Multiple Nucleation and Crystal Growth of Barium Titanate - Crystal

Article pubs.acs.org/crystal

Multiple Nucleation and Crystal Growth of Barium Titanate Hongquan Zhan,†,§ Xianfeng Yang,† Chaomin Wang,† Jian Chen,† Yuping Wen,† Chaolun Liang,† Heather F. Greer,‡ Mingmei Wu,*,† and Wuzong Zhou*,‡ †

MOE Key Laboratory of Bioinorganic and Synthetic Chemistry, State Key Laboratory of Optoelectronic Materials and Technologies, School of Chemistry and Chemical Engineering, Instrumental Analysis and Research Centre, Sun Yat-Sen University, Guangzhou, 510275, P. R. China ‡ EAStCHEM, School of Chemistry, University of St Andrews, St Andrews, Fife KY16 9ST, United Kingdom § Department of Material Science and Engineering, Jingdezhen Ceramic Institute, Jingdezhen 333001, P. R. China S Supporting Information *

ABSTRACT: Crystal growth of cubic BaTiO3 in the presence of polyethylene glycol-200 (PEG-200) is investigated step by step using powder X-ray diffraction, scanning electron microscopy, and transmission electron microscopy. Titanium precursor Ti(OC4H9)4 aggregates with PEG to form spherical colloidal particles at the very beginning. Multiple nucleation of BaTiO3 takes place on the surface of these colloidal particles. The nanocrystallites then selfadjust their orientations likely under dipole−dipole interaction and/or intercrystallite interactions enhanced by surface adsorbed polymers, followed by an orientated connection and crystal extension via an Ostwald ripening process. The final BaTiO3 crystals have a novel dodecahedral morphology. The formation mechanism is proposed to be attributed to the selective adsorption of PEG molecules on the {110} crystal planes, significantly reducing the crystal growth rate on these surfaces. A kinetic model is proposed based on the calculated crystallite sizes using the Scherrer equation. The physical meaning of the model and a significant fake reduction of the crystallite size is discussed.

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INTRODUCTION Nucleation and early stage crystal growth are of crucial importance in relation to crystal engineering and synthesis of new materials. According to the classical theory of crystal growth, nucleation in a hydrothermal system is normally associated with a supersaturation phenomenon and is initiated by the aggregation of sub-nanosized chemical species, for example, ions and molecules (monomers). After a nucleus reaches a critical size, the growth typically takes place by further attachment of monomers to its surface, and the final morphology of a free crystal in a synthetic solution is dominated by the slow-growing faces because the fast-growing faces may grow out and not be represented in the final crystal habit.1 In contrast, the achievement in the growth of various nanostructured materials in the past decade has suggested several nonclassical pathways where crystals may develop from an initial mesoscale solid species.2−7 For example, a faceted nanocrystal could evolve from an amorphous colloidal particle by nucleation beginning at its core and extending to its edge or vice versa. During the incubation period, one single crystal is developed from each colloidal particle (Scheme 1a).8 Surface crystallization of a disordered aggregate may lead to a reversed crystal growth route (Scheme 1b).9−11 The formation of crystalline shells with a faceted polyhedral morphology indicates that Curie and Wulff’s theory12,13 is more general than the Bravais−Friedel−Donnay−Harker (BFDH) law.14−16 The latter produces a kinetic measure of the crystal growth rates © 2012 American Chemical Society

along different crystallographic orientations. The former gives a thermodynamic view in order to predict that the equilibrium shape of a free crystal is the shape that minimizes its surface free energy. These assumptions can explain the formation of polyhedral habits in both the classic crystal growth route and the reversed crystal growth route. When multiple nuclei are developed within an aggregate, several crystals can grow simultaneously with random orientations (Scheme 1c).17 If these crystals undergo orientated aggregation, a single crystal can probably be achieved containing a large quantity of structural defects (Scheme 1d).18 The latest progress in nanochemistry addressed that monocrystal-like mesocrystals and orientated nanocrystal arrays can be grown in a solution with the assistance of some organic surfactants.19−21 Recently, we reported our investigation of the early stage crystal growth of perovskite CaTiO3 in poly(ethylene glycol) 200 (PEG-200) solution.22 We observed orientated aggregation of cubic nanocrystallites, surface recrystallization, and reversed crystal growth via Ostwald ripening. It is interesting to see whether BaTiO3, an isostructural compound of CaTiO3 with a lower symmetry, would have a similar crystal growth behavior. BaTiO3 is a remarkably important electronic material with a long-standing history of applications in electronic industries Received: September 24, 2011 Revised: December 7, 2011 Published: January 10, 2012 1247

dx.doi.org/10.1021/cg201259u | Cryst. Growth Des. 2012, 12, 1247−1253

Crystal Growth & Design

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present work is of interest and the possible explanation of its formation is discussed.

Scheme 1. Schematic Drawing of Various Crystal Growth Routesa

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EXPERIMENTAL SECTION

Synthesis. To grow BaTiO3 crystals, tetrabutyl titanate [titanium n-butoxide, Ti(OC4H9)4, TNB] (analytical grade) was slowly added to the polymer PEG-200 (5.0 mL), achieving final concentrations of 0.05 M and 2.81 M of [Ti] and PEG, respectively. 188 mg of Ba(OH)2·8H2O (analytical grade) was dissolved in 3.83 mL of doubledistilled water, which had been preboiled for 15 min to remove any dissolved CO2. The TNB/PEG solution was slowly added into the Ba(OH)2·8H2O solution under stirring. The Ba:Ti ratio of the mixture was 1.2 in order to ensure a complete conversion of the titanium precursor into BaTiO3. NaOH solution was then added to keep the batch at a designated pH value of ca. 11. The final volume ratio of PEG to water is 1:1. The suspension was then transferred to a 20-mL Teflonlined autoclave, which was immediately sealed. The hydrothermal reaction was conducted at 180 °C in an oven for times ranging from 15 min to 20 days. After the reaction, the autoclave was removed from the oven and cooled down to room temperature. Soluble impurities were removed by repeatedly washing the precipitate with hot double-distilled water. The final powder specimens were recovered via filtration and washed extensively, first with water, followed by dilute acetic acid, and finally with ethanol, in an attempt to remove any adsorbed impurities such as the excess barium components. The powder specimens were ultimately placed into a desiccator for overnight drying at 60 °C. Characterization. Initial specimen characterization was performed using X-ray diffraction (XRD) on a Rigaku D/MAX 2200 VPC diffractometer, operating at 40 kV and 20 mA, with steps of 0.02° at 10° min−1 in a 2θ range from 20° to 80°. Scanning electron microscopic (SEM) images were recorded on a FEI Quanta 400 Thermal FE environment scanning electron microscope. Samples for transmission electron microscopic (TEM) examination were prepared by dispersing specimen powder on a carbon film supported on a copper grid. TEM and high resolution TEM (HRTEM) images were recorded on a JEOL JEM-2010HR electron microscope equipped with a Gatan GIF Tridiem system. The Ba:Ti ratios of the produced particles were examined by energy dispersive X-ray spectroscopy (EDS) using an Oxford Inca system. Although the commonly used XRD peaks for the calculation of the elemental ratio of Ba:Ti, Ba Lα, and Ti Kα are heavily overlapped, the system can separate them according to their different shapes. The Brunauer−Emmett−Teller (BET) nitrogen physisorption experiments were carried out on a Micromeritics ASAP 2010 system. The pore size distributions of the materials were determined by using the Barrett−Joyner−Halenda (BJH) algorithm according to the desorption data of the N2 isotherms. Fourier transform infrared (FT-IR) spectra, in a range of 400−4000 cm−1 with a resolution of 0.4 cm−1, were obtained from an FTIR-Avatar 350 spectrometer. Thermogravimetric analysis (TGA) was performed in N2 atmosphere with a flow rate of 20 mL/min and with a temperature control from room temperature to 800 °C at a rate of 20 °C/min.

a

(a) The evolution of an amorphous colloidal particle into a single crystal through nucleation at the core or outer surface. (b) The development of an amorphous colloidal particle into a single-crystal like core-shell nanostructure. (c) Growth of an amorphous colloidal particle into several crystallites through multiple nucleation. (d) Orientated aggregation of nanocrystallites and further growth into single crystals.

due to its unique and microstructure-dependent di- and ferroelectric properties.23−26 Detailed crystal growth processes and morphology control may have significant influences on its physicochemical properties. In addition, the improved knowledge of the crystal growth of BaTiO3, a member of the huge perovskite family, is expected to have a large impact on the study of other perovskite materials. Among a variety of fabrication processes of barium titanate, the one-step hydrothermal synthesis method has attracted the most interest whereby the growth mechanism has been proposed by several groups.27,28 Typically, it can be classified into two approaches. One is the so-called dissolution−precipitation approach and the other is an in situ heterogeneous transformation. Disagreement regarding the formation mechanism of BaTiO3 has often been raised. More detailed studies of the early stage crystal growth are therefore required for a better understanding. The studies of the early crystal growth stages of BaTiO3 without the presence of surfactant were reported by Testino et al.29,30 It was observed that irregular BaTiO3 polycrystalline particles formed via primary and secondary nucleation processes. Further, more interesting results could be attained if a correlation could be made between structural domains and the development of the particle morphology. Herein, we present our recent investigation of early stage crystal growth of perovskite-type BaTiO3 from barium hydroxide and tetrabutyl titanate when polyethylene glycol-200 (PEG-200) is present. A new crystallization process is proposed, that is, “aggregation” − “multiple nucleation” − “surface recrystallization” − “single crystal”. Bearing in mind that BaTiO3 crystals usually have a cubic shape,31,32 the formation of dodecahedral crystals of BaTiO3 with 12 {110} facets in the

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RESULTS AND DISCUSSION The Growth Procedure. The XRD pattern from the sample after a hydrothermal reaction time of 15 min does not show any diffraction peaks, indicating that no crystalline phase was present in the sample. With longer reaction times, from 20 min to 48 h, diffraction peaks attributed to the cubic BaTiO3 with a = 4.03 Å, space group Pm3m ̅ (JCPDS card No. 31-0174) appeared in the XRD patterns of the as-synthesized products. The intensity and sharpness of the diffraction peaks increased with the reaction time, indicating a continuous increase of the crystallinity and the crystal size (Figure 1a). No peak splitting in the (h00) and (hk0) diffraction peaks is observed, indicating that the BaTiO3 phase is cubic. The crystal sizes of the specimens were calculated from the Scherrer equation (details see 1248



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Figure 1. (a) Typical XRD patterns of BaTiO3 specimens synthesized at 180 °C with different reaction times ranging from 15 min to 480 h. (b) The crystal sizes calculated using the Scherrer equation (the dots). The inset is an enlarged magnification for stage one from A to B. The curve was calculated from eq 1 with d0 = 5 nm, m = 6.26, and k1 = 1.37 h−1.

Figure 2. SEM images of the specimens prepared at 180 °C for different reaction times: (a) 15 min, (b) 20 min, (c) 30 min, (d) 12 h, and (e) 48 h. The upper insets are typical TEM images of individual colloidal particles. The scale bars are 20 nm. The corresponding SAED patterns from the whole particles are shown in the lower inserts with the diffraction spots indexed to the cubic unit cell of BaTiO3 with a = 4.03 Å. The edge areas of the particles marked by rectangles were further investigated by HRTEM as shown in Figure 3. (f) The Ba:Ti ratios from the results of EDS analysis.

Supporting Information Part 1). As shown in Figure 1b, the calculated crystal sizes rapidly increase between the reaction times of 20 min and 12 h, a significant decrease from 12 to 48 h, followed by a slow increase. A possible kinetic model corresponding to this novel curve is discussed below. SEM and TEM images from the specimen with a reaction time of 15 min reveal that the specimen contains spherical colloidal particles with a size about 60 nm in diameter (Figure 2a). No diffraction spots are visible on the selected area electron diffraction (SAED) pattern as shown in the inset of Figure 2a, in a good agreement with the XRD results. Extending the hydrothermal reaction time from 15 min up to 48 h, the colloidal particle sizes do not change significantly (Figure 2b−e). It is interesting to see that very weak (110) diffraction spots are visible on the SAED pattern from the sample after a reaction time of only 20 min (Figure 2b). The intensities of the diffraction spots on the SAED patterns from the samples with longer reaction times increase notably. The most extraordinary phenomenon is that almost all the SAED patterns show a single-crystal property even when the colloidal particles are truly aggregates of smaller particles as shown by both the SEM and TEM images in Figure 2. It is also noted that a regular dodecahedral morphology started to appear in the sample with the reaction time of 48 h (Figure 2e). More TEM images of these specimens together with a sample produced after a reaction for 480 h are shown in Supporting Information (Figure S1). Another interesting phenomenon observed in the present work is that the ratio of Ba:Ti of the colloidal particles changes from 0.4 to 1.0 at the early stage of the reaction as detected by EDS (Figure 2f). According to previous research results,29,30,33

the formation process of BaTiO3 consists of the rapid formation of a titanium hydroxide gel phase followed by a reaction between the gel phase and the Ba ions in the solution. At high pH values, the gel phase from the hydrolysis of titanium salts is built of negatively charged entangled networks composed of polymeric titanium hydroxide chains. Positively charged barium cations can be adsorbed on the surface or trapped in the spare spaces of the networks. In the present work, the combination of barium and titanium occurred in the colloidal particles. Bearing in mind that the original ratio of Ba:Ti in the starting suspension was 1.2, the initial colloidal particles consisted of much less Ba than we expected. During the crystal growth, Ba cations gradually moved from the solution into the colloidal particles to join the multiple nucleation and further crystal growth. HRTEM images from the colloidal particles grown for 20 min reveal that a large part of the particles is still amorphous with some nanocrystallites developed on surface of the particles, but the location of some nanocrystallites embedded in the colloidal particles cannot be ruled out (Figure 3a). The crystallite size observed, in a range of 3−8 nm, is typical according to the average crystallite size from XRD (Figure 1b). These nanocrystallites seem to be separated from each other by the amorphous or granular matrix. However, a high degree of concordant 1249



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Figure 4. (a) SEM and (b) TEM images of BaTiO3 crystals grown at 180 °C for 480 h. The inset in (b) is the corresponding SAED pattern from the entire crystallite shown, indexed to the cubic BaTiO3 unit cell. (c) HRTEM image and related FFT pattern (inset) from the white rectangle in (b). (d) Schematic illustration of a dodecahedral crystal with 12 {110} facets.

Figure 3. HRTEM images of specimens recorded from the areas marked by rectangles in Figure 2 with different reaction times, (a) 20 min, (b) 30 min, (c) 12 h, and (d) 48 h, respectively. The insets are the corresponding FFT patterns, obtained from the whole image.

molecules are adsorbed to the surface metal atoms in BaTiO3. The density of metal atoms (Ba and Ti) on the {110} planes is 1.414/a2, while that on the {100} surface is 1/a2, where a is the unit cell parameter of BaTiO3 (4.03 Å). This selective adsorption of PEG results in a protective layer on the {110} surfaces, significantly suppressing the crystal growth along the ⟨110⟩ zone axes. A similar phenomenon was observed from the formation of nanoplatelets of zeolite analcime where ethylamine was believed to be selectively adsorbed on the {111} surfaces.9 The ideal {110} atomic planes of BaTiO3 are either positively charged when they terminate at the metal/oxygen layers, designated (110) planes, or negatively charged if the terminated planes contain oxygen anions only, designated (220) planes (Supporting Information, Figure S2). A dipolar moment is possible in the nanocrystallites. When the crystallite size is very small, the dipole−dipole interactions would probably play an important role in the self-orientation of nanocrystallites as observed in the present work and also in the previous work.35−37 When the nanocrystallites grew up, the adsorbed PEG molecules on the {110} surfaces may depress the dipolar−dipolar interaction. On the other hand, the adsorbed PEG molecules can also enhance the attraction between the nanocrystallites through the intermolecular interaction. Consequently, the orientated connection between the {110} planes of the crystallites minimizes the total energy of the system. This process most likely takes place on the surface of the colloidal particles because the surface crystallites have a relatively high mobility. Crystallization Behavior. This process supports the proposed reversed crystal growth route, that is, surface crystallization of amorphous colloid particles followed by a surface-tocore extension of crystallization. Observation of this reversed crystal growth route in the present work was more difficult than the previous work in the zeolite systems, because the colloidal particles (ca. 60 nm in diameter) are much smaller than the disordered aggregates in the synthetic systems for zeolite analcime (ca. 60 μm)9 and zeolite A (ca. 2 μm).4 Nevertheless, HRTEM images of the particles still reveal different levels of crystallinity

crystal orientations of these nanocrystallites implies that they have already undergone some type of interaction and selfadjusted their orientations. It is much easier for such a process to happen on the surface of the colloidal particles. A similar phenomenon of surface crystallization was observed during the reversed crystal growth of zeolite analcime and zeolite A.9,10 With longer hydrothermal treatment times, the nanocrystallites tend to join together. Consequently, the single-crystal areas become larger, although a large number of defects can be detected. In specimens with a reaction time of 30 min, HRTEM images revealed such a connection of nanocrystallites. The overall structure of the particles looks like mesoporous crystals (Figure 3b).34 The pores were filled by further crystallization of the samples with longer reaction times (Figure 3c,d). Dodecahedral Crystals of BaTiO3. When the crystals are large enough, HRTEM images indicate that the terminal planes of the crystals are {110} (Figure 3d). The dodecahedral morphology with 12 {110} facets becomes more apparent when the reaction time is as long as 20 days (Figure 4). It has been established that the crystal growth rate along a crystallographic orientation is proportional to the surface attachment energy, which is defined as a fraction of the total lattice energy released on the attachment of a growth slice of thickness dhkl onto a growing crystal surface.1 Normally a small surface attachment energy is associated with a large d-spacing. According to both the BFDH law14−16 and Curie and Wulff’s theory,12,13 a free crystal of BaTiO3 should have a cubic morphology with six {100} facets, since crystal growth along the ⟨100⟩ zone axes is the slowest, as often seen from as synthesized BaTiO3 crystals following the classic growth route. In the present work, PEG polymer molecules would have a strong interaction with the crystals. Although PEG can be adsorbed on all surfaces of the crystals, the coverage of PEG on the {110} surfaces would be much higher than that on the {100} surfaces, since the density of metal atoms in the {110} planes is higher. We assume PEG 1250



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in Supporting Information, Figure S3. The colloidal particles were initially aggregates of titanium precursor and polymer PEG-200 molecules. With the migration of Ba cations into the colloidal particles to form BaTiO3, the PEG and other molecules/ anions in the colloidal particles were continuously moving out. Consequently, the colloidal particles after short reaction times contained a large amount of PEG and H2O, and underwent a large weight loss (Supporting Information, Figure S3). Such a large mass transportation was not possible in the crystal growth of zeolite analcime where a highly dense single-crystalline shell completely covered the particle surface.9 From the HRTEM images, it can be seen that BaTiO3 crystallites are mainly spherical and separated at a short reaction time, for example, 15 min or 20 min (Figure 3a). After growing for 30 min, the crystallites start to connect to each other (Figure 3b). Therefore, after nucleation, the first stage of the crystal growth was dominated by an orientated aggregation process. The colloidal particles at this stage undergo a transition from a porous to nonporous state, which can be confirmed by nitrogen adsorption/desorption isotherms as shown in Supporting Information (Figure S4). The 20 min specimen clearly shows a mesoporous property, which is lost in the 12 and 240 h samples (Figure S4a). At the same time, the specific surface areas of the specimens reduced very quickly at this stage (from 15 min to 12 h) and then reduced slowly (Figure S4b). For such an orientated aggregation process, a kinetic model was proposed (see part 6, Supporting Information),38

in their cores compared to their surface areas. For example, in the HRTEM image in Figure 5, we can clearly see that the surface

Figure 5. HRTEM image of a BaTiO3 particle after crystal growth at a lower temperature, 120 °C for 24 h, showing that the core and the surface area have different crystallinities. Two d-spacings of 3.96 and 2.76 Å are measured, corresponding to the (001) and (110) planes of BaTiO3, respectively.

region of this particle has become single-crystalline, while the core is still in a state of aggregated nanocrystallites with a large number of defects and grain boundaries. Furthermore, the mass density of the core is much lower than that in the shell. If further hydrothermal treatment is performed, we can expect a surface-to-core extension of recrystallization until the whole particle becomes a single crystal. The behavior of the BaTiO3 growth is certainly different from the previous descriptions.18,38−40 The whole process can be divided into three stages according to the XRD and HRTEM results obtained in the present work. These three stages can be identified from the non-monotonic increase of the crystallite sizes with the reaction time, calculated from the (110) peak broadening using the Scherrer equation (Figure 1b). In the first stage from the beginning of reaction (A) to the peak point (B) as shown in Figure 1b, the crystal size rapidly increased to a size of ca. 22 nm at 1 h and then gradually increased to a size of ca. 30 nm when the reaction time was 12 h. It is interesting to see that the curve of the Ba:Ti ratio in the colloid particles as a function of the reaction time (Figure 2f) resembles the curve of the crystallite size increase very well (Figure 1b). The ratio of Ba:Ti quickly increases in the first hour and then becomes relatively stable, indicating that the diffusion of barium cations from the solution to the colloid particles dominated this very early process. The crystallization of BaTiO3 after the arrival of barium cations in the colloid particles was relatively faster. Since the size of the colloidal particles remained the same during the whole process as shown in Figure 2, the crystallization took place in the colloidal particles, which must be accompanied by a change in the overall composition of the colloidal particles. In addition to the change of the Ba:Ti ratio, the gradual loss of water and organic molecules during crystallization could be predicted according to the TGA and FT-IR results from the specimens with different crystal growth times, as shown

d = d0

1 + mk1t 1 + k1t

(1)

where d is the average crystal size at time t, d0 is the initial average crystal size at the starting point, m is defined as the aggregation factor which represents the degree of crystal combination, k1 represents the crystal growth rate constant. The crystal size d0 is about 5 nm at point A. The first stage of crystal growth can be fitted well to eq 1 and the resultant fitting parameters listed in Table 1, that is, d0 = 4.90 nm, m = 6.26, Table 1. Simulated Data for the Three Stages of Crystal Growth of BaTiO3 Nanoparticlesa stage the first stage

the second stage

the third stage

a

T (°C)

220

180

140

m d0 (nm) k1 (h−1) R2 dh (nm) k2 (h−1) R2 dm (nm) tm (h) k3 (h−1/3) 1/n R2

6.86 4.49 2.49 0.93 28.99 0.32 0.91 22.15 23.60 1.87 0.39 0.96

6.26 4.90 1.37 0.91 29.77 0.094 0.97 25.70 47.93 1.45 0.32 0.95

5.62 4.85 0.72 0.91 28.85 0.048 0.99 22.79 240.0 0.87 0.35 0.82

Ea (kJ/mol) 26.42

40.10

16.40

Note: Ea is deduced from Arrhenius equation, ln k = −((Ea)/(RT)) + A0.

and k1 = 1.37 h−1. The crystal size curve shown in the inset of Figure 1b remarkably matches the experiment results, indicating that the above model described by eq 1 can actually address crystal growth by an orientated aggregation process. When t is very small, the crystallite size changes almost linearly with 1251



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the growth time with a gradient of mk1. When t is large, d approaches a maximum value of md0. The parameters such as those deduced from the experimental results at 140 and 220 °C (Figure S5) are also listed in Table 1. With the increase of reaction temperature (T), both the aggregation factor (m) and rate constant (k) tend to be greater. This implies that at a higher temperature more nucleation sites are initiated at a much earlier stage for crystallization; hence orientated growth tends to be enhanced. The reduction of the crystallite size from B to C in Figure 1b seems to have no support from TEM observations. In a previous report, such a reduction was attributed to the shrinkage of particles when they were losing their porous property.38 Examination of the HRTEM images show that, in the second stage, the aggregation process of nanocrystallites was completed (Figure 3d); that is, all the nanocrystallites have aggregated together. Two principal changes which dominated this stage were (1) the dodecahedral morphology of the particle became more obvious, and (2) the porous property of the particles declined as the pores were filled up by crystalline BaTiO3 (Figure 3d). We can give kinetic models for simulating stage two and stage three as previously. For stage 2 from B to C in Figure 1b, the calculated crystallite size can be expressed by a simplified equation as follows:

d = dh − k 2(t − th)

energy can be calculated based on the yield of BaTiO3 product,28 the Ea of individual stages of the crystal growth reported for the first time in the present work enables us to study more details of the kinetic behavior of crystal growth. The highest Ea value was recorded for stage 2 due to the difficulty of mass transportation in and out the particles when the pores become smaller due to the limited space after further crystallization. Another possible reason is the formation of a large number of defects in the grain boundaries. The larger Ea value for the first stage than that for the third stage is believed to be attributed to the presence of surface adsorbed polymer, depressing the growth of individual crystallites. How the polymer molecules interfere with the crystal growth has been tested by changing the concentration of polymer PEG in the synthetic system (Supporting Information, Figure S6). When no polymer was added, the crystals are irregular in shape (Figure S6a). A low concentration of polymer (10%) led to dodecahedral crystals with diameters of hundreds of nanometers (Figure S6b). Further increase of the polymer to 30% and 50% resulted in smaller dodecahedral crystals (Figures S6c,d), because smaller colloidal particles formed. When the concentration of polymer was very high, instead of disordered colloidal particles forming, individual nanocrystals protected by the polymer molecules developed (Figures S6e−h). These images in Figure S6 clearly confirm the significant effect of PEG molecules on the crystallization of BaTiO3 crystals.

(2)

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where t is time, th is the beginning time of the second stage (ca. 12 h). dh is the initial particle size at the beginning of the second stage (ca. 30 nm). The obtained parameters are listed in the middle row of Table 1. The datum of k2 is obtained to be 0.094. Such a small value of k2 suggests a slow change of the calculated crystallite size. In the third stage, the size increase is reinitiated, but the increase rate is much slower than that at the first stage. The particles reduced their defects and distortion via Ostwald ripening. The progress can be simulated by the equation below.38

d = k3(t − t m)1/ n + d m

CONCLUSION Dodecahedral crystals of perovskite-type BaTiO3 have been produced in the presence of polyethylene glycol, which plays two important roles during the crystal growth. First, it enhances the aggregation of precursor molecules to form spherical colloidal particles, allowing multiple nucleation to take place in these particles. Second, PEG is selectively adsorbed on the {110} planes of BaTiO3, leading to the dodecahedral morphology. The crystal growth has been recognized to be nonclassic reversed crystal growth, following the route of “disordered aggregation” − “multiple nucleation” − “surface crystallization” − “crystal extension from surface to core” − “single crystal” (Scheme 2). This overall crystal growth can be further divided

(3)

in which t is time, k3 is a temperature-dependent reaction rate constant, n is an exponent, dm is the crystal size at starting time point of tm, herein tm = 48 h for point C in Figure 1b. Table 1 and Figure 1b show the fitted data matches well with the experimental results. Interestingly, the values of dm and n are almost identical for the three different temperatures, but tm decreases rapidly with increasing temperature and the k3 value increases with temperature (Table 1, Figure 1b and Figure S5). This implies that both the starting state and the nature of the third stage of crystal growth are independent of temperature, but starting point (tm) shifts to an early time and the growth process of the third stage becomes faster with a higher temperature. Consequently, phenomenological kinetic energy analysis shows that the crystal growth of BaTiO3 in the presence of polyethylene glycol-200 exhibits three distinct stages after multiple nucleation in the disordered aggregates: (1) orientated aggregation of nanocrystallites, (2) filling of the pores by further crystallization, and (3) perfection of crystals via Oswald ripening. According to the Arrhenius equation and the above deduced data of the reaction rate constants in Table 1 for the three stages, the deduced activation energies (Ea) are derived to be 26.42, 40.1, and 16.4 kJ mol−1. Although some overall activation

Scheme 2. Schematic Drawing to Show the Proposed Crystal Growth of BaTiO3 in the Presence of PEGa

a

(a) Individual precursor monomers and PEG, (b) amorphous colloidal particle, (c) multiple nucleation on the surface of BaTiO3, (d) orientated connection of nanocrystallites, (e) surface crystallization to form a dodecahedron, (f) single crystal.

into three stages with different kinetic behaviors. The new knowledge of the crystal growth will help researchers to have a better control of the crystallite size and crystal morphology. 1252



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ASSOCIATED CONTENT

S Supporting Information *

TEM images of specimens prepared under different conditions. Models of surface atomic layers of BaTiO3. TGA, FT-IR results. Gas adsorption/desorption results. Kinetic modeling of the crystal growth. Temperature-dependent crystal size changes. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (M.W.) or wzhou@ st-andrews.ac.uk (W.Z.).

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ACKNOWLEDGMENTS This work was financially supported by National Natural Science Foundation of China (NSFC) and the Government of Guangdong Province and Guangzhou City (No. U0734002, No. 50872158, No. 8251027501000010 and No. 2010GNC011), and industry program (2007B090400001). W.Z. thanks the Royal Society for financial support to an International Collaboration project in this field. The sample for HRTEM imaging in Figure 5 was prepared by a group of undergraduates at St Andrews University in their third year mini-project. The authors thank the group members for their contribution: Louise McCulloch, Aidan Rooney, Katherine Self, James Squires, and Izaak Watson.

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REFERENCES

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Multiple Nucleation and Crystal Growth of Barium Titanate - Crystal

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