The synthesis of novel lanthanum hydroxyborate at extreme conditions

The novel structure of lanthanum hydroxyborate La₂B₂O₅(OH)₂ was synthesized by the reaction of partially hydrolyzed lanthanum and boron oxide in a diamond anvil cell under high-pressure/high-temperature (HPHT) conditions of 30 GPa and ∼2,400 K. The single-crystal X-ray structure determination of the lanthanum hydroxyborate revealed: $P\overline{3}c1$, a = 6.555(2) Å, c = 17.485(8) Å, Z = 6, R₁ = 0.056. The three-dimensional structure consists of discrete planar BO₃ groups and three crystallographically different La ions: one is surrounded by 9, one by 10, and one by 12 oxygen anions. The band gap was estimated using ab initio calculations to be 4.64 eV at ambient pressure and 5.26 eV at 30 GPa. The current work describes the novel HPHT lanthanum hydroxyborate with potential application as a deep-ultraviolet birefringent material.

1 Introduction

In recent decades, borates have garnered significant interest as versatile materials due to their varied crystal structures, impressive linear and nonlinear optical (NLO) properties, and favorable machining characteristics (Chen et al., 1995; Wu et al., 1996; Chénais et al., 2002; Jia et al., 2017; Zou and Ok, 2020; Guo et al., 2022). Notably, considerable research efforts have been devoted to the development of novel borate-based birefringent materials for potential application in the deep-ultraviolet (DUV) region (longer wavelength portion of UV-C; 190 nm ≤ λ₀ ≤ 280 nm; 4.43 eV ≤ E₀ ≤ 6.53 eV) (Zhang et al., 2020).

Despite the different principles in crystal symmetries of NLO and birefringent materials, sufficiently large optical anisotropy plays a crucial role in the applications for both types (Guo et al., 2022). It is widely recognized that the small double refraction of NLO crystals limits their ability to achieve the shortest phase-matching wavelength, thereby negatively affecting potential applications in the DUV region (Jiang et al., 2015). Birefringent materials play an important role in modulating light polarization in the optical communication and laser industries (Li and Ma, 2012). Several commercially available crystals like calcite (Ghosh, 1999), YVO₄ (DeShazer, 2002), α-BaB₂O₄ (Guoqing et al., 1998; Solntsev et al., 2002), and MgF₂ (Dodge, 1984) have found utility in the optical spectrum spanning from the infrared (IR) to the UV range with wavelengths below 400 nm. However, these four compounds are not suitable for application in the DUV region because:

• The low transmittance in the DUV range of α-BaB₂O₄, calcite, and YVO₄ restricts their application in shorter-wavelength regions;

• An extremely small birefringence (Δn = 0.0128 at 235.7 nm) limits the application of MgF₂ in the DUV region (Scott, 1962; Dodge, 1984).

Consequently, an ideal crystal must possess high transmittance in the DUV range, large birefringence (Δn > 0.08) (Gong et al., 2020), and a short UV cutoff edge (the smaller the better) (Guo et al., 2022). Today, the scarcity of such materials meeting these criteria underscores the importance of exploring novel DUV crystals with substantial birefringence.

In terms of borates, there are three basic groups that form unique structures: linear BO₂, trigonal-planar BO₃ and tetrahedral BO₄, which occur as discrete oxyanions or polymerize to form finite clusters, chains, sheets, and frameworks. Anionic group theory gives the understanding of structure-property relationships. The key factor that affects optical properties is if the anionic unit is capable to produce a wide band gap, high polarizability anisotropy, and hyperpolarizability (Huang et al., 2021; Mutailipu et al., 2021). The triangle π-conjugated BO₃ group has the largest hyperpolarizability (β_max = 10.80) among BO₂ (β_max = 0) and BO₄ (β_max = 3.61), and a good relation between the other two parameters: band gap (E_g = 8.48 eV) and polarizability anisotropy (δ = 7.01) (Mutailipu et al., 2021). The birefringence originates from the dependence of dipole oscillators and refractive index, and it can be considered as a result of the functional unit`s arrangement (Wang F. et al., 2021). Therefore, the solution for the large optical anisotropy lies in metal cations and the type of functional anion (Jin et al., 2021). The metal cations can form MO_n polyhedra with large deformability and thereby increase the optical anisotropy (Wu et al., 2019). But with the positive influence on birefringence, there is a negative effect on DUV transmittance: the crystals with big metal cations have a smaller band gap and as a consequence may hardly transmit in the DUV spectral region. The birefringence is not sensitive to the exact orientation of the BO₃ groups because it is almost optically isotropic within the BO₃ plane (Chen et al., 2012). It was shown that all borates crystal structures with only triangle borate groups could be divided into three structural types according to the arrangement of these groups: 1) the BO₃ planes arranged in a nearly coplanar pattern, 2) in a coaxial pattern, 3) and in the other inclined patterns (Jiang et al., 2015). The crystals with coplanar arrangement generally have the largest birefringence, while those with disordered patterns have the smallest (Jiang et al., 2014; Lin et al., 2014).

Along with alkali and transition metals borates, rare-earth (RE) borates (and lanthanum borates in particular) have raised significant interest due to their stable physical and chemical properties, wide bandwidth, and good light transmittance. The system La-B-O is represented by several compositionally different borates: λ-LaBO₃ (Sari et al., 2017), high-temperature modification H-LaBO₃, LaB₃O₆ (ambient pressure), and its two high-pressure modifications γ-LaB₃O₆ (Emme et al., 2004) and δ-LaB₃O₆ (Heymann et al., 2006), La₄B₁₄O₂₇ (Nikelski et al., 2008), La₂₆O₂₇(BO₃)₈ (Lin et al., 1996), La₄B₁₀O₂₁ (isotypic to Pr₄B₁₀O₂₁) (Hinteregger et al., 2012) and La₂B₈O₁₅ (isotypic to Ce₂B₈O₁₅) (Glätzle et al., 2016). Except for the high-pressure modifications (γ-LaB₃O₆, δ-LaB₃O_6, and La₄B₁₀O₂₁), all known lanthanum borates are synthesized by heating stoichiometric mixtures of La₂O₃ and B₂O₃ under ambient pressure conditions. However, this simple synthesis fails to produce pure crystalline phases (Shmyt’ko et al., 2013). Hence, HPHT synthesis serves as a viable alternative. There is a common trend in high-pressure borates where the boron atoms tend to prefer four-fold coordination as pressure increases. Typically, trigonal-planar BO₃ groups transform into tetrahedral BO₄ groups beyond 10 GPa pressure (Hinteregger et al., 2012). However, a few compounds are known to contain trigonal-planar BO₃ groups beyond this pressure threshold, for example, in Ho₃₁O₂₇(BO₃)₃(BO₄)₆ (Hering et al., 2010).

In the present study, we have applied methods of single-crystal X-ray diffraction in laser-heated diamond anvil cell (DAC) to synthesize lanthanum hydroxyborate La₂B₂O₅(OH)₂ for the first time and characterize its crystal structure. We performed ab initio calculations of the band gap and compared both: the band gap and its structural properties with literature. The structural organization of La₂B₂O₅(OH)₂ allows us to propose that the lanthanum borates with isolated BO₃ groups can be used as a potential DUV birefringent material.

2 Materials and methods

2.1 Sample preparation

For the synthesis, we used a non-stoichiometric mixture of partially hydrolyzed La (a piece of lanthanum 99.9% purity from Fisher Scientific left on humid air for 3 days) and B₂O₃ (99.999% purity, purchased from Fisher Scientific), finely grounded and pre-pressed into pellets between two diamonds. The pre-pressed pellet of size 10*15*5 μm³ was loaded in the symmetric DAC (Symm100 by Almax EasyLab) equipped with Boehler–Almax diamonds with a 200 μm culet size. Rhenium gasket was pre-indented to the thickness of 26 μm, and a hole with the diameter of about 110 μm was drilled with a laser-drilling system at GeoSoilEnviroCARS (GSECARS), Advanced Photon Source (APS), Argonne National Laboratory (ANL). A 4 μm piece of gold and a 15 μm ruby ball (DACtools, LLC) were used as pressure calibrants (Ye et al., 2018). Neon was loaded using the COMPRES/GSECARS gas loading system available at APS (Rivers et al., 2008) and served as a pressure-transmitting medium.

2.2 Laser-heating experiments

Double-sided laser-heating experiments coupled with X-ray diffraction (XRD) measurements were conducted at the 13ID-D beamline at GSECARS of the APS, ANL. The laser heating system at the beamline is equipped with two 1,064 nm wavelength infrared lasers that produce a flat-top spot size of around 10 µm in diameter (full width at half-maximum) (Goncharov et al., 2010). We used double-sided laser heating in the burst mode with a heating duration of 1 or 3 s, collecting XRD of the sample during and after heating. The surface temperatures of both sides were measured by the standard spectroradiometry method (Heinz and Jeanloz, 1987) using an IsoPlane SCT 320 spectrometer with a PI-MAX3 1024i ICCD camera from Princeton Instruments.

The DAC was compressed stepwise to a maximum pressure of 30(1) GPa and laser-heated at 3.3(5) and 13.3(5) GPa to a maximum temperature of 2,285(325) and 2,430(130) K, respectively. After each heating cycle, a detailed X-ray diffraction map was collected around the heated spot in order to determine the occurrence of the reaction and the phase composition. At each pressure point, single crystal X-ray diffraction images were collected in a few spots with decent quality for phase composition determination.

2.3 X-ray data analysis

The crystal structures of the sample in the DAC were investigated through in situ XRD measurements using synchrotron radiation performed at the 13ID-D beamline of the APS, ANL. A monochromatic X-ray beam of 42 keV (λ = 0.2952 Å) was used to collect powder and single crystal data on a Pilatus 1M CdTe large area detector.

2.3.1 Powder diffraction

Powder collection was performed as a single image in the omega scanning range of ±20° with an exposure time of 40 s. Detector parameters were calibrated using LaB₆.

The data for powder analysis was prepared and converted into the required file extension using Dioptas software (Prescher and Prakapenka, 2015). Powder XRD data analysis consisted of structure refinement by the Le Bail method using the GSAS II software (Toby and Von Dreele, 2013).

2.3.2 Single crystal diffraction

Single crystal collection included 120 frames in the omega scanning range of ±34° with a step of 0.5° and an exposure time of 1 s per step. Sample-to-detector distance, coordinates of the beam center, tilt angle, and tilt plane rotation angle of the detector images were calibrated using an orthoenstatite crystal.

Single-crystal XRD data (unit cell determination, integration of the reflection intensities, absorption corrections) were processed using CrysAlisPro software (Rigaku Oxford Diffraction, 2019). For the search of the domains during data reduction, the DAFi software was used (Aslandukov et al., 2022). The structure was determined by SHELXT (Sheldrick, 2015), a structure solution package that uses the method of intrinsic phasing. The crystal structure was refined against F² on all data by full-matrix least-squares using SHELXL software (Sheldrick, 2015). SHELXT and SHELXL were implemented in the Jana2006 software package (Petříček et al., 2014). Crystal structure visualization was made using VESTA (Momma and Izumi, 2011) and Diamond software (Putz and Brandenburg, 1999).

Because more than 50% of the diffraction reflections were blocked by the body of the diamond anvil cell, the data sets of the reflections were incomplete. To improve the data/parameter ratio, only the atomic thermal parameters of lanthanum and oxygen were refined using anisotropic approximation, leading to an R₁ value of 5.6%. Due to the presence of high-Z lanthanum atoms, the residual electron density peaks were on the order of 2–6 e/ų, which is comparable with the number of electrons in boron and oxygen atoms. Assignment of the residual density peaks to boron or oxygen atoms did not improve the final R-values, and therefore, the high residuals likely originate from the incompleteness of the XRD data sets. The typical data/parameter ratios were on the order of 10–15. The detailed summary of the crystal structure refinement, along with unit cell parameters, atomic coordinates, and atomic displacement parameters, is shown in Table 1 and Supplementary Tables S1, S2.

TABLE 1

TABLE 1. Crystal data and structure refinement parameters for La₂B₂O₅(OH)₂.

2.4 Scanning electron microscopy

The composition of the sample mixture prior to loading in the DAC was analyzed by means of scanning electron microscopy using the JOEL JSM-IT500HR scanning electron microscope (JEOL USA, Inc., Peabody, MA, United States). The chemical composition was checked at 15 kV using energy-dispersive X-ray spectroscopy (EDS) of QUANTAX EDS System with XFlash 6160 detector (Bruker Nano GmbH, Berlin, Germany). No impurities or traces of any other elements were found. The detailed summary is shown in Supplementary Figure S1.

2.5 Band gap calculations

Density functional theory (DFT) calculations were performed using Vienna ab initio simulation package (VASP 6.3) (Kresse and Furthmüller, 1996a; Kresse and Furthmüller, 1996b). Local Density Approximation (LDA) and Generalized Gradient Approximation (GGA) were used to describe exchange and correlation effects. Electron wave functions were expanded by plane wave with a cutoff energy of 520 eV. Monkhorst-Pack (Monkhorst and Pack, 1976) k-point grids were set as 12 × 12 × 4 for the structure relaxation and 24 × 24 × 8 for the electronic structure calculations. Atomic relaxation was performed until the change in the electronic and ionic steps were less than 10⁻⁶ and 10⁻⁵ eV, respectively. VASPKIT package (Wang V. et al., 2021) was used to extract and analyze the VASP raw output files. Calculations were performed at ambient pressure and external pressure of 30.0 GPa.

3 Results

The synthesis of new lanthanum hydroxyborate was performed from the mixture of partially hydrolyzed lanthanum powder and boron oxide. The initial mixture has irregular composition (insert in Supplementary Figure S1). As lanthanum can oxidize on air to either oxide, hydroxide, carbonate, or hydroxycarbonate depending on the conditions and humidity, we performed EDS analysis to confirm the composition of starting mixture. The brief inspection of the EDS spectrum of the initial mixture shows that the sample is composed of the elements La, B, and O. We used carbon tape as a sample mount which may account for the carbon present in the spectra.

To confirm the composition of the initial mixture, we performed powder XRD analysis at the pressure of 3.3(5) GPa. The powder pattern can be found in Figure 1. There are characteristic peaks of La(OH)₃, B₂O₃, and Re. The unit cell parameters for La(OH)₃ (P6₃/m) are: a = 6.506(4) Å, c = 3.8673(7) Å, V = 141.75(12) Å³; for B₂O₃ (P3₁) are: a = 4.3789(11) Å, c = 8.2888(16) Å, V = 137.64(5) Å³; and for Re (P6₃/mmc) are: a = 2.716(7) Å, c = 4.396(30) Å, V = 28.09(20) Å³. The R-factor is equal to 0.6%. Thus, the source of lanthanum in the system was lanthanum hydroxide. Our sample is very close to the gasket; therefore, the presence of rhenium is not surprising. No characteristic peaks of other compounds exist, such as lanthanum carbonate, lanthanum hydroxycarbonate, or lanthanum oxycarbonate. We did not observe the characteristic peaks of various lanthanum borate phases either. As a result, we can rule out the possibility of a reaction occurring during compression at 3.3(5) GPa without heating.

FIGURE 1

FIGURE 1. Powder XRD pattern of the mixture prior to heating at 3.3(5) GPa: blue crosses are experimental data from this study, the green line corresponds to the calculated curve, the red one represents the background, and the black one shows the difference between observed and calculated curves. The ticks represent the different phases: red is B₂O₃ (ICSD 16021), blue is La(OH)₃ (ICSD 239411), and teal one is Re (ICSD 291898).

Laser heating up to 2,285(325) K at 3.3(5) GPa led to a pressure jump to 6.6(5) GPa, however, the reaction did not occur. Data collection at 13.3(5) GPa before and after heating to 2,430(130) K did not produce good-quality crystalline samples either. Fortunately, the diffraction pattern after increasing pressure up to 30(1) GPa confirmed the chemical reaction by forming a new, previously unknown structure.

By employing single crystal diffraction analysis, the new compound crystallizes in the centrosymmetric trigonal space group $P\overline{3}c1$ (no. 165) with lattice parameters a = 6.555(2) Å, c = 17.485(8) Å (Table 1). It consists of a dense, three-dimensional network (Figure 2) composed of planar triangles of BO₃ connected with three crystallographically independent lanthanum ions. The lanthanum atoms possess different coordination spheres (Supplementary Figure S2): La01 is coordinated by 10 oxygen atoms, La02 is coordinated by 12 oxygen atoms, and La03 is coordinated by 9 oxygen atoms. The distances La-O are in the range of 2.27(2)–2.614(12) Å. The B-O bond lengths are in the range of 1.26(2)–1.321(15) Å (for all bond lengths in the structure, see Supplementary Table S3). These bond distances are slightly smaller than those published for alkali- and rare-earth borates which can be explained by the higher pressure reached during this experiment.

FIGURE 2

FIGURE 2. Crystal structure of La₂B₂O₅(OH)₂ (hydrogen atoms are not shown): (A) along a axis, (B) along c axis. Lanthanum atoms are shown in grey, oxygens are pink, and boron atoms are in the center of each planar triangle and are shown in dark purple.

As the amount of water absorbed by the lanthanum is unknown, for the structure solution, we used only three elements: La, B, and O. According to the structure refinement, our formula ended up as La₂B₂O₇. To achieve charge balance, instead of two oxygen atoms, there should be two hydroxyl groups. This agrees well with our XRD data of the starting compositions. Therefore, the new borate has a composition of La₂B₂O₅(OH)₂.

The band gap calculated by DFT method is 3.40 eV (GGA)/4.64 eV (LDA) at ambient pressure and 5.31 eV (GGA)/5.26 eV (LDA) at 30 GPa pressure (Figure 3 for LDA and Supplementary Figure S4 for GGA). These values correspond to the short cutoff edge in the range from 365 to 233 nm. Commonly, the GGA and LDA method-based calculations tend to slightly underestimate the band gap, therefore the real value might be slightly higher and, consequently, the cutoff edge smaller (Bagayoko, 2014; Baiheti et al., 2021).

FIGURE 3

FIGURE 3. The electronic band structure calculated by using LDA method: (A) for ambient pressure, and (B) for 30 GPa.

4 Discussion

The starting mixture for the reaction consisted of La(OH)₃ and B₂O₃. During laser heating up to 2,430(130) K, the hydroxide partially decomposed to La₂O₃ and H₂O without subsequent melting of La₂O₃ [T_{m (amb)} = 2588 K (Grundy et al., 2000)], while boron oxide melted [T_{m (8 GPa)} ∼ 1,800 K (Solozhenko et al., 2015)]. The behavior of B₂O₃ melt is similar to SiO₂, and it readily dissolves metallic oxides with the formation of borates (Huppertz, 2011), so the lanthanum borate was synthesized by dissolving La₂O₃ and La(OH)₃ in B₂O₃ with subsequent reaction.

The structure of La₂B₂O₅(OH)₂ is based on La-O layers identical to those in the A-type La₂O₃ structure ($P\overline{3}m$) and La(OH)₃ (P6₃/m) (Figure 4). During HP synthesis, the lanthanum-oxygen layers of La(OH)₃ were integrated between similar layers of La₂O₃. The oxide layers are rotated by 180° relative to each other along the c axis. The coordination numbers for La in La(OH)₃ frame increase from 9 to 10 and 12 [La01 and La02 in La₂B₂O₅(OH)₂]; while for La in La₂O₃ pattern—from 7 to 9 [La03 in La₂B₂O₅(OH)₂]. Boron atoms have three-fold coordination and are located in the cavities between La01/02-O and La03-O layers. The positional disorder of the BO₃ groups is unusual for known RE borates and has never been described before. In terms of a three-fold coordinated boron atom, in RE borates BO₃ group can form either linked chains [for example, in α-Sm(BO₃)₂ (Fuchs et al., 2020a) or in LaB₂O₄F (Hinteregger et al., 2013b)], or isolated triangles [for instance, in NdBO₃ (Müller-Bunz et al., 2003) or in Dy₅(BO₃)₂F₉ (Hinteregger et al., 2013a)]. The arrangement of boron groups in most cases is coplanar (parallel to one plane) or slightly distorted. In La₂B₂O₅(OH)₂ boron groups have a coaxial arrangement: each BO₃ triangle occupies one of three possible positions along C₃ axis and lies in the glade n plane (Supplementary Figure S5). BO₃ group exhibits C₂ symmetry as it represents an isosceles triangle.

FIGURE 4

FIGURE 4. The comparison of La-O frame (hydrogen and boron atoms are not shown) for: (A) La₂B₂O₅(OH)₂ (present work), (B) La₂O₃ (ICSD 56771), and (C) La(OH)₃ (ICSD 239411). For convenience, the lanthanum atoms with different pattern are shown in different shades of grey: for La₂O₃ pattern in violetish grey, for La(OH)₃ pattern in greenish grey.

There are known structures of RE hydroxyborates, for example, high-pressure La₃B₆O₁₃(OH) (Fuchs et al., 2020b), and LaB₂O₄(OH) (Bashir et al., 2017). However, both are composed of edge-sharing BO₄ tetrahedra which distinguishes them from the newly synthesized La₂B₂O₅(OH)₂. We found only two lanthanum borates with similar structure: H-LaBO₃ (Böhlhoff et al., 1971) and La₂₆(BO₃)₈O₂₇ (Lin et al., 1996). Both these structures consist of repeated La-O and BO₃ patterns: the orientation of planar BO₃ groups in H-LaBO₃ is coplanar, while in La₂₆(BO₃)₈O₂₇ the BO₃ groups have a slightly distorted arrangement (Figure 5). The bond distances in La₂B₂O₅(OH)₂ correspond well to typical bond lengths in lanthanum borates (Figure 6). For example, in comparison with La₂₆(BO₃)₈O₂₇ at ambient pressure where the bond distances for La-O are in the range 2.272(10)–3.047(9) Å, and for B-O are in the range 1.34(2)–1.42(2) Å (Lin et al., 1996), the newly synthesized La₂B₂O₅(OH)₂ at 30(1) GPa have the bond lengths 2.27(2)–2.612(14) Å and 1.26(2)–1.319(15) Å for La-O and B-O, respectively.

FIGURE 5

FIGURE 5. The comparison of BO₃ polyhedra arrangement for: (A) La₂B₂O₅(OH)₂ (present work), (B) H-LaBO₃ (ICSD 15383), and (C) La₂₆(BO₃)₈O₂₇ (ICSD 82308). For convenience, only BO₃ polyhedra are shown.

FIGURE 6

FIGURE 6. The comparison of the bond distances for La-O and B-O (in trigonal planar orientation) from publications (Böhlhoff et al., 1971; Lin et al., 1996; Emme et al., 2004; Hinteregger et al., 2012) and for La₂B₂O₅(OH)₂ (present work). The ranges from the literature are shown in grey bars, the red squares are corresponding to the smallest value of the bond length of the La₂B₂O₅(OH)₂, while the black dots are representing the biggest value.

While the borates with parallel arrangement of planar BO₃ groups have the largest birefringence (Jiang et al., 2015), the situation with coaxial BO₃ arrangement is slightly different. The value for optical anisotropy depends not only on BO₃ pattern, but also on the detailed orientation and spatial density of the planar BO₃ groups (Jiang et al., 2015). Additionally, the presence of hydroxyl anions linked with isolated triangular boron groups may enlarge the birefringence by delocalization of π electrons (Jin et al., 2021). Our calculated band gap values for ambient [3.40 eV (GGA)/4.64 eV (LDA)] and high pressure [5.31 eV (GGA)/5.26 eV (LDA)] are typical for lanthanum borates with three-fold coordinated boron. For example, the calculated (GGA) and experimental band gap at ambient conditions for LaBO₃ with two-dimensional BO₃ layers are 4.81 and 5.23 eV (Sha et al., 2021) respectively. As mentioned earlier, the presence of rare-earth elements may positively affect the birefringence but at the same time decreases the band gap. As we are looking at the combination of factors, there is a good probability that synthesized La₂B₂O₅(OH)₂ has high birefringence with the cutoff edge short enough to transmit in the longer wavelength portion of UV-C.

5 Conclusion

During the HPHT synthesis at 30(1) GPa and 2,430(130) K, we were able to obtain a new structure of lanthanum hydroxyborate [La₂B₂O₅(OH)₂] with planar BO₃ groups. In contrast with the most known RE borates (including high-pressure structures), La₂B₂O₅(OH)₂ does not form a B-O framework and does not have BO₄ tetrahedra: trigonal-planar BO₃ groups occupy the cavities between La-O layers and create the coaxial pattern. The estimated band gap for lanthanum hydroxyborate is 4.64 eV (for ambient pressure) and 5.26 eV (for 30 GPa), which fits well into the acceptable range for DUV transparency. The structural organization of La₂B₂O₅(OH)₂ and its electronic properties allows us to propose that this class of lanthanum borates can be used as a potential DUV birefringent material.

Data availability statement

The datasets presented in this study can be found in online repositories. The names of the repository/repositories and accession number(s) can be found below: the joint CCDC/FIZ Karlsruhe online deposition service: https://www.ccdc.cam.ac.uk/structures/; the deposition number CSD-2280897.

Author contributions

OI: Investigation, Conceptualization, Data curation, Software, Visualization, Writing–original draft. LV: Investigation, Writing–review and editing. ZH: Investigation, Writing–review and editing. VD: Writing–review and editing, Resources, Software. SC: Methodology, Supervision, Writing–review and editing. VP: Methodology, Supervision, Writing–review and editing. IC: Methodology, Supervision, Writing–review and editing, Funding acquisition, Investigation, Project administration, Data curation, Validation.

Funding

The authors declare financial support was received for the research, authorship, and/or publication of this article. Funding was provided by Florida International University.

Acknowledgments

This research used resources of the Advanced Photon Source, a U.S. Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under Contract No. DE-AC02-06CH11357. We acknowledge the support of GeoSoilEnviroCARS (Sector 13), which is supported by the National Science Foundation—Earth Sciences (EAR-1634415). This work used Bridges-2 at Pittsburgh Supercomputing Center through allocation Discover MAT230033 from the Advanced Cyberinfrastructure Coordination Ecosystem: Services and Support (ACCESS) program, which is supported by National Science Foundation grants #2138259, #2138286, #2138307, #2137603, and #2138296. The Bridges-2 system is supported by NSF award number ACI-1928147, at the Pittsburgh Supercomputing Center (PSC) (Towns et al., 2014). The authors are grateful to Florida International University for financial support.

Conflict of interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Publisher’s note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

Supplementary material

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fchem.2023.1259000/full#supplementary-material

References

Aslandukov, A., Aslandukov, M., Dubrovinskaia, N., and Dubrovinsky, L. (2022). Domain auto finder (DAFi) program: the analysis of single-crystal X-ray diffraction data from polycrystalline samples. J. Appl. Crystallogr. 55 (5), 1383–1391. doi:10.1107/S1600576722008081

PubMed Abstract | CrossRef Full Text | Google Scholar

Bagayoko, D. (2014). Understanding density functional theory (DFT) and completing it in practice. AIP Adv. 4 (12). doi:10.1063/1.4903408

CrossRef Full Text | Google Scholar

Baiheti, T., Han, S., Jin, W., Yang, Z., and Pan, S. (2021). Cs₂AlB₅O₁₀: a short-wavelength nonlinear optical crystal with moderate second harmonic generation response. Dalton Trans. 50 (3), 822–825. doi:10.1039/D0DT04020G

PubMed Abstract | CrossRef Full Text | Google Scholar

Bashir, B., Zhang, B., Lee, M.-H., Pan, S., and Yang, Z. (2017). DFT-based comparative study about the influence of fluorine and hydroxyl anions on opto-electric properties of borate crystals: Choice for better anion. Inorg. Chem. 56 (10), 5636–5645. doi:10.1021/acs.inorgchem.7b00120

PubMed Abstract | CrossRef Full Text | Google Scholar

Böhlhoff, R., Βambauer, H. U., and Hoffmann, W. (1971). Die kristallstruktur von Hoch-LaBO₃. Z. fur Kristallogr. 133 (1-6), 386–395. doi:10.1524/zkri.1971.133.16.386

CrossRef Full Text | Google Scholar

Chen, C., Sasaki, T., Li, R., Wu, Y., Lin, Z., Mori, Y., et al. (2012). Nonlinear optical borate crystals. John Wiley & Sons, 15–115.

Google Scholar

Chen, C., Wang, Y., Xia, Y., Wu, B., Tang, D., Wu, K., et al. (1995). New development of nonlinear optical crystals for the ultraviolet region with molecular engineering approach. J. Appl. Phys. 77 (6), 2268–2272. doi:10.1063/1.358814

CrossRef Full Text | Google Scholar

Chénais, S., Druon, F., Balembois, F., Georges, P., Gaumé, R., Haumesser, P. H., et al. (2002). Spectroscopy and efficient laser action from diode pumping of a new broadly tunable crystal: Yb:Sr₃Y(BO₃)₃. J. Opt. Soc. Am. B 19 (5), 1083. doi:10.1364/JOSAB.19.001083

CrossRef Full Text | Google Scholar

DeShazer, L. G. (2002). “Improved midinfrared polarizers using yttrium vanadate,” in Polarization analysis and measurement IV, proc. SPIE 4481 (SPIE). doi:10.1117/12.452881

CrossRef Full Text | Google Scholar

Dodge, M. J. (1984). Refractive properties of magnesium fluoride. Appl. Opt. 23 (12), 1980. doi:10.1364/AO.23.001980

PubMed Abstract | CrossRef Full Text | Google Scholar

Emme, H., Despotopoulou, C., and Huppertz, H. (2004). High-pressure synthesis and crystal structure of the structurally new orthorhombic rare-earth Meta-oxoborates γ-RE(BO₂)₃ (RE = La - Nd). Z. Fur Anorg. Und Allg. Chem. 630 (13–14), 2450–2457. doi:10.1002/zaac.200400202

CrossRef Full Text | Google Scholar

Fuchs, B., Heymann, G., Wang, X., Lkhamsuren Bayarjargal, A. T., Siegel, R., Schmutzler, A., et al. (2020a). La₃B₆O₁₃(OH): The first acentric high-pressure borate displaying edge-sharing BO₄ tetrahedra. Chem. – A Eur. J. 26 (30), 6851–6861. doi:10.1002/chem.201905419

CrossRef Full Text | Google Scholar

Fuchs, B., Kindler, R. O., Heymann, G., and Huppertz, H. (2020b). High-pressure synthesis and crystal structure of the samarium meta-oxoborate γ-Sm(BO₂)₃. Z. Für Naturforsch. B 75 (6–7), 589–595. doi:10.1515/znb-2020-0045

CrossRef Full Text | Google Scholar

Ghosh, G. (1999). Dispersion-equation coefficients for the refractive index and birefringence of calcite and quartz crystals. Opt. Commun. 163 (1–3), 95–102. doi:10.1016/S0030-4018(99)00091-7

CrossRef Full Text | Google Scholar

Glätzle, M., Hoerder, G. J., and Huppertz, H. (2016). RE₂B₈O₁₅ (RE = La, Pr, Nd) - syntheses of three new rare earth borates isotypic to Ce₂B₈O₁₅. Zeitschrift Fur Naturforschung - Sect. B J. Chem. Sci. 71 (5), 535–542. doi:10.1515/znb-2016-0027

CrossRef Full Text | Google Scholar

Gong, P., Kang, L., and Lin, Z. (2020). Realizing deep-ultraviolet second harmonic generation by first-principles-guided materials exploration in hydroxyborates. J. Am. Chem. Soc. 142 (35), 15157–15163. doi:10.1021/jacs.0c07256

PubMed Abstract | CrossRef Full Text | Google Scholar

Grundy, A. N., Hallstedt, B., and Gauckler, L. J. (2000). Thermodynamic assessment of the lanthanum-oxygen system. J. Phase Equilibria 22, 105–113. doi:10.1361/105497101770338950

CrossRef Full Text | Google Scholar

Guo, R., Jiang, X., Guo, S., Xia, M., Liu, L., Lin, Z., et al. (2022). Realization of enlarged birefringence from BaCdBe₂(BO₃)₂F₂ to NaMgBe₂(BO₃)₂F via the cation size effect as a potential deep-ultraviolet birefringent material. Inorg. Chem. 61 (19), 7624–7630. doi:10.1021/acs.inorgchem.2c00880

PubMed Abstract | CrossRef Full Text | Google Scholar

Guoqing, Z., Jun, X., Xingda, C., Heyu, Z., Siting, W., Ke, X., et al. (1998). Growth and spectrum of a novel birefringent α-BaB₂O₄ crystal. J. Cryst. Growth 191 (3), 517–519. doi:10.1016/S0022-0248(98)00162-6

CrossRef Full Text | Google Scholar

Heinz, D. L., and Jeanloz, R. (1987). “Temperature measurements in the laser-heated diamond cell,” in High-pressure research in mineral physics: A volume in honor of syun-iti akimoto. Editors M. H. Manghnani, and Y. Syono (Terra Scientific Publishing Company). doi:10.1029/GM039p0113

CrossRef Full Text | Google Scholar

Hering, S. A., Haberer, A., Kaindl, R., and Huppertz, H. (2010). High-pressure synthesis and crystal structure of the new holmium oxoborate Ho₃₁O₂₇(BO₃)₃(BO₄)₆. Solid State Sci. 12 (12), 1993–2002. doi:10.1016/j.solidstatesciences.2010.08.016

CrossRef Full Text | Google Scholar

Heymann, G., Soltner, T., and Huppertz, H. (2006). δ-La(BO₂)₃ (≡δ-LaB₃O₆): A new high-pressure modification of lanthanum meta-oxoborate. Solid State Sci. 8 (7), 821–829. doi:10.1016/j.solidstatesciences.2006.03.002

CrossRef Full Text | Google Scholar

Hinteregger, E., Böhler, G., Hofer, T. S., and Huppertz, H. (2013a). High-pressure syntheses and characterization of the rare earth borates RE₅(BO₃)₂F₉ (RE=Dy, Ho). Z. Für Naturforsch. B 68 (1), 29–38. doi:10.5560/znb.2013-2313

CrossRef Full Text | Google Scholar

Hinteregger, E., Heymann, G., Hofer, T. S., and Huppertz, H. (2012). High-pressure synthesis and characterization of the rare-earth borate La₄B₁₀O₂₁. Z. Für Naturforsch. B 67b, 605–613. doi:10.5560/znb.2012-0001

CrossRef Full Text | Google Scholar

Hinteregger, E., Kocsis, K., Hofer, T. S., Heymann, G., Perfler, L., and Huppertz, H. (2013b). High-pressure synthesis and characterization of the rare-earth fluoride borate LaB₂O₄F. Z. Fur Naturforsch. B 68 (9), 951–959. doi:10.5560/ZNB.2013-3177

CrossRef Full Text | Google Scholar

Huang, C., Mutailipu, M., Zhang, F., Griffith, K. J., Hu, C., Yang, Z., et al. (2021). Expanding the chemistry of borates with functional [BO₂]⁻ anions. Nat. Commun. 12 (1), 2597. doi:10.1038/s41467-021-22835-4

PubMed Abstract | CrossRef Full Text | Google Scholar

Huppertz, H. (2011). New synthetic discoveries via high-pressure solid-state chemistry. Chem. Commun. 47 (1), 131–140. doi:10.1039/c0cc02715d

PubMed Abstract | CrossRef Full Text | Google Scholar

Jia, Z., Zhang, N., Ma, Y., Zhao, L., Xia, M., and Li, R. (2017). Top-seeded solution growth and optical properties of deep-UV birefringent crystal Ba₂Ca(B₃O₆)₂. Cryst. Growth Des. 17 (2), 558–562. doi:10.1021/acs.cgd.6b01428

CrossRef Full Text | Google Scholar

Jiang, X., Kang, L., Luo, S., Gong, P., Lee, M.-H., and Lin, Z. (2014). Development of nonlinear optical materials promoted by density functional theory simulations. Int. J. Mod. Phys. B 28 (27), 1430018. doi:10.1142/S0217979214300187

CrossRef Full Text | Google Scholar

Jiang, X., Luo, S., Kang, L., Gong, P., Huang, H., Wang, S., et al. (2015). First-principles evaluation of the alkali and/or alkaline earth beryllium borates in deep ultraviolet nonlinear optical applications. ACS Photonics 2 (8), 1183–1191. doi:10.1021/acsphotonics.5b00248

CrossRef Full Text | Google Scholar

Jin, C., Shi, X., Zeng, H., Han, S., Chen, Z., Yang, Z., et al. (2021). Hydroxyfluorooxoborate Na[B₃O₃F₂(OH)₂]⋅[B(OH)₃]: Optimizing the optical anisotropy with heteroanionic units for deep ultraviolet birefringent crystals. Angew. Chem. - Int. Ed. 60 (37), 20469–20475. doi:10.1002/anie.202107291

CrossRef Full Text | Google Scholar

Kresse, G., and Furthmüller, J. (1996a). Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput. Mater. Sci. 6 (1), 15–50. doi:10.1016/0927-0256(96)00008-0

CrossRef Full Text | Google Scholar

Kresse, G., and Furthmüller, J. (1996b). Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54 (16), 11169–11186. doi:10.1103/PhysRevB.54.11169

PubMed Abstract | CrossRef Full Text | Google Scholar

Li, R. K., and Ma, Y. (2012). Chemical engineering of a birefringent crystal transparent in the deep UV range. CrystEngComm 14 (17), 5421. doi:10.1039/c2ce25240f

CrossRef Full Text | Google Scholar

Lin, J. H., Su, M. Z., Wurst, K., and Schweda, E. (1996). The structure of La₂₆(BO₃)₈O₂₇: A structure with a distorted fluorite type arrangement of atoms. J. Solid State Chem. 126 (2), 287–291. doi:10.1006/jssc.1996.0339

CrossRef Full Text | Google Scholar

Lin, Z., Jiang, X., Kang, L., Gong, P., Luo, S., and Lee, M.-H. (2014). First-principles materials applications and design of nonlinear optical crystals. J. Phys. D Appl. Phys. 47 (25), 253001. doi:10.1088/0022-3727/47/25/253001

CrossRef Full Text | Google Scholar

Momma, K., and Izumi, F. (2011). VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data. J. Appl. Crystallogr. 44 (6), 1272–1276. doi:10.1107/S0021889811038970

CrossRef Full Text | Google Scholar

Monkhorst, H. J., and Pack, J. D. (1976). Special points for Brillouin-zone integrations. Phys. Rev. B 13 (12), 5188–5192. doi:10.1103/PhysRevB.13.5188

CrossRef Full Text | Google Scholar

Müller-Bunz, H., Nikelski, T., and Schleid, T. (2003). Einkristalle des Neodym(III)-meta-Borats Nd(BO₂)₃ und -ortho-Borats Nd[BO₃]/Single Crystals of the Neodymium(III) meta-Borate Nd(BO₂)₃ and ortho-Borate Nd[BO₃]. Z. Für Naturforsch. B 58 (5), 375–380. doi:10.1515/znb-2003-0503

CrossRef Full Text | Google Scholar

Mutailipu, M., Poeppelmeier, K. R., and Pan, S. (2021). Borates: A rich source for optical materials. Chem. Rev. 121 (3), 1130–1202. doi:10.1021/acs.chemrev.0c00796

PubMed Abstract | CrossRef Full Text | Google Scholar

Nikelski, T., Schäfer, M. C., and Schleid, T. (2008). La₄B₁₄O₂₇: Ein Lanthan-ultra-Oxoborat mit Raumnetzstruktur. Z. Für Anorg. Und Allg. Chem. 634 (1), 49–55. doi:10.1002/zaac.200700303

CrossRef Full Text | Google Scholar

Petříček, V., Dušek, M., and Palatinus, L. (2014). Crystallographic computing system JANA2006: General features. Z. Für Kristallogr. - Cryst. Mater. 229 (5), 345–352. doi:10.1515/zkri-2014-1737

CrossRef Full Text | Google Scholar

Prescher, C., and Prakapenka, V. B. (2015). Dioptas: a program for reduction of two-dimensional X-ray diffraction data and data exploration. High Press. Res. 35 (3), 223–230. doi:10.1080/08957959.2015.1059835

CrossRef Full Text | Google Scholar

Putz, H., and Brandenburg, K. (1999). Diamond - crystal and molecular structure visualization.

Google Scholar

Rigaku Oxford Diffraction (2019). CrysAlisPro software system. Version 1.171.40.84a.

Google Scholar

Rivers, M., Prakapenka, V., Kubo, A., Pullins, C., Holl, C., and Jacobsen, S. (2008). The COMPRES/GSECARS gas-loading system for diamond anvil cells at the Advanced Photon Source. High Press. Res. 28 (3), 273–292. doi:10.1080/08957950802333593

CrossRef Full Text | Google Scholar

Sari, S., Senberber, F. T., Yildirim, M., Kipcak, A. S., Yuksel, S. A., and Derun, E. M. (2017). Lanthanum borate synthesis via the solid-state method from a La₂O₃ precursor: Electrical and optical properties. Mater. Chem. Phys. 200, 196–203. doi:10.1016/j.matchemphys.2017.07.056

CrossRef Full Text | Google Scholar

Scott, W. D. (1962). Purification, growth of single crystals, and selected properties of MgF₂. J. Am. Ceram. Soc. 45 (12), 586–587. doi:10.1111/j.1151-2916.1962.tb11065.x

CrossRef Full Text | Google Scholar

Sha, H., Li, B., Xiong, Z., Wang, Z., Liu, C., Su, R., et al. (2021). A new rare-earth borate birefringent crystal with quasi-two-dimensional [BO₃] layers. J. Mater. Chem. C 9 (44), 15886–15890. doi:10.1039/D1TC04256D

CrossRef Full Text | Google Scholar

Sheldrick, G. M. (2015). Shelxt – integrated space-group and crystal-structure determination. Acta Crystallogr. Sect. A Found. Adv. 71 (1), 3–8. doi:10.1107/S2053273314026370

PubMed Abstract | CrossRef Full Text | Google Scholar

Shmyt’ko, I. M., Kiryakin, I. N., and Strukova, G. K. (2013). Features of LaBO₃ phase formation during solid-phase synthesis from the amorphous precursor state. Phys. Solid State 55 (7), 1468–1475. doi:10.1134/S1063783413070305

CrossRef Full Text | Google Scholar

Solntsev, V. P., Tsvetkov, E. G., Gets, V. A., and Antsygin, V. D. (2002). Growth of α-BaB₂O₄ single crystals from melts at various compositions: comparison of optical properties. J. Cryst. Growth 236 (1–3), 290–296. doi:10.1016/S0022-0248(01)02216-3

CrossRef Full Text | Google Scholar

Solozhenko, V. L., Kurakevych, O. O., Le Godec, Y., and Brazhkin, V. V. (2015). Thermodynamically consistent p-T phase diagram of boron oxide B₂O₃ by in situ probing and thermodynamic analysis. J. Phys. Chem. C 119 (35), 20600–20605. doi:10.1021/acs.jpcc.5b07088

CrossRef Full Text | Google Scholar

Toby, B. H., and Von Dreele, R. B. (2013). GSAS-II: the genesis of a modern open-source all purpose crystallography software package. J. Appl. Crystallogr. 46 (2), 544–549. doi:10.1107/S0021889813003531

CrossRef Full Text | Google Scholar

Towns, J., Cockerill, T., Dahan, M., Foster, I., Gaither, K., Grimshaw, A., et al. (2014). Xsede: Accelerating scientific discovery. Comput. Sci. Eng. 16 (5), 62–74. doi:10.1109/MCSE.2014.80

CrossRef Full Text | Google Scholar

Wang, F., Huber, L., Maehrlein, S. F., and Zhu, X.-Y. (2021a). Optical anisotropy and phase transitions in lead halide perovskites. J. Phys. Chem. Lett. 12 (20), 5016–5022. doi:10.1021/acs.jpclett.1c00918

PubMed Abstract | CrossRef Full Text | Google Scholar

Wang, V., Xu, N., Liu, J.-C., Tang, G., and Geng, W.-T. (2021b). Vaspkit: A user-friendly interface facilitating high-throughput computing and analysis using VASP code. Comput. Phys. Commun. 267, 108033. doi:10.1016/j.cpc.2021.108033

CrossRef Full Text | Google Scholar

Wu, B.-L., Hu, C.-L., Mao, F.-F., Tang, R.-L., and Mao, J.-G. (2019). Highly polarizable Hg²⁺ induced a strong second harmonic generation signal and large birefringence in LiHgPO₄. J. Am. Chem. Soc. 141 (26), 10188–10192. doi:10.1021/jacs.9b05125

PubMed Abstract | CrossRef Full Text | Google Scholar

Wu, B., Tang, D., Ye, N., and Chen, C. (1996). Linear and nonlinear optical properties of the KBe₂BO₃F₂ (KBBF) crystal. Opt. Mater. 5 (1–2), 105–109. doi:10.1016/0925-3467(95)00050-X

CrossRef Full Text | Google Scholar

Zhang, C., Divitt, S., Fan, Q., Zhu, W., Agrawal, A., Lu, Y., et al. (2020). Low-loss metasurface optics down to the deep ultraviolet region. Light Sci. Appl. 9 (1), 55. doi:10.1038/s41377-020-0287-y

PubMed Abstract | CrossRef Full Text | Google Scholar

Zou, G., and Ok, K. M. (2020). Novel ultraviolet (UV) nonlinear optical (NLO) materials discovered by chemical substitution-oriented design. Chem. Sci. 11 (21), 5404–5409. doi:10.1039/D0SC01936D

PubMed Abstract | CrossRef Full Text | Google Scholar