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Crystallization kinetics of Bi1.7V0.3Sr2Ca2Cu3Ox glass-ceramic
ARTICLE IN PRESS
Physica B 355 (2005) 64–71 www.elsevier.com/locate/physb
Crystallization kinetics of Bi1.7V0.3Sr2Ca2Cu3Ox glass-ceramic H. Koralaya,, F. Yakuphanoglub, S. Cavdara, A. Gu¨nenc, E. Aksua a Ankara Nuclear Research and Training Center, TAEA, 06100-Besevler/Ankara,Turkey Department of Physics, Faculty of Arts and Science, Fırat University, Elazıg 23169, Turkey c Department of Physics, Gazi University, Teknik Okullar Ankara, Turkey
b
Received 25 July 2004; received in revised form 4 October 2004; accepted 12 October 2004
Abstract Crystallization kinetics of Bi1.7V0.3Sr2Ca2Cu3Ox glass-ceramic was investigated using the differential scanning calorimetry (DSC) technique. Three characteristic phenomena were observed in the studied temperature range. The activation energies for glass transition temperature and crystallization phenomena were determined by different theoretical models. Applying the modified Johnson–Mehl–Avrami (JMA) equation reasonably suggests that crystallization process of the Bi1.7V0.3Sr2Ca2Cu3Ox glass-ceramic is carried out by a bulk growth in three dimensions. r 2004 Elsevier B.V. All rights reserved. PACS: 61.43.Fs; 64.70.Pf Keywords: Glass-ceramic; Crystallization kinetics; Avrami parameter; Glass transitions
1. Introduction The thermal behavior of glass-ceramics plays an important role in determining the transport mechanism, thermal stability and practical applications. Thermal analysis techniques such as differential scanning calorimetry (DSC) and thermogravimetry analysis (TG) methods have been widely used to determine the thermal behavior of solid materials [1–6]. In general, these methods are Corresponding author. Tel.:+90 312 212 7719; fax: +90
312 223 4439. E-mail address: [email protected] (H. Koralay).
used to constantly measure the changes occurring in the physical properties of a material. Differential thermal analysis (DTA) and DSC are of particular importance. Both procedures permit the amount of heat to be determined that are taken up from or emitted to the surroundings per unit time during isothermal procedures or during heating and cooling. In this manner, heat capacities, melt enthalpies and transition temperatures can be measured, and from this information further indications regarding phase transitions and crystallization processes can be derived. The crystallization kinetics of non-crystalline solids are extensively studied by thermal analysis methods
0921-4526/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2004.10.023
ARTICLE IN PRESS H. Koralay et al. / Physica B 355 (2005) 64–71
such as DTA, DSC or hot-stage X-ray diffraction. Experimental data are usually analyzed by means of the nucleation and growth model proposed by Johnson et al. [7–10]. Activation energy is the most important parameter for crystallization kinetics and it is associated with the nucleation and growth process. This work reports the study of the crystallization kinetics and evaluation of the activation energy of the amorphous–crystallization transformation of Bi1.7V0.3Sr2Ca2Cu3Ox glass-ceramic.
2. Theoretical background
65
If one takes the logarithm at both sides of this equation, the equation can be written as ! b 1 DE : (8) ¼ ln K ln n nkT p T 2p This equation is used to obtain the activation energy using the linear relationship between lnðb=T 2p Þ and 1=T p : The slope and intercept of the straight line give DE=nk and ð1=nÞln K; respectively. On the other hand, Eqs. (1) and (2) can be written as K DE lnð lnð1 xÞÞ ¼ ln n þ 2n ln T : (9) b kT
The classical Johnson–Mehl–Avrami (JMA) theoretical model [11] is defined as follows:
Taking the derivative with respect to 1=T gives [12]
x ¼ 1 expðKt2n Þ
d lnð lnð1 xÞÞ DE DE ¼ 2nT ; dð1=TÞ k k
with
DE n K ¼ K 0 b exp ; kT
(1)
(2)
where b is the heating rate. The Avrami parameter n and activation energy DE are described as [12] n ¼ a þ bc;
(3)
DE ¼ aE n þ bcE g :
(4)
Taking the second derivative of Eqs. (1) and (2) with respect to time and setting it to zero gives [12] DE DE þ 2n 2 ¼ þ 2 xe ðT p Þ: (5) kT p kT p Assuming, as before, that DE=2nbkT ; we see that xe ðT p Þ 1:
(6)
The true importance of this equation lies in the fact that the fraction transformed at the peak in the transformation rate is equal to xðT P Þ ¼ 1 e1 ¼ 0:63; regardless of the heating rate. This fact lies at the heart of the peak shift methods such as Kissinger analysis [13,14]. Form Eqs. (2) and (6), we have, !n T 2p DE K exp ¼ 1: (7) kT p b
(10)
where DE=2nbkT is used; hence, we can plot a curve of lnðlnð1 xÞÞ vs. 1=T p ; which should give a straight line with slope DE=k: So, having obtained values for DE=n and DE; we can calculate n.
3. Experimental The starting materials are Bi2O3, SrCO3, CaCO3, CuO and V2O5 powders which were used for production of the sample. These powders were mixed to obtain a homogeneous mixture for 1 h. The mixture was melted at 1150 1C for 90 min. The obtained sample was rapidly quenched between two copper plates. The sample was produced as black glass sheet having 1 mm thickness [15]. The surface morphology of the sample was investigated by SEM technique (using a JEOL 5600 scanning electron microscope). X-ray diffraction (XRD) pattern of the sample was obtained with a Rigaku DMAX 2200 diffractometer. DSC measurements of the sample were carried out using a TA Instrument DSC 2010. DSC measurements were performed at heating rates of 5, 10, 15 and 20 K/min under nitrogen atmosphere using an aluminum crucible.
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4. Results and discussion
4.2. Crystallization kinetics
4.1. Microstructure and XRD study
Fig. 3 shows the DSC curves of the sample at different heating rates. It is evaluated that when the sample studied is heated at a constant heating rate in a DSC experiment, it undergoes structural changes and eventually crystallizes.
The XRD study shows the amorphous structure of the as-prepared sample. The sample annealed in air for 90 min at 1150 1C shows the existence of crystalline peaks indicating the transformation from amorphous to crystalline material (Fig. 1). The crystal structure and crystalline phases were identified by XRD. The crystal structure of the sample was found to be orthorhombic with the lattice parameters a ¼ 5:390; b ¼ 5:413; c ¼ ( for the low T phase and a ¼ 5:435; b ¼ 30:813 A c ( for the high T phase. The 5:412; c ¼ 36:926 A c phases that occur in microstructure of the sample are BSCCO 2212 (low Tc) and BSCCO 2223 (high Tc) phases [15]. The micrograph of the sample is given in the Fig. 2. It is observed in the figure that there are crystals having different orientation. The sample shows weak intercrystal connectivity in some regions; however, it shows better intercrystal connectivity in the other regions. It is also observed that there are voids between crystals.
Fig. 2. Micrograph of the ceramic.
Fig. 1. X-ray diffraction pattern of the ceramic.
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Fig. 3. DSC curves of the ceramic at different heating rates.
Three characteristic phenomena were observed in the studied temperature range. The first one corresponds to the glass transition temperature Tg which appears as an endothermic peak and the others correspond to crystallization peaks which follow as an exothermic formation. The glass transition temperature is a thermodynamic characteristic temperature for the sample. This calorimetric glass transition is generally considered to be due to changes in the amorphous structure, which approaches a thermodynamic equilibrium state as the temperature of the system is increased [16–18]. It is seen that the position of the glass transition peak depends on the heating rate. It is well-known that Tg is a temperature at which the relaxation time, t, becomes equal to an experimental time of observation, tobs, and Tg is inversely proportional to the relaxation time. tobs decreases with increasing heating rate. Thus, Tg increases with increasing heating rate. It is observed that there are two crystallization peaks (Tc1 and Tc2), which may be due to the presence of distinct phase transformations. The maximum temperature of peak 1 (Tp1) increases from 486.15 to 502.4 1C, while the
maximum temperature of peak 2 (Tp2) increases from 530.61 to 552.67 1C, when the heating rate is increased from 5 to 20 K/min. The peak temperature shifts to higher temperatures with increasing heating rate. Another important parameter for the crystallization mechanism is the peak height. As seen in Fig. 3, after 5 K/min heating rate, the height of the first crystallization peak is greater than the height of the second peak. It is wellknown that the height of the crystallization peak is proportional to the concentration of nuclei in the sample. The shift of peak temperature may be associated with particle size effects on heat transfer. Larger particles would have greater heat transfer resistance when a given heating rate is considered. It takes longer for the center of the particle to reach the furnace temperature. Thus, this process results in a higher crystallization. It is important to know the activation energies involved in glass transition and crystallization processes. The activation energy of the sample can be obtained via the modified Kissinger method [14]. Plotting ln(b/T2g) vs. 1000/T gives a straight line. The value of Eg can be obtained from the
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Fig. 4. ln(b/T2g) and ln b vs. 1000/T plots for the ceramic. Fig. 5. Variation of Tg with ln b for the ceramic.
slope of this straight line (Fig. 4). The Eg value can also be obtained from the following equation: lnðbÞ ¼
Eg þ C; RT g
(11)
where Tg is the glass transition temperature, Eg is the activation energy for structural relaxation and R is the gas constant. This equation can be used when the variation of lnð1=T 2g Þ ln b is much slower than that of 1/Tg with ln b. The ln b vs. 1000/T plot for the sample is shown in Fig. 4. The activation energies of the glass transition were found as 350.9 for the Kissinger method and 363.0 kJ/mol for Mahadevan et al. [19]. The glass transition activation energy, Eg, is the amount of energy absorbed by a group of atoms in the glassy region. This activation energy provides molecular motion and rearrangement of atoms around the glass transition temperature and helps in a jump from one metastable state to another. The glass transition temperature dependence of heating rate can be expressed by the relation [20] T g ¼ A þ B lnðbÞ;
(12)
where A and B are constants. The Tg vs. ln b plot for the sample is shown in Fig. 5. This plot confirmed the validity of the relation and A and B were 1.601 and 688.3 K, respectively. The kinetics of the crystallization can be obtained by the formal theory developed by Johnson and Mehl [21]. In the non-isothermal
method, the fraction x crystallized at any temperature is given as RT AT T ðdH=dTÞ dT ; (13) ¼ x ¼ R T 10 A1 T 0 ðdH=dTÞ dT where T0 and TN are temperatures at which crystallization starts and ends. AN is the total area of the exothermic peak, and AT is the area under the exothermic peak at any temperature. Eq. (10) can be applied to obtain crystallization parameters. A plot of ln[ln(1x)] vs. 1000/T for the sample at different heating rates gives nearly parallel straight lines for the first peak, but this parallel nature disappeared for the second peak [Fig. 6(a and b)]. These plots show linearity over most of the temperature range. At high temperatures or in regions of large crystallization fractions, a slight deviation in the linearity or rather a decrease in slope of the initial slope is observed for all heating rates. This deviation could be attributed to the saturation of the nucleation sites in the final stages of crystallization [22,23]. The other possibility to explain such a behavior could be the restriction of crystal growth by the small size of the particles [24]. The DE C values were obtained from the slope of Fig. 6(a and b) and are given in Table 1. The average activation energy values, DE C ; were found as 1860.23 kJ/mol for the first peak and 1528.22 kJ/mol for the second peak. On the other
ARTICLE IN PRESS H. Koralay et al. / Physica B 355 (2005) 64–71
Fig. 6. ln(ln(1x)) vs. 1000/T plots for the ceramic at different heating rates: (a) peak, 1 (b) peak 2.
Table 1 Kinetics parameters of the ceramic Heating rate (K/min)
DE C (kJ/mol) for 1st peak
DE C (kJ/mol) for 2nd peak
5 10 15 20
2310.20 1873.81 1765.43 1491.51
2354.38 2009.80 1070.84 677.86
hand, the DE=n values for the first and second peaks were respectively found as 407.42 and 338.33 kJ/mol. The activation energy and the crystal growth index (Avrami parameter) are
69
important kinetics parameters to evaluate crystallization capability the sample. It is well-known that if activation energy is lower, it is easier to crystallize the sample. The crystallization activation energy of the sample decreases with increasing heating rate. This suggests that it is easier to crystallize the sample with a higher heating rate. On the other hand, Eqs. (8) and (10) were used to obtain Avrami parameter n for each peak. The n values were approximately found to be 4.5 using the calculated DE C and DE=n values. The Avrami parameter is expressed as n ¼ a þ bc; where a determines nucleation rate (a ¼ 0 for no nucleation, ao1 for decreasing nucleation rate, a41 for increasing nucleation rate) [25]. The parameter c refers to the dimensionality of growth (c ¼ 1; 2 and 3 for one-dimensional growth, two-dimensional growth and three-dimensional growth, respectively). The b parameter determines the mechanism of the growth (b ¼ 0:5 for diffusioncontrolled growth (parabolic) and b ¼ 1 for interfacial control of growth (linear)). The value of n 4:5 provides c ¼ 3; b ¼ 1 (linear growth) and the value of a ¼ 1:5 (increasing nucleation rate) indicating the crystallization process occurs in the sample by means of three-dimensional growth. The higher the Avrami parameter, the easier the crystallization. The n parameters obtained suggest that crystallization takes place easily in structure and the crystallization mechanism is the bulk crystallization mechanism, in which nucleation occurs in the bulk of the sample. The sharp crystallization peaks seen in Fig. 3 confirm the bulk crystallization. Formation enthalpy is an important parameter to understand the structure of the sample and physical properties. The enthalpy values of glass transition and crystallization temperature were calculated by the following relation: DH ¼ kAr =M;
(14)
where Ar is the area under the peak, k is the instrument constant and M is the mass of the sample. The enthalpy values for the glass transition temperature and crystallization peaks were calculated. The variation of enthalpy values with temperature for these peaks is shown in Fig. 7. It is seen that the enthalpy values increase with
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vestigated using the DSC technique. Three characteristic phenomena were observed in the studied temperature range. The activation energies for glass transition temperature and crystallization phenomena were calculated. It is seen that the activation energy of the first crystallization peak is higher than that of the second peak. The activation energy values of crystallization peaks decrease with increasing heating rates. The Avrami parameter for the sample was found as n 4:5 which suggests that the crystallization process occurs in the sample by means of three-dimensional growth.
Fig. 7. Variation of enthalpy with peak temperatures.
increasing heating rates. The values of DH were determined by a least-squares linear regression analysis. The resultant correlations for the formation enthalpy dependence of peak temperature were experimentally determined as DHðJ=gÞ ¼ 0:651373 TðKÞ þ 462:145
for T g ;
ð15Þ
DHðJ=gÞ ¼ 0:540054 TðKÞ þ 402:714 for T P1 ;
ð16Þ
DHðJ=gÞ ¼ 0:636007 TðKÞ þ 504:383 for T P2 :
ð17Þ
These results suggest that the formation enthalpy values vary linearly with peak temperature. Thus, an experimental equation can be proposed as DH ¼ D T þ E: The D values in Eqs. (16) and (17) increase when these equations were compared with each other and these values are associated with entropy which is a measure of order. This indicates that the entropy value for the Tp1 peak is lower than that of the Tp2 peak.
5. Conclusions The crystallization kinetics of the Bi1.7V0.3Sr2Ca2Cu3Ox glass-ceramic superconductor was in-
Acknowledgements This study was supported by TAEA’s DPT project no AP2. The authors also thank Kırıkkale University for SEM measurements. References [1] M. Zayed, F.A. Nour El-Dien, Thermochim. Acta 114 (1987) 359. [2] A.A. Salman, J. Therm, Anal. Calorim. 63 (2001) 22. [3] L. Nunez, F. Fraga, M.R. Nunez, M.T. Villanueva, Polymer 41 (2000) 4635. [4] X. Wang, K. Yang, Y. Wang, B. Wu, Y. Liu, B. Yang, Polym. Degrad. Stabil. 81 (2003) 415. [5] .M.I. Nad-Elrahman, M.O. Ahmed, S.M. Ahmed, T. Aboul-Fadl, A. El-Shorbagi, Biophys. Chem. 97 (2000) 113. [6] N. Bmanaragan, N.S. Saxena, D. Bhandari, M.M. Imran, D.D. Paudyal, Bull. Mater. Sci. 23 (5) (2000) 369. [7] W.A. Johnson, K.F. Mehl, Trans. Am. Inst. Min. Metall. Eng. 135 (1939) 416. [8] M. Avrami, J. Chem. Phys. 7 (1939) 1103. [9] M. Avrami, J. Chem. Phys. 8 (1940) 212. [10] M. Avrami, J. Chem. Phys. 9 (1941) 177. [11] H. Yinnan, D.R. Uhlmann, J. Non-Cryst. Solids 54 (1983) 253. [12] G. Ruitenberg, E. Woldt, A.K. Petford-Long, Thermochim. Acta 378 (2001) 97–105. [13] D.W. Henderson, J. Non-Cryst. Solids 30 (1979) 301. [14] H.E. Kissinger, Anal. Chem. 29 (1957) 32. [15] T.S. Kayed, N. Calınlı, E. Aksu, H. Koralay, A. Gu¨nen, I˙. Ercan, S. Aktu¨rk, S. C - avdar, Crys. Res. Technol., in press (2004). [16] C.A. Agnell, W. Sichina, Ann. N.Y. Acad. Sci. 279 (1976) 53. [17] M.H. Cohen, G.S. Grest, Phys. Rev. B 21 (1980) 4113. [18] J. Ja¨ckle, Rep. Prog. Phys. 49 (1986) 171.
ARTICLE IN PRESS H. Koralay et al. / Physica B 355 (2005) 64–71 [19] S. Mahadevan, A. Giridhar, A.K. Singh, J. Non-cryst. Solids 88 (1986) 11. [20] M. Lasocka, Mater. Sci. Eng. 23 (1973) 173. [21] W.A. Johnson, R.F. Mehl, Trans. Am. Inst. Min. Metall. Eng. 135 (1939) 416. [22] M.G. Scott, J. Mater. Sci. 13 (1978) 291.
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[23] V.R.V. Raman, G.E. Fish, J. Appl. Phys. 53 (1982) 2273. [24] J. Colemenero, J.M. Barandiaran, J. Non-Cryst. Solids 30 (1978) 263. [25] R. Jain, N.S. Saxena, D. Bhandari, S.K. Sharma, K.V.R. Rao, Physica B 301 (2001) 341.
Physica B 355 (2005) 64–71 www.elsevier.com/locate/physb
Crystallization kinetics of Bi1.7V0.3Sr2Ca2Cu3Ox glass-ceramic H. Koralaya,, F. Yakuphanoglub, S. Cavdara, A. Gu¨nenc, E. Aksua a Ankara Nuclear Research and Training Center, TAEA, 06100-Besevler/Ankara,Turkey Department of Physics, Faculty of Arts and Science, Fırat University, Elazıg 23169, Turkey c Department of Physics, Gazi University, Teknik Okullar Ankara, Turkey
b
Received 25 July 2004; received in revised form 4 October 2004; accepted 12 October 2004
Abstract Crystallization kinetics of Bi1.7V0.3Sr2Ca2Cu3Ox glass-ceramic was investigated using the differential scanning calorimetry (DSC) technique. Three characteristic phenomena were observed in the studied temperature range. The activation energies for glass transition temperature and crystallization phenomena were determined by different theoretical models. Applying the modified Johnson–Mehl–Avrami (JMA) equation reasonably suggests that crystallization process of the Bi1.7V0.3Sr2Ca2Cu3Ox glass-ceramic is carried out by a bulk growth in three dimensions. r 2004 Elsevier B.V. All rights reserved. PACS: 61.43.Fs; 64.70.Pf Keywords: Glass-ceramic; Crystallization kinetics; Avrami parameter; Glass transitions
1. Introduction The thermal behavior of glass-ceramics plays an important role in determining the transport mechanism, thermal stability and practical applications. Thermal analysis techniques such as differential scanning calorimetry (DSC) and thermogravimetry analysis (TG) methods have been widely used to determine the thermal behavior of solid materials [1–6]. In general, these methods are Corresponding author. Tel.:+90 312 212 7719; fax: +90
312 223 4439. E-mail address: [email protected] (H. Koralay).
used to constantly measure the changes occurring in the physical properties of a material. Differential thermal analysis (DTA) and DSC are of particular importance. Both procedures permit the amount of heat to be determined that are taken up from or emitted to the surroundings per unit time during isothermal procedures or during heating and cooling. In this manner, heat capacities, melt enthalpies and transition temperatures can be measured, and from this information further indications regarding phase transitions and crystallization processes can be derived. The crystallization kinetics of non-crystalline solids are extensively studied by thermal analysis methods
0921-4526/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2004.10.023
ARTICLE IN PRESS H. Koralay et al. / Physica B 355 (2005) 64–71
such as DTA, DSC or hot-stage X-ray diffraction. Experimental data are usually analyzed by means of the nucleation and growth model proposed by Johnson et al. [7–10]. Activation energy is the most important parameter for crystallization kinetics and it is associated with the nucleation and growth process. This work reports the study of the crystallization kinetics and evaluation of the activation energy of the amorphous–crystallization transformation of Bi1.7V0.3Sr2Ca2Cu3Ox glass-ceramic.
2. Theoretical background
65
If one takes the logarithm at both sides of this equation, the equation can be written as ! b 1 DE : (8) ¼ ln K ln n nkT p T 2p This equation is used to obtain the activation energy using the linear relationship between lnðb=T 2p Þ and 1=T p : The slope and intercept of the straight line give DE=nk and ð1=nÞln K; respectively. On the other hand, Eqs. (1) and (2) can be written as K DE lnð lnð1 xÞÞ ¼ ln n þ 2n ln T : (9) b kT
The classical Johnson–Mehl–Avrami (JMA) theoretical model [11] is defined as follows:
Taking the derivative with respect to 1=T gives [12]
x ¼ 1 expðKt2n Þ
d lnð lnð1 xÞÞ DE DE ¼ 2nT ; dð1=TÞ k k
with
DE n K ¼ K 0 b exp ; kT
(1)
(2)
where b is the heating rate. The Avrami parameter n and activation energy DE are described as [12] n ¼ a þ bc;
(3)
DE ¼ aE n þ bcE g :
(4)
Taking the second derivative of Eqs. (1) and (2) with respect to time and setting it to zero gives [12] DE DE þ 2n 2 ¼ þ 2 xe ðT p Þ: (5) kT p kT p Assuming, as before, that DE=2nbkT ; we see that xe ðT p Þ 1:
(6)
The true importance of this equation lies in the fact that the fraction transformed at the peak in the transformation rate is equal to xðT P Þ ¼ 1 e1 ¼ 0:63; regardless of the heating rate. This fact lies at the heart of the peak shift methods such as Kissinger analysis [13,14]. Form Eqs. (2) and (6), we have, !n T 2p DE K exp ¼ 1: (7) kT p b
(10)
where DE=2nbkT is used; hence, we can plot a curve of lnðlnð1 xÞÞ vs. 1=T p ; which should give a straight line with slope DE=k: So, having obtained values for DE=n and DE; we can calculate n.
3. Experimental The starting materials are Bi2O3, SrCO3, CaCO3, CuO and V2O5 powders which were used for production of the sample. These powders were mixed to obtain a homogeneous mixture for 1 h. The mixture was melted at 1150 1C for 90 min. The obtained sample was rapidly quenched between two copper plates. The sample was produced as black glass sheet having 1 mm thickness [15]. The surface morphology of the sample was investigated by SEM technique (using a JEOL 5600 scanning electron microscope). X-ray diffraction (XRD) pattern of the sample was obtained with a Rigaku DMAX 2200 diffractometer. DSC measurements of the sample were carried out using a TA Instrument DSC 2010. DSC measurements were performed at heating rates of 5, 10, 15 and 20 K/min under nitrogen atmosphere using an aluminum crucible.
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4. Results and discussion
4.2. Crystallization kinetics
4.1. Microstructure and XRD study
Fig. 3 shows the DSC curves of the sample at different heating rates. It is evaluated that when the sample studied is heated at a constant heating rate in a DSC experiment, it undergoes structural changes and eventually crystallizes.
The XRD study shows the amorphous structure of the as-prepared sample. The sample annealed in air for 90 min at 1150 1C shows the existence of crystalline peaks indicating the transformation from amorphous to crystalline material (Fig. 1). The crystal structure and crystalline phases were identified by XRD. The crystal structure of the sample was found to be orthorhombic with the lattice parameters a ¼ 5:390; b ¼ 5:413; c ¼ ( for the low T phase and a ¼ 5:435; b ¼ 30:813 A c ( for the high T phase. The 5:412; c ¼ 36:926 A c phases that occur in microstructure of the sample are BSCCO 2212 (low Tc) and BSCCO 2223 (high Tc) phases [15]. The micrograph of the sample is given in the Fig. 2. It is observed in the figure that there are crystals having different orientation. The sample shows weak intercrystal connectivity in some regions; however, it shows better intercrystal connectivity in the other regions. It is also observed that there are voids between crystals.
Fig. 2. Micrograph of the ceramic.
Fig. 1. X-ray diffraction pattern of the ceramic.
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Fig. 3. DSC curves of the ceramic at different heating rates.
Three characteristic phenomena were observed in the studied temperature range. The first one corresponds to the glass transition temperature Tg which appears as an endothermic peak and the others correspond to crystallization peaks which follow as an exothermic formation. The glass transition temperature is a thermodynamic characteristic temperature for the sample. This calorimetric glass transition is generally considered to be due to changes in the amorphous structure, which approaches a thermodynamic equilibrium state as the temperature of the system is increased [16–18]. It is seen that the position of the glass transition peak depends on the heating rate. It is well-known that Tg is a temperature at which the relaxation time, t, becomes equal to an experimental time of observation, tobs, and Tg is inversely proportional to the relaxation time. tobs decreases with increasing heating rate. Thus, Tg increases with increasing heating rate. It is observed that there are two crystallization peaks (Tc1 and Tc2), which may be due to the presence of distinct phase transformations. The maximum temperature of peak 1 (Tp1) increases from 486.15 to 502.4 1C, while the
maximum temperature of peak 2 (Tp2) increases from 530.61 to 552.67 1C, when the heating rate is increased from 5 to 20 K/min. The peak temperature shifts to higher temperatures with increasing heating rate. Another important parameter for the crystallization mechanism is the peak height. As seen in Fig. 3, after 5 K/min heating rate, the height of the first crystallization peak is greater than the height of the second peak. It is wellknown that the height of the crystallization peak is proportional to the concentration of nuclei in the sample. The shift of peak temperature may be associated with particle size effects on heat transfer. Larger particles would have greater heat transfer resistance when a given heating rate is considered. It takes longer for the center of the particle to reach the furnace temperature. Thus, this process results in a higher crystallization. It is important to know the activation energies involved in glass transition and crystallization processes. The activation energy of the sample can be obtained via the modified Kissinger method [14]. Plotting ln(b/T2g) vs. 1000/T gives a straight line. The value of Eg can be obtained from the
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Fig. 4. ln(b/T2g) and ln b vs. 1000/T plots for the ceramic. Fig. 5. Variation of Tg with ln b for the ceramic.
slope of this straight line (Fig. 4). The Eg value can also be obtained from the following equation: lnðbÞ ¼
Eg þ C; RT g
(11)
where Tg is the glass transition temperature, Eg is the activation energy for structural relaxation and R is the gas constant. This equation can be used when the variation of lnð1=T 2g Þ ln b is much slower than that of 1/Tg with ln b. The ln b vs. 1000/T plot for the sample is shown in Fig. 4. The activation energies of the glass transition were found as 350.9 for the Kissinger method and 363.0 kJ/mol for Mahadevan et al. [19]. The glass transition activation energy, Eg, is the amount of energy absorbed by a group of atoms in the glassy region. This activation energy provides molecular motion and rearrangement of atoms around the glass transition temperature and helps in a jump from one metastable state to another. The glass transition temperature dependence of heating rate can be expressed by the relation [20] T g ¼ A þ B lnðbÞ;
(12)
where A and B are constants. The Tg vs. ln b plot for the sample is shown in Fig. 5. This plot confirmed the validity of the relation and A and B were 1.601 and 688.3 K, respectively. The kinetics of the crystallization can be obtained by the formal theory developed by Johnson and Mehl [21]. In the non-isothermal
method, the fraction x crystallized at any temperature is given as RT AT T ðdH=dTÞ dT ; (13) ¼ x ¼ R T 10 A1 T 0 ðdH=dTÞ dT where T0 and TN are temperatures at which crystallization starts and ends. AN is the total area of the exothermic peak, and AT is the area under the exothermic peak at any temperature. Eq. (10) can be applied to obtain crystallization parameters. A plot of ln[ln(1x)] vs. 1000/T for the sample at different heating rates gives nearly parallel straight lines for the first peak, but this parallel nature disappeared for the second peak [Fig. 6(a and b)]. These plots show linearity over most of the temperature range. At high temperatures or in regions of large crystallization fractions, a slight deviation in the linearity or rather a decrease in slope of the initial slope is observed for all heating rates. This deviation could be attributed to the saturation of the nucleation sites in the final stages of crystallization [22,23]. The other possibility to explain such a behavior could be the restriction of crystal growth by the small size of the particles [24]. The DE C values were obtained from the slope of Fig. 6(a and b) and are given in Table 1. The average activation energy values, DE C ; were found as 1860.23 kJ/mol for the first peak and 1528.22 kJ/mol for the second peak. On the other
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Fig. 6. ln(ln(1x)) vs. 1000/T plots for the ceramic at different heating rates: (a) peak, 1 (b) peak 2.
Table 1 Kinetics parameters of the ceramic Heating rate (K/min)
DE C (kJ/mol) for 1st peak
DE C (kJ/mol) for 2nd peak
5 10 15 20
2310.20 1873.81 1765.43 1491.51
2354.38 2009.80 1070.84 677.86
hand, the DE=n values for the first and second peaks were respectively found as 407.42 and 338.33 kJ/mol. The activation energy and the crystal growth index (Avrami parameter) are
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important kinetics parameters to evaluate crystallization capability the sample. It is well-known that if activation energy is lower, it is easier to crystallize the sample. The crystallization activation energy of the sample decreases with increasing heating rate. This suggests that it is easier to crystallize the sample with a higher heating rate. On the other hand, Eqs. (8) and (10) were used to obtain Avrami parameter n for each peak. The n values were approximately found to be 4.5 using the calculated DE C and DE=n values. The Avrami parameter is expressed as n ¼ a þ bc; where a determines nucleation rate (a ¼ 0 for no nucleation, ao1 for decreasing nucleation rate, a41 for increasing nucleation rate) [25]. The parameter c refers to the dimensionality of growth (c ¼ 1; 2 and 3 for one-dimensional growth, two-dimensional growth and three-dimensional growth, respectively). The b parameter determines the mechanism of the growth (b ¼ 0:5 for diffusioncontrolled growth (parabolic) and b ¼ 1 for interfacial control of growth (linear)). The value of n 4:5 provides c ¼ 3; b ¼ 1 (linear growth) and the value of a ¼ 1:5 (increasing nucleation rate) indicating the crystallization process occurs in the sample by means of three-dimensional growth. The higher the Avrami parameter, the easier the crystallization. The n parameters obtained suggest that crystallization takes place easily in structure and the crystallization mechanism is the bulk crystallization mechanism, in which nucleation occurs in the bulk of the sample. The sharp crystallization peaks seen in Fig. 3 confirm the bulk crystallization. Formation enthalpy is an important parameter to understand the structure of the sample and physical properties. The enthalpy values of glass transition and crystallization temperature were calculated by the following relation: DH ¼ kAr =M;
(14)
where Ar is the area under the peak, k is the instrument constant and M is the mass of the sample. The enthalpy values for the glass transition temperature and crystallization peaks were calculated. The variation of enthalpy values with temperature for these peaks is shown in Fig. 7. It is seen that the enthalpy values increase with
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vestigated using the DSC technique. Three characteristic phenomena were observed in the studied temperature range. The activation energies for glass transition temperature and crystallization phenomena were calculated. It is seen that the activation energy of the first crystallization peak is higher than that of the second peak. The activation energy values of crystallization peaks decrease with increasing heating rates. The Avrami parameter for the sample was found as n 4:5 which suggests that the crystallization process occurs in the sample by means of three-dimensional growth.
Fig. 7. Variation of enthalpy with peak temperatures.
increasing heating rates. The values of DH were determined by a least-squares linear regression analysis. The resultant correlations for the formation enthalpy dependence of peak temperature were experimentally determined as DHðJ=gÞ ¼ 0:651373 TðKÞ þ 462:145
for T g ;
ð15Þ
DHðJ=gÞ ¼ 0:540054 TðKÞ þ 402:714 for T P1 ;
ð16Þ
DHðJ=gÞ ¼ 0:636007 TðKÞ þ 504:383 for T P2 :
ð17Þ
These results suggest that the formation enthalpy values vary linearly with peak temperature. Thus, an experimental equation can be proposed as DH ¼ D T þ E: The D values in Eqs. (16) and (17) increase when these equations were compared with each other and these values are associated with entropy which is a measure of order. This indicates that the entropy value for the Tp1 peak is lower than that of the Tp2 peak.
5. Conclusions The crystallization kinetics of the Bi1.7V0.3Sr2Ca2Cu3Ox glass-ceramic superconductor was in-
Acknowledgements This study was supported by TAEA’s DPT project no AP2. The authors also thank Kırıkkale University for SEM measurements. References [1] M. Zayed, F.A. Nour El-Dien, Thermochim. Acta 114 (1987) 359. [2] A.A. Salman, J. Therm, Anal. Calorim. 63 (2001) 22. [3] L. Nunez, F. Fraga, M.R. Nunez, M.T. Villanueva, Polymer 41 (2000) 4635. [4] X. Wang, K. Yang, Y. Wang, B. Wu, Y. Liu, B. Yang, Polym. Degrad. Stabil. 81 (2003) 415. [5] .M.I. Nad-Elrahman, M.O. Ahmed, S.M. Ahmed, T. Aboul-Fadl, A. El-Shorbagi, Biophys. Chem. 97 (2000) 113. [6] N. Bmanaragan, N.S. Saxena, D. Bhandari, M.M. Imran, D.D. Paudyal, Bull. Mater. Sci. 23 (5) (2000) 369. [7] W.A. Johnson, K.F. Mehl, Trans. Am. Inst. Min. Metall. Eng. 135 (1939) 416. [8] M. Avrami, J. Chem. Phys. 7 (1939) 1103. [9] M. Avrami, J. Chem. Phys. 8 (1940) 212. [10] M. Avrami, J. Chem. Phys. 9 (1941) 177. [11] H. Yinnan, D.R. Uhlmann, J. Non-Cryst. Solids 54 (1983) 253. [12] G. Ruitenberg, E. Woldt, A.K. Petford-Long, Thermochim. Acta 378 (2001) 97–105. [13] D.W. Henderson, J. Non-Cryst. Solids 30 (1979) 301. [14] H.E. Kissinger, Anal. Chem. 29 (1957) 32. [15] T.S. Kayed, N. Calınlı, E. Aksu, H. Koralay, A. Gu¨nen, I˙. Ercan, S. Aktu¨rk, S. C - avdar, Crys. Res. Technol., in press (2004). [16] C.A. Agnell, W. Sichina, Ann. N.Y. Acad. Sci. 279 (1976) 53. [17] M.H. Cohen, G.S. Grest, Phys. Rev. B 21 (1980) 4113. [18] J. Ja¨ckle, Rep. Prog. Phys. 49 (1986) 171.
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