Synthesis and characterization of a disordered variant of KB₅O₇(OH)₂

2.1 Synthesis

The title compound was synthesized hydrothermally by charging a Teflon-lined stainless-steel autoclave (8 mL) with KNO₃ (435.3 mg), B₂O₃ (302.8 mg), and Ce(NO₃)₃·6H₂O (125.9 mg) with a molar ratio of 1:1:0.07. The chemicals were obtained from Carl Roth GmbH (Karlsruhe, Germany, KNO₃ and Ce(NO₃)₃·6H₂O), and Strem Chemicals (Newburyport, MA, USA, B₂O₃) exhibiting at least p.a. quality. Prior to and after the use of the aforementioned chemicals, powder patterns of the educts were collected to control their stability, especially with regard to the water content of Ce(NO₃)₃·6H₂O. The latter nitrate displayed reflections according to pentaaquatrinitratocerium(III) monohydrate Ce(NO₃)₃(H₂O)₅·H₂O [15]. This compound exhibits five molecules of water in close coordination to the cerium cation, and one water molecule formulated as crystal water confirming the compsition of the educt. The educt mixture was then ground together, heated to and kept at 513 K for 3 days, cooled slowly down to 393 K (1 K h^–1), and finally quenched to room temperature. Colorless block-shaped crystals of disordered and ordered KB₅O₇(OH)₂ were obtained alongside traces of another, unknown phase. The product mixture was washed with hot deionized water to remove excess educts.

2.2 Crystal structure analysis

The powder X-ray diffraction pattern of the disordered phase KB₅O₇(OH)₂ was collected with a STOE Stadi P powder diffractometer with transmission geometry and MoK_α1 (λ = 70.93 pm) radiation applying a focusing Ge(111) primary beam monochromator and a linear PSD detector. Figure 1 (top) shows the experimental powder pattern of the disordered variant of KB₅O₇(OH)₂ with the according theoretical pattern simulated from the single-crystal data [Fig. 1 (center)]. For comparison, the theoretical pattern stemming from the single crystal data of the ordered structure reported by Wu is also given in Fig. 1 (bottom).

Fig. 1:

Top: Experimental powder pattern of the hydrothermal synthesis product containing the disordered variant of KB₅O₇(OH)₂; the reflections marked with a cross stem from the ordered variant of KB₅O₇(OH)₂, reflections marked with asterisks result from traces of boric acid, and reflections with a circle stem from an unknown side phase. Center: theoretical powder pattern derived from single-crystal data of the disordered variant of KB₅O₇(OH)₂. Bottom: theoretical powder pattern obtained from single-crystal data of the ordered compound KB₅O₇(OH)₂.

The corresponding reflections of the powder pattern were indexed and refined [16]. The lattice parameters fit well with the parameters obtained from the single-crystal data (see Table 1).

For the single-crystal structure analysis, irregularly shaped crystals (40 × 35 × 30 μm) of the disordered variant of KB₅O₇(OH)₂ were picked and isolated through polarization contrast microscopy. Collection of the single-crystal data using a Nonius Kappa-CCD diffractometer with graphite-monochromatized MoK_α radiation (λ = 71.073 pm) was conducted at room temperature as well as at –50 °C employing liquid nitrogen cooling. No change of the crystal structure was observed while cooling, therefore only data obtained from the room temperature experiment are presented in the following. From the systematic extinctions, the centrosymmetric space group P2₁/n (no. 14:b2) was derived. For reasons of comparability with the structure variant reported by Wu, a space group transformation to P2₁/c (no. 14:b1) was performed following a suggested unit cell transformation of (–a, –b, a + c) and an origin shift of (+1/2, +1/2, 0) obtained by the Structure Tidy routine implemented in Platon [17].

All non-hydrogen atoms were refined with anisotropic displacement parameters. The final difference Fourier syntheses did not reveal any significant peaks in the refinement (Shelxl-2013, full-matrix least-squares on F²) [18, 19]. The hydrogen atoms at the hydroxyl groups O7–H1 and O8–H2 were refined isotropically, employing a bond restraint of 83 pm.

All relevant details of the data collection and evaluation are listed in Table 1. Tables 2–6 show the positional parameters, the anisotropic displacement parameters, selected interatomic distances, bond angles, and characteristic data of the hydrogen bond system, respectively.

Further details of the crystal structure investigation may be obtained from the Fachinformationszentrum Karlsruhe, D-76344 Eggenstein-Leopoldshafen, Germany (fax: +49-7247-808-666; e-mail: crysdata@fiz-karlsruhe.de, http://www.fiz-karlsruhe.de/request_for_deposited_data.html) on quoting the deposition number CSD-429423.

2.3 Vibrational spectroscopy

The transmission FT-IR spectrum of a single-crystal of the title compound was measured in the spectral range of 600–4000 cm^–1 with a Bruker Vertex 70 FT-IR spectrometer (spectral resolution 4 cm^–1), equipped with an MCT (Mercury Cadmium Telluride) detector and attached to a Hyperion 3000 microscope. As mid-infrared source, a Globar (silicon carbide) rod was used, whereby 32 scans of the single-crystal placed on a BaF₂ sample holder were acquired. Primary data was recorded supported by the spectrometer software Opus[20].

The confocal Raman spectrum of the same single-crystal of the disordered variant of KB₅O₇(OH)₂ was recorded from 100–2000 cm^–1 with a HORIBA Jobin Yvon LabRam-HR 800 Raman micro-spectrometer. The sample was excited using a frequency doubled 100 mW Nd-YAG-laser (λ = 532.22 nm) under an Olympus 100× objective lens with a numerical aperture of 0.9. The scattered light was dispersed by an optical grating with 1800 lines mm^–1, and collected by a 1024 × 256 open electrode CCD detector. Three ranges with a measurement time of 10 s each were measured with a spectral resolution higher than 2 cm^–1 determined by measuring the Rayleigh line. A background correction was applied [21].

2.4 DFT calculations

In addition to the experimental recording of vibrational spectra, quantum-chemical energy minimizations and computations of the harmonic vibrational frequencies were performed. The minimum geometry and the theoretical spectra were calculated using the program Crystal09 [22, 23]. For all atoms, a triple zeta basis set was chosen [24]. Exchange and correlation contributions were calculated with the Pbesolfunctional using a shrinking factor of eight [25]. All calculations were performed on the MACH Supercomputer with 256 processors of the type Intel Westmere EX 2.66 GHz.

3.1 Synthetic conditions

The title compound was obtained through a hydrothermal synthesis as described in the experimental section. To promote single-crystal growth, a low cooling rate of 1 K h^–1 was applied. We also varied the educts with respect to the synthesis of the ordered structure variant KB₅O₇(OH)₂ published by Wu substituting boron oxide B₂O₃ with boric acid H₃BO₃, whereby the title compound was not formed. A reduction of the reaction temperature from 513 to 483 K as applied by Wu did not lead to product formation either. Furthermore, a reduced reaction time of two days (instead of three) at the maximum temperature of 513 K did not lead to the formation of the desired product. In our experimental approach to yield the disordered variant of KB₅O₇(OH)₂, we employed a small amount of cerium nitrate hexahydrate (0.07 equivalents based on boron), which possibly acted upon the reaction mixture as a mineralizer accelerating or enabling the reaction. Wu reported the addition of GaO(OH) (also 0.07 equivalents relative to boron) to obtain the ordered variant of KB₅O₇(OH)₂. The related compound K[B₅O₇(OH)₂]·H₂O reported by Zhang et al., which is not a structural variant but shows great resemblance to the dehydrated KB₅O₇(OH)₂, was, however, obtained by addition of pyridine (14 equivalents based on boron) to the reaction mixture containing boric acid, potassium hydroxide, and water [26].

We were able to isolate single crystals of the disordered variant of KB₅O₇(OH)₂, but only as a minor side phase. As the system is strongly inclined towards formation of the ordered structure variant as reported by Wu, further promotion of the formation of the disordered structure variant appears to be not very promising.

3.2 Crystal structure discussion

The disordered potassium pentaborate KB₅O₇(OH)₂ crystallizes with four formula units (Z = 4) in the monoclinic space group P2₁/c (no. 14) with the lattice parameters a = 904.8(2), b = 753.2(2), and c = 1214.9(5) pm, β = 117.16(2)° and V = 0.73663(5) nm³. The Figs. 2 and 3 show the crystal structure of the title compound in direct comparison to the ordered structure obtained by Wu along [001] and [100], respectively. The disorder of the cation position results in a remarkable elongation of the crystallographic a axis (766.90(3) → 904.8(2) pm) and a shortening of the b axis [904.45(3) → 753.2(2) pm]. The c axis and the monoclinic angles are similar in both forms: c = 1214.9(5) pm/β = 117.16(2)° and c = 1223.04(4) pm/β = 119.132(2)° for the disordered and the ordered pentaborate, respectively. Interestingly, the volume of the disordered variant [V = 0.73663(5) nm³] is slightly smaller than the volume of the ordered variant (V = 0.74102 nm³).

Fig. 2:

Left: Crystal structure of the disordered variant of KB₅O₇(OH)₂ down [001]. K⁺: large grey spheres; both possible potassium positions are displayed centering the corrugated channels along the b axis; O^2–: small blue spheres at the corners of the tetrahedral and of the trigonal-planar groups; B³⁺: center of tetrahedra and BO₃ groups (depicted without polyhedra) as small red spheres; H⁺: small yellow spheres; Right: ordered structure variant KB₅O₇(OH)₂ by Wu; K⁺: large white spheres; color scheme of the remaining atoms as aforementioned.

Fig. 3:

Crystal structure of the disordered variant of KB₅O₇(OH)₂ down [100] (top). Color scheme as mentioned. For comparison, KB₅O₇(OH)₂ by Wu is given below.

A more detailed view of the structure of the disordered variant of KB₅O₇(OH)₂ is depicted in the left part of Fig. 4; all relevant positions referred to in the following are highlighted. The disordered phase KB₅O₇(OH)₂ consists of chains of four trigonal-planar BO₃ units (Δ), whereby the chain is terminated at both ends by protonated oxygen positions. These chains are interconnected by BO₄ tetrahedra (□), of which all four corners are connected to adjacent BO₃ units. Thereby, the obtained fundamental building block (FBB) in the disordered variant of KB₅O₇(OH)₂ can be written as <2Δ□>–<2Δ□>–· (after Burns et al. [27]). Fig. 4 (left) shows the representation of the asymmetric unit with displacement ellipsoids (relevant values are given in Tables 2 and 3). For comparison, the ordered phase KB₅O₇(OH)₂reported by Wu is also given in Fig. 4 (right). In the disordered phase KB₅O₇(OH)₂, chains composed of BO₃ groups display an angle of 133.5(2)° formed by the positions B3–O9–B5 of adjacent FBBs, resulting in slightly bent chains. The equivalent positions B5–O5–B1 in the ordered variant form a slightly smaller angle of 131.2(2)°. A torsion angle of –7.6(3)° in the Dreierringe [28] (formed by the positions B5–O5–B4–O4) gives rise to a helical wrapping of the disordered structure. In the ordered structure variant, the corresponding torsion angle is very small [–0.7(3)° formed by the positions B1–O3–B2–O1]. At the opposite side of the central tetrahedron, the terminal borate group is connected with a small torsion angle of –0.3(3)° for O1–B2–O2–B3. The ordered structure variant of KB₅O₇(OH)₂, however, shows an angle of 3.6(3)° for the equivalent structural feature (O6–B3–O4–B5) [9].

Fig. 4:

Asymmetric units in both variants of KB₅O₇(OH)₂. Left: the disordered variant of KB₅O₇(OH)₂; right: KB₅O₇(OH)₂reported by Wu. Displacement ellipsoids are presented at a 50 % probability level.

Bond angles within the trigonal-planar and tetrahedral borate groups (listed in Table 5) concur well with the normal values of 120.0 and 109.4°, respectively [3, 4]. The B–O bond lengths [146.8(3)–148.6(2) pm] are within the normal range commonly reported for BO₄ tetrahedra in borates [3]. In the BO₃ units, the observed distances range from 133.7(2) to 138.9(2) pm (average value in borates: 137.0 pm [4]).

The terminal oxygen atoms of the BO₃ groups are protonated enabling hydrogen bonds as an interconnection between the infinite borate strings. In Table 6, bond lengths, distances, and angles of the three different OH donor and acceptor groups are listed. In the disordered phase KB₅O₇(OH)₂, the O–H distance was restrained to a value of 83(2) pm, which corresponds to the value reported in the ordered structure variant (84 pm). Therefore, also the formed hydrogen bonds (average lengths for the distances H···A and D···A in the disordered form of KB₅O₇(OH)₂ are 228 and 295.8 pm compared to 239 and 313 pm in the ordered form) are comparable [9]. Only the mean hydrogen bond angle of 140° found for the title compound is slightly smaller in comparison to the previously reported average angle of 150° [9] in the ordered phase of KB₅O₇(OH)₂.

In the disordered pentaborate, the positions K1 and K2 are occupied by 46 and 54 %, respectively. Single-crystal diffraction experiments below room temperature (at 213 K) showed no convergence of the cations to a single position. Figure 5 shows the coordination environment of K1 and K2 in direct comparison to the coordination sphere of the K1 position in the ordered structure of KB₅O₇(OH)₂. The K–O coordination distances ranging from 259.6(2) to 340.9(2) pm (average value for K1 and K2 is 300.7 pm) are given in Table 4. The average K1–O distance of 286.9 pm in the ordered form of KB₅O₇(OH)₂ is significantly smaller [9]. The K1 and K2 cations in the title compound exhibit a seven- and nine-fold coordination by oxygen anions, respectively.

Fig. 5:

Coordination spheres of the two potassium positions K1 and K2 in the disordered variant of KB₅O₇(OH)₂ (left) in comparison to the coordination sphere of the K1 position in the ordered variant of KB₅O₇(OH)₂ (right).

The bond-valence sums of all ions for the disordered variant of KB₅O₇(OH)₂ were calculated from the single-crystal data using the bond-length/bond-strength concept (ΣV) [29, 30]. The results of the calculations (Table 7) correspond well with the expected values for the formal ionic charges of the atoms.

3.3 Vibrational spectroscopy

The IR and the Raman spectra of the disordered variant of KB₅O₇(OH)₂are given in Figs. 6 and 7, respectively. The calculations of the irreducible representation of the title compound in the space group P2₁/c yielded 204 theoretically possible modes: Γ = 51 A_u + 51 B_u + 51 A_g + 51 B_g. One B_u and one A_u mode are acoustic, the remaining 100 optical u-modes are excitable by IR radiation. The remaining 51 A_g and 51 B_g modes are purely Raman-active.

Fig. 6:

FT-IR absorbance spectrum of a single-crystal (top curve) and theoretical bands (red lines) of the disordered variant of KB₅O₇(OH)₂ in the range of 600–3500 cm^–1.

Fig. 7:

Single-crystal Raman spectrum (top curve) and theoretical bands (red lines) of the disordered variant of KB₅O₇(OH)₂ in the range of 400 to 3600 cm^–1.

IR and Raman active bands below 200 cm^–1 can be assigned to lattice vibrations involving the cation. Bending and coupled vibrations of BO₃ and BO₄ units are located between 200 and 900 cm^–1 [31]. Due to experimental limitations, an IR characterization below 600 cm^–1 was not possible. From 850 to 1600 cm^–1, stretching vibrations of B–O units are detected, whereby absorptions of BO₄ tetrahedra dominate between 850–1100 cm^–1 [32–34]. Absorptions of BO₃ units are expected from 1200 to 1450 cm^–1 [33–36]. The broad band around 3300 cm^–1 can be assigned to O–H groups involved in hydrogen bonding [37, 38]. A more detailed correlation of the observed bands and the according vibrations is given in the following.

3.4 Quantum-mechanical calculations of harmonic vibrational frequencies

For the vibrational band assignment, quantum mechanical calculations were performed using the program Crystal09 [22, 23]. The disordered position of the potassium cation is challenging for quantum chemical calculations. As a consequence, multiple calculations were necessary. Two independent calculations were performed: firstly with a full occupation of the K1 site and secondly with a fully occupied position K2. The similar positions of the vibrational bands in the spectra can be found in the Supplementary Material (Fig. S1). Qualitative band assignments based on the two spectra described above are given in the following. A band-to-band assignment is difficult, as the density of the modes is very high.

The hydrogen stretching bands can clearly be assigned as they represent the only modes showing wavenumbers higher than 3000 cm^–1. Around 1600 cm^–1, an absorption was found experimentally, which was not obtained in the theoretical work. A possible explanation for this effect could be traces of water on the surface of the measured crystal. The stretching mode of the tetrahedally coordinated boron atoms can theoretically be found between 780 and 1030 cm^–1 in the Raman spectrum and between 880 and 1060 cm^–1 in the IR spectrum. Stretching frequencies stemming from trigonally coordinated B³⁺ appear at higher wavenumbers: 1390–1540 and 1300–1480 cm^–1 in the IR and Raman spectrum, respectively. Bending modes for the BO₄ groups are widespread between 300 and 1000 cm^–1. Absorptions resulting from bending of the BO₃ groups are located in a more narrow range between 330 and 600 cm^–1. In the region between 1050 and 1250 cm^–1, H–O–B bending bands are expected. At wavenumbers lower than 250 cm^–1, motions in which the potassium cation is involved are dominant, e.g. K–O stretching and O–K–O bending. Table 8 gives all experimentally and theoretically observed frequencies and their assignment. The complete Table of calculated IR and Raman vibrational modes can be obtained as Supporting Information available online (Table S1; see note at the end of the paper for availability).