1.   Introduction

Barium–sodium metaborate Ba₂Na₃(B₃O₆)₂F (P6₃/m) found as a reaction product in the BaB₂O₄−NaF system [1] is known for its prominent birefringent properties both in the ultraviolet [2–4] and terahertz regions [5]. It belongs to the so-called metaborates as its main structural element is an isolated metaboric ring, [B₃O₆]³⁻, consisting of three [BO₃]³⁻ triangles linked via three bridging oxygen atoms. Known metaborates, which are the salts of the low-temperature modification of metaboric acid α-HBO₂ (Pbnm), include alkaline metals salts with structural formula M₃[BO₂]₃ (M = Na, K, Rb, Cs) (R$\bar{3}$c) [6–9], alkaline-earth and transition metals salts such as α-BaB₂O₄ (R$\bar{3}$c) [10], β-BaB₂O₄ (R3c) [11], and Ba₂M(B₃O₆)₂ (M = Ca, Cd, Mg, Co, Ni) (R$\bar{3}$) [12]. The structure of barium–sodium metaborate Ba₂Na₃(B₃O₆)₂F is similar to the structure of a high-temperature modification of barium metaborate α-BaB₂O₄: both structures have pseudolayered arrangement of metaboric rings perpendicular to the c axis, with the difference that in the structure of Ba₂Na₃(B₃O₆)₂F six-coordinated barium atoms are replaced by [Na₃F]²⁺ groups according to the scheme Ba²⁺ → [Na₃F]²⁺ [4].

The effect of high pressure on the crystal structure and properties of borates has been an actively developing area of research for many years [13–15]. The study of high-pressure borates aids in the understanding of both their crystal-chemical regularities as well as their potential to create new functional materials. Our recent attempt to assess the stability of the BaB₂O₄ compound at pressures up to 10 GPa using first-principles calculations [16] in conjunction with subsequent experiment at a pressure of 3 GPa led to the discovery of γ-BaB₂O₄ (P2₁/n) modification [17]. The central role in its structure is played by edge-sharing BO₄ tetrahedra, first described in the Dy₄B₆O₁₅ compound by Huppertz and von der Eltz [18].

In this paper, we address the electronic properties of the Ba₂Na₃(B₃O₆)₂F compound, establish a connection between the structure and Raman scattering based on the comparison of experimental and calculated spectra, and provide the evidence for Ba₂Na₃(B₃O₆)₂F high-pressure decomposition into sodium fluoride, sodium borate, NaBO₂, and new high-pressure modification of barium borate, δ-BaB₂O₄.

2.   Computational and experimental details

2.1   Computational methods

All calculations were performed within the density functional theory (DFT) implemented in the VASP 5.4.4 [19–20]. The exchange–correlation interaction was taken into account in the generalized gradient approximation in the form of the Perdew–Burke–Ernzerhof (PBE) functional [21]. The electron–ion interaction was described by applying the projector–augmented–wave (PAW) method with the following valence electron configurations of atoms: 5s²5p⁶6s² for Ba, 3s¹3p⁰ for Na, 2s²2p¹ for B, 2s²2p⁴ for O, and 2s²2p⁵ for F. The total energies of the structures were minimized by relaxing the structural parameters and atomic coordinates at different pressures using a conjugated gradient optimization method. The relaxation of the structure was performed with maximum tolerances for the energy of 1.0 × 10⁻⁷ eV and stress of 0.01 GPa. Forces between atoms are minimized down to 0.001 eV/Å. The energy cutoff was set to 700 eV. By adopting the Γ-centered Monkhorst-Pack method [22], the Brillouin zone was sampled with a k-mesh density of 2π × 0.03 Å⁻¹. Electron smearing was employed using the Gaussian-smearing technique with smearing parameter σ = 0.05 eV. The elastic constants C_ij were calculated from the stress (σ)–strain (ε) relation σ_i = C_ij × ε_j, where i, j = 1–6. Since the use of the PBE functional tends to severely underestimate the width of the band gap, the HSE06 hybrid functional [23] was used to calculate the density of states (DOS) and band structure of Ba₂Na₃(B₃O₆)₂F. A high-symmetry path for the calculation of electronic band structure was generated by the VASPKIT tool [24]. It is worth nothing that hybrid DFT is limited by tradeoffs between over-delocalization and under-binding, and thus, it can still underestimate width of the band gaps. There are some approaches, such as self-interaction corrections, localized orbital scaling corrections, and rung-3.5, that can help mitigate these tradeoffs’ impact the electronic structure [25–27].

To calculate the phonon spectra and pressure–temperature (P–T) phase diagram, the PHONOPY [28] program was exploited. The temperature effect was considered within the quasiharmonic approximation (QHA). Real-space force constants were calculated using supercell and finite-displacement approaches with a 2 × 2 × 1 supercell.

The Raman spectra were obtained using vasp_raman.py code [29] by calculating the dielectric tensors for each vibrational mode. To match the experimental spectrum, the calculated Raman spectrum was calibrated using a scaling factor, which is the ratio of Raman shifts of the most intensive peaks in experimental and calculated Raman spectra. In the present study, the scaling factor was 1.033. The animations and visualization of Raman active vibrations were made by VaspVib2XSF [30], PHONOPY [28], and OVITO tools [31].

2.2   Experimental techniques

2.2.1   High-pressure high-temperature synthesis

The synthesis of β-BaB₄O₇ was carried out on the ‘Discoverer-1500’ DIA-type apparatus at the Sobolev Institute of Geology and Mineralogy SB RAS in Novosibirsk, Russia. The design and characteristics of the high-pressure cell used in this work were described in detail in Ref. [17].

As initial samples for high-pressure high-temperature (HPHT) experiments we used grounded Ba₂Na₃(B₃O₆)₂F crystal, grown in the BaB₂O₄–NaF system [1], and the polycrystalline sample obtained by solid phase synthesis (SPS) according to reaction (1):

The samples were placed in a graphite cassette with holes of 0.9 mm in diameter and 1.1 mm deep. Experiments were carried out by compressing to 3 MN and 6 MN (corresponding to a pressure of 3 GPa and 6 GPa, respectively), and heating to the temperature of 1173 K at a rate of 100 K/min. The heating was stopped by switching off the voltage supplied to the heater. The maximum temperature gradient in the working volume with samples is estimated at 4–5 K/mm at 1073 K. Accordingly, in the working volume of the sample we distinguish high (HT) and low (LT) temperature zones. The temperature drop rate was about 100 K/s. Decompression to ambient-pressure conditions took 180 min. The duration of the experiment at 3 GPa, 1173 K was 44.5 h, and at 6 GPa, 1173 K was 64 h.

2.2.2   Scanning electron microscopy

Annealed samples were studied using a MIRA 3 LMU scanning electron microscope (Tescan Orsay Holding, Brno-Kohoutovice, Czech Republic) coupled with an INCA energy-dispersive X-ray microanalysis system 450 equipped with the liquid nitrogen-free Large area EDS X-Max-80 Silicon Drift Detector (Oxford Instruments Nanoanalysis Ltd., High Wycombe, UK) at IGM SB RAS.

2.2.3   Raman spectroscopy

The Raman spectra were recorded on a Horiba Jobin Yvon LabRAM HR800 (France) spectrometer with 1024 pixel LN/CCD detector using the 532 nm wavelength (tunable Ar⁺ laser) in IGM SB RAS and collected in a backscattering geometry using Olympus BX41 confocal microscope. The spectral resolution of the recorded Stokes side of the Raman spectrum was set to ~2.0 cm⁻¹ at a Raman shift of 1300 cm⁻¹.

3.   Results and discussion

3.1   Structure stability and electronic properties

The stability of the Ba₂Na₃(B₃O₆)₂F compound in the pressure range of 0–10 GPa has been considered relative to two possible reactions of decomposition:

For the calculations, the structures of known polymorphs of BaB₂O₄ (${\text{β}} { \xrightarrow {\rm 0.8\;GPa}} {\text{γ}} { \xrightarrow {\rm 6.8\;GPa}} Pa \bar 3$) [17] and BaF₂ ($Fm\bar{3}m { \xrightarrow {\rm 3.5\;GPa}} Pnma$) [16,32] were taken into account. NaF and NaBO₂ were considered in the form of Fm$\bar{3}$m [33] and R$\bar{3}$c [34] structures, respectively, in the entire considered pressure range.

Fig. 1 depicts enthalpy–pressure dependencies calculated without taking into account zero-point energy (ZPE). It can be seen that the decomposition of Ba₂Na₃(B₃O₆)₂F in accordance with reaction (2) occurs at a pressure of 2.8 GPa. Reaction (3) is energetically unfavorable relative to reaction (2) over the entire pressure range. This result suggests that above 2.8 GPa Ba₂Na₃(B₃O₆)₂F should decompose to 2BaB₂O₄ + 2NaBO₂ + NaF.

Figure  1.  Relative enthalpy–pressure dependencies of Ba₂Na₃(B₃O₆)₂F and two isochemical mixtures.

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To estimate the mechanical stability of Ba₂Na₃(B₃O₆)₂F, the elastic constants C_ij were calculated (Table S1) and then the Born stability criteria were applied. The Born stability criteria form a set of necessary and sufficient conditions that determine whether a given material is stable. For hexagonal crystal under a hydrostatic pressure P, there are three Born stability criteria [35]:

In our case, the first and second stability criteria are satisfied in the entire considered pressure range. The third stability criterion is met up to ~5 GPa (Fig. 2). Above this pressure, the value of (C₄₄ – P) becomes negative (Fig. 2) which indicate the mechanical instablity of Ba₂Na₃(B₃O₆)₂F above 5 GPa.

Figure  2.  Born stability criteria as a function of the applied pressure.

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To assess the dynamic stability and the effect of temperature on the decomposition pressure of Ba₂Na₃(B₃O₆)₂F, phonon spectra were calculated at various pressures. The absence of imaginary modes in phonon spectra indicates that Ba₂Na₃(B₃O₆)₂F is dynamically stable at 0–5 GPa (Fig. 3), which lends support to the use of QHA in this pressure range. Above 5 GPa, imaginary modes appear, indicating dynamic instability. In addition, the absence of imaginary modes and meeting Born stability criteria imply that Ba₂Na₃(B₃O₆)₂F can be metastably compressed without heating up to 5 GPa.

Figure  3.  Calculated phonon spectra of Ba₂Na₃(B₃O₆)₂F at (a) 0, (b) 5, and (c) 10 GPa.

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Based on the calculations of Gibbs free energy at different temperatures, P–T diagram of Ba₂Na₃(B₃O₆)₂F was constructed (Fig. 4). The consideration of ZPE increases the decomposition pressure from 2.8 to 3.1 GPa at zero temperature. According to the obtained results, at 300 K the decomposition of Ba₂Na₃(B₃O₆)₂F occurs at 3.4 GPa with a positive Clapeyron slope of 0.9 MPa/K. It should be noted that constructed P–T diagram is valid in case of the absence of phase transitions of Ba₂Na₃(B₃O₆)₂F.

Figure  4.  P–T phase diagram of Ba₂Na₃(B₃O₆)₂F.

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According to the band-structure calculation, Ba₂Na₃(B₃O₆)₂F is an insulator with an indirect band gap (E_g) of 6.289 eV along the Γ–K direction (Fig. 5(a)). The obtained value of the band gap is in good agreement with the experimentally obtained UV transmittance cut-off edge, which is located according to different studies at about 200 nm (6.20 eV) [1], 186 nm (6.66 eV) [2] and 175 nm (7.08 eV) [3].

Figure  5.  Calculated (a) band structure and (b) total and partial DOS of Ba₂Na₃(B₃O₆)₂F.

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The calculation of the density of states (Fig. 5(b)) shows that the bottom of the valence band is composed of occupied Ba 5p states (about −10 eV). The band centered at −8.3 eV is formed by O 2p and B 2s states, and the bands from −7.6 to −2.7 eV are formed by O 2p and B 2p states. This implies that O 2p orbitals are hybridized with the B 2s and 2p orbitals. It is worth noting that the contributions of B 2s and 2p states are smaller than the contribution of O 2p states. The valance band region from −2.6 eV to −2.0 eV is contributed by O 2p states and F 2p states. In the upper part of the valence band above −2.0 eV, the O 2p states make the main contribution. The conduction band consists of unoccupied Ba 5d states with a small contribution from unoccupied B 2p, O 2p, and Na 3s states. These results indicate that the main optical transition occurs from O 2p orbitals to Ba 5d levels with a change in the orbital angular momentum Δl = 1. Such transitions generally are characteristic of barium borates [17,36–38].

3.2   Raman spectroscopy of Ba₂Na₃(B₃O₆)₂F

Since the number of experimental methods suitable for studying HPHT synthesis products is limited by the small size of the samples, Raman spectroscopy has gained increasing prominence for the identification of polymorphs.

From the group analysis of Ba₂Na₃(B₃O₆)₂F, the optical modes at the Γ point belong to the following irreducible representations: Γ_optical = 12A_g + 11A_u + 12B_g+ 12B_u + 11E_1g + 12E_1u + 13E_2g + 11E_2u, where 36 modes, Γ_Raman = 12A_g + 13E_2g + 11E_1g, are Raman-active modes. Fig. 6 and Table 1 show the experimental Raman spectra of Ba₂Na₃(B₃O₆)₂F synthesized at ambient pressure in comparison with the results of DFT calculation in the range from 50 to 1700 cm⁻¹. All calculated Raman shifts are close to the experimental value.

Figure  6.  Experimental and calculated (DFT) unoriented Raman spectra of Ba₂Na₃(B₃O₆)₂F.

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Table  1.  Experimental and calculated Raman active modes of Ba₂Na₃(B₃O₆)₂F

Observed / cm−1	Calculated / cm−1	Mulliken symbol		Observed / cm−1	Calculated / cm−1	Mulliken symbol
1559	1561	Ag		215	214	E2g
778	771	Ag		171	171	E2g
764	748	Ag		164	163	Ag
672	676	E1g		137	133	Ag
628	628	Ag		120	124	E1g
605	602	Ag		108	107	E2g
476	479	E2g		97	95	E2g
392	385	E2g		80	77	E1g
232	235	E1g		—	—	—

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Generally, in metaborates peaks below ~300 cm⁻¹ are attributed to the external modes of the crystal, while the peaks above ~300 cm⁻¹ are attributed to the internal vibrational modes of (B₃O₆)³⁻ rings [39]. The Raman peak at about 1559 cm⁻¹ arises from the symmetric stretching vibration of B–O bonds (Fig. 7(a)). In the experimental spectrum, it splits into several peaks (Fig. 6). In Ba₂Mg(B₃O₆)₂ the splitting of the peak at about 1525 cm⁻¹ related to the stretching vibration of B–O bonds into four peaks, is accounted for by an isotopic effect [40]. The peak at 764 cm⁻¹ is associated with bending vibrations of B–O bonds (Fig. 7(b)). The strongest Raman mode in the spectra of all studied metaborates is accounted for by the breathing vibration of (B₃O₆)³⁻ ring. Its position is believed to be insensitive to the surrounding atoms, which is confirmed by several experimental studies [39–41]. In Ba₂Na₃(B₃O₆)₂F, the breathing vibration is observed at 628 cm⁻¹ (Fig. 7(c)). The modes at 476 cm⁻¹ (Fig. 7(d)) and 392 cm⁻¹ (Fig. 7(e)) are attributed to the mixed bending and libration vibration of (B₃O₆)³⁻, while at 392 cm⁻¹ vibrations of F⁻ and Na⁺ are also attending. The Raman shifts below 232 cm⁻¹ are related to mixed libration and translation vibrations of the (B₃O₆)³⁻ ring together with translations of F⁻, Na⁺, and Ba²⁺ ions (Fig. 7(f)–(i)).

Figure  7.  Atom displacements in selected Raman modes of Ba₂Na₃(B₃O₆)₂F at (a) 1559 cm⁻¹, (b) 764 cm⁻¹, (c) 628 cm⁻¹, (d) 476 cm⁻¹, (e) 392 cm⁻¹, (f) 215 cm⁻¹, (g) 121 cm⁻¹, (h) 97 cm⁻¹, and (i) 80 cm⁻¹. Arrows represent displacement vectors. Animated harmonic modes are available in the Supporting Information.

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3.3   Study of the products of high-pressure high-temperature synthesis

Here we would like to draw attention to the results of two HPHT experiments conducted at a temperature of 1173 K and pressure of 3 GPa and 6 GPa, respectively (Fig. 8, Table 2). In both experiments grounded Ba₂Na₃(B₃O₆)₂F crystal and synthesized Ba₂Na₃(B₃O₆)₂F were used as starting materials.

Figure  8.  Backscattered electron images of the products of HPHT experiments at 3 GPa (a–c) and 6 GPa (d–f), 1173 K.

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Table  2.  Compositions of the products of HPHT experiments determined by energy-dispersive X-ray microanalysis

Experimental conditions	Starting mater	Phase	Composition / mol%
			Ba	B	F	Na	O
3 GPa, 1173 K, 44.5 h	Crystal	Ba2Na3(B3O6)2F	9.2(1)	23.9(2)	4.1(1)	13.2(1)	49.6(1)
	SPS	Ba2Na3(B3O6)2F	9.2(1)	23.8(1)	4.2(1)	13.3(1)	49.5(1)
		BaB2O4 (trace amount)	16(2)	27(4)	—	—	57(2)
3 GPa, 1173 K, 64 h	Crystal	BaB2O4	18(1)	22(1)	—	—	60(2)
		NaBO2	0.9(2)	23.9(2)	0.2(5)	25.5(5)	49.4(3)
		NaF	2.8(3)	4(3)	48(3)	52(4)	10(4)
	SPS	BaB2O4	19(2)	21(1)	—	—	60(1)
		NaBO2	0.5(4)	24.2(7)	1(1)	25(1)	49(1)
		NaF	0.9(4)	0.9(2)	47(2)	48.3(1)	3(2)
Note: The numbers in the parentheses represent the standard error in the last digit shown.

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At 3 GPa, a single-phase sample with a composition close to Ba₂Na₃(B₃O₆)₂F was observed for the grounded crystal (Fig. 8(a)), while for the synthesized starting material small inclusions of the second phase, BaB₂O₄, were also present (Fig. 8(b) and (c)). We put emphasis on the fact that the Raman spectrum of Ba₂Na₃(B₃O₆)₂F phase at 3 GPa coincided with the spectrum at atmospheric pressure which suggests that no phase transition occurs (Fig. 9(a) and (b)).

Figure  9.  Raman spectra of Ba₂Na₃(B₃O₆)₂F at (a) atmospheric pressure and (b) 3 GPa; (c,d) reaction products at 6 GPa.

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In contrast to the results of the experiment at 3 GPa, we have not found Ba₂Na₃(B₃O₆)₂F in the reaction products of the experiment at 6 GPa. Based on the results of energy-dispersive X-ray microanalysis, the phases formed at 6 GPa are BaB₂O₄, NaBO₂, and NaF, which lends support to the correctness of the calculated P–T diagram (Fig. 4). It is worth noting that the size of BaB₂O₄ crystals formed is very small and does not exceed several microns (Fig. 8(d)–(f)). The most intriguing results have been revealed with the use of Raman scattering. As the NaF compound, being an ionic one, provides a very weak or no Raman signal, the observed Raman peaks might belong to NaBO₂ and BaB₂O₄ compounds (Fig. 9(c) and (d)). Fig. S1 shows the Raman spectrum of the reaction products at 6 GPa in comparison with the Raman spectra of the NaBO₂ (R$\bar{3}$c) phase [42]. Based on the comparison, we can draw the conclusion that peaks at about 126, 401, 475, 625, 680, 770, 1549, and 1577 cm⁻¹ belong to the NaBO₂ phase. Correspondingly, an intense peak at 906 cm⁻¹, and less intense peaks at about 181, 203, and 1202 cm⁻¹, which do not coincide with the Raman peaks of the γ-BaB₂O₄ phase [17], might belong to a new high-pressure modification of barium borate, δ-BaB₂O₄. According to a recent numerical study [16–17], γ-BaB₂O₄ should undergo a phase transition at the pressure of about 6 GPa. Further HPHT study is needed to obtain δ-BaB₂O₄ crystals large enough for structure refinament.

4.   Conclusion

In this work, a high-pressure stability limit of barium–sodium metaborate, Ba₂Na₃(B₃O₆)₂F, was studied. Performed DFT calculations showed that Ba₂Na₃(B₃O₆)₂F decompose to 2BaB₂O₄ + 2NaBO₂ + NaF at zero temperature above 2.8 GPa without ZPE and 3.1 GPa with ZPE. Phonon calculations suggest that Ba₂Na₃(B₃O₆)₂F could be compressed metastable without heating up to 5 GPa. Taking into account the temperature effect, the P–T boundary of the decomposition reaction was obtained. In addition, electronic properties were studied. The width of the band gap is 6.289 eV with indirect transition along the Γ–K direction. The main optical transition occurs from O 2p to Ba 5d levels. Experimental Raman spectrum of Ba₂Na₃(B₃O₆)₂F synthesized at ambient pressure was compared with calculated spectrum which made it possible to attribute the observed modes. The conducted HTHP experiments showed that Ba₂Na₃(B₃O₆)₂F remains stable at 3 GPa, and decomposes to NaF, NaBO₂, and BaB₂O₄ at 6 GPa, thereby confirming the correctness of the calculated P–T diagram. According to the Raman spectra from 6 GPa, there is a new high-pressure modification of BaB₂O₄, named δ-BaB₂O₄. Since the size of δ-BaB₂O₄ crystals does not exceed several microns, it is currently impossible to solve the structure.