Phase transitions among four BiB₃O₆ polymorphs: a detailed investigation

Abstract

The stability and phase transformations of the four BiB₃O₆ polymorphs, i.e., α-, β-, γ- and δ-BiB₃O₆, were investigated under different temperatures and pressures. β-BiB₃O₆ is a metastable phase which can only be obtained by boric acid flux method in a sealed system at low temperature. The other polymorphs, α-, γ- and δ-BiB₃O₆, are thermodynamic stable phases. Owing to the large kinetic effect, the phase transformations of the BiB₃O₆ polymorphs are generally slow, thus an extensive annealing process was used in this study. The study shows that α-BiB₃O₆ is the high-temperature phase and its stable area is narrow (710–715 °C) in atmospheric conditions, while γ-BiB₃O₆ is a stable phase in the intermediate temperature range (∼680–710 °C). The results also confirm that δ-BiB₃O₆ is a high-pressure phase and all other polymorphs may transfer to δ-phase under high pressure. However, the δ-phase can be obtained by annealing α- or β-BiB₃O₆ at relatively low temperature under ambient pressure. Therefore, δ-BiB₃O₆ can also be regarded as the low-temperature phase in this system. Based on the experimental results, as well as the thermodynamic principles, a pressure–temperature (P–T) phase diagram for the BiB₃O₆ system is proposed.

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Introduction

BIBO, first identified in Bi₂O₃-B₂O₃ phase diagram as α-BiB₃O₆ in early 1960s,¹ has been demonstrated as one of the most promising nonlinear optical materials. The synthesis,^2,3 structure,^2–5 crystal growth^3,6–8 and physical properties of a series of compounds based on this formula have attracted considerable attention.^3,9–13 Up to now, four different polymorphs have been identified in BiB₃O₆ system, i.e., monoclinic α-BiB₃O₆ (C2),¹ β-BiB₃O₆ (P2₁/n), γ-BiB₃O₆ (P2₁/n)² and orthorhombic δ-BiB₃O₆ (Pca2₁).³ The structure of α-BiB₃O₆ consists of borate layers with a BO₄/BO₃ ratio of 1/2 (Fig. 1a).^4,5 β-BiB₃O₆ also contains a 2D borate layer, which can be depicted as an innerlayer condensation of α-BiB₃O₆, with a BO₄/BO₃ ratio of 2/1 (Fig. 1b).² The borate network in γ-BiB₃O₆, which can be expressed as interlayer condensation of the borate layers in β-BiB₃O₆, is a 3D structure that is completely constructed of BO₄groups (Fig. 1c).² The fourth modification, δ-BiB₃O₆, known as a high-pressure phase, also contains a 3D borate framework constructed exclusively of BO₄groups (Fig. 1d).³ From the structural point of view, the dimensionality of the borate framework increases from 2D in α- and β-phases to 3D in γ- and δ-phases and the BO₄/BO₃ ratio also shows a similar increasing tendency. The effective coordination numbers (ECoN, as described by Hoppe¹⁴) of bismuth cation also increase from α- to δ-phase (α: 5.1, β: 5.6, γ: 5.9 and δ: 6.8). As a consequence, the density of these four polymorphs increases accordingly (Fig. 1).

Fig. 1 Crystal structures of α-, β-, γ- and δ-BiB₃O₆. (a) α-BiB₃O₆: C2, a = 7.116 Å, b = 4.993 Å, c = 6.508 Å, β = 105.6°, ρ = 5.033 g cm⁻³; (b) β-BiB₃O₆: P2₁/n, a = 14.1664 Å, b = 6.7514 Å, c = 4.4290 Å, β = 102.125°, ρ = 5.411 g cm⁻³; (c) γ-BiB₃O₆: P2₁/n, a = 8.4992 Å, b = 11.7093 Å, c = 4.2596 Å, β = 121.141°, ρ = 6.177 g cm⁻³; (d) δ-BiB₃O₆: Pca2₁, a = 18.448 Å, b = 4.4495 Å, c = 4.2806 Å, ρ = 6.378 g cm⁻³; triangles, BO₃; tetrahedra, BO₄; large spheres, Bi³⁺.

It is known that α-BiB₃O₆ crystals were grown mainly using a top-seeded method from a melt.^6–8 Both β- and γ-BiB₃O₆ were identified by boric acid flux method in sealed systems,² while δ-BiB₃O₆ was found under high pressure.³ A natural question arises for the phase relationship of the BiB₃O₆ polymorphs, i.e., whether the phase transitions may occur and under what conditions. A preliminary study in our group revealed that β-BiB₃O₆ converted to γ-BiB₃O₆ at about 660 °C, while the in-situ temperature-variable X-ray diffraction indicated that γ-BiB₃O₆ sustained up to a temperature near its melting point.² The detailed study on α-BiB₃O₆ using temperature-variable neutron and X-ray diffraction techniques on powder and single-crystalline samples revealed the anisotropic thermal behavior of this phase, but did not find any evidence of structural phase transformations from α-BiB₃O₆ to any other polymorphs between 3.5 and 999 K at ambient pressure.¹⁵ However, our further work indicated that the solid state reaction at about 700 °C might give out a sample in the mixture, which contained both α- and γ-BiB₃O₆ phases. The inconsistent results caught our attention. In the study on borates, we noticed that the kinetic effect often plays an important role in the processes of phase transition. Hysteresis is often encountered in the phase transformation process for borate systems, particularly when the formation/breakage of the B–O bonds is involved. A convincing example is YBO₃, a potential luminescent material in PDP display, which has two polymorphs.¹⁶ The transformation from LT-YBO₃ to HT-YBO₃ occurs at 965 °C, involving a B–O bond break from the B₃O₉ ring to isolated BO₃ triangles. The reverse transition, however, occurs at far lower temperature (580 °C) on cooling.

Regarding to the technological importance of the α-polymorph, it is desirable to learn the chemistry behind these polymorphs. Therefore, we carried out a systematic study on BiB₃O₆ polymorphs under different temperatures and pressures. Since the phase transitions in the BiB₃O₆ system also involved a considerable B–O bond breakage and formation, a long-time annealing treatment and seed-induced technique were applied in the study in order to reduce the kinetic effect. In this paper, we will present intriguing phase transition processes and propose a schematic pressure–temperature diagram to show the relationship among α-, γ-, and δ-phases.

Experimental

Synthesis

A powder sample of α-BiB₃O₆ was prepared by conventional solid-state reactions.^1,17 A stoichiometric mixture of Bi₂O₃ and H₃BO₃ (with 1 mol% excess H₃BO₃) was fully mixed and pre-heated at 550 °C for 10 h (forming a mixture of Bi₂B₈O₁₅ and Bi₃B₅O₁₂). Then, the precursor was re-ground and heated to 700 °C at a rate of 1 °C min⁻¹ and kept at this temperature for 10 h. β-BiB₃O₆ was prepared under hydrothermal conditions.² Typically, 0.5 g of Bi₂O₃ and 3.32 g of H₃BO₃ were ground and put into a 50 mL Teflon container, and 0.4 mL distilled water was added. The container was sealed and kept at 240–260 °C statically for 3–7 d in an oven. The solid product was washed by hot distilled water (80 °C) to remove the residual boric acid and dried at 100 °C. γ-BiB₃O₆ was prepared in a similar way but at higher temperature, 270 °C. A specially designed PPL modified Teflon container (25 mL) was used for this high temperature synthesis. Since a small amount of Cl⁻ ions might be released from the PPL modified Teflon, BiOCl often appeared in the product as impurity. The high pressure phase, δ-BiB₃O₆ was synthesized by treating α-, β- or γ-BiB₃O₆ under high-pressure and high-temperature, i.e., 2GPa/800 °C for 30 min.

Heating treatments under ambient pressure

Polycrystalline samples of certain BiB₃O₆ polymorphs were heated from room temperature to the annealing temperature at 1 °C min⁻¹ heating rate in a muffle furnace and kept at that temperature for a certain time. The temperature and its gradient distribution inside the furnace were calibrated by observation of the melting evidence of α-BiB₃O₆. In order to induce the reaction and increase the reaction rate, small amount (generally less than 2 wt%) crystal seeds were added into the initial samples in some batches. A few of the samples were even mixed with a considerable amount of seed crystals, as shown in the results.

Heating treatments under high pressure

The high-pressure experiments were performed with a cubic anvil apparatus under different high pressure and heat temperature. The starting polycrystalline material (∼0.2 g) was ground into fine powder, and then pressed into a cylinder (5 mm in diameter) and encapsulated in Ag foil to prevent contamination. During the experiment, the sample was placed in the center of a pyrophyllite cube (25 × 25 × 25 mm³ in size) surrounded by a pressure transmitting medium (boron nitride) to keep a constant quasihydrostatic pressure. A graphite tube and two Mo sheets attached to the top and bottom of the anvil were served as heater and contacts. The pyrophyllite cube was placed in the center cavity of the cubic anvil apparatus which could generate pressure up to 5 GPa. The pressure was increased gradually to a certain value first, then the system was heated through the Joule effect using a graphite furnace and the temperature was measured with a Ni–Cr/Ni–Si thermocouple. No correction was made for the pressure effect on the thermocouple wires. The solid–solid phase transition of a certain metal (i.e., Bi, Ba) under pressure was employed to determine the pressure inside the cell with an accuracy of ±0.05 GPa. The reaction was terminated by temperature quenching followed by pressure releasing. The high-pressure cell was opened under ambient conditions and the product was analysed by powder X-ray diffraction.

Characterization

Powder X-ray diffraction data were collected at room temperature on a Rigaku D/Max-2000 diffractometer using a rotating anode (Cu Kα, 40 kV and 100 mA), a graphite monochromator and a scintillation detector. X-Ray diffraction profiles of the four BiB₃O₆ polymorphs are shown in Fig. 2, where the marked peaks are used for the identification of each phase. Quantitative analysis was done by Rietveld refinements using the program TOPAS.¹⁸ The DSC (differential scanning calorimetric) measurements were carried out on a NETZSCH STA449C instrument at a heating rate of 10 or 2 °C min⁻¹ from room temperature to certain temperatures under Ar atmosphere.

Fig. 2 The observed XRD patterns of four polymorphs of BiB₃O₆ (selected peaks with different marks are used to identify the presence of the corresponding phases in the products. △: α-phase; ▲: β-phase; ⋄: γ-phase; ♦: δ-phase).

Results

DSC analysis

Fig. 3 shows the DSC curves of the four polymorphs. In each curve of α-, γ- and δ-BiB₃O₆, there is only a single endothermal peak at 710 °C (γ- and δ-BiB₃O₆) and 715 °C (α-BiB₃O₆), while there are three peaks at about 693, 707 and 715 °C for β-BiB₃O₆. The single endothermal peak in the DSC curves of α-, γ- and δ-BiB₃O₆ corresponds to the melting point of each phase. As to the three peaks for β-BiB₃O₆, the first endothermal peak corresponds to the decomposition of the β-phase into Bi₂B₈O₁₅ and Bi₃B₅O₁₂, which is proved by the XRD pattern of the sample heated to 692 °C at a rate of 2 °C min⁻¹ and quenched quickly (Fig. 4). For comparison, the DSC curve of a mixture of Bi₂B₈O₁₅ and Bi₃B₅O₁₂ is also shown in Fig. 3. One can see that an eutectic melting phenomenon occurs in the mixture at about 707 °C, which is in accordance with the shoulder (the second peak) in the DSC curve of β-BiB₃O₆. The third peak (715 °C) in the DSC curve of β-BiB₃O₆ is very close to the melting point of α-BiB₃O₆, one would reasonably suggest that Bi₂B₈O₁₅ and Bi₃B₅O₁₂ react around the eutectic melting to form α-phase. In fact, α-BiB₃O₆ was synthesized by the mixture of Bi₂B₈O₁₅ and Bi₃B₅O₁₂ in a furnace (see the insert of Fig. 4). The DSC results unambiguously indicate that β-BiB₃O₆ is a metastable modification, which decomposes at ∼693 °C, and then α-phase forms by the combination of the decomposition products at higher temperature. Although the DSC analysis did not show any evidence of phase transition among α-, γ- and δ-phases because of the kinetic effect, it did provide useful information on the phase relations. The melting point of the α-phase is the highest, which indicates that the α-phase might be stable at high temperature. Furthermore, since the γ- and δ-phases melt almost at the same temperature, the transition from δ- to γ-phase may have occurred before the melting point but be hidden by the melting process. Since the DSC analysis was performed in a relatively short time for a given sample, it may be difficult to get more information on the phase relationship due to kinetic hysteresis. Thus series of experiments for treating different BiB₃O₆ polymorphs at different temperatures and pressures were performed. Long-time annealing treatment and/or crystal seeds addition were used when necessary.

Fig. 3 DSC curves of α-, β-, γ-, δ-BiB₃O₆ and the mixture of Bi₂B₈O₁₅ and Bi₃B₅O₁₂ (heating rate: 10 °C min⁻¹).

Fig. 4 Powder X-ray diffraction profile of the product from β-BiB₃O₆ by DSC analysis (heating rate: 2 °C min⁻¹); the insert is the XRD profile of α-BiB₃O₆ synthesized from the mixture of Bi₂B₈O₁₅ and Bi₃B₅O₁₂.

Treatment of β-BiB₃O₆ in atmospheric conditions

β-BiB₃O₆ underwent a series of complex changes in the temperature range 650–710 °C in atmospheric conditions, as shown in Scheme 1. β-BiB₃O₆ decomposed to Bi₂B₈O₁₅ and Bi₃B₅O₁₂ at 680∼710 °C in about 1 h, and then these two compounds reacted further, forming a mixture in which α-BiB₃O₆ was the major phase and γ-BiB₃O₆ and Bi₃B₅O₁₂ were the minor phases at the stage after 10-h treatment, which coincided with the phenomenon observed in the DSC analysis. However, further prolonging the reaction time (about 50 h) resulted in the formation of γ-BiB₃O₆ with minor Bi₃B₅O₁₂, while α-BiB₃O₆ disappeared totally, which implied that the phase transformation from α-BiB₃O₆ to γ-BiB₃O₆ occurred at this temperature range. The presence of Bi₃B₅O₁₂ in the final product might be due to the evaporation of the boron oxide. In the batches with the addition of a small amount (<2%) of certain seed crystals, the phase transition processes were indeed influenced by different polymorph seeds, especially at the early stage of the reactions. For example, α-BiB₃O₆ became a major phase only in ca 1 h by using α-BiB₃O₆ as the seed crystals, and γ- or δ-BiB₃O₆ phases also appeared if the corresponding seed crystals were used. However, γ-BiB₃O₆ was always the major phase in the final products no mater what kind of seed crystals was used if the treatment time was long enough. It shows that γ-BiB₃O₆ is the stable phase in the temperature range of 680–710°C at ambient pressure. In the lower temperature range (650–670 °C), thermal treatment of β-BiB₃O₆ for ca 100 h always results in a mixture of α-, γ-, δ-BiB₃O₆ and Bi₃B₅O₁₂. However, the ratio of these phases varied with the seed crystals and the seed-induced phase existed as the major phase. The high-pressure phase δ-BiB₃O₆ seems to be more stable in this lower temperature range, since it appears as a major phase without seed-crystals (see the reactions under 650–670 °C in Scheme 1). It should be noted that δ-BiB₃O₆, which was known as a high-pressure phase previously, can in fact be realized under ambient pressure via phase transformations.

Scheme 1 The change of the β-phase treated in atmospheric conditions with temperature and time. (Subscript ‘s’ means seed crystals, and the datum below each phase is the weight percent of the phase in the product.)

Treatment of δ-BiB₃O₆ in atmospheric conditions

δ-BiB₃O₆ is a high-pressure phase and one would expect its transformation to low pressure polymorphs at ambient pressure. In the experiments, δ-BiB₃O₆ behaved quite inertly and a pure δ-BiB₃O₆ sample did not show any evidence of phase transition except for a small amount of decomposition to Bi₃B₅O₁₂ and B₂O₃, as listed in Table 1 (B₂O₃ is not taken into account due to its evaporation and relatively weak scattering ability to X-ray). The inertness of δ-BiB₃O₆ may be due to the kinetic hindrance of the break of the B–O bond. With the increase of the annealing temperature, the phase transition from δ- to γ-BiB₃O₆ was observed above 680 °C if γ-seeds were added to the starting materials. The density difference between γ- and δ-BiB₃O₆ is not very large (6.177 vs 6.378 g cm⁻³), therefore, seed crystals and high annealing temperature are necessary to induce the phase transformation. This might also be the reason that one could observe the growing of the δ-phase when δ-BiB₃O₆ was used as a seed during the heat treatment of β-BiB₃O₆.

Table 1 Thermal treatment results of α- and δ-phases

Starting material^a	Temperature/°C	Time/h	Product^b
a Subscript ‘s’ means seed crystals. b The ratio in parentheses is the quantitative analytical result of each phase in the corresponding product from powder X-ray diffraction data.
δ	650–700	50	δ + Bi3B5O12 (85/15)
δ + γs (43/57)	650–670	50	δ + γ + Bi3B5O12 (32/57/11)
δ + γs (43/57)	680–710	50	γ + δ + Bi3B5O12 (81/6/13)
α	650–670	50	α + Bi3B5O12 (86/14)
α	680–710	50	α + γ + Bi3B5O12 (79/12/9)
α + γs (98/2)	650–670	50	α + γ + Bi3B5O12 (78/16/6)
α + γs (98/2)	680–710	50	γ + Bi3B5O12 (83/17)
α + δs (98/2)	650–670	100	α + δ + Bi3B5O12 (39/36/25)
α + δs (98/2)	680–710	50	α + δ + γ + Bi3B5O12 (55/12/19/14)
α + δs (98/2)	680–710	100	γ + Bi3B5O12 (78/22)

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Treatment of α-BiB₃O₆ in atmospheric conditions

In the treatment of the β-phase at 680∼710 °C, we have observed a series of phase transitions from β- to α-, then to γ-BiB₃O₆ with time. Further investigation of the thermal behavior of the α-phase at a temperature below 710 °C (the melting point of γ-BiB₃O₆) revealed more information about the transformation of α-BiB₃O₆, as listed in Table 1. During the treatment, α-BiB₃O₆ decomposed to Bi₃B₅O₁₂ and B₂O₃ slowly below 670 °C, and no evidence related to a phase transition was observed even after 50 h treatment. At higher temperatures (680∼710 °C) and with prolonging the reaction time, γ-BiB₃O₆ emerged but in low yield. As expected, introducing γ-crystal seeds accelerated the reaction rate and promoted the formation of γ-BiB₃O₆. If δ-BiB₃O₆ was added to the initial material as seed, δ-phase formed at 650–670 °C. In the temperature range of 680∼710 °C, δ-phase appeared at the early stages together with the γ-phase, and disappeared with time while the γ-phase became the major phase, which also revealed the phase transition process from δ- to γ-BiB₃O₆, as happened in the treatment of β- or δ-phase.

Heat treatments of γ-BiB₃O₆ in atmospheric conditions

From the above results, it can be concluded that γ-BiB₃O₆ was the most stable phase in the temperature range of 680–710 °C. Further treatment of the γ-phase in the same conditions confirmed this conclusion. In the present work, it was observed that γ-BiB₃O₆ melts at 710 °C, and the cooled product was glass-likely amorphous. No α-phase was obtained at 710 °C even if the process was kept going for a long time.

Treatments of γ-BiB₃O₆ under high pressure

γ-BiB₃O₆ is a stable phase under 680–710 °C in ambient pressure, but it should transfer to δ-phase under high pressure due to its less density. The experimental results of the treatment of γ-BiB₃O₆ under high pressures at different temperature are summarized in Table 2. As expected, the transformation from γ-BiB₃O₆ to δ-BiB₃O₆ occurred at relatively high temperature and pressure. The addition of δ-BiB₃O₆ seeds induced the phase transformation and significantly reduced the reaction pressure and temperature (i.e. 0.6 GPa and 600 °C).

Table 2 Products of high-temperature/high-pressure treatments on the γ-phase

Starting material	Pressure/GPa	Temperature/°C	Time/min	Product
γ	0.6	600–700	30	γ
γ	2	400–600	30	γ
γ	2	800	30	δ
γ	5	400	30	γ
γ + δs (68/32)	0.6	600	30	γ + δ
				(59/41)

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Treatments of α-BiB₃O₆ under high pressure

α-BiB₃O₆ has the lowest density among the polymorphs. Using α-BiB₃O₆ as starting material, a series of phase transformations were observed with the increase of pressure. As shown in Table 3, in most cases, γ- and δ-phases exist together in the products. Considering the small density differences between γ- and δ-phases, the co-formation of these two phases from α-BiB₃O₆ under relatively mild conditions is reasonable. Under extreme conditions (2GPa, 800 °C), the final product was δ-phase. No β-BiB₃O₆ was observed because of the metastable nature of this phase, although the density of β-BiB₃O₆ is higher than that of α-BiB₃O₆.

Table 3 Products of high-temperature/high-pressure treatments on the α-phase

Pressure/GPa	Temperature/°C	Time/min	Product
0.6	400	30	α
0.6	550	30	α + γ + δ (44/39/17)
0.6	550	60	α + γ + δ (24/35/41)
0.6	600	30	γ + δ (68/32)
0.6	600	60	γ + δ (59/41)
2	300	30	α + γ + δ (96/2/2)
2	400	30	α + γ + δ (36/46/18)
2	600	30	γ + δ (32/68)
2	800	30	δ

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Treatments of β-BiB₃O₆ under high pressure

Different from the complex performance of β-BiB₃O₆ during the heating treatment under ambient pressure, the transformation process of β-BiB₃O₆ under high pressure is quite simple. As shown in Table 4, β-BiB₃O₆ transformed to other higher density phases (γ- and δ-BiB₃O₆) directly without decomposition. At a relatively low pressure (0.4∼1GPa) and low temperature (490∼600 °C), γ- and δ-phases always coexisted in the products after 30 min treatment. The content of the δ-phase increased with pressure, temperature and time, and almost pure δ-BiB₃O₆ was obtained at 600 °C and 2 GPa after 30 min reaction.

Table 4 The change of the β-phase with temperature and pressure

Pressure/GPa	Temperature/°C	Time/min	Product
0.4	600	30	γ + δ (34/66)
0.5	570	30	γ + δ (44/56)
0.55	550	30	β + γ + δ (4/68/28)
0.55	550	90	γ + δ (65/35)
0.6	550	30	β + γ + δ (27/55/18)
0.6	700	30	γ + δ (7/93)
0.75	520	20	β + γ + δ (20/10/70)
0.85	490	20	β + γ + δ (41/27/32)
1	600	30	γ + δ (2/98)
2	400	30	β + δ (97/3)
2	440	30	β + δ (80/20)
2	600	30	δ
2	800	30	δ
5	400	30	β + δ (74/26)
5	615	30	δ
5	800	30	δ

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Discussion

From a thermodynamic view, the possible phase transition could be estimated by the Gibbs free energy ΔG. For a given system, ΔG depends on temperature (T), enthalpy change (ΔH) and entropy change (ΔS), here the latter two quantities are further affected by temperature and pressure. For a system at consistent pressure, the Gibbs free-energy change can be expressed as follows:

ΔG^o(T) = ΔH^o(T) − TΔS^o(T) (1)

If pressure is variable, the equation becomes:^19,20In a reaction with a change in volume, pressure can play an important effect on the reaction process.

It is known that β-BiB₃O₆ can only be obtained by hydrothermal synthesis. The present study shows that β-BiB₃O₆ is very reactive and may easily transform to the other polymorphs under appropriate conditions. In fact, there is no evidence of the inverse transformation to β-phase, thus, β-BiB₃O₆ should be regarded as a metastable phase that cannot be expressed in the P–T phase-diagram. However, the high reactivity of β-BiB₃O₆ provides it as a useful precursor to get other polymorphs.

The transformations of the other three BiB₃O₆ polymorphs can be expressed in a P–T phase diagram. There are two structural parameters that may influence the phase transformation, i.e., density (α: 5.033 g cm⁻³, γ: 6.177 g cm⁻³, δ: 6.378 g cm⁻³) and structure dimensionality (α is 2D, γ and δ are 3D). The density difference gives rise to a volume change of the reaction, which provides a driven force for the pressure-induced phase transformation. From the density of BiB₃O₆ polymorphs, one expects phase transitions α → γ → δ with the increase of pressure. The dimensionality of the structures, on the other hand, is another factor which may influence the enthalpy and entropy change, and then influence the transformation process. In general, one expects phase transformations of δ → γ → α as the increase of temperature. The real processes are much more complicated, particularly in solid state reactions the kinetic effect often plays an important role, then higher temperature is necessary to facilitate the reaction occurrence.

α-BiB₃O₆ was initially identified in the Bi₂O₃-B₂O₃ system.¹ Our experimental results show that a pure phase sample of α-BiB₃O₆ can be synthesized with a conventional solid state reaction at temperature very close to the melting point. At lower temperature (<710 °C), α-BiB₃O₆ could also be formed at the initial stage (<10 h), but it transformed to γ-BiB₃O₆ if the reaction was prolonged. One of the interesting facts is that there was no report about the formation of γ-BiB₃O₆ in the past many years, although studies on the synthesis, structure and crystal growth of the α-phase have been carried out extensively.^1,4–8 Possible reasons might be that the crystal of α-BiB₃O₆ was synthesized mostly by the top-seed crystal growth method^6–8 and the α-polymorph is quite inert. Once it forms, it maintains. As far as the structure is concerned, α-BiB₃O₆ exhibits the lowest density (5.033 g cm⁻³) and a 2D structure framework, thus one could expect that both ΔH > 0 and ΔS > 0 for the γ → α transition. All evidence confirms that the α-polymorph is a high-temperature phase, and its stable range is very narrow, probably in a range between the melting points of the γ- and α-phases (710–715 °C).

γ-BiB₃O₆ was identified first in a boric flux system at low temperature (∼270 °C).² However, as indicated, γ-BiB₃O₆ is a very stable phase that is encountered most frequently in our experiments; it is always the final product if the reaction time was long enough in the temperature range of 680–710 °C, no mater what polymorphs (either α or δ) were used as the starting materials. γ-BiB₃O₆ has a 3D borate framework and a lower melting point (710 °C) than that of α-BiB₃O₆, thus it is thermodynamically reasonable that γ-BiB₃O₆ is a stable phase in this intermediate temperature range under ambient pressure. On the other hand, the phase transition α → γ was also observed under high pressure. In fact, γ-BiB₃O₆ always appeared as one of the major phases when the α-phase was used as a starting material under high pressure (Table 3). The density of γ-BiB₃O₆ (6.177 g cm⁻³) is much higher than that of the α-phase but slightly lower than that of the δ-phase, thus it is possible that the γ-polymorph is an intermediate species in the high pressure phase transformation α → γ → δ. Unfortunately, we have not yet experimentally observed the phase transition from γ- to α-phase under ambient pressure. This is understandable from the inert nature and the lower melting point of the γ-phase, thus the γ-phase may melt before phase transformation, which ends up with an amorphous glass.

The δ-phase, first identified in the high-pressure synthetic studies, adopts a compact structure (3D borate framework) with the highest density (6.378 g cm⁻³) among the BiB₃O₆ polymorphs.³ This phase can be conventionally synthesized under high pressure at high temperature. In our study, we did find that the β-phase can easily transform to the δ-phase in relatively mild conditions (1GP, 600 °C) (Table 4), but the transformation from α- and γ-BiB₃O₆ can be realized only at higher temperature (2GP, 800 °C) (Table 2, 3), which demonstrates again the inert nature of α- and γ-phases. More interestingly, we also found that, starting from β-BiB₃O₆, δ-BiB₃O₆ could be formed as the major phase after 100 h annealing at 650–670 °C under ambient pressure (Scheme 1). Similarly δ-BiB₃O₆ also appeared in the product when α-BiB₃O₆, together with the δ-seeds, was used as starting material under the same conditions (Table 1). This means that, although δ-BiB₃O₆ is a high-pressure phase, the stability range of this phase may extend through to ambient pressure below 670 °C. At higher temperatures (680–710 °C), a reverse transition from δ- to γ- phase can also be detectable under ambient pressure when a large amount of γ-seeds were used. Further considering the small density difference between γ- and δ-phase, one could reasonably conclude that δ-BiB₃O₆ is a high-pressure and low-temperature phase in this system.

Based on the experimental results and thermodynamic principles, we propose a sketch P–T phase-diagram for the BiB₃O₆ system (Fig. 5). We already knew that the phase transformations δ → γ → α may occur on heating under ambient pressure. We also knew that the phase transformations α → γ → δ can be realized along the pressure axis at an appropriate temperature. It is also well-known that melting points may increase along with pressure, so does the phase transition boundary between solid phases. Although the boundaries may not be accurately defined, this sketched P–T phase diagram is very useful for understanding the chemical behavior of the polymorphs in the BiB₃O₆ system. For example, regarding the narrow stable area of α-BiB₃O₆, the crystals can be grown from a melt by the top-seeded method, but the overcooling temperature has to be carefully controlled.^6–8 In addition, from the phase-diagram, it can be expected that crystals of δ-BiB₃O₆ can be grown from a melt using a high pressure and high temperature apparatus.³

Fig. 5 Schematic drawing of the phase-diagram of BiB₃O₆.

In fact, polymorphism is a common phenomenon in borate systems because of the BO₃/BO₄ coordination modes and diverse linkages of polyborates.^16,21–24 Another interesting example that is comparable to BiB₃O₆ is LnB₃O₆, rare earth polyborate. LnB₃O₆ also has four polymorphs: α-LnB₃O₆ (Ln = La - Tb, except Pm) is a low-pressure form;^25–30 additionally, there are two high-pressure forms, γ-LnB₃O₆ (Ln = La - Nd)^31,32 and δ-LnB₃O₆ (Ln = La, Ce),^33,34 and one metastable orthorhombic variation β-LnB₃O₆ (Ln = Nd, Sm, Gd, Tb - Lu).^35–37 The structures of LnB₃O₆ and BiB₃O₆ are also closely related (see Fig. S1 in the ESI†). Though α-LnB₃O₆ has a 1D borate chain structure, which is different from the layer structure in α-BiB₃O₆,^4,5 the BO₃/BO₄ ratio and their alternative connectivity are principally the same (Fig. S1a).† β-LnB₃O₆ is built up from corrugated layers by corner-shared BO₄ tetrahedra, but the stacking way of the layers is similar to that in β-BiB₃O₆. Finally, γ- and δ-LnB₃O₆ are exactly isostructural with δ- and γ-BiB₃O₆,^2,3 respectively. Therefore, one could expect that LnB₃O₆ has a similar P–T phase diagram as that of the BiB₃O₆ system. Although the details of the phase relationship have not yet been established for the LnB₃O₆ system, it was reported that the high-pressure forms, γ- and δ-LnB₃O₆, may transform to α-LnB₃O₆ at high temperature under ambient pressure,^32,33 which is rather similar to the BiB₃O₆ system. Owing to the higher melting points of LnB₃O₆ in comparison with that of BiB₃O₆, the study of the phase relationship can proceed in a wider temperature range, which could effectively eliminate the kinetic effect of the phase transformations. Further investigating the details of a phase relationship of the phases for the LnB₃O₆ system will be very interesting not only for the chemistry of the LnB₃O₆ system itself but also for providing a comprehensive understanding of the whole MB₃O₆ (M = Bi, Ln)³⁸ system.

Conclusion

The phase relationship of the four BiB₃O₆ polymorphs, i.e., α-, β-, γ- and δ-BiB₃O₆, is important for understanding the chemistry and synthetic process, particularly for the crystal growth of α-BiB₃O₆, a promising nonlinear optical material. However, the study of the phase transition is complicated by the kinetic effect for this borate system, thus extensive annealing and seed-inducing were used in the practical processes. Although there still are some uncertainties, the fundamental ground of the phase relationship is clearly defined. First of all, β-BiB₃O₆ is a metastable phase which can be synthesized by the boric acid flux method but cannot be expressed in the P–T phase diagram. α-BiB₃O₆ is a high-temperature phase, which is stable in a narrow temperature range (710–715 °C) under ambient pressure. δ-BiB₃O₆ is a high-pressure phase, but can be present at low temperature (<670 °C) under ambient pressure. γ-BiB₃O₆, on the other hand, is a stable phase in an intermediate temperature range (∼680–710 °C). The phase stability under pressure is simply reverse, i.e., δ > γ > α, which means that the phase transition α → γ → δ may occur as the increase of the pressure. Based on these observations, a schematic P–T phase diagram has been proposed for the BiB₃O₆ system, which can be used to understand the chemistry behavior of this system.

Acknowledgements

This study is financially supported by National Natural Science Foundation of China. The authors thank the Institute of Crystal Materials, Shandong University for providing α-BiB₃O₆ single crystal.

References

1. E. M. Levin and C. L. McDaniel, J. Am. Ceram. Soc., 1962, 45, 355.
2. L. Y. Li, G. B. Li, Y. X. Wang, F. H. Liao and J. H. Lin, Inorg. Chem., 2005, 44, 8243.
3. J. S. Knyrim, P. Becker, D. Johrendt and H. Huppertz, Angew. Chem., Int. Ed., 2006, 45, 8239.
4. J. Z. Liebertz, Crystallogr. Rep., 1982, 158, 319.
5. R. Fröhlich, L. Bohatý and J. Liebertz, Acta Crystallogr., Sect. C: Cryst. Struct. Commun., 1984, 40, 343.
6. P. Becker, J. Liebertz and L. Bohatý, J. Cryst. Growth, 1999, 203, 149.
7. B. Teng, J. Y. Wang, Z. P. Wang, H. D. Jiang, X. B. Hu, R. B. Song, H. Liu, Y. G. Liu, J. Q. Wei and Z. S. Shao, J. Cryst. Growth, 2001, 224, 280.
8. B. Teng, J. Y. Wang, Z. P. Wang, X. B. Hu, H. D. Jiang, H. Liu, X. F. Cheng, S. M. Dong, Y. G. Liu and Z. S. Shao, J. Cryst. Growth, 2001, 233, 282.
9. H. Hellwig, J. Liebertz and L. Bohatý, J. Appl. Phys., 2000, 88, 240.
10. H. Hellwig, J. Liebertz and L. Bohatý, Solid State Commum., 1999, 109, 249.
11. Z. S. Lin, Z. Z. Wang, C. T. Chen and M. H. Lee, J. Appl. Phys., 2001, 90, 5585.
12. A. A. Kaminskii, P. Becker, L. Bohatý, K. Ueda, K. Takaichi, J. Hanuza, M. Maczka, H. J. Eichler and G. M. A. Gad, Opt. Commun., 2002, 206, 179.
13. S. Haussühl, L. Bohatý and P. Becker, Appl. Phys. A: Mater. Sci. Process., 2006, 82, 495.
14. R. Hoppe, Angew. Chem., Int. Ed. Engl., 1970, 9, 25.
15. W. D. Stein, A. Cousson, P. Becker, L. Bohatý and M. Braden, Z. Kristallogr., 2007, 222, 680.
16. J. H. Lin, D. Sheptyakov, Y. X. Wang and P. Allenspach, Chem. Mater., 2004, 16, 2418.
17. Yu. F. Kargin, V. P. Zhereb and A. V. Egorysheva, Russ. J. Inorg. Chem. (Transl. of Zh. Neorg. Khim.), 2002, 47, 1240.
18. TOPAS V2.1: General Profile and Structure Analysis Software for Powder Diffraction Data, Bruker AXS, Karlsruhe, Germany.
19. R. J. Hemley, Ultrahigh-pressure Mineralogy: Physics and Chemistry of the Earth's Deep Interior, Mineralogical Society of America, Washington, DC, 1998.
20. (a) Z. Matvei, Prog. Mater. Sci., 2007, 52, 597; (b) Q. X. Guo, Y. S. Zhao, C. Jiang, W. L. Mao, Z. W. Wang, J. Z. Zhang and Y. J. Wang, Inorg. Chem., 2007, 46, 6164.
21. A. V. Egorysheva, A. S. Kanishcheva, Yu. F. Kargin, Yu. E. Gorbunova and Yu. N. Mikhailov, Russ. J. Inorg. Chem. (Transl. of Zh. Neorg. Khim.), 2002, 47, 1804.
22. (a) H. Emme and H. Huppertz, Chem.–Eur. J., 2003, 9, 3623; (b) H. Huppertz, S. Altmannshofer and G. J. Heymann, Solid State Chem., 2003, 170, 320.
23. (a) H. Z. Bauer, Z. Anorg. Allg. Chem., 1963, 320, 306; (b) H. Huppertz and G. Heymann, Solid State Sci., 2003, 5, 281.
24. H. Kimura, T. Numazawa and M. Sato, J. Mater. Sci., 1996, 31, 2361.
25. (a) J.-St. Ysker and W. Hoffmann, Naturwissenschaften, 1970, 57, 129; (b) G. K. Abdullaev, Kh. S. Mamedov and G. G. Dzhfarov, Sov. Phys. Crystallogr., 1981, 26, 473.
26. F. Goubin, Y. Montardi, P. Deniard, X. Rocquefelte, R. Brec and S. Jobic, J. Solid State Chem., 2004, 177, 89.
27. C. Sieke, T. Nikelski and Th. Schleid, Z. Anorg. Allg. Chem., 2002, 628, 819.
28. (a) V. I. Pakhomov, G. B. Sil'nitskaya, A. V. Medvedev and B. F. Dzhurinskii, Inorg. Mater., 1972, 8, 1107; (b) H. Müller-Bunz, T. Nikelski and Th. Schleid, Z. Naturforsch., 2003, 58b, 375.
29. G. D. Abdullaev, Kh. S. Mamedov and G. G. Dzhafarov, Sov. Phys. Crystallogr., 1975, 20, 161.
30. A. Goriounova, P. Held, P. Becker and L. Bohatý, Acta Crystallogr., Sect. E: Struct. Rep. Online, 2003, 59, i83.
31. H. Emme, C. Despotopoulou and H. Huppertz, Z. Anorg. Allg. Chem., 2004, 630, 1717.
32. H. Emme, C. Despotopoulou and H. Huppertz, Z. Anorg. Allg. Chem., 2004, 630, 2450.
33. G. Heymann, T. Soltner and H. Huppertz, Solid State Sci., 2006, 8, 821.
34. A. Haberer, G. Heymann and H. Huppertz, Z. Naturforsch., 2007, 62b, 759.
35. T. Nikelski and Th. Schleid, Z. Anorg. Allg. Chem., 2003, 629, 1017.
36. H. Emme, G. Heymann, A. Haberer and H. Huppertz, Z. Naturforsch., 2007, 62b, 765.
37. H. Emme, T. Nikelski, Th. Schleid, R. Pöttgen, M. H. Möller and H. Huppertz, Z. Naturforsch., 2004, 59b, 202.
38. J. Yang and M. Dolg, J. Solid State Chem., 2007, 180, 2763.

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Footnote

† Electronic supplementary information (ESI) available: Structures of LnB₃O₆ (Fig. S1). See DOI: 10.1039/b903567m

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