Journal of Non-Crystalline Solids 429 (2015) 164–170

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Journal of Non-Crystalline Solids

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Thermal stability and non-isothermal crystallization kinetics ofTi41.5Cu42.5Ni7.5Zr2.5Hf5Si1 bulk metallic glass

S. Haratian ⁎, M. Haddad-SabzevarMetallurgical and Materials Engineering Department, Ferdowsi University of Mashhad, P.O. Box 91775-1111, Mashhad, Iran

⁎ Corresponding author.E-mail address: Saberharatian@yahoo.com (S. Haratia

http://dx.doi.org/10.1016/j.jnoncrysol.2015.09.0090022-3093/© 2015 Elsevier B.V. All rights reserved.

a b s t r a c t

a r t i c l e i n f o

Article history:Received 8 July 2015Received in revised form 27 August 2015Accepted 1 September 2015Available online xxxx

Keywords:Ti-based bulk metallic glass;Activation energy;Non-isothermal crystallization kinetics;Nucleation and growth mechanism

In this research, an investigation has been carried out to determine the non-isothermal crystallization kinetics ofTi41.5Cu42.5Ni7.5Zr2.5Hf5Si1 bulk metallic glass prepared via copper mold casting. X-ray diffraction (XRD), energydispersive spectroscopy (EDS), differential thermal analysis (DTA) and differential scanning calorimetry (DSC)were used to determine its characterization and non-isothermal crystallization kinetics. The DSC curves revealedthree stages of the crystallization. The microstructure evolution through annealing at three-stage crystallizationof the bulk glassy alloywas characterized. The apparent activation energies for the first exothermic crystallizationpeakwere calculated as 281.33 and 279.11 kJ/mol using Kissinger and Ozawa equations, respectively. The nucle-ation and growthmechanismswere determined by the local Avrami exponent at heating rates ranging from 5 to80 K/min using Jhonson–Mehl–Avrami–Kolomogrov (JMAK) method. The local Avrami exponent gradually de-creases as the crystallization proceeds implying that the nucleation rate decreases. Nucleation and growth acti-vation energies were estimated by Ozawa–Flynn–Wall (OFW) equation.

© 2015 Elsevier B.V. All rights reserved.

1. Introduction

Bulk metallic glasses (BMGs) are a new class of the advanced mate-rials that have attracted a lot of attention in the recent years due to theirspecific capability in engineering applications [1]. Metallic glasses areknown for their unique properties such as high strength and hardness,low Young's modulus and in some cases high wear and corrosion resis-tance [2–4]. Although metallic glasses bear noticeable properties, theyare metastable and tend to transform into the crystalline state duringcontinuous heating [5]. Therefore, it seems significant to determinetheir thermal stability from scientific and technological points of viewthat reflects how stable the BMGs are against the thermal treatmentsthat may be present in the practical applications. Since the overall crys-tallization of the glassy alloys happens through nucleation and growthprocesses the kinetics of the overall transformation reflects how theseprocesses depend on time and temperature. Recently, widespreadstudies on crystallization kinetics have been conductedwith applicationof isothermal and non-isothermal analysis techniques. The non-isothermal DSC experiments are highly efficient due to detecting rapidphase transformations occurring in the crystallization process [6–9].The crystallization transformation can be studied by investigating thenumber of exothermic crystallization peaks, microstructure evolution,

n).

required activation energy, crystallized volume fraction and reaction ki-netics [5,10,11]. Several methods have been utilized to describe the pa-rameters determinant in the kinetics of the crystallization process suchas Kissinger method [12], Ozawa method [13], Augis–Bennett method[14] and Friedman method [15] aiming to estimate the crystallizationactivation energy (Ec) and Johnson–Mehl–Avrami–Kolomogrov(JMAK) method [16,17] for determining crystallization mechanism.

Nowadays, Ti-based bulk metallic glasses have been widelyresearched due to their capability in structural engineering and biomed-ical applications [4]. Several research works have been carried out inorder to synthesize Ti-based glassy alloy systems such as Ti–Zr–Be[18], Ti–Ni–Cu–Sn [19], Ti–Zr–Cu–Ni [20], Ti–Ni–Cu–Si–Sn [21], Ti–Zr–Be–Al [22] and Ti–Zr–Cu–Pd [23] and improve their glass forming ability(GFA) and thermal stability but less concentration on the crystallizationtransformation of Ti-based BMGs during thermal treatment has beendone. Recently, some research works have been carried out to fabricatenanocrystalline BMG composites benefitting high plasticity throughcontrolled crystallization transformation. Khalifa et al. [24] reportedprecipitation of Ti(Ni,Cu) nanocrystalline phase atfirst exothermic crys-tallization peakwith nucleation and diffusion-controlled growth duringisothermal crystallization of Ti–Ni–Cu–Si–Sn bulk glassy system.

In the present research, the experimental and analytical study on thecrystallization behavior of Ti41.5Cu42.5Ni7.5Zr2.5Hf5Si1 BMG was investi-gated in order to determine the crystallization kinetics and the crystal-line phase evolution during this process using non-isothermal DSCtechnique. The crystallization kinetic parameters such as activation

Fig. 1. XRD pattern of as-cast Ti41.5Cu42.5Ni7.5Zr2.5Hf5Si1 bulk metallic glass.

Fig. 2. EDS pattern of as-cast rods of Ti41.5Cu42.5Ni7.5Zr2.5Hf5Si1 bulk metallic glass.

165S. Haratian, M. Haddad-Sabzevar / Journal of Non-Crystalline Solids 429 (2015) 164–170

energy, local Avrami exponents and frequency factor have been calcu-lated. The nucleation and growth mechanisms have been determinedusing Ranganathan–Heimendahl equation.

2. Experimental

2.1. Sample preparation

The alloy ingots with the nominal composition ofTi41.5Cu42.5Ni7.5Zr2.5Hf5Si1 (at.%) were prepared by vacuum arc meltingof high pure elements (99.9 wt.%) of Ti, Cu, Ni, Zr, Hf and Si underargon atmosphere. The alloy ingots were remelted four times to ensurecompositional homogeneity. Cylindrical rods with 1 mm in diameterand 15 mm in height were produced by suction casting into a coppermold.

2.2. Structure characterization

The amorphous structure was examined using Philips X'pert PW3040/60 X-ray diffractometer (XRD) with CuKα radiation and was re-corded in 2θ ranging 20°–90°. In order to ensure the composition ofthe Ti-based bulk glassy alloy the energy dispersive electron spectrom-eter (EDS) attached to Philips XL20 scanning electron microscopy(SEM) was used.

2.3. Thermal analysis

Thermal properties and the non-isothermal crystallization kineticsof the bulk glassy alloy were characterized by continuous heatingat heating rates ranging from 5 to 80 K/min in Shimadzu DSC-60 differ-ential scanning calorimeter (DSC) and BAHR STA503 differential ther-mal analysis (DTA) under a flow of purified argon at a flow rate of60 cm3/min. The temperature accuracy of DSC equipment was ±0.1 Kwith an average standard error of about 1 K in the measured values.About 6 mg of the bulk glassy samples were cut from the as-cast rodsof Ti41.5Cu42.5Ni7.5Zr2.5Hf5Si1 BMG. Aluminum (Al) and alumina(Al2O3) pans were utilized for continuous heating in DSC and DTA, re-spectively. The temperature range covered in DSC was from 298 K to873 K. The DSC system was calibrated for temperature and heat fluxwith an indium standard. To identify the crystalline phases at differentexothermic crystallization peaks, the annealing of specimens was car-ried out at three onset crystallization temperatures in a heat treatmentfurnace. The Ti-based glassy alloy samples were put into the quartz cap-sule under a high vacuum atmosphere. The capsulation was done inorder to prevent oxidation of the specimens. XRD technique was usedto characterize the nature of the crystalline phases generated during an-nealing treatment.

3. Results and discussion

3.1. Characterization

Fig. 1 illustrates the XRD pattern of the Ti-based bulk glassy alloywhich exhibits a diffuse halo peak at 2θ ≈ 40° and no diffractionpeaks suggesting its amorphous state without any crystalline phases.Fig. 2 presents the result of EDS analysis obtained from as-cast rods ofTi41.5Cu42.5Ni7.5Zr2.5Hf5Si1 BMG. As seen from EDS result, there is no im-purity in composition and also that indicate the chemical elements usedin the glassy alloy are highly pure. Fig. 3 shows the DSC and DTA curvesof the bulk glassy alloy in continuous heating condition at a heating rateof 20 K/min, respectively. A glass transition temperature (Tg) followedby a supercooled liquid region (ΔTx = Tx − Tg), the onset exothermicpeak of crystallization temperature (Tx) (Fig. 3-a) and solidus (Tm) andliquidus (Tl) temperatures (Fig. 3-b) were distinguished in these pat-terns. The thermal properties of this glassy alloy at a heating rate of20 K/min are listed in Table 1. These values are in good agreement

with the results of the researchwork conducted byHuang et al. [25]. An-other feature observed in DSC curve is that there are three exothermiccrystallization peaks, so the Ti–Cu–Ni–Zr–Hf–Si glassy alloy crystallizedin multiple stages. According characteristic transformation tempera-tures obtained by DSC and DTA analysis, some criteria such as (Trg =Tg/Tl) [26], (γ = Tx/(Tg + Tl)) [27], (δ = Tx/(Tl − Tg)) [28] and (β =1 + (Tx/Tl)) [29] can be proposed to explain glass forming ability(GFA) of Ti–Cu–Ni–Zr–Hf–Si BMG. These calculated parameters thatare listed in Table 1 indicate good GFA for this Ti-based BMG that tendto cast into the fully amorphous rods with 2 mm in diameter accordingto Huang et al. study [25].

3.2. Annealing of Ti41.5Cu42.5Ni7.5Zr2.5Hf5Si1 bulk metallic glass

Due to the existence of several compositions in bulkmetallic glasses,it is possible to form different crystalline phases in continuous heatingat temperatures above onset crystallization temperatures. The DSC pat-tern of crystallization processes of Ti41.5Cu42.5Ni7.5Zr2.5Hf5Si1 indicatesthree exothermic peaks of crystallization at a heating rate of 5 K/minas presented in Fig. 4. To identify themicrostructure evolution and crys-talline phase products during the crystallization process at each exo-thermic peak, XRD experiments were carried out on samples annealedat onset crystallization temperatures at a heating rate of 5 K/min for2 h. The XRD patterns for annealed glassy samples as seen in Fig. 5.For the sample annealed at Tx1, the first onset crystallization tempera-ture at a heating rate of 5 K/min, 700 K, TiCu crystalline phase can be

Fig. 3. DSC (a) and DTA (b) curves obtained from as-cast Ti41.5Cu42.5Ni7.5Zr2.5Hf5Si1 bulkglassy alloy at a heating rate of 20 K/min.

Fig. 4.DSC curves of Ti41.5Cu42.5Ni7.5Zr2.5Hf5Si1 bulk glassy alloy at a heating rate of5 K/min.

166 S. Haratian, M. Haddad-Sabzevar / Journal of Non-Crystalline Solids 429 (2015) 164–170

detected. By annealing sample at Tx2, the second crystallization temper-ature at a heating rate of 5 K/min, 760 K, the crystalline peak of TiCu be-comes distinct and Ti2Ni indicated. By increasing annealing temperatureat Tx3, the third crystallization temperature at a heating rate of 5 K/min,800 K, the XRD pattern exhibiting sharper and higher intensity peaks ofcrystalline phases. Finally, two distinct Cu2Ti and Cu3Ti crystallinephases detected beside the two phases (TiCu, Ti2Ni) formed in the pre-vious steps. The driving force of Ti41.5Cu42.5Ni7.5Zr2.5Hf5Si1 BMG crystal-lization process supply from increasing temperature that causes theglassy state with a higher energy level transformed to crystalline statewith a lower energy level. Thus controlled crystalline microstructurecan be obtained through controlling time and temperature during an-nealing process.

3.3. Non-isothermal crystallization behavior

DSC curves of Ti41.5Cu42.5Ni7.5Zr2.5Hf5Si1 bulkmetallic glass recordedduring continuous heating at heating rates of 5, 20, 40, 60 and 80 K/min

Table 1Thermal properties of Ti41.5Cu42.5Ni7.5Zr2.5Hf5Si1 bulk metallic glass at a heating rate of20 K/min.

Tg (K) Tx (K) Tm (K) Tl (K) ΔTx (K) Trg γ δ β

684 719 1128 1193 35 0.57 0.38 1.41 1.60

are shown in Fig. 6. The results of DSC analysis are presented in Table 2.According to Fig. 6, with an increase in heating rates the DSC traces andall characteristic temperatures (Tg, Tx, Tp and ΔTx) are displaced tohigher temperatures, suggesting that the glass transition (Tg) and crys-tallization temperature (Tx) show a dependence on the heating ratewhich is caused by the fact that the nucleation and growth are thermallyactivated processes, whereas the glass transition kinetics is due to therelaxation process in the glass transition region. At lower heatingrates, there is enough time for stabilization and formation of crystallinenucleus so the crystallization occurred at lower temperatures. By in-creasing heating rate, the atoms rapidly face the temperature levelchanges and don't have sufficient time to locate at defined crystallinesites and form stable crystalline nucleus so the crystallization happenedat higher temperatures. Indeed, it indicates the effect of diffusion

Fig. 5. XRD patterns for Ti41.5Cu42.5Ni7.5Zr2.5Hf5Si1 bulk glassy samples annealed at threeonset crystallization peaks at 5 K/min.

Fig. 6.DSC curves of Ti41.5Cu42.5Ni7.5Zr2.5Hf5Si1 bulkmetallic glass at various heating rates. Fig. 7. Crystallized volume fraction of Ti41.5Cu42.5Ni7.5Zr2.5Hf5Si1 bulk metallic glass as afunction of temperature at different heating rates.

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parameters; time and temperature on the crystallization transformationof the glassy alloy.

Before analyzing the crystallization kinetic parameters during thefirst crystallization peak, the crystallized volume fraction of non-isothermal crystallization, x, should be obtained. According to DSCcurves, the crystallized volume fraction can be plotted against tempera-ture using the following equation [30,31]:

x ¼

Z T

Ti

dHdT

� �dT

Z T f

Ti

dHdT

� �dT

ð1Þ

where Ti and Tf are the onset and final crystallization temperatures, re-spectively. Fig. 7 depicts the plots of crystallized volume fraction, x asa function of temperature at different heating rates. All these curves rep-resent S-shape indicating bulk crystallization of the glassy alloy. At stage(a) random nucleation of crystalline phase occurs, then at stage(b) crystalline nucleus grow rapidly and at final stage (c) coalescenceof crystalline grains happens.

3.4. Non-isothermal crystallization kinetics

3.4.1. Activation energyOneof themost important kinetic parameters for crystallization pro-

cess is the activation energy. In this study, analytical methods such asKissinger andOzawa have been used to determine the activation energyvalues for thefirst exothermic crystallization peak. Kissinger proposed amethod for determining the activation energy of a simple decomposi-tion reaction by making differential thermal analysis patterns at differ-ent heating rates. He related the heating rate of a reaction to the peaktemperature recorded by thermal analysis. By considering the variation

Table 2DSC results of Ti41.5Cu42.5Ni7.5Zr2.5Hf5Si1 bulk metallic glass at various heating rates.

Heating rate (K/min) Tg (K) Tx (K) ΔTx (K) Tp (K)

5 671 700 29 71320 684 719 35 73340 690 728 38 74560 694 734 40 75080 696 737 41 755

of each temperature event (Tg, Tx and Tp) with heating rates (β), the ac-tivation energies (E) can be calculated by Kissinger method:

lnβT2

� �¼ −

ERT

þ lnARE

� �ð2Þ

where β is the heating rate, T is the variation of Tg, Tx and Tp tempera-tures, A is the frequency factor and R is a gas constant. Fig. 8 presentsthe plots of ln(β/T2) versus 1000/RT which gives a straight line withslope of Eg, Ex and Ep, respectively and intercept of ln(A/E). The obtainedactivation energies (Eg, Ex and Ep) for the first crystallization process are415.90, 301.30 and 281.33 kJ/mol, respectively. It is found that the valueof Eg is considerably higher than Ex and Ep, implying that Ti–Cu–Ni–Zr–Hf–Si BMG must overcome the higher barrier energy for atomic rear-rangement and diffusion of atoms in the supercooled liquid region be-cause the temperature during the glass transition process is lowerthan crystallization process. The frequency factors that estimate theprobability that an atom attends in the crystallization process can be de-termined from the intercept of straight lines showed in Fig. 8. The fre-quency factor values for glass transition, onset crystallization and first

Fig. 8.Kissinger plot of ln(β/T2) versus 1000/RT for Ti41.5Cu42.5Ni7.5Zr2.5Hf5Si1 bulkmetallicglass.

Table 3Activation energies calculated using Kissinger and Ozawa methods.

Activation energy (kJ/mol)

Methods Eg r2 Ex r2 Ep r2

Kissinger 415.90 0.9953 301.30 0.9973 281.33 0.9981Ozawa 406.30 0.9956 297.86 0.9975 279.11 0.9983

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crystallization peak are 1.28 × 1032, 1.09 × 1022 and 1.35 × 1020 min−1,respectively. These values are in good agreement with other previousresearch works in this field [24,32].

In order to confirm the result of theKissingermethod, the other non-isothermal equation is used to estimate the activation energy calledOzawa method:

lnβ ¼ −1:0516ERT

þ const: ð3Þ

where β, T, E and R are heating rate, the variation of Tg, Tx and Tp temper-atures, the activation energy and gas constant, respectively. Fig. 9 showsthe plots of ln(β) against 1000/RT that the slope of −1.0516E derivedfrom these straight lines. The values of Eg, Ex and Ep are 406.30, 297.86and 279.11 kJ/mol based on Ozawa equation, respectively. It can beseen that the value of Eg is higher than the values of Ex and Ep. It is gen-erally known that the barrier energy for glass transformation is higherthan crystallization transformation. The derived activation energyvalues from Kissinger and Ozawa methods are listed in Table 3. Thevalues of activation energy based on Ozawa method are less that thosevalues estimated by Kissinger method. In this respect, through analyz-ing the activation energies obtained by these two methods, we couldfind that these values were close to each other, even if there was a littlediscrepancy between them.

3.4.2. Local activation energyThe previous calculation of activation energy usually gives the aver-

age value of this energy but it is considerably important to estimate thelocal activation energy at any crystallized volume fraction as the crystal-lization proceeding. It can help us to make clear the nucleation andgrowth activation energies required for the non-isothermal crystalliza-tion. Therefore, the Ozawa–Flynn–Wall (OFW)was applied for estimat-ing the local activation energy [33]:

lnβ ¼ −1:0516E xð ÞRT xð Þ

þ const: ð4Þ

where β is heating rate, T(x) is a temperature matching to the values ofcrystallized volume fractions at different heating rates. By using exper-imental data of temperature at different heating rates, we can plotln(β) versus 1000/RT(x) (Fig. 10). The value of E(x) is obtained fromthe slope of the straight line for a certain amount of x. Fig. 11 presentsthe local activation energy at any crystallized volume fractions (x). As

Fig. 9. Ozawa plot of ln(β) against 1000/RT for Ti41.5Cu42.5Ni7.5Zr2.5Hf5Si1 bulk metallicglass.

can be observed from Fig. 11, at the initial stage of crystallizationtransformation (x b 0.05), the value of local activation energy is about282 kJ/mol. As the crystallization proceeds and the crystallized volumefraction goes into the range of 0.2–0.8, the local activation energy de-creases slowly and then becomes almost constant. At the end of crystal-lization (x N 0.8) for the first exothermic peak, the local activationenergy decreases rapidly and the value of local activation energy forx = 0.95 is about 239 kJ/mol. The crystallization process is controlledby both nucleation and growth mechanism, therefore the local activa-tion energy is composed of nucleation and growth activation energies.At early stages of crystallization (x b 0.2) the crystals begin to nucleatefrom the amorphous matrix and the large local activation energy im-plies that the nucleation process is activated. Then by the crystallizationproceeding both nucleation and growth of crystalline phase occur withalmost constant local activation energy. At the final stages (x N 0.8),crystallization is dominated by the growth of crystalline phases. There-fore, it is found that the required activation energy for crystalline phasenucleation in Ti–Cu–Ni–Zr–Hf–Si bulk metallic glassy system is higherthan growth activation energy.

3.4.3. Crystallization mechanismThe Avrami exponent commonly is used to determine the details of

nucleation and growth mechanism during the crystallization process.For isothermal condition JMAK equation is used to calculate the crystal-lization exponent [34]:

x ¼ 1− exp − k tð Þ½ �n� � ð5Þ

where x is the crystallized volume fraction, n is the Avrami exponentthat is associated with the geometry of the crystallization transforma-tion andK is the reaction constant rate that is followed by this Arrheniusequation:

K Tð Þ ¼ K0 exp −EcRT

� �ð6Þ

Fig. 10. Ozawa–Flynn–Wall plots for different crystallization volume fractions (x) inTi41.5Cu42.5Ni7.5Zr2.5Hf5Si1 bulk metallic glass (ranging from 0.1 to 0.9).

Fig. 11.Dependence of the local activation energy E(x) on crystallized volume fractions (x). Fig. 13. Local Avrami exponents at each heating rate.

169S. Haratian, M. Haddad-Sabzevar / Journal of Non-Crystalline Solids 429 (2015) 164–170

whereK0 is constant, Ec is apparent activation energy,R is a gas constant,T is the temperature. The value of n can be obtained by plottingln(− ln(1 − x)) against ln(t). It is considered that the nucleation andgrowth behavior are not constant during crystallization transformationso the local Avrami exponent was introduced. For non-isothermal crys-tallization condition the local Avrami exponent can be estimated by thisequation [35,36]:

n xð Þ ¼ −R∂ ln − ln 1−xð Þð Þ

Ex∂1T

� � ð7Þ

where n(x) is the local Avrami exponent, Ex is variation of local activa-tion energy calculated by OFWmethod, R is a gas constant, T is the tem-perature and x is crystallized volume fraction. Hence, by plottingln(− ln(1 − x)) versus 1000/T the value of n(x) at each heating ratecan be obtained from the slope of these straight lines. Fig. 12 showsthe ln(− ln(1 − x)) against 1000/T at different heating rates. The plotsof the local Avrami exponent n(x) versus the crystallized volume frac-tion (x) at different heating rates ranging from 5 to 80 K/min for Ti–Cu–Ni–Zr–Hf–Si BMG are shown in Fig. 13. It can be seen that the valuesof n(x) at different heating rates show the same tendency and they vary

Fig. 12. Plots of ln(−ln(1 − x)) against 1/T at different heating rates.

with the increasing of crystallized volume fraction (x) during the wholecrystallization process. The mechanism of nucleation and growth ateach heating rate can be determined by Ranganathan–Heimendahlequation [37–40]:

n ¼ N dimg þ B ð8Þ

where n is Avrami crystallization exponent,Ndim is growth dimension, gis growth indexwith values of 1 and 0.5 for interfaced anddiffusion con-trolled growth, respectively, and B is a nucleation index (B= 0 for zeronucleation rate, 0 b B b 1 for decreasing nucleation rate, B = 1 for con-stant nucleation rate and B N 1 for increasing nucleation rate).

According to the calculated local Avrami exponent showed in Fig. 13,the value of n(x) decreases as the crystallized fraction increases at differ-ent heating rates. When the 0 b x b 0.8 the value of n(x) is larger than2.5, whichmeans that the three-dimensional growthwith an increasingnucleation rate occurs. When the crystallized volume fraction (x)reaches to 0.8 the value of n(x) decreases, implying that the nucleationrate decreases and the crystallization is mainly governed by a three-dimensional diffusion controlled growth with decreasing nucleationrate.

4. Conclusions

In the present work, the non-isothermal crystallization kinetics ofTi41.5Cu42.5Ni7.5Zr2.5Hf5Si1 BMG was investigated. The followings areamong the main conclusions:

(1) Crystallization of Ti41.5Cu42.5Ni7.5Zr2.5Hf5Si1 BMG occurs at threestages. During the first crystallization peak TiCu formation oc-curs, while at higher annealing temperatures Ti2Ni, Cu2Ti andCu3Ti nucleate from the amorphous phase.

(2) Apparent activation energy values for the first exothermic crys-tallization peak of Ti41.5Cu42.5Ni7.5Zr2.5Hf5Si1 BMG, which obtain-ed according to Kissinger and Ozawa equations were 281.33 and279.11 kJ/mol, respectively.

(3) According to local activation energies estimated byOFWmethod,the nucleation and growth activation energies are about 282 and239 kJ/mol, respectively.

(4) Based on JMAK equation for non-isothermal condition, the localAvrami exponent gradually decreases as the crystallization pro-ceeds. The crystallization mechanism is mainly controlled bythree-dimensional growth with an increasing nucleation rate.At the final stages of crystallization the nucleation rate decreases.

170 S. Haratian, M. Haddad-Sabzevar / Journal of Non-Crystalline Solids 429 (2015) 164–170

Acknowledgments

The authors are grateful to the financial support from Ferdowsi uni-versity ofMashhad provision of laboratory facilities during this researchwas conducted.

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