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On the glass transition phenomenon in Se–Te and Se–Ge based ternary chalcogenide glasses
ARTICLE IN PRESS Physica B 404 (2009) 1835–1839
Contents lists available at ScienceDirect
Physica B journal homepage: www.elsevier.com/locate/physb
On the glass transition phenomenon in Se–Te and Se–Ge based ternary chalcogenide glasses N. Mehta a,, K. Singh a, A. Kumar b a b
Department of Physics, Banaras Hindu University, Varanasi 221005, India Department of Physics, Harcourt Butler Technological Institute, Kanpur, India
a r t i c l e in fo
abstract
Article history: Received 16 February 2009 Received in revised form 25 February 2009 Accepted 28 February 2009
The present paper reviews the results of non-isothermal differential scanning calorimetry (DSC) measurements on some ternary glassy systems of Se–Te and Se–Ge chalcogenide alloys for evaluation of activation of glass transition. The activation energy of glass transition (Eg) is calculated using Kissinger’s relation, which is basically derived for amorphous to crystalline phase transition. The results show that Eg values obtained from Kissinger’s relation are in good agreement with the Eg values which are obtained using Moynihan’s relation based on the concept of thermal relaxation. This proves the applicability of Kissinger’s relation for determination of activation energy of glass transition. & 2009 Elsevier B.V. All rights reserved.
Keywords: Chalcogenide glasses Glass transition kinetics Differential scanning calorimetry
1. Introduction In the past three decades, significant interest in chalcogenide glasses has been shown by various workers because of their interesting physical properties as well as their wide technological applications. Though, glassy materials are not in equilibrium, yet their properties strongly depend on the thermal history of samples. In the glass transition region, the properties are dependent on time because, in this region, the experimental time scale becomes comparable to the time scale for structural rearrangements; the material will relax towards equilibrium, this phenomenon being called structural relaxation. One of the most important problems in the area of glasses is the understanding of glass transition kinetics [1–3] which can be studied in terms of glass transition temperature (Tg) and activation energy of thermal relaxation (Eg). The evaluation of Eg using the theory of glass transition kinetics and structural relaxation as developed by Moynihan et al. [4–6] from the heating rate dependence of glass transition temperature is widely discussed in literature [7–10]. However, the Eg values determined from this relation can depend substantially on the thermal history because of the dependence of relaxation time on temperature as well as structure. Hence, Eg values determined from this relation must be viewed as apparent activation energy. Some attempts have also been made to evaluate Eg using Kissinger’s relation [11–29], which is originally derived for
Corresponding author. Tel.: +91 542 2307308; fax.: +91 542 2368174.
E-mail address: [email protected] (N. Mehta). 0921-4526/$ - see front matter & 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2009.02.032
determination of activation energy of crystallization [30–32]. Since Eg evaluated from this relation has less dependence on thermal history [13], this method seems to have some extra advantage. Since this method is basically used for amorphous to crystalline transition, the validity of its use for glass transition kinetics has always been questionable. The application of this relation for glass transition means that some kind of transition is assumed in this case also. Some authors have given the name of this transition as glass to amorphous transition [19,24]. It is, therefore, interesting to see whether Kissinger’s relation can be applied in general for chalcogenide glasses for evaluating the activation energy of structural relaxation, which is normally obtained by Moynihan’s relation. This motivates us to compare the values of activation energy of glass transition process by both the relations in a large number of glassy alloys prepared in our laboratory to check the validity of Kissinger’s relation for glass transition phenomenon. Our results show that Eg values obtained for these glasses using Kissinger’s relation are in good agreement with that obtained using Moynihan’s relation.
2. Theoretical basis 2.1. Moynihan’s relation The heating rate dependence of the glass transition temperature in chalcogenide glasses is interpreted by Moynihan et al. [6] in terms of thermal relaxation phenomenon. In this kinetic interpretation, the enthalpy at a particular temperature and time H (T, t) of the glassy system, after an instantaneous isobaric
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change in temperature, relaxes isothermally toward a new equilibrium value He(T). The relaxation equation can be written in the following form [4]: dH ¼ ðH He Þ=t (1) dt T Here t is a temperature dependent structural relaxation time and is given by the following relation: Eg exp½cðH He Þ t ¼ t0 exp (2) RT where t0 and c are constants and Eg is the activation energy of relaxation time. Using the above equations, it can be shown [5,6] that Eg dðln bÞ ¼ (3) R dð1=T g Þ Eq. (3) states that ln b vs I/Tg plot should be straight line and the activation energy involved in the molecular motions and rearrangements around Tg can be calculated from the slope of this plot. 2.2. Kissinger’s relation This method is most commonly used in analyzing crystallization data in DSC. Kissinger showed that for first order reactions a linear dependence is obtained between ln b/Tc2 and 1/Tc. The conditions of applying Kissinger’s relation are [30]: 1. The crystal growth rate has Arrhenian temperature dependence. 2. Over the temperature range where the thermo-analytical measurements are carried out, the nucleation rate is negligible. 3. Both the crystal growth and nucleation frequency have Arrhenian temperature dependence. During the isothermal transition, the extent of crystallization (a) of a certain material is represented by Avrami’s equation [33,34]:
aðtÞ ¼ 1 expðKtn Þ
(4)
where ‘K’ is rate constant and ‘n’ is the order parameter which depends upon the mechanism of crystal growth. The rate constant K is given by Arrhenius equation: Ec (5) K ¼ K 0 exp RT Here K0 is pre-exponential factor. According to Kissinger, Eq. (4) can be approximated as da ¼ ð1 aÞnK n t n1 dt
The derivative of K with respect to time can be obtained from Eqs. (5) and (8) as follows: dK dK dT bEc (9) ¼ ¼K 2 dt dT dt RT Using Eqs. (7) and (9) Kissinger showed that ! b Ec þ constant ln 2 ¼ RT c Tc
Here Tc is peak crystallization temperature. Although originally derived for the crystallization process, it is suggested that this relation is valid for glass transition process [12,13] and hence the above equation takes the following form for its use in glass transition kinetics: ! Eg b þ constant (11) ln 2 ¼ RT g Tg
3. Experimental Glassy alloys were prepared by quenching technique. The exact proportions of high purity (99.999%) elements, in accordance with their atomic percentages, were weighed out using an electronic balance (LIBROR, AEG-120) with a sensitivity of 104 g. The materials were then sealed in evacuated (105 Torr) quartz ampoules (length 5 cm and internal diameter 8 mm). Each ampoule was kept inside the furnace at a temperature of 1000 1C (where the temperature was raised at a rate of 3–4 1C/min). During heating, all the ampoules were constantly rocked by rotating a ceramic rod to which the ampoules were attached in the furnace. This was done to obtain homogeneous glassy alloys. After rocking for about 12 h, the obtained melts were cooled rapidly by removing the ampoules from the furnace and dropping rapidly into ice-cooled water. The ingots were then taken out by breaking the quartz ampoules. The size of the samples was 3 cm in length and 8 mm in diameter. The glassy nature of the alloys was ascertained by X-ray diffraction. The XRD pattern of glassy Se70Te28Zn2 alloys is shown in Fig. 1. Absence of any sharp peak confirms the glassy nature of the sample. Similar XRD patterns were obtained for other glassy alloys. The glasses, thus prepared, were ground to make fine powder for DSC studies; 10–20 mg of the powder was heated at constant heating rate, and the changes in heat flow with respect to an empty reference pan were measured. Fig. 2 shows the typical DSC scans for glassy Se80Te19Sb1 alloy at different heating rates. It is clear from these figures that well defined peaks are observed at glass transition temperatures (Tg). Similar DSC scans were obtained for the other glassy alloys.
(6)
Expressing t in terms of a from Eq. (4), the crystallization rate da/dt becomes da ¼ AnKð1 aÞ dt
(7) ðn-1Þ=n
. Here A ¼ ½ lnð1 aÞ In non-isothermal crystallization, it is assumed that there is a constant heating rate in the experiment. The relation between the sample temperature T and the heating rate b can be written in the form T ¼ T i þ bt where Ti is the initial temperature.
(10)
(8) Fig. 1. XRD pattern of glassy Se70Te28Zn2 alloy.
ARTICLE IN PRESS N. Mehta et al. / Physica B 404 (2009) 1835–1839
1837
Se80Te19.5Ag0.5
Exothermic
Y
Se80Te19Sb1
25 K/min 20 K/min
4 2 0 -2 -4 -6 -8 -10 -12 2.9
Y = ln β Moynihan's Method Kissinger's Method
Y = ln (β / Tg2) 2.92
2.94 2.96 1000 / Tg (K)-1
2.98
3
Fig. 3. Plots of ln b and ln(b/Tg2) against 103/Tg for glassy Se80Te19.5Ag0.5 alloy.
Endothermic
15 K/min
Se70Ge20As10 4
Y = ln β
2 0
10 K/min
Y
-2 -4
Moynihan's Method Kissinger's Method
-6
5 K/min
-8 Y = ln (β / Tg2)
-10 -12 2.03
2.04
2.05 2.06 2.07 1000 / Tg (K)-1
2.08
2.09
Fig. 4. Plots of ln b and ln(b/Tg2) against 103/Tg for glassy Se70Ge20As10 alloy.
313
333
353
373
393
413
433
453
473
Temperature (K)
Table 1 Activation energy of glass transition for ternary glasses of Se–Te systems.
Fig. 2. DSC scans of glassy Se80Te19Sb1 alloy for different heating rates. Sample
4. Results Using Moynihan’s relation (Eq. (3)), the plots of ln b against 103/Tg are plotted for various glassy alloys of Se–Te and Se–Ge systems. Such plots are shown in Figs. 3 and 4 for glassy Se80Te19.5Ag0.5 and Se70Ge20As10 alloys. Similar plots were obtained for the other glassy alloys. The slopes of these plots were used to calculate the activation energy of glass transition process. Tables 1 and 2 show the Eg values obtained from Eq. (3) for glassy alloys of Se–Te and Se–Ge systems. The values of Eg are also evaluated using Kissinger’s relation (Eq. (11)) from the slopes of plots of ln(b/Tg2) against 103/Tg for various glassy systems. Such plots are shown in Figs. 3 and 4 for glassy Se80Te19.5Ag0.5 and Se70Ge20As10 alloys. Similar plots were obtained for the other glassy alloys. These values are also given in Tables 1 and 2 for glassy alloys of Se–Te and Se–Ge systems. It is clear from Tables 1 and 2 that Eg values obtained from Kissinger’s relation are in good agreement with the Eg values obtained using Moynihan’s relation. The Eg values obtained from these two relations for various glassy alloys are plotted against the composition of chalcogenide glassy systems. Such plots are shown in Figs. 5 and 6 for glassy Se70Te30xZnx and Se80xGe20Asx systems. It is clear from Figs. 5 and 6 that the composition dependence of Eg values obtained using the two relations are similar in both glassy systems. Similar results were obtained for other glassy systems. It is interesting to note that Eq. (3) can also be obtained using the Mahadevan et al. approximation [29] in Eq. (11). According to
Se80Te20 Se80Te19.5Sb0.5 Se80Te19Sb1 Se70Te30 Se70Te28Zn2 Se70Te26Zn4 Se70Te24Zn6 Se70Te22Zn8 Se80Te19.5Ag0.5 Se80Te19.5Cd0.5 Se80Te19.5In0.5 Se80Te19.5Sb0.5
Eg (eV) Moynihan’s method
Kissinger’s method
1.91 1.81 1.31 1.59 1.53 1.62 1.58 1.12 1.75 1.45 1.71 1.71
1.85 1.75 1.33 1.53 1.47 1.57 1.51 1.06 1.69 1.39 1.66 1.65
Table 2 Activation energy of glass transition for ternary glasses of Se–Ge systems. Sample
Se80Ge20 Se75Ge20As5 Se70Ge20As10 Se78Ge22 Se74Ge22Bi4 Se70Ge22Bi8 Se78Ge22Cd10 Se78Ge22In10 Se78Ge22Pb10
Eg (eV) Moynihan’s method
Kissinger’s method
1.11 1.20 1.34 3.15 7.24 5.25 7.90 7.80 6.90
1.04 1.12 1.25 3.07 7.16 5.17 7.80 7.70 6.80
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Chalcogenide glasses may be considered as amorphous semiconductors, since they have no long range order. However, many glass technologists object to this definition as they prepare a glass by cooling a melt in such a way that it does not crystallize and feel that this process is an essential characteristic of a glass. Solids lacking long range positional order are called noncrystalline solids. Non-crystalline solids produced by melt-cooling are generally referred to as glass. Non-crystalline solids made by non-conventional methods, such as vapor deposition, sol–gel and solid-state amorphization processes are sometimes referred to as glass and other times as amorphous solids. A non-crystalline solid is defined as a glass if it satisfies the condition [35]:
Se70Te30-xZnx 1.8 Moynihan’s method Kissinger’s method
Eg (eV)
1.6 1.4 1.2 1 0
2
4
6
8
10
x (at %)
SRO ðglassÞ ¼ SRO ðmeltÞ
However, amorphous solids (a-solids) are the non-crystalline solids, which violate condition (13). In other words [32]
Fig. 5. Composition dependence of Eg in glassy Se70Te30xZnx alloys.
SRO ða-solidsÞa SRO ðmeltÞ
Se80-xGe20Asx 1.4 Moynihan’s method Kissinger’s method
Eg (eV)
1.3 1.2 1.1 1 0
2
4
6 x (at %)
8
10
(13)
12
Fig. 6. Composition dependence of Eg in glassy Se80xGe20Asx alloys.
this approximation, when the variation of ln(1/Tg2) with ln b is much slower than that of 1/Tg then Eq. (11) converts into the form Eg þ constant (12) ln b ¼ RT g which is exactly similar to Eq. (3). This indicates that the structural relaxation phenomenon during glass transition can also be explained by Kissinger’s relation. According to Moharram et al. [19,24], glass transition kinetics can be treated as pre-crystallization kinetics and the analysis of endothermic (glass transition) peaks can be made in the same way as those made on exothermic (crystallization) peaks using Kissinger’s relation.
5. Discussion Glassy solid state has a large viscosity; the relaxation kinetics are very slow leaving a few opportunities for local arrangements of bonds and atomic displacements. This type of thermal relaxation depends upon the annealing temperature and may be quite fast near the glass transition temperature. Thus, it is reasonable to associate the glass transition temperature with the structural rearrangements. On the basis of this, the glass transition phenomenon can be divided into the following three regimes:
(14)
Thus, we see that ‘amorphous’ and ‘glass’ are the two different phases of non-crystalline solids. A chalcogenide glass can, therefore, said to be in ‘glass’ phase before the glass transition (ToTg) which transforms into a new phase after the glass transition (T4Tg). Though, it faces structural rearrangements in glass transition process, yet it retains short range order structure in this new phase. The phase from glass transition temperature to crystallization temperature may be called ‘amorphous’ phase as on heating further, a transition takes place from amorphous phase to crystalline phase. From the above discussion, it is clear that the glass transition phenomenon can be treated as glass to amorphous phase transition. For ToTg, the sample is in glassy phase, while it transforms into amorphous phase for T4Tg. Since Kissinger’s relation is derived for crystallization process, which is also a phase transition from amorphous phase to crystalline phase, it may be valid for glass to amorphous transition process also. The present results support this argument as the Eg values obtained from the two relations are in good agreement with each other.
6. Conclusions The activation energy of glass transition process has been determined using Kissinger’s relation for various glassy alloys in order to compare the Eg values obtained from this relation with the Eg values evaluated by us in our previous work using Moynihan’s relation. The results show that Eg values obtained from Kissinger’s relation are in good agreement with the Eg values which were obtained using Moynihan’s relation. It has also been found that the composition dependence of Eg values obtained using the two relations are similar in most of the glassy systems. Thus, one can use any of the two relations (Kissinger’s relation and Moynihan’s relation) for the evaluation of Eg values. The major conclusion of the present work is that, analogous to crystallization process, the glass transition phenomenon is also a phase transition process in chalcogenide glasses. Hence, Kissinger’s relation can be used for evaluation of activation energy of glass transition as well as crystallization processes in chalcogenide glasses. References
(i) T4Tg ) it describes liquid equilibrium region where the return to equilibrium is almost instantaneous. (ii) TTg ) it describes glass transition region. (iii) ToTg ) it describes glass region, where the structure is frozen.
[1] C. Bergman, I. Avramov, C.V. Zahra, J.C. Mathieu, J. Non-Cryst. Solids 70 (1985) 367. [2] A.N. Sreeram, D.R. Swiler, A.K. Varshneya, J. Non-Cryst. Solids 127 (1991) 77. [3] S.R. Joshi, A. Pratap, N.S. Saxena, M.P. Saksena, A. Kumar, J. Mater. Sci. 13 (1994) 287.
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Contents lists available at ScienceDirect
Physica B journal homepage: www.elsevier.com/locate/physb
On the glass transition phenomenon in Se–Te and Se–Ge based ternary chalcogenide glasses N. Mehta a,, K. Singh a, A. Kumar b a b
Department of Physics, Banaras Hindu University, Varanasi 221005, India Department of Physics, Harcourt Butler Technological Institute, Kanpur, India
a r t i c l e in fo
abstract
Article history: Received 16 February 2009 Received in revised form 25 February 2009 Accepted 28 February 2009
The present paper reviews the results of non-isothermal differential scanning calorimetry (DSC) measurements on some ternary glassy systems of Se–Te and Se–Ge chalcogenide alloys for evaluation of activation of glass transition. The activation energy of glass transition (Eg) is calculated using Kissinger’s relation, which is basically derived for amorphous to crystalline phase transition. The results show that Eg values obtained from Kissinger’s relation are in good agreement with the Eg values which are obtained using Moynihan’s relation based on the concept of thermal relaxation. This proves the applicability of Kissinger’s relation for determination of activation energy of glass transition. & 2009 Elsevier B.V. All rights reserved.
Keywords: Chalcogenide glasses Glass transition kinetics Differential scanning calorimetry
1. Introduction In the past three decades, significant interest in chalcogenide glasses has been shown by various workers because of their interesting physical properties as well as their wide technological applications. Though, glassy materials are not in equilibrium, yet their properties strongly depend on the thermal history of samples. In the glass transition region, the properties are dependent on time because, in this region, the experimental time scale becomes comparable to the time scale for structural rearrangements; the material will relax towards equilibrium, this phenomenon being called structural relaxation. One of the most important problems in the area of glasses is the understanding of glass transition kinetics [1–3] which can be studied in terms of glass transition temperature (Tg) and activation energy of thermal relaxation (Eg). The evaluation of Eg using the theory of glass transition kinetics and structural relaxation as developed by Moynihan et al. [4–6] from the heating rate dependence of glass transition temperature is widely discussed in literature [7–10]. However, the Eg values determined from this relation can depend substantially on the thermal history because of the dependence of relaxation time on temperature as well as structure. Hence, Eg values determined from this relation must be viewed as apparent activation energy. Some attempts have also been made to evaluate Eg using Kissinger’s relation [11–29], which is originally derived for
Corresponding author. Tel.: +91 542 2307308; fax.: +91 542 2368174.
E-mail address: [email protected] (N. Mehta). 0921-4526/$ - see front matter & 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2009.02.032
determination of activation energy of crystallization [30–32]. Since Eg evaluated from this relation has less dependence on thermal history [13], this method seems to have some extra advantage. Since this method is basically used for amorphous to crystalline transition, the validity of its use for glass transition kinetics has always been questionable. The application of this relation for glass transition means that some kind of transition is assumed in this case also. Some authors have given the name of this transition as glass to amorphous transition [19,24]. It is, therefore, interesting to see whether Kissinger’s relation can be applied in general for chalcogenide glasses for evaluating the activation energy of structural relaxation, which is normally obtained by Moynihan’s relation. This motivates us to compare the values of activation energy of glass transition process by both the relations in a large number of glassy alloys prepared in our laboratory to check the validity of Kissinger’s relation for glass transition phenomenon. Our results show that Eg values obtained for these glasses using Kissinger’s relation are in good agreement with that obtained using Moynihan’s relation.
2. Theoretical basis 2.1. Moynihan’s relation The heating rate dependence of the glass transition temperature in chalcogenide glasses is interpreted by Moynihan et al. [6] in terms of thermal relaxation phenomenon. In this kinetic interpretation, the enthalpy at a particular temperature and time H (T, t) of the glassy system, after an instantaneous isobaric
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change in temperature, relaxes isothermally toward a new equilibrium value He(T). The relaxation equation can be written in the following form [4]: dH ¼ ðH He Þ=t (1) dt T Here t is a temperature dependent structural relaxation time and is given by the following relation: Eg exp½cðH He Þ t ¼ t0 exp (2) RT where t0 and c are constants and Eg is the activation energy of relaxation time. Using the above equations, it can be shown [5,6] that Eg dðln bÞ ¼ (3) R dð1=T g Þ Eq. (3) states that ln b vs I/Tg plot should be straight line and the activation energy involved in the molecular motions and rearrangements around Tg can be calculated from the slope of this plot. 2.2. Kissinger’s relation This method is most commonly used in analyzing crystallization data in DSC. Kissinger showed that for first order reactions a linear dependence is obtained between ln b/Tc2 and 1/Tc. The conditions of applying Kissinger’s relation are [30]: 1. The crystal growth rate has Arrhenian temperature dependence. 2. Over the temperature range where the thermo-analytical measurements are carried out, the nucleation rate is negligible. 3. Both the crystal growth and nucleation frequency have Arrhenian temperature dependence. During the isothermal transition, the extent of crystallization (a) of a certain material is represented by Avrami’s equation [33,34]:
aðtÞ ¼ 1 expðKtn Þ
(4)
where ‘K’ is rate constant and ‘n’ is the order parameter which depends upon the mechanism of crystal growth. The rate constant K is given by Arrhenius equation: Ec (5) K ¼ K 0 exp RT Here K0 is pre-exponential factor. According to Kissinger, Eq. (4) can be approximated as da ¼ ð1 aÞnK n t n1 dt
The derivative of K with respect to time can be obtained from Eqs. (5) and (8) as follows: dK dK dT bEc (9) ¼ ¼K 2 dt dT dt RT Using Eqs. (7) and (9) Kissinger showed that ! b Ec þ constant ln 2 ¼ RT c Tc
Here Tc is peak crystallization temperature. Although originally derived for the crystallization process, it is suggested that this relation is valid for glass transition process [12,13] and hence the above equation takes the following form for its use in glass transition kinetics: ! Eg b þ constant (11) ln 2 ¼ RT g Tg
3. Experimental Glassy alloys were prepared by quenching technique. The exact proportions of high purity (99.999%) elements, in accordance with their atomic percentages, were weighed out using an electronic balance (LIBROR, AEG-120) with a sensitivity of 104 g. The materials were then sealed in evacuated (105 Torr) quartz ampoules (length 5 cm and internal diameter 8 mm). Each ampoule was kept inside the furnace at a temperature of 1000 1C (where the temperature was raised at a rate of 3–4 1C/min). During heating, all the ampoules were constantly rocked by rotating a ceramic rod to which the ampoules were attached in the furnace. This was done to obtain homogeneous glassy alloys. After rocking for about 12 h, the obtained melts were cooled rapidly by removing the ampoules from the furnace and dropping rapidly into ice-cooled water. The ingots were then taken out by breaking the quartz ampoules. The size of the samples was 3 cm in length and 8 mm in diameter. The glassy nature of the alloys was ascertained by X-ray diffraction. The XRD pattern of glassy Se70Te28Zn2 alloys is shown in Fig. 1. Absence of any sharp peak confirms the glassy nature of the sample. Similar XRD patterns were obtained for other glassy alloys. The glasses, thus prepared, were ground to make fine powder for DSC studies; 10–20 mg of the powder was heated at constant heating rate, and the changes in heat flow with respect to an empty reference pan were measured. Fig. 2 shows the typical DSC scans for glassy Se80Te19Sb1 alloy at different heating rates. It is clear from these figures that well defined peaks are observed at glass transition temperatures (Tg). Similar DSC scans were obtained for the other glassy alloys.
(6)
Expressing t in terms of a from Eq. (4), the crystallization rate da/dt becomes da ¼ AnKð1 aÞ dt
(7) ðn-1Þ=n
. Here A ¼ ½ lnð1 aÞ In non-isothermal crystallization, it is assumed that there is a constant heating rate in the experiment. The relation between the sample temperature T and the heating rate b can be written in the form T ¼ T i þ bt where Ti is the initial temperature.
(10)
(8) Fig. 1. XRD pattern of glassy Se70Te28Zn2 alloy.
ARTICLE IN PRESS N. Mehta et al. / Physica B 404 (2009) 1835–1839
1837
Se80Te19.5Ag0.5
Exothermic
Y
Se80Te19Sb1
25 K/min 20 K/min
4 2 0 -2 -4 -6 -8 -10 -12 2.9
Y = ln β Moynihan's Method Kissinger's Method
Y = ln (β / Tg2) 2.92
2.94 2.96 1000 / Tg (K)-1
2.98
3
Fig. 3. Plots of ln b and ln(b/Tg2) against 103/Tg for glassy Se80Te19.5Ag0.5 alloy.
Endothermic
15 K/min
Se70Ge20As10 4
Y = ln β
2 0
10 K/min
Y
-2 -4
Moynihan's Method Kissinger's Method
-6
5 K/min
-8 Y = ln (β / Tg2)
-10 -12 2.03
2.04
2.05 2.06 2.07 1000 / Tg (K)-1
2.08
2.09
Fig. 4. Plots of ln b and ln(b/Tg2) against 103/Tg for glassy Se70Ge20As10 alloy.
313
333
353
373
393
413
433
453
473
Temperature (K)
Table 1 Activation energy of glass transition for ternary glasses of Se–Te systems.
Fig. 2. DSC scans of glassy Se80Te19Sb1 alloy for different heating rates. Sample
4. Results Using Moynihan’s relation (Eq. (3)), the plots of ln b against 103/Tg are plotted for various glassy alloys of Se–Te and Se–Ge systems. Such plots are shown in Figs. 3 and 4 for glassy Se80Te19.5Ag0.5 and Se70Ge20As10 alloys. Similar plots were obtained for the other glassy alloys. The slopes of these plots were used to calculate the activation energy of glass transition process. Tables 1 and 2 show the Eg values obtained from Eq. (3) for glassy alloys of Se–Te and Se–Ge systems. The values of Eg are also evaluated using Kissinger’s relation (Eq. (11)) from the slopes of plots of ln(b/Tg2) against 103/Tg for various glassy systems. Such plots are shown in Figs. 3 and 4 for glassy Se80Te19.5Ag0.5 and Se70Ge20As10 alloys. Similar plots were obtained for the other glassy alloys. These values are also given in Tables 1 and 2 for glassy alloys of Se–Te and Se–Ge systems. It is clear from Tables 1 and 2 that Eg values obtained from Kissinger’s relation are in good agreement with the Eg values obtained using Moynihan’s relation. The Eg values obtained from these two relations for various glassy alloys are plotted against the composition of chalcogenide glassy systems. Such plots are shown in Figs. 5 and 6 for glassy Se70Te30xZnx and Se80xGe20Asx systems. It is clear from Figs. 5 and 6 that the composition dependence of Eg values obtained using the two relations are similar in both glassy systems. Similar results were obtained for other glassy systems. It is interesting to note that Eq. (3) can also be obtained using the Mahadevan et al. approximation [29] in Eq. (11). According to
Se80Te20 Se80Te19.5Sb0.5 Se80Te19Sb1 Se70Te30 Se70Te28Zn2 Se70Te26Zn4 Se70Te24Zn6 Se70Te22Zn8 Se80Te19.5Ag0.5 Se80Te19.5Cd0.5 Se80Te19.5In0.5 Se80Te19.5Sb0.5
Eg (eV) Moynihan’s method
Kissinger’s method
1.91 1.81 1.31 1.59 1.53 1.62 1.58 1.12 1.75 1.45 1.71 1.71
1.85 1.75 1.33 1.53 1.47 1.57 1.51 1.06 1.69 1.39 1.66 1.65
Table 2 Activation energy of glass transition for ternary glasses of Se–Ge systems. Sample
Se80Ge20 Se75Ge20As5 Se70Ge20As10 Se78Ge22 Se74Ge22Bi4 Se70Ge22Bi8 Se78Ge22Cd10 Se78Ge22In10 Se78Ge22Pb10
Eg (eV) Moynihan’s method
Kissinger’s method
1.11 1.20 1.34 3.15 7.24 5.25 7.90 7.80 6.90
1.04 1.12 1.25 3.07 7.16 5.17 7.80 7.70 6.80
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Chalcogenide glasses may be considered as amorphous semiconductors, since they have no long range order. However, many glass technologists object to this definition as they prepare a glass by cooling a melt in such a way that it does not crystallize and feel that this process is an essential characteristic of a glass. Solids lacking long range positional order are called noncrystalline solids. Non-crystalline solids produced by melt-cooling are generally referred to as glass. Non-crystalline solids made by non-conventional methods, such as vapor deposition, sol–gel and solid-state amorphization processes are sometimes referred to as glass and other times as amorphous solids. A non-crystalline solid is defined as a glass if it satisfies the condition [35]:
Se70Te30-xZnx 1.8 Moynihan’s method Kissinger’s method
Eg (eV)
1.6 1.4 1.2 1 0
2
4
6
8
10
x (at %)
SRO ðglassÞ ¼ SRO ðmeltÞ
However, amorphous solids (a-solids) are the non-crystalline solids, which violate condition (13). In other words [32]
Fig. 5. Composition dependence of Eg in glassy Se70Te30xZnx alloys.
SRO ða-solidsÞa SRO ðmeltÞ
Se80-xGe20Asx 1.4 Moynihan’s method Kissinger’s method
Eg (eV)
1.3 1.2 1.1 1 0
2
4
6 x (at %)
8
10
(13)
12
Fig. 6. Composition dependence of Eg in glassy Se80xGe20Asx alloys.
this approximation, when the variation of ln(1/Tg2) with ln b is much slower than that of 1/Tg then Eq. (11) converts into the form Eg þ constant (12) ln b ¼ RT g which is exactly similar to Eq. (3). This indicates that the structural relaxation phenomenon during glass transition can also be explained by Kissinger’s relation. According to Moharram et al. [19,24], glass transition kinetics can be treated as pre-crystallization kinetics and the analysis of endothermic (glass transition) peaks can be made in the same way as those made on exothermic (crystallization) peaks using Kissinger’s relation.
5. Discussion Glassy solid state has a large viscosity; the relaxation kinetics are very slow leaving a few opportunities for local arrangements of bonds and atomic displacements. This type of thermal relaxation depends upon the annealing temperature and may be quite fast near the glass transition temperature. Thus, it is reasonable to associate the glass transition temperature with the structural rearrangements. On the basis of this, the glass transition phenomenon can be divided into the following three regimes:
(14)
Thus, we see that ‘amorphous’ and ‘glass’ are the two different phases of non-crystalline solids. A chalcogenide glass can, therefore, said to be in ‘glass’ phase before the glass transition (ToTg) which transforms into a new phase after the glass transition (T4Tg). Though, it faces structural rearrangements in glass transition process, yet it retains short range order structure in this new phase. The phase from glass transition temperature to crystallization temperature may be called ‘amorphous’ phase as on heating further, a transition takes place from amorphous phase to crystalline phase. From the above discussion, it is clear that the glass transition phenomenon can be treated as glass to amorphous phase transition. For ToTg, the sample is in glassy phase, while it transforms into amorphous phase for T4Tg. Since Kissinger’s relation is derived for crystallization process, which is also a phase transition from amorphous phase to crystalline phase, it may be valid for glass to amorphous transition process also. The present results support this argument as the Eg values obtained from the two relations are in good agreement with each other.
6. Conclusions The activation energy of glass transition process has been determined using Kissinger’s relation for various glassy alloys in order to compare the Eg values obtained from this relation with the Eg values evaluated by us in our previous work using Moynihan’s relation. The results show that Eg values obtained from Kissinger’s relation are in good agreement with the Eg values which were obtained using Moynihan’s relation. It has also been found that the composition dependence of Eg values obtained using the two relations are similar in most of the glassy systems. Thus, one can use any of the two relations (Kissinger’s relation and Moynihan’s relation) for the evaluation of Eg values. The major conclusion of the present work is that, analogous to crystallization process, the glass transition phenomenon is also a phase transition process in chalcogenide glasses. Hence, Kissinger’s relation can be used for evaluation of activation energy of glass transition as well as crystallization processes in chalcogenide glasses. References
(i) T4Tg ) it describes liquid equilibrium region where the return to equilibrium is almost instantaneous. (ii) TTg ) it describes glass transition region. (iii) ToTg ) it describes glass region, where the structure is frozen.
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