Formation of Ba2NaNb5O15 Crystal and Crystallization Kinetics in

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Formation of Ba2NaNb5O15 crystal and crystallization kinetics in BaO-Na2O-Nb2O5-SiO2-B2O3 glass C. G. Baek, M. Kim, O. H. Kwon, H. W. Choi, and Y. S. Yang Cryst. Growth Des., Just Accepted Manuscript • DOI: 10.1021/acs.cgd.7b00576 • Publication Date (Web): 06 Oct 2017 Downloaded from http://pubs.acs.org on October 8, 2017

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Crystal Growth & Design

Formation of Ba2NaNb5O15 crystal and crystallization kinetics in BaONa2O-Nb2O5-SiO2-B2O3 glass C. G. Baek, M. Kim, O. H. Kwon, H. W. Choi, and Y. S. Yang* Department of Nano Fusion Technology, College of Nanoscience and Nanotechnology, Pusan National Univ., Busan 46241, Korea * email: [email protected]

Abstract

We have synthesized Ba2NaNb5O15 (BNN) crystal by annealing 25.6BaO-6.4Na2O–32Nb2O5– 24SiO2–12B2O3 (BNNSB) glass and investigated the crystallization kinetics from the glass. The glass sample was prepared by a plate quenching method. Thermal, structural, vibrational and surface properties have been studied by using differential thermal analysis, X-ray diffraction, Raman spectroscopy and atomic force microscopy, respectively. It is found that the crystallite sizes of the orthorhombic Ba2NaNb5O15 crystal occurred in the BNNSB glass are confined within 30~70 nm. The Williamson-Hall plot is applied to estimate the effect of crystallite size and strain to Bragg peak broadening. The isothermal model of the JohnsonMehl-Avrami-Kolmogorov function is applied to characterize the kinetics of the crystallization process. The Avrami exponent 4.5 indicates that the crystallization mechanism belongs to an increasing nucleation rate with the diffusion-controlled growth. The activation energy of crystallization, 5.0 eV obtained from the isothermal model, show the similar value to that resulted from the isoconversion method. The Raman scattering patterns, which are very different between the crystalline and glass phases, have been deconvoluted and the various vibrational modes have been explained based on the network dimensionality, nonbridging oxygen and the degree of structural order.

Keywords: Ba2NaNb5O15 crystal, BaO-Na2O–Nb2O5–SiO2–B2O3 glass, crystallization kinetics, Raman spectroscopy

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Introduction Barium sodium niobate (Ba2NaNb5O15, BNN) crystal has attracted attention long time because of its important physical properties of ferroelectricity, high nonlinear optical coefficient and intense photoluminescence.1-3 BNN crystal possesses a sequence of structural phase transitions accompanying the change of dielectric properties. The ferroelectric orthorhombic Pba2 structure BNN with the lattice parameters a=12.425, b=12.484, c=3.997 Å at room temperature transforms to the ferroelectric tetragonal 4mm at 260 oC, and with further heating, to the paraelectric tetragonal 4/mmm at 560 oC. 4,5 At room temperature, BNN has the useful values of dielectric constant ε=250 and spontaneous polarization P=0.40 C/m2,6 which can be compared with those of LiNbO3 (ε=80, P=0.71 C/m2),7,8 LiTaO3 (50, 0.5 C/m2),9 BaTiO3 (3000, 0.25 C/m2).10 BNN has been used in second harmonic generation and electro-optic devices because of its high nonlinear coefficient and resistance to optical damage.11,12 In spite of useful ferroelectricity and optical properties, there exists limitation in applying BNN crystals, caused by twinning defects and a lack of high quality crystallinity during synthesizing process. It is naturally required to broaden the sample preparation method and the types of samples for the further development of BNN applications.13,14 Crystallization of glass is one of the ways to produce various types of samples such as glass, glass-ceramics, ceramics and nano crystals, which can reveal different kinds of physical characteristics. In the scientific point of view, understanding the crystallization process from a glass is important and useful because it enables us to control the production specifications of crystal size, crystallinity, crystal structure, and crystal volume fraction in the glass.15-17 In

this

paper,

25.6BaO-6.4Na2O–32Nb2O5–24SiO2–12B2O3

(BNNSB,

the

stoichiometric composition of BNN in borosilicate, which can be written as 2BaO+0.5Na2O+2.5Nb2O5+ borosilicate) glass was synthesized by rapidly quenching the melt. The data obtained from isothermal measurements at 697~703 oC have been analyzed using the Johnson-Mehl-Avrami-Kolmogorov (JMAK) model to determine the crystallization mechanism of the glass. We also have conducted isoconversional analysis to find the change of activation energy for the conversion fraction x and to get information about the transition complexity during crystallization. Raman spectroscopy measurements have been performed to investigate the vibrational modes of the glass and crystal. Comparison between those modes provides the information of the internal binding and structural changes.


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Experimental section BaCO3 (Sigma-Aldrich Chemistry), Na2CO3, Nb2O5, B2O3, SiO2 with the mole ratio 25.6:6.4:32:12:24 were well mixed for 1 h, melted at 1300 oC, and quenched to produce a glass. The formation of the glass was confirmed by using X-ray diffraction (XRD, Rigaku) of CuKα and differential thermal analysis (DTA, Mac Sci.). The isothermal crystallization kinetics of the glass was carried out by DTA under a pure argon atmosphere. For isothermal experiments, the sample of 5 mg was encapsulated into platinum pan and was heated at 697, 699, 701, 703 oC. The surface morphology was taken by atomic force microscopy (AFM, Park Sys.). The average crystallite sizes were calculated by using the Scherrer equation from the XRD data, obtained with the step-scan mode scanned with 0.05o per 5 s in the scattering angle range 20o~60o, and by the image calculating program of AFM. Raman spectroscopy (Dongwoo Co.) measurements for the glass and the fully crystallized samples were performed to investigate and compare the local vibrational modes.

Results and Discussion Figure 1 shows the isothermal exothermic curves at 697, 699, 701, 703 oC, measured with DTA during the crystallization of the 25.6BaO-6.4Na2O–32Nb2O5–24SiO2–12B2O3 (BNNSB) glass. The inset of the figure represents the non-isothermal crystallization curve with the heating rate 10 oC/min. The only one exothermic peak in the inset is caused by the heat release during the phase transition from the BNNSB glass to a crystalline phase and the crystallization mechanism of the glass can be determined with this peak. We select the proper temperatures to conduct isothermal measurements, based on this non-isothermal crystallization curve in which the glass transition temperature Tg, the crystallization temperature Tc and the maximum crystallization temperature Tp are shown. Figure 2(a) shows the XRD patterns measured at room temperature for the rapidly cooled samples when temperatures reach at 710, 725, 740 and 750 oC with the heating rate 10 o

C/min. The XRD pattern at 710 oC is from the BNNSB glass state. The low intensity of

crystalline peak appears at the beginning of crystallization at 725 oC and the intensity becomes stronger when the crystallization is fully finished at 750 oC. We have obtained a



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series of XRD patterns for the samples quenched at different temperatures during crystallization, and a progressive increase of crystalline peak intensity, which is proportional to the transformed volume fraction from the glass to the crystalline phase, is measured. The crystal structure corresponding to the diffraction patterns in the figure is orthorhombic Ba2NaNb5O15 (BNN) with the lattice parameters a=12.399±0.013, b=12.532±0.054 and c=3.939±0.002 Å, the same structure in JCPDS No 86-0739. Considering the initial compositions of the glass 25.6BaO-6.4Na2O–32Nb2O5–24SiO2–12B2O3 (BNNSB), all of the cations Ba, Na and Nb are consumed to form the BNN crystal but non of the Si and B species contribute to the crystal formation but remains as a silico-borate glass phase within the reached annealing temperature of 800 oC. The size variation of nano crystallites during the phase transition at different temperatures is shown on the upper part of Fig. 2(a). The crystallite size is calculated using the Scherrer equation R=pλ/βcosθ, where R is the crystallite size, λ the X-ray wavelength, p the shape factor, β the full width half maximum of Bragg peak and θ the scattering angle. The inset of the figure is a magnified view of the (231) peak, taken from the XRD pattern of 3-dimensional plot in Fig. 2(a) at 750 oC. The crystallite size 62±5 nm is obtained from the broad peak width of 0.258. The change of the calculated peak width for different Miller indices can be seen in the Williamson-Hall plot in Fig. 2(b). Only the crystallite size effect is considered for XRD peak broadening in the plot of crystallite size variation on the upper part of Fig. 2(a), because the strain effect is not so pronounced as can be seen in the Williamson-Hall plot in Fig. 2(b). Considering the XRD line shape, peak broadening mostly occurs due to crystal size and strain effects. One of the models to separate each effect is the Williamson-Hall plot.18-19 In this model, the peak broadening of full width at the half maximum β can be written as β=βsize+βstrain= pλ/Rcosθ + ηtanθ, where βsize is the size effect, βstrain the strain effect and η the apparent strain (η/4; maximum strain). From the plot βcosθ versus sinθ, for different Bragg peaks, the intercept of a linear extrapolation to this plot gives the crystallite size λ/R for the shape factor p=1.0 and the slope gives the strain η. In the Williamson-Hall plot in Fig. 2(b), the peak width at each Bragg reflection is obtained from the XRD data shown in Fig. 2(a). The comparison of two plots for 725 oC and 750 oC in Fig. 2(b) clearly shows the size-


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strain relationship; in the early stage of crystallization at 725 oC, the average crystallite size 33.6 nm is small with the large strain 3.2Å10-3 (0.3%), meanwhile, in the late stage of crystallization at 750 oC, the crystallite size 61.3 nm is large but the strain 6.3Å10-4 is small. One of the models to estimate a critical nucleus size from the variation of crystallite size on the isothermal process of nucleation and growth, under a few assumptions such as; the particles are spherical; nucleation occurs homogeneously; growth is controlled by diffusion; a system is in isotropic solid solution, can be written as R=(Ro2+ct)1/2, where R is the crystallite size, Ro the critical size, c the growth constant, t is the time after incubation.20-22 The application of this model to the BNNSB system may be too idealized, but this approach allows for the simple account of nucleation and growth process, including the rough estimation of critical size. Figure 3 is the variation of crystallite size as a function of time at 697 oC. The fit with the above-mentioned model shows the critical nucleus size 6.7 nm. The inset of the figure is intended to show the growth mechanism is in the diffusion controlled process in the measured time range with the time exponent 0.5. Concerning the crystal size of early stage crystallization at different isothermal temperatures, in the thermodynamic point of view, an incubation time is dependent on the combination of driving force (increase with deep undercooling) and viscosity (decrease with increasing temperature) for nucleation. From the simple model of crystal formation energy in glass, G=4/3πr3∆g+4πr2γ, where r is the crystal radius, ∆g is the free energy difference between glass and crystal at a given temperature, γ is the surface energy of a grain, the critical nucleus size, which can be thought as a grain formed at the incubation time, is obtained as 2γ/∆g.23 In this thermodynamic reason, we can say that the crystal size at the incubation time becomes smaller with increasing undercooling (large ∆g, low isothermal temperature). Figure 4 shows the normalized integrated exothermic heat of DTA curve at each isothermal temperature, obtained from Fig. 1, which is proportional to the transformed crystalline BNN volume fraction from the BNNSB glass. In the figure, the symbols are data and the lines are the fit with the Johnson-Mehl-Avrami-Kolmogorov (JMAK) equation24,25 which can be written as () = 1 − exp(− )

(1)

with

( ) = exp (− )

(2)



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where x(t) is the transformed crystalline volume fraction after time t, k(T) is the crystallization rate constant with isothermal parameter ko, n is the Avrami exponent which describes a transition mechanism, E is the activation energy of crystallization, kB is the Boltzmann constant. As can be seen in the figure, eq. (1) is relatively well fit to the data up to x~0.6 and slightly deviate thereafter. In the late stage crystallization, when the crystallites keep growing and the sizes become larger, normally impingement occurs and this effect of growth interruption appears as a delayed crystallization, and the time to reach to certain x is longer in the experimental data, compared with the time in the JMAK model. Meanwhile, when the grain growth is disturbed and the grains are restricted to nano size, the data are rather well fit to eq. (1) even at the late stage of crystallization, and often the time to reach to a certain x is shorter in the experimental data compared to the time in eq. (1), as the case of this figure, because the released heat during crystallization can act as an increased thermal fluctuation and accelerate crystallization. As seen in the figure, the Avrami exponents at different temperatures are close each other with the average value n=4.5. The meaning of the value will be discussed below. Figure 5 is the plot to calculate the activation energy of crystallization using eqs. (1) and (2). The plot ln[-ln(1-x)] versus ln t of eq. (1) intercepts at ln k, and then E can be obtained from eq. (2). The inset of the figure shows the activation energy of nucleation, obtained from the incubation time, the onset time ti of crystallization, with the Arrhenius relation ti=to exp (En/kBT), where to is the prefactor and En is the activation energy of nucleation. The Avrami exponent n and the activation energy of crystallization E can be combined together to get better understanding of crystallization mechanism with the relationship; n=a+bc (a=0; zero, o1 indicates that the crystallization involves an increasing nucleation rate whether the growth is under interface or diffusion control.23 And from the fact that the time exponent of the growth is 0.5 in the experimental result shown in the inset of Fig. 3, c can be set as 0.5. The effect of the increasing nucleation rate is appeared


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in the late stage crystallization in Fig. 4, where the volume fraction of the data at certain time is larger than the value from the JMAK model, meaning that the crystallization occurs faster than the model predicted. Concerning the activation energy of crystallization, with the obtained values from experiments, E=5.0 eV (Fig. 5), En=1.1 eV (the inset of Fig. 5), b=3 (Fig. 7), and with E=En+bcEg, Eg=2.6 eV for c= 0.5. The smaller value of the nucleation activation energy En compared with the growth activation energy Eg indicates that the nucleation rather than the growth dominates the BNN crystallization of the BNNSB glass. Figure 6 shows the isoconversion plot of activation energy as a function of crystallized volume fraction. It is seen that the values exist within 10% against 5.0 eV obtained with JMAK model, indicating that the time-temperature-transition relationship is relatively well kept through the entire crystallization process. The JMAK model of thermally activated reaction kinetics in homogeneous systems, written in eqs. (1) and (2) is normally assumed that the activation energy E and pre-exponential factor ko do not vary during phase transition. But it has been known that those parameters may vary with the progressive change of x, and the variation can be recognized by the isoconversion E variation method. There have been several proposed explanations of E variation in solid state reactions such as; complex reactions, the heterogeneous nature of the samples, defect formation, intra-crystal strain, reactivity change due to heat or mass transfer at reaction interfaces. A brief explanation of isoconversion method which is used in this isothermal study of crystallization of glass is described as follows. The reaction rate of solid state kinetics can be generally described by dx/dt=hu(x), where h=Dexp(-E/kBT) is the reaction rate constant with the pre-exponential frequency factor D and kB is the Boltzmann constant. The integration of this rate equation is written as v(x)=ht=Dtexp(-E/kBT). By taking the logarithm of v(x), the standard isoconversion method is obtained; ln t=-ln(D/v(x))+E/kBT. And thus, the slope of the plot ln t vs. 1/T at each x yields E. 26-27 The process to obtain E from the slope mentioned above at x=0.45 is shown in the inset of Fig. 6. And the variation of E with the progressive change of volume fraction x is seen in Fig. 6, with the value 4.8~5.6 eV. Even the values of E do not vary drastically through the whole process of transformation, the result of E variation indicates that the crystallization kinetics of the BNNSB glass involves one or more effects mentioned above. Figure 7 shows the AFM surface morphology taken at room temperature for (a) the asquenched glass sample and (b) the crystallized sample quenched at 750 oC after annealing the BNNSB glass with the heating rate of 10 oC/min which is the same heating rate shown in Fig.



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1. In the glass sample, only a flat surface morphology is seen, but the crystallites with round shapes clearly appear in the crystallized sample. The crystallite sizes in the figure are distributed within 30~70 nm, which are obtained using the pre-installed size measurement program in AFM. In Figure 8, Raman spectra of the (a) BNNSB glass and (b) crystal taken at room temperature, with the incident wavelength of 532 nm, are shown. Different vibrational modes existing in the network structures, originated from the relative arrangement of atomic or molecular units, and the amounts of bridging and non-bridging oxygen atoms, are overlapped and are appeared as broad peaks in the spectra. A pronounced difference in the scattering patterns between two phases can be seen in the figure. We have deconvoluted the spectra, only by changing the peak intensity without peak position variation, and attached a label to each peak based on the characterized vibrational mode. The excitation modes of each peak are summarized on Table 1, where Qz represents the structural unit of silica network, Q is the Si tetrahedron and z the number of bridging oxygen per tetrahedron, varying between 0 and 4. Fig. 8(c) is the simplified view of the Raman scattering intensity change of each peak for the crystal and glass phases. As can be seen in Table 1, Raman scattering in the high wavenumber range (P10, P11, P12), where the intensity from the glass phase is much higher than that of the crystal phase, is related to the vibration of low ordered network binding and disconnected network structure of Qo, Q1, [NbO6]7-. Meanwhile, Raman scattering in the low wavenumber region (P4, P5, P7), in which the scattering from the crystal phase is much denser than that of the glass state is concerned with the vibrations of high dimensional network binding of NbO6 octahedron. The results indicate that the difference of the vibrational modes between the glass and crystalline phases from the internal network structure can be clearly manifested by the Raman scattering patterns. Raman peak width is related to structural disorder and broadens with the increase of disorderliness. Each deconvoluted Raman peak from the BNNSB glass in Fig. 8(a) is very broad, caused by highly disordered structure of the glass phase. In the case of the deconvoluted peak width in Fig. 8(b), even narrower than that in 8(a), Both BNN nano crystallites and borosilicate glass may contribute to peak broadening.

Conclusions We have synthesized the orthorhombic Ba2NaNb5O15 (BNN) crystal by annealing the


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25.6BaO-6.4Na2O–32Nb2O5–24SiO2–12B2O3 (BNNSB) glass. There occurs nano formation during the crystallization of the glass and the average crystallite sizes calculated using the Scherrer equation with the XRD data and AFM morphology are 30~70 nm. The analysis of the Johnson-Mehl-Avrami-Kolmogorov parameters insures us that the crystallization mechanism is governed by an increasing nucleation rate with the process of crystallization. The calculated activation energy relationship En

Formation of Ba2NaNb5O15 Crystal and Crystallization Kinetics in

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