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Variation of Avrami parameter during non-isothermal surface crystallization of glass powders with different sizes
Journal of Non-Crystalline Solids 358 (2012) 1486–1490
Contents lists available at SciVerse ScienceDirect
Journal of Non-Crystalline Solids journal homepage: www.elsevier.com/ locate/ jnoncrysol
Variation of Avrami parameter during non-isothermal surface crystallization of glass powders with different sizes Alexander Karamanov a,⁎, Isak Avramov a, Lorenzo Arrizza b, Radost Pascova a, Ivan Gutzow a a b
Institute of Physical Chemistry, Bulgarian Academy of Sciences, G. Bonchev Str. Block 11, 1113 Sofia, Bulgaria Microscopy Centrum, University of L'Aquila, 67100, Monteluco di Roio, L'Aquila, Italy
a r t i c l e
i n f o
Article history: Received 23 January 2012 Received in revised form 2 April 2012 Available online 28 April 2012 Keywords: Crystallization kinetics; Reaction order; Differential thermal analysis; Crystallization induced porosity
a b s t r a c t The influence of grain size on the surface crystallization kinetics is investigated by non-isothermal Differential Thermal Analysis and Scanning Electron Microscopy. For this purpose, different powder fractions of a model glass forming diopside via surface crystallization and crystallization induced porosity, are used. The activation energy of crystallization, EC, is determined from Kissinger plot, and the Avrami parameter, m, is estimated by both Ozawa and of Augis–Bennett methods. The values of EC decrease from 530 to 300 kJ/mol when grain size increases. Simultaneously, the m value drops from 2.5 to 1.3. This result contradicts to the widespread fallacy that the reaction order should be equal to one in the case of surface crystallization. During the initial stage of surface crystallization three dimensional growth takes place, a fact confirmed by the SEM investigations. Later on, one dimensional growth inwards the grain is observed, leading to the reaction order changes from 3 to 1. © 2012 Elsevier B.V. All rights reserved.
1. Introduction During the last 40–50 years, the crystallization kinetics of glasses under non-isothermal conditions is commonly investigated by Differential Thermal Analysis (DTA) and Differential Scanning Calorimetry (DSC) and analyzed using models, developed in the framework of the classical Kolmogorov–Johnson–Mehl–Avrami (KJMA) equation of overall crystallization [1–3]. Notwithstanding, in the case of surface crystallization of glass powders it is often assumed that the value of the so called Avrami kinetic coefficient, m, is equal to one [4–8], which means that only onedimensional growth can takes place. Actually, growth of needle-like crystals in direction perpendicular to the grain surface is observed only in some large glass particles, while in fine powders the crystals remain more or less isometric until the end of the crystallization process. In our previous work on the kinetics of isothermal surface crystallization of glass powders [9], based on the ideas of Mampel and Todes for the surface controlled phase formation [10,11], it was shown that the parameter m can vary between 1 and 3 as a function of the particle size, crystal growth rate and density of active centers on the surface, NS. The larger are the grains and/or the higher is the NS density, the lower is the m value. Later, this phenomenon was also confirmed and discussed in details by other colleagues [12–14].
⁎ Corresponding author. Tel.: + 359 2 979 2552. E-mail address: [email protected] (A. Karamanov). 0022-3093/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2012.04.003
The aim of present communication is to demonstrate that under conditions of non-isothermal surface crystallization, studied by DTA, the Avrami parameter also varies between 1 and 3 as a function the particle size of the used glass fractions. 2. Basic equations The kinetics of overall isothermal crystallization is usually analyzed employing the KJMA (Kolmogorov–Johnson–Mehl–Avrami) equation [1–3]: n m α ðτÞ ¼ 1− exp −const Io U τ
ð1Þ
where α (τ) is the degree of transformation till time τ, and Io and U are the rates of steady-state nucleation and of crystal growth, respectively. Power m is called Avrami parameter and plays role of reaction order. The parameter n has value between 0.5 and 3 depending on the growth mechanisms and on the crystal shape. In the case of simultaneous nucleation and growth m = n + 1. However, when the melt contains athermal nuclei or other insoluble crystallization cores with a bulk concentration NB Eq. (1) is transformed into: n n α ðt Þ ¼ 1− exp −const NB U t :
ð2Þ
The kinetics of surface isothermal crystallization might be described in similar way, assuming that the crystallization starts from a constant number NS of active centers on the surface [2,9,12–15].
A. Karamanov et al. / Journal of Non-Crystalline Solids 358 (2012) 1486–1490
EC T2 ¼ ln P RT P v
! ð3Þ
where TP is the temperature of the crystallization exothermal peak and v is again the heating rate. The Avrami parameter m can be estimated employing the Ozawa equation [17]: d½ lnð− lnð1−α ðTÞÞÞ ¼ −m dð lnvÞ
ð4Þ
T
from the degree α(Τ) of overall crystallization at a fixed temperature and at different heating rates v. The value of α is proportional to the partial area of the crystallization peak till the temperature T. An alternative way to determine m is given by the Augis–Bennett equation [18]: ð2:5=ΔwÞ m¼ EC =RT P 2
ð5Þ
where Δw is the width of the crystallization exotherm at half peak height. 3. Experimental A model glass with composition (in mol%) SiO2-54, Al2O3-2, CaO21, MgO-21, and Na2O-2 is used. This glass is characterized by surface crystallization of ~ 60 wt.% diopside (CaO·MgO·2SiO2) and by formation of 8–10 vol.% crystallization induced porosity, PCR [19,20]. This additional porosity is a consequence of the significant density difference between the parent glass and the newly formed crystal phase and of the huge increase of apparent viscosity due to the crystallization. Recently, several experimental results [21–25] and theoretical approaches [26,27] related to the phenomenon of PCR formation were published. The crystallization induced pores in the studied composition are formed in the centers of each grain and their diameter is about 0.4– 0.5 of the grain's diameter. This means that the pore creation decreases the length of crystal front at about two times and in this way significantly reduces the time for overall crystallization. After melting at 1500 °C and water quenching the obtained frits were milled and sieved into different fractions with grain sizes of 32–40 μm, 75–125 μm and 850–1180 μm. About 100 mg samples of each fraction, as well as single particles with the same mass (labeled as bulk samples), were heated at 5, 7.5, 10 and 20 K/min (Linseiz L81 DTA instrument). “Green” samples with initial size of 7/10/10 mm were prepared by mixing glass powders (fractions 75–175 μm and fraction b 40 μm) with PVA solution and pressing at 100 MPa. After drying and a 30 min heat-treatment at 270 °C (to eliminate the PVA), the samples were sintered at 800 and 900 °C using heating and cooling rates of 20 °C/min. Scanning electron microscopy investigations (Philips XL30CP) were performed using freshly fractured or polished sintered samples. Some of the samples were treated with 2% HF solution for 3 s, while others were directly studied without employment of etching procedure. The fractured samples were observed by SE technique after metallization with gold, while the polished ones were investigated by BSE technique (without metallization and at controlled vacuum of 0.5 mBar).
4. Results DTA curves, obtained with the finer fraction (between 32 and 40 μm) and with the bulk samples, are presented in Fig. 1. The results show a significant temperature shift (of about 150 °C) of the exoeffects between these two series, which is typical at surface crystallization. The figure also highlights a remarkably change in the crystallization peak shape: the exotherms of fine fraction are significantly sharper, which clearly indicates a higher value of the Avrami parameter in this case. The activation energies of crystallization EC were determined according to Eq. (3) from the dependences ν/Tp2 vs. 1/Tp, using the data obtained at different heating rates (see Fig. 2). The values of activation energies EC are summarized in Table 1 together with the temperature ranges in which they were determined. It is seen that the larger are the grains the higher are the peak temperatures and the lower is the activation energy. This finding is in agreement with the decrease of activation energy of viscous flow with the temperature rise [20]. The Ozawa plots of the studied fractions are shown in Fig. 3. The values of the Avrami parameter, determined from the slopes of corresponding ln(1 − (1 − α)) − lnν dependences, are reported in Table 2, together with the ones obtained using the August–Bennet equation. In the last case each data is an average of the four measurements, carried out at every heating rate used. Fig. 4a to c shows SE-SEM images of a fractured sample, obtained using glass powder fraction with grain sizes in the range of 75–125 μm after 2 h heat-treatment at 800 °C. Well sintered grains with thin front of initial surface crystallization and some residual intergranular pores are shown in Fig. 4a. Images at higher magnification (Figs. 4b and c) highlight the morphology of the surface crystallization fronts between two sintered glass particles and around a residual pore, respectively. It is well seen that all individual crystals of the crystal fronts have nearly isometric three dimensional shapes and sizes of about 2–4 μm. Fig. 5 shows BSE-SEM images, obtained after completed sintercrystallization at 900 °C. Photos in Figs. 5a and b are obtained from
exo =>
Usually, the kinetics of non-isothermal crystallization is studied by DTA/DSC methods employing a series of experiments, carried out at different heating rates v. The activation energy of crystallization, EC, is evaluated by the classical Kissinger equation [16]:
1487
20oC/min
10oC/min
7.5oC/min
5oC/min 700
fraction 32-40 μm 800
900
bulk samples 1000
1100
Temperature ( oC) Fig. 1. DTA results of fraction 32–40 μm and bulk samples at heating rates of 5, 7.5, 10 and 20 K/min.
1488
A. Karamanov et al. / Journal of Non-Crystalline Solids 358 (2012) 1486–1490
-11.0
Table 2 Values of Avrami parameter vs. fractional size.
32-40 μm 850-1180 μm
97
6
ln ( ν / T2p )
5 2 0.99 R=
9 2 0. R=
9 2 0. R=
-12.0
6 2 0.98 R=
-11.5
Fraction (μm)
August–Bennet
Ozawa
32–40 75–125 850–1180 Bulk
2.54 ± 0.08 1.83 ± 0.05 1.64 ± 0.11 1.35 ± 0.09
2.48 ± 0.12 1.79 ± 0.08 1.68 ± 0.09 1.34 ± 0.04
(at (at (at (at
900 °C) 920 °C) 975 °C) 1040 °C)
-12.5 75-125 μm
bulk
-13.0
9.0
9.5
10.5
10.0
105 / RTp Fig. 2. Kissenger plots of the studied glass powder fractions.
analysis of the surface crystallization under isothermal conditions and demonstrates that the assumption for m = 1 at non-isothermal surface crystallization is not always valid. Practically, in the initial stage of each surface crystallization the crystals grow three dimensionally, 3D, till the formation of a hardcore because of crystals impinge. Then, after a short intermediate stage,
a
Table 1 Activation energy of crystallization vs. fractional size (μm). Fraction (μm)
32–40
75–125
850–1180
Bulk (~3500)
EC (kJ/mol) Temperatures (°C)
509 ± 34 892–922
485 ± 19 915–948
349 ± 10 960–1009
296 ± 32 1034–1096
etched samples, using fractions 75–175 μm and below 40 μm, respectively. Photo in Fig. 5c is taken from sample from fraction below 40 μm without chemical treatment. In all images the individual sintered grains are traced with a white dashed line. In the sample with larger grains (Fig. 5a) dendrite-like diopside crystals with sizes of 20–25 μm, growing perpendicular to the surfaces, are well evidenced as well as a part of a typical intragranular crystallization induced pore with diameter of about 40 μm. Image in Fig. 5b demonstrates a smaller grain, where the crystal size is about 5–10 μm and the crystallization pore is ~ 10 μm. Photo in Fig. 5c shows a particle with a diameter less than 10 μm, where the formed crystals are practically three dimensional (with size of 2–4 μm) and the tiny crystallization induced pore has an irregular shape.
b
5. Discussion The SEM images highlight that in the initial stage of crystal growth as well as in the fine particles the crystals are three dimensional, while with the progress of the phase formation in the larger particles dendrite growth with a significant anisotropy takes place. In the same time, both methods for evaluation of the Avrami parameter give very similar m values and demonstrate that the reaction order rises when the particle size decreases. This finding is in coincidence with the results of experimental investigations and theoretical
c
1 32-40 μm 75-125 μm 850-1180 μm bulk
ln(-ln(1- α))
0
-1
-2
-3 1.5
2.0
2.5
3.0
ln ν Fig. 3. Ozawa plots of the studied fractions.
Fig. 4. SE-SEM images taken from the fractured surface of a sample, sintered at 800 °C for 2 h.
A. Karamanov et al. / Journal of Non-Crystalline Solids 358 (2012) 1486–1490
a
1489
percentage of crystallization induced porosity (at fixed particle size and NS) higher is the “average” m value. In glasses forming diopside, where the density difference between glassy and crystal state is extremely high (~16 vol.%), the phenomenon of PCR formation is well presented. The relative amount of 3D crystals can be estimated by the following simple relationship:
R3 −ðR−hÞ3 X ¼ 100 R3 −r 3
b
c
ð6Þ
where X is the percentage of 3D crystals in vol.%, R is particle radius, h is the thickness of formed hardcore layer of 3D crystals and r is the radius of crystallization induced pore. Fig. 6 shows X vs. R dependences, calculated by Eq. (6), using three different values for h (2, 4 and 6 μm) in the case when no crystallization induced porosity is formed. At particles with radius R of 8–10 μm the amount of 3D crystals is predominant even at a very thin hardcore layer of 2 μm, while at h of 6 μm 50% of the crystals are threedimensional even at R of 30 μm. A similar approach was already published and discussed by Ferreira et al. [14]. Fig. 7 presents the percentage of 3D crystals as a function of R at 3D layer with a thickness of 4 μm and r/R ratios of 0.3, 0.4 and 0.5 (corresponding to 2.7, 6.4 and 12.5 vol.% crystallization induced porosity, respectively). The figure demonstrates that at small percentage of crystallization induced porosity the variation of m is insignificant, while in glasses with 8–10% PCR (as in the case of the studied composition) a considerable increase of the average Avrami parameter can be expected. It is also evident that the effect is stronger in the finer glass fractions. 6. Conclusion
Fig. 5. BSE-SEM images of polished samples, heat-treated at 900 °C for 1 h.
Non-isothermal kinetic studies with different fractions of model glass, forming diopside by surface crystallization, are performed. It is shown that the Avrami parameter, m, increases with the decrease of the particle size, reaching m value of 2.5 at a fraction of 32–40 μm. This demonstrates that the widely used assumption for m = 1 at non-isothermal surface crystallization is not always valid. SEM observations elucidate that in the beginning of phase formation and in the fine particles the growth of the crystals is threedimensional, while in the larger particles dendrite-like crystals with a significant anisotropy are formed. It is also highlighted that the formation of crystallization induced porosity additionally increases the effective value of Avrami parameter in the finer fractions. 100 90 80 70
X3D (vol%)
the crystal growth becomes nearly one dimensional, 1D. When the number of active centers on the surface, NS, is small the 3D crystals become relatively large and an important degree of crystallization proceeds at m ~ 3. The smaller is the particle, the stronger is this effect and higher is the average m value. The thickness, h, at which the crystalline hardcore is formed depends on the surface concentration, c, of active centers NS per 1 μm 2 (i.e. h ~ c − 0.5). For large grains, the amount of material in the firstly formed 3D crystalline core is small, so that m tends to 1. On the other hand, when the grain radius is comparable to h, the crystallization process takes part predominantly three-dimensionally and the subsequent one-dimensional crystal growth has negligible role for the average m value. In the cases, when crystallization induced porosity is created, the relative part of crystal phase, formed at m ~ 1 decreases, which additionally raises the effective value of Avrami parameter. Higher is the
60 50 h=6 μ m
40
h=4 μ m
30
h=2 μ m
20 10 0
0
10
20
30
40
50
60
70
80
90
100
R (μm) Fig. 6. Variations of vol.% 3D crystals (X) versus particle radius (R) at different thickness h of 2, 4 and 6 μm and in absence of crystallization induced porosity (r = 0).
1490
A. Karamanov et al. / Journal of Non-Crystalline Solids 358 (2012) 1486–1490
100 h=4 μ m
90 80
X3D (vol %)
r=0.5R
70
r=0.4R r=0.3R
60 50 40 30 20
0
5
10
15
20
25
30
35
40
45
50
R (μm) Fig. 7. Variations of percentage of 3D crystals (X) (in vol.%) versus particle radius (R) at h of 4 μm and r/R ratios of 0.3, 0.4 and 0.5.
Acknowledgments The authors gratefully acknowledge the financial support within Project DID 02-40 (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) 207–224. [5] H. Chen, J. Non-Cryst. Solids 27 (1978) 257–263. [6] K. Matusita, S. Sakka, J. Non-Cryst. Solids 38 (1980) 741–745. [7] X.J. Xu, C.S. Ray, D.E. Day, J. Am. Ceram. Soc. 74 (1991) 909–914. [8] A. Marotta, S. Saiello, F. Branda, A. Buri, J. Mater. Sci. 17 (1982) 105–108. [9] I. Gutzow, R. Pascova, A. Karamanov, J. Schmelzer, J. Mater. Sci. 33 (1998) 5265–5273. [10] K. Mampel, Z. Phys. Chem. Abt. A 187 (43) (1940) 225. [11] K.M. Todes, Zh. Fiz. Khim. (USSR) 14 (1940) 1224. [12] J. Vazquez, D. Garciıa, G. Barreda, P.L. Lopez-Alemany, P. Villares, R. JimenezGaray, Thermochim. Acta 430 (2005) 173. [13] E.B. Ferreira, M.L.F. Nascimento, H. Stoppa, E.D. Zanotto, Phys. Chem. Glasses 49 (2008) 81. [14] E.B. Ferreira, V. Lopez-Richard, E.D. Zanotto, G.E. Marques, J. Am. Ceram. Soc. 92 (2009) 2616. [15] R. Müller, E.D. Zanotto, V.M. Fokin, J. Non-Cryst. Solids 274 (2000) 208–231. [16] H. Kissinger, Anal. Chem. 29 (1957) 1702–1706. [17] T. Ozawa, Polymer 12 (1971) 150–158. [18] J.A. Augis, J.E. Bennett, J. Therm. Anal. 13 (1978) 283–292. [19] A. Karamanov, M. Pelino, J. Eur. Ceram. Soc. 26 (2006) 2511–2517. [20] A. Karamanov, M. Pelino, J. Eur. Ceram. Soc. 26 (2006) 2519–2526. [21] H. Yang, C. Chen, H. Sun, H. Lu, X. Hu, J. Mater. Process. Technol. 197 (2008) 206. [22] A. Goel, R.R. Rajagopal, J.M.F. Ferreira, Acta Biomater. 7 (2011) 4071. [23] E. Bernardo, R. Dal Maschio, Waste Manage. 31 (2011) 2245. [24] W.Y. Zhang, H. Gaoa, Y. Xub, J. Eur. Ceram. Soc. 31 (2011) 1669. [25] L.M. Schabbach, F. Andreola, E. Karamanova, I. Lancellotti, A. Karamanov, L. Barbieri, J. Non-Cryst. Solids 357 (2011) 10. [26] A. Karamanov, I. Georgieva, R. Pascova, I. Avramov, J. Non-Cryst. Solids 356 (2010) 117. [27] A.S. Abyzova, J.W.P. Schmelzer, V.M. Fokin, J. Non-Cryst. Solids 357 (2011) 3474.
Contents lists available at SciVerse ScienceDirect
Journal of Non-Crystalline Solids journal homepage: www.elsevier.com/ locate/ jnoncrysol
Variation of Avrami parameter during non-isothermal surface crystallization of glass powders with different sizes Alexander Karamanov a,⁎, Isak Avramov a, Lorenzo Arrizza b, Radost Pascova a, Ivan Gutzow a a b
Institute of Physical Chemistry, Bulgarian Academy of Sciences, G. Bonchev Str. Block 11, 1113 Sofia, Bulgaria Microscopy Centrum, University of L'Aquila, 67100, Monteluco di Roio, L'Aquila, Italy
a r t i c l e
i n f o
Article history: Received 23 January 2012 Received in revised form 2 April 2012 Available online 28 April 2012 Keywords: Crystallization kinetics; Reaction order; Differential thermal analysis; Crystallization induced porosity
a b s t r a c t The influence of grain size on the surface crystallization kinetics is investigated by non-isothermal Differential Thermal Analysis and Scanning Electron Microscopy. For this purpose, different powder fractions of a model glass forming diopside via surface crystallization and crystallization induced porosity, are used. The activation energy of crystallization, EC, is determined from Kissinger plot, and the Avrami parameter, m, is estimated by both Ozawa and of Augis–Bennett methods. The values of EC decrease from 530 to 300 kJ/mol when grain size increases. Simultaneously, the m value drops from 2.5 to 1.3. This result contradicts to the widespread fallacy that the reaction order should be equal to one in the case of surface crystallization. During the initial stage of surface crystallization three dimensional growth takes place, a fact confirmed by the SEM investigations. Later on, one dimensional growth inwards the grain is observed, leading to the reaction order changes from 3 to 1. © 2012 Elsevier B.V. All rights reserved.
1. Introduction During the last 40–50 years, the crystallization kinetics of glasses under non-isothermal conditions is commonly investigated by Differential Thermal Analysis (DTA) and Differential Scanning Calorimetry (DSC) and analyzed using models, developed in the framework of the classical Kolmogorov–Johnson–Mehl–Avrami (KJMA) equation of overall crystallization [1–3]. Notwithstanding, in the case of surface crystallization of glass powders it is often assumed that the value of the so called Avrami kinetic coefficient, m, is equal to one [4–8], which means that only onedimensional growth can takes place. Actually, growth of needle-like crystals in direction perpendicular to the grain surface is observed only in some large glass particles, while in fine powders the crystals remain more or less isometric until the end of the crystallization process. In our previous work on the kinetics of isothermal surface crystallization of glass powders [9], based on the ideas of Mampel and Todes for the surface controlled phase formation [10,11], it was shown that the parameter m can vary between 1 and 3 as a function of the particle size, crystal growth rate and density of active centers on the surface, NS. The larger are the grains and/or the higher is the NS density, the lower is the m value. Later, this phenomenon was also confirmed and discussed in details by other colleagues [12–14].
⁎ Corresponding author. Tel.: + 359 2 979 2552. E-mail address: [email protected] (A. Karamanov). 0022-3093/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2012.04.003
The aim of present communication is to demonstrate that under conditions of non-isothermal surface crystallization, studied by DTA, the Avrami parameter also varies between 1 and 3 as a function the particle size of the used glass fractions. 2. Basic equations The kinetics of overall isothermal crystallization is usually analyzed employing the KJMA (Kolmogorov–Johnson–Mehl–Avrami) equation [1–3]: n m α ðτÞ ¼ 1− exp −const Io U τ
ð1Þ
where α (τ) is the degree of transformation till time τ, and Io and U are the rates of steady-state nucleation and of crystal growth, respectively. Power m is called Avrami parameter and plays role of reaction order. The parameter n has value between 0.5 and 3 depending on the growth mechanisms and on the crystal shape. In the case of simultaneous nucleation and growth m = n + 1. However, when the melt contains athermal nuclei or other insoluble crystallization cores with a bulk concentration NB Eq. (1) is transformed into: n n α ðt Þ ¼ 1− exp −const NB U t :
ð2Þ
The kinetics of surface isothermal crystallization might be described in similar way, assuming that the crystallization starts from a constant number NS of active centers on the surface [2,9,12–15].
A. Karamanov et al. / Journal of Non-Crystalline Solids 358 (2012) 1486–1490
EC T2 ¼ ln P RT P v
! ð3Þ
where TP is the temperature of the crystallization exothermal peak and v is again the heating rate. The Avrami parameter m can be estimated employing the Ozawa equation [17]: d½ lnð− lnð1−α ðTÞÞÞ ¼ −m dð lnvÞ
ð4Þ
T
from the degree α(Τ) of overall crystallization at a fixed temperature and at different heating rates v. The value of α is proportional to the partial area of the crystallization peak till the temperature T. An alternative way to determine m is given by the Augis–Bennett equation [18]: ð2:5=ΔwÞ m¼ EC =RT P 2
ð5Þ
where Δw is the width of the crystallization exotherm at half peak height. 3. Experimental A model glass with composition (in mol%) SiO2-54, Al2O3-2, CaO21, MgO-21, and Na2O-2 is used. This glass is characterized by surface crystallization of ~ 60 wt.% diopside (CaO·MgO·2SiO2) and by formation of 8–10 vol.% crystallization induced porosity, PCR [19,20]. This additional porosity is a consequence of the significant density difference between the parent glass and the newly formed crystal phase and of the huge increase of apparent viscosity due to the crystallization. Recently, several experimental results [21–25] and theoretical approaches [26,27] related to the phenomenon of PCR formation were published. The crystallization induced pores in the studied composition are formed in the centers of each grain and their diameter is about 0.4– 0.5 of the grain's diameter. This means that the pore creation decreases the length of crystal front at about two times and in this way significantly reduces the time for overall crystallization. After melting at 1500 °C and water quenching the obtained frits were milled and sieved into different fractions with grain sizes of 32–40 μm, 75–125 μm and 850–1180 μm. About 100 mg samples of each fraction, as well as single particles with the same mass (labeled as bulk samples), were heated at 5, 7.5, 10 and 20 K/min (Linseiz L81 DTA instrument). “Green” samples with initial size of 7/10/10 mm were prepared by mixing glass powders (fractions 75–175 μm and fraction b 40 μm) with PVA solution and pressing at 100 MPa. After drying and a 30 min heat-treatment at 270 °C (to eliminate the PVA), the samples were sintered at 800 and 900 °C using heating and cooling rates of 20 °C/min. Scanning electron microscopy investigations (Philips XL30CP) were performed using freshly fractured or polished sintered samples. Some of the samples were treated with 2% HF solution for 3 s, while others were directly studied without employment of etching procedure. The fractured samples were observed by SE technique after metallization with gold, while the polished ones were investigated by BSE technique (without metallization and at controlled vacuum of 0.5 mBar).
4. Results DTA curves, obtained with the finer fraction (between 32 and 40 μm) and with the bulk samples, are presented in Fig. 1. The results show a significant temperature shift (of about 150 °C) of the exoeffects between these two series, which is typical at surface crystallization. The figure also highlights a remarkably change in the crystallization peak shape: the exotherms of fine fraction are significantly sharper, which clearly indicates a higher value of the Avrami parameter in this case. The activation energies of crystallization EC were determined according to Eq. (3) from the dependences ν/Tp2 vs. 1/Tp, using the data obtained at different heating rates (see Fig. 2). The values of activation energies EC are summarized in Table 1 together with the temperature ranges in which they were determined. It is seen that the larger are the grains the higher are the peak temperatures and the lower is the activation energy. This finding is in agreement with the decrease of activation energy of viscous flow with the temperature rise [20]. The Ozawa plots of the studied fractions are shown in Fig. 3. The values of the Avrami parameter, determined from the slopes of corresponding ln(1 − (1 − α)) − lnν dependences, are reported in Table 2, together with the ones obtained using the August–Bennet equation. In the last case each data is an average of the four measurements, carried out at every heating rate used. Fig. 4a to c shows SE-SEM images of a fractured sample, obtained using glass powder fraction with grain sizes in the range of 75–125 μm after 2 h heat-treatment at 800 °C. Well sintered grains with thin front of initial surface crystallization and some residual intergranular pores are shown in Fig. 4a. Images at higher magnification (Figs. 4b and c) highlight the morphology of the surface crystallization fronts between two sintered glass particles and around a residual pore, respectively. It is well seen that all individual crystals of the crystal fronts have nearly isometric three dimensional shapes and sizes of about 2–4 μm. Fig. 5 shows BSE-SEM images, obtained after completed sintercrystallization at 900 °C. Photos in Figs. 5a and b are obtained from
exo =>
Usually, the kinetics of non-isothermal crystallization is studied by DTA/DSC methods employing a series of experiments, carried out at different heating rates v. The activation energy of crystallization, EC, is evaluated by the classical Kissinger equation [16]:
1487
20oC/min
10oC/min
7.5oC/min
5oC/min 700
fraction 32-40 μm 800
900
bulk samples 1000
1100
Temperature ( oC) Fig. 1. DTA results of fraction 32–40 μm and bulk samples at heating rates of 5, 7.5, 10 and 20 K/min.
1488
A. Karamanov et al. / Journal of Non-Crystalline Solids 358 (2012) 1486–1490
-11.0
Table 2 Values of Avrami parameter vs. fractional size.
32-40 μm 850-1180 μm
97
6
ln ( ν / T2p )
5 2 0.99 R=
9 2 0. R=
9 2 0. R=
-12.0
6 2 0.98 R=
-11.5
Fraction (μm)
August–Bennet
Ozawa
32–40 75–125 850–1180 Bulk
2.54 ± 0.08 1.83 ± 0.05 1.64 ± 0.11 1.35 ± 0.09
2.48 ± 0.12 1.79 ± 0.08 1.68 ± 0.09 1.34 ± 0.04
(at (at (at (at
900 °C) 920 °C) 975 °C) 1040 °C)
-12.5 75-125 μm
bulk
-13.0
9.0
9.5
10.5
10.0
105 / RTp Fig. 2. Kissenger plots of the studied glass powder fractions.
analysis of the surface crystallization under isothermal conditions and demonstrates that the assumption for m = 1 at non-isothermal surface crystallization is not always valid. Practically, in the initial stage of each surface crystallization the crystals grow three dimensionally, 3D, till the formation of a hardcore because of crystals impinge. Then, after a short intermediate stage,
a
Table 1 Activation energy of crystallization vs. fractional size (μm). Fraction (μm)
32–40
75–125
850–1180
Bulk (~3500)
EC (kJ/mol) Temperatures (°C)
509 ± 34 892–922
485 ± 19 915–948
349 ± 10 960–1009
296 ± 32 1034–1096
etched samples, using fractions 75–175 μm and below 40 μm, respectively. Photo in Fig. 5c is taken from sample from fraction below 40 μm without chemical treatment. In all images the individual sintered grains are traced with a white dashed line. In the sample with larger grains (Fig. 5a) dendrite-like diopside crystals with sizes of 20–25 μm, growing perpendicular to the surfaces, are well evidenced as well as a part of a typical intragranular crystallization induced pore with diameter of about 40 μm. Image in Fig. 5b demonstrates a smaller grain, where the crystal size is about 5–10 μm and the crystallization pore is ~ 10 μm. Photo in Fig. 5c shows a particle with a diameter less than 10 μm, where the formed crystals are practically three dimensional (with size of 2–4 μm) and the tiny crystallization induced pore has an irregular shape.
b
5. Discussion The SEM images highlight that in the initial stage of crystal growth as well as in the fine particles the crystals are three dimensional, while with the progress of the phase formation in the larger particles dendrite growth with a significant anisotropy takes place. In the same time, both methods for evaluation of the Avrami parameter give very similar m values and demonstrate that the reaction order rises when the particle size decreases. This finding is in coincidence with the results of experimental investigations and theoretical
c
1 32-40 μm 75-125 μm 850-1180 μm bulk
ln(-ln(1- α))
0
-1
-2
-3 1.5
2.0
2.5
3.0
ln ν Fig. 3. Ozawa plots of the studied fractions.
Fig. 4. SE-SEM images taken from the fractured surface of a sample, sintered at 800 °C for 2 h.
A. Karamanov et al. / Journal of Non-Crystalline Solids 358 (2012) 1486–1490
a
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percentage of crystallization induced porosity (at fixed particle size and NS) higher is the “average” m value. In glasses forming diopside, where the density difference between glassy and crystal state is extremely high (~16 vol.%), the phenomenon of PCR formation is well presented. The relative amount of 3D crystals can be estimated by the following simple relationship:
R3 −ðR−hÞ3 X ¼ 100 R3 −r 3
b
c
ð6Þ
where X is the percentage of 3D crystals in vol.%, R is particle radius, h is the thickness of formed hardcore layer of 3D crystals and r is the radius of crystallization induced pore. Fig. 6 shows X vs. R dependences, calculated by Eq. (6), using three different values for h (2, 4 and 6 μm) in the case when no crystallization induced porosity is formed. At particles with radius R of 8–10 μm the amount of 3D crystals is predominant even at a very thin hardcore layer of 2 μm, while at h of 6 μm 50% of the crystals are threedimensional even at R of 30 μm. A similar approach was already published and discussed by Ferreira et al. [14]. Fig. 7 presents the percentage of 3D crystals as a function of R at 3D layer with a thickness of 4 μm and r/R ratios of 0.3, 0.4 and 0.5 (corresponding to 2.7, 6.4 and 12.5 vol.% crystallization induced porosity, respectively). The figure demonstrates that at small percentage of crystallization induced porosity the variation of m is insignificant, while in glasses with 8–10% PCR (as in the case of the studied composition) a considerable increase of the average Avrami parameter can be expected. It is also evident that the effect is stronger in the finer glass fractions. 6. Conclusion
Fig. 5. BSE-SEM images of polished samples, heat-treated at 900 °C for 1 h.
Non-isothermal kinetic studies with different fractions of model glass, forming diopside by surface crystallization, are performed. It is shown that the Avrami parameter, m, increases with the decrease of the particle size, reaching m value of 2.5 at a fraction of 32–40 μm. This demonstrates that the widely used assumption for m = 1 at non-isothermal surface crystallization is not always valid. SEM observations elucidate that in the beginning of phase formation and in the fine particles the growth of the crystals is threedimensional, while in the larger particles dendrite-like crystals with a significant anisotropy are formed. It is also highlighted that the formation of crystallization induced porosity additionally increases the effective value of Avrami parameter in the finer fractions. 100 90 80 70
X3D (vol%)
the crystal growth becomes nearly one dimensional, 1D. When the number of active centers on the surface, NS, is small the 3D crystals become relatively large and an important degree of crystallization proceeds at m ~ 3. The smaller is the particle, the stronger is this effect and higher is the average m value. The thickness, h, at which the crystalline hardcore is formed depends on the surface concentration, c, of active centers NS per 1 μm 2 (i.e. h ~ c − 0.5). For large grains, the amount of material in the firstly formed 3D crystalline core is small, so that m tends to 1. On the other hand, when the grain radius is comparable to h, the crystallization process takes part predominantly three-dimensionally and the subsequent one-dimensional crystal growth has negligible role for the average m value. In the cases, when crystallization induced porosity is created, the relative part of crystal phase, formed at m ~ 1 decreases, which additionally raises the effective value of Avrami parameter. Higher is the
60 50 h=6 μ m
40
h=4 μ m
30
h=2 μ m
20 10 0
0
10
20
30
40
50
60
70
80
90
100
R (μm) Fig. 6. Variations of vol.% 3D crystals (X) versus particle radius (R) at different thickness h of 2, 4 and 6 μm and in absence of crystallization induced porosity (r = 0).
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A. Karamanov et al. / Journal of Non-Crystalline Solids 358 (2012) 1486–1490
100 h=4 μ m
90 80
X3D (vol %)
r=0.5R
70
r=0.4R r=0.3R
60 50 40 30 20
0
5
10
15
20
25
30
35
40
45
50
R (μm) Fig. 7. Variations of percentage of 3D crystals (X) (in vol.%) versus particle radius (R) at h of 4 μm and r/R ratios of 0.3, 0.4 and 0.5.
Acknowledgments The authors gratefully acknowledge the financial support within Project DID 02-40 (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.
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