A new polymorph of Cd₃B₂O₆: synthesis, crystal structure and phase transformation

Abstract

A new polymorph of Cd₃B₂O₆ (β-Cd₃B₂O₆) has been grown through spontaneous crystallization with the flux system. β-Cd₃B₂O₆ crystallizes in triclinic space group P1̄ and features a three-dimensional Cd–O network composed of CdO_n (n = 5, 6) distorted polyhedra and isolated planar BO₃ groups. The phase transformation of Cd₃B₂O₆ has been studied by the structure analysis and powder X-ray diffraction. TG-DSC measurement reveals the melting behavior and phase transformation temperature. Furthermore, the IR spectrum was measured. The detailed structure comparison between Cd₃B₂O₆ and other cadmium-containing borates, such as CdB₄O₇, CdB₂O₄ and Cd₂B₂O₅ was also carried out.

---

Introduction

Polymorphism, the ability for a substance to adopt several distinct crystalline phases of identical composition, is observed for a variety of materials.¹ This phenomenon has become increasingly important and is attracting more attention because of the promising applications in pharmaceuticals, pigments, foods, dyestuffs and so forth.² Industrially, disastrous consequences can be speculated by a sudden unexplained switch of polymorph. Technologically, the structural variants exhibit different physical properties reflecting in optical characteristics, chemical reactivity, crystal morphology, etc.³ α- and β-ZnS give a good example that the two polymorphs belong to different crystal systems and thus own different physical properties, which make them to possess different applications in nano materials and semiconductor materials.⁴ Understanding polymorphism is valuable for the research of structure–property relationships. Extensive polymorphism has been reported in many inorganic materials, such as α-BaTeMo₂O₉ (ref. 5) and β-BaTeMo₂O₉,⁶ α-Cs₂I₄O₁₁ (ref. 7) and β-Cs₂I₄O₁₁,⁸ α-KMoO₃(IO₃) (ref. 9) and β-KMoO₃(IO₃).¹⁰

In the study, we mainly focus on the borate polymorphs because they possess rich chemistry structures, generally, the B atoms can be coordinated by either three or four O atoms to form a BO₃ triangle or BO₄ tetrahedron, which can be further linked by sharing O atoms to form isolated rings and cages or to construct infinite chains, sheets, or networks. The rich structure chemistry of borates favors them to exhibit the phenomenon of polymorphs, which make borates ideal candidates for the research of the phase transformation. In addition, borates also exhibit many attractive properties such as efficient frequency conversion capability in nonlinear optical crystals, high electrical conductivity in ion conductors, and large birefringence in controlling the polarization of illuminating lasers.¹¹ And borate polymorphs with different crystal structures exhibit different physical properties and thus possess different applications. For example, BaB₂O₄ has two polymorphs with different space groups and distinct crystal structures. The low-temperature phase (β-BaB₂O₄) is a widely used nonlinear optical material, while the high-temperature phase (α-BaB₂O₄) also has excellent property for its large birefringence.¹²

In this work, a new Cd₃B₂O₆ phase was found in CdO–B₂O₃ system, it crystallizes in triclinic space group P1̄. The other phase Cd₃B₂O₆ has been reported.¹³ According to their crystallization temperature from low to high, the new Cd₃B₂O₆ phase can be regarded as the high-temperature phase β-Cd₃B₂O₆. TG-DSC of α-Cd₃B₂O₆ and IR spectra of α- and β-Cd₃B₂O₆ were measured. Furthermore, to better understand the phase transformation of Cd₃B₂O₆, polycrystalline samples of β-Cd₃B₂O₆ were synthesized by traditional solid-state reaction techniques at different reaction temperatures. The detailed comparison between Cd₃B₂O₆ and other cadmium-containing borates, such as CdB₄O₇, CdB₂O₄ and Cd₂B₂O₅ was also carried out.¹⁴

Experimental

Reagents

CdO (99%, Sinopharm Chemical Reagent Co., Ltd.) and H₃BO₃ (99%, Sinopharm Chemical Reagent Co., Ltd.) were used as received.

Crystal growth

Small single crystals were grown from a high-temperature solution with the PbO–MoO₃ flux system in air. A mixture of raw materials CdO–H₃BO₃–PbO–MoO₃ with molar ratio 3.3 : 2 : 1 : 1 was loaded in a platinum crucible and heated in a muffle furnace at 700 °C until the solution became transparent and clear. The homogenized solution was then cooled quickly (20 °C h⁻¹) to the crystallization temperature (580 °C), then slowly cooled (3 °C h⁻¹) to 500 °C, followed by cooling to room temperature after the furnace was powered off. Small colorless crystals of β-Cd₃B₂O₆ were obtained.

X-ray crystallography

A colorless and transparent plate crystal of β-Cd₃B₂O₆ with dimensions of 0.063 × 0.128 × 0.161 mm³ was selected and mounted on a thin glass fiber of the Bruker SMART APEX II CCD diffractometer. Data were collected using monochromatic Mo Kα radiation (λ = 0.71073 Å) at 296(2) K and integrated with the SAINT program.¹⁵ All calculations were performed with programs from the SHELXTL crystallographic software package.¹⁶ The structure was solved by direct methods using SHELXS-97.¹⁷ The final full-matrix least-squares refinement was on F_o² with data having F_o² ≥ 2σ(F_o²) and all of the atoms were refined with anisotropic thermal parameters. The final refinement was converged with R₁ = 0.0149 and wR₂ = 0.0435. The β-Cd₃B₂O₆ structure was checked for missing symmetry elements with PLATON.¹⁸ The crystal data and structure refinement for β-Cd₃B₂O₆ are presented in Table 1. The atomic coordinates, related anisotropic displacement parameters, the bond valence calculation¹⁹ for all atoms and selected bond lengths (Å) and angles (deg.) are summarized in Tables S1–S3 in the ESI.† The results of bond valence calculations (Cd, 1.93–2.08; B, 2.90–2.92) indicate that the Cd and B atoms are in oxidation states of +2 and +3, respectively.

Table 1 Crystal data and structure refinement for β-Cd₃B₂O₆

a R1 = ∑||Fo| − |Fc||/∑|Fo| and wR2 = [∑w(Fo^2 − Fc^2)^2/∑wFo^4]^1/2 for Fo^2 > 2σ(Fo^2).
Empirical formula	β-Cd3B2O6
Formula weight	454.82
Crystal system	Triclinic
Space group, Z	P1̄, 2
Unit cell dimensions
a	6.1114(5) Å
b	6.1463(5) Å
c	7.4232(6) Å
α	76.521(3)°
β	80.730(3)°
γ	82.461(3)°
Volume	266.34(4) Å^3
Density (calculated)	5.671 Mg m^−3
Theta range for data collection	2.85° to 27.59°
Limiting indices	−7 ≤ h ≤ 7, −8 ≤ k ≤ 8, −9 ≤ l ≤ 9
Reflections collected/unique	3827/1205 [R(int) = 0.0194]
Completeness to theta	98.1%
Goodness-of-fit on F^2	1.189
Final R indices [Fo^2 > 2σ(Fo^2)]^a	R1 = 0.0149, wR2 = 0.0435
R indices (all data)^a	R1 = 0.0157, wR2 = 0.0439
Extinction coefficient	0.0213(9)
Largest diff. peak and hole (e Å^−3)	0.955 and −0.674 e Å^−3

---

Powder X-ray diffraction

Powder X-ray diffraction (XRD) analysis of β-Cd₃B₂O₆ was performed in flat plate at room temperature in the angular range of 10° < 2θ < 70° with a scan step width of 0.02° and fixed counting time of 1 s per step with a Bruker D8 ADVANCE X-ray diffractometer with graphite monochromatized Cu Kα (λ = 1.5418 Å) radiation.

Thermal analysis

Thermal analysis was carried out on a simultaneous NETZSCH STA 449C thermal analyzer instrument with a heating rate of 5 °C min⁻¹. The measurement range extended from 35 to 1200 °C in an atmosphere of flowing N₂.

IR spectroscopy

The IR absorption spectra were recorded on a Shimadzu IR Affinity-1 Fourier transform IR spectrometer to analyze the presence of functional groups in the α- and β-Cd₃B₂O₆ compounds. The samples were mixed thoroughly with dried KBr (1 mg of the sample, 100 mg of KBr). The spectra were collected in the range from 400 to 4000 cm⁻¹ with a resolution of 2 cm⁻¹.

Results and discussion

Synthesis and phase transformation

Polycrystalline samples of β-Cd₃B₂O₆ were synthesized by traditional solid-state reaction techniques. Pure polycrystalline β-Cd₃B₂O₆ was not obtained, even with different proportions of raw materials and various dwell times at temperature. For example, superfluous CdO was also tried owing to its high vapor pressure. However, the experimental results were still not satisfactory. The polycrystalline β-Cd₃B₂O₆ was always mixed with some α-Cd₃B₂O₆, while pure polycrystalline α-Cd₃B₂O₆ has been obtained easily. To investigate the phase transformation, TG-DSC of pure α-Cd₃B₂O₆ was measured as shown in Fig. 1. The DSC curve exhibits two endothermic peaks at 862 and 985 °C upon heating to 1200 °C. There is weight loss on the TG curve from 985 °C. 862 and 985 °C are the phase transformation temperature and melting temperature, respectively. For confirmation of this and investigation of its phase transformation, a series of experiments at different reaction temperatures (850–1000 °C) were conducted. Stoichiometric mixture of CdO and H₃BO₃ were thoroughly ground in an agate mortar and then packed into a platinum crucible. The crucible was heated in air from room temperature to 850 °C at a rate of 20 °C min⁻¹ and allowed to dwell at the temperature for 24 h, grounded three times during the sintered process, and then quenched in air. The phase purity of the resultant solid was confirmed by powder XRD. When the temperatures were higher than 880 °C, the powder XRD patterns were similar. Then, the XRD patterns at 850–880 °C are shown in Fig. 2. As shown in Fig. 2, the phase transformation begins at about 860 °C. When the temperature was raised to 1000 °C, the powders melted. The result is consistent with our previous prediction that 862 °C and 985 °C are the phase transformation temperature and melting temperature of β-Cd₃B₂O₆, respectively.

Fig. 1 TG-DSC curves of α-Cd₃B₂O₆.

Fig. 2 Powder XRD traces showing the influence of reaction temperature on polymorph formation. Denotation ★ represents the α-Cd₃B₂O₆ crystalline phase.

In order to further research the phase transformation of Cd₃B₂O₆, the sample after melting has been characterized by the powder XRD. The powder of β-Cd₃B₂O₆ melted at 1000 °C for 10 h, the different cooling rates of melt were explored. For sample 1 in Fig. 3, the temperature decreased from 1000 to 800 °C at a rate of 2 °C h⁻¹, and allowed to cool to room temperature after the furnace was turned off. Powder XRD revealed that the main product was α-Cd₃B₂O₆ with some β-Cd₃B₂O₆. For sample 2, the melting β-Cd₃B₂O₆ powder was directly quenched in ice-water mixture. Powder XRD revealed that the main product was β-Cd₃B₂O₆ with some α-Cd₃B₂O₆. The above results indicate that β-Cd₃B₂O₆ is a congruent melting compound and the energy barrier from β-Cd₃B₂O₆ to α-Cd₃B₂O₆ is very low. Hence, the crystallized β-Cd₃B₂O₆ products always include some α-Cd₃B₂O₆ and the pure polycrystalline β-Cd₃B₂O₆ is difficult to obtain. In addition, the before and after melting XRD patterns also indicate that the weight loss on the TG curve was just due to the volatilization.

Fig. 3 Calculated XRD patterns of α- and β-Cd₃B₂O₆ and the before and after melting XRD patterns of β-Cd₃B₂O₆. Lines 1 and 2 represent the after melting XRD patterns. Line 1 represents the result that adopts the slow decreasing temperature program while line 2 is the result of quenching experiment. Denotation ★ represents the α-Cd₃B₂O₆ crystalline phase.

Structural description

β-Cd₃B₂O₆ crystallizes in the centrosymmetric triclinic system with space group P1̄, and its structure is illustrated in Fig. 4. β-Cd₃B₂O₆ features a three-dimensional (3D) Cd–O network composed of CdO_n (n = 5, 6) distorted polyhedra and isolated planar BO₃ groups. In the asymmetric unit, Cd, B, and O each occupy three, two, and six crystallographically unique positions, respectively. In the CdO_n (n = 5, 6) polyhedra, the bond lengths vary from 2.143(2) to 2.424(2) Å, with O–Cd–O bond angles from 59.43(8)° to 173.31(8)°. In the BO₃ triangles, the bond lengths and angles range from 1.366(4) to 1.391(4) Å and from 116.4(3)° to 123.4(3)°, respectively. The mean bond length in the BO₃ triangle is 1.383 Å. These bond lengths and angles in β-Cd₃B₂O₆ are comparable with those reported in other borates.²⁰

Fig. 4 View of the β-Cd₃B₂O₆ crystal structure along the b-axis. B1O₃ and B2O₃ groups are shown in pink and blue, respectively. The bonds of Cd–O are removed for clarity.

In β-Cd₃B₂O₆, there are three unique Cd–O polyhedra: Cd1O₆, Cd2O₅, Cd3O₆. These CdO_n (n = 5, 6) polyhedra are linked through common corners and edges to form a 3D framework. Among Cd–O groups, each Cd1-centered octahedron shares corners with two Cd2-centered hexahedra and four Cd3-centered octahedra and simultaneously shares one edge with two Cd1 and one Cd3-centered octahedra. Each Cd2-centered hexahedron shares corners with two Cd1-centered octahedra and three Cd3-centered octahedra and shares one edge with two Cd2-centered hexahedra. Each Cd3-centered octahedron is linked with four Cd1-centered octahedra and three Cd2-centered hexahedra and shares one edge with one Cd1 and one Cd3-centered octahedra (Fig. S1 in the ESI†). The Cd⋯Cd distances of two adjacent Cd–O polyhedra contacted across the shared edges (the average is 3.3917 Å) are markedly shorter than those associated with shared corners (the average is 3.9273 Å), and the O–Cd–O angles in the Cd–O polyhedron contacted across the shared edges (the average is 82.644°) are also significantly smaller than those associated with shared corners (the average is 109.57°) due to the constraint of the Cd–O–Cd–O four-membered rings (Fig. S1 and Table S3 in the ESI†).

Two adjacent isolated planar B1O₃ and B2O₃ groups are parallel to each other with totally opposite orientation, respectively. Each B1O₃ triangle shares its three vertices with six neighboring CdO₆ octahedra and two CdO₅ hexahedra, while each B2O₃ triangle shares its three vertices with four neighboring CdO₆ octahedra and three CdO₅ hexahedra (Fig. S1 in the ESI†). It is also worth noting that each BO₃ triangle shares its one edge with neighboring CdO₆ octahedra developing Cd–O–B–O four-membered rings which lead to distinct small O–Cd–O angles. As mentioned above, Cd–O–Cd–O and Cd–O–B–O four-membered rings are responsible for the highly distorted CdO_n (n = 5, 6) polyhedra. To better understand the distortion of the CdO_n (n = 5, 6) polyhedra, we further calculated their dipole moments by the simple valence method.²¹ The approximate directions of the dipole moments for CdO_n (n = 5, 6) polyhedra are shown in Fig. 5 and the magnitudes of dipole moments of CdO_n (n = 5, 6) polyhedra in α- and β-Cd₃B₂O₆ are shown in Table S4 in the ESI.† The result reveals that the distortions of CdO_n (n = 5, 6) polyhedra in β-Cd₃B₂O₆ are larger than those in α-Cd₃B₂O₆.

Fig. 5 The approximate directions of the dipole moments for CdO_n (n = 5, 6) polyhedra in β-Cd₃B₂O₆. The unit of Cd–O bond length is Å.

Comparing the structures with α-Cd₃B₂O₆

To further well understand the structure of β-Cd₃B₂O₆, we compared the structures between the two phases in detail. The structure of α-Cd₃B₂O₆ is built up of a 3D Cd–O network composed of solely CdO₆ distorted polyhedra and isolated planar BO₃ groups.¹³ The different orientation of the BO₃ groups and the variation of the connection modes of Cd–O groups contribute for the structural versatility of Cd₃B₂O₆. It is worth noting that in α- and β-Cd₃B₂O₆, the Cd–O frameworks both consist of the Cd–O four- and six-membered rings, however, the ratio of four-membered rings in α-Cd₃B₂O₆ is higher than that in β-Cd₃B₂O₆. And in β-Cd₃B₂O₆, the large eight-membered rings are observed, as shown in Fig. 6. In addition, in β-Cd₃B₂O₆, two kinds of Cd–O coordination-sphere (CdO₅, CdO₆) are observed, while only one kind of CdO₆ octahedra is observed in α-Cd₃B₂O₆. The different structural features could cause the loose structure of β-Cd₃B₂O₆ when compared with α-Cd₃B₂O₆. Based on the calculated densities, β-Cd₃B₂O₆ is 5.671 g cm⁻³, while α-Cd₃B₂O₆ is 5.870 g cm⁻³. The result is consistent with above structure analysis. We think that the higher crystallization temperature of β-Cd₃B₂O₆ results in more vigorous atomic thermal motion, which further drives the formation of different loose Cd–O framework and realizes the phase transition.

Fig. 6 The Cd–O frameworks in α- and β-Cd₃B₂O₆. The yellow Cd–O bonds represent the eight-membered rings emerged in β-Cd₃B₂O₆. The BO₃ groups are removed for clarity.

Other cadmium-containing borates

A further crystal structure research was performed on other cadmium-containing borates to investigate the reason of the formation of different Cd₃B₂O₆ polymorphs. CdB₄O₇, CdB₂O₄, Cd₂B₂O₅, α-Cd₃B₂O₆ and β-Cd₃B₂O₆ can be written as CdO·2B₂O₃ and xCdO·B₂O₃ (x = 1, 2, 3) to reflect the rising proportion of Cd²⁺ cations. There are rule changes in the connecting patterns of B–O groups. As shown in Fig. 7, when Cd/B < 1 (in CdO·2B₂O₃, Cd/B = 0.25 and in CdO·B₂O₃, Cd/B = 0.5), the B–O groups include BO₃ triangles or BO₄ tetrahedra, which can be further linked by sharing O atoms to form 3D networks. When Cd/B = 1 (in 2CdO·B₂O₃), two BO₃ triangles sharing one O atom form the B₂O₅ unit. When Cd/B > 1 (in α- and β-Cd₃B₂O₆, Cd/B = 1.5), B and O atoms only form the isolated BO₃ triangles. We think that the solely isolated BO₃ triangles possess more flexible arrangement modes which further contribute to the formation of different Cd₃B₂O₆ polymorphs. Moreover, it might appear isolated BO₄ tetrahedra or O²⁻ ions which are not linked to B atoms when the Cd/B ratio is increased higher than 1.5. This conclusion will give a meaningful guide to ensuing experiments in CdO–B₂O₃ system.

Fig. 7 The B–O groups in CdO·2B₂O₃ (a), CdO·B₂O₃ (b), 2CdO·B₂O₃ (c), α-3CdO·B₂O₃ (d), β-3CdO·B₂O₃ (e), BO₄ tetrahedra and BO₃ triangles are shown in blue and pink, respectively.

IR spectroscopy

IR spectra of α- and β-Cd₃B₂O₆ are presented in Fig. S2 in the ESI† and they are similar. Referring to the literatures,²² the peaks at 1453, 1267, and 1106 cm⁻¹ for α-Cd₃B₂O₆, 1438, 1202, and 1154 cm⁻¹ for β-Cd₃B₂O₆ can be assigned to the asymmetric stretching and symmetric stretching vibrations of BO₃, while the peaks located at 804, 697 and 612 cm⁻¹ for α-Cd₃B₂O₆, 877, 709 and 615 cm⁻¹ for β-Cd₃B₂O₆ are likely to be from the out-of-plane bending of B–O in BO₃, respectively. The peaks at 568 cm⁻¹ for α-Cd₃B₂O₆, 580 and 508 cm⁻¹ for β-Cd₃B₂O₆ are attributed to bending vibrations. IR spectra indicate that only BO₃ groups are included in α- and β-Cd₃B₂O₆.

Conclusion

A new high-temperature phase of Cd₃B₂O₆, namely, β-Cd₃B₂O₆, has been discovered. It crystallizes in the triclinic space group P1̄, and displays a 3D framework composed of CdO_n (n = 5, 6) distorted polyhedra and isolated BO₃ groups. The phase transformation process between α- and β-Cd₃B₂O₆ was presented and their crystal structures were compared. TG-DSC and polycrystalline samples synthesis of β-Cd₃B₂O₆ at different reaction temperatures by traditional solid-state reaction techniques reveal that 862 and 985 °C are the phase transformation temperature and melting temperature, respectively. IR spectra of α- and β-Cd₃B₂O₆ indicate that only BO₃ groups are included in the two polymorphs. Furthermore, the crystal structures of other cadmium-containing borates have also been discussed to understand the formation of different Cd₃B₂O₆ polymorphs. We think that the solely isolated BO₃ triangles, which possess more flexible arrangement modes, contribute to the formation of different Cd₃B₂O₆ polymorphs. Our future research efforts will be devoted to exploring other borate polymorphs.

Acknowledgements

This work is supported by the High Technology Research & Development Program of Xinjiang Uygur Autonomous Region of China (Grant nos 201315103, 201116143), 973 Program of China (Grant nos 2014CB648400, 2012CB626803), the National Natural Science Foundation of China (Grant nos 21201176, U1129301, U1303392, 51172277, 51202287), the Western Light Program of CAS (Grant no. XBBS201214), Main Direction Program of Knowledge Innovation of CAS (Grant no. KJCX2-EW-H03-03) and the Science and Technology Project of Urumqi (Grant no. G121130002).

Notes and references

1. W. C. McCrone, Phys. Chem. Org. Solid State, 1965, 2, 725.
2. (a) W. H. Streng, Drug Discovery Today, 1997, 2, 415; (b) S. R. Vippagunta, H. G. Brittain and D. J. W. Grant, Adv. Drug Delivery Rev., 2001, 48, 3; (c) H. G. Brittain, J. Pharm. Sci., 2007, 96, 705.
3. (a) J. Bernstein, Org. Solid State Chem., 1987, 32, 471; (b) P. H. v. Groth, Chemische Kristallographie, Wilhelm Engelmann, Leipzig, 1917, vol. 4; (c) P. H. v. Groth, Chemische Kristallographie, Wilhelm Engelmann, Leipzig, 1919, vol. 5.
4. E. Monroy, F. Omnes and F. Calle, Semicond. Sci. Technol., 2003, 18, R33.
5. J. J. Zhang, Z. H. Zhang, W. G. Zhang, Q. X. Zheng, Y. X. Sun, C. Q. Zhang and X. T. Tao, Chem. Mater., 2011, 23, 3752.
6. W. G. Zhang, X. T. Tao, C. Q. Zhang, H. J. Zhang and M. H. Jiang, Cryst. Growth Des., 2009, 9, 263.
7. K. M. Ok and P. S. Halasyamani, Angew. Chem. Int. Ed., 2004, 43, 5489.
8. K. M. Ok and P. S. Halasyamani, Inorg. Chem., 2005, 44, 9353.
9. R. E. Sykora, K. M. Ok, P. S. Halasyamani and T. E. Albrecht-Schmitt, J. Am. Chem. Soc., 2002, 124, 1951.
10. R. E. Sykora, D. M. Wells and T. E. Albrecht-Schmitt, J. Solid State Chem., 2002, 166, 442.
11. (a) H. P. Wu, H. W. Yu, S. L. Pan, Z. J. Huang, Z. H. Yang, X. Su and K. R. Poeppelmeier, Angew. Chem. Int. Ed., 2013, 52, 3406; (b) H. P. Wu, H. W. Yu, Z. H. Yang, X. L. Hou, S. L. Pan, X. Su, K. R. Poeppelmeier and J. M. Rondinelli, J. Am. Chem. Soc., 2013, 135, 4215.
12. (a) C. T. Chen, Y. C. Wu, A. D. Jiang, B. C. Wu and G. M. You, Sci. Sin., Ser. B, 1985, 28, 235; (b) S. F. Wu, G. F. Wang, J. L. Xie, X. Q. Wu, Y. F. Zhang and X. Lin, J. Cryst. Growth, 2002, 245, 84.
13. Y. H. Zhao, X. A. Chen, X. A. Chang, J. L. Zuo and M. Li, Acta Crystallogr., Sect. E: Struct. Rep. Online, 2007, 63, i50.
14. (a) M. Ihara and J. Krogh-Moe, Acta Crystallogr., 1966, 20, 132; (b) M. Weil, Acta Crystallogr., Sect. E: Struct. Rep. Online, 2003, 59, i95; (c) J. S. Knyrim, H. Emme, M. Döblinger, O. Oeckler, M. Weil and H. Huppertz, Chem.–Eur. J., 2008, 14, 6149.
15. SAINT-Plus, version 6.02A, Bruker Analytical X-ray Instruments, Inc., Madison, WI, 2000.
16. G. M. Sheldrick, SHELXTL, version 6.14, Bruker Analytical X-ray Instruments, Inc., Madison, WI, 2003.
17. G. M. Sheldrick, SHELXS-97, Program for X-ray Crystal Structure Solution, University of Göttingen, Göttingen, Germany, 1997.
18. A. L. Spek, J. Appl. Crystallogr., 2003, 36, 7.
19. (a) N. E. Brese and M. Okeeffe, Acta Crystallogr., Sect. B: Struct. Sci., 1991, 47, 192; (b) I. D. Brown and D. Altermatt, Acta Crystallogr., Sect. B: Struct. Sci., 1985, 41, 244.
20. (a) C. T. Chen, Y. B. Wang, Y. N. Xia, B. C. Wu, D. Y. Tang, K. C. Wu, W. R. Zeng and L. H. Yu, J. Appl. Phys., 1995, 77, 2268; (b) H. W. Huang, J. Y. Yao, Z. S. Lin, X. Y. Wang, R. He, W. J. Yao, N. X. Zhai and C. T. Chen, Angew. Chem. Int. Ed., 2011, 50, 9141.
21. P. S. Halasyamani, Chem. Mater., 2004, 16, 3586.
22. (a) Y. Yang, S. L. Pan, J. Han, X. L. Hou, Z. X. Zhou, W. W. Zhao, Z. H. Chen and M. Zhang, Cryst. Growth Des., 2011, 11, 3912; (b) L. Wang, S. L. Pan, L. X. Chang, J. Y. Hu and H. W. Yu, Inorg. Chem., 2012, 51, 1852; (c) Y. J. Wang, S. L. Pan, X. L. Tian, Z. X. Zhou, G. Liu, J. Wang and D. Z. Jia, Inorg. Chem., 2009, 48, 7800.

---

Footnote

† Electronic supplementary information (ESI) available: ICSD-number 427222 for β-Cd₃B₂O₆ crystal data (CIF file); checkCIF; atomic coordinates, related anisotropic displacement parameters, the bond valence calculation for all atoms; selected bond lengths (Å) and angles (deg.); coordinated environments of the Cd and B atoms in β-Cd₃B₂O₆; IR spectra of α- and β-Cd₃B₂O₆. CCDC 982763. For ESI and crystallographic data in CIF or other electronic format see DOI: 10.1039/c4ra00671b

---