Non-isothermal crystallization kinetics of ternary ...

Journal of Crystal Growth 436 (2016) 125–133

Contents lists available at ScienceDirect

Journal of Crystal Growth journal homepage: www.elsevier.com/locate/jcrysgro

Non-isothermal crystallization kinetics of ternary Se90Te10 xPbx glasses H.E. Atyia n, A.S. Farid Physics Department, Faculty of Education, Ain Shams University, Cairo, Egypt

art ic l e i nf o

a b s t r a c t

Article history: Received 16 September 2015 Received in revised form 26 November 2015 Accepted 2 December 2015 Communicated by K. Jacobs Available online 12 December 2015

Ternary Se90Te10 xPbx with (x ¼2 and 6 at% ) glass compositions have been prepared using a melt quenching technique and performed the non-isothermal kinetics by differential thermal analysis (DTA) at various heating rates. The glassy state of the studied samples has been characterized using x-ray diffraction analysis. The glass transition temperature Tg, the onset temperature of crystallization Tc and the peak temperature of crystallization Tp are found to be composition and heating rate dependent. From heating rate dependence of Tg and Tp, the glass transition activation energies Eg and the crystallization activation energies Ec have been determined according to different methods. The transformation mechanisms have been examined by the values of Avrami exponent n and dimensionality of growth m. Thermal stability and glass formation ability have been monitored through the calculation of the thermal stability S, temperature difference ΔT, Hurby parameter Hr, frequency factor Ko, crystallization rate factor K and fragility index F. The compositional dependence of the above–mentioned parameters indicate that, the stability of the studied glass samples decreases with increasing Pb at% content. & 2015 Elsevier B.V. All rights reserved.

Keywords: Glassy compositions Non-isothermal method Glass transition temperature Crystallization kinetics Thermal stability

1. Introduction Recently amorphous chalcogenide materials have raised great importance in the field of material science mainly due to their broad applications such as ultrafast optical switches, electronic memories and optical recording. Crystallization of chalcogenide glasses plays an important role in determining the transport mechanism, thermal stability and practical application. Thermal analysis are valuable for the quantitative analysis of crystallization in chalcogenide glasses. Thermal analysis methods including differential thermal analysis (DTA) and differential scanning calorimetric (DSC) are particularly important as they easy to carry out and require little samples preparation. Thermally activated transformations in the solid state can be investigate by isothermal or non-isothermal experiments [1–3]. In isothermal method, this is disadvantage of reaching a test temperature instantaneously during the time in which the system needs to stabilize, no measurements are possible. Experiments were performed at a constant heating rate (non-isothermal) are the most rapid way for studying the transformation, while isothermal experiments are generally time consuming [4]. Chalcogenide compositions used Se atom as a major content are more useful due to its wide commercial applications because of its unique property of reversible transformation [5]. Unfortunately pure Se atoms, in an amorphous state, has disadvantage n

Corresponding author. Tel.: þ 20 966 506591713; fax: þ20 966 028221115. E-mail address: [email protected] (H.E. Atyia).

http://dx.doi.org/10.1016/j.jcrysgro.2015.12.004 0022-0248/& 2015 Elsevier B.V. All rights reserved.

because of its tendency to recrystalline and low photosensitivity. The addition of certain element such as Te to pure glassy Se atoms overcomes the observable proplem. The binary Se–Te alloy is preferred due to their higher photosensitivity, greater harness, higher crystallization temperature, appreciable conductivity and smaller aging as compared to pure glassy Se [6]. The addition of the third element to Se–Te alloy will create compositional and configuration disorder in the material with respect to the binary alloy. The lead Pb element is the last element in radioactive series, which is most stable and most difficult to form a glass [7]. The addition of the heavy metallic element as Pb in certain chalcogenide glasses, shows a transition from p-type to n-type conduction at a certain atomic percentage of Pb. 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 [8,9]. Various workers [10–13] have been studied and discussed the kinetics study of Se–Te based ternary compositions with different elements like Sn, Ag, In, Bi …etc. Thermal stability and crystallization kinetics of Se92Te8 xSnx (x ¼0, 1, 2, 3, 4, 5) chalcogenide glasses using differential scanning calorimetry were studied by Kumar et al. [10]. Tripathi et al. [11] studied the glass transition and crystallization of Se70Te15In15 chalcogenide glass. Glass-crystal transformation in Se80 xTe20Agx glasses was studied by Naqvi et al. [12]. Farid et al. [13] studied and discussed the glass transition and crystallization of Te additive Se–Bi chalcogenide glasses.

126

H.E. Atyia, A.S. Farid / Journal of Crystal Growth 436 (2016) 125–133

The thermal stability and crystallization kinetics have been reported for the Se–Te–Pb system for different ratios. The kinetics of a-Se80Te20 xPbx compositions using non-isothermal crystallization studied by Khan et al. [14]. Differential scanning calorimetry of Se85Te15 xPbx (x¼ 4, 6, 8 and 10) glasses studied by Maharajan et al. [15]. Ram et al. [16] studied the glass transition kinetics of Pb-modified Se80In20 system by using non-isothermal differential scanning calorimetry. In the present work, the glass transition and crystallization kinetics of Se90Te10 xPbx (x ¼2 and 6) has been studied under nonisothermal conditions at different heating rates (β ¼ 10, 20, 30, 40 and 50 K/min). The effects of Pb-addition and heating rate on the crystallization mechanism and thermal stability parameters have been reported and discussed.

2. Experimental details Ingots of glassy alloys of Se90Te10 xPbx with (x¼ 2 and 6 at% ) were prepared by melt quenching technique. High purity specimens (99.999% pure) were used to prepare the amorphous materials. The studied materials were weighted according to their atomic percentages and sealed in quartz ampoules under high vacuum of 10 5 Torr. Then the sealed ampoules were placed in an oscillatory furnace. The temperature of the furnace was increased for 3 °C min 1 up to 1273 K and kept at this temperatures for 12 h [17] with frequent rocking to ensure the homogenization of the melt. Then, the melt was rapidly quenched in icy water to have a glassy form. The bulk samples were taken out by breaking the silica ampoules. This ingots were then ground into a fine powder using a pestle and mortar. The chemical compositions of the investigated samples were checked by energy dispersive x-ray (EDX) spectrum analysis using scanning electron microscope (Joel 5400). The obtained data of the percentage of the studied compositions show that, the percentages of the constituent elements are approximately the same Se90Te8Pb2 and Se90Te4Pb6 compositions. The structure of the investigated samples was checked by x-ray diffraction analysis (shimadzu XD-D2) with Cu target and Ni filter. Fig. 1 shows the XRD patterns for Se90Te8Pb2 and Se90Te4Pb6 compositions. The obtained patterns are characterized by the absence of any diffraction lines, which revealed the amorphous nature of the studied samples. The study of glass transition and crystallization behaviors of the considered samples were performed under non-isothermal measurements, using a Shimadzu DTA-50 device. Typically, 10 mg of

sample in powder form was sealed in standard aluminum sample pans and heated at different rates ranging from 10 to 50 °C min 1. The glass transition, crystallization and melting temperatures were measured by the DTA curves. The temperature precision of this equipment is 71 °C with an average standard error of about 70.02 in the measured values of Tg and Tp. All lines in the obtained figures were fitted using least square method [18].

3. Results and discussion 3.1. Thermal analysis To evaluate the phase transformation and the level of thermal stability, the differential thermal analysis (DTA) experiments were recorded at different heating rates β ¼10, 20, 30, 40 and 50 °C min 1. Fig. 2 shows the thermal curve for Se90Te4Pb6 glassy composition at heating rate 10 °C min 1 as an example. The obtained DTA curves in Fig. 2 are characterized by three important phenomena: the first one is the appearance of endothermic peak, corresponding to the glass transition temperature Tg. That indicates a large change of viscosity marking a transformation from amorphous solid phase to super cooled liquid state. The second phenomena is exothermic peak refers to the crystallization of the sample. This exothermic peak has three characteristics temperature points, the onset crystallization temperature Tc, The peak crystallization temperature Tp and the finish crystallization temperature Tf. The third phenomena appears at higher temperatures in DTA trace as endothermic peak corresponding to the melting temperature Tm. Fig. 3(a and b) depicts the a typical DTA traces of glassy Se90Te8Pb2 and Se90Te4Pb6 compositions respectively at different heating rates β ¼10, 20, 30, 40 and 50 °C min 1. The obtained characteristic transition temperatures Tg, Tc, Tp, Tf and Tm for the studied compositions at different heating rates are reported in Table 1. It is clear from Table 1 that, the glass transition and crystallization temperatures for the studied compositions were shifted towards higher temperature with increasing heating rate. The increase of the values of Tg with increasing heating rate may be attributed to the relaxation dynamics in the glass transition period. Moreover, the variation of Tg takes the form of a power low behavior and represented by the following expression [19]. T g ¼ T o ðβ Þy

ð1Þ

where the exponent y is given by, y¼ log[(Tg)10/(Tg)1].(Tg)1 and 20

Se90Te4Pb6 10

Se90Te8Pb2

Intensity, arbitrary units

Tp

Se90Te4Pb6

Tc

ΔT

0

Tg -10

-20

Tm

-30 0

0

20

40 60 Diffraction angle (2θ)

80

100

Fig. 1. XRD patterns for glassy Se90Te8Pb2 and Se90Te4Pb6 compositions.

100

200 0

300

400

t, c

Fig. 2. Differential thermal analysis (DTA) trace for glassy Se90Te4Pb6 composition at constant heating rate 10 °C min 1.


(Tg)10 are the glass transition temperatures Tg at β ¼ 1 and 10 °C min 1 respectively. Eq. (1) gives another evidence for the increase of Tg with increasing heating rates. The shift of Tp towards the higher temperature with increasing heating rates can be attributed to the fact that, when the heating rate increases, the system does not get sufficient time for nucleation and crystallization [20]. On the other hand, It is observed that the values of Tg decrease with increasing Pb at% content in Se90Te10 xPbx glassy system. This behavior can be explained on the basic of structural change due to the introduction of Pb atoms in Se–Te system. The addition of Pb atoms in Se–Te system reduces the effective bond energies of Se–Se bonds (79.5 kcal mol 1) and Se–Te bonds (64 kcal mol 1) by forming the lower bond energies as Se–Pb bonds

a

120

10 K/min 20 K/min 30 K/min 40 K/min 50 K/min

Se 90Te8Pb 2

ΔT

80

40

0

100

200

300

400

500

600

0

t, c

b

(72.4 kcal mol 1) and Te–Pb bonds (60 kcal mol 1) [21]. The similar behavior has been observied by considering the decrease of Te% by increasing of Pb% in the studied Se90Te10 xPbx system. The same results was obtained in another works of Se–Te–Pb system [14,15] and for another compositions [22,11,13]. 3.2. Thermal Stability and glass formation ability The thermal stability of glasses has been checked on the basic of calorimetric measurements using DTA track. The glass transition temperature Tg represents the strength and rigidity of the glass structure in chalcogenide glasses. Tg offers valuable information on the thermal stability of the glassy states. However, Tg does not gives any information about glass formation ability. It is found that the temperature difference ΔT ¼Tc Tg consider a good indicator of thermal stability, because of the higher the value of ΔT coddles the delay in nucleation [23]. The values of ΔT criterion of glassy Se90Te8Pb2 and Se90Te4Pb6 compositions at different heating rates are listed in Table 2. It is found that the values of ΔT decrease with increasing heating rates as well as increasing Pb% content in the investigated system. It means decreasing in the thermal stability with increasing Pb% content. According to Zanotto [24,25], the glass tendency to homogeneous and heterogeneous nucleation can be distinguished on bases of reduced glass transition temperature Trg where T rg ¼ T g =T m

0

-40

127

80 Se 90Te4Pb 6

10 K/min 20 K/min 30 K/min 40 K/min 50 K/min

40

ð2Þ

The estimated values of Trg have been listed in Table 2. The values of Trg are found to be of order (2/3) for all studied sample compositions at different heating rate, which indicate a good glass formation tendency [26]. Turnbull [27] give more details about the case of larger values than 2/3 of Trg, the homogenous crystal nucleation will be essentially suppressed due to the sluggishness of crystallization kinetics. Therefore Trg becomes a criterion to evaluate glass formation ability GFA as a good formation shows a low Trg values and vise verse. Glasses have Trg values greater than 0.58–0.6 values display only surface crystallization, while glasses showing volume nucleation have Trg less than 0.58–0.6 values [28].

ΔT

Table 2 Compositional dependences of ΔT, Hr, S and Trg for glassy Se90Te8Pb2 and Se90Te4Pb6 compositions at different heating rates.

0

-40

0

100

200

300

400

500

600

0

t, c Fig. 3. DTA thermograms for glassy (a) Se90Te8Pb2 and (b) Se90Te4Pb6 compositions with different heating rates.

Heating rate Se90Te8Pb2 β (°C min 1) ΔT (K) Hr Tc Tg

S (K) Trg (K) ΔT (K) Tc Tg

Hr

S (K)

Trg (K)

10 20 30 40 50

2.12 2.40 3.20 3.06 3.23

0.197 0.189 0.193 0.221 0.234

1.29 1.31 1.32 0.735 0.983

0.656 0.662 0.663 0.669 0.668

38.11 47.03 47.39 48.88 49.75

0.330 0.436 0.466 0.485 0.505

Se90Te4Pb6

0.661 0.662 0.664 0.667 0.669

25.65 24.17 24.66 28.99 30.13

Table 1 Compositional and heating rate dependences of the characteristic transition temperatures for glassy Se90Te8Pb2 and Se90Te4Pb6 compositions. Heating rate β (°C min 1)

Se90Te8Pb2

10 20 30 40 50

336.217 0.02 374.32 7 0.02 393.05 7 0.02 406.087 0.02 508.377 0.02 328.09 7 0.02 353.747 0.02 338.03 7 0.02 385.067 0.02 402.32 7 0.02 416.34 7 0.02 510.25 7 0.02 333.157 0.02 357.32 7 0.02 340.077 0.02 387.4 7 0.026 410.43 7 0.02 428.167 0.02 512.08 7 0.02 335.047 0.02 359.7 7 0.02 343.247 0.02 392.127 0.02 413.58 7 0.02 431.197 0.02 514.3 7 0.02 341.42 7 0.02 370.417 0.02 345.52 7 0.02 395.277 0.02 417.7 7 0.02 434.047 0.02 516.147 0.02 342.187 0.02 372.317 0.02

Tg (K)

Se90Te4Pb6 Tc (K)

Tp (K)

Tf (K)

Tm (K)

Tg (K)

Tc (K)

Tp (K)

Tf (K)

Tm (K)

370.27 70.02 388.167 0.02 500.38 7 0.02 375.41 70.02 398.067 0.02 503.517 0.02 377.64 70.02 401.56 7 0.02 505.42 7 0.02 379.0770.02 411.197 0.02 510.05 7 0.02 383.47 70.02 424.04 7 0.02 512.4 7 0.02

128


The thermal stability parameter S can be defined by the following expression [25] ð3Þ S ¼ T p T c T c T g =T g

350

The parameter S reflects the resistance to diversification after formation of glass. The difference ΔT is connected to the rate of diversification transformation of the glass phases. Hruby [29] was presented a parameter known as Hruby number Hr developed mostly for chalcogenide systems [30] ð4Þ Hr ¼ T c T g = T m T p

340

Tg, K

345

335 330

Se90Te8Pb2 Se90Te4Pb6

325

The Hruby number Hr incorporates the nucleation and growth features of the phase transformation as a glass formation ability. According to Eq. (4) it is clear that, the Hruby number Hr has an almost matching implication as the temperature difference ΔT [31] more rabidly when crystallization peak is shifted and taking also in to account ease of melting. The values of S and Hr parameters have been reported in Table 2 for glassy Se90Te8Pb2 and Se90Te4Pb6 compositions at different heating rates. The maximum value of parameters S and Hr occurs for Se90Te8Pb2 glassy composition, which indicate that the glassy composition with the little Pb at% content (Se90Te8Pb2) is thermally more stable than that with more Pb at% content. It is observable from Table (2) that, the thermal stability parameters (S, Hr, Trg and ΔT) have a minimum values at highest value of heating rate and for glassy composition with the lowest Pb content. This results indicate that the thermal stability of the studied sample compositions increases with increasing heating rates and decreases with increasing Pb at% addition in Se90Te10 xPbx system. The inversions relation between the thermal stability and Pb at.% content may be attributed to decrease of effective band energy with increasing the lower Te–Pb and Se–Pb bonds energies by increasing Pb at% content in the studied system. 3.3. Heating rate dependence of Tg The kinematical studies are always connected with the concept of the activation energy. In general, separate activation energies must be identified with individual nucleation and growth steps in a transformation. Although they usually have been combined in to one activation energy representative of the overall crystallization process. Losocka [32] suggested an empirical relationship describes the glass transition temperature Tg dependence of heating rate as follows: T g ¼ A þ B ln β

ð5Þ

Where A and B are constants. The value of the constant A indicates the glass transition temperature for the heating rate of 1 °C min 1. The value of the constant B indicates the temperature that is 0.693 times the glass transition temperature when the sample is scanned at a heating rate of 10 °C min 1 [33]. The constant B is also related to the cooling rate of the melt; the lower the cooling rate of melt the lower the value B. This signifies that the constant B is related with the response of the configurationally changes within the glass transition region. The variation of Tg vs. lnβ for glassy Se90Te4Pb6 and Se90Te8Pb2 compositions is shown in Fig. 4. The driving values of the constants A and B from Fig. 4 are listed in Table 3 for the studied glassy compositions. It is clear from Table 3 that, the values of the constant B are depended on the composition. This dependence refers to structure changes take place with increasing Pb at% content.

320

2

2.5

3

3.5

4

4.5

5

ln (β) Fig. 4. Plot of glass transition temperature Tg vs. lnβ for Se90Te8Pb2 and Se90Te4Pb6 glassy compositions. Table 3 Deduced Values of activation energy of glass transition Eg (kJ mol 1) and Kinetic parameters A and B for glassy Se90Te8Pb2 and Se90Te4Pb6 compositions according to different methods. Composition Activation energy of glass transition Eg (kJ mol 1)

Se90Te8Pb2 Se90Te4Pb6

Kissinger method

Moynihan method

156.127 0.05 96.077 0.01

158.32 70.05 98.21 70.01

A (K)

B (min)

322.43 7 0.11 5.517 0.07 307.03 7 0.11 8.3 7 0.07

3.4. Evaluation of the activation energy of glass transition Eg The activation energy of glass transition is the amount of energy that is absorbed by a group of atoms in the glassy region so a jump from one metastable state to another [22]. In other words, the activation energy is involved in the molecular motions and rearrangements of the atoms around the glass transition temperature. The glass transition temperature represents the strength or rigidity of the glass structure of the alloy, which depends on several independent parameters such as the band gap, effective molecular mass, cohesive energy and average coordination number [34]. The heating rate dependence of the glass transition temperature in chalcogenide glasses may be interpreted in terms of thermal relaxation phenomenon. Moynihan et al. [35] arise a relation to evaluate the activation energy of glass transition Eg as follows: lnðβ Þ ¼ Const: Eg =RT g

ð6Þ

where R is the universal gas constant. According to Eq. (6), the plots of ln β vs. 1=T g for glassy Se90Te4Pb6 and Se90Te8Pb2 compositions should be straight lines as apparent in Fig. 5(b). The deduced values of glass transition activation energies Eg are listed in Table 3. Soliman [36] derived three methods to applicability of the Kissinger's model [37] to evaluate the values of Eg dependent on the Kissinger's relation lnðβ =T g 2 Þ ¼ Const: Eg =RT g

ð7Þ

All these methods to derivate the Kissinger's equation, given nearly the same values of Eg and different values of the constant [36]. A plots of ln(β/T 2g ) vs. 1000/Tg for Se90Te4Pb6 and Se90Te8Pb2 glassy compositions are displayed in Fig. 5(a). The values of the glass transition activation energies Eg have been calculated from the slopes of straight lines and reported in Table 3.


30

-7.6

Se 90Te 4Pb 6

-8.0

-8.4

Se90Te8Pb2 Fragility parameter F

Se 90Te 8Pb 2

ln(β/Tg2)

129

25

Se90Te4Pb6

20 15 10

-8.8

5 0.2

0.25

0.3

0.35

0.4

0.45

1/ln(β β)

-9.2

Fig. 6. Variation of fragility index F vs. (1/ln(β)) for Se90Te8Pb2 and Se90Te4Pb6 glassy compositions.

2.92

2.96

3.00

3.04

1000/Tg,K-1

Se90Te8Pb2

4.0

Se90Te4Pb6

lnβ

3.6

3.2

2.8

2.4

2.92

2.96

3.00

3.04

-1 1000/Tg,K Fig. 5. Plots of (a) ln (β/Tg2) and (b) ln(β) vs. 1000/Tg for Se90Te8Pb2 and Se90Te4Pb6 glassy compositions.

It is observable from Table 3 that, the values of activation energies of glass transition obtained by Kissinger's and Moynihan's models are quite closed and their tends of variation with composition are nearly similar. Moreover, the differences in the values of Eg are within average of experimental errors. It is clear from Table 3 that, the values of Eg have been decreased with increasing Pb at% content in Se90Te10 xPbx system. This behavior can be attributed to that, in the glasses containing Se there is tendency to form polymerized network. The structure of the Se–Te system prepared by melt quenching is regarded as a mixture of Se8 member rings, Se6Te2 mixed rings and Se–Te chains. A strong covalent bonds exist between the atoms in the ring, whereas in between the chains only the Vander Waals forces are dominant [38]. The addition of Pb at% content to the Se–Te system leads to its entry into the cross link chains, therefore increasing the stability in the glass [39] and hence causing a decrease in rigidity of the glass matrix by formation of additional Pb–Se and Pb–Te bonds with lower bond energy replacing the Se–Te and Te–Te bonds with the higher bonds energies. This explanation performs to decrease of the glass transition temperatures Eg with increasing Pb at% content in studied Se90Te10 xPbx glassy system. 3.5. Glass fragility Fragility index (F) characterizes and quantifies the anomalous non-Arrhenius transport behavior of glassy materials as they

approach the randomness-breaking glass transition region [40]. Fragile glasses are materials with non-directional inter-atomic or intermolecular bonds. Strong glasses show resistance to structural degradation and usually with a small enthalpy of the structural relaxation kinetics. The fragility index F has been calculated using the following relation [41]: F ¼ Eg =RT g ln β ð8Þ The variation of the index F vs. heating rate is shown in Fig. 6 for Se90Te4Pb6 and Se90Te8Pb2 glassy compositions. It is observable that, the values of the fragility index F increase with increasing Pb at% content in the investigated compositions and decrease with increasing heating rates. The increase of F with increasing Pb at% content means that the glass becomes more fragile, and its tendency to structural arrangement increases with increasing nondirectional inter-atomic bonds. The decrease in the values of F with increasing heating rate can be discussed according to decrease in relaxation time with increasing heating rates. Moreover, the low values of fragility index F (FE16) for investigated glassy compositions indicate that, the glassy Se90Te4Pb6 and Se90Te8Pb2 compositions are obtained from the strong glassforming liquid [42]. 3.6. Kinetics of Crystallization processes Differential thermal analysis (DTA) are the thermal method to study the behavior of glass crystallization. The heat flow ϕ was evolved during crystal growth expressed by the following equation [43]

φ ¼ ΔHdx=dt

ð9Þ

where ΔΗ is the heat of crystallization. The crystallization fraction χ can be expressed according to the Johnson–Mehl–Avarmi (JMA) transformation equation as a function of time [44] xðtÞ ¼ 1 exp ðkTÞn

ð10Þ

where k is the effective reaction rate constant. The isothermal transformation rate dχ(t)/dt can be given from Eq. (10) as 1 1=n dxðtÞ=dt ¼ nkð1 xÞ lnð1 xÞ ð11Þ where n is the Avrami exponent. The validity of the JMA equation can be extended to non–isothermal kinetics, if the crystallization rate is defined only by temperature and does not depended on the previous thermal history [45]. Sestak–Berggen SB (m,n) model [31] suggested an empirical models as a special case of (JMA) model [46] in the case for JMA equations are not valid. SB (m,n) model was descriped the crystallization kinetics process, where m is an integer that depends on the dimensionality of the crystal.

130


According to Vyazovkin [47] have been faulted the term of activation energy in the case of crystallization processes and stressed that, it should be the effective activation energy, means an average activation energy taking in to account the individual energy of all the multiple steps involved in the crystallization process. Matusita et al. [48] have been suggested a method for nonisothermal experiments. The precipitated volume fraction of crystallites χ in a glass heated at constant heating rate β is related to the activation energy of crystalization Ec according to the following double-logarithmic equation: ð12Þ ln ln 1 χ ¼ n ln β 1:052mEc =RT þ cons tan t where χ is given as χ ¼A/AT, AT is the total area of the exothermal peak between Tc (the crystallization just begins) and the temperature Tf (the crystallization is completed) represented as a shaded area in Fig. (2) and A is the area between the initial temperature Tc and generically T selected between Tc and Tf. If the crystallization fraction χ is determined at a fixed temperature but at different heating rates. The Avrami exponent n can be obtained from the slope of the following equation: d ln ln 1 χ ¼ n ð13Þ dðln β Þ T According to Eq. (13), a plot of ln{ ln(1 χ)} vs. lnβ, at fixed temperatures,yield a straight line with slope equal to the exponent n as shown in Fig. 7(a and b) for glassy Se90Te4Pb6 and Se90Te8Pb2 compositions respectively. The values of the constants m and n are dependent on the mechanism of the growth and the dimensionality of the crystal respectively. For the quenched glass samples containing no nuclei, m is equal to (n 1). On the other hand, for glass contain 5 396 K 392 K 388 K 385 K

3

ln[-ln(1-χ)

1 -1 -3 -5 -7 -9 -11 2.5

2.7

2.9

3.1

3.3

3.5

3.7

3.9

4.1

ln (β) 8

367 K 363 K 360 K 370 K

6

ln[-ln(1-χ)

4 2 0 -2 -4 -6 -8 -10 -12 1.8

2

2.2 2.4

2.6 2.8

3 3.2 3.4 ln (β)

3.6 3.8

4

4.2

Fig. 7. Plots of ln[ ln(1 χ)] vs. lnβ for (a) Se90Te8Pb2 and (b) Se90Te4Pb6 glasses compositions at different fixed temperatures during the DTA exothermic peaks.

Table 4 The values of Avrami index n and dimensionality of growth m for different crystallization mechanisms. Mechanism

Avrami index n

Dimensionality of growth m

Three-dimensional growth Two-dimensional growth One-dimensional growth Surface nucleation

4 3 2 1

3 2 1 1

sufficiently large number of nuclei, which might occur due to the annealing of the asquenched glass (i.e.) when nuclei formed during any previous heat treatment prior to thermal analysis are dominant, m is taken equal to n. Mahadevan et al. [49] showed that, the Avarim exponent n may be equal to 4, 3, 2 or 1 depended on the glas–crystal transformation mechanisms. The values of n and m for different crystallizations [49] are given in Table 4. The values of Avrami exponent (n) and dimensionality of growth m (m ¼ n 1, since the asquenched samples are studied) for glassy Se90Te4Pb6 and Se90Te8Pb2 compositions at different temperatures have been listed in Table 5. The values of n and m reveal that, the mechanism of crystal growth changes with increasing of Pb at% amount in Se90Te10 xPbx glass system. It is observable from Table (5) that, for Se90Te8Pb2 glassy composition the average value of n¼ 3.99 70.01 E4, which gives m ¼ 2.99 70.01 E3 suggested the bulk nucleation with three-dimensional growth. for Se90Te4Pb6 glassy composition the average value of n ¼3.26 70.01 E3, which gives m ¼2.26 70.01 E2 suggested the bulk nucleation with twodimensional growth. The kinetic analysis of crystallization reaction is related to the reaction rate constant as a function of temperature. In the amorphous crystalline transformation process, the activation energies are the activation energy of nucleation En and activation energy of growth Eg. The activation energy for the whole process is called the activation energy of crystallization and is denoted by Ec. The activation energy of crystallization is a measure of potential for crystallization and a recipe for consideration during applications. As shown in Eq. (12), the plot of ln[ ln(1 χ)] against 1000/T should give a straight lines for all heating rates. Fig. 8(a and b) shows the plots of ln[ ln(1 χ)] vs. 1000/T at different heating rates for Se90Te4Pb6 and Se90Te8Pb2 glassy compositions respectively. It is observed that the obtained relations are linear over a wide range of temperature. At higher temperature range, a break in linearity is seem for all heating rates. The break in linearity behavior may be due to the saturation of nucleation sites in the final stages of crystallization of crystal growth by small size of the particles. The values of the activation energies of crystallization Ec have been calculated from the slope of each straight lines in Fig. 8 (a and b) for the investigated compositions and listed in Table 6. It is found that the values of Ec seem to be independent of the heating rate. There are another different methods to determine Ec based on the crystallization temperature dependence of the heating rate. The kinetics equation of chemical reaction in the linear heating process can be described as follows

dα E ð14Þ β ¼ Af ðαÞexp RT dt where f(α) is the differential function of conversion, A is the preexponent factor and E is the activation energy. According to the Kissinger method [50], which generalized by Elder [51] at the condition of maximum reaction rate (d2α/dT2) ¼0, Eq. (14) can be rewritten as lnðβ =T p 2 Þ ¼ lnðAR=EÞ þ ln δp E=RT p

ð15Þ


131

Table 5 The values of Avrami index n and dimensionality of growth m for glassy Se90Te8Pb2 and Se90Te4Pb6 compositions at different selected temperatures during the DTA exothermic peaks. Composition

T (K)

n

m

Average (n)

Average (m)

Se90Te8Pb2

385 388 392 396 360 363 367 370

3.85 7 0.01 3.917 0.01 4.05 7 0.01 4.167 0.01 3.137 0.01 3.25 7 0.01 3.217 0.01 3.487 0.01

2.85 7 0.01 2.917 0.01 3.05 7 0.01 3.167 0.01 2.137 0.01 2.25 7 0.01 2.217 0.01 2.487 0.01

3.99 7 0.01E4

2.99 7 0.01E3

3.26 7 0.01E3

2.26 7 0.01E2

Se90Te4Pb6

2

Se 90Te8Pb2

10 K/min 20 K/min 30 K/min 40 K/min 50 K/ min

ln(-(ln(1-χ))

0

-2

-4

-6

-8

2.4

2.6

2.5

1000/ T, K 3

2.7

2.8

-1

10 K/min 20 K/min 30 K/min 40 K/min

ln(-(ln(1-χ))

-1

50 K/min

-3 `

-7

2.6

2.65

2.7

2.75

1000/ T, K

where xp ¼E/RTp. From the last equation, the activation energies have been estimated from the slope of the straight lines of ln(β/ Tp2) vs. 1000/Tp plot, should be corrected with the factor 1/[1 (dlnδp/dxp). At the case of ΔTo150 K, the factor of [dlnδp/dxp] exhibits a rather smaller change around an average value [52],then the approximate value of activation energy according to Kissinger's method is given by h i d lnðβ=T 2p Þ Eapprox ¼ R ð17Þ dð1=T p Þ With condition

e% ¼

1

-9

ð16Þ

1 1 ½dðln δp Þ=dðxp Þ

1 the relative error of Eapprox

with respect to real values E can given as [52]

Se 90 Te 4 Pb 6

-5

the activation energy calculated as h i d lnðβ =T 2p Þ 1 E ¼ R dð1=T p Þ 1 dðln δp Þ=dðxp Þ

2.8

2.85

2.9

-1

Fig. 8. The plots of ln[ ln(1 χ)] vs. 1000/T for (a) Se90Te8Pb2 and (b) Se90Te4Pb6 glassy compositions at different heating rates. Table 6 Evaluation Values of activation energy of crystallization Ec (kJ mol 1) glassy Se90Te8Pb2 and Se90Te4Pb6 compositions according to different methods. Composition

Se90Te8Pb2

Se90Te4Pb6

Kissinger method Augis and Bennet method Augis and Bennet approximated method Mahadevan method Ozawa and Chen method Matusita method

84.0770.05 82.59 70.07 83.14 70.012 83.98 70.03 78.99 70.06 95.02 70.02

138.58 7 0.05 135.107 0.07 137.917 0.012 134.117 0.03 122.78 7 0.06 176.487 0.02

where δp is a correction term which dependence on the kinetics model and equal to 0 δp¼ df(αp)/dα ¼ f . The effect of this term on the values of activation parameters (E and A) was also investigated [51]. Then,

Eapprox E 100 E

ð18Þ

Some authors [53,54] have shown that, for some kinetic models the error in the activation energy directly calculated from the slopes of ln(β/Tp2) vs. 1000/Tp plot does not exceed 5%. Llopiz et al. [55] consider that, the correction of lnδp term used for the correct evaluation of A from the intercept of the straight lines in ln(β/Tp2) vs. 1000/Tp plot. For Se90Te4Pb6 and Se90Te8Pb2 glassy compositions, the shift in peak temperature of crystallization Tp with the heating rate can be used to evaluate the approximate values of activation energy for crystallization Ec. Plots of lnðβ =T p 2 Þ vs. 1=T p for the studied glassy compositions are shown in Fig. 9(a and b). The data are fitted by straight lines. The estimated values of Ec for the studied compositions, which have been derived from Fig. 9(a and b) according to Eq. (17) are listed in Table 6. Augis and Bannett [56] developed a method to evaluate the values of activation energy for crystallization Ec and frequency factor Ko, according to the following equation ð19Þ ln β=ðT p T c Þ ¼ Ec =RT p þ ln ko ; where the values of the frequency factor Ko is defined as the number of attempts mode by nuclei per second to overcome the energy barrier and provides an information for the calculation of nucleation site, present in the material for crystal growth [57]. According to Eq. (19), ln β=ðT p T c Þ has been plotted against 1000/Tp for the investigated glassy composition as shown in Fig. 9 (a and b). The values of Ec have been evaluated from the slops of this function fitted to the data and reported in Table 6. In the case of T p g g T c , Eq. (19) can be approximated as follows [58]: lnðβ =T p Þ ¼ Ec =RT p þ ln ko ;

ð20Þ

The plots of lnðβ=T p Þ vs. 1000/Tp are shown in Fig. 9(a and b) for Se90Te8Pb2 and Se90Te4Pb6 glassy compositions respectivily. From the slopes of the linear fitting of the data of Fig. 9(a and b) for this

132


indication of the retardation of the crystallization, while its higher value diminishes the glass formation ability [49]. It is observable from Table 7 that, the values of K increase with decreasing Pb at% content in the studied system, which suggested the increase of the glass forming ability and stability of glass for Se90Te8Pb2 glassy composition. Therefore one can concluded that, the addition of Pb atoms to the binary Se90Te10 system, decreases the rate of crystallization and hence its thermal stability. The values of the activation energy for crystallization Ec can be calculated also using the approximation of Mahadevan et al. [49], where the variation of ln(1/Tp2) with ln β is much slower than ln (1/Tp) [49] as follows

6 3

ln (β)

Y

0

ln β/ (Tp-Tc)

-3

ln β/ Tp

-6 -9

ln β/ T2p

-12 2.35

2.45

ln β ¼ Ec =RT p þCons tan t; 2.65

2.55

1000/Tp,K-1

6

Y

3 0

ln β/ (Tp-Tc)

-3

ln β/ Tp

-12 2.57

ln β/ T2p 2.62

2.67

2.72

1000/Tp,K

ð23Þ

At a fixed value of the crystallized fraction χ and for a set of temperature in exothermic peaks in the DTA trace at different heating rates. Plots of lnðβ=T 2 Þ vs. st 1/T for the studied glassy compositions is shown in Fig. 10(a and b). The values of Ec can be obtained from the slops of the straight lines in Fig. 10(a and b). The deduced values of Ec for Se90Te4Pb6 and Se90Te8Pb2 glassy compositions are listed in Table 6. One can observed from Table 6 that, the values of activation energy of crystallization Ec for Se90Te4Pb6 and Se90Te8Pb2 glassy compositions that determined according to Kissinger, Augis and Bannett, Augis and Bannett approximation and Mahadevan methods are in good agreement with each other but different from

-6 -9

Fig. 9(a and b) shows the variation of ln β vs.1=T p for studied compositions. The values of Ec can be calculated from the slopes of the obtained straight lines. The deduced values of Ec for the studied compositions are listed in Table 6. Ozawa [59] and Chen [60] suggested a method to evaluate Ec using the following formula lnðβ =T 2 Þ ¼ Ec =RT þ Cons tan t

ln (β)

ð22Þ

2.77

-1

Y ¼ ln(β/T2p),

Fig. 9. Plots of function ln(β/Tp), ln β/(Tp Tc) and ln(β) vs. 1000/Tp for (a) Se90Te8Pb2 and (b) Se90Te4Pb6 glassy compositions.

Table 7 The average values of frequency factor (Ko) and crystallization rate factor (K) for glassy Se90Te8Pb2 and Se90Te4Pb6 compositions. Composition Ko (min 1) according to Ko (min 1) according to K (min 1) Eq. (19) Eq. (20) Se90Te8Pb2 Se90Te4Pb6

6.48 1012 7.07 1020

1.96 1011 1.56 1020

1.87 1012 2.61 1020

approximated formula, the values of the activation energy for crystallization Ec can be evaluated. The values of Ec for the studied compositions are listed in Table 6. The values of the frequency factor Ko have been calculated according to Eqs. (19) and (20) for Se90Te4Pb6 and Se90Te8Pb2 glassy compositions are listed in Table 7, which are in a good agreement with each others. The values of Ko provide an information for the calculation of nucleation sites, present in the material for crystal growth. The minimum values of Ko confirm the fact that, glass is most stable, as the number of attempts made by nuclei are lowest for a glass [57]. The value of Ko(min) was found for Se90Te8Pb2 composition with the lower Pb at% content. Using the values of Ko, the crystallization rate factor K have been evaluated according to Arrhenius equation: K ¼ K o expð Ec =RT c Þ

ð21Þ

The values of crystallization rate factor K for the studied compositions are listed in Table 7. The importance of crystallization rate factor can be attributed to its minimum value gives an

Fig. 10. Plots of lnðβ=T 2 Þ vs. (1000/T) at fixed values of the crystallized fraction χ for (a) Se90Te8Pb2 and(b) Se90Te4Pb6 glassy compositions.


their value obtained according to Ozawa and Chen as well as Matusita methods. This difference may be due to the different approximations used in this methods [61]. It is clear from Table 6 that, the values of Ec increase with increasing Pb at% content. This increase in Ec of Pb doped ternary alloys Se90Te10 xPbx can be explained in terms of atomic weights of Te and Pb atoms. It is well known that the activation energy of crystallization is associated with the nucleation and growth processes that dominate the devitrification of most glassy solids [62]. The atomic weight of Pb (207.2 g mol 1) is much than that of Te (127.60 g mol 1). In the present work, Pb is added in binary Se–Te composition at the cost of Te, thus, the mean atomic weight of ternary alloys is increased which a decrease in the nucleation and growth rate is possible. This is probably the reason why crystallization occurs in present ternary alloys at comparatively higher activation energies. On the other hand, the increase in activation energy of crystallization with increasing Pb% addition to Se90Te10 xPbx glassy system, indicating that the rate of crystallization is faster as the Pb content increases.

4. Conclusion The glass transition and crystallization kinetics of Se90Te10 xPbx (x¼2,6) glasses compositions, have been studied by differential thermal analysis (DTA) under non-isothermal condition with different heating rates (10,20,30,40,50 °C min 1). The values of glass transition activation energy Eg have been calculated using the Kissinger and Moynihan methods based on the heating rate dependence of glass transition temperature Tg. The values of Eg are reduced with increasing Pb content, which is accredited to variation in chemical bonding by increasing of Pb at% content. The variation of activation energy of crystallization with increase of Pb content in the investigated compositions has been studied according to Kissinger, Augis and Bennett, Augis and Bennet approximated, Mahadevan, Ozawa and Chen and Matusita methods. Difference in values of activation energy Ec using different models may be attributed to the different approximation used in these models. The lowest value of Eg and the highest value of Ec for Se90Te8Pb2 glassy composition indicate that. it is more stable as compared to Se90Te4Pb6 glassy composition. The values of Avrami index n obtained from Matusita's model are 3.9970.01E4 for Se90Te8Pb2 glassy composition and 3.2670.01E3 for Se90Te4Pb6 glassy composition. It was suggested the three and two dimensional nucleation growth for Se90Te8Pb2 and Se90Te4Pb6 glassy composition respectively during its amorphous to crystalline transformation. The values of various kinetic parameters such as thermal stability S, temperature difference ΔT, Hurby parameter Hr, frequency factor Ko, crystallization rate factor K and fragility index F have been estimated under non-isothermal condition. Their values have been found increase with increasing heating rate and decrease with increasing Pb at% content in the studied system. It means that the thermal stability decreases with increasing Pb at% content. This result can be attributed to the effective bands energies with increasing Pb at% content in Se90Te10 xPbx system.

References [1] [2] [3] [4]

A. Sharm, P.B. Barman, J. Therm. Anal. Calorim. 96 (2009) 413. N. Rysava, T. Spasov, L. Tichy, J. Therm. Anal. 32 (1987) 1015. N. Afify, J. Non-Cryst. Solids 128 (1991) 279. F.A. Al-Agel, S.A. Khan, E.A. Al-Arfaj, A.A. Al-Ghamdi, J. Non-Cryst. Solids 358 (2012) 564. [5] K. Tanaka, Phys. Rev. B 39 (1989) 1270. [6] V.S. Kushwaha, A. Kumar, J. Mat. Sci. 42 (2007) 2712.

133

[7] N. Kushwaha, R.K. Shukla, A. Kumar, J. Optoelectron. Adv. Mater. 8 (2006) 794. [8] Y. Abbe, S. Furukawa, K. Mochizuki, K. Masumato, J. Jpn. Inst. Met. 58 (1994) 346. [9] M. Agne, A. Lambrecht, U. Schiessl, M. Tacke, Infrared Phys. Technol. 35 (1994) 47. [10] R. Kumar, P. Sharma, P.B. Barman, V. Sharma, S.C. Katyal, V.S. Rangra, J. Therm. Anal. Calorim. 110 (2012) 1053. [11] S.K. Tripathi, B.S. Patial, N. Thakur, J. Therm. Anal. Calorim. 107 (2012) 31. [12] S.F. Naqvi, Deepika, N.S. Saxena, K. Sharma, D. Bhandri, J. Alloy. Compd. 506 (2010) 956. [13] A.S. Farid, H.E. Atyia, J. Non-Cryst. Solids 408 (2015) 123. [14] A. Khan, Z.H. Khan, M. Zulfequar, M. Husain, Phys. B 400 (2007) 180. [15] N.B. Maharajan, N.S. Saxena, D. Bhandari, M.M. Mimran, D.D. Paudyal, Bull. Mater. Sci. 23 (2000) 369. [16] I.S. Ram, K. Singh, Int. J. Thermophys. 35 (2014) 123. [17] S.A. Khan, M. Zulfequar, M. Husain, Curr. Appl. Phys. 5 (2005) 583. [18] D. Moore, G. McCabe, W.H. Freeman. Co., London, 2003. [19] M.K. Rabinal, K.S. Sangunni, E.S.R. Gopal, J. Non-Cryst. Solids 188 (1994) 77. [20] S.A. Khan, J.K. Lal, F.A. Al-Agel, M.A. Alvi, J. Non-Cryst. Solids 554 (2013) 227. [21] R.R. Daived, CRC Hand Book of Chemistry and Physics, Chemical Rubber Publishing Co., Cleve Land, Ohio, 1977. [22] B.S. Patial, N. Thakur, S.K. Tripathi, J. Therm. Anal. Calorim. 106 (2011) 845. [23] N. Mehta, S.R. Tiwari, A. Kumar, Mat. Res. Bull. 41 (2006) 1664. [24] E.D. Zanotto, J. Non-Cryst. Solids 89 (1987) 10. [25] E.D. Zanotto, J. Non-Cryst. Solids 74 (1985) 373. [26] M.L.F. Nascimento, L.A. Souza, E.B. Ferreira, E.D. Zanotto, J. Non–Cryst. Solids 351 (2005) 3296. [27] D. Turnbll, Contemp. Phys. 10 (1969) 473. [28] M. Saad, M. Pouling, Mater. Sci. Foum. 19 (1987) 11. [29] A. Hruby, C Zech, J. Phys. B. 22 (1972) 187. [30] A. Hruby, Czech, J. Phys. B 53 (1973) 1263. [31] J. Sestak, Elsivier, Amesterdam, 2006. [32] M. Lasocka, Mater. Sci. Eng. 23 (1976) 173. [33] M.M.A. Imran, D. Bhandari, N.S. Saxena, J. Therm. Anal. Calorim. 65 (2001) 257. [34] M.K. Rabinal, K.S. Sangunni, E.S.R. Gopal, J. Non-Cryst. Solids 188 (1995) 98. [35] C.T. Moynihan, A.J. Easteal, J. Wilder, J. Tucke, J. Phys. Chem. 78 (1974) 2673. [36] A.A. Soliman, J. Therm. Anal. 89 (2007) 389. [37] E.H. Kissinger, Nat. Bur. Stand. 57 (1956) 217. [38] T. Ozawa, Polymer 12 (1971) 150. [39] P.K. Dwivedi, Ph.D. thesis, Department of Physics, HBTI, Kanpur, 1996. [40] C.A. Angell, J. Non-Cryst. Solids 73 (1988) 7818. [41] L.K. Nagi, R.W. Rendell, L.D. Pye, W.C. LaCourse, H.J. Sevens, The Physics of Non-crystalline Solids, Taylor and Francis, London, 1992. [42] T.A. Vilgis, Phys. Rev. B 47 (1993) 2882. [43] E. Cernoskova, Z.G. Ivanova, V. Pamukchieva, Thermochim. Acta 316 (1998) 97. [44] J. Vazquez, R. Gonzalez-Palma, P. Villares, R. Jimenez-Garay, Phys. B 336 (2003) 97. [45] D.W. Henderson, J. Therm. Anal. 325 (1979) 325. [46] P. Simon, Thermochim. Acta. 300 (2011) 156. [47] S. Vyaovkin, Macromol. Rapid Commun. 23 (2002) 771. [48] K. Mutusita, T. Komatsu, R. Yokota, J. Mater. Sci. 19 (1984) 291. [49] S. Mahadevan, A. Giridhar, A.K. Singh, J. Non-Cryst. Solids 88 (1986) 11. [50] H.E. Kissinger, Anal. Chem. 29 (1957) 1702. [51] J.P. Elder, J. Therm. Anal. 30 (1985) 30. [52] P. Budrugeac, E. Segal, J. Therm. Anal. 88 (2007) 703. [53] G.M. Criado, A. Ortega, J. Non-Cryst. Solids 87 (1986) 302. [54] J. Malek, J. Sestak, F. Rouquerol, J.M. Criado, A. Ortega, J. Therm. Anal. 38 (1992) 71. [55] J. Llopiz, M.M. Romero, A. Jerez, Y. Laureiro, Thermochim. Acta. 256 (1995) 205. [56] J.A. Augis, J.E. Bennett, J. Therm. Anal. 13 (1978) 283. [57] A. Kaswan, V. Kumari, D. Patidar, N.S. Saxena, K. Sharma, Process. Appl. Ceram. 8 (2014) 25. [58] H. Yinnon, D.R. Uhlmann, J. Non-Cryst. Solids 54 (1983) 291. [59] T. Ozawa, Bull. Chem. Soc. Jpn. 38 (1965) 1881. [60] H.S. Chen, J. Non-Cryst. Solids 27 (1987) 257. [61] M.M. Heireche, M. Belhadji, N.F. Hakiki, J. Therm. Anal. Calorim. 114 (2014) 195. [62] R. Chiba, N. Funakoshi, J. Non-Cryst. Solids 105 (1998) 105.