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The crystallization kinetics of Se_{80}In_{10}Pb_{10} chalcogenide glass is studied using differential scanning calorimeter (DSC) at different heating rates (5, 10, 15 and 20 K/min) under non-isothermal conditions. Four iso-conversional methods (Kissinger-Akahira-Sunose, Flynn-Wall-Ozawa, Tang and Straink) were used to determine various kinetic parameters: crystallization temperature (T_{α}), activation energy of crystallization (E_{α}), Avrami exponent (n_{α}) in non-isothermal mode. The transformation from amorphous to crystalline phase in Se_{80}In_{10}Pb_{10} is considered as a single step reaction mechanism.

The chalcogenide glasses have drawn a great attention since last 5 - 6 decades due to their wide range of applications in various fields [

The thermal behavior of the chalcogenide glasses plays an important role in determining the transport mechanism, thermal stability and useful applications. The differential scanning calorimeter (DSC) technique has so for been employed to study the crystallization process in amorphous alloys and proved to be the most effective method for such studies [

In the present study, we report the crystallization kinetics of Se_{80}In_{10}Pb_{10} chalcogenide glass. The activation energy was determined using four iso-conversional methods (Kissinger-Akahira-Sunose (KAS), Flynn-WallOzawa (FWO), Tang and Straink). The Avrami exponent also has been determined to study nucleation and growth during crystallization process.

The investigated Se_{80}In_{10}Pb_{10} chalcogenide glass was prepared from high purity (99.999%) Se, In and Pb elements by melt quenching technique. The desired amounts of constituent elements were weighed according to their atomic weight percentage and put into cleaned quartz ampoule. The ampoule was evacuated and sealed under a vacuum of 10^{−5} Torr to exclude reaction of alloying materials with Oxygen at higher temperature. The sealed ampoule was heated in a furnace at rate of 4 - 5 K/min and raised the temperature up to 1100 K and kept it at that temperature for 12 hours. During the melting process the ampoule was frequently rocked to ensure the homogeneity of alloying materials. After the above said period, the ampoule with molten materials was rapidly quenched into ice cooled water. The ingot of glassy material was taken out from ampoule by breaking them. The X-ray diffraction pattern of as prepared material was recorded using Philips PW-1830 Diffractometer with Cu-K_{α}_{ }(λ = 1.54 Å) to confirm the amorphous nature of prepared glass. The XRD pattern of Se_{80}In_{10}Pb_{10} chalcogenide glass is shown in _{80}In_{10}Pb_{10} chalcogenide glass. The surface morphology of Se_{80}In_{10}Pb_{10} chalcogenide glass was done by using Scanning Electron Microscopy (SEM) (Model: Quanta 200). The SEM image is shown in _{80}In_{10}Pb_{10} chalcogenide glass is also confirmed by using an energy dispersive X-ray analysis (EDAX). The EDAX spectrum of Se_{80}In_{10}Pb_{10} is shown in

The DSC thermograms of Se_{80}In_{10}Pb_{10} chalcogenide glass at different heating rates (5, 10, 15 and 20 K/min) are shown in _{g} and an exothermic peak at the crystallization temperature T_{c}. The crystallized fraction α at a given temperature T is given as α = (A_{T}/A), where A is the total area of the exothermic

peak between the onset temperature (T_{i}) where crystallization just begins and the temperature (T_{f}) where the crystallization is completed. A_{T} is the area between T_{i} and T. The values of T corresponding to α are listed in

_{80}In_{10}Pb_{10} chalcogenide glass at different heating rates.

shown in

The kinetics of crystallization in amorphous material can be described by the following rate equation [

where, K is the reaction rate constant usually has Arrhenius temperature dependence, is the reaction model, t is time and α is the crystallized fraction.

But reaction rate constant K is given by following equation:

where, K_{0} is pre-exponential factor of rate constant, E is activation energy, T is temperature and R is universal gas constant.

Under non-isothermal condition with a constant heating rate and using Equation (2), Equa-

tion (1) can be written as:

There is a variety of theoretical models and mathematical equations to explain the estimation of crystallization kinetics. The following four iso-conversional methods have been used in present study to analyze the crystallization kinetics of Se_{80}In_{10}Pb_{10} chalcogenide glass. All the four methods require the determination of the temperature T_{αi} at which a fixed fraction α of the total amount is transformed.

In KAS method, the relation between the temperature T_{αi}_{ }and heating rate β_{i} is given by [20,21];

The subscript i denotes different heating rates. For each degree of the conversion α, a corresponding T_{αi}_{ }and heating rates are used. The graphs of versus 1000/T_{αi}_{ }for Se_{80}In_{10}Pb_{10} chalcogenide glass are shown in _{α}._{ }The obtained values of E_{α}_{ }are listed in

In FWO method, the relation between the temperature T_{αi}_{ }and heating rate β_{i} is given by [22-24];

The graphs of ln(β_{i}) versus 1000/T_{αi}_{ }for Se_{80}In_{10}Pb_{10} chalcogenide glass are shown in _{α}._{ }The obtained values of E_{α}_{ }are listed in

_{80}In_{10}Pb_{10} chalcogenide glass at different crystallized fraction (α) for different iso-conversional methods.

In Tang method [_{αi}_{ }and heating rate β_{i} is given by;

The graphs of versus 1000/T_{αi}_{ }for Se_{80}In_{10}Pb_{10} chalcogenide glass are shown in _{α}. The obtained values of E_{α}_{ }are listed in

In Straink method [26,27], the relation between the temperature T_{αi}_{ }and heating rate β_{i} is given by;

The graphs of versus 1000/T_{αi}_{ }for Se_{80}In_{10}Pb_{10} chalcogenide glass are shown in _{α}. The obtained values of E_{α}_{ }are listed in

The purpose of apply four different iso-conversional methods for evaluation of E_{α} is to check the validity of the four methods. The values of E_{α} obtained by the four methods are in good agreement. There is an about 1% experimental error in the evaluation of E_{α} by all four methods. The Kissinger-Akahira-Sunose (KAS) method is sometimes called generalized Kissinger method is one of the best iso-conversional method [_{α} are independent of α, the crystallization process is dominated by a single step reaction mechanism [_{α} with α could

be explained in terms of multi-step reaction mechanism [30,31]. If the relative error of the E_{α} evaluated from iso-conversional method is lower than 10%, then the values of E_{α} can be considered as independent of α [_{α} at different crystallized fraction evaluated by four iso-conversional methods vary here by about 7.9, 6.2, 7.7 and 8.1%, respectively. So, the crystallization process could be considered as a single step reaction mechanism. The variation of the activation energy with temperature demonstrates that the rate of crystallization is actually determined by the rates of two processes; nucleation and diffusion. Because these two mechanisms are likely to have different activation energies, the effective activation energy of the transformation will vary with temperature [17,33]. This interpretation is based on the nucleation theory proposed by Fisher and Turnbull [_{80}In_{10}Pb_{10 }glass that the amorphous to crystallization can be described by single-step reaction mechanism.

The Avrami exponent can be calculated from the following equation [

The evaluated values of the Avrami exponent n_{α} are listed in _{α} decreases with increasing temperature. It is well known that crystallization of chalcogenide glasses is associated with nucleation and growth process. The degree of crystallization increases with increase in temperature. In other words, it attains its maximum value 1. The decrease in value of n_{α} with increasing temperature suggests that the character of crystallization changes from nucleation-driven in the beginning to essentially a growth-driven regime by the end of crystallization process.

_{α}) of Se_{80}In_{10}Pb_{10} chalcogenide glass at different crystallized fraction (α) for different heating rates.

1) The activation energy as determined from the four iso-conversional methods was found to be varying in the same way and show a little variation with crystallized fraction and temperature.

2) The Avrami exponent n_{α}_{ }also show a little variation with crystallized fraction and temperature.

3) The transformation from amorphous to crystalline phase in Se_{80}In_{10}Pb_{10 }is a single-step mechanism.

ISR is thankful to the Principal, Dyal Singh College, University of Delhi, New Delhi for sanctioned study leave to carry out research work. We are also thankful to CSIR, New Delhi for providing financial assistance under research project no. 01(2456)/11/EMR-II to carry out research work.