A thermal analysis study of melt-quenched Zn5Se95 chalcogenide glass

Journal Pre-proof A thermal analysis study of melt-quenched Zn5Se95 chalcogenide glass Alaa M. Abd-Elnaiem, Gh Abbady PII:

S0925-8388(19)34126-X

DOI:

https://doi.org/10.1016/j.jallcom.2019.152880

Reference:

JALCOM 152880

To appear in:

Journal of Alloys and Compounds

Received Date: 31 July 2019 Revised Date:

13 October 2019

Accepted Date: 30 October 2019

Please cite this article as: A.M. Abd-Elnaiem, G. Abbady, A thermal analysis study of melt-quenched Zn5Se95 chalcogenide glass, Journal of Alloys and Compounds (2019), doi: https://doi.org/10.1016/ j.jallcom.2019.152880. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier B.V.

A thermal analysis study of melt-quenched Zn5Se95 chalcogenide glass Alaa M. Abd-Elnaiem*, Gh. Abbady Physics Department, Faculty of Science, Assiut University, Assiut 71516, Egypt.

Abstract Thermal analysis of chalcogenide glass similar to other materials is of great importance in order to increase the knowledge about its phase transitions, thermal stability, etc. The current study reports on the thermal kinetics of melt-quenched Zn5Se95 chalcogenide glass using differential thermal analysis (DTA) techniques under non-isothermal conditions. The glass-forming ability (GFA) and the relation between the glass transition and onset crystallization temperatures are found to show a linear behavior. In addition, Moynihan et al., Kissinger's, and other approaches of Johnson-Mehl-Avrami utilized to determine the activation energy of the amorphous-crystalline and glass transition. It is found that the glass transition process cannot be concluded in terms of single activation energy, and that variation with the extent of conversion was analyzed using various iso-conventional methods. Therefore, the observed change of the activation energy throughout the glass transition reveals that the transition from amorphous to the supercooled liquid phase of Zn5Se95 glass is a complex process. The crystallization process at different heating rates is simulated using the Málek method, and Šesták–Berggren SB(M,N) model, in which the SB model show fairly good matching with the experimental DTA data. Moreover; the fragility index is a measure of the GFA of Zn5Se95 chalcogenide glass, which has been estimated using the glass transitions and activation energy values. We have found that the fragility index of Zn5Se95 glass values in between ~13 and 30, depending on the heating rate, revealing that the synthesized glass is a strong liquid with excellent GFA.

Keywords: Zn-Se, chalcogenide glass, DTA, glass transition, thermal analysis, fragility index.

*Corresponding author: E-mail: [email protected]

1

1. Introduction Glassy chalcogenides can be characterized by the crystal structure as well as the energy gap. In general, insulators are transparent and having energy gaps of 5-10 eV, while the amorphous chalcogenide semiconductors are having energy gaps of 1-3 eV. On structurally view and compared to other materials, polymers such as polyethylene (–CH2–) are characterized by one dimension (1D) chains, i.e., the network dimension is one [1]. However, chalcogenide glasses such as As2S(Se)3 and GeS(Se)2 are proposed to have 2D (distorted layers as crumpled paper) structures, though there may be some controversy. In addition, oxide glasses and tetrahedral materials have 3D network structures. The structure of glasses can be considered more rigid compared to polymers, chalcogenides, and oxides. Furthermore, semiconductor properties, such as carrier mobility, and material price per unit area become better and higher compared to organic, chalcogenide, tetrahedral, and crystalline materials. Cooling glass materials from an equilibrium liquid state leads to a decrease in the molecular mobility, and the time scale for conformational changes becomes comparable to the time scale of cooling and the material deviates from the liquid line and begins to form a glass. The glass transition can be considered a kinetic rather than a thermodynamic transition and depends on the heating and/or cooling rate [2-6]. It is well-known, the glass transition temperature (Tg) for amorphous materials is a temperature at which the extrapolated glass and liquid equilibrium lines cross. Structural relaxation is a general phenomenon taking place when a glass is maintained at a temperature below Tg. Therefore, a glassy material has at least two important characteristics: its glass-transition temperature and its sub-Tg relaxation kinetics. The glass-forming liquids can be divided, according to the temperature dependence of their viscosity, into two parts: strong and fragile glass-forming liquids. The strong glassforming liquids show an Arrhenius temperature dependence of the viscosity, while fragile glass-forming liquids exhibit a non-Arrhenius behavior. The dynamic of the structural relaxation above Tg can be characterized by the strong fragile classification scheme for glassforming liquids, originally introduced by Angle [7], and extensively used to describe the relaxation process in supercooled liquids. The differential scanning calorimetric (DSC) and differential thermal analysis (DTA) techniques are commonly used, among other thermal analysis techniques, to determine the glass transition in glasses with high accuracy [2-4,8,9]. Moreover, the kinetic aspect of the glass transition is evident from the strong dependence of the glass transition on the heating rate. One of the key kinetic parameters which can also be determined by DTA is the 2

activation energy of the glass transition. Understanding the glass transition kinetics in chalcogenide systems is of great importance to get information about their thermal stability and to determine the useful range of operating temperatures for specific technological applications. The glass transition of glass is taking place before the crystallization process upon the heating. Moynihan et al. [10] demonstrated that the apparent activation energy doesn’t vary through the glass transition for several glasses. Therefore they proposed a single value of the activation energy for the entire transition process. However, by employing a similar analysis of DSC heating traces, other researchers [11-14] have reported a decrease in activation energy through the heating over the glass transition region. In addition, Hancock et al. [11] determined the apparent activation energies using the onset (Tg(on)), midpoint or peak (Tgp), and offset (Tg(off)) temperatures in DSC cooling curves and found the values to generally increase from the liquid state to the glass state and small molecule glass formed. They show that (Tg(on)) and (Tg(off)) may vary significantly depending on the temperature range of the tangents drawn to determine them. The free volume model since proposed by Cohen et al. [15] has been widely employed to elucidate various properties of glasses. The free volume theory assumes that a supercooled liquid can be divided into liquid-like and solid-like parts and a molecule can move by diffusion if it has a certain free volume in its surroundings. Therefore, it is assumed that the free volume can propagate freely through the liquid, hence no activation energy is required for free volume redistribution [15,16]. Recently, we have reported on the non-isothermal crystallization kinetics of Zn10Se90 glass using the DTA technique [9]. On the other side, some studies on the crystallization kinetics of the Se-Zn system over a wide composition using the DSC technique have been reported [17,18]. In addition, the vibrational and thermal properties of binary Zn-Se have been investigated [19]. For instant, the heat capacities of Zn-Se comprehensively estimated over the temperature range 2-150 K is maintaining and the obtained data have compared to the calculated. Other studies on the physical properties of binary Zn-Se which prepared by different techniques such as ball milling, melt quenching, chemical bath method, etc. are available elsewhere [9,17,21-23]. The main objective of the present work is to investigate the thermal kinetics, thermal stability, and the variation of the activation energy throughout the glass transition region and during the amorphous-crystallization transformation for Zn5Se95 chalcogenide glass. The activation energy of the mentioned transition is extracted from DTA measurements and the experimental data are used to test a number of theoretical models proposed to describe the 3

thermal kinetics. In particular, different iso-conversional methods are used to evaluate the values of activation energies at different stages of the transformation.

2. Experimental details Bulk Zn5Se95 chalcogenide glass is fabricated by the melt quenching technique. Commercial Zn and Se of ~99.999% purity are weighted according to their atomic percentage (at.%) and sealed in a quartz glass ampoule (1.2 cm in diameter) under a vacuum of 10-4 Torr. Then, the contents are heated with a slow rate from room temperature (RT) and kept at 823 K for 50 h. During the melting process, the tube is frequently shaken to ensure the homogeneity of the resulting alloy. Thereafter, the melt is quenched in ice-cold water to obtain the glassy state of Zn5Se95. The thermal characterization of the prepared sample is done under non-isothermal conditions (5, 10, 15, 20 and 30 K/min) using a Shimadzu DTG-60H Differential Thermal Analyzer. The DTA and thermal gravimetric analysis (TGA) measurements are performed under dry N2 atmosphere supplied at a rate of 30 ml/min. For this purpose, the bulk samples were ground to form Zn5Se95 powder and ~25 mg of powder is sealed in the standard aluminum crucible in a dry nitrogen atmosphere. Non-isothermal DTA curves are recorded with mentioned heating rates ranging from RT up to 625 K. The accuracy of the heat flow is ±0.01 mW/cm while the temperature precision is ±0.1 K as determined by the microprocessor of the thermal analyzer. The values of characteristic temperatures such as Tg, the onset temperature of crystallization (Tc), and the peak temperature of crystallization (TP) are determined from the DTA curves at different heating rates. In addition, the glassy nature of the melt-quenched Zn5Se95 samples is confirmed using a Philips X-ray diffractometer of 1710-type with CuKα radiation of the wavelength of 1.5418 Å. The scanning angle range 4º-90º at a scanning step 0.02º and speed of 0.06º/s.

3. Results and discussion 3.1. Structural analysis Fig. 1 shows the X-ray diffraction (XRD) pattern for the as-prepared Zn5Se95 chalcogenide system. It is noticed that only a broad diffraction peak can be observed and no appreciable diffraction peaks corresponding to any crystalline phase are detected, indicating a fully amorphous nature of the prepared composition. The DTA traces of Zn5Se95 glass at various heating rates (5≤β≤30 K/min) are presented in Fig. 2 and show the evolution of the thermal properties of glass. It is clear from 4

the DTA curve that a single glass transition (~318.2K), single crystallization peak (~353.3K) and melting point (~494.5K) can be observed at heating rate 5 K/min in the temperature range of 300-650 K and their values shift toward higher temperatures with increasing the heating rate as seen in Table 1. For a small concentration of Zn (~2at.%) in Zn-Se glass, two glass transition peaks through the DSC curves are observed [17,24]. Such glasses have single endothermic and exothermic peaks, are more stable than those that have two or more multi endothermic and exothermic peaks. The observed peaks in the DTA curve at each heating rate can be attributed to three processes. The first one corresponds to the glass transition region which appears as an endothermic reaction, the second part is related to the crystallization process of the considered glass indicated by one exothermic reaction, and the third peaks correspond to an endothermic peak resulted of Se phase melting. The appearance of the glass transition in the DTA curve confirms the production of an amorphous Zn5Se95 powder by melt quenching technique. This observation is in good agreement with our previous

published work [9]. The characteristic temperatures Tg, Tc, and Tp increase with increasing heating rate (β), while the melting point of Se (Tm) slightly increases with increasing the heating rate. Other important thermal parameters such as (Tc-Tg), and (

=

) are

determined to check the glass thermal stability and the ability to form glass, respectively. The calculated values of these parameters at different heating rates are summarized in Table 1. It can be seen that the thermal stability as well as the glass-forming ability (GFA) are enhanced by the addition of a small amount of Zn compared to unary Se [25]. Based on Hr values (>0.1), it refers to the possibility of the GFA of this composition. The estimated data is slightly changed comparing to our previous study on Zn10Se90 glass, due to the change of alloying elements compositions [9]. For example, as the Zn increases from 5 to 10 at.% in the Zn-Se system, the thermal stability and the GFA are enhanced, while the values of Tc at different β decreased. In addition and although that changes in elemental composition in the Zn-Se glass, the average value of Tm is maintaining constant around 498 K, which good agreement with the calculated equilibrium phase diagram of the Zn-Se system [26]. The value of thermal stability is too closed to that observed for Zn2Se98 glass at a heating rate of 20 K/min [17]. However, further increasing of Zn up to 20 at.% in the mixture reduces the thermal stability [18].

3.2. Glass transition and the Kauzmann temperature

5

Determination of the glass transition is important for understanding the mechanism of glass transformation and it is essential for investigating the structural rigidity of the glasses. It's well-known, at the glass transition, a significant increase in the specific heat of glasses taking place due to an increased relaxation upon reaching the supercooled liquid state. It is evident from Fig. 3 and Table 1 that, Tg increases with β due to an increase in structural relaxations and decreases in relaxation time with increasing β [10]. The data have been plotted and fitted to a linear relation according to Lasocka formula [27]: Tg=Bg ln(β) + Ag

(1)

Here Ag and Bg are empirical constants with values of 309.2 K and 5.38, respectively, for Zn5Se95 glass. Furthermore, Lasock's relation for the glass transition has also been found to be valid for the heating rate dependence of the onset as well as the crystallization temperatures: Tc=Bc ln(β) + Ac ; and Tp=Bp ln(β) + Ap

(2)

It is noticed from Fig. 4 that, the variation of Tc and Tp with ln(β) is steeper than that of Tg. Since crystallization, being a kinetic process is controlled by atomic diffusion, however, glass transition encounters configurationally changes due to the structural relaxation. The values of Ac, Ap, and Bc, Bp for the Zn5Se95 glass are 335.2, 341.5 K and 12, 15.75, respectively. To correlate the glass transition and the onset crystallization temperatures of the present glasses, one could derive a linear correlation between Tg and Tc or Tp using Eqs. 1 & 2: =

+

(3)

For the studied glass Tg= 0.42Tc+167.1, while Tg=0.34Tp+192.3. It can be seen that the glass transition and onset and/or crystallization temperatures are dependent on each other and Tg increases linearly with both Tc and Tp. Indeed a similar correlation was deduced for amorphous alloys by Yao et al. [28]. The Lasocka equations for Tg and Tc can be used to estimate Kauzmann temperature (Tk). The Kauzmann temperature can be defined as the lowest theoretical boundary for the glass transition. Determination of Tk is quite important to characterize glassy materials from a thermodynamic viewpoint. At temperature equal to Tk the entropy of supercooled liquid becomes equal to that of the crystal [29]. Moreover, at a temperature below Tk, a liquid cannot be supercooled even at the slowest cooling rate. One can assume that Tg=Tc=Tk [30] at a heating rate βk. After replacing Tg and Tc by Tk in Eq. (1) and Eq. (3), one would deduce: = 10

(4) 6

And: =

(5)

Based on Eqs. 4 and 5, we obtain βk= 1.18×10-4 K/min and Tk=288.07 K for the studied glass. These values show that Zn5Se95 supercooled liquid has high thermal stability as well as good GFA. This observation can be confirmed from the TGA analysis, see supplementary file Fig. S1.

3.3. Evaluate activation energy for the glass transition Kinetics of the glass transition is considered as one of the most desirable problems in the glasses science and technologies, which can be accomplished through the determination of Tg and activation energy of thermal relaxation. The transformation to a glass state does not occur at one, strictly defined temperature, but over a temperature range which is represented as the transformation region as shown in Fig. 3. The activation energy of the glass transition was determined using different kinetic models as well as iso-conversional methods. The most frequently used approach for the kinetics of the glass transition is based on the Moynihan method [10]. The relation between Tg and β is given by: ( ) (

)

= − "!

(6)

Here Et is the activation energy for the structural relaxation associated with the glass transition and R is the universal gas constant (8.314 J mol-1 K-1). Based on the free volume model of the glass transition, Ruitenberg [31] showed that the Kissinger approach [32] can be used to determine the glass transition activation energy by the following equation: #

( $ ) (

)

= − "!

(7)

The free volume model for Kissinger's equation utilized to determine the glass transition using three different definitions [8,33]. Fig. 5 shows these definitions of the glass transition through the DTA curve of the Zn5Se95 glass a heating rate of 10 K/min: on-set glass transition (Tg(on)), peak glass transition (Tg(peak)), and off-set glass transition (Tg(off)) temperatures. The different definitions of the glass transition considered in this work correspond to a different degree of conversion. By applying Eqs. (6) and (7), the activation energy for different the glass transition assignments can be determined by plotting ln(β) and ln(β/Tg2) versus 1/Tg, respectively, as 7

presented in Figs 6 and 7. The slopes of these plots are used to calculate the activation energy required to the glass transition process and their numerical values are given in Table 2. It is useful to compare the values of the activation energy as determined using the various stages of the glass transition. This will demonstrate if Et varies with the extent of conversion or simply conversion (α) or remains constant throughout the transition. It is clear that Et values obtained from Moynihan and Kissinger equations are dissimilar in the Zn5Se95 glass. Our results indicate that the value of Et is not constant over the whole glass transition range. This agreement with the results obtained by Hancock et al. [11]. But not agree well with Moynihan et al. [10], as they observed good agreement between the values of activation energies obtained from heating rate dependence of the onset temperature, inflection temperature, and the maximum in the peak temperature from the DTA curve. Similar investigations for the Zn-Se glass over a wide range of composition (020at.%Zn) were carried out by Nasir et al. [18]. In their study, the value of Tg was increased as the concentration of Zn increased up to 10 at.%, and then decreased for further increase in the concentration. In this study, the activation energies for the structural relation are determined and found to be significant influence by the elemental composition of the glass alloy, however, there is not a clear trend that can be deduced to control the change. Moreover, there are obvious discrepancies in these values obtained by numerous methods and relations. The obtained results can be understood on the basis of the free volume theory. The glass transition phenomenon can be treated as glass to amorphous phase transformation. It is reasonable to divide the glass transition region into following three regimes and associate the glass transition stage with the structural rearrangements: i. The glassy behavior is observed below Tg since the free volume has a constant value that is too small to allow the conformational arrangements associated with amorphous behavior. ii. Above Tg, the free volume increases with increasing temperature and facilitates the large–scale conformational rearrangements that define the amorphous phase. iii. The attainment of a critical free volume is the definition of the glass transition temperature. From the above discussion, one can see that the glass transition phenomena can be concluded as a glass-amorphous phase transition. Thus we cannot generalize the constancy of the glass transition activation energy, through the glass transition range as observed for Zn5Se95 glass.

8

3.4. Activation energy as a function of α and Tg To investigate the variation of the activation energy of the glass transition, throughout the glass transition region, the iso-conversional methods are used. Iso-conversional methods are used for evaluating activation energies with α and temperature (T). The values of α used in the iso-conversional analysis is determined using the partial area method. In this method, the value of α at any value of T in the glass transition region is defined as α=AT/A, where A is the area under the curve of the endothermic between temperature Tg(on) and Tg(off) and AT is the area between Tg(on) and T. We supposed the conversion to be 1 in the liquid state and 0 in the glass state. The respective values of temperature Tgα in the glass transition region are calculated at different values of α at different heating rates as shown in Fig. 8. Based on the experimental data shown in Fig. 8, four iso-conversional methods are used to evaluate the activation energy of the glass transition throughout the glass transition region. These methods are Kissinger-Akahira-Sunose (KAS) [34], Flynn-Wall-Ozawa (FWO) [35,36], Straink [37] and Tang method [38]. All of the iso-conversional methods require the determination of the temperature Tαi at which a fixed fraction α of the total transformed amount. To address this concern, in the KAS [34] method, the relation between Tαi and βi is given by: (

ln ' $) + = − " *)

*

*)

+ ,-./0.

(8)

The subscript i denotes different heating rates. For each value of α, a corresponding Tαi and βi are used. In the FWO method the relation between Tαi and βi is given by [35]: ln( 2 ) = ,-./0. −1.0518 " *)

*)

(9)

In Straink method [37], the relation between Tαi and βi is given by: ln '

()

.5$ *)

+ = −1.0008 "

*

*)

+ ,-./0.

(10)

A more precise formula for the temperature integral has been suggested by Tang et al. [38] which is as follows: ln '

() .65788 *)

+ = ,-./0. −1.00145033 "

The Plots of ln ' ln '

() .65788 *)

()

$ *)

*

(11)

*)

+ against 1000/Tαi, ln(βi) versus 1000/Tαi, ln '

()

.5$ *)

+ against 1000/Tαi and

+ versus 1000/Tαi across different heating rates are shown in Fig. 9. From these

plots, one can see the straight line. This confirms the validity of Eqs. 8-11 in the studied glass. 9

From the slopes of these straight lines, it is possible to deduce the value of the activation energy of the glass transition, Eα. The values of activation energy calculated from the iso-conversional methods are given in Table 3. Also, the variation of the glass activation energy, Eαg, as a function of α is shown in Fig. 10a, while the temperature dependence of Eαg is shown in Fig. 10b. It can be seen that all methods reveal a decrease of the activation energy with increasing α and T. The value of activation energy Eαg is found to decrease by more than 50 % from the glassy state to the equilibrium liquid state. The observed decrease of the activation energy with increasing temperature is consistent with the prediction of the free volume model of the glass transition. According to this model, the activation energy of the process depends on the amount of free volume in the sample. For example, more free volume is related to the lower activation energy. The remarkable feature of the Eα(T) dependence for the transition in the Zn5Se95 sample indicates that the glass transition temperature cannot be described by a single-step mechanism. Indeed, the glass transition demonstrates a complex multi-step reaction involving relaxation processes with different activation energies and mechanisms [39]. Based on the free volume model, it can be shown that the temperature dependence of the activation energy of the glass transformation is given by the Williams-Landel-Ferry (WLF) equation [40]: ; = 2.303= (

$>

$

$

)$

(12)

where c1 and c2 are constants. Using T0=320K as a reference temperature, the universal values (c1=17.44 and c2=51.6) are normally assigned to these constants. Sopade et al. [41] reported different values of c1 and c2 in their investigation for the applicability of the WLF model. It is evident from Fig. 10b that the WLF model can account for the variation of the activation energy with temperature as obtained using the KAS method. In this work, a significant variation of Eαg is observed as a function of α, this attributed to the glassy structure continues to evolve towards equilibrium as a result of the kinetic nature of the glass transition.

3.5. The relaxation time and fragility index For the Zn5Se95 system, the values of Tg are found to increase with the increased β. The reason behind that is when β increases; the system doesn't get abundance time for nucleation and growth. In addition, the relaxation time (τ) of atoms is directly proportional to β. Therefore, as β increases, the value of τ decreases leads to an increase in Tg as the product 10

of both τ and Tg should be constant. Hence, Tg shifts towards higher values with an increase in β. Through the heating of material from the glassy state into the supercooled liquid zone, one can deduce a relation between a particular average structural relaxation time and β. The total relaxation time for the glass transition (? ) can be approximated as [37]: ?

=

∆

(

(13)

where ∆Tg is the width of the glass transition region (the difference between Tg(off) and Tg(on) determined from the DSC or DTA curves). The obtained values of ? β are given in Table 4. It is observed that the value of ?

for Zn5Se95 at different

decreases (while ∆Tg increases)

with increasing β; this is a good agreement with the above discussion. In the present study, it is noticed that decreasing interval between Tg(on) and Tg(off), with increasing β indicates a faster glass transition process. Another important parameter concerning the GFA is the fragility index (Fi), it is a measure the rate at which the relaxation time decreases with the increasing temperature around Tg. Fragility is specified as the increasing rate of the viscosity of an under-cooled liquid at Tg in the cooling process. According to the value of Fi, the glass-forming liquid can be classified into two categories: strong liquid and fragile liquid [7,42]. The value of Fi for a glass as a function of β can be approximately evaluated [43] as: A2 = " ! ln ( )

(14)

According to Vigils [44], glass-forming liquids exhibit an approximate Arrhenius temperature dependence of their relaxation and specified which a low value of Fi (Fi~16) then the system is known as "strong" glass former. On the other hand, if 16 ˂ Fi ˂ 200, then that system is classified as "fragile'. The fragility indices are calculated for Zn5Se95 glass using activation energies obtained by Moynihan's and Kissinger's methods and listed in Table 4. It is clear that the values of Fi decrease with increasing β and their values below 16 for β>15 K/min indicates that the present glass falls in the class of "strong" glass-forming liquids.

3.6. Thermal analysis of the amorphous-crystallization transformation In order to describe the amorphous-crystallization transition by means of full kinetic analysis, it is necessary to determine the activation energy required to that transition, estimate the pre-exponential factor, and select an appropriate thermal analysis model or the kinetic 11

model f(α) to describe the crystallization peak. Based on the Johnson-Mehl-Avrami (JMA) equation, the crystallization kinetic parameters such as the Avrami exponent (n) and the crystallization activation energy (Ec) can be calculated using different approaches. For example, the Ec of amorphous-crystalline transformation is calculated using the equation derived by Kissinger [32]: ln ' $ + = − BC

DE

FBC

+ CH

(15)

This formula is similar to Eq. (7) which is used to investigate the glass transition process. Fig. 11a shows the plot of ln( $ ) versus BC

IJK BC

for the studied composition, and the deduced value of

Ec equal to 70.15 kJ/mol. In addition, the Ec, m and n values are calculated using the Matusita et al. method [45]: lnL− ln(1 − α)N = −nln(β) − 1.052

PDE FB



(16)

Where α is the volume fraction crystallized at the corresponding temperature (T) and m is constant related to the crystallization mechanism. Fig. 11b shows the α as a function of T at different β. One can use the data in Fig. 11b, for plotting of lnL− ln(1 − α)N versus

IJK B

as

shown in Fig. 11c for the Zn5Se95 samples at various β. From the slope of the fitted straight lines, the average mEc values are calculated and equal to 234.76 kJ/mol. It is clear that the fitted curves show a linear behavior over a wide range of temperatures. For glasses containing no nuclei; n =m+1, and for glasses containing a sufficiently large number of nuclei m = n. The calculated n values were not integers and the average value being = 2.85. This indicates that the crystallization process takes place by more than one mechanism [46,47]. Also, the values of n may be accounted for the possibility of a combination of one and two-dimensional crystal growth with heterogeneous nucleation [46]. By using the average n value and the average mEc, the activation energy for crystallization was calculated to be 82.37 kJ/mol. Also, the Ec can be determined, Fig. 12, using numerous methods such as the KAS method [34,48]: (

ln ' $¡ + = − " * + const. *¡

(17)

*¡

In this method, one can calculate the local activation energy of crystallization Eαc at specific α corresponds to different β. Moreover, this process can be repeated for various degrees of conversion. Fig. 13 shows the calculated activation energy of the crystallization process as a 12

function of transformed fraction α using the KAS and FWO methods. Results show that Ec(α) slightly increases with α as it changes from 67 to 71.5 kJ/mol for increasing α from 0.1 to 0.9. A general view, the Ec(α) should be practically independent of the fraction conversion in the range of 0.3 ≤ α ≤ 0.7, and some changes may be expected for the lower and higher values of α, particularly for the faster processes (i.e. higher values of β). In addition, the slight difference between the activation energies estimated by the KAS and FWO methods may be attributed to the different approximations used in these models. According to Malek proposal [49], the validity of the JMA model to describe the crystallization process can be tested by checking the maximum of the Z(α) function at αS R . If the maximum of the Z(α) function falls into the range of 0.63±0.02, then the experimental data could be presented by using the JMA model, if αS R is shifted to a lower value, and then the condition of the validity is not fulfilled [50]. Both of Y(α) and Z(α) functions are calculated according to the following equations: D

Y(α) = φ exp YFBE Z

(8)

Z (α) = φ T ]

(9)

Where φ is the specific heat flow. These two functions are normalized within the (0, 1)

range, and reach their maxima when α is equal to αM and αS R , respectively. The value of αM is

always lower than the maximum of the Z(α) function αS R . The average value of Ec

determined by the KAS method and then is used to calculate Y(α) function for the studied glass. The variations of Y(α) and Z(α) functions versus α are shown in Fig. 14 for the Zn5Se95 system. From the plot of Y(α) and Z(α) versus α, the values of αM and αS R corresponds to their maxima, respectively, were determined at different β and are summarized in Table 5. The value of αS R exhibits strong heating rate dependence, for example when β increases from

5 to 30 K/min, the value of αS R decreases from 0.589 to 0.452, respectively, for the

crystallization process. On the other hand, all the values of αS ^ are lower than their S corresponding values of αS R , and the value of αR is assumed to be constant at around 0.632

S for the JMA model. However, in the current study the average values of αS ^ and are αR are

0.407 and 0.519, respectively. This observation implies a more complicated crystallization process and thus the JMA model is not suitable for describing the crystallization process of Zn5Se95 chalcogenide glass. Accordingly, if the JMA model is applied to describe the thermal kinetics in this case, inappropriate results will be obtained. This observation is in good agreement with other studies for other compositions or systems [9,51]. Such behavior of the crystallization stage could be quantitatively described by the Šesták–Berggren SB(M,N) 13

model. The kinetics exponents M and N are two parameters that define the relative contribution of the acceleratory and deceleratory part of the crystallization process. The conversion corresponding to the maximum of Y(α) function, α^ , can be used to calculate the quotient of parameters M and N [49]: ^ _

= I

`a

`a



(20)

The N values can be estimated using the following equation [49]: a

D

ln bφ exp Y E Zc = ln(ΔHA) + N lnLα h (1 − α)N

(21)

FB

Where A is the frequency factor, depends on the number of successful collisions of the reacting molecules, and ∆H is the crystallization enthalpy. This equation is valid in the interval of 0.2 ≤ α ≤ 0.8. The parameter N is determined directly from the slope of the plot of a

D

ln bφ exp YFBE Zc versus lnLα h (1 − α)N, Fig. 15, and then the parameter M was deduced by using Eq. 20. Also, the pre-exponential factor (A) was calculated from the section of the dependence by using Eq. 21. The numerical values of M, N, and A at different β for the studied Zn5Se95 system are listed in Table 5. Theoretical DTA curves can be calculated based on the JMA and SB models. In the i

solid-state reaction, the conversion rate Y Z of reaction single-stage process of transformation or decomposition in the solids is usually determined by the following expression: l

i

Y Z = (jk m )n(o)

(22)

Where the left-hand side part presents the temperature-dependent rate constant, and for the JMA model, the function ƒ(α) is defined as [52]: ƒ(α) = n (1 − α)L− ln(1 − α)NI

q

(23)

Here n is a kinetic exponent related to the dimensionality of the crystal growth. The degree of crystallization or conversion α implies the relative volume of the crystalline part transformed during the crystallization process. On the other side, in the empirical kinetic model of SB, the function ƒ(α) is described by [53]: ƒ(α) = α^ (1 − α)_ (− ln(1 − α))r

(24)

The terms α^ , (1 − α)_ , and (− ln(1 − α))r in Eq. (24) describe the diffusion, interface, and nucleation mechanisms, respectively. The value of M is limited to the interval (1˃M˃0). Although this model has little kinetic meaning, it covers various kinetics functions as for 14

every value of M, and N one can obtain a wide range of models [54]. For simplicity and as no more than two kinetic exponents are necessary, Eq. (24) can be rewritten after eliminating the third exponential part: ƒ(α) = α^ (1 − α)_

(25)

The values of M and n in Eq. (25) may differ in value from those in Eq. (24). The SB model can be used with other thermal models to determine n, M and N exponents and to estimate the invariant activation energy as well as describing the single-step mechanism. Therefore it can be used to describe the crystallization process by means of full kinetic analysis. In order to confirm the established above values, the calculated and experimental DTA curves are shown in Fig. 16. The DTA curves calculated using the SB model are in good agreement with the experimental data at all heating rates. The higher value of N exponent (~1.048) as observed at β=5 K/min, reveals the increasing of reaction complexity. However, as can be seen from Table 5, the values of M and N can be controlled by adjusting β, therefore, controlling the reaction mechanism without complementary measurements. Based on Eq. 25 the entire nucleation process must take place during the early stages of the transformation and become negligible afterward [55]. This site saturation assumption is necessary for the process where the crystallization rate is only defined by the temperature and shows little dependence on thermal history [55]. At low β, the nuclei have more time to form before starting the growth process. This making the entire nucleation occurs basically in the early stages of the S transformation. As the following conditions (0˂αM˂αS R ; and αR ≠0.632) are satisfied through

the studied system this implies that the SB model is appropriate to fit the non-isothermal reaction rate of amorphous-crystallization transition. From the above, the SB kinetic model can be used for the quantitative description of more complicated phase transformations. In general, the values of M, and N exponents in Eq. (25) may not reflect the reaction mechanism, however, they help to understand the kinetic data and modeling the kinetics of the overall process without a deeper insight into its mechanism. The SB equation gives a purely formal description of the kinetics and it should be applied and understood in this way.

4. Conclusion Various thermal kinetics such as glass transition and amorphous-crystallization kinetics of Zn5Se95 glass are systematically investigated by non-isothermal DTA technique with some comparisons with the published data. Linear correlation is found between the glass transition and crystallization temperatures. In addition, the Kauzman temperature is

15

calculated and revealed the lower bound for the kinetically observed glass transition. The observed variation in the activation energy required for the glass transition over the glass transition region is expected, however, its constancy through the glass transition region is expected but its constancy through the glass transition temperature range is not proved. Its value determined by four different iso-conversional methods and shows a decrease with temperature and the extent of conversion and that change was explained in the light of the free volume theory. Moreover, the fragility index of the given glass is less than 16 indicates that the given glass is classified as a strong glass type. The crystallization activation energy is found to be 70.15 kJ/mol estimated by the KAS method, while 82.38 kJ/mol estimated by Matusita's method. The calculated DTA curves at various heating rates indicate a good consistency by the SB model. In addition, the determined kinetic was validated by a composite differential method and the comparison of the calculated and experimental data.

References 1. 2. 3.

4.

5. 6. 7. 8. 9.

10.

11.

Zallen, Richard. The physics of amorphous solids. John Wiley & Sons, 2008. Abbady, Gh, and Alaa M. Abd-Elnaiem. "Thermal stability and crystallization kinetics of Ge13In8Se79 chalcogenide glass." Phase Transitions , 92(7), (2019): 667-682. Dabban, M. A., Nema M. Abdelazim, Alaa M. Abd-Elnaiem, S. Mustafa, and M. A. Abdel-Rahim. "Effect of Sn substitution for Se on dispersive optical constants of amorphous Se–Te–Sn thin films." Materials Research Innovations 22, no. 6 (2018): 324-332. Abd-Elnaiem, Alaa M., and Samar Moustafa. "Optical properties of annealed As30Te67Ga3 thin films grown by thermal evaporation." PROCESSING AND APPLICATION OF CERAMICS 12, no. 3 (2018): 209-217. Rowlands, John, and Safa Kasap. "Amorphous semiconductors usher in digital x-ray imaging." Physics Today 50, no. 11 (1997): 24-30. Jackle, J. "Models of the glass transition." Reports on Progress in Physics 49, no. 2 (1986): 171. Angell, C. A. "Relaxation in liquids, polymers and plastic crystals—strong/fragile patterns and problems." Journal of Non-Crystalline Solids 131 (1991): 13-31. Abdel-Rahim, M. A. "A study of the crystallization kinetics of some Se–Te–Sb glasses." Journal of non-crystalline solids 241, no. 2-3 (1998): 121-127. Abdel-Rahim, M. A., M. M. Hafiz, A. Y. Abdel-Latief, Alaa M. Abd-Elnaiem, and A. Elwhab B. Alwany. "A study of the non-isothermal crystallization kinetic of Zn 10 Se 90 glass." Applied Physics A 119, no. 3 (2015): 881-890. Moynihan, Cornelius T., Allan J. Easteal, James Wilder, and Joseph Tucker. "Dependence of the glass transition temperature on heating and cooling rate." The Journal of Physical Chemistry 78, no. 26 (1974): 2673-2677. Hancock, Bruno C., Chad R. Dalton, Michael J. Pikal, and Sheri L. Shamblin. "A pragmatic test of a simple calorimetric method for determining the fragility of some amorphous pharmaceutical materials." Pharmaceutical research 15, no. 5 (1998): 762767.

16

12.

13. 14.

15. 16. 17.

18.

19.

20. 21.

22.

23.

24.

25.

26. 27. 28.

29.

Angell, C. A., R. C. Stell, and W. Sichina. "Viscosity-temperature function for sorbitol from combined viscosity and differential scanning calorimetry studies." The Journal of Physical Chemistry 86, no. 9 (1982): 1540-1542. Lacey, D., G. Nestor, and M. J. Richardson. "Structural recovery in isotropic and smectic glasses." Thermochimica acta 238 (1994): 99-111. Vyazovkin, Sergey, and Nicolas Sbirrazzuoli. "Isoconversional kinetic analysis of thermally stimulated processes in polymers." Macromolecular Rapid Communications 27, no. 18 (2006): 1515-1532. Cohen, Morrel H., and David Turnbull. "Molecular transport in liquids and glasses." The Journal of Chemical Physics 31, no. 5 (1959): 1164-1169. Paluch, M., R. Casalini, and C. M. Roland. "Cohen-Grest model for the dynamics of supercooled liquids." Physical Review E 67, no. 2 (2003): 021508. Dohare, C., and N. Mehta. "Determination of kinetics parameters of glass transition in glassy Se and glassy Se98M2 alloys using DSC technique." Applied Physics A 114, no. 2 (2014): 597-603. Nasir, Mohd, Mohd Abdul Majeed Khan, Mushahid Husain, and Mohammad Zulfequar. "Thermal properties of Se100–xZnx glassy system." Materials Sciences and Applications 2, no. 05 (2011): 289. Kremer, R. K., M. Cardona, R. Lauck, G. Siegle, and A. H. Romero. "Vibrational and thermal properties of Zn X (X= Se, Te): density functional theory (LDA and GGA) versus experiment." Physical Review B 85, no. 3 (2012): 035208. De Lima, J. C., V. H. F. Dos Santos, and T. A. Grandi. "Structural study of the Zn-Se system by ball milling technique." Nanostructured materials 11, no. 1 (1999): 51-57. Leppert, Valerie J., Shailaja Mahamuni, N. R. Kumbhojkar, and Subhash H. Risbud. "Structural and optical characteristics of ZnSe nanocrystals synthesized in the presence of a polymer capping agent." Materials Science and Engineering: B 52, no. 1 (1998): 8. Heireche, Lamia, Mohamed Heireche, and Maamar Belhadji. "Kinetic Study of NonIsothermal Crystallization in Se90-xZn10Sbx (x= 0, 2, 4, 6) Chalcogenide Glasses." Journal of Crystallization Process and Technology 4, no. 02 (2014): 111. Nasir, Mohd, and M. Zulfequar. "DC Conductivity and Dielectric Behaviour of Glassy Se100–xZnx Alloy." Open Journal of Inorganic Non-metallic Materials 2, no. 02 (2012): 11. Singh, Abhay Kumar, Neeraj Mehta, and Kedar Singh. "Correlation between Meyer– Neldel rule and phase separation in Se98−xZn2Inx chalcogenide glasses." Current Applied Physics 9, no. 4 (2009): 807-811. Peng, Shuai, Guowu Tang, Kaimin Huang, Qi Qian, Dongdan Chen, Qinyuan Zhang, and Zhongmin Yang. "Crystalline selenium core optical fibers with low optical loss." Optical Materials Express 7, no. 6 (2017): 1804-1812. Sharma, R. C., and Y. A. Chang. "The Se-Zn (selenium-zinc) system." Journal of phase equilibria 17, no. 2 (1996): 155-160. Lasocka, Maria. "The effect of scanning rate on glass transition temperature of splatcooled Te85Ge15." Materials Science and Engineering 23, no. 2-3 (1976): 173-177. Yao, B., H. Ma, H. Tan, Y. Zhang, and Y. Li. "Correlations between the glass transition, crystallization, apparent activation energy and glass forming ability in Fe based amorphous alloys." Journal of Physics: Condensed Matter 15, no. 45 (2003): 7617. Kauzmann, Walter. "The nature of the glassy state and the behavior of liquids at low temperatures." Chemical reviews 43, no. 2 (1948): 219-256.

17

30.

31. 32.

33.

34. 35. 36. 37.

38. 39. 40.

41.

42.

43.

44. 45. 46. 47. 48. 49.

Ichitsubo, Tetsu, Eiichiro Matsubara, Hiroshi Numakura, Katsushi Tanaka, Nobuyuki Nishiyama, and Ryuichi Tarumi. "Glass-liquid transition in a less-stable metallic glass." Physical Review B 72, no. 5 (2005): 052201. Ruitenberg, G. "Applying Kissinger analysis to the glass transition peak in amorphous metals." Thermochimica acta 404, no. 1-2 (2003): 207-211. Kissinger, Homer E. "Variation of peak temperature with heating rate in differential thermal analysis." Journal of research of the National Bureau of Standards 57, no. 4 (1956): 217-221. Lankhorst, M. H. R. "Modelling glass transition temperatures of chalcogenide glasses. Applied to phase-change optical recording materials." Journal of non-crystalline solids 297, no. 2-3 (2002): 210-219. Kissinger, Homer E. "Reaction kinetics in differential thermal analysis." Analytical chemistry 29, no. 11 (1957): 1702-1706. Ozawa, Takeo. "A new method of analyzing thermogravimetric data." Bulletin of the chemical society of Japan 38, no. 11 (1965): 1881-1886. Ozawa, Takeo. "Temperature control modes in thermal analysis." Pure and applied chemistry 72, no. 11 (2000): 2083-2099. Starink, M. J. "Comments on “Precipitation kinetics of Al–1.12 Mg2Si–0.35 Si and Al– 1.07 Mg2Si–0.33 Cu alloys”." Journal of alloys and compounds 433, no. 1-2 (2007): L4-L6. Tang, Wanjun, Yuwen Liu, Hen Zhang, and Cunxin Wang. "New approximate formula for Arrhenius temperature integral." Thermochimica Acta 408, no. 1-2 (2003): 39-43. Birge, Norman O., and Sidney R. Nagel. "Specific-heat spectroscopy of the glass transition." Physical Review Letters 54, no. 25 (1985): 2674. Williams, Malcolm L., Robert F. Landel, and John D. Ferry. "The temperature dependence of relaxation mechanisms in amorphous polymers and other glass-forming liquids." Journal of the American Chemical society 77, no. 14 (1955): 3701-3707. Sopade, P. A., P. Halley, B. Bhandari, B. D’arcy, Caffin Doebler, and N. Caffin. "Application of the Williams–Landel–Ferry model to the viscosity–temperature relationship of Australian honeys." Journal of Food Engineering 56, no. 1 (2003): 6775. Wang, W-M., A. Gebert, S. Roth, U. Kuehn, and L. Schultz. "Glass formability and fragility of Fe61Co9− xZr8Mo5WxB17 (x= 0 and 2) bulk metallic glassy alloys." Intermetallics 16, no. 2 (2008): 267-272. Lafi, Omar A. "Correlation of some opto-electrical properties of Se–Te–Sn glassy semiconductors with the average single bond energy and the average electronegativity." Journal of Alloys and Compounds 660 (2016): 503-508. Vilgis, Thomas A. "Strong and fragile glasses: A powerful classification and its consequences." Physical Review B 47, no. 5 (1993): 2882. K. Matusita, S. Sakka,. "Kinetic study of the crystallization of glass by differential scanning calorimetry". Physics and Chemistry of Glasses, 20 (4) (1979), 81. A. Hrubý, "Evaluation of glass-forming tendency by means of DTA". Czechoslovak Journal of Physics B, 22(11), (1972)1187-1193. M. Rahim, A. El-Korashy, S. Al-Ariki, "Crystallization Studies on Se-Te-Cd Chalcogenide Glasses". Materials transactions, 51(2), (2010) 256-260. T. Akahira, T. Sunose. "Joint convention of four electrical institutes."Res Rep Chiba Inst Technol 16 (1971): 22-31. J. Málek, "Kinetic analysis of non-isothermal calorimetric data". Sci. Papers Univ. Pardubice, 2, (1996)177-209.

18

50. 51.

52. 53. 54.

55.

J. Málek,. "The applicability of Johnson-Mehl-Avrami model in the thermal analysis of the crystallization kinetics of glasses". Thermochimica Acta, 267, (1995) 61-73. Mohamed, Mansour, Alaa M. Abd-Elnaiem, R. M. Hassan, M. A. Abdel-Rahim, and M. M. Hafiz. "Non-isothermal crystallization kinetics of As30Te60Ga10 glass." Applied Physics A 123, no. 8 (2017): 511. M. Avrami,. "Granulation, phase change, and microstructure kinetics of phase change. III". The Journal of chemical physics, 9(2), (1941)177-184. J. Šesták, G. Berggren, "Study of the kinetics of the mechanism of solid-state reactions at increasing temperatures" Thermochimica Acta, 3(1), (1971) 1-12. Perez-Maqueda, L. A., J. M. Criado, and P. E. Sanchez-Jimenez. "Combined kinetic analysis of solid-state reactions: a powerful tool for the simultaneous determination of kinetic parameters and the kinetic model without previous assumptions on the reaction. D. W. Henderson,. "Thermal analysis of non-isothermal crystallization kinetics in glass forming liquids". Journal of Non-Crystalline Solids, 30(3), (1979) 301-315.

19

List of Tables: Table 1: List of characteristic temperatures Tg, Tc, Tp, Tc-Tg, and Hr for the Zn5Se95 glass at different heating rates (β).

β (K/min)

Tg (K)

Tc (K)

Tp (K)

Tm (K)

Tc-Tg (K)

Hr

5 10 15 20 30

318.2 321.2 323.7 325.1 327.9

353.3 365.5 366.3 371.3 375.6

367.5 376.9 383.7 388.7 395.6

494.5 496.4 498.2 500.7 501.9

35.1 44.3 42.6 46.2 47.7

0.25 0.34 0.32 0.36 0.38

Table 2: The glass transition activation energy (Eg) determined using the Moynihan and Kissinger equations at different assignments (or different degrees of conversion). Activation energy (kJ/mol) Tg assignment Moynihan equation Kissinger equation Tg(on) 152.38 145.85 Tg(peak)

129.83

121.71

Tg(off)

70.36

68.32

Table 3: List of activation energy of glass transition (Eαg) as a function of the extent of conversion (α) determined by different iso-conversional methods. α 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

KAS 142.07 132.30 125.55 116.96 107.22 105.52 98.93 90.09 82.83

FWO 147.48 137.05 137.05 123.22 112.69 111.00 104.43 95.62 88.39

1

Eαg (kJ/mol) Tang 142.36 131.91 131.61 118.05 107.51 105.81 99.22 90.38 83.12

Straink 142.29 131.84 131.54 117.98 107.44 105.74 99.15 90.31 83.05

Table 4: List of the width of the glass transition (∆Tg), relaxation time (τTg), and dynamic fragility index (Fi) at different heating rates (β).

β (K/min) 5 10 15 20 30

∆Tg (K) 12.70 10.91 24.76 24.87 23.37

τTg (s) 2.54 1.09 1.65 1.24 0.78

Fi (Moynihan method) 29.97 20.85 17.53 15.74 13.76

Fi (Kissinger method) 28.30 19.55 16.44 14.76 12.81

Table 5: The crystallization enthalpy (∆H), conversion values (αM) and (αp∞) corresponding to the maxima of functions Y(α) and Z(α), respectively, and the parameters N and M of the SB(M,N) model at the different heating rates (β). β (K/min)

∆H (J/g)

αM

5 10 15 20 30

63.48 61.06 66.30 68.23 67.52

0.468 0.431 0.430 0.376 0.328

Average

65.32

0.407

N

M

ln(A) (min-1)

0.589 0.541 0.529 0.486 0.452

1.191 0.898 1.182 1.120 1.140

1.048 0.680 0.892 0.675 0.556

21.51 21.64 21.61 20.97 20.92

0.519

1.106

0.770

21.33

2

Intensity (Arb. units)

List of figures and figure captions:

0

10

20

30

40

50

60

70

80

90

2θ (°)

Endo Heat flow Exo

Fig. 1. XRD chart of the as-prepared Zn5Se95 chalcogenide glass.

300

Tm Tx

Tc

Tg

β 5 K/min 10 K/min 15 K/min 20 K/min 30 K/min 350

400

450

500

550

600

Temperature (K) Fig. 2. DTA traces for the Zn5Se95 chalcogenide glass at different heating rates (β).

1

Endo Heat flow Exo 310

β 5K/min 10K/min 15K/min 20K/min 30K/min

320

330

340

350

Temperature (K) Fig. 3. DTA curves show the endothermic peak of the glass transition region for the Zn5Se95 chalcogenide glass at different heating rates (β).

330

400

Tg (K)

325

360

Tg Tc Tp

320

315 1.5

2.0

2.5

ln (β)

3.0

340

Tp & Tc (K)

380

320 3.5

Fig. 4. The relation between the glass transition temperature (Tg), left-hand side, onset crystallization temperature (Tc), and crystallization peak temperature (Tp) right-hand side, versus ln(β) for the Zn5Se95 chalcogenide glass.

2

Heat flow

Tg(on) Tg(off)

Tg(Peak) 315

320

325

330

335

340

Temperature (K) Fig. 5. A typical DTA plot of the Zn5Se95 chalcogenide glass showing on-set glass transition temperature Tg(on), peak glass transition temperature Tg(peak) and off-set glass transition temperature Tg(off) at a heating rate 10 K/min.

3.12

ln (β)

3.06

3.00

2.94

Tg(on) 2.88

Tg(peak) Tg(off)

2.82 1.4

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

3.2

3.4

3.6

1000/Tg (K-1) Fig. 6. ln(β) versus 1000/Tg for the Zn5Se95 chalcogenide glass. The straight lines represent least-squares fittings to the Moynihan model.

3

-8.1 -8.4

ln (β/T2 g)

-8.7 -9.0 -9.3 -9.6

Tg(on) Tg(peak)

-9.9

Tg(off) -10.2 2.85

2.90

2.95

3.00

3.05

3.10

3.15

1000/Tg (K-1) Fig. 7. plot of ln( / ) versus 1000/Tg for the Zn5Se95 chalcogenide glass. The straight lines represent least-squares fitting to the Kissinger equation. 1.0

0.8

α

0.6

β

0.4

5 K/min 10 K/min 15 K/min 20 K/min 30 K/min

0.2

0.0 320

325

330

335

340

345

350

Tg (K) Fig. 8. degree of transformation or extent of conversion (α) versus the glass transition temperature (Tg) for the Zn5Se95 chalcogenide glass at different heating rates (β).

4

4

2

Method

Y

KAS FWO Tang Straink

-8

-10

2.98

3.00

3.02

3.04

3.06

3.08

3.10

3.12

1000/Tαg (K-1) Fig. 9. plots of Y: (■) ln (

), (●) ln ( ), (▲) ln (

.

), and (▼) ln (

.

), versus 1000/Tαg

for Zn5Se95 chalcogenide glass at α=0.5.

(a) 150

Eαg (kJ/mol)

140 130 120 110

Method KAS FWO Tang Straink

100 90 80 0.0

0.2

0.4

α

5

0.6

0.8

1.0

(b) 150 140

Eg (kJ/mol)

130 120 110 100 90 80

Method KAS FWO Tang Straink WLF 330

332

334

336

338

340

342

344

T (K) Fig. 10. activation energy required for the glass transition (Eg) as a function of (a) α as determined using different iso-conversional methods, (b) the temperature (T) in the glass transition region for the Zn5Se95 chalcogenide glass.

(a)

-8.4 -8.7

ln (β/T2 p)

-9.0 -9.3 -9.6 -9.9 -10.2 2.50

2.55

2.60

2.65 -1

1000/Tp (K )

6

2.70

2.75

(b)

1.0

α

0.5

5 K/min 10 K/min 15 K/min 20 K/min 30 K/min

0.0 340

360

380

400

420

2.8

2.9

T (K)

(c)

ln[-ln(1-α)]

0

-2

β -4

5 K/min 10 K/min 15 K/min 20 K/min 30 K/min

-6 2.5

2.6

2.7

1000/T (K -1) Fig. 11. plots of (a) ln

versus 1000/TP, (b) the crystalline volume fraction (α) as a

function of temperature (T) and (c) ln [− ln(1 − )] versus 1000/T at different heating rates (β) for the Zn5Se95 chalcogenide glass.

7

(a)

3.5

α

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

ln(β)

3.0

2.5

2.0

1.5

2.45

2.50

2.55

2.60

2.65

2.70

2.75

2.80

2.85

1000/Tα (K-1)

(b)

-8.4

α 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

-8.8

ln(β / Τ2α)

-9.2

-9.6

-10.0

-10.4 2.48

2.52

2.56

2.60

2.64

2.68

1000/Tα (K-1)

2.72

2.76

2.80

Fig. 12. plots of (a) ln(β) and (b) ln ( ), versus 1000/Tα for Zn5Se95 chalcogenide glass for different crystalline volume fraction (α).

8

80

KAS FWO

(kJ/mol.)

65

αc

70

E

75

60 0.0

0.2

0.4

0.6

0.8

1.0

α

0.8

0.8

0.6

0.6

0.4

0.2

0.0 0.0

0.4

5K/min 10K/min 15K/min 20K/min 25K/min 0.2

0.4

α

0.6

Z(α)

1.0

Y(α)

1.0

Z(α)

Y(α)

Fig. 13. the change of activation energy for crystallization (Eα) with the fractional conversion (α) for the Zn5Se95 chalcogenide glass using KAS and FWO approaches.

0.2

0.8

0.0 1.0

Fig. 14. normalized Y(α), and Z(α) functions obtained from the DTA data for the crystallization process in the Zn5Se95 chalcogenide glass at various heating rates (β).

9

ln [φ exp(Ec/RT)]

24

23

β 5 K/min 10 K/min 15 K/min 20 K/min 25 K/min

22

21

20 -4.0

Fig. 15. plots of ln [

-3.5

-3.0

ln [αM/N (1- α)]

-2.5

-2.0

!"

(1 − )] against ln [ #$ ] at different heating rates (β) for the Zn5Se95 chalcogenide glass.

25 EXP.

∆Τ (K)

20

15

SB

5 K/min 10K/min 15K/min 20K/min 25K/min

10

5

0 340

360

380

400

420

440

T (K) Fig. 16. non-isothermal crystallization curves, temperature difference (∆T) versus T, of Zn5Se95 chalcogenide glass for different heating rates (β) together with the calculated (dots) using the SB(M,N) model.

10

Highlights: •

•

• •

The thermal kinetics of melt-quenched Zn5Se95 chalcogenide glass using differential thermal analysis (DTA) techniques under non-isothermal conditions is studied. The glass transition process cannot be concluded in terms of single activation energy, and that variation with the extent of conversion was analyzed using various iso-conventional methods. The calculated DTA curves at different heating rates show fairly good consistency by SB(M,N) model. The fragility index is a measure of glass-forming ability, of Zn5Se95 composition, has been calculated using the glass transitions and activation energy values.

Declaration of interests The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.