** Journal of Crystallization Process and Technology** Vol.4 No.2(2014), Article ID:45163,10 pages DOI:10.4236/jcpt.2014.42014

Kinetic Study of Non-Isothermal Crystallization in Se_{90−x}Zn_{10}Sb_{x} (x = 0, 2, 4, 6) Chalcogenide Glasses

Lamia Heireche, Mohamed Heireche, Maamar Belhadji

Physics Department, Faculty of Science, Oran University, Oran, Algeria

Email: heirechelamia80@yahoo.f, heirechemohamed@yahoo.fr, nmaamar@yahoo.fr

Copyright © 2014 by authors and Scientific Research Publishing Inc.

This work is licensed under the Creative Commons Attribution International License (CC BY).

http://creativecommons.org/licenses/by/4.0/

Received 25 February 2014; revised 25 March 2014; accepted 1 April 2014

ABSTRACT

Crystallization and glass transition kinetics of Se_{90−x}Zn_{10}Sb_{x }(x = 0, 2, 4, 6) chalcogenide glasses prepared by conventional melt-quenching technique were studied under non-isothermal condition using a differential scanning Calorimeter (DSC) measurement at different heating rates 5, 7, 10 and 12˚C/min. The glass transition temperatures T_{g}, the crystallization temperatures T_{c} and the peak temperatures of crystallization T_{p} were found to be dependent on the compositions and the heating rates. From the dependence on the heating rates of T_{g} and T_{p}, the activation energy for glass transition, E_{g}, and the activation energy for crystallization, E_{c}, are calculated and their composition dependence is discussed. The activation energy of glass transition E_{g}, Avrami index n, dimensionality of growth m and activation energy of crystallization E_{c }have been determined from different models.

**Keywords:**Crystallization Kinetics, Chalcogenide Glasses, Crystallization Temperature, Activation Energy, Differential Scanning Calorimetry

1. Introduction

Chalcogenide glasses are of wide-ranging importance in a variety of technological. They are based on chalcogen elements S, Se and Te. These glasses are formed by the addition of other elements such as Ga, In, Si, Ge, Sn, As, Sb, Bi, Ag, Cd, Zn. Many researchers have studied the structure, electrical properties, photoconductivity, glass formation and crystallization kinetics of the glassy system [1] -[7] . The current interest in chalcogenide materials centers on X-ray imaging [8] , xerography [9] , optical recording [10] , memory switching [11] and electrographic applications such as photoreceptors in photocopying and laser printing [12] -[14] . The binary Se-Zn alloys have more advantages due to their wide band gap; they are an example of potential applications in optoelectronic devices like blue light emitting diodes and blue diode lasers [15] and white Light Emitting Diodes (LEDs) and infrared lenses [16] . The proprieties of binary SeZn can be modified by adding a third element. The work presented in this paper has been done with the purpose of studying the effect of Sb on various thermal parameters in binary Se-Zn system, the crystallization kinetics and the evaluation of the crystallization parameters of Se_{90-x}Zn_{10}Sb_{x} (x = 0, 2, 4, 6) glassy alloy under non-isothermal conditions. Using the differential scanning calorimetry (DSC) measurement, the kinetic parameters such as activation energy of glass transition E_{g}, Avrami index n, dimensional growth m and activation energy of crystallization E_{c} have been determined from different models.

2. Experimental

Bulk sample of the Se_{90-x}Zn_{10}Sb_{x }(x = 0, 2, 4, 6) were prepared by the melt quenching technique. High purity materials (99.999%) were weighted according to their atomic percentages and were sealed in quartz ampoules under the vacuum of 10^{−5} Torr. The sealed ampoules are kept inside the furnace where the temperature was raised to 800˚C for 10 h. The ampoule was frequently rocked to ensure the homogeneity of the melt. The quenching was done in ice water to obtain the composition in the glass state.

The amorphocity of the samples was confirmed by the absence of any sharp peak in the X-ray diffraction pattern, Figure 1 shows the X-ray diffraction pattern of Se_{86}Zn_{10}Sb_{4} glass at room temperature.

3. Results and Discussions

DSC therograms of glassy alloys Se_{90-x}Zn_{10}Sb_{x }(x = 0, 2, 4, 6) were recorded at different heating rate 10˚C/min is shown in Figure 2. The endothermic peak of glass transition, exothermic peak of crystallization and endothermic pick present the melting of sample have been clearly observed in the Figure 2. The values of the glass transition temperature T_{g} and the crystallization temperature T_{c} for each sample at different heating rates 5, 7, 10, 12˚C/min are given in Table 1. From the Table 1 it is clear that glass transition temperature T_{g} and crystallization temperature T_{c} both shift towards higher temperatures as the heating rate increases from 5 to 12˚C/min. is found that the glass transition temperature T_{g} decreases as Sb concentration increases and the crystallization temperature T_{c} increases with increasing Sb.

Glass transition region Two approaches have been used to study the dependence of T_{g} on the heating rate α the first approach is the empirical relation suggested by Lasocka [17]

(1)

where A and B are constants for a given glass composition. The value of A indicates the glass transition temperature for the heating rate of 1˚C/min, while B is proportional to the time taken by the system to reduce its glass transition temperature, when its heating rate is lowered from 10 to 1 K/min [18] . Figure 3 depicts the

Figure 1. XRD pattern of Se_{86}Zn_{10}Sb_{4} glassy alloy.

Figure 2. DSC thermograms of Se_{90-x}Zn_{10}Sb_{x }(x = 0, 2, 4, 6) glassy alloys at heating rate of 10˚C/min.

Table 1. The values of glass transition temperature T_{g} and crystallization temperature T_{c} at different heating rates 5, 7, 10, 12˚C/min for Se_{90-x}Zn_{10}Sb_{x }(x = 0, 2, 4, 6) glassy alloys.

variation of the glass transition temperature T_{g} with lnα for the investigated Se_{90-x}Zn_{10}Sb_{x }(x = 0, 2, 4, 6) glassy systems. from Figure 3 the value of A and B can be obtained form the slop of straight line of the plot T_{g} versus lnα.

The calculated values of A and B for the different compositions are listed in Table 1.

The second approach is the evaluation of the activation energy for the glass transition E_{g} using Kissinger equation [19]

(2)

where α is the heating rate, T_{gp} is the peak glass transition temperature, E_{g} is the activation energy for the glass transition and R is the gas constant. Figure 4 shows ln(α/T^{ }_{gp}^{2}) versus 1000/T_{gp} plots for different composition Se_{90-x}Zn_{10}Sb_{x }(x = 0, 2, 4, 6) glassy systems.

The values of activation energy of glass transition E_{g }calculated from the slope of the straight line of the plots between ln(α/T_{gp}^{2}) and 1000/T_{gp} are listed in Table 2. From Table 2 the value of E_{g} decreases with increasing Sb.

Figure 3. Plots of T_{g} versus lnα for Se_{90-x}Zn_{10}Sb_{x }(x = 0, 2, 4, 6) glasses.

Figure 4. Plots of ln(α/T_{gp}^{2}) versus T_{g} for Se_{90-x}Zn_{10}Sb_{x }(x = 0, 2, 4, 6) glasses.

Table 2. The values of A, B and Activation energy of glass transition E_{g} for Se_{90-x}Zn_{10}Sb_{x }(x = 0, 2, 4, 6).

Crystallization region The crystallization fraction x, can be expressed as a function of time according to the Johnson–Mehl–Avrami equation [20] -[22] :

(3)

where n is the Avrami exponent which depends on the mechanism of the growth and dimensionality of crystal growth and K is defined as the reaction rate constant and is given by:

(4)

where E_{c} is the activation on energy of crystallization, k is the Boltzmann constant, T is the isothermal temperature and K_{0} is the frequency factor. The activation energy of crystallization E_{c} for Se_{90-x}Zn_{10}Sb_{x} (x = 0, 2, 4, 6) glassy system have been determined using Matusita, Kissinger and Ozawa methods.

3.1. Matusita Model

In the non-isothermal method, the crystallized fraction x, precipitated in a glass heated at constant rate α, is related to the activation energy for crystallization E_{c }through the following expression [23] [24]

(5).

where n is the Avrami index depending on the nucleation process, m is an integer which depends on the dimensionality of the crystal. Here n = m + 1 is taken for a quenched glass containing no nuclei and n = m for a preheated glass containing sufficiently large number of nuclei, the values of n and m for different crystallization are given in Table 3. The fraction volume x crystallized at any temperature T is given as x = S/S_{T}, where S_{T} is the total area of the exotherm between T_{i} where the crystallization just begins and the temperature T_{f} where the crystallization is completed and S is the area between T_{i} and T as shown by the hatched portion in Figure 5.

Figure 6 shows linear plots of ln [−ln(1 − x)] versus lnα at three fixed temperatures for Se_{90-x}Zn_{10}Sb_{x }(x = 0,

Table 3. The Values of n and m for different crystallization mechanism.

Figure 5. The DSC curve indicating the estimation of volume fraction crystallized.

2, 4, 6) glasses system .Using Equation (5), the values of n have been determined from the slopes of these curves at each temperature and are given in Table 4 for Se_{90-x}Zn_{10}Sb_{x }(x = 0, 2, 4, 6) glassy system, the observed values reveal the dimension growth is two dimensional for the binary Se_{90}Zn_{10} and three for the ternaries Se_{90-x}Zn_{10}Sb_{x }(x = 2, 4, 6).

Figure 7 shows the plot of ln[−ln(1 − x)] versus 1000/T for Se_{90-x}Zn_{10}Sb_{x} (x = 0, 2, 4, 6 ) at different heating rates 5, 7, 10 and 12˚C/min. The deviation from the straight line nature at higher temperature is due to saturation of nucleation sites during the latter stage in the process of crystallization [25] or to the restriction of crystal growth by the small size of the particles [26] . From Figure 7, the value of activation energy of crystallization E_{c} was calculated from the slope of the ln[−ln(1 − x)] versus 1000/T for all heating rates, the values are given in

Figure 6. The plots of ln[−ln(1 − x)] versus lnα for different composition Se_{90-x}Zn_{10}Sb_{x }(x = 0, 2, 4, 6) at any fixed temperature.

Table 4. The values of Avrami index n and dimensionality of growth m.

Table 5. From Table 5 the value of activation energy of crystallization E_{c} of Se Zn Sb glassy increases with decreasing Sb.

3.2. Kissinger Method

The activation energy for crystallization E_{c} can be obtained from the heating-rate dependence on the peak temperature of crystallization T_{p}, using the Kissinger equation [19] .

(6)

Figure 7. The plots of ln[−ln(1 − x)] versus lnα at different heating rates for Se_{90-x}Zn_{10}Sb_{x} (x = 0, 2, 4, 6) glasses.

Table 5. The values of activation energy of crystallisation obtained from Matusita method.

A plot of ln(α/T_{p}^{2}) versus 1/T_{p} for compositions Se_{90-x}Zn_{10}Sb_{x} (x = 0, 2, 4, 6 ) is shown in Figure 8 The slope of these straight lines gives the activation energy of crystallization E_{c}, the values of E_{c} for all compositions are given in Table 6.

3.3. Ozawa Method

The activation energy of crystallization E_{c} can also be obtained from the variation of the temperature at maximum peak T_{p} with heating rate by using Ozawa’s [27] relation as

(7)

The plots of lnα versus 1/T_{p} for different compositions are shown in Figure 9. The Values of the activation energy E_{c} for the crystallization processes are listed in Table 6.

4. Conclusion

The crystallization kinetics in glassy Se_{90-x}Zn_{10}Sb_{x} (x = 0, 2, 4, 6) alloys have been studied under non-isothermal conditions using the DSC technique. The glass transition temperature T_{g} decreases with an increase in the Sb

Figure 8. The plots of ln(α/T_{p}^{2}) versus 1/T_{p} for Se_{90-x}Zn_{10}Sb_{x} (x = 0, 2, 4, 6) glasses.

Figure 9. The plots of ln α versus 1/T_{p} for Se_{90-x}Zn_{10}Sb_{x} (x = 0, 2, 4, 6) glasses.

Table 6. The values of activation energy of crystallisation obtained from Kissinger and Ozawa methods.

contents and the crystallization temperature T_{c} increase with increase in Sb. The activation energy of glass transition E_{g} calculated from Kissinger model decreases with the increase in Sb. The calculated values of the kinetic exponent n suggest two dimensional growth for the binary Se_{90}Zn_{10} and three dimensional growth for ternaries Se_{90-x}Zn_{10}Sb_{x} (x = 0, 2, 4, 6 ), the activation energy of crystallization E_{c} has been calculated using Kissinger, Ozawa and Matusita models there are in good agreement with each other.

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