Kinetic Study of Non-Isothermal Crystallization in Se 90 − xZn 10 Sbx ( x = 0 , 2 , 4 , 6 ) Chalcogenide Glasses

Crystallization and glass transition kinetics of Se90−xZn10Sbx (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 Tg, the crystallization temperatures Tc and the peak temperatures of crystallization Tp were found to be dependent on the compositions and the heating rates. From the dependence on the heating rates of Tg and Tp, the activation energy for glass transition, Eg, and the activation energy for crystallization, Ec, are calculated and their composition dependence is discussed. The activation energy of glass transition Eg, Avrami index n, dimensionality of growth m and activation energy of crystallization Ec have been determined from different models.


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.

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.

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] 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].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] ( ) 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.

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

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] ( ) 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.

Mechanism n m
Three-dimensional growth 4 3 Two-dimensional growth 3 2 One-dimensional growth 2 1 Surface nucleation 1 1 100 150 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).

Heat Flow (mW)
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

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].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.

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] 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.

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 4 2 )
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 and 1000/T gp are listed in

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

Table 1 .
The values of glass transition temperature T glass transition temperature T g with lnα for the investigated Se 90-x Zn 10 Sb x (x = 0, 2, 4, 6) glassy systems.fromFigure3thevalue of A and B can be obtained form the slop of straight line of the plot T g versus lnα.

Table 2 .
From Table2the value of E g decreases with increasing Sb.

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).

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

Table 5 .
From Table5the value of activation energy of crystallization E c of Se Zn Sb glassy increases with decreasing Sb.

Table 5 .
The values of activation energy of crystallisation obtained from Matusita method.T p for compositions Se 90-x Zn 10 Sb x (x = 0, 2, 4, 6 ) is shown in Figure

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