Crystal structures of anhydrous borax α-Na₂B₄O₇ and γ-Na₂B₄O₇ and ab initio quantum chemical calculations of structural stability on their fundamental building blocks

Abstract

The crystal structures of α-Na₂B₄O₇ and γ-Na₂B₄O₇ formed during the heating of borax were investigated by single-crystal X-ray diffraction. In addition, the structural stability of the fundamental building blocks (FBBs) was examined using ab initio quantum chemical calculations. α-Na₂B₄O₇ crystallized into the triclinic space group P1 with unit cell dimensions of a = 6.5489(7) Å, b = 8.6261(9) Å, c = 10.4909(11) Å, α = 93.2540(10)°, β = 94.8660(10)°, γ = 90.8380(10)°, V = 589.45(11) ų. γ-Na₂B₄O₇ crystallized into the triclinic space group P1 with unit cell dimensions of a = 6.7123(11) Å, b = 9.6052(17) Å, c = 13.270(2) Å, α = 104.183(4)°, β = 91.560(4)°, γ = 106.501(4)°, and V = 791.0(2) ų. In both α-Na₂B₄O₇ and γ-Na₂B₄O₇, Na coordination polyhedra with the same coordination numbers have similar coordination volumes; however, the Na polyhedra in γ-Na₂B₄O₇ possess more distortable environments than those in α-Na₂B₄O₇. The flexibility of the Na coordination environment allows these materials to adopt favorable oxygen positions, leading to an α-γ phase transition. The structural stability of the FBBs in α-Na₂B₄O₇ and γ-Na₂B₄O₇ was lowered by dehydration and recrystallization. Consequently, α-Na₂B₄O₇ and γ-Na₂B₄O₇ possess FBBs with readily changeable connection geometries, which causes a phase transformation between α-Na₂B₄O₇ and γ-Na₂B₄O₇ without requiring a significant amount of energy.

INTRODUCTION

Naturally occurring borates are a major economic source of boron. Currently, the most common commercial sources of borate are colemanite, CaB₃O₄(OH)₃·H₂O, ulexite, NaCaB₅O₆(OH)₆·5H₂O, kernite, Na₂B₄O₆(OH)₂·3H₂O, and borax, Na₂B₄O₅(OH)₄·8H₂O (Helvaci and Palmer, 2017). These are most abundant in Turkey, the United States, and Russia, which supply over 80% of the world’s borates. Borax is one of the most important minerals used in the borate industry. Anhydrous borax, Na₂B₄O₇, has long been studied because of its importance in various applications, such as in borosilicate glasses, glass wool, ceramics, cement enamels, and detergents (Garrett, 1998). From structural and thermodynamic perspectives, studying the dehydration of borax is essential because nearly 50% of the total weight is released from the structure as water (Waclawska, 1995; Ekmekyapar et al., 1997; Dumanli et al., 2022). There are four stages in the thermal transformation of borax to anhydrous borax, which occur over a temperature range of 50-750 °C (Waclawska, 1995). (1) Dehydration of borax starts at 74 °C; upon further heating to 133 °C, (2) it changes to tincalconite Na₂B₄O₅(OH)₄·3H₂O with the release of 5 mol H₂O. Upon heating to 200 °C, (3) tincalconite decomposes into an amorphous phase. Subsequently, (4) the remaining H₂O is continuously released. At approximately 420 °C, a part of the amorphous phase crystallizes and finally transforms to anhydrous borax Na₂B₄O₇ at 575 °C. Before Na₂B₄O₇ melts at 723 °C, it undergoes a complicated crystallization process in which many polymorphic modifications occur (Morey and Mervin, 1936; Krogh-Moe, 1974; Li and Liang, 1995; Sennova et al., 2007; Fofanova et al., 2013). Li and Liang (1995) reported that β-Na₂B₄O₇ is formed when the temperature is maintained at 550 °C for 2 days or more, and γ-Na₂B₄O₇ is formed at a temperature range of 560-640 °C. Although the authors proposed that the γ-Na₂B₄O₇ crystallized into the monoclinic space group P2, Pm, or P2/m, it was later corrected by Kanishcheva et al. (2004) to the triclinic space group P1. Above this temperature, γ-Na₂B₄O₇ transforms into stable α-Na₂B₄O₇ with a triclinic space group P1 (Krogh-Moe, 1974). In addition, metastable δ- and ε-Na₂B₄O₇ phases appear depending on the annealing temperature and heating time (Li and Liang, 1995).

Despite their industrial and technological importance, there have been no reports on the crystal structures of anhydrous borax phases formed during the heating process. The crystal structure of α-Na₂B₄O₇ was determined using a specimen crystallized from a melt heated at 800 °C (Krogh-Moe, 1974), whereas that of γ-Na₂B₄O₇ was determined using a crystal grown from a mixture of sodium oxide and borate oxide (Kanishcheva et al., 2004; Fofanova et al., 2013). Borates are known to exhibit extreme structural complexity based on fundamental building blocks (FBBs) consisting of Bϕ₃ triangles and Bϕ₄ tetrahedra (ϕ: O²⁻, OH⁻). FBBs form many types of rings consisting of corner-sharing Bϕ₃ triangles and Bϕ₄ tetrahedra (Hawthorne et al., 1996; Grice et al., 1999). In this study, we investigated the crystal structures of α-Na₂B₄O₇ and γ-Na₂B₄O₇ formed during the heating of borax using single-crystal X-ray diffraction (XRD). In addition, we examined various connection modes between the Bϕ₃ triangles and Bϕ₄ tetrahedra and their structural stabilities using ab initio quantum chemical calculations.

EXPERIMENTAL METHODS

Commercially available borax, sodium tetraborate decahydrate (guaranteed reagent grade, Fujifilm Wako Pure Chemical Co., Inc., Osaka, Japan) was used as the starting material. It was placed in a Pt crucible and heated in an electronic furnace in the presence of air at temperatures ranging from 40 to 750 °C. After heating for 1 h, the samples were cooled naturally to room temperature. The samples were then stored in a vacuum desiccator until use.

Synchrotron powder XRD measurements were performed at BL8B at the Photon Factory (PF), High-Energy Accelerator Research Organization (KEK), Japan. The samples were removed from the vacuum desiccator, powdered, and inserted into Lindemann glass capillaries (φ = 0.7 mm). The incident beam was monochromatized using an Si(111) double-crystal monochromator. The X-ray beam was collimated to 0.5 mm in diameter. The exposure time was 5 min. The samples were rotated at a 10° φ angle during each exposure. The X-ray wavelength used in this study was determined to be 0.6840(1) Å using CeO₂ (NIST Standard Reference Material 674a).

Thermal analysis was performed using thermogravimetric (TG) and differential thermal analysis (DTA) (TG/DTA-7300, Seiko Instruments Inc. Chiba, Japan). Approximately 15 mg of borax was placed in a flat-bottomed platinum pan. The sample was heated from 50 to 800 °C at a rate of 10 °C/min under an argon gas flow at a rate of 200 mL/min.

Single crystals were obtained from samples heated at 600 and 650 °C for 12 h. Single crystals suitable for single-crystal XRD were selected under an optical microscope (SMZ1270, Nikon Corporation, Tokyo, Japan) and mounted on glass fibers. The lattice parameters and intensity data were measured using a single-crystal diffractometer (SMART APEX II ULTRA; Bruker AXS Inc., Germany) equipped with a CCD detector, multilayer optics, and graphite monochromatized MoKα radiation (λ = 0.71073 Å) generated by a rotating anode. The initial lattice parameters and orientation matrix were determined from the 36 frames collected with an exposure time of 10 s. A total of 720 frames were collected with an exposure time per frame of 10 s in the ω-scan mode with Δω = 0.5° at three different ϕ positions. The intensity data were integrated and corrected for Lorentz and polarization effects using the Bruker APEX3 software suite (Bruker, 2018). The collected data was reduced using the SAINT software (Bruker, 2017). Empirical absorption correction was also applied using the SADABS software (Sheldrick, 2012). The structure was solved by combining the direct and difference Fourier methods provided by the program SHELXS-2013/1 (Sheldrick, 2015). The atomic coordinates and atomic displacement parameters were refined using full-matrix least-squares methods on F² using the software SHELXL-2013/1 (Sheldrick, 2015). The atomic labels for α-Na₂B₄O₇ and γ-Na₂B₄O₇ were obtained from previous studies (Krogh-Moe, 1974; Kanishcheva et al., 2004). All atoms were refined based on an anisotropic displacement model. The details of the data collection and crystal structure refinement are listed in Table 1. The polyhedral parameters were calculated using IVTON software (Balić-Žunić and Vickovic, 1996).

Table 1. Crystal data and summary of parameters describing data collection and refinement for α- and γ-Na₂B₄O₇

	α-Na2B4O7	γ-Na2B4O7
	Crystal data
Crystal size (mm)	0.20 × 0.10 × 0.10	0.10 × 0.05 × 0.05
Crystal system	Triclinic	Triclinic
Space group	P1	P1
a (Å)	6.5489(7)	6.7123(11)
b (Å)	8.6261(9)	9.6052(17)
c (Å)	10.4909(11)	13.270(2)
α (o)	93.2540(10)	104.183(4)
β (o)	94.8660(10)	91.560(4)
γ (o)	90.8380(10)	106.501(4)
V (Å3)	589.45(11)	791.0(2)
Z	4	2
	Data collection and refinement
Radiation, wavelength (Å)	MoKα, λ = 0.71073	MoKα, λ = 0.71073
Temperature (°C)	20	20
Maximum observed 2θ (o)	57.84	55.72
Measured reflections	3539	30984
Unique reflections	2690	3746
Reflections Fo > 4σ(Fo)	2393	2615
Range of h, k, l	−8 ≤ h ≤ 8	−8 ≤ h ≤ 8
	−10 ≤ k ≤ 11	−12 ≤ k ≤ 12
	−13 ≤ l ≤ 12	−17 ≤ l ≤ 17
R1 [Fo > 4σ(Fo)]	0.0320	0.0451
wR2	0.0853	0.1182
Goodness of fit	1.066	1.018
Number of l.s. parameters	236	353
Residual highest and deepest peaks (e/Å3)	0.74, −0.67	0.41, −0.46

Ab initio quantum chemical calculations were performed using the quantum chemical calculation software package Gaussian-16 (Frisch et al., 2016). The total energies of the FBBs comprising α-Na₂B₄O₇, γ-Na₂B₄O₇, and representative borate minerals were calculated using the second-order Møller-Plesset perturbation theory (MP2) with the 6-311+G(d,p) basis set. The FBB geometries of the borates used in this study were not composed of infinite extended arrays, such as one-dimensional chains, two-dimensional sheets, and three-dimensional frameworks, but unconnected, isolated borate polyanions. Generally, the edges of FBBs are terminated by adding hydrogen atoms to the terminal oxygen atoms instead of repeating structural unit. However, because the isolated borate polyanions were composed of a single structural unit, no hydrogen atoms were placed at the terminal oxygen atoms of the FBBs. In this study, the total energies of the FBBs were divided by the number of electrons in the FBBs to compare their structural stability (Bochvar et al., 1989; Jiang and Zhang, 1989; Koskinen et al., 1995).

RESULTS AND DISCUSSION

Figure 1 shows the continuous variation in the XRD patterns with temperature. Borax is closely related to tincalconite Na₂B₄O₅(OH)₄·3H₂O, the dehydration product of borax. Borax and tincalconite are rapidly and reversibly interconverted at a relative humidity of 60% and temperature of 20-25 °C (Christ and Garrels, 1959). The XRD pattern at 40 °C exhibited diffraction peaks for both borax and tincalconite. With increasing temperature, the borax diffraction peaks gradually weakened and finally disappeared at 80 °C. The diffraction peaks of tincalconite decreased at 120 °C and became almost zero at 180 °C. Upon further heating, slight diffraction peaks were observed in the amorphous halo pattern. The slight diffraction peaks remained largely unchanged up to 450 °C but appeared to temporarily increase at 500 °C. As the diffraction peak positions observed between 200 and 550 °C were fully consistent with those of tincalconite, the crystalline phase would possess FBBs similar in structure to those of tincalconite. Above 600 °C, strong diffraction peaks appeared, indicating the crystallization of anhydrous borax Na₂B₄O₇. However, these diffraction patterns corresponded to neither α-Na₂B₄O₇ nor γ-Na₂B₄O₇. This suggests that the XRD patterns show a mixture of several anhydrous borax phases, including α-, β-, γ-, δ-, and ε-Na₂B₄O₇ phases (Li and Liang, 1995). Thereafter, the diffraction peaks weakened at 700 °C and disappeared entirely at 750 °C.

Figure 1. Variation of X-ray diffraction (XRD) pattern on thermal dehydration and decomposition process of borax.

Figure 2 shows the TG and DTA curves of borax. The two dehydration temperatures of borax and tincalconite are consistent with those reported by Waclawska (1995). The first and second mass losses of approximately 25% and 10% agree with the theoretical mass losses of 23.6% corresponding to 5H₂O in borax and 9.4% corresponding to 2H₂O in tincalconite. Thereafter, the TG curve showed a continuous mass loss of the remaining water molecules, finally showing a mass loss of 49.5%, which is in approximate agreement with the mass of ten water molecules in borax corresponding to 47.2%. The exothermic peak not accompanied by a clear mass loss was observed at approximately 530 °C, which indicates that dehydrated borax crystallized at this temperature. The XRD result supported this result that the diffraction peaks temporarily increased at 500 °C (Fig. 1). Sharp endothermal peaks were observed at approximately 670 °C, indicating that the Na₂B₄O₇ phases began to decompose at these temperatures. After a small mass loss at 700 °C, the anhydrous borax melted at approximately 725 °C. The melting temperature was consistent with that reported by Waclawska (1995); however, the cause of the mass loss just before melting requires further detailed study.

Figure 2. Thermogravimetry (TG) and differential thermal analysis (DTA) curves of borax. Two insets show magnification of areas where any endothermic or exothermic reaction was observed.

Single crystals extracted at 600 and 650 °C were investigated using single-crystal XRD measurements. The crystal structures of the crystals extracted at 600 and 650 °C matched those of γ-Na₂B₄O₇ and α-Na₂B₄O₇, respectively. γ-Na₂B₄O₇ crystallized in triclinic space group P1 with unit cell dimensions of a = 6.7123(11) Å, b = 9.6052(17) Å, c = 13.270(2) Å, α = 104.183(4)°, β = 91.560(4)°, γ = 106.501(4)°, and V = 791.0(2) ų (Table 1). α-Na₂B₄O₇ crystallized into the triclinic space group P1 with unit cell dimensions of a = 6.5489(7) Å, b = 8.6261(9) Å, c = 10.4909(11) Å, α = 93.2540(10)°, β = 94.8660(10)°, γ = 90.8380(10)°, V = 589.45(11) ų (Table 1). The fractional atomic coordinates, displacement parameters, and selected bond distances are listed in Supplementary Tables S1 and S2 (Tables S1 and S2 are available online from https://doi.org/10.2465/jmps.230112), respectively. Figure 3 shows the crystal structures of α-Na₂B₄O₇ and γ-Na₂B₄O₇. The crystal structure of α-Na₂B₄O₇ is characterized by a framework structure with open channels, whereas that of γ-Na₂B₄O₇ is characterized by a complicated three-dimensional framework. The Na-O and B-O bond distances in α-Na₂B₄O₇ and γ-Na₂B₄O₇ were identical to those reported by Krogh-Moe (1974) and Kanishcheva et al. (2004). The broad distribution of Na-O distances is a characteristic of borate structures (Krogh-Moe, 1974; Fofanova et al., 2013). Moreover, the Na-O interatomic distances around the Na4 site in γ-Na₂B₄O₇ are continuously distributed up to 3.187 Å, forming 10-fold coordination. However, as this is unrealistic, it is difficult to determine the coordination number only from the coordination environments around the Na atoms. In this study, the bond valence sum (Brese and O’Keeffe, 1991) was used as an indicator to estimate the coordination number of the Na atom. The bond valence analysis results are listed in Supplementary Tables S3 and S4 (Tables S3 and S4 are available online from https://doi.org/10.2465/jmps.230112). Consequently, we concluded that the Na atom at the Na4 site in γ-Na₂B₄O₇ is coordinated by six oxygen atoms in the 2.320-2.643 Å. The seven-fold coordination at the Na2 site in α-Na₂B₄O₇ exhibits a low bond valence sum (0.930 v.u.), but the next neighbor Na-O interatomic distance of 3.638 Å is too large to form a bond between Na and O atoms. The polyhedral parameters of the coordination environments of the Na atoms are presented in Table 2. In α-Na₂B₄O₇ and γ-Na₂B₄O₇, Na coordination polyhedra with the same coordination number have similar coordination volumes and radii as the fitted spheres. Na polyhedra with the largest and smallest cation eccentricities (distance between the centroid position and the Na atom in the Na polyhedron) are formed in γ-Na₂B₄O₇. However, the average eccentricity in γ-Na₂B₄O₇ is almost equal to that in α-Na₂B₄O₇, which implies that the Na polyhedra in γ-Na₂B₄O₇ possess more distortable environments than those in α-Na₂B₄O₇. The flexibility of the Na coordination environment allows these materials to adopt favorable oxygen positions, which leads to the α-γ phase transition.

Figure 3. Crystal structure of (a) α-Na₂B₄O₇ and (b) the fundamental building blocks (FBBs) consisting of BO₃ triangles and BO₄ tetrahedra. (c) γ-Na₂B₄O₇ and (d) the FBBs consisting of BO₃ triangles and BO₄ tetrahedra. Na, B, and O atoms are represented by yellow, green, and red squares, respectively. The crystal structures were drawn using the VESTA program (Momma and Izumi, 2011).

Table 2. Polyhedral parameters of α- and γ-Na₂B₄O₇

	α-Na2B4O7				γ-Na2B4O7
	Na1O6	Na2O7	Na3O6	Na4O6	Na1O7	Na2O7	Na3O6	Na4O6	Na5O7	Na6O6
V	14.91 Å3	22.81 Å3	13.82 Å3	12.84 Å3	20.27 Å3	21.18 Å3	14.72 Å3	13.72 Å3	21.37 Å3	14.11 Å3
r	2.495 Å	2.575 Å	2.470 Å	2.414 Å	2.488 Å	2.534 Å	2.401 Å	2.420 Å	2.579 Å	2.476 Å
s	0.9455	0.9495	0.9385	0.9499	0.9277	0.9104	0.9796	0.9731	0.9488	0.9305
Δ	0.153 Å	0.225 Å	0.277 Å	0.148 Å	0.065 Å	0.357 Å	0.198 Å	0.164 Å	0.290 Å	0.181 Å

V, polyhedron volume; r, radius of the least-squares sphere fitted to the polyhedron; s, sphericity equals to (1 − σ_r/r), where σ_r is standard deviation of r; Δ, distances between the centroid and central atom of the polyhedron (cation eccentricity).

Figure 4 shows the connection modes between BO₃ triangles and BO₄ tetrahedra. The crystal structure of α-Na₂B₄O₇ comprises two types of FBBs. One consists of a three-membered ring composed of two BO₃ triangles and one BO₄ tetrahedron (Fig. 4a). According to the description proposed by Burns et al. (1995), this FBB is expressed by ⟨2△□⟩, where △ and □ indicate Bϕ₃ triangles and Bϕ₄ tetrahedra (ϕ: O²⁻, OH⁻), respectively. The other consists of a double three-membered ring connected by two types of three-membered rings. One comprises two BO₃ triangles and one BO₄ tetrahedron, and the other comprises one BO₃ triangle and two BO₄ tetrahedra connected by a common BO₄ tetrahedron (Fig. 4b). The FBB is expressed as ⟨2△□⟩-⟨△2□⟩. The crystal structure of γ-Na₂B₄O₇ comprises only one type of FBB: a double three-membered ring observed in α-Na₂B₄O₇ expressed by ⟨2△□⟩-⟨△2□⟩ (Fig. 4b). It is important to emphasize that the double three-membered rings are a common connection mode in α-Na₂B₄O₇ and γ-Na₂B₄O₇. Considering the phase transition between α-Na₂B₄O₇ and γ-Na₂B₄O, it is reasonable to assume that they consist of common FBBs. In addition, this suggests the possibility that the β-, δ-, and ε-Na₂B₄O₇ phases include the same double three-membered rings expressed by ⟨2△□⟩-⟨△2□⟩ in the structures.

Figure 4. Fundamental building blocks (FBBs) in α-Na₂B₄O₇ and γ-Na₂B₄O₇. α-Na₂B₄O₇ constitutes (a) a three-membered ring and (b) a double three-membered ring, whereas γ-Na₂B₄O₇ constitutes only (b) a double three-membered ring. B and O atoms are represented by green and red squares, respectively.

Structural stability of FBBs in borate minerals

The total energies of the FBBs in anhydrous borates and representative borate minerals are listed in Table 3. Burns (1995) previously performed molecular orbital calculations for FBBs in borax using the Hartree-Fock method with the 3-21G* basis set. The total energy obtained by Burns (1995) was −771.24 Hartree, almost identical to our result (Table 3). The relative structural stability of the FBBs is shown in Figure 5. Borax comprises two three-membered rings, each containing a BO₃ triangle and two BO₄ tetrahedra. Because these rings have two BO₄ tetrahedra in common, this FBB is expressed by ⟨△2□⟩=⟨△2□⟩, where = indicates two polyhedra common to both rings. Tincalconite Na₂B₄O₅(OH)₄·3H₂O, which is formed by the dehydration of borax, is composed of the same FBB as borax (Giacovazzo et al., 1973). The connection mode of borax shows relatively low energy in the diagram (Fig. 5). Colemanite CaB₃O₄(OH)₃·H₂O, one of the most common borate minerals, includes three-membered rings composed of one Bϕ₃ triangle and two Bϕ₄ tetrahedra, expressed by ⟨△2□⟩. The colemanite connection mode exhibited the lowest total energy among the borate minerals (Fig. 5). Ulexite, NaCaB₅O₆(OH)₆·5H₂O, and kernite, Na₂B₄O₆(OH)₂·3H₂O, are also common borate minerals. They are composed of double three-membered rings consisting of two three-membered rings of one Bϕ₃ triangle and two Bϕ₄ tetrahedra, expressed by ⟨△2□⟩-⟨△2□⟩. The relatively low total energies of FBBs in borax, ulexite, and kernite are consistent with their widespread occurrence. Notably, these major borate minerals possess common FBBs of three-membered rings of one Bϕ₃ triangle and two Bϕ₄ tetrahedra, expressed by ⟨△2□⟩. Burns et al. (1995) examined the frequency of occurrence of various FBB geometries in borate minerals and concluded that ⟨△2□⟩ rings are strongly favored in FBBs. Burns et al. (1995) concluded that three-membered rings occur in the following order of preference: ⟨△2□⟩ >> ⟨2△□⟩ > ⟨3□⟩ > ⟨3△⟩. This order of frequency is partially consistent with the ab initio quantum chemical calculations. As mentioned above, the ⟨△2□⟩ ring in colemanite exhibits the lowest total energy, which is in good agreement with the results of Burns et al. (1995). The ⟨2△□⟩ ring, consisting of two Bϕ₃ triangles and one Bϕ₄ tetrahedron in ameghinite, also exhibits relatively lower total energy. Unexpectedly, sborgite had an FBB composed of two ⟨2△□⟩ rings, with the second lowest total energy. This was because sborgite is a rare mineral. Thus far, sborgite has been found in only two known locations: California, USA, and Larderello, Italy (Cipriani, 1957; McAllister, 1961), and no relationship has been found between the frequency of occurrence and structural stability. Metaborite possesses an FBB of the ⟨3□⟩ ring consisting of three BO₄ tetrahedra with relatively high total energy. The ⟨3△⟩ ring is the least common structure in borate minerals (Burns et al., 1995; Hawthorne et al., 1996). To the best of our knowledge, no borate minerals with an FBB consisting of only 3△ rings have been reported. However, one of the most noteworthy findings of this study was that the total energy of the ⟨3△⟩ ring in NaBO₂ was lower than that of the ⟨2△□⟩ ring in ameghinite. The FBB of the ⟨3△⟩ ring is not necessarily an energetically unstable arrangement in the borate structures. Therefore, borate minerals with ⟨3△⟩ rings may be found.

Table 3. Total energies of fundamental building blocks (FBBs) constituting of representative borates and borate minerals

		FBB
Name	Chemical formula	Chemical formula	Connectivity (Burns et al., 1995)
α-Na2B4O7	Na2B4O7	[B5O11]7−	⟨2△□⟩-⟨△2□⟩
α-Na2B4O7	Na2B4O7	[B3O7]5−	⟨2△□⟩
γ-Na2B4O7	Na2B4O7	[B5O11]7−	⟨2△□⟩-⟨△2□⟩
Borcarite	Ca4MgB4O6(CO3)2(OH)6	[B4O6(OH)6]6−	⟨4□⟩
Uralborite	CaB2O2(OH)4	[B4O4(OH)8]4−	⟨3□⟩□
Metaborite	CaB3O4(OH)3·H2O	[B3O3(OH)6]3−	⟨3□⟩
Priceite	Ca2B5O7(OH)5·H2O	[B5O8(OH)5]6−	⟨△2□⟩-⟨3□⟩
Sassolite	H3BO3	B(OH)3	1△
Hydrochlorborite	Ca2B3O3(OH)4·BO(OH)3Cl·7H2O	[B3O3(OH)4·BO(OH)3]3−	⟨△2□⟩□
Biringuccite	Na2B5O8(OH)·H2O	[B5O10(OH)]6−	⟨2△□⟩-⟨△2□⟩
Ulexite	NaCaB5O6(OH)6·5H2O	[B5O6(OH)6]3−	⟨△2□⟩-⟨△2□⟩
Ameghinite	NaB3O3(OH)4	[B3O3(OH)4]−	⟨2△□⟩
Borax	Na2B4O5(OH)4·8H2O	[B4O5(OH)4]2−	⟨△2□⟩=⟨△2□⟩
NaBO2	NaBO2	[B3O6]3−	⟨3△⟩
Sborgite	NaB5O6(OH)4·3H2O	[B5O6(OH)4]−	⟨2△□⟩-⟨2△□⟩
Colemanite	CaB3O4(OH)3·H2O	[B3O5(OH)3]2−	⟨△2□⟩

	FBB
Name	# of atoms	# of electrons	Total energy (Hartree)	Total energy/ electrons (Hartree)	References
α-Na2B4O7	16	120	−948.30	−7.903	This study
α-Na2B4O7	10	76	−597.22	−7.858	This study
γ-Na2B4O7	16	120	−945.43	−7.879	This study
Borcarite	22	128	−1002.59	−7.833	Burns and Hawthorne (1995)
Uralborite	24	128	−1004.72	−7.849	Simonov et al. (1977)
Metaborite	18	96	−753.81	−7.852	Freyhardt et al. (2000)
Priceite	23	140	−1102.10	−7.872	Sun et al. (2011)
Sassolite	7	32	−251.97	−7.874	Gajhede et al. (1986)
Hydrochlorborite	22	118	−929.51	−7.877	Brown and Clark (1978)
Biringuccite	17	120	−949.51	−7.913	Corazza et al. (1974)
Ulexite	23	130	−1028.78	−7.914	Ghose et al. (1978)
Ameghinite	14	76	−602.81	−7.932	Dal Negro et al. (1975)
Borax	17	98	−777.83	−7.937	Levy and Lisensky (1978)
NaBO2	9	66	−524.83	−7.952	Borisova et al. (1978)
Sborgite	19	110	−877.91	−7.981	Merlino and Sartori (1972)
Colemanite	14	84	−676.94	−8.059	Burns and Hawthorne (1993)

Figure 5. Relative structural stability of fundamental building blocks consisting of Bϕ₃ triangles and Bϕ₄ tetrahedra (ϕ: O²⁻, OH⁻) in representative borates and borate minerals. Red triangles and blue squares show the Bϕ₃ triangle and BϕO₄ tetrahedron, respectively. Small circles at the vertex of triangles or squares indicate hydrogen atoms bonded to the vertex oxygen. The description method for the connection mode was modeled after Burns et al. (1995).

As shown in Figure 5, the total energies of the FBBs in both α-Na₂B₄O₇ and γ-Na₂B₄O₇ are higher than those in borax. Upon thermal treatment, borax transforms to α-Na₂B₄O₇ or γ-Na₂B₄O₇, but the ⟨△2□⟩ ring in borax survives as part of the FBBs in α-Na₂B₄O₇ and γ-Na₂B₄O₇. One of the FBBs in α-Na₂B₄O₇ consists of three-membered rings, expressed as ⟨2△□⟩. This is the same FBB found in ameghinite. The critical difference between α-Na₂B₄O₇ and ameghinite is the bonding of oxygen atoms on the vertices to hydrogen. The FBBs in α-Na₂B₄O₇ and γ-Na₂B₄O₇ contained no hydrogen at the oxygen vertices of the FBBs. Dehydration and recrystallization reduces the structural stability of the FBBs in α-Na₂B₄O₇ and γ-Na₂B₄O₇ from that of borax. Consequently, α-Na₂B₄O₇ and γ-Na₂B₄O₇ possess FBBs with readily changeable connection geometries, which would cause phase transformations among the α-, β-, γ-, δ-, and ε-Na₂B₄O₇ phases without requiring a significant amount of energy. Grew et al. (2017) proposed that boron mineral diversity increases with geological time and is accelerated during supercontinent assembly accompanied by high-temperature metamorphism. Our results suggest that new borate minerals may be found where borates are exposed to high temperatures because borates dehydrated at high temperatures are highly likely to reconstruct the connection mode of BO₃ triangles and BO₄ tetrahedra.

ACKNOWLEDGMENTS

The synchrotron radiation experiment performed at BL8B at KEK-PF was approved by the Photon Factory Program Advisory Committee (Proposal Nos. 2019G115 and 2021G521). This study was partially supported by the JSPS KAKENHI Grant Number JP20K04124.

SUPPLEMENTARY MATERIALS

Supplementary Tables S1-S4 are available online from https://doi.org/10.2465/jmps.230112.

REFERENCES

•  Balić-Žunić,  T. and  Vickovic,  I. (1996) IVTON-program for the calculation of geometrical aspects of crystal structures and some crystal chemical applications. Journal of Applied Crystallography, 29, 305-306.
•  Bochvar,  D.A.,  Gal’pern,  E.G. and  Stankevich,  I.V. (1989) MO LCAO studies on the structures and stability of some framework molecules and inclusion compounds. Journal of Structural Chemistry, 30, 388-392.
•  Borisova,  N.V.,  Vedishcheva,  N.M. and  Pivovarov,  M.M. (1978) On compounds forming in sodium borate system. Zhurnal Neorganicheskoj Khimii, 23, 703-706.
•  Brese,  N.E. and  O’Keeffe,  M. (1991) Bond-valence parameters for solids. Acta Crystallographica, B47, 192-197.
•  Brown,  G.E. and  Clark,  J.R. (1978) Crystal structure of hydrochlorborite, Ca₂[B₃O₃(OH)₄·OB(OH)₃]Cl·7H₂O, a seasonal evaporite mineral. American Mineralogist, 63, 814-823.
• Bruker (2017) SAINT Version 8.38A. Bruker Analytical X-ray Instruments Inc., Madison, Wisconsin, USA.
• Bruker (2018) APEX3, Version 2018.1. Bruker Analytical X-ray Instruments Inc., Madison, Wisconsin, USA.
•  Burns,  P.C. (1995) Borate clusters and fundamental building blocks containing four polyhedra: Why few clusters are utilized as fundamental building blocks of structures. Canadian Mineralogist, 33, 1167-1176.
•  Burns,  P.C. and  Hawthorne,  F.C. (1993) Hydrogen bonding in colemanite: An X-ray and structure-energy study. Canadian Mineralogist, 31, 297-304.
•  Burns,  P.C. and  Hawthorne,  F.C. (1995) Hydrogen bonding in borcarite, an unusual borate-carbonate mineral. Mineralogical Magazine, 59, 297-304.
•  Burns,  P.C.,  Grice,  J.D. and  Hawthorne,  F.C. (1995) Borate minerals I. Polyhedral clusters and fundamental building blocks. Canadian Mineralogist, 33, 1131-1151.
•  Christ,  C.L. and  Garrels,  R.M. (1959) Relations among sodium borate hydrates at the Kramer deposit, Boron, California. American Journal of Science, 257, 516-528.
•  Cipriani,  C. (1957) Un nuovo minerale fra i prodotti boriferi di Larderello. Atti della Accademia Nazionale dei Lincei. Rendiconti della Classe di Scienze Fisiche, Matematiche e Naturali, 22, 519-525.
•  Corazza,  E.,  Menchetti,  S. and  Sabelli,  C. (1974) The crystal structure of biringuccite, Na₄[B₁₀O₁₆(OH)₂]·2H₂O. American Mineralogist, 59, 1005-1015.
•  Dal Negro,  A.,  Pozas,  J.M.M. and  Ungaretti,  L. (1975) The crystal structure of ameghinite. American Mineralogist, 60, 879-883.
•  Dumanli,  F.T.S.,  Kipcak,  A.S. and  Derun,  E.M. (2022) Microwave dehydration of borax: Characterization, dehydration kinetics, and modelling. Glass Physics and Chemistry, 48, 210-218.
•  Ekmekyapar,  A.,  Baysar,  A. and  Kunkul,  A. (1997) Dehydration kinetics of tincal and borax by thermal analysis. Industrial & Engineering Chemistry Research, 36, 3487-3490.
•  Fofanova,  M.,  Bubnova,  R.,  Abert,  B.,  Filatov,  S., et al (2013) Structural changes in metastable γ-Na₂B₄O₇ between −150 °C and 720 °C. Zeitschrift für Kristallographie-Crystalline Materials, 228, 520-525.
•  Freyhardt,  C.C.,  Wiebcke,  M. and  Felsche,  J. (2000) The monoclinic and cubic phases of metaboric acid (precise redeterminations). Acta Crystallographica, C56, 276-278.
• Frisch, M.J., Trucks, G.W., Schlegel, H.B., Scuseria, G.E., et al. (2016) Gaussian 16, Revision C.01, Gaussian, Inc., Wallingford Connecticut, USA.
•  Gajhede,  M.,  Larsen,  S. and  Rettrup,  S. (1986) Electron density of orthoboric acid determined by X-ray diffraction at 105 K and ab initio calculations. Acta Crystallographica, B42, 545-552.
• Garrett, D.E. (1998) Borates: handbook of deposits, processing, properties, and use. pp. 483, Academic Press, London.
•  Ghose,  S.,  Wan,  C. and  Clark,  J.R. (1978) Ulexite, NaCaB₅O₆(OH)₆·5H₂O: Structure refinement, polyanion configuration, hydrogen bonding, and fiber optics. American Mineralogist, 63, 160-171.
•  Giacovazzo,  C.,  Menchetti,  S. and  Scordari,  F. (1973) The crystal structure of tincalconite. American Mineralogist, 58, 523-530.
•  Grew,  E.,  Hystad,  G.,  Hazen,  R.M.,  Krivovichev,  S.V., et al (2017) How many boron minerals occur in Earth’s upper crust? American Mineralogist, 102, 1573-1587.
•  Grice,  J.D.,  Burns,  P.C. and  Hawthorne,  F.C. (1999) Borate minerals. II. A hierarchy of structures based upon the borate fundamental building block. Canadian Mineralogist, 37, 731-762.
•  Hawthorne,  F.C.,  Burns,  P.C. and  Grice,  J.D. (1996) The crystal chemistry of boron. Reviews in Mineralogy and Geochemistry, 33, 41-115.
•  Helvaci,  C. and  Palmer,  M.R. (2017) Origin and distribution of evaporite borates: The primary economic sources of boron. Elements, 13, 249-254.
•  Jiang,  Y. and  Zhang,  H. (1989) Stability and reactivities based on moment analysis. Theoretica Chimica Acta, 75, 279-297.
•  Kanishcheva,  A.S.,  Egorysheva,  A.V.,  Gorbunova,  Y.E.,  Kargin,  Y.F., et al (2004) Crystal structure of the metastable polymorph γ-Na₂O·2B₂O₃. Russian Journal of Inorganic Chemistry, 49, 919-924.
•  Koskinen,  M.,  Lipas,  P.O. and  Manninen,  M. (1995) Electron-gas clusters: the ultimate jellium model. Zeitschrift für Physik D Atoms, Molecules and Clusters, 35, 285-297.
•  Krogh-Moe,  J. (1974) The crystal structure of sodium diborate, Na₂O·2B₂O₃. Acta Crystallographica B30, 578-582.
•  Levy,  H.A. and  Lisensky,  G.C. (1978) Crystal structures of sodium sulfate decahydrate (Glauber’s salt) and sodium tetraborate decahydrate (borax). Redetermination by neutron diffraction. Acta Crystallographica, B34, 3502-3510.
•  Li,  H. and  Liang,  J. (1995) Dependence of crystallization behavior of sodium diborate (Na₂O·2B₂O₃) on its glass structure and the characteristics of phase transformation. Journal of the American Ceramic Society, 78, 470-478.
• McAllister, J.F. (1961) Sborgite in the Furnace Creek area, California. United States Geological Survey Professional Paper, 424B, 299-301.
•  Merlino,  S. and  Sartori,  F. (1972) The crystal structure of sborgite, NaB₅O₆(OH)₄·3H₂O. Acta Crystallographica, B28, 3559-3567.
•  Momma,  K. and  Izumi,  F. (2011) VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data. Journal of Applied Crystallography, 44, 1272-1276.
•  Morey,  G.W. and  Mervin,  H.E. (1936) Phase equilibrium relationships in the binary system, sodium oxide-boric oxide, with some measurements of the optical properties of the glasses. Journal of the American Chemical Society, 58, 2248-2254.
•  Sennova,  N.A.,  Bubnova,  R.S.,  Filatov,  S.K. and  Polyakova,  I.G. (2007) High-temperature crystal chemistry of α-Na₂B₄O₇ and β-NaB₃O₅ layered borates. Glass Physics and Chemistry, 33, 217-225.
• Sheldrick, G.M. (2012) SADABS Version 2012/1. Bruker Analytical X-ray Instruments Inc., Madison, Wisconsin, USA.
•  Sheldrick,  G.M. (2015) Crystal structure refinement with SHELXL. Acta Crystallographica, C71, 3-8.
•  Simonov,  M.A.,  Egorov-Tismenko,  Y.K. and  Belov,  N.V. (1977) Accurate crystal structure of uralborite, Ca₂[B₄O₄(OH)₈]. Doklady Akademii Nauk SSSR, 234, 822-825.
•  Sun,  W.,  Huang,  Y.X.,  Li,  Z.C.,  Pan,  Y.M., et al (2011) Hydrothermal synthesis and single-crystal X-ray structure refinement of three borates: sibirskite, parasibirskite and priceite. Canadian Mineralogist, 49, 823-834.
•  Waclawska,  I. (1995) Thermal decomposition of borax. Journal of Thermal Analysis and Calorimetry, 43, 261-269.