nm shorter than that of β-BBO (189 nm). c The refractive index dispersion curves for the Pna2₁-Ba₃Mg₃(BO₃)₃F₃ crystal. d The refractive index dispersion curves for fundamental (blue lines) and the second-harmonic (red lines) light. Based on the Sellmeier equations, when considering the type I phase-matching condition, n(ω) = n(2ω), the shortest type I phase-matching wavelengths in the xz and xy plane are evaluated to be 310 and 322 nm

The refractive indices of Pna2₁-BMBF were measured using prism coupling method. As it follows the inequality n_z − n_y < n_y − n_x, which depicts that Pna2₁-BMBF is a negative biaxial crystal (consistent with results of conoscopic interference patterns), with the birefringence (Δn = n_z − n_x) ranging from 0.044@1064 nm to 0.045@532 nm and the values are comparable with those of the commercial UV NLO materials LiB₃O₅ and CsLiB₆O₁₀ (Δn = 0.045 and 0.049@1064 nm)¹⁰. A least-square method was used to fit the dispersion parameters of the refractive indices, n_i, using the Sellmeier Eq. (1):

$$n_i^2 = {{A}} + \frac{{{B}}}{{\lambda ^2 - {{C}}}} - {{D}}\lambda ^2$$

(1)

where λ represents the wavelength in units of µm, and A, B, C, and D are the Sellmeier parameters. The Sellmeier Eq. (1) deduced by the least-square fitting of all the measured refractive indices have been fitted as:

$$\begin{array}{ccccc}\\ n_x^2 = & 2.58654 + \frac{{0.01672}}{{\lambda ^2 - 0.00904}} - 0.00987\lambda ^2\\ \\ n_y^2 = & 2.71284 + \frac{{0.02264}}{{\lambda ^2 + 0.01829}} - 0.00486\lambda ^2\\ \\ n_z^2 = & 2.72604 + \frac{{0.01908}}{{\lambda ^2 - 0.01344}} - 0.00819\lambda ^2\\ \end{array}$$

(2)

The calculated and experimental values of the refractive indices at five different wavelengths are summarized in Supplementary Table 9. The calculated values are consistent with experimental ones to the fourth decimal place, which indicates that the fitted Sellmeier equations based on the current data are reliable (Fig. 4c). Based on above fitted Sellmeier equations, when considering the type I phase-matching condition, n(ω) = n(2ω), the shortest type I phase-matching wavelengths in the xz and xy plane are evaluated to be 310 and 322 nm (Fig. 4d), respectively. Therefore, the Pna2₁-BMBF crystal can generate 532 and 355 nm light by direct second and third harmonic generation from a 1064 nm laser.

In order to determine the individual NLO coefficients of Pna2₁-BMBF, Maker fringe measurements were carried out. The schematic of the Maker fringe measurement system is shown in Fig. 5. For the SHG coefficient measurements, the orientation of the crystals and the relationships of P_ω and P_2ω are shown in Fig. 6a, c. The (001)-cut and (100)-cut plane-parallel uncoated plates of Pna2₁-BMBF crystals (4 mm × 4 mm × 1 mm) were used to measure the related NLO coefficients. And also a (110)-cut plate (5 mm × 5 mm × 2 mm) of the KDP crystal was used to measure the d₃₆ (KDP) NLO coefficient as the reference. By fitting the calculated Maker fringes based on the current measurements and calculations, the NLO coefficient of the Pna2₁-BMBF crystal relative to d₃₆ (KDP) has been determined as d₃₃ = 1.3 × d₃₆ (KDP) (Fig. 6b, d). However, the Maker fringe for d₃₁ is too weak to be observed. As d₃₆ coefficient of KDP is 0.39 pm/V, the absolute NLO coefficients of Pna2₁-BMBF crystal based on the measurements and calculations are evaluated to be d₃₃ = 0.51 pm/V.

Fig. 5

Schematic diagram of the Maker fringe experiment using an Nd:YVO₄ laser. A Q-switched Nd:YVO₄ laser system was adopted as fundamental light source with the following experimental conditions: fundamental wavelength: 1064 nm; repetition frequency: 10 kHz; and pulse width: 10 ns. The second-harmonic signal, which changed with rotation angle of Pna2₁-Ba₃Mg₃(BO₃)₃F₃ crystal, was detected by a photomultiplier tube, averaged by a fast-gated integrator and boxcar integrator, and then recorded by computer system. The Pna2₁-Ba₃Mg₃(BO₃)₃F₃ crystal is at the waist of the fundamental light with a beam diameter of 1.0 mm

Fig. 6

Maker fringe measurement for Pna2₁-Ba₃Mg₃(BO₃)₃F₃ crystal. a, c The orientations of as-grown crystal plates for measuring the NLO coefficients. b, d The measured and calculated Maker fringe data as well as fitted envelope for d₃₆ of KH₂PO₄ (KDP) and d₃₃ of Pna2₁-Ba₃Mg₃(BO₃)₃F₃. The data were fitted according to the Maker fringe theory and the detailed fitting procedure is available in the Methods section

Discussion

In order to achieve a deep investigation about the structure-property relationship, theoretical calculations based on density functional theory methods were performed^42,43,44. The total and partial density of states projected on the constitutional atoms of Pna2₁-BMBF crystal are given in Fig. 7a. Clearly, the energy bands can be divided into several regions. The uppermost part of valence bands from −7.5 to 0 eV is essentially dominated by O 2p states and an appreciable contribution of F 2p orbitals with a small amount of B 2p states. The obvious narrow band with sharp peak locates at about −10.7 eV entirely dominated by Ba 5p orbitals and also with a small contribution of O 2p states. The last part from −19.4 to −15.9 eV is mainly generated from O 2s, O 2p, and B 2s, B 2p, indicating strong sp hybridization of the B and O orbitals in the [BO₃]³⁻ groups. While the bottom of the conduction band is essentially composed of Ba 5d, Ba 5s, B 2p, and O 2p orbitals. In principle, the optical properties are mainly determined by the electronic transitions among the states near Fermi level, which are mainly occupied by the O 2p nonbonding orbitals, B–O hybridization states and Ba 5d states in Pna2₁-BMBF. Besides, the interatomic interactions within the BO₃ units and MgO₄F₂ octahedra can be clearly visualized by the electron localization function diagrams. Results show the ionic character of Mg–O and Mg–F bonds in the MgO₄F₂ octahedra as well as the covalent nature of B–O bonds in the [BO₃]³⁻ units (Fig. 7b). Through the Mulliken population analysis, the same conclusions can also be substantiated by the calculated overlap populations for Mg–F, Mg–O and B–O, which are 0.12–0.21, 0.21–0.55, and 0.85–0.97, respectively (higher populations reflect stronger covalence).

Fig. 7

Theoretical calculation results of Pna2₁-Ba₃Mg₃(BO₃)₃F₃. a Partial and total density of states with the energy region from −22 to 15 eV. b The electron localization function diagrams slice along the bc plane (top of b) with the slice position of (5.70841, 7.67893, 4.35171) and ab plane (bottom of b) with the slice position of (4.02830, 7.63500, 7.43644), respectively. Isovalue increases from blue to red, and the maximum electron localization function value is scaled to 4.209 × 10⁻² for the two electron localization function diagrams

The NLO properties of Pna2₁-BMBF were also calculated using a theoretical technique under the static limit within the length gauge. The calculated SHG tensors are evaluated to be d₃₃ = 0.47, d₃₂ = −0.39, and d₃₁ = 0.09 pm/V, respectively. These values are well consistent with experimental values presented above (d₃₃ = 0.51 pm/V). The SHG density analysis can be used to intuitively and accurately display the SHG-contributed orbitals for an NLO crystal. Furthermore, we investigated the SHG origin of Pna2₁-BMBF from the perspective of orbital analysis using SHG density analysis. And the SHG process is denoted by two virtual transition processes, namely virtual electron (VE) and virtual hole processes. The contributions of VE process to d₃₁, d₃₂, and d₃₃ SHG tensors are up to 83.7%, 81.6%, and 86.5%, respectively, indicating that the SHG effects of three tensors mainly originate from the VE processes. Thus, only the largest d₃₃ SHG tensor of VE process is analyzed and the results are drawn in Fig. 8. In the occupied states, the nonbonding 2p orbitals of O (1, 2, 3, 5, 8, 9) atoms in [B(2)O₃]³⁻ and [B(3)O₃]³⁻ groups give more dominant contributions to the SHG effects, while for the occupied states, π orbitals of the [B(1, 2, 3)O₃]³⁻ units as well as 2p orbitals of F (1, 2, 3) atoms in the MgO₄F₂ octahedra give more dominant contributions for the SHG effects, revealing the p–(p, π*) charge-transfer excitation mechanism in Pna2₁-BMBF. Both occupied and unoccupied states of the Ba cations, in analogy to alkali metal and alkali earth metal ions in other NLO crystals, have very little contribution on the SHG effect, which agrees well with the anionic group theory¹⁰. To sum up, the large SHG response of Pna2₁-BMBF can be regarded as the synergistic effects of the planar [BO₃]³⁻ and distorted MgO₄F₂ octahedra.

Fig. 8

The second-harmonic generation density analysis of Pna2₁-Ba₃Mg₃(BO₃)₃F₃. a The density maps of the occupied orbitals in virtual electron process of the second-harmonic generation tensor d₃₃. b The density maps of the unoccupied orbitals in virtual electron process of the second-harmonic generation tensor d₃₃ of Pna2₁-Ba₃Mg₃(BO₃)₃F₃. Isovalue increases from blue to red, and the maximum electron localization function values are scaled to 5.823 × 10⁻² for occupied orbitals (a) and 5.095 × 10⁻² for unoccupied orbitals (b), respectively

In summary, by starting from the SBBO structure, we designed and synthesized two beryllium-free SBBO-like borates through chemical cosubstitution strategy. A high-quality Pna2₁-BMBF crystal with dimensions up to 16 × 14 × 8 mm³ has been grown by the top-seeded solution growth method with a BaF₂-H₃BO₃-LiF flux system. Linear and nonlinear optical measurements reveal a sufficiently large SHG coefficient (d₃₃ = 0.51 pm/V), suitable birefringence (0.045@532 nm), type I phase-matchability, and chemical stability. Remarkably, Pna2₁-BMBF has a large LDT (~6.2 GW/cm²), a deep-UV cutoff edge (λ ~ 184 nm), a weak anisotropic thermal expansion as well as the capacity of insolubility in water, these optical properties could be comparable or superior to that of commercial NLO materials β-BBO (Supplementary Table 10). Thus, these merits on optical properties make Pna2₁-BMBF a promising UV NLO material.

Methods

Synthesis and crystal growth

Polycrystalline samples of targeted Pna2₁-BMBF were synthesized through solid-state reaction method by mixing the raw materials BaF₂, BaCO₃, MgO, and H₃BO₃ according to the molar ratio of 3:3:6:6. The mixture was preheated at 400 °C for 48 h. After that, the temperature was gradually raised to 600 °C for Pna2₁-BMBF, with several intermediate mixings and grindings. Single crystals of Pna2₁-BMBF were grown by top-seeded solution growth method with the flux BaF₂-H₃BO₃-LiF at a molar ratio of Pna2₁-BMBF/H₃BO₃/BaF₂/LiF = 1:1:0.5:3. A mixture of Pna2₁-BMBF polycrystalline samples, BaF₂, H₃BO₃, and LiF were placed into a Φ 30 × 30 mm platinum crucible and melted at 750 °C in a temperature-programmable electric furnace. The solution was held at 750 °C for 24 h to form a homogeneous solution. After that, cooled to 715 °C and dipped the Pna2₁-BMBF seed crystal into the solution and held for 2 h that allowed the seed crystal surface to melt. The solution was slowly cooled to the saturation temperature about 712 °C. Then the Pna2₁-BMBF crystal was grown by cooling the solution at a rate of 0.2 °C/d to 706 °C. When the growth procedure finished, the Pna2₁-BMBF crystal was drawn out of the solution and cooled down to room temperature at a rate of 20 °C/h. While for P$\bar 6$2m-BMBF single crystals, the loaded compositions are Ba(NO₃)₂ (0.5227 g, 2 mmol), BaF₂ (0.3507 g, 2 mmol), MgO (0.0403 g, 1 mmol) and H₃BO₃ (0.4328 g, 7 mmol). All the reagents were mixed homogeneously and transferred to a platinum crucible. The samples were heated to 880 °C in 24 h and held at this temperature for 72 h and then cooled to 700 °C at a rate of 1.0 °C/h, after that, cooled to room temperature at a rate of 15 °C/h. During the process of crystallization, colorless and transparent P$\bar 6$2m-BMBF crystals were formed in the platinum crucible.

Characterization

The selected single crystals with dimensions up to 0.12 × 0.10 × 0.01 mm³ for Pna2₁-BMBF and 0.16 × 0.07 × 0.06 mm³ for P$\bar 6$2m-BMBF were glued on glass fibers for structure determination by single-crystal X-ray diffractometer. An APEX II CCD diffractometer equipped with monochromatic Mo Kα radiation was used for the single-crystal data collection. The Bruker Suite software package was used to reduce the collected data. The numerical absorption corrections were carried out with the SADABS program and integrated with the SAINT program⁴⁵. The original structures were established by the direct method and refined by the full-matrix least-squares program on SHELXL⁴⁶. The PLATON program was used for checking the possible missing symmetry elements, but no higher symmetries were found⁴⁷. Investigation of the thermal behavior Pna2₁-BMBF crystal was performed using a NETZSCH STA 449 C simultaneous thermal analyzer. The sample of 6.5 mg was enclosed in a platinum crucible and heated from 40 to 1200 °C at a rate of 5 °C/min. The measurements were carried out in an atmosphere of flowing N₂. The powder X-ray diffraction data of Pna2₁-BMBF were collected at room temperature using an automated Bruker D2 X-ray diffractometer (Supplementary Figure 4). The transmittance spectra of Pna2₁-BMBF water were collected by a Solid Spec-3700DUV spectrophotometer for the range of 180–2500 nm in an atmosphere of flowing N₂ and by a Shimadzu IRAffinity-1 Fourier spectrometer for the range extended from 2500 to 4000 nm (Supplementary Figure 5). The powder SHG measurements for targeted Pna2₁- and P$\bar 6$2m-BMBF were carried out on the basis of the Kurtz–Perry method⁴¹. Polycrystalline samples of Pna2₁- and P$\bar 6$2m-BMBF were ground and sieved into the following particle size ranges: 20–38; 38–55; 55–88; 88–105; 105–150; 150–200; and 200–250 μm. During the measurement, Pna2₁- and P$\bar 6$2m-BMBF samples were irradiated with a Q-switched Nd:YAG laser with light wavelength of 1064 nm. Then the intensity of the frequency-doubled of 532 nm output emitted from Pna2₁- and P$\bar 6$2m-BMBF were recorded by a digital oscillometer equipped with a photomultiplier tube. The microcrystalline KDP samples with the same particle sizes were used as references. For LDT test, the crystals were cut plane parallel and polished to optical quality using a Unipol-300 grinding/polishing machine. A Q-switched Nd:YAG laser with a pulse width of 10 ns and repetition frequency of 10 kHz was employed as the fundamental light source (1064 nm). The second-harmonic signal generated from the sample wafer was detected by a side window photomultiplier tube, averaged by a fast-gated integrator and boxcar average, and then automatically recorded by a computer. A cut-KDP (110) wafer was used as a reference. The refractive index measurements of Pna2₁-BMBF were carried out using (100), (010), and (001) crystal plates on the Metricon model 2010/M prism coupler (Metricon Co.) at five wavelengths (406.9, 514.0, 636, 964.8, and 1546.7 nm), and the accuracy of the measurements is estimated to be 2 × 10⁻⁴. Maker fringe measurements of Pna2₁-BMBF were performed on two crystal wafers cut perpendicular to the a- and b-crystallographic axes in order to measure d₃₁, d₃₂, and d₃₃ NLO coefficients. Then, the data were fitted according to the Maker fringe theory. The detected second-harmonic power P_2ω is expressed as the following Eq.(3):

$$P_{2\omega }\left( \theta \right) = \frac{{512\pi ^2}}{{cw^2}}d^2P_\omega ^2f\left( {n,\theta } \right)\sin ^2\Psi$$

(3)

$$f\left( {n,\theta } \right) = \frac{1}{{\left( {n_\omega ^2 - n_{2\omega }^2} \right)^2}}t_\omega ^4T_{2\omega }p^2\left( \theta \right)R\left( \theta \right)\beta \left( \theta \right)$$

(4)

where c is the speed of light in vacuum, w is the radius of light beam, n_ω and n_2ω are the refractive indices under the fundamental and harmonic wavelength, d is the NLO coefficient, P_ω is the fundamental beam power, Ψ = 2πL(n_ωcosθ_ω − n_2ωcosθ_2ω)/λ_ω, and sin²Ψ determines the minima oscillating position. t_ω and t_2ω are the transmission coefficients of fundamental wave and harmonic wave, p(θ) is the projection factor, R(θ) is the incident multiple-reflection correction, and β(θ) is the beam size correction. The f (n, θ) part depicts the envelope of the Maker fringe. By fitting the calculated and measured Maker fringes, a constant, C = 512πd²P²_ω/(cω²) can be obtained. The magnitude of NLO coefficients of Pna2₁-Ba₃Mg₃(BO₃)₃F₃ can be determined relatively to d₃₆ of KDP crystal, and the coefficient equation can be expressed as:

$$d_{{\mathrm{sample}}} = \sqrt {\frac{{C_{{\mathrm{sample}}}}}{{C_{\mathrm{KDP}}}}} d_{36}\left( {{\mathrm{KDP}}} \right)$$

(5)

Computational methods

First-principles calculations of Pna2₁-BMBF based on density functional theory were performed by a planewave pseudopotential calculation package CASTEP⁴⁸. The exchange and correlation effects were treated by Perdew–Burke–Ernzerhof in the generalized gradient approximation⁴⁹. The interactions between the ionic cores and electrons were described by norm-conserving pseudopotentials⁵⁰. The cutoff energy for the planewave basis was 990 eV and the Brillouin zone was sampled by 4 × 2 × 3 Monkhorst-Pack k-point.

Data availability

The authors declare that the data supporting the findings of this study are available within the article and Supplementary Information files, or from the corresponding authors upon reasonable request.