DETERMINATION OF AVRAMI PARAMETER IN THE CASE OF NON-ISOTHERMAL SURFACE CRYSTALLIZATION OF POWDERED GLASSES

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1 1 Proceedings of 16 -th International conference of Glass and Ceramics, Varna, Bulgaria, 26-30,09,Varna 2008 DETERMINATION OF AVRAMI PARAMETER IN THE CASE OF NON-ISOTHERMAL SURFACE CRYSTALLIZATION OF POWDERED GLASSES Alexander Karamanov, Radost Pascova, Isak Avramov, Ivan Gutzow Institute of Physical Chemistry, Bulgarian Academy of Sciences, G. Bonchev Str. Block 11, 1113 Sofia, Bulgaria, Abstract: The influence of grain size on the crystallization kinetics of glass powders with diopside-albite composition is investigated by non-isothermal Differential Thermal Analysis and Scanning Electron Microscopy. For this purpose, different fractions of a glass, forming diopside crystals via surface crystallization were used. The activation energy of crystallization, E cr, is determined from Kissinger plot, while the reaction order, m, is estimated both by the methods of Ozawa and of Augis-Bennett. The values of E cr thus determined, decrease, when grain size increases, from 530 to 300 kj/mol; simultaneously, the m value drops from 2.5 to 1.3. This result contradicts to the widespread fallacy that the reaction order, in the case of surface crystallization, should be equal to one. In fact, as it is confirmed by the SEM investigations, during the initial stage of crystallization a three dimensional growth takes place. Later on, one dimensional growth inwards the grain is possible. Thus, the reaction order changes from 3 to 1. Keywords: crystallization kinetics, reaction order, differential thermal analysis, crystallization porosity INTRODUCTION In the last 40 years, the transformation kinetics of glasses into glass ceramics has been very thoroughly investigated under isothermal as well as under non-isothermal conditions. The experimental results were commonly analyzed in the framework of the Kolmogorov-Johnson-Mehl-Avrami (KJMA) theoretical model [1-3]. In the case of non-isothermal crystallization Differential Thermal Analysis (DTA) and Differential Scanning Calorimetry (DSC) have been widely used [4]. Up to now, in these studies it 1

2 is supposed that in the case of surface crystallization of glass powders the so called Avrami kinetic coefficient, m, has a value of one [4-8]. However, in our previous work, discussing isothermal crystallization [9], it is shown, that in the case of overall crystallization of ensembles of glass particles, the parameter m varies between 1 and 3 as a function of the particle size, crystal growth rate and density of active centres on the surface, N S. The larger are particles and the N S density, the lower is the m value. In fact, in large particles, a growth of needle-like crystals perpendicular to the grain surface is observed. On the other hand, in fine powders the crystals remain more or less isometric until the end crystallization process. The aim of present communication is to demonstrate that under conditions of non-isothermal heat treatment, studied by DTA, the Avrami parameter also varies between 1 and 3 as a function the particle size of the powder fraction used. SUMMARY OF BASIC EQUATIONS The kinetics of overall isothermal crystallization is usually analyzed employing the KJMA (Kolmogorov-Johnson-Mehl-Avrami) equation [1-3]: α n m ( τ ) 1 exp ( const I o U τ ) = (1) where α (τ) is the degree of transformation till time τ, I o and U are the rates of steadystate nucleation and of crystal growth, respectively, and m called Avrami parameter is the reaction order. The parameter n has different values (from 0.5 to 3) depending on the growth mechanisms and crystal shape. In the case of simultaneous nucleation and crystallization m = n+1, while when the melt contains athermal nuclei or other insoluble crystallization cores with bulk concentration N B, eq.1 transforms into: α n ( τ ) 1 exp ( const τ ) = (2). By relationships, similar to Eq.2, the kinetics of surface crystallization might also be described, assuming that the crystallization starts by a constant number N S of active centres on the particles surface [2, 9,10]. The kinetics of non-isothermal crystallization is commonly studied by DTA/DSC techniques employing a series of experiments, carried out at different heating rates, v. The activation energy of crystallization, E C, could be evaluated by the Kissinger equation [11] N B 2

3 EC RT P 2 T P = ln (3) v where T P is the temperature of the crystallization exothermal peak. The Avrami parameter m could be estimated by the Ozawa equation [12]: d [ ln( ln( 1 α ))] d( lnv) T = m (4) where the degree of transformation α is determined at a fixed temperature, T, from exothermal peaks obtained at different v. The value of α is calculated as the ratio of partial area of the crystallization peak at the temperature T to its total area. When the activation energy of crystallization is known, m can be estimated by the Augis-Bennett equation [13]: ( 2.5/ w) ( E 2 / ) m = (5) C RT P where w is the width of the crystallization exotherm at half peak height. EXPERIMENTAL A glass with composition (in mol %) SiO 2-54, Al 2 O 3-2, CaO-21, MgO-21, Na 2 O-2 was used. It forms by surface crystallization about 60 wt % diopside (CaO.MgO.2SiO 2 ) and is characterised by formation of crystallization induced pores in the centres of each glass particle [14-15]. After melting at 1500 C and water quenching the frit obtained was milled and sieved into different fractions: <26 µm, <40 µm, µm, µm and µm. About 100 mg samples of each fraction, as well as single particles with mg mass (labelled bulk samples), were heated at 5, 7.5, 10 and 20 C/min (Linseiz L81 DTA apparatus). RESULTS AND CONCLUSIONS 889 (<40 µm) 886 (<26 µm) 909 (32-40 µm) 930 ( µm) 982 ( µm) 1170 (bulk) Figure 1. DTA results at 10 C/min exo -> Temperature ( o C)

4 -11-11, µm µm <26 µm DTA traces of different glass fractions are shown in -11,4-11,6 Fig.1, whereas Fig. 2 ln[v/(t p 2 )] -11, ,2 presents the obtained Kissenger plots; the E C -12,4-12, µm <40 µm -12,8 bulk -13 0, , , , , , /(RT p) values are summarized in Table 1 together with the corresponding temperature ranges of the DTA runs. Figure 2. Kissenger plots of the fractions studied Table 1. Activation energy of crystallization vs. fractional size Fraction (µm) <26 < Bulk E C (KJ/mol) Temperatures ( o C) As seen in Fig.1, the peak temperature increases with the grain size. Therefore, the activation energy, E C is lowered. This finding is in a good agreement with the decrease of the activation energy of viscous flow with the temperature rise [15]. ln (-ln (1- a)) 1 0,5 0-0,5-1 -1,5-2 bulk Figure 3. Ozawa plots of some of the studied fractions The Ozawa plots, related to the bulk samples and -2, µm µm 1,5 1,7 1,9 2,1 2,3 2,5 2,7 2,9 3,1 ln v the fractions µm, and µm are shown in Fig. 4

5 3. Table 2 summarizes the values of Avrami parameter, obtained by the August Bennet relationship (average of the four measurements at different heating rates) and by the Ozawa method. Table 2. Values of Avrami parameter vs. fractional size Fraction (µm) August Bennet Ozawa < (at 880 o C) < (at 890 o C) (at 900 o C) (at 920 o C) (at 975 o C) Bulk (at 1040 o C) For the bulk samples and the fractions µm, and µm the Ozawa and August Bennet methods give similar m values and highlight that the reaction order rises when the decreasing of particle size. This confirms both the results of the isothermal experiments and the theory, presented in Ref. [9] and elucidates that the assumption m = 1 for surface crystallization is not always valid. At the same time, for the fractions <26 µm and <40 µm both methods (especially one of Ozawa) give lower m values than those obtained for the fraction µm. The apparent discrepancy can be explained by the higher dispersity of these two fractions, which leads to broadening of the exothermal peaks and to a lower m value. 5

6 a b Fig. 4 SEM images of fraction <40 µm: a after 2 h at 800 o C b after 1 h the 900 o C Fig. 4 shows SEM photos of samples obtained by sintering of fraction <40 µm at different stages of crystallization. The SE-SEM image, presented in Fig 4-a, demonstrates the three dimensional shape of the growing crystals during the initial stages of phase formation. At the same time, the BSE-SEM image, shown in Fig. 4-b, highlights that at final stages of crystallization the three-dimensional growth is transformed into one-dimensional: a needle-like shape of the crystals is well observed together with the crystallization induced pores, formed in the centers of the grains. ACKNOWLEDGMENTS: The authors gratefully acknowledge the financial support within Project TK-X-1713/07 (Bulgarian Ministry of Science and Education). REFERENCES 1. Z. Strnad, Glass-Ceramic Materials, Elsevier, Amsterdam (1986). 2. I. Gutzow, J. Shmelzer, The Vitreous State- Structure, Thermodynamics, Rheology and Crystallisation, Springer Verlag, Berlin, New York (1995). 3. W. Höland, G. Beall, Glass-Ceramics Technology, The American Ceramics Society, Westerville (2002). 4. C. S. Ray, D.E Day, In Nucleation and Crystallization in Liquids and Glasses, Am. Ceram. Soc. 30 (1992)

7 5. H. Chen, J. Non-Cryst. Solids 27 (1978) K. Matusita, S.Sakka, J. Non-Cryst. Solids 38 (1980) X. J. Xu, C.S. Ray, D.E. Day, J. Am. Ceram. Soc. 74 (1991) A. Marotta, S. Saiello, F. Branda, A. Buri, J. Mater. Sci. 17 (1982) I. Gutzow, R. Pascova, A. Karamanov, J. Schmelzer, J. Mater. Sci. 33 (1998) R. Müller, E.D. Zanotto, V.M. Fokin, J. Non-Cryst. Solids 274 (2000) H. Kissinger, Analytic Chemistry 29 (1957) T. Ozawa, Polymer 12 (1971) J. A. Augis, J. E. Bennett, J. Therm. Anal. 13 (1978) A. Karamanov, M.Pelino, J. Europ. Ceram. Soc. 26 (2006) A. Karamanov, M.Pelino, J. Europ. Ceram. Soc. 26 (2006)