Kinetics of non-isothermal crystallization and glass transition phenomena in Ga10Se87Pb3 and Ga10Se84Pb6 chalcogenide glasses by DSC

Journal of Non-Crystalline Solids 358 (2012) 564–570

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Kinetics of non-isothermal crystallization and glass transition phenomena in Ga10Se87Pb3 and Ga10Se84Pb6 chalcogenide glasses by DSC F.A. Al-Agel a,⁎, Shamshad A. Khan b, E.A. Al-Arfaj c, A.A. Al-Ghamdi a a b c

Department of Physics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Kingdom of Saudi Arabia Department of Physics, St. Andrews College, Gorakhpur, UP 273001, India Department Physics, College of Applied Sciences, Umm Al-Qura University, Makkah, Kingdom of Saudi Arabia

a r t i c l e

i n f o

Article history: Received 13 August 2011 Received in revised form 20 October 2011 Available online 19 November 2011 Keywords: Chalcogenide glasses; Glass transition temperature; Activation energy; Thermal stability

a b s t r a c t The crystallization process affects solid properties through the crystal structure and morphology established during the transition process. An important aspect of the crystallization process is its kinetics, both from the fundamental point of view of amorphous material as well as the modeling and phase transition. In the present research work, non-isothermal crystallization data in the form of heat flow vs. temperature curves has been studied by using some well known models for amorphous Ga10Se87Pb3 and Ga10Se84Pb6 chalcogenide glasses, prepared by the melt quenching technique. The glass transition phenomena and crystallization of these glasses have been studied by using non-isothermal differential scanning calorimetery (DSC) measurements at constant heating rates of 5, 10, 15, 20, 25 and 30 K/min. The glass transition temperature (Tg), crystallization temperature (Tc), and melting temperature (Tm) were determined from DSC thermograms. The dependence of Tg and Tc on the heating rate was used to determine different crystallization parameters such as the order parameter (n), the glass transition energy (ΔEg) and the crystallization activation energy (ΔEc). The results of crystallization were discussed on the basis of different models such as Kissinger's approach and the modification for non-isothermal crystallization in addition to Johnson, Mehl, Ozawa and Avrami. © 2011 Elsevier B.V. All rights reserved.

1. Introduction The great development of modern science and technology has led to the synthesis of new chalcogenide alloys with different compositions to fabricate new materials which can be used to make more advanced and cheap solid state electronic devices. Chalcogenide glasses based on chalcogen elements (S, Se and Te) are attractive and widely investigated materials as they possess high optical transparency in the IR region. They have low phonon energy, high photosensitivity, easy fabrication and good chemical durability. So, they are used in ultrafast optical switches, frequency converters, optical amplifiers, optical recording devices, integrated optics, infrared lasers etc. Kinetic studies are always connected with the concept of activation energy. The activation energy in the glass transition phenomenon is associated with nucleation and growth process. Studies of the glass transition and crystallization of a glass upon heating can be interpreted in terms of several theoretical models. The study of crystallization kinetics using the differential scanning calorimetry (DSC) methods has been widely used. Thermally activated transformations in the solid state can be investigated by isothermal or non-

⁎ Corresponding author. Tel.: + 966 26952000; fax: + 966 26951106. E-mail address: [email protected] (F.A. Al-Agel). 0022-3093/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2011.10.029

isothermal experiments. Experiments performed at constant heating rate are the most rapid way for studying the transformation, while isothermal experiments are generally time consuming. DSC is one of the important tools to study of glass transition phenomena and crystallization kinetics, which has been widely discussed in the literature [1–9]. Zhang et al. [10] has studied the crystallization kinetics of Si15Te85 and Si20Te80 chalcogenide glasses, El-Raheem et al. [11] has studied the crystallization kinetics determination of Pb15Ge27Se58 chalcogenide glass by using the various heating rates method, Elabbar et al. [12] has studied the crystallization kinetics study of Pb4.3Se95.7 chalcogenide glass using DSC technique, Aly et al. [13] has studied the effect of Te additions on the glass transition and crystallization kinetics of (Sb15As30Se55)100 − xTex amorphous solids. The work on structural characterization and phase transformation kinetics of Se58Ge42 − xPbx chalcogenide glasses by Deepika et al. [14], crystallization kinetics and composition dependence of some physical properties of Sn–Sb–Bi–Se chalcogenide glasses by Ahmad et al. [15], studying the crystallization behavior of Se85S10Sb5 chalcogenide semiconducting glass by Shapaan et al. [16], on the glass transition phenomenon in Se–Te and Se–Ge based ternary chalcogenide glasses by Mehta et al. [17], kinetics of crystallization in glassy Se70Te30 − xZnx using DSC technique by Srivastava et al. [18], calorimetric studies of Se75Te15Cd10 and Se75Te10Cd10In5 multicomponent chalcogenide glasses by Kumar et al. [19], measurements of DSC isothermal

F.A. Al-Agel et al. / Journal of Non-Crystalline Solids 358 (2012) 564–570

2. Experimental The glassy samples of Ga10Se87Pb3 and Ga10Se84Pb6 chalcogenide glasses were prepared by traditional melt quenching technique. High purity (5 N) of gallium, selenium and lead were weighed according to their atomic percentages and sealed in quartz ampoules under a vacuum of 10 − 6 Torr. Alloying of the elements was accomplished by putting the sealed ampoules in a furnace with a rocking mechanism. The rocked motion ensures that a complete mixing of the materials takes place. To assure complete chemical reactions between the constituents, the furnace temperature program was adjusted first at 573 K for 3 h, secondly at 773 K for 2 h and at last to 1223 K for 10 h. Rapid quenching in ice-water bath was used to obtain the bulk amorphous material. The amorphous nature of the samples was verified by XRD. Differential Scanning Calorimeter DSC (Model– DSC plus, Rheometric Scientific Company, U.K) was used to determine glass transition (Tg), crystallization temperature (Tc) and melting temperature (Tm). The temperature precision of this equipment is ±0.1 K with an average standard error of about 1 K in the measured values of Tg, Tc and Tm. The DSC scans were taken at six different heating rates 5, 10, 15, 20, 25 and 30 K/min. The masses of the samples varied between 5 to 10 mg. The powder sample pan was covered by a lid which acts as a radiation shield. The DSC equipment was calibrated prior to measurements, using high purity standards Pb, Sn and In with well-known melting points. 3. Results 3.1. Structural studies A Philips Model PW 1710 X-ray diffractometer was employed for studying the structure of the material. The copper target was used as a source of X-rays with λ = 1.5404 Å (Cu Kα1). The scanning angle was in the range of 10°–70°. A scan speed of 2°/min and a

chart speed of 1 cm/min were maintained. The X-ray diffraction traces of Ga10Se87Pb3 and Ga10Se84Pb6 chalcogenide glasses are shown in Fig. 1. 3.2. Glass transition (Tg) and crystallization (Tg) temperature The DSC curves of the crystallization process of Ga10Se87Pb3 and Ga10Se84Pb6 chalcogenide glasses obtained at different heating rates are shown in Figs. 2, 3 and 4. The DSC thermograms are characterized by three phenomena; the first one is the appearance of an endothermic hump, corresponding to the glass transition, which arises due to an abrupt increase in specific heat of the sample. The second is the exothermic peak, which arises due to the crystallization of the sample. The third endothermic peak corresponds to the melting of the material. The latent heat of fusion of Ga10Se87Pb3 and Ga10Se84Pb6 chalcogenide glasses were calculated by numerical integration of the area under the melting peak of the DSC curve shown in Fig. 4, using a computer program supplied with the equipment and the melting point was estimated by the tangent at the point of intersection of the highest slope with the base line [35]. The melting temperature and the latent heat of fusion for Ga10Se87Pb3 are found to be 495.46 K and 41.30 kJ/kg, while for Ga10Se84Pb6 it is found to be 499.17 K and 36.07 kJ/kg. 3.3. Surface morphology Small amount of amorphous Ga10Se87Pb3 and Ga10Se84Pb6 glasses in the form of powder were annealed at 433 K for two hours in a vacuum furnace. The surface microstructure of amorphous and thermally annealed bulk samples were examined by means of a Field Emission Scanning Electron Microscope (FESEM) (QUANT FEG 450, Amsterdam, Netherlands). The microscope was operated at an accelerating voltage of 20 kV with 10 mm work distance. Figs. 5(a) and 6(a) shows the FESEM of as-prepared bulk specimen of Ga10Se87Pb3 and Ga10Se84Pb6 glasses while Figs. 5(b) and 6(b) shows the FESEM of annealed samples Ga10Se87Pb3 and Ga10Se84Pb6 glasses. 3.4. Evaluation of Avrami index (n) The kinetics of isothermal crystallization involving nucleation and growth is usually analyzed using Kolmogorov–Johnson–Mehl– Avrami (KJMA) model. According to this model, the volume fraction of crystallites (α) is given by [36–40]:  n α ðtÞ ¼ 1−exp: −ðktÞ

ð1Þ

where α(t) is the volume fraction crystallized after time t, n is the Avrami exponent which is associated with the nucleation and growth

Relative Intensity (Arb. Units)

crystallization kinetics in amorphous selenium bulk samples by AbuSehly et al. [20] are also worth mentioning. A lot of research work [21–26] on crystallization kinetics and thermal properties of chalcogenide glasses has been done by various workers. In the present research work, the crystallization kinetics and the evaluation of the activation energies of Ga10Se87Pb3 and Ga10Se84Pb6 chalcogenide glasses, prepared by the melt quenching technique were carried out by means of non-isothermal DSC measurement. In the earlier published work [27], one of our co-author has studied the kinetics of non-isothermal crystallization in Ga10Se90 chalcogenide glass. Now, in our present study, we have decided to make doping of Pb in Ga–Se system. We have used Se as a major content because of its wide commercial applications in many industrial fields, such as photo elements, solar technology, metal coatings as well as lubricants and pharmaceuticals. It also exhibits a unique property of reversible transformation. This property makes its use in optical memory devices. But in pure state it has disadvantages because of its short lifetime and low sensitivity. To overcome these difficulties certain additives are used with Se. Here we have chosen Ga as an additive to overcome these problems. It has one of the longest liquid ranges of any metal and has a low vapor pressure even at high temperature. There is a strong tendency for Ga to supercool below its freezing point, so, seeding may be necessary to initiate solidification [28]. We have incorporated lead in Ga–Se system. Metallic additive such as Pb and Bi in chalcogenide glasses enter the network as charged species, altering the concentration of positively and negativity of valence alternation pairs [29–31]. Selenium-lead chalcogenides are considered to be mainly utilized for detecting hydrocarbon pollutant in atmosphere, higher solution spectroscopy, trace gas analysis, optical fiber analysis and optical communication system over super long distances [32–34].

565

10

Ga10 Se 84Pb6

Ga10 Se 87 Pb3 20

30

40

50

60

Angle (2θ) (Degree) Fig. 1. X-ray pattern of Ga10Se87Pb3 and Ga10Se84Pb6 chalcogenide glasses.

70

F.A. Al-Agel et al. / Journal of Non-Crystalline Solids 358 (2012) 564–570

Ga10Se87Pb3

5 K/min Ga10 Se87 Pb3

Exo

Exo

566

Heat Flow (mW)

Heat Flow (mW)

10 K/min

15 K/min

20 K/min

Ga10 Se84 Pb6

Endo

Endo

25 K/min

30 K/min

300 300

320

340

360

380

400

420

440

350

400

450

500

550

Temperature (oK)

460

Temperature (oK) Fig. 4. DSC plot for Ga10Se87Pb3 and Ga10Se84Pb6 glasses at the heating rate of 10 K/min showing the melting temperature of the samples.

Fig. 2. DSC plot for Ga10Se87Pb3 glass at different the heating rates.

mechanisms and k is the reaction rate constant.In the thermally activated process the reaction rate constant k is related to temperature T and is given by, k ¼ ν exp:ð−ΔEc =RTÞ

ð2Þ

crystallization temperature T1, where crystallization just begins and the temperature T2 where the crystallization is completed. ‘AT’ is the partial area of exothermic peak between the temperature ‘T1’ and ‘T2’. The temperature T is selected between T1 and T2.

(a)

where ΔEc is the activation energy of crystallization and R is the gas constant. However, as pointed out by Vyazovkin [41], the crystallization process is generally determined by nucleation and growth, which are likely to have different activation energies. It is also possible that different growth mechanisms are operating at different degrees of crystallization leading to temperature dependent activation energy. The activation energy for crystallization as well as the Avrami exponent can be obtained using a method suggested specifically for non-isothermal experiments by Matusita et al. [42]. The fraction ‘α’ crystallized at any temperature ‘T’ is given as α = AT/A, where ‘A’ is the total area of exotherm between the onset Ga10Se87Pb3 As-prepared

Exo

Ga10Se84Pb6

(b)

5 K/min

Heat Flow (mW)

10 K/min

15 K/min

20 K/min

Endo

25 K/min

300

30 K/min Ga10 Se87 Pb3 Annealed at 433 K

320

340

360

380

400

420

440

460

480

o

Temperature ( K) Fig. 3. DSC plot for Ga10Se84Pb6 glass at different the heating rates.

Fig. 5. Field Emission Scanning Electron Micrograph of Ga10Se87Pb3 specimen that was as-prepared (a) and annealed at 433 K for 2 h (b).

F.A. Al-Agel et al. / Journal of Non-Crystalline Solids 358 (2012) 564–570

(a)

567

3 2

ln -[ln (1-α)]

1

Ga10Se87Pb3 Ga10Se84Pb6

0 -1 -2 -3 -4 -5 1.5

1.7

1.9

2.1

2.3

2.5

2.7

2.9

3.1

3.3

3.5

ln β Ga10Se84Pb6 As-prepared

Fig. 7. Plot of ln [− ln(1 − α)] as a function of lnβ of Ga10Se87Pb3 and Ga10Se84Pb6 chalcogenide glasses.

(b) 3.5. Activation energy of crystallization (ΔEc) The interpretation of the experimental crystallization data is given on the basis of Kissinger's, Matusita's and modified Ozawa's equations for non-isothermal crystallization. The activation energy (ΔEc) for crystallization can therefore be calculated by using Kissinger's equation [45],   2 ln β=Tc ¼ −ΔEc =RTc þ D

Ga10Se84Pb6 Annealed at 433 K

Fig. 6. Field Emission Scanning Electron Micrograph of Ga10Se84Pb6 specimen that was as-prepared (a) and annealed at 433 K for 2 h (b).

ð4Þ

The plot of ln (β/Tc2) versus 1000/Tc for Ga10Se87Pb3 and Ga10Se84Pb6 chalcogenide glasses are shown in Fig. 8, which come to be straight lines. The value of ΔEc may be calculated from the slope of each curve and is given in Table 2. The activation energy of crystallization can also be obtained from the variation of the onset crystallization temperature with heating rate by using Ozawa's [46] relation as, ln β ¼ −ΔEc =RTc þC

The volume fraction of crystallites (α) precipitated in a glass heated at constant heating rate (β) is related to the effective activation energy for crystallization (ΔE) through the following expression: ln½−lnð1−α Þ ¼ −n ln ðβÞ–1:052mðΔEÞ=RT þ constant

ð3Þ

where m is an integer, which depends upon the dimensionality of the crystal and n is a numerical factor depending on the nucleation process. When the nuclei formed during the heating at a constant rate are dominant, n is equal to (m + 1) and when nuclei formed during any previous heat treatment prior to thermal analysis are dominant, n is equal to m. According to Eq. (3), a plot of ln [−ln (1 − α)] versus ln β yield a straight line with slope equal to n (order parameter). Fig. 7 shows the variation of ln [−ln(1 − α)] against ln β for Ga10Se87Pb3 and Ga10Se84Pb6 chalcogenide glasses. The value of order parameter (n) for Ga10Se87Pb3 and Ga10Se84Pb6 chalcogenide glasses are listed in Table 1. Since as-quenched sample is studied, the value of m is taken [43] as m = n − 1. The value of m is two in case of Ga10Se87Pb3 and Ga10Se84Pb6 chalcogenide glasses, which indicate a twodimensional growth of ternary samples [44].

ð5Þ

where C is a constant. Fig. 9 shows ln β versus 1000/Tc curve, which come to be linear for the entire heating rate. The value of ΔEc is calculated from the slope of each curve and is given in Table 2. It is clear from this table that the activation energy of crystallization calculated by two methods is in good agreement with each other. The average value of activation energy of crystallization is found to be 98.5 kJ/mol for Ga10Se87Pb3 glass, while 88.0 kJ/mol for Ga10Se84Pb6 chalcogenide glass. Table 1 Compositional dependence of Tg (K) and Tc (K) of Ga10Se87Pb3 and Ga10Se84Pb6 glasses from non-isothermal DSC experiments. Heating rate (K/min)

Ga10Se90a

5 10 15 20 25 30

Tg (K) 319.56 320.42 321.38 322.18 323.61 326.23

a

Ref. [27]

Tc (K) 378.48 386.04 391.78 394.63 398.21 401.49

Ga10Se87Pb3

Ga10Se84Pb6

Tg (K) 317.82 318.34 320.51 321.67 322.54 324.14

Tg (K) 319.89 320.72 321.58 323.31 325.12 327.71

Tc (K) 382.53 392.72 397.91 402.05 405.12 407.69

Tc (K) 375.58 379.09 386.91 396.04 400.96 405.91

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4

-13

Ga10Se87Pb3

Ga10Se87Pb3 Ga10Se84Pb6

Ga10Se84Pb6

3.5 3

-11.4

ln (β)

ln (β/Tc2)

-12.2

-10.6

2.5 2

-9.8 -9 2.45

1.5 2.5

2.55

2.6

2.65

1 2.45

2.7

-1

2.5

1000/Tc (K )

2.55 2.6 1000/ Tc (K-1)

2.65

2.7

Fig. 8. Plot of ln (β/Tc2) as a function of 1000/Tc (K− 1) of Ga10Se87Pb3 and Ga10Se84Pb6 chalcogenide glasses.

Fig. 9. Plot of ln β as a function of 1000/Tc (K-1) of Ga10Se87Pb3 and Ga10Se84Pb6 chalcogenide glasses.

3.6. Activation energy of glass transition (ΔEg)

3.7. Crystallization enthalpy (ΔHc)

The activation energy of glass transition (ΔEg) for Ga10Se87Pb3 and Ga10Se84Pb6 chalcogenide glasses can be calculated by using Kissinger's Eq. (45) as,

The crystallization enthalpy (ΔHc) is evaluated by using the formula,

ð6Þ

It is evident from this equation that a plot of ln (β/Tg2) against 1000/Tg should be straight line (shown in Fig. 10) and that the activation energy involved in the molecular motions and rearrangements around Tg can be calculated from the slope of this plot and are given in Table 2. The heating rate (β) dependence of the glass transition temperature in chalcogenide glasses may be interpreted in terms of thermal relaxation phenomena and it has been shown by Moynihan [47] that the activation energy of structural relaxation (ΔEg) can also be related to Tg and β by,   d ln β=d 1=Tg ¼ −ΔEg =R

ð7Þ

From this equation, a plot of lnβ against 1000/Tg should be straight line (shown in Fig. 11). The activation energy involved in the molecular motions and rearrangements around Tg can be calculated from the slope of this plot (given in Table 2). The activation energy involved in the molecular motions and rearrangements around Tg has been calculated by two well known methods and are given in Table 2. It is clear from this table that the activation energy of glass transition (structural relaxation) decreases with increasing Pb content in Ga–Se system in both methods. The average value of activation energy of glass transition (ΔEg) is found to be 138.0 kJ/mole for Ga10Se87Pb3 glass, while 112.0 kJ/mole for Ga10Se84Pb6 chalcogenide glass.

Table 2 Compositional dependence of ΔEc (kJ/mol) and ΔEg (kJ/mol) of Ga10Se87Pb3 and Ga10Se84Pb6 glasses from non-isothermal DSC experiments. Sample

Ga10Se87Pb3 Ga10Se84Pb6

ΔEg (kJ/mol)

ΔEc (kJ/mol)

lnβ versus 1000/Tg

ln(β/Tg2) versus 1000/Tg

lnβ versus 1000/Tc

ln(β/Tc2) versus 1000/Tc

146 ± 2 124 ± 3

130 ± 3 100 ± 5

93 ± 1 83 ± 1

104 ± 2 93 ± 2

ΔHc ¼ KA=M

ð8Þ

where K (=1.5) is the constant of the instrument used. The value of K was deduced by measuring the total area of the complete melting endotherm of high purity tin and indium and used the well known enthalpy of melting of these standard materials. A is the area of the crystallization peak and M is the mass of the sample. The value of ΔHc for Ga10Se87Pb3 and Ga10Se84Pb6 chalcogenide glasses at different heating rates are shown in Table 3. 4. Discussion The X-ray diffraction traces of Ga10Se87Pb3 and Ga10Se84Pb6 chalcogenide glasses were taken at room temperature and found to show similar trends and are shown in Fig. 1. The absence of sharp structural peak confirms the amorphous nature of the samples. The variation of glass transition temperature (Tg) and crystallization temperature (Tc) of Ga10Se90 [27] and the studied glasses with Pb composition for all heating rates is given in Table 1. It is evident from Table 1 that Tg shifts to higher temperatures with increasing heating rate. The pronounced variation of Tg with heating rate is a manifestation of the kinetic nature of the glass transition. The relatively large endothermic peaks observed in the present work are most likely due to aging effect. The samples used in this study were stored at room temperature

-11.2 Ga10Se87Pb3

-10.8

ln (β/Tg2)

  2 ln β=Tg ¼ −ΔEg =RTg þ constant

Ga10Se84Pb6

-10.4

-10

-9.6

-9.2 3.04

3.06

3.08

3.1

3.12

3.14

3.16

1000/Tg (K-1) Fig. 10. Plot of ln (β/Tg2) as a function of 1000/Tg (K-1) of Ga10Se87Pb3 and Ga10Se84Pb6 chalcogenide glasses.

F.A. Al-Agel et al. / Journal of Non-Crystalline Solids 358 (2012) 564–570

4 Ga10Se87Pb3 Ga10Se84Pb6

3.5

ln β

3 2.5 2 1.5 3.04

3.06

3.08

3.1

3.12

3.14

3.16

1000/Tg (K-1) Fig. 11. Plot of ln β as a function of 1000/Tg (K-1) of Ga10Se87Pb3 and Ga10Se84Pb6 chalcogenide glasses.

for a considerable period of time. As the output of the DSC during heating is proportional to the heat capacity, it is a straightforward and convenient method of detecting the glass transition and investigating its kinetics. For example, the heating/cooling rate dependence of the glass transition temperature can be used to determine the activation energy of the transition from glassy to liquid state. The onset of the endothermic change is commonly used to define the glass transition temperature. Other definitions for Tg were used by different workers. For instance, Moynihan et al. [47] used three different definitions of Tg that included the extrapolated onset, the inflection point and the maximum of the DSC output curve obtained on heating. Using these definitions of Tg, the result of extracting the activation energy for three different glasses was found to be the same [47]. The value of Tg and therefore the rigidity of the lattice increase with increasing heating rates. The heating rate dependence of glass transition temperature Tg is an experimentally observed [43, 48–49] fact. Theoretically, Tg is defined as the temperature at which the relaxation time (τ) becomes equal to the relaxation time of observation (τobs). At the same time, Tg varies inversely [48] as the relaxation time. With increasing heating rate, τobs decreases and hence the glass transition temperature increases. It is also observed from Table 1 that the crystallization temperature (Tc) shift towards higher temperature as the heating rate is increased from 5 to 30 K/min. A sharp peak is observed during the crystallization process. The height of crystallization peaks are shifted to higher temperatures with increasing heating rates, indicating that the crystallization behavior is clearly different. Enhancement of the thermal stability in the amorphous chalcogenide glasses appears due to the presence of a relatively high degree of short range order. Such a structure provides an increased resistance against disruption of existing ordered grains. In the case of Ga10Se87Pb3 and Ga10Se84Pb6 chalcogenide glasses, a short range order is known to exist, which has also been confirmed through the peak crystallization temperature in the present study. For all heating rates, it is clearly observed that, the studied materials have a single exothermic crystallization peak, which means these glasses are homogeneous. From FESEM pictures (Figs. 5 and 6), it is clear that there is a change in the structure of the materials due to the annealing at temperature above the crystallization temperature. From Figs. 5(b) and 6

569

(b), it is clear that there is a crystal growth during annealing of the samples. The activation energy of crystallization (shown in Table 2) decreases with increasing Pb content in Ga-Se system, indicating that the rate of crystallization is slower as the Pb content increases. The decrease in activation energy of crystallization may be interpreted in terms of decreased hoping conduction in impurity induced states [50]. At higher concentration, alloying effect observed which could change the mobility gap and various other parameters of the original materials. The activation energy of crystallization is an indication of the speed of rate of crystallization. It is useful for the characterization of glassy alloys for different applications. The activation energy of glass transition is found to be decreases with increasing Pb content in Ga-Se system. When the sample is heated, in DSC furnace, the atom undergoes infrequent transitions between the local potential minima separated by different energy barriers in the configurationally space where each local minimum represent a different structure. The most stable local minima in the glassy region have lower internal energy. Accordingly, the atoms in a glass having minimum activation energy have higher probability to jump to the metastable (or local minimum) state of lower internal energy The value of ΔHc for studied glass at different heating rates are shown in Table 3. The enthalpy release is related to the metastability of the glasses and the least stable glasses are supposed to have maximum ΔHc. It is observed that Ga10Se87Pb3 glass has more enthalpy than Ga10Se84Pb6 glass at all heating rates and hence Ga10Se87Pb3 glass is a lesser stable glass than Ga10Se84Pb6 glass.

5. Conclusion Calorimetric measurements were performed on Ga10Se87Pb3 and Ga10Se84Pb6 chalcogenide glasses, which indicate that the glass transition and crystallization temperatures depend on the heating rate and on Pb concentration. The value of order parameter (n) for studied glasses indicates a two-dimensional growth of ternary samples. The interpretation of the experimental crystallization data is given on the basis of Kissinger's, Matusita's and modified Ozawa's equations. By employing different methods, the activation energy of crystallization (ΔEc) and activation energy of structural relaxation (ΔEg) were determined from the heating rate dependence of crystallization and glass transition temperature. The results of crystallization kinetics indicate that the degree of crystallization under non-isothermal conditions fits well with the theory of Matusita, Sakka and Kissinger. A multiple scanning technique was used to calculate ΔEc and ΔEg. It was found that the value of ΔEc and ΔEg by both techniques are in good agreement with each other. The activation energy is found to vary with compositions indicating a structural change due to the addition of Pb. The enthalpy released is found to be maximum for Ga10Se87Pb3 glass as compared to Ga10Se84Pb6 glass at all heating rates and hence Ga10Se87Pb3 glass is a lesser stable glass than Ga10Se84Pb6 glass. The activation energy of crystallization decreases with increasing Pb content in Ga–Se system in both methods, indicating that the rate of crystallization is slower as Pb content increases. The activation energy of structural relaxation decreases with increasing Pb content, which can be explained in terms of change in chemical bonding at higher concentrations.

Table 3 Compositional dependence of order parameter (n), m and Enthalpy released (ΔHc) of Ga10Se87Pb3 and Ga10Se84Pb6 glasses from non-isothermal DSC experiments. Sample

n

m

Ga10Se87Pb3 Ga10Se84Pb6

2.68 2.95

2 2

ΔHc (J/mg) 5 K/min

10 K/min

15 K/min

20 K/min

25 K/min

30 K/min

6924 ± 8 3876 ± 7

5586 ± 8 4659 ± 9

6098 ± 9 5884 ± 8

7258 ± 8 7065 ± 11

6784 ± 11 5094 ± 8

5974 ± 8 4999 ± 7

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