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Crystallization behaviour of glass-ceramic sealant for solid oxide fuel cells
Materials Letters 141 (2015) 284–287
Contents lists available at ScienceDirect
Materials Letters journal homepage: www.elsevier.com/locate/matlet
Crystallization behaviour of glass-ceramic sealant for solid oxide fuel cells A.G. Sabato, M. Salvo, A. De Miranda,, F. Smeacetto n Department of Applied Science and Technology, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
art ic l e i nf o
a b s t r a c t
Article history: Received 12 September 2014 Accepted 22 November 2014 Available online 2 December 2014
The crystallization behaviour of a glass-ceramic suitable as SOFCs sealant has been investigated using differential thermal analysis (DTA). Glass powders of two different particle sizes ( o 38 mm and 38–75 mm) have been considered. The exothermic peak in DTA thermographs has been associated with the crystallization of the diopside phase, as revealed by X-ray diffraction analysis (XRD). Avrami exponents (n) have been calculated for both particle sizes using the Ozawa equation, while Matusita and Sakka equation has been used to calculate the activation energy for the crystallization (Ec). The values found for n are 2.6 ( o 38 mm) and 2.1 (38–75 mm). The obtained values for Ec are 403 kJ/mol and 262 kJ/ mol for the finest and the coarsest glass powders, respectively. As a comparison, the activation energies for the viscous flow (Eη) have been also evaluated: 349 kJ/mol for powders sized o38 mm and 265 kJ/mol for those sized 38–75 mm. & 2014 Elsevier B.V. All rights reserved.
Keywords: Glass-ceramic Sealant Differential thermal analysis
1. Introduction In the modern challenge to developing a competitive way to produce “clean” energy, solid oxide fuel cells (SOFCs) can occupy a decisive role. SOFCs are devices able to convert chemical energy into electrical energy by red-ox reactions between a fuel and an oxidant. In order to obtain a satisfying output power it is necessary to build a SOFC stack [1,2]. Some of the stack elements (i.e. metallic interconnect and ceramic cell) are joined by a sealant. Recently many studies have pointed out glass-ceramic sealants among the most promising materials for this application [3–8]. This is mainly due to the possibility of tailoring their proprieties by changing their composition or thermal treatments. Glass-ceramics are materials in which a residual glass phase and a crystalline phase deriving from a devitrification process coexist together. In general, they have superior mechanical proprieties compared to their parent glasses. A reliable glass-ceramic sealant for SOFCs should have an excellent gas tightness, a high resistance to relevant SOFC operating conditions (i.e. reducing and oxidizing atmospheres) and a thermal expansion coefficient (TEC) as much as possible closest to that of materials to which they are in contact with [4]. The activation energy for the crystallization and the Avrami exponent (n) are the most important parameters in order to evaluate the crystallisation mechanism of glass-ceramic materials. They can be obtained from differential thermal analysis (DTA)
n
Corresponding author. E-mail address: [email protected] (F. Smeacetto).
http://dx.doi.org/10.1016/j.matlet.2014.11.128 0167-577X/& 2014 Elsevier B.V. All rights reserved.
conducted at different heating rates. Many studies have been carried out on different glass systems (also for different applications) in order to evaluate these parameters and how they could affect the crystallization mechanisms [9–13]. A better understanding of these factors, including the effect of the mean particle size on crystallization kinetics, could lead to improved knowledge in varying glass-ceramic properties. In this study, Kissinger [9], Matusita and Sakka [5] and Ozawa [10] equations were used to determine the crystallization mechanism and the activation energy values for the crystallization of a glass-ceramic composition designed and preliminary tested as SOFC sealant elsewhere [14].
2. Experimental The composition of the glass in wt% was: 54.39% SiO2, 13.78% Na2O, 9.02 CaO, 8.37% MgO, 11.26% Al2O3, 1.67% K2O, 0.9% B2O3 and 0.61% Y2O3. This glass was labelled as KMBY. The sealant was produced as glass by melting the appropriate oxides and carbonates raw materials in different proportions (as reported above) and by heating at 1500 1C for 1 h in a platinum-rhodium crucible. The melt was cast on a brass plate and the transparent glass was ground for differential thermal analysis. The resulting powders were sieved, obtaining two different particle sizes: o38 mm and 38–75 mm. DTA analyses (Netzsch DTA 404 PC) have been carried out on both particle sizes, using Al2O3 as reference, at different heating rates (10 1C/min, 20 1C/min, 40 1C/min) from room
A.G. Sabato et al. / Materials Letters 141 (2015) 284–287
temperature to 1200 1C. The distribution of sizes (vol % vs particle diameter) has been obtained by a particle size analyser (LS230, Coulter Corporation, USA) on two different particle sizes (o 38 μm and 38–75 μm respectively). SEM (JEOL 5700) and EDS analyses have been carried out on the KMBY glass-ceramic obtained after sintering at 850 1C for 30 min in air atmosphere. The sintering behaviour (shrinkage %) has been determined by heating stage microscopy (Expert System Solutions, Italy) at heating rate of 20 1C/min.
3. Results and discussion The DTA thermographs of the KMBY powder (o38 mm) are reported in Fig. 1, together with the glass transition temperature (Tg). The DTA analyses of the glass powder (size o38 mm and 38–75 mm) show that the crystallization peak (Tp) shifts to higher values with increasing the heating rate. In a previous study [14] we observed that the crystallization peak is also affected by the particle size; the peak shifted to lower temperatures with decreasing particle size, suggesting an effect associated with the surface nucleation of the glass. According to XRD analyses, Ca0.89Mg1.11Si2O6 (diopside) was found as the dominant crystalline phase, potassium containing nepheline (Na3K (Al0.44Si0.56)8O16) and traces of akermanite (Ca2MgSi2O7) were also detected, as reported in reference [14], after a heat treatment at 850 1C for 30 min; the shaped DTA exothermic crystallization peak can be assigned to the diopside. The activation energy for crystallisation, related to Tp can be estimated by the Kissinger equation (Eq. (1)) [15]: ! α E Ln 2 ¼ ck þ constant ð1Þ RT p Tp
285
the activation energy for the crystallization; n and m parameters have to be calculated in order to obtain the value of Ec. The Avrami coefficient can be derived from the Ozawa equation (Eq. (3)) [18], d ln ln 1 χ ð3Þ n ¼ dðlnαÞ T where χ is the volume fraction of crystallized phase at a fixed temperature T. χ was evaluated from the exothermic peak in the DTA thermographs and was calculated as the ratio between the partial area under the peak (at a chosen temperature) and the total area of the peak. The Ozawa plots ln(-ln(1 χ)) versus lnα, at different temperatures (930 1C, 940 1C, 950 1C, 970 1C) for KMBYo38 μm are reported in Fig. 2. The value of n has been calculated as the mean value of the slopes of the plots and it was found to be 2.6, while for KMBY powders size 38o mmo 75 the n value was 2.1 (graph not reported here). Assuming that the number of nuclei is not constant with the heating rate, n and m are related to each other through the relation m¼n 1 [9–11,19]. Values of m for the finest and the coarsest powders are 1.6 and 1.1, respectively, suggesting a bulk crystallization with dimensionality of crystal growth between 1 (i.e. rod like) and 2 (i.e. plate like) [11,17,20]. Fig. 3 shows the particle size distribution of the two different particle sizes batches used for the study (o 38 mm and 38–75 mm). The average size for particles sieved ato38 μm was found to be 21 μm while the average size for the powder in the 38–75 μm range was 51 μm. In Table 1, kinetics parameters, activation energies for crystallization (Eck and Ec), activation energy for viscous flow (Eη) and sintering behaviour (shrinkage %) for two different sizes of KMBY powders are reported. In case of surface crystallization opposite results would be expected, since the lower the particle size the greater is the tendency to devitrification by growth from surface nuclei, thus leading to the
where α is the heating rate, R is the gas constant and Eck is the value of activation energy obtained by this method. The value of Eck can be deduced from the linear plot between Ln(α/T2p) and 1/Tp. The Eck for KMBY o38 mm and 38–75 mm were found to be 233 kJ/mol and 126 kJ/mol, respectively. As stated by Matusita and Sakka [16,17], the Kissinger equation is valid only if crystallization is completely from surface sites. Otherwise, Matusita and Sakka equation should be used (Eq. (2)). ! αn mEc Ln 2 ¼ þ constant ð2Þ RT p Tp where n is the Avrami coefficient which depends from the mechanisms of growth, m is the dimensionality of growth of the crystalline phase (i.e. rod-like, disk-like or sphere-like) and Ec is
∆ T (endo down) (°C)
Tp
Fig. 2. Plots in accordance with Ozawa equation (Eq. (3)) for KMBY with powders sizeo 38 mm.
Tg
T (°C) Fig. 1. DTA thermographs of KMBY powders ( o 38 mm) collected at different heating rates: (a) 10 1C/min, (b) 20 1C/min, (c) 40 1C/min.
Fig. 3. Particle size distribution of the two different particle sizes batches used for the study ( o 38 mm and 38–75 mm).
286
A.G. Sabato et al. / Materials Letters 141 (2015) 284–287
Table 1 Comparison of kinetics parameters (n and m), activation energies for crystallization (Eck and Ec), activation energy for viscous flow (Eη) and shrinkage obtained for two different sizes of KMBY powders. Powders size
Eck (kJ/ n mol)
o 38 mm 38–75 mm
233 126
m
Ec (kJ/ mEc mol) (kJ/ mol)
2.6 1.6 406 2.1 1.1 262
658 286
nEck (kJ/ mol)
Eη (kJ/ Shrinkage (%) mol)
612 264
349 265
E 45 E 35
values of n¼m ¼1. As observed also in other glass-based systems [9], an effective sintering (by viscous flow) before the crystal growth explains how nuclei formed on surfaces sites can act as bulk nuclei during the growth after the sintering. For the KMBY system this hypothesis is supported by: the KMBY sintering behaviour, where the temperature of the maximum shrinkage is always lower than the onset of the crystallization for both particle sizes [14] and the fact that in the case of the coarsest powders (38o mmo 75), that showed a worse sintering behaviour (lower shrinkage %, as reported in Table 1), lower values of n and m were obtained.
Fig. 4 shows the Matusita and Sakka plot for both powders sizes; the values of mEc were obtained from the slopes of the straight line. The Ec value was found to be 403 kJ/mol for finest powders and 262 kJ/mol for coarsest ones; both values were significantly higher than Eck. Furthermore, some authors suggest that the values of nEck and mEc can be considered similar with an error lower than 10% [11,20]. It is evident from Table 1 that, in our glass system, these values are very similar, thus supporting the accuracy of these results. Besides, many authors pointed out that a relationship between the activation energy for crystallization and the activation energy for viscous flow (Eη) exists [10,17]. A.A. Francis et al. [10], and E. Ercenk [21] reported the calculation of Eη obtained from the variation of Tg with the heating rate. Eη /R value has been calculated as the slope of the Ln(T2g/α) versus 1/Tg plot. Eη values were found 349 kJ/mol and 265 kJ/mol for the finest and the coarsest powders, respectively. Some authors showed that Eη is approximately equal to Ec [17], while other authors pointed out a value of Ec higher than Eη [10], owing this effect to the complex stoichiometry of crystalline phase (diopside) combined with a diffusion controlled bulk growth. In the glass-ceramic system that is presented here, Eη and Ec were found to be similar for the coarsest powders and slightly different for the finest particles, thus suggesting that for the glass-ceramic obtained with the finest particles the energy needed for diffusion to progress the crystallization is greater than that for the viscous flow. This observation is in agreement with literature results on glass-ceramic systems similar to the one studied here [10]. To summarize, the powder size seems to affect the crystallization mechanism (n, m) and the activation energy for crystallization. The same influence of the particle size has been reported in other works [9,22,23]. In our system nucleation preferentially occurs at the surface, but, as observed also in other glass-based systems [9], an effective sintering (by viscous flow) before the crystal growth explains how nuclei formed on surfaces sites can act as bulk nuclei during the growth after the sintering. Surface nuclei behave as bulk nuclei in finely powdered samples (i.e. o38 mm) that efficiently sinter before devitrifying.
Fig. 4. Matusita and Sakka plot (Eq. (2)) for KMBY powderso 38 mm (a) and 38–75 mm (b).
4. Conclusions A study on the crystallization mechanism and kinetics of a novel glass-ceramic sealant for SOFCs has been conducted using non-isothermal DTA analysis. Although this glass system shows a surface nucleation of diopside, m and n parameters suggest a bulk growth of crystals. This might be explained by the effective glass sintering before the crystal growth, thus leading to surface nuclei acting as bulk nuclei. The data obtained from this study are useful to better understand the crystallization mechanism and kinetic and to have a better control on this process (variation in thermal treatment or particle size) in order to tailor the properties of the final glassceramic sealant.
Acknowledgements The research leading to these results has received funding from the European Union's Seventh Framework Programme managed by REA-Research Executive Agency http://ec.europa.eu/research/ rea and it participates in a Marie Curie Action (GlaCERCo GA 264526). References [1] EG & G Technical service. Fuel cells handbook. 7th ed.. . Morgantown, West Virginia: U.S. Department of Energy, Office of Fossil Energy, National Energy Technology Laboratory; 2004. [2] Shingal SC, Kendall K. High temperature solid oxides fuel cells: fundamental, design and application. London: Elsevier Ltd;; 2003. [3] Mahapatra MK, Lu K. Seal glass for solid oxide fuel cell. J Power Sources 2010;195:7129–39. [4] Tulyaganov DU, Reddy AA, Kharton VV, Ferreira JMF. Aluminosilicate-based sealants for SOFCs and other electrochemical applications – a brief review. J Power Sources 2013;242:486–502. [5] Fergus JW. Sealants for solid oxide fuel cells. J Power Sources 2005;147:46–57. [6] Smeacetto F, Salvo M, Leone P, Santarelli M, Ferraris M. Performance and testing of joined crofer22APU-glass-ceramic sealant-anode supported cell in SOFC relevant conditions. Mater Lett 2011;65:1048–52. [7] Smeacetto F, et al. Performance of a glass-ceramic sealant in SOFC short stack. Int J Hydrogen Energ 2013;38:588–96. [8] Reddy, et al. Bi-Layer glass-ceramic sealant for solid oxide fuel cells. J Eur Ceram Soc 2014;34:1449–55. [9] Costantini A, Luciani G, Branda F. Thermal and devitrification behavior of CaOGa2O-SiO2 glasses. J Eur Cer Soc 2000;20:1403–7. [10] Francis AA, Rawlings RD, Sweeney R, Boccaccini AR. Crystallization kinetic of glass particles prepared from a mixture of coal ash and soda-lime cullet glass. J Non-Cryst Solids 2004;333:187–93.
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[11] Ghasemzadeh M, Nemati A, Nozad A, Hamnabard Z, Baghshahi S. Crystallization kinetics of glass-ceramics by differential thermal analysis. Ceram Silikaty 2011;55:188–94. [12] Smeacetto F, Salvo M, Ferraris M, Cho J, Boccacini AR. Glass–ceramic seal to join crofer 22 APU alloy to YSZ ceramic in planar SOFCs. J Eur Ceram Soc 2008;28:61–7. [13] Arora A, Shaaban ER, Singh K, Pandey OP. Non-isothermal crystallization kinetics of ZnO–BaO–B2O3–SiO2 glass. J Non-Cryst Solids 2008;354:3944–51. [14] Smeacetto F, De Miranda A, Chrysanthou A, Bernardo E, Secco M, Bindi M, et al. Novel glass-ceramic composition as sealant for SOFCs. J Am Ceram Soc in press, DOI: 10.1111/jace.13219. [15] Kissinger HE. Variation of peak temperature with heating rate in differential thermal analysis. J Res Natl Bur Stand 1956;57:217–21. [16] Matusita K, Sakka S. Kinetic study of the crystallisation of glass by differential scanning calorimetry. Phys Chem Glasses 1979;20:81–4. [17] Matusita K, Sakka S. Kinetic study on non-isothermal crystallization of glass by thermal analysis. Bull Inst Chem Res Kyoto Univ 1981;59:159–71.
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[18] Ozawa T. Kinetics of non-isothermal crystallization. Polymers 1971;12:150. [19] Çelikbilek M, Ersundu AE, Solak N, Aydin S. Crystallization kinetics of the tungsten–tellurite glasses. J Non-Cryst Solids 2011;357:88–95. [20] Erol M, Kucukbayrak S, Ersoy-Mericboyu A. The application of differential thermal analysis to the study of isothermal and non-isothermal crystallization kinetics of coal fly ash based glasses. J Non-Cryst Solids 2009;355:569–76. [21] Ercenk E. The crystallization kinetics of the CaO-SiO2-P2O5-MgO-Al2O3 base glass system. J Non-Cryst Solids 2014;387:101–6. [22] Erol M, Kucukbayrak S, Ersoy-Mericboyu A. Influence of particle size on the crystallization kinetics of glasses produced from waste materials. J Non-Cryst Solids 2011;357:211–9. [23] Karamanov A, Avramov I, Arrizza L, Pascova R, Gutzow I. Variation of Avrami parameter during non-isothermal surface crystallization of glass powders with different sizes. J Non-Cryst Solids 2012;358:1486–90.
Contents lists available at ScienceDirect
Materials Letters journal homepage: www.elsevier.com/locate/matlet
Crystallization behaviour of glass-ceramic sealant for solid oxide fuel cells A.G. Sabato, M. Salvo, A. De Miranda,, F. Smeacetto n Department of Applied Science and Technology, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
art ic l e i nf o
a b s t r a c t
Article history: Received 12 September 2014 Accepted 22 November 2014 Available online 2 December 2014
The crystallization behaviour of a glass-ceramic suitable as SOFCs sealant has been investigated using differential thermal analysis (DTA). Glass powders of two different particle sizes ( o 38 mm and 38–75 mm) have been considered. The exothermic peak in DTA thermographs has been associated with the crystallization of the diopside phase, as revealed by X-ray diffraction analysis (XRD). Avrami exponents (n) have been calculated for both particle sizes using the Ozawa equation, while Matusita and Sakka equation has been used to calculate the activation energy for the crystallization (Ec). The values found for n are 2.6 ( o 38 mm) and 2.1 (38–75 mm). The obtained values for Ec are 403 kJ/mol and 262 kJ/ mol for the finest and the coarsest glass powders, respectively. As a comparison, the activation energies for the viscous flow (Eη) have been also evaluated: 349 kJ/mol for powders sized o38 mm and 265 kJ/mol for those sized 38–75 mm. & 2014 Elsevier B.V. All rights reserved.
Keywords: Glass-ceramic Sealant Differential thermal analysis
1. Introduction In the modern challenge to developing a competitive way to produce “clean” energy, solid oxide fuel cells (SOFCs) can occupy a decisive role. SOFCs are devices able to convert chemical energy into electrical energy by red-ox reactions between a fuel and an oxidant. In order to obtain a satisfying output power it is necessary to build a SOFC stack [1,2]. Some of the stack elements (i.e. metallic interconnect and ceramic cell) are joined by a sealant. Recently many studies have pointed out glass-ceramic sealants among the most promising materials for this application [3–8]. This is mainly due to the possibility of tailoring their proprieties by changing their composition or thermal treatments. Glass-ceramics are materials in which a residual glass phase and a crystalline phase deriving from a devitrification process coexist together. In general, they have superior mechanical proprieties compared to their parent glasses. A reliable glass-ceramic sealant for SOFCs should have an excellent gas tightness, a high resistance to relevant SOFC operating conditions (i.e. reducing and oxidizing atmospheres) and a thermal expansion coefficient (TEC) as much as possible closest to that of materials to which they are in contact with [4]. The activation energy for the crystallization and the Avrami exponent (n) are the most important parameters in order to evaluate the crystallisation mechanism of glass-ceramic materials. They can be obtained from differential thermal analysis (DTA)
n
Corresponding author. E-mail address: [email protected] (F. Smeacetto).
http://dx.doi.org/10.1016/j.matlet.2014.11.128 0167-577X/& 2014 Elsevier B.V. All rights reserved.
conducted at different heating rates. Many studies have been carried out on different glass systems (also for different applications) in order to evaluate these parameters and how they could affect the crystallization mechanisms [9–13]. A better understanding of these factors, including the effect of the mean particle size on crystallization kinetics, could lead to improved knowledge in varying glass-ceramic properties. In this study, Kissinger [9], Matusita and Sakka [5] and Ozawa [10] equations were used to determine the crystallization mechanism and the activation energy values for the crystallization of a glass-ceramic composition designed and preliminary tested as SOFC sealant elsewhere [14].
2. Experimental The composition of the glass in wt% was: 54.39% SiO2, 13.78% Na2O, 9.02 CaO, 8.37% MgO, 11.26% Al2O3, 1.67% K2O, 0.9% B2O3 and 0.61% Y2O3. This glass was labelled as KMBY. The sealant was produced as glass by melting the appropriate oxides and carbonates raw materials in different proportions (as reported above) and by heating at 1500 1C for 1 h in a platinum-rhodium crucible. The melt was cast on a brass plate and the transparent glass was ground for differential thermal analysis. The resulting powders were sieved, obtaining two different particle sizes: o38 mm and 38–75 mm. DTA analyses (Netzsch DTA 404 PC) have been carried out on both particle sizes, using Al2O3 as reference, at different heating rates (10 1C/min, 20 1C/min, 40 1C/min) from room
A.G. Sabato et al. / Materials Letters 141 (2015) 284–287
temperature to 1200 1C. The distribution of sizes (vol % vs particle diameter) has been obtained by a particle size analyser (LS230, Coulter Corporation, USA) on two different particle sizes (o 38 μm and 38–75 μm respectively). SEM (JEOL 5700) and EDS analyses have been carried out on the KMBY glass-ceramic obtained after sintering at 850 1C for 30 min in air atmosphere. The sintering behaviour (shrinkage %) has been determined by heating stage microscopy (Expert System Solutions, Italy) at heating rate of 20 1C/min.
3. Results and discussion The DTA thermographs of the KMBY powder (o38 mm) are reported in Fig. 1, together with the glass transition temperature (Tg). The DTA analyses of the glass powder (size o38 mm and 38–75 mm) show that the crystallization peak (Tp) shifts to higher values with increasing the heating rate. In a previous study [14] we observed that the crystallization peak is also affected by the particle size; the peak shifted to lower temperatures with decreasing particle size, suggesting an effect associated with the surface nucleation of the glass. According to XRD analyses, Ca0.89Mg1.11Si2O6 (diopside) was found as the dominant crystalline phase, potassium containing nepheline (Na3K (Al0.44Si0.56)8O16) and traces of akermanite (Ca2MgSi2O7) were also detected, as reported in reference [14], after a heat treatment at 850 1C for 30 min; the shaped DTA exothermic crystallization peak can be assigned to the diopside. The activation energy for crystallisation, related to Tp can be estimated by the Kissinger equation (Eq. (1)) [15]: ! α E Ln 2 ¼ ck þ constant ð1Þ RT p Tp
285
the activation energy for the crystallization; n and m parameters have to be calculated in order to obtain the value of Ec. The Avrami coefficient can be derived from the Ozawa equation (Eq. (3)) [18], d ln ln 1 χ ð3Þ n ¼ dðlnαÞ T where χ is the volume fraction of crystallized phase at a fixed temperature T. χ was evaluated from the exothermic peak in the DTA thermographs and was calculated as the ratio between the partial area under the peak (at a chosen temperature) and the total area of the peak. The Ozawa plots ln(-ln(1 χ)) versus lnα, at different temperatures (930 1C, 940 1C, 950 1C, 970 1C) for KMBYo38 μm are reported in Fig. 2. The value of n has been calculated as the mean value of the slopes of the plots and it was found to be 2.6, while for KMBY powders size 38o mmo 75 the n value was 2.1 (graph not reported here). Assuming that the number of nuclei is not constant with the heating rate, n and m are related to each other through the relation m¼n 1 [9–11,19]. Values of m for the finest and the coarsest powders are 1.6 and 1.1, respectively, suggesting a bulk crystallization with dimensionality of crystal growth between 1 (i.e. rod like) and 2 (i.e. plate like) [11,17,20]. Fig. 3 shows the particle size distribution of the two different particle sizes batches used for the study (o 38 mm and 38–75 mm). The average size for particles sieved ato38 μm was found to be 21 μm while the average size for the powder in the 38–75 μm range was 51 μm. In Table 1, kinetics parameters, activation energies for crystallization (Eck and Ec), activation energy for viscous flow (Eη) and sintering behaviour (shrinkage %) for two different sizes of KMBY powders are reported. In case of surface crystallization opposite results would be expected, since the lower the particle size the greater is the tendency to devitrification by growth from surface nuclei, thus leading to the
where α is the heating rate, R is the gas constant and Eck is the value of activation energy obtained by this method. The value of Eck can be deduced from the linear plot between Ln(α/T2p) and 1/Tp. The Eck for KMBY o38 mm and 38–75 mm were found to be 233 kJ/mol and 126 kJ/mol, respectively. As stated by Matusita and Sakka [16,17], the Kissinger equation is valid only if crystallization is completely from surface sites. Otherwise, Matusita and Sakka equation should be used (Eq. (2)). ! αn mEc Ln 2 ¼ þ constant ð2Þ RT p Tp where n is the Avrami coefficient which depends from the mechanisms of growth, m is the dimensionality of growth of the crystalline phase (i.e. rod-like, disk-like or sphere-like) and Ec is
∆ T (endo down) (°C)
Tp
Fig. 2. Plots in accordance with Ozawa equation (Eq. (3)) for KMBY with powders sizeo 38 mm.
Tg
T (°C) Fig. 1. DTA thermographs of KMBY powders ( o 38 mm) collected at different heating rates: (a) 10 1C/min, (b) 20 1C/min, (c) 40 1C/min.
Fig. 3. Particle size distribution of the two different particle sizes batches used for the study ( o 38 mm and 38–75 mm).
286
A.G. Sabato et al. / Materials Letters 141 (2015) 284–287
Table 1 Comparison of kinetics parameters (n and m), activation energies for crystallization (Eck and Ec), activation energy for viscous flow (Eη) and shrinkage obtained for two different sizes of KMBY powders. Powders size
Eck (kJ/ n mol)
o 38 mm 38–75 mm
233 126
m
Ec (kJ/ mEc mol) (kJ/ mol)
2.6 1.6 406 2.1 1.1 262
658 286
nEck (kJ/ mol)
Eη (kJ/ Shrinkage (%) mol)
612 264
349 265
E 45 E 35
values of n¼m ¼1. As observed also in other glass-based systems [9], an effective sintering (by viscous flow) before the crystal growth explains how nuclei formed on surfaces sites can act as bulk nuclei during the growth after the sintering. For the KMBY system this hypothesis is supported by: the KMBY sintering behaviour, where the temperature of the maximum shrinkage is always lower than the onset of the crystallization for both particle sizes [14] and the fact that in the case of the coarsest powders (38o mmo 75), that showed a worse sintering behaviour (lower shrinkage %, as reported in Table 1), lower values of n and m were obtained.
Fig. 4 shows the Matusita and Sakka plot for both powders sizes; the values of mEc were obtained from the slopes of the straight line. The Ec value was found to be 403 kJ/mol for finest powders and 262 kJ/mol for coarsest ones; both values were significantly higher than Eck. Furthermore, some authors suggest that the values of nEck and mEc can be considered similar with an error lower than 10% [11,20]. It is evident from Table 1 that, in our glass system, these values are very similar, thus supporting the accuracy of these results. Besides, many authors pointed out that a relationship between the activation energy for crystallization and the activation energy for viscous flow (Eη) exists [10,17]. A.A. Francis et al. [10], and E. Ercenk [21] reported the calculation of Eη obtained from the variation of Tg with the heating rate. Eη /R value has been calculated as the slope of the Ln(T2g/α) versus 1/Tg plot. Eη values were found 349 kJ/mol and 265 kJ/mol for the finest and the coarsest powders, respectively. Some authors showed that Eη is approximately equal to Ec [17], while other authors pointed out a value of Ec higher than Eη [10], owing this effect to the complex stoichiometry of crystalline phase (diopside) combined with a diffusion controlled bulk growth. In the glass-ceramic system that is presented here, Eη and Ec were found to be similar for the coarsest powders and slightly different for the finest particles, thus suggesting that for the glass-ceramic obtained with the finest particles the energy needed for diffusion to progress the crystallization is greater than that for the viscous flow. This observation is in agreement with literature results on glass-ceramic systems similar to the one studied here [10]. To summarize, the powder size seems to affect the crystallization mechanism (n, m) and the activation energy for crystallization. The same influence of the particle size has been reported in other works [9,22,23]. In our system nucleation preferentially occurs at the surface, but, as observed also in other glass-based systems [9], an effective sintering (by viscous flow) before the crystal growth explains how nuclei formed on surfaces sites can act as bulk nuclei during the growth after the sintering. Surface nuclei behave as bulk nuclei in finely powdered samples (i.e. o38 mm) that efficiently sinter before devitrifying.
Fig. 4. Matusita and Sakka plot (Eq. (2)) for KMBY powderso 38 mm (a) and 38–75 mm (b).
4. Conclusions A study on the crystallization mechanism and kinetics of a novel glass-ceramic sealant for SOFCs has been conducted using non-isothermal DTA analysis. Although this glass system shows a surface nucleation of diopside, m and n parameters suggest a bulk growth of crystals. This might be explained by the effective glass sintering before the crystal growth, thus leading to surface nuclei acting as bulk nuclei. The data obtained from this study are useful to better understand the crystallization mechanism and kinetic and to have a better control on this process (variation in thermal treatment or particle size) in order to tailor the properties of the final glassceramic sealant.
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