Critical analysis of endo-thermal effect in the glass transition process in chalcogenide glasses
Highlights
► The constancy of the glass transition activation energy has been checked. ► The applicability of Kissinger relation has been verified. ► The selection of peak value of the glass transition endotherm is established.
Introduction
Theories based on the concepts of free volume model are used by various workers in the past to understand the glass transition and relaxation in different types of glasses and polymers [1], [2], [3], [4]. Lipatov and Privalko [1] explained the dependence of free volume fraction at the glass transition temperature on the molecular parameters of linear polymers. Possible experimental equivalence of the Gibbs–DiMarzio and free volume theories of the glass transition was proposed by Eisenberg and Saito [2]. Grenberg and Kusy [3] reported the quantities evaluation of the Gibbs–DiMarzio theory of the glass transition using the assumption that both the inter-/intramolecular energy ratio and the effective chain segment density remain constant while the fractional free volume at glass transition temperature varies as a function of reciprocal degree of polymerization. Chow [4] described the glass relaxation in terms of collapse of a series of free volume having different creation energies but having equal volume.
The evaluation of Eg using the theory of glass transition kinetics and structural relaxation as developed by Moynihan and other workers [5], [6], [7] from the heating rate dependence of glass transition temperature is widely discussed in literature. 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 [8], [9], [10], [11], [12], [13]. Since Eg evaluated from this relation has less dependence on thermal history [9], this method seems to have some extra advantage. Since this method is basically given for amorphous to crystalline transformation, 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 transformation is assumed in this case also. Some authors have given the name of this transformation as glass to amorphous transformation [10], [11]. It is, therefore, interesting to see whether the 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. We have already proved that Eg values obtained for chalcogenide glasses using Kissinger's relation are in good agreement with that obtained using Moynihan's relation [12], [13].
Soliman has derived the Kissinger's equation in terms of the free volume model [14]. He also tested the activation energy for constancy throughout the glass transition for granted this model. For this, a particular Cu0.3(SSe20)0.7 chalcogenide glass was used. In the present work, the constancy of Eg is tested for three glassy systems Se80-xTe20Mx (0 ≤ x ≤ 15; M = Ag, Cd, Sb) of chalcogenide glasses to check the generalization of free volume model for derivation of Kissinger's relation. The present manuscript puts an end by a convincing way to a longstanding disputation about the nature of the endo-thermal effect related to the glass transition temperature. The reason behind the selection of chalcogenide glasses is the facility of sharp glass transition peaks as compared to oxide and metallic glasses; where generally, we observe a bump as glass transition peak.
Section snippets
Theoretical basis
A general picture of the glass transition naturally leads to an idea that the motion of a molecule in a densely packed configuration needs some cooperative motion of the surrounding molecules. The first major development in the direction of understanding of glass transition phenomenon was the formulation of free volume theory of liquid viscosities. The free volume model since proposed by Cohen and Turnbull [15] and developed by Cohen and Spaepen [16], [17] has been widely employed to explain
Material preparation
Glassy alloys of Se80-xTe20Mx (0 ≤ x ≤ 15; M = Ag, Cd, Sb) systems were prepared by quenching technique. The exact proportions of high purity (99.999%) Se, Te, Ag, Cd and Sb elements, in accordance with their atomic percentages, were weighed using an electronic balance (LIBROR, AEG-120) with the least count of 10− 4 g. The material was then sealed in evacuated (~ 10− 5 Torr) quartz ampoules (length ~ 5 cm and internal diameter ~ 8 mm). The ampoules containing material were heated to 1000 °C and were held at
Experimental
After rocking for about 12 h, the obtained melts were cooled rapidly by removing the ampoules from the furnace and dropping to ice-cooled water rapidly. The quenched samples were then taken out by breaking the quartz ampoules. The glassy nature of the alloys was ascertained by X-ray diffraction (XRD) technique. The XRD pattern of glassy Se70Te20Sb10 is shown in Fig. 1. Absence of any sharp peak in XRD pattern in Fig. 1 confirms the glassy nature of Se70Te20Sb10 alloy. Similar XRD patterns were
Results
To check the application of free volume model for the Kissinger's equation to the glass transition endothermic peak, Tg is determined by using three different definitions [26], [27]. This is shown in Fig. 2 for glassy Se75Te20Cd15 at a heating rate of 20 °C/min. The extrapolated onset of the heat capacity break is designated as on-set glass transition temperature (Tg)on, where the auxiliary line through the ascending peak slope intersects the interpolated baseline. The inflection point in the
Discussion
It is clear from Fig. 5 that the composition dependence of Eg values obtained using the three different definitions of glass transition temperature are also dissimilar in the present glassy systems. This shows that the value of Eg is not constant throughout the whole glass transition temperature range. This can be understood as follows:
Glassy solid state has a large viscosity, the relaxation kinetics are very slow leaving a few opportunities for local arrangements of bonds and atomic
Conclusions
The activation energy of glass transition process has been determined by Kissinger's relation for various glassy alloys using heating rate dependence of on-set glass transition temperature (Tg)on, peak glass transition temperature (Tg)p and off-set glass transition temperature (Tg)off in order to compare the Eg values obtained for the three different definitions of glass transition temperature. The major conclusions of the present work are as follows:
- 1.
Kissinger approach, which has been shown to
Acknowledgments
One of us, NM is thankful to the Board of Research in Nuclear Sciences (BRNS), Mumbai, India for providing financial assistance under DAE Research Award for Young Scientists [Scheme No. 2011/20/37P/02/BRNS].
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