Determination of activation energy of amorphous to crystalline transformation for Se90Te10 using isoconversional methods

Journal of Non-Crystalline Solids 387 (2014) 79–85

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Determination of activation energy of amorphous to crystalline transformation for Se90Te10 using isoconversional methods N.M. Abdelazim ⁎, A.Y. Abdel-Latief, A.A. Abu-Sehly, M.A. Abdel-Rahim Physics Department, Faculty of Science, Assiut University, Assiut, Egypt

a r t i c l e

i n f o

Article history: Received 31 August 2013 Received in revised form 1 January 2014 Available online xxxx Keyword: DSC; Crystallization kinetics; Chalcogenide glass; Activation energy; Isoconversional methods

a b s t r a c t The activation energies of crystallization of Se90Te10 glass were studied at different heating rates (4–50 K/min) under non-isothermal conditions using a differential scanning calorimetric (DSC) technique. The activation energy was determined by analyzing the data using the Matusita et al. method. A strong heating rate dependence of the activation energy was observed. The variation of the activation energy was analyzed by the application of the three isoconversional methods, of Kissinger–Akahira–Sunose (KAS), Flynn–Wall–Ozawa (FWO), and Vyazovkin. These methods confirm that the activation energy of crystallization is not constant but varies with the degree of crystallization and hence with temperature. This variation indicates that the transformation from amorphous to crystalline phase is a complex process involving different mechanisms of nucleation and growth. On the other hand, the validity of the Johnson–Mehl–Avrami (JMA) model to describe the crystallization process for the studied composition was discussed. Results obtained by directly fitting the experimental DSC to the calculated DSC curve indicate that the crystallization process of the Se90Te10 glass cannot be satisfactorily described by the JMA model. In general, simulation results indicate that the Sestak–Berggren (SB) model is more suitable to describe the crystallization kinetics. © 2014 Elsevier B.V. All rights reserved.

1. Introduction Studies on amorphous chalcogenide glasses are of great interest due to their importance in preparing optical memories [1] and their optical applications are good for IR transmitting materials [2–4]. Moreover, they are interesting as core materials for optical fibers for transmission especially when short length and flexibility are required [5,6]. Many amorphous semiconducting glasses in particular selenium (Se) exhibit a unique property of reversible transformation [7]. The selection of Se is because of its wide commercial applications in xerography photocell switching and memory devices etc. But its pure state has disadvantages because of its short lifetime and low sensitivity. To overcome this difficulty, several workers [8–10] have used certain additives (Ge, Te, Bi, Zn etc.) to make binary alloys with selenium which in turn gives high sensitivity at high crystallization temperature and smaller aging effects. Recently, it has been pointed out that the Se–Te system based on Se has become materials of considerable commercial scientific and technological importance. They are widely used for various applications in many fields as optical recording media because of their excellent laser writer sensitivity xerography and electrographic applications such as photoreceptors in photocopying, laser printing infrared

⁎ Corresponding author. E-mail address: [email protected] (N.M. Abdelazim). 0022-3093/$ – see front matter © 2014 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jnoncrysol.2014.01.012

spectroscopy, and laser fiber techniques [11,12]. Furthermore, amorphous Se–Te alloys have greater hardness, higher crystallization temperature, higher photosensitivity and smaller aging effects than pure Se [11]. Structural studies of chalcogenide glasses are important in determining their transport mechanisms, thermal stability and practical applications. Different techniques have been used to study the structure of chalcogenide glasses, such as scanning electron microscopy (SEM), X-ray diffraction (XRD) and differential scanning calorimetry (DSC) [13–16]. The variation of the activation energy E with the degree of crystallization is an important issue in the kinetics of amorphous to crystalline transformation. It can provide useful information about the different mechanisms involved in the transformation process as indicated by Vyazovkin [17]. Liu et al. [18] have considered a generalization of the Johnson–Mehl–Avrami (JMA) model to account the variation of the activation energy. In contrast to the original formalism of the JMA theory, where only nucleation site saturation or continuous nucleation was assumed, Liu et al. model predicts that the activation energy is not constant throughout the crystallization process when mixed nucleation (a combination of pre-existing nuclei and continuous nucleation modes, with site saturation and continuous nucleation as two extremes) is considered. In order to reveal this variation of the activation energy of crystallization, two approaches are normally used. The first approach is to use the Matusita et al. [19] method to determine the kinetic parameters such as the activation energy E and the Avrami exponent n of the

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crystallization process. The variation of the activation energy can be analyzed using isoconversional methods which were widely used by different authors to investigate different kinetic processes associated with this transformation [20–23]. In the present work, the kinetics of crystallization of amorphous Se90Te10 alloy is studied using the differential scanning calorimetry (DSC) technique at different constant heating rates. The DSC data are analyzed using Matusita as well as the isoconversional methods to investigate the growth processes involved in the transformation. The heating rate dependence of the activation energy of crystallization (E) is discussed. 2. Theoretical background Model-free isoconversion methods are the most reliable methods for the calculation of the activation energy of thermally activated reactions [24–28]. A large number of isoconversion methods have been conducted for polymer materials, but only a few studies on chalcogenide glasses. The assumption that the transformation rate of a solid-state reaction in isothermal conditions is the product of two functions, one dependent on the temperature, T, and the other dependent on the conversion fraction, α, can be generally described by [24–28]: dα ¼ kðT Þ f ðαÞ; dt

ð1Þ

where k(T) is the reaction rate constant, f(α) is the reaction model, and α is the conversion fraction that represents the volume of the crystallized fraction. The rate constant, k(T), usually has an Arrhenian temperature dependence: k ¼ A expð−E=RT Þ;

ð2Þ

where A(s−1) is the pre-exponential (frequency) factor, E(kJ mol−1) is the activation energy, and R is the universal gas constant. Thus, the kinetic equation combined with the Arrhenius approach can be described as: dα ¼ A expð−E=RT Þ f ðαÞ: dt

ð3Þ

There is a wide range of theoretical models and mathematical treatments to estimate the activation energy of a reaction. These models can be categorized into the two most popular (linear) and (non-linear) methods, as described below.

The most popular models used for calculation of activation energy are: 1- The Kissinger–Akahira–Sunose (KAS) method [29–31], which takes the form:

βi T 2αi

! ¼ C K ðαÞ−

Eα RT αi

ð4Þ

2- The Flynn–Wall–Ozawa (FWO) method [32,33], this method is given by:

lnβi ¼ C W ðαÞ−1:0518

Eα : RT αi

A second way of extracting the same information is by using the advanced isoconversional method (non-linear) developed by Vyazovkin [22,26]. This method is given by:

Ω¼

n X n X IðEα ; T αi Þβ j   ; i¼1 j≠i I E α ; T α j βi

ð6Þ

where n is the number of experiments carried out at different heating rates. The activation energy can be determined at any particular value of α by finding the value of Eα which minimizes the objective function Ω. The temperature integral, I, was evaluated using an approximation suggested by Gorbachev [34]: Z

    −E RT 2 −E exp exp dT ¼ : E þ 2RT RT RT 0 T

ð7Þ

3. Experimental technique Bulk material was prepared by the well-established melt-quench technique. The high purity (99.999%) Se and Te in appropriate at.% proportion were weighed in a quartz glass ampoule (12 mm diameter). The contents of the ampoule were sealed under a vacuum of 10−4 Torr and heated at around 950 K for 24 h. The melt was quenched in water at 273 K to obtain the glassy state. The structure of the sample was examined using the Shimadzu XRD-6000 X-ray diffractometer using Cu Kα radiation (λ = 1.5418 Ǻ). The surface microstructure was revealed by SEM (Shimadzu Superscan SSX-550). The content of the alloy was checked by Energy Dispersive X-ray (EDX) using the scanning electron microscope (Shimadzu Superscan SSX-550). The composition of the elements (Se and Te) was determined by EDX at different locations of the sample and average values were used. The differential scanning calorimetry, DSC, was carried out on approximately 5 mg quantities of powder samples using a Shimadzu DSC-60 with sensitivity of ± 10 μW. The heating rates were varied from 4 to 50 K/min under dry nitrogen supplied at the rate 30 ml/min. To minimize the temperature gradient the samples were well granulated to form a uniform fine powder and spread as thinly as possible on the bottom of the sample pan. 4. Results and discussion

2.1. Isoconversion methods

ln

2.2. The Vyazovkin method

ð5Þ

4.1. Structural studies The X-ray diffraction examination indicates the amorphous structure of the as-prepared Se90Te10 bulk as shown in Fig. 1(a). Fig. 1(b) shows the SEM of a fractured as-prepared bulk specimen. Conchoidal contours of the fractured specimen indicate the glass structure. DSC curves of the crystallization process of the Se90Te10 chalcogenide glass obtained at different heating rates are shown in Fig. 2. The DSC thermo-grams are characterized by two temperatures. The glass temperature Tg as defined by the endothermic change in the DSC trace indicates a large change of viscosity, marking a transformation from amorphous solid phase to super cooled liquid state. The exothermic peak temperature Tp is used to identify the crystallization process. It is evident from this figure that both Tp and Tg shift to higher temperatures with increasing heating rate. The shift of Tp arises from the dependence of the induction time, tin associated with nucleation process. Crystallization is controlled by nucleation and there exist an induction time for nucleation. Furthermore, the volume of crystallization fraction, α, was calculated using the partial area method as shown in Fig. 3.

N.M. Abdelazim et al. / Journal of Non-Crystalline Solids 387 (2014) 79–85

(a)

81

1.0

Intinsity (Arb. Unit )

0.8

β

(K/min) 4 5 7 10 15 20 30 40 50

α

0.6 0.4 0.2 0.0 0

20

40

60

360 370 380 390 400 410 420 430 440 450

80

T (K)

2θ (deg.)

Fig. 3. Extent of crystallization, α, as a function of temperature at different heating rates.

(b)

The activation energy for crystallization (E) as well as the Avrami exponent (n) were obtained using a method specifically suggested for non-isothermal conditions by Matusita et al. [19] as: ln ½− ln ð1−αÞ ¼ −n ln β−1:052

Fig. 1. (a) X-ray diffractometer and (b) SEM micrograph of the as-prepared bulk specimen.

4.2. Crystallization kinetics Based on the Johnson–Mehl–Avrami (JMA) equation, the crystallization kinetic parameters namely the crystallization activation energy (E) and the Avrami exponent (n) can be calculated using different approximated methods. Fig. 3 shows the plot of α against T at different heating rates. From this figure we notice a systematic shift in α to higher temperature with an increase in heating rate β. JMA model implies that the Avrami exponent, n, and the activation energy, E, should be constant during the transformation process. Recent investigations indicated that n and E are not necessarily constants, but vary during the transformation [35,36].

mE þ constant; RT

ð8Þ

where m is an integer which depends on the dimensionality of the crystal. When the nuclei formed during the heating at a constant rate dominate, n = m + 1 and when the nuclei formed during any previous heat treatment prior to thermal analysis are dominant, n = m. In this work the values of the indices n and m are considered to be equal because the sample was pre-annealed for a period of time before each experimental run at a temperature below the glass transition temperature, Tg, thus ensuring that the site was saturated. Fig. 3 shows the extent of crystallization (α) as a function of temperature at different heating rates. Using the data of Fig. 3, plots of ln[−ln(1 − α)] against 1/T at different heating rates are shown in Fig. 4. The straight lines in this graph are linear fittings according to Eq. (8). From the slopes of each straight line the mE values was calculated. In addition to evaluate the E values dimensionality of growth m and Avrami exponent n were calculated from the following equation df ln ½− ln ð1−αÞg dð lnβÞ

j

¼ −n:

ð9Þ

T

β (K/min)

0.0

4 5

Heating rates (K/min.)

50

DSC

40 30 20 15 10 7 5 4

Endo

300

350

400

450

500

7

-0.5

ln[-ln(1-α)]

Exo

10 15 20 30 40 50

-1.0

-1.5

-2.0

2.40

2.45

2.50

2.55

2.60

1000/T

2.65

2.70

2.75

2.80

(K-1)

T (K) Fig. 2. DSC curves of the Se90Te10 chalcogenide glass at different heating rates.

Fig. 4. ln[−ln(1 − α)] versus 1/T plots at different heating rates for the Se90Te10 chalcogenide glass.

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N.M. Abdelazim et al. / Journal of Non-Crystalline Solids 387 (2014) 79–85

T= 396 K T= 389 K T= 381 K T= 374 K

15

200

E (kJ/mole)

ln[-ln(1-α])

10

250

5 0

100 50

-5

0

-10 1.0

150

1.5

2.0

2.5

3.0

3.5

4.0

0

ln (β)

10

20

30

40

50

Heating Rate (K/min.)

Fig. 5. ln[−ln(1 − α)] versus ln(β) plots at different temperatures for the Se90Te10 chalcogenide glass.

The value of n can be obtained by plotting ln[−ln(1 − α)] versus lnβ at different temperatures. Fig. 5 shows these plots for the studied composition. It is clear from this figure that n is temperature dependent as shown in Fig. 6. The average value of n is 2.74 ± 0.03. The calculated n value was not integers. This means that the crystallization occurs by more than one mechanism [37]. The value of n may be accounted for the possibility of a combination of two and three dimensional crystal growth with heterogeneous nucleation [38]. From the average n value and mE the effective activation energies E for the composition Se90Te10 were calculated. Fig. 7 shows the variation of the activation energy for crystallization with the heating rate. The result shows a dramatic decrease in E as the heating rate increases. A similar behavior was observed by other workers [35,36]. The observed dependence of the effective activation energy on the heating rate can be attributed to the possible variation of E with temperature. In order to investigate the variation of the activation energy with the extent of conversion and hence with temperature, KAS, FWO, and Vyazovkin isoconversional methods were used. Using the experimental data shown in Fig. 3, the three isoconversional methods are used to evaluate the activation energies at different values of α. According to the KAS and FWO methods, the effective activation energy of crystallization can be obtained by plotting ln(β/T2) versus 1000/T and ln(β) versus 1000/T respectively for all heating rates used, the results are shown in Figs. 8 and 9. On the other hand, according to the Vyazovkin method,

Fig. 7. Effective activation energy (E) as a function of heating rate for the Se90Te10 chalcogenide glass.

Fig. 10 shows the minimization factor, Ω, versus the effective activation energy of crystallization, Eα, at different crystallization fraction α. Fig. 11 shows the variation of the effective activation energy using the three isoconversional methods. It can be seen that the three methods yield a decrease of the activation energy with increasing α. The KAS and Vyazovkin methods give similar values of Eα. The FWO method gives values of Eα of only 2% higher than the values obtained by the other two methods. The temperature dependence of Eα can be obtained [39] by replacing α with a corresponding average temperature calculated from Fig. 3. This temperature dependence is shown in Fig. 12. It is evident from the observed temperature dependence of the activation energy in the present system that the amorphous to crystalline transformation cannot be described by a single-step mechanism. The transformation demonstrates complex multi-step reactions involving several processes of growth with different activation energies and mechanisms. The observed decrease of the activation energy with temperature demonstrates that the rate constant of crystallization is in fact determined by the rates of two processes, nucleation and diffusion. Because these two mechanisms are likely to have different activation energies, the effective activation energy of the transformation will vary with temperature. This interpretation is based on the nucleation theory proposed by Turnbull and Fisher [40]. According to this

-8.0 4

ln (β/T2)

-8.5 3

n

-9.0 α

-9.5

2

0.05 0.25 0.5 0.75 0.95

-10.0 1 -10.5 0 370

2.3 375

380

385

390

395

400

2.4

2.5

2.6

2.7

1000/T (K-1)

T (k) Fig. 6. Variation of the exponent n with temperature.

Fig. 8. A plot of ln(β/T2) versus 1000/T (for α = 0.05, 0.25, 0.50, 0.75 and 0.95). The straight lines are fit to the Kissinger–Akahira–Sunose (KAS) equation.

N.M. Abdelazim et al. / Journal of Non-Crystalline Solids 387 (2014) 79–85

83

120

4.0

FWO method KAS method Vyazovkin method

3.5

E (kJ/mole)

ln (β)

100 3.0 α

2.5

0.05 0.25 0.5 0.75 0.95

2.0 1.5 2.3

80

60

2.4

2.5

2.6

1000/T

40

2.7

0.0

0.2

0.4

(K-1)

Fig. 9. A plot of ln(β) versus 1000/T (for α = 0.05, 0.25, 0.50, 0.75 and 0.95). The straight lines are fit to the Flynn–Wall–Ozawa (FWO) equation.

α

0.6

0.8

1.0

Fig. 11. The effective activation energy as a function of α as determined using different isoconversional methods.

theory, the temperature dependence of the crystallization rate r is given by:

where Φ is the heat flow evaluated during the crystal growth and can be expressed by the following kinetic equation [42]

    −ED −Δ F exp r ¼ r ∘ exp kB T kB T

Φ ¼ ΔHA expð−E=RTÞ f ðaÞ:

ð10Þ

where ro is the pre-exponential factor, kB is the Boltzmann constant, ED is the activation energy for diffusion and ΔF is the maximum free energy necessary for nucleus formation. According to Malek proposal [41], the validity of the JMA model to describe the crystallization process can be tested by checking the maximum of the z(α) function at α ∞p, if the maximum of z(α) function falls in to the range (0.61–0.65) then the experimental data could be presented by using the JMA model, and if α ∞p shifted to a lower value, then the condition of the validity is not fulfilled. Both y(α) and z(α) function are calculated according to the following equation [42] yðaÞ ¼ Φ expðE=RT Þ zðaÞ ¼ Φ T

ð11Þ

2

ð12Þ

ð13Þ

The average value of E(α) determined by the isoconversion method of Kissinger–Akahira–Sunose (KAS) was used to calculate the y(α) function for the studied composition. The variation of y(α) and z(α) functions with the fractional conversions (α) is shown in Fig. 13. From the plot of y(α) and z(α) versus α the value of α ∞p and αM at which z(α) and y(α) reaching its maximum exhibits strong heating rate dependence. When the heating rate is increased from 4 to 50 K/min α ∞p decreases from 0.565 to 0.505 and αM from 0.414 to 0.252 for the crystallization process. On the other hand, the value of α ∞p is significantly smaller than the fingerprint of JMA model. Thus we conclude that the JMA model is not suitable for studying the isochronal crystallization kinetics of Se90Te10 glass. If the JMA model is used in these cases inappropriate results will be obtained. In general, the more generalized SB (M, N) model should be used to analyze the isochronal crystallization kinetics of this amorphous alloy. The kinetics exponents M and N are parameters that define relative contribution of acceleratory and deceleratory part of the crystallization process. The parameters of this model can be determined in a simply way.

α FWO method KAS method Vyazovkin method

120

E (kJ/mole)

Minimization Factor Ω

0.05 0.15 0.35 0.55 0.75 0.95

100

80

60

65

70

75

80

85

90

95

100

Eα(kJ/mol) Fig. 10. The minimization factor, Ω, against the activation energy for crystallization, Eα (for α = 0.05, 0.15, 0.35, 0.55, 0.75 and 0.95) for glassy Se90Te10.

40

380

385

390

395

400

T (K) Fig. 12. The temperature dependence of the effective activation energy.

405

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N.M. Abdelazim et al. / Journal of Non-Crystalline Solids 387 (2014) 79–85

5 7

0.4

0.4

10 15 20 30 40 50

0.2 0.0 0.0

0.2

0.4

0.6

α

0.8

0.0

26.00

1.0

-0.65-0.60-0.55-0.50-0.45-0.40-0.35-0.30-0.25-0.20-0.15-0.10 ln{[n(1-α)[-ln(1-α)]1-1/n}

M aM ¼ N ð1−aM Þ

ð14Þ

Using the average values of E calculated by the KAS method and M/N calculated according the previous equation, the N values can be determined from the dependence [43] M=N

ln ½ϕ expðE=RT Þ ¼ ln ½ΔHA þ N ln α

i ð1−αÞ

n o 1−1=n : ln ½φ expðE=RT Þ ¼ ln ½ΔHA þ ln nð1−αÞ½− ln ð1−αÞ

ln[ϕ exp(E/RT)]

Fig. 15 shows the plots of ln[Φexp(E/RT)] versus ln{n(1 − α) [− ln(1 − α)] 1 − 1/n } for the Se90Te10 glass. The calculated values of parameters M and N, the pre- exponential factor A, the enthalpy (ΔH), n and ln A corresponding to the appropriate activation energy are listed in Table (1). Furthermore, we calculated theoretical DSC based on the JMA and SB models using the following equations respectively [43–46]

1−1=n

ð17Þ

ð15Þ

ð16Þ

β (K/min ) 4

5 7

27.00

Fig. 15. The plots of ln[Φexp(E/RT)] versus ln{n(1 − α)[−ln(1 − α)]1–1/n} at different heating rates for Se90Te10.

f ðaÞ ¼ nð1−αÞ½− ln ð1−αÞ

where ΔH is the heat of crystallization and A is the exponential frequency factor. This equation is valid in the interval of 0.2 ≤ α ≤ 0.8. The parameter N is determined directly from the slope of this dependence as shown in Fig. 14 and then the parameter M can be deduced using Eq. (14). Also the pre-exponential factor A can be calculated from the section of the dependence [44]. On the other hand, the Avrami exponent (n) and the pre- exponential factor A can be calculated according to the JMA model from the dependence [43]

27.25

7 10 15 20 30 40 50

26.50 26.25

The conversion corresponding to the maximum of y(α) function can be used to calculate the quotient of parameters M and N [43].

27.50

26.75

0.2

Fig. 13. Normalized y(α) and z(α) functions obtained by the transformation of non-isothermal data for the crystallization of the studied composition at different heating rates.

h

ln[ϕ exp(E/RT)]

0.6

z (α)

β (K/min) 4

0.6

β (K/min ) 4

5

27.00

0.8

0.8

y (α)

27.25

1.0

1.0

10 15 20 30 40 50

26.75 26.50 26.25 26.00 -1.30 -1.25 -1.20 -1.15 -1.10 -1.05 -1.00 -0.95 -0.90 -0.85 -0.80

ln[αM/N(1-α)] Fig. 14. The plots of ln[Φexp(E/RT)] versus ln[αM/N(1 − α)] at different heating rates for Se90Te10.

M

N

f ðaÞ ¼ α ð1−αÞ :

ð18Þ

The deduced theoretical and experimental DSC curves are shown in Fig. 16 (a, b). It is obvious that the DSC curves calculated using the JMA model is nearly in agreement with the measured data only when the heating rate is low. At high heating rates, the discrepancies become large. On the other hand, the DSC curves calculated using the SB model fit quite well with the experimental data at all heating rates. The reason that DSC curves calculated from JMA model show large deviations from experiments at high heating rates may be due to the fact that some approximations used for deriving Eq. (17) are not held for the crystallization of Se90Te10 glass. To extend the validity of Eq. (18) to non-isothermal condition the entire nucleation process must take place during the early stages of the transformation and become negligible afterwards [47]. This site saturation assumption is important for the process where the crystallization rate is only defined by the temperature and shows little dependence on the thermal history [48]. At low heating rates, the nuclei have more time to form before their growth process starts making the entire nucleation occur basically in early stages of the transformation. Therefore, only at low heating rates can the situation under that the JMA model is valid in non-isothermal conditions be reasonably satisfied. On the other hand, after the nucleation process, the nuclei grow very slowly. At high heating rates, the temperature increases so fast that the growth process may not obey the linear or parabolic growth rule as assumed in the JMA analysis. In general, the JMA model is a specific case of the two parameters (M, N) SB kinetic model. It can be shown [42] that there is a combination of parameters M and N corresponding to a given value of kinetic exponent for the JMA model (when n ≥ 1). Therefore, the SB kinetic model can be used for a quantitative description of more complicated phase transformation involving both nucleation and growth.

N.M. Abdelazim et al. / Journal of Non-Crystalline Solids 387 (2014) 79–85

85

Table 1 The crystallization enthalpy (ΔH), the parameters of the SB (M, Nnn model and JMA model) for the composition Se90Te10 at different heating rates. SB Heating rate (K/min)

ΔH

N

4 5 7 10 15 20 30 40 50

14.75 19.65 33.82 41.05 65.80 85.03 117.53 132.88 180.92

1.15 0.67 0.77 0.86 0.88 0.91 0.93 0.98 1.10

a

Heat Flow

9

JMA M ± ± ± ± ± ± ± ± ±

0.04 0.02 0.03 0.02 0.02 0.04 0.03 0.03 0.01

0.81 0.38 0.42 0.45 0.46 0.45 0.40 0.47 0.37

± ± ± ± ± ± ± ± ±

0.45 0.35 0.25 0.36 0.30 0.42 0.33 0.25 0.27

8

4 K/min

4 K/min

5 K/min

5 K/min

7

7 K/min

7 K/min

10 K/min

10 K/min

6

15 K/min

15 K/min

20 K/min

20 K/min

5

30 K/min

30 K/min

40 K/min

40 K/min

4

50 K/min

50 K/min

n

27.92 27.60 27.64 27.51 27.11 27.63 27.32 27.25 27.04

2.69 2.97 3.52 3.71 4.18 4.44 4.76 4.88 5.19

25.22 24.62 24.12 23.80 22.93 23.19 22.55 22.36 21.85

2.14 1.82 1.77 1.72 1.72 1.68 1.56 1.64 1.41

[1] [2] [3] [4] [5] [6] [7] [8]

2 1 0 -1 350 360 370 380 390 400 410 420 430 440 450 Temp (K)

[9] [10] [11]

10 Exp JMA 4 K/min 4 K/min 9 8 7

Heat Flow

ln A

6 5

5 K/min

5 K/min

7 K/min

7 K/min

10 K/min

10 K/min

15 K/min

15 K/min

20 K/min

20 K/min

30 K/min

30 K/min

40 K/min

40 K/min

50 K/min

50 K/min

± ± ± ± ± ± ± ± ±

0.89 0.84 0.65 0.62 0.62 0.52 0.58 0.46 0.43

ln (dHA)

ln A

26.74 27.08 27.07 26.91 26.50 27.05 26.81 26.64 26.59

24.05 24.10 23.55 23.20 22.32 22.60 22.04 21.75 21.401

References

3

b

ln ΔH

involving different mechanisms of nucleation and growth. On the other hand, the experimental DSC is in agreement with the JMA model only at low heating rates, while the Sestak–Berggren (SB) model provides a better fitting to the measured DSC curves at all heating rates.

S.B

Exp

ln (ΔHA)

[12] [13]

4 3 2 1 0 -1 350 360 370 380 390 400 410 420 430 440 450

Temp (K) Fig. 16. (a, b) Experimental non-isothermal crystallization at different heating rates compared with the calculated data using SB model and JMA using the appropriate activation energy.

[14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37]

5. Conclusions The crystallization kinetics for Se90Te10 glass was analyzed by the isoconversion models under non-isothermal condition. The effective activation energy E of crystallization was determined by using the Matusita et al. Furthermore, the effective activation energy E(α) is deduced by the isoconversional methods various slightly with transformed fraction. The present work shows that the transformation from amorphous to crystalline phase in Se90Te10 is a complex process

[38] [39] [40] [41] [42] [43] [44] [45] [46] [47] [48]

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