Iso-conversional approach for study of glass transition and crystallization kinetics of ternary glassy Se98−xAg2Inx (x = 0, 2, 4, 6) system

Journal of Alloys and Compounds 587 (2014) 565–572

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Iso-conversional approach for study of glass transition and crystallization kinetics of ternary glassy Se98xAg2Inx (x = 0, 2, 4, 6) system C. Dohare, N. Mehta ⇑ Department of Physics, Banaras Hindu University, Varanasi 221 005, India

a r t i c l e

i n f o

Article history: Received 30 May 2013 Received in revised form 24 September 2013 Accepted 17 October 2013 Available online 30 October 2013 Keywords: Glass transition Crystallization kinetics Non-isothermal Differential scanning calorimetry Scanning electron microscope

a b s t r a c t The glass transition and crystallization kinetics of Se98xAg2Inx (x = 0, 2, 4, 6) glasses have been studied under non-isothermal condition using differential scanning calorimetry (DSC). Using model free approach [Kissinger–Akahira–Sunose (KAS), Flynn–Wall–Ozawa (FWO), Tang and Straink], the activation energy of glass transition, DEag and crystallization kinetics, DEac have been plotted as a function of extent of conversion, a. The kinetic parameters such as the activation energy (E), Avrami exponent (n), and rate of crystallization (K) have been determined using Kolmogorov–Johnson–Mehl–Avrami (KJMA) model. Glassy nature of as prepared samples was confirmed by XRD (X-ray diffraction), surface morphology and diffraction pattern by SEM and TEM, respectively. Ó 2013 Elsevier B.V. All rights reserved.

1. Introduction The kinetics of glass transition and crystallization process can be investigated with the assist of thermo-analytical technique namely, differential scanning calorimetry (DSC). The kinetic analysis of glassy systems is generally based on either the iso-kinetic hypothesis or the iso-conversional principle. These two approaches can be accordingly categorized as (1) iso-kinetic methods, where the transformation mechanism is assumed to be the same throughout the temperature/time range of interest and, the kinetic parameters are assumed to be constant with respect to time and temperature; (2) iso-conversional methods, which are generally used for non-isothermal analysis, assume that the reaction (transformation) rate at extent of conversion, a (degree of transformation) is only a function of temperature [1,2]. Therefore, the activation energy for such processes can logically vary with the degree of conversion. The kinetic parameters, in this case, are considered to be dependent on the degree of transformation at constant temperature [3,4]. It has been experimentally demonstrated that the model free equations give rise to reliable predictions where as the substitution of kinetic triplets, obtained from single heating rate run, yields fundamentally erroneous predictions. Iso-conversional methods are used in the physical chemistry for the determination of the kinetics of thermally activated solid-state ⇑ Corresponding author. Tel.: +91 542 2307308x244; fax: +91 542 2368174. E-mail address: [email protected] (N. Mehta). 0925-8388/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jallcom.2013.10.131

reactions. Physicochemical changes during an exothermic or endothermic event in DSC are complex and involve multi-step (serial or parallel) processes occurring simultaneously at different heating rates [5,6]. These methods are very functional for the analysis of chemical or physical process and give some hidden clue for the mechanism of various chemical reactions, cross-linking, polymer crystallization, phase transition kinetics, glass aging and protein denaturation [7,8]. Data simulations are also very necessary for these methods for large scale or industrial purposes because these simulations do not need any assumptions on the reaction mechanism. Selenium based multi-component system exhibits a unique property of reversible transformation. Silver makes the structure more stable in chalcogenide matrix by bridging chalcogenide chains. It is found that the addition of Ag modifies the band structure as well as it enhances the electrical and optical properties of the materials [9]. Silver incorporated chalcogenide glasses can be used as, materials for holography and also be used as sensitive electrochemical electrodes [24]. The structure of glassy Se and, the effect of Indium into glassy Se have been pointed out in the literature, and studies signify its coordination requirement after the incorporation of Indium into glassy Se to form a cross-linked structure, which retards the crystallization probability and enhanced thermal stability [10]. Sewry and Brown [11] showed the dependence of activation energy, Ea and temperature, Tai on the extent of conversion, a by model-free kinetic analysis. Vyazovkin and Sbirrazzuoli [12]

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explained the iso-conversional kinetic analysis for thermally stimulated processes in polymers. In the present study, we report the effect of Indium additive in binary Se–Ag glassy system in term of iso-conversional kinetics. 2. Material preparation and characterization Glassy Se98xAg2Inx (x = 0, 2, 4, 6) system was prepared by quenching technique as discussed in the paper [13]. The surface morphology and chemical composition of synthesized desired sample were characterized by using SEM, XRD and EDS. The structure of the as-prepared samples were verified by X-ray diffractometer using Cu Ka radiation (k = 1.5405 Å). The X-ray tube voltage and current were 30 kV and 20 mA, respectively. The scan range was 5–80° (2h) and the scan speed was 1°/min. The XRD patterns of as-prepared Se98xAg2Inx (x = 0, 2, 4, 6) system are shown in Fig. 1. These XRD patterns clearly show that peaks are not very sharp. This confirms the glassy nature of samples. Surface morphology is characterized by Scanning Electron Microscope [Inspect S-50 (FEI Company of USA (SEA) PTE Ltd., Singapore), FP 2017/12 scanning electron microscope]. The SEM micrograph clarifies the formation of agglomerated conchoidal contours (3D microstructure) in chalcogenide Se96Ag2In2 alloy which is an indication of glass structure (see Fig. 2). Transmission electron microscopy (TEM) and high resolution transmission electron microscopy (HRTEM) investigations were carried out using a Tecnai 20G2-TEM, employing 200 kV typical e-beam voltage using JEOL-JSM-5600. Diffraction pattern was confirmed by TEM analysis. Diffraction pattern of glassy Se96Ag2In2 system does not show such sharp spots in a particular manner that could form ring. This further indicates the glassy nature of present samples (see Fig. 3). Surface analysis shows the diffusion and interface controlled growth with decreasing nucleation rate as confirmed by dimensionality and growth parameters. Energy dispersion spectrums (EDS) of glassy Se96Ag2In2 system show the high evidence of the presence of Se, Ag and In elements with proper weight of percentages. The Energy spectrum of Se96Ag2In2 system is shown in Fig. 4. Similar results were obtained for other glasses. The accuracy of the heat flow in DSC was ±0.01 mW and the temperature precision as determined by the microprocessor of the thermal analyser was ±0.1 K. Measurements were made under almost identical conditions at four different heating rates 5, 10, 15 and 20 K/min so that, a comparison of various kinetic parameters of crystallization could be made in order to understand the effect of indium in ternary glassy Se98xAg2Inx (x = 0, 2, 4, 6) system. Fig. 5 shows the characteristic DSC scans for Se92Ag2In6 system with different heating rates.

Fig. 2. SEM image of as prepared glassy Se96Ag2In2 alloy.

3. Theoretical formulation The kinetics of amorphous alloys have been extensively studied using the classical Johnson–Mehl–Avrami (JMA) theoretical model [14]. According this model, the crystallization fraction (a) is described as a function of time, t:



aðtÞ ¼ 1  exp ðKtÞn



ð1Þ

Here, n is the Avrami exponent (order parameter), which depends on the mechanism of growth and dimensionality and K is the effective (overall) reaction rate constant which is given by

Fig. 3. TEM and HRTEM (diffraction pattern) image as prepared glassy Se96Ag2In2 alloy.

Fig. 1. XRD pattern of glassy Se98XAg2InX (X = 0, 2, 4, 6) alloys.

Fig. 4. Energy dispersion image of Se96Ag2In2 (X = 0, 2, 4, 6) alloy by EDX.

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3.1. Kissinger–Akahira–Sunose (KAS) method

0.6

5 K/min 10K/min 15K/min 20K/min

Se 92 Ag 2 In 6

Heat Flow (mW)

0.4

Iso-conversion methods require the determination of the temperature Tai at which a fixed fraction of, a, of the total amount is transformed. In (KAS) method, the relation between the temperature, Tai and heating rate, b is given by [17]:

Tc

0.2

ln 0.0

!

b

¼

T 2ai

Ea þ const RT ai

ð7Þ

Evaluation of the activation energy from the plot of the left side of Eq. (7) vs. 1/Tai at constant conversion degree for the i heating rates used will be called the Kissinger–Akahira–Sunose (KAS) method.

-0.2

To

Tg

3.2. Flynn–Wall–Ozawa (FWO) method

-0.4 320

340

360

380

400

420

440

Fig. 5. DSC scans at different (5, 10, 15, 20 K/min) heating rates for Se92Ag2In6 alloy.

Flynn–Wall–Ozawa method [19,20] has been used for the determination of non-isothermal analysis of crystallization in which the temperature integral in Eq. (5) is simplified by using the Doyle’s approximation [21] and the relation is estimated as follow:

  Ec K ¼ K o exp  RT

ln bi ¼ 1:052

Temperature (K)

ð2Þ

Here, Ec is the activation energy for crystallization and Ko is the frequency factor. In non-isothermal mode, the activation energy of crystallization, Ec has been calculated by Kissinger, Augis-bennett and Matusita-Sakka [27,30,31] and glass transition activation energy, Eg is estimated by Kissinger and Moynihan methods [13,27,28]. Recently, model-free Iso-conversional methods are more reliable than model-fitting methods for determining activation energy for thermally complex process. It is observed that model free prediction compares very well with the actual measurement and emphasizes the reaction complexity for iso-conversional dependence of, Ea on, a determined for the curing process [12]. Iso-conversional methods are categorized as differential and integral form proposed by Freidman (FR), Ozawa–Flyn-Wall (OFW) and Kissinger–Kahira–Sunose (KAS) [16,17]. The kinetics of crystallization in amorphous material can be described by the following rate equation [18]:

  da E f ðaÞ ¼ A exp  RT dt

gðaÞ ¼

a

0

da A ¼ f ðaÞ b

Z

T t0

  E A dT ¼ IðE; TÞ exp  RT b

IðE; TÞ ¼

T

t0

  E dt exp  RT

and determined by direct numerical integration.

þ const

ð8Þ

3.3. Tang method Temperature integral relation has been suggested by Tang and is given as [22]:

ln

!

bi RT 1:895 ai

 ¼ 1:00145

Ea RT ai



þ const

ð9Þ

Evaluation of the activation energy from the plot of the left side of Eq. (9) vs. 1/Tai at constant conversion degree for the i heating rates used will be called the Tang method. 3.4. Starink method

ln

ð4Þ

ð5Þ

where to is the initial temperature, and T is the temperature at an equivalent (fixed) state of transformation. Using an advanced isoconversional method [18], numbers of experiments are carried out at different heating rates and, effective activation energy can be determined at any particular value of a. The temperature integral I(E, T) in Eq. (5) is given as:

Z



The method proposed by Starink is given as [23]:

The integral form of reaction model can be obtained by integrating Eq. (4) as:

Z

Ea RT ai

Evaluation of the activation energy from the plot of the left side of Eq. (8) vs. 1/Tai at constant conversion degree for the i heating rates used will be called the Flynn–Wall–Ozawa (FWO) method.

ð3Þ

where f(a) is the reaction model. Under non-isothermal condition with a constant heating rate b ¼ dT , Eq. (3) may be written as: dt

    da da 1 A E ¼ exp  f ðaÞ ¼ b RT dT dt b



ð6Þ

bi

!

T 1:92 ai

  Ea ¼ 1:0008 þ const RT ai

ð10Þ

Evaluation of the activation energy from the plot of the left side of Eq. (10) vs. 1/Tai at constant conversion degree for the i heating rates used will be called the Starink method. 4. Results and discussions Characteristic temperatures such as glass transition, Tg and crystallization, Tc are recorded by DSC scans at different heating rates (5, 10, 15 and 20 K/min). Their values are given in Table 1.

Table 1 Glass transition and crystallization temperature for glassy Se98xAg2Inx (X = 0, 2, 4, 6) system at different heating rates in non-isothermal mode. Systems

Se98Ag2 Se96Ag2In2 Se94Ag2In4 Se92Ag2In6

10 K/min

15 K/min

20 K/min

Tg (K)

5 K/min Tc (K)

Tg (K)

Tc (K)

Tg (K)

Tc (K)

Tg (K)

Tc (K)

306.5 318.4 319.4 319.7

355.7 387.8 389.2 392.3

310.6 320.8 321.4 321.5

362.1 396.3 397.9 401.1

312.5 321.9 323.2 323.4

364.3 401.8 404.6 408.2

314.8 322.7 324.4 324.9

367.3 407.8 410.2 414.6

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The peak values of crystallization, Tc denotes the exothermic change in crystallization process at various heating rates. The values of glass transition, Tg obtained from the endothermic peaks in

Table 2 Activation energy of glass transition of glassy Se98xAg2Inx (X = 0, 2, 4, 6) system in non-isothermal mode. System

Kissinger method

Moynihan method

Eg (kJ/mol) Se98Ag2 Se96Ag2In2 Se94Ag2In4 Se92Ag2In6

131.3 ± 2.1 265.4 ± 2.1 230.2 ± 2.1 220.5 ± 2.1

136.5 ± 2.2 270.7 ± 2.2 235.6 ± 2.2 225.8 ± 2.2

Table 3 Activation energy and pre-factor of crystallization of glassy Se98xAg2Inx (X = 0, 2, 4, 6) system in non-isothermal mode. System

Kissinger method

Se98Ag2 Se96Ag2In2 Se94Ag2In4 Se92Ag2In6

125.7 ± 2.0 85.7 ± 2.0 81.2 ± 1.9 77.2 ± 1.9

Augis– Bennett

Matusita– Sakka

ln Ko (min1)

128.7 ± 2.1 89.0 ± 2.1 84.4 ± 2.1 80.8 ± 2.1

131.6 ± 2.2 92.3 ± 2.2 87.7 ± 2.2 84.1 ± 2.2

39.3 23.3 21.8 20.5

Ec (kJ/mol)

Table 4 Determination of Avrami index, Thermal stability and glass forming ability (GFA) for glassy Se98xAg2Inx (X = 0, 2, 4, 6) system. System

Avrami index (n)

Thermal stability (DT)

GFA

Se98Ag2 Se96Ag2In2 Se94Ag2In4 Se92Ag2In6

1.0 ± 0.12 1.6 ± 0.20 2.7 ± 0.05 2.8 ± 0.20

49.2 69.4 69.8 72.6

0.75 0.35 0.47 0.50

the DSC scans indicate a large change of viscosity, marking a transformation from amorphous solid phase to super-cooled liquid state. It is evident from Fig. 5 that all the Tc and Tg are shifting towards higher temperature with increasing temperature. The difference, DT between, Tc–Tg indicates the thermal stability of the system [24]. From DSC scans it is clear that thermal stability of ternary alloys is higher after the incorporation of Indium additive in Se98Ag2 system. The increasing sequence is ðDTÞx¼2 < ðDTÞx¼4 < ðDTÞx¼6 respectively (see Table 4). The value of glass forming ability GFA [25] is also given in Table 4 for all glassy alloys. The activation energy of the crystallization process is obtained using Kissinger’s, Augis–Bennett’s and Matusita–Sakka’s equation [26,27,31]. A straight line is obtained by plotting ln (b=T 2c ) vs. 1000/Tc, ln (b/Tc) vs. 1000/Tc and ln(b) vs. 1000/Tc for above discussed glassy system. It is possible to derive the value of the activation energy of crystallization, yielding Se98Ag2 > Se96Ag2In2 > Se94Ag2In4 > Se92Ag2In6 respectively, is listed in Table 2. Pre-exponential factor, lnKo has been determined by Augis-Bennett’s relation [26,31]. The decreasing sequence of pre-exponential factor, lnKo is Se98Ag2 > Se96Ag2In2 > Se96Ag2In4 > Se96Ag2In6 (Table 2). The compensation effect has been observed in present system and the value of pre-exponential factor, lnKo is in good correlation with activation energy of crystallization, Ec. Plotting the graph between Ec vs. lnKo, the value of characteristic pre-exponential crystallization factor, lnKo is found 13.1 min1. In the same way, we have calculated the activation energy of glass transition by Kissinger’s and Moynihan’s method [28,29]. The results are given in Table 3.

4.1. Extent of conversion, a as a function of glass transition, Tag and crystallization temperature, Tac In DSC scan, the crystallization temperature is exhibited as a temperature corresponding to extent of conversion, a due to a sudden change in specific heat. The plots of a, against Tag and a, against Tac at different heating rates for Se98xAg2Inx (x = 0, 2, 4, 6) system are shown in Figs. 6 and 7. The values of Tag and Tac corresponding to a at all heating rates (5, 10, 15, 20 K/min) show a systematic increase in temperature.

Fig. 6. Dependence of extent of conversion, a on glass transition temperatures, Tag for glassy Se98XAg2InX (X = 0, 2, 4, 6) alloys.

C. Dohare, N. Mehta / Journal of Alloys and Compounds 587 (2014) 565–572

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Fig. 7. Dependence of extent of conversion, a on crystallization temperatures, Tac for glassy Se98XAg2InX (X = 0, 2, 4, 6) alloys.

1000/Tai, lnðb=T 1:895 Þ vs 1000/Tai and lnðb=T 1:92 ai ai Þ vs 1000/Tai are shown in Figs. 8 and 9 at extent of conversion, a = 0.5 for both glass transition and crystallization phenomenon, respectively. Above mentioned relations show the straight line of good correlation coefficients for obtaining the activation energy. These plots clearly show that the activation energy of crystallization and glass transition with respect to, a, for glassy Se98xAg2Inx (x = 0, 2, 4, 6) system is not constant, but shows a systematic variation in different stages of transformations. 4.3. Activation energy, Ea as a function of extent of conversion, a and temperature, Ta Fig. 8. Plots of ln ðbi =T 2ai Þ vs. 103/Tag, ln (b) vs 103/Tag, ln (bi =T 1:895 ) vs.103/Tag ln and ai 3 ðbi =T 1:92 ai Þ vs. 10 /Tag for glassy Se92Ag2In6 alloy at a = 0.5.

Iso-conversional methods (described in Section 3) were used for evaluation of activation energies with extent of conversion and temperature. Figs. 10 and 11 show a pronounced variation in the activation energy, Eai as a function of the degree of conversion, a. All the methods show a gradual decrease in Eai as ai increase for both crystallization as well as glass transition in Se98xAg2Inx (x = 0, 2, 4, 6) system. Figs. 12 and 13 show the variation in the activation energy, Eai as a function of crystallization temperature, Ta, at 5 K/min. The reasonable decrement in the activation energy with temperature demonstrates that the rate constant of crystallization is actually determined by the rate of nucleation and growth process. The effective activation energy, DEa of crystallization and glass transition for KAS method is 75.5 ± 3.3 kJ/mol (see Fig. 12) and 222.9 ± 3.6 kJ/mol (see Fig. 13), respectively. Error bar has been taken as standard calculation at 5% for all data points. 4.4. Estimation of local Avrami index (order parameter)

Fig. 9. Plots of ln ðbi =T 2ai Þ vs. 103/Tac, ln (b) vs 103/Tac, ln ðbi =T 1:895 Þ vs.103/Tac ln and ai 3 ðbi =T 1:92 ai Þ vs. 10 /Tac for glassy Se92Ag2In6 alloy at a = 0.5.

4.2. Estimation of activation energy of glass transition, Eag and crystallization, Eag The activation energy of crystallization and glass transition are obtained using KAS, FWO, Tang and Starink methods have been discussed in section 3. The plots of lnðb=T 2ai Þ vs 1000/Tai, ln(b) vs

The extent of conversion ‘a’ at any temperature, T is given as a = AT/A, where A is the total area of exothermic peak or endothermic between the temperature Ti where, the peak begins (i.e., the crystallization or glass transition started) and the temperature T where, the peak ends (i.e., the crystallization or glass transition completed). AT is the partial area of exothermic or endothermic peak between the temperatures Ti and T. For constant temperature, Avrami exponent can be estimated [15,30–32] as:

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Fig. 10. Plots of activation energy Eag vs. extent of conversion, a for glassy Se98XAg2InX (X = 0, 2, 4, 6) alloys.

Fig. 11. Plots of activation energy Eac vs. extent of conversion, a for glassy Se98XAg2InX (X = 0, 2, 4, 6) alloys.

ln ½ lnð1  aÞ ¼ n lnðbÞ  1:052

E þ Const RT

ð11Þ

According to above equation, the value of n can be determined by plotting ln [ln(1a)] vs ln(b) as a slope of straight line at fixed temperatures (Tag and Tac) for Se98xAg2Inx (x = 0, 2, 4, 6) system. The obtained values of Avrami index, n for crystallization are listed in Table 3, and plots are shown in Fig. 14. For determining the value

of m, the slope of the plot of ln[ln(1a)] against 1000/Tai at different heating rates for Se98xAg2Inx glass is shown in Fig. 15 [33]. It is observed that the plots are linear over a wide temperature range. For As-quenched glass, containing no nuclei n = m + 1, however, for a glass containing a sufficiently large number of nuclei n = m. The values of m for increasing Indium concentration (0, 2, 4 and 6) is 1.0, 1.4, 2.5 and 2.5, respectively. Dimensionality, m and growth parameter, n for parent and Indium based compositions

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C. Dohare, N. Mehta / Journal of Alloys and Compounds 587 (2014) 565–572 4

100

5 K/min. 10 K/min. 15 K/min 20 K/min.

2

ln (-ln(1-α))

90

ΔE αc , (kJ/mol)

Se92 Ag2 In6

KAS method FWO method Tang method Straink method

Se92 Ag2 In6

80

70

0

-2

-4

60

-6

50 380

385

395

390

400

2.30

405

2.35

Ταc (K)

2.40

2.45

2.50

2.55

2.60

2.65

2.70

1000/Tc (K -1) Fig. 15. Plots of ln [ln (1a)1] with 1000/Tai for Se92Ag2In6 alloy.

Fig. 12. Plot of Eag vs. Tag at 5 K/min for Se92Ag2In6 alloy.

show the bulk nucleation with varying number of nuclei in two dimensional plates [34–36]. 250

Se92Ag 2In6

240

KAS method FWO method Tang method Straink method

5. Conclusions The crystallization and glass transition kinetics of glassy Se98xAg2Inx system are studied by model fitting and model free assumptions. The major conclusions are listed below:

ΔE αg (kJ/mol)

230 220 210 200 190 180 317

318

319

320

321

322

323

Tαg (K)

(1) Thermal stability and glass forming ability of ternary alloys are found maximum in case of higher concentration of Indium composition (x = 6). (2) The activation energy determined from iso-conversional methods is decreased with extent of conversion, a as well as temperature, Tai. (3) Avrami index n is found to be increased after the incorporation of Indium additive and it decreases with increasing heating rates.

Fig. 13. Plot of Eac vs. Tac at 5 K/min for Se92Ag2In6 alloy.

Acknowledgement NM is thankful to the Department of Science and Technology (DST), Delhi, India for providing financial assistance under Fast Track Young Scientists Scheme [Scheme No. SR/FTP/PS-054/ 2010]. We are also thankful to Hon’ble Professor O. N. Srivastava of our department for providing us SEM, TEM and XRD facilities in his laboratory.

0.5 395.2 K

Se92 Ag2 In6

0.0

399.2 K 401.5 K

ln (-ln(1-α))

-0.5 -1.0

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-1.5

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-2.0 -2.5 -3.0 2.2

2.3

2.4

2.5

2.6

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2.8

2.9

3.0

3.1

ln (β) Fig. 14. Plots of ln [ln (1a)1] with ln b for Se92Ag2In6 alloy at constant temperature in crystallization regime.

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