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Thermochimica Acta 570 (2013) 27– 32

Contents lists available at ScienceDirect

Thermochimica Acta

jo ur nal ho me page: www.elsev ier .com/ locate / tca

he kinetic analysis of the non-isothermal crystallization process ofZr46Cu42Al7Y5)95Be5 metallic glass

iaochao Lua, Hongying Lia,b,∗, Peilu Xiaoc, Ronghai Wua,d, Dewang Lia

School of Material Science and Engineering, Central South University, Changsha, 410083 Hunan, PR ChinaKey Laboratory of Non-ferrous Materials, Ministry of Education, Central South University, Changsha, 410083 Hunan, PR ChinaPowder Metallurgy Research Institute, Central South University, Changsha, 410083 Hunan, PR ChinaUniversity of Erlangen-Nuremberg, Institute of Materials Simulation, Dr.-Mack-Street 77,90762 Furth, Germany

r t i c l e i n f o

rticle history:eceived 27 May 2013eceived in revised form 24 July 2013ccepted 28 July 2013vailable online 6 August 2013

a b s t r a c t

The crystallization processes of three clearly separated crystallization peaks of (Zr46Cu42Al7Y5)95Be5

metallic glass, under non-isothermal condition, are studied using differential scanning calorimetry (DSC)technique. It was found that the crystallization processes of (Zr46Cu42Al7Y5)95Be5 metallic glass repre-sent the complex processes, where there are conversion regions with a constant value of the activationenergy (E˛). The pre-exponential frequency A(˛) was determined from the linear relation, known as the

eywords:Zr46Cu42Al7Y5)95Be5 glassifferential scanning calorimetryon-isothermal crystallizationyazovkin methodaster plots method

kinetic compensation effect. The invariant kinetic parameters (ln Ainv, E˛,inv) for the three crystallizationprocesses were calculated, which is approximately the average values obtained by the Vyazovkin methodin the considered interval. Finally, the master plots method was successfully utilized to determine thereaction model, and the best reaction models for describing the three crystallization kinetic processesare A2, A3/2 and A3/2, respectively.

© 2013 Elsevier B.V. All rights reserved.

. Introduction

Amorphous alloys have received considerable attention inecent years due to their superior physical and chemical prop-rties [1]. Bulk metallic glass alloys with different sizes andhapes have been produced by a variety of techniques in theast few decades. Among all the created bulk metallic glasses,r-based metallic glasses have been widely investigated due toheir good glass-forming ability and mechanical properties, suchs high strength, high elastic strain, and low Young’s modulus2,3]. Zr-based metallic glasses have been successfully applieds sporting goods, surgical instrument electronic devices, etc.he studies of crystallization kinetics are of great important forhe determination of the stability of amorphous materials andheir possible practical applications [4,5]. It is also helpful innderstanding the crystallization mechanism and directing the

ubsequent annealing processing of amorphous glass [6]. Differen-ial scanning calorimetry (DSC) is the most commonly used methodor studying the behavior of crystallization kinetics in Zr-based

∗ Corresponding author at: School of Material Science and Engineering, Centralouth University, Changsha, 410083 Hunan, PR China. Tel.: +86 731 8883328; fax: +86 731 8883 6328.

E-mail address: lhying@csu.edu.cn (H.Y. Li).

040-6031/$ – see front matter © 2013 Elsevier B.V. All rights reserved.ttp://dx.doi.org/10.1016/j.tca.2013.07.028

metallic glasses [7–9]. There are a lot of research works on thecrystallization kinetics of Zr-based metallic glasses in recent years.However, the research report on the behavior of crystallizationkinetics of (Zr46Cu42Al7Y5)95Be5 glass has not been found in pre-vious literatures. In present work, the behavior of crystallizationkinetics of (Zr46Cu42Al7Y5)95Be5 glass was studied by the DSCtechnique under non-isothermal conditions for different heatingrates. From DSC data, the kinetic parameters, such as activationenergy E, pre-exponential factor ln A and analytical form of reac-tion model function g(˛), was estimated using the isoconversional,isokinetic, invariant kinetic parameters (IKP) methods and masterplots method.

2. Theoretical basis

2.1. Isoconversional (model-free) methods

Any kinetic analysis (DSC, DTA, TG, etc.) of non-isothermal datais based on the rate equation [10]:

d˛ =(

A)

exp(

− E)

f (˛) (1)

dT ˇ RT

where is the transformed fraction, T the temperature, the heat-ing rate, A the pre-exponential factor, E the activation energy, f(˛)a dependent kinetic model function, and R the gas constant.

2 imica

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˚

wivf

I

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2

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l

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vm

2

aaw

8 X.C. Lu et al. / Thermoch

This equation can be integrated by separation of variables:

(˛) =∫ ˛

0

d˛

f (˛)=

(A

ˇ

)∫ T

T0

exp(

− E

RT

)dT

= AE

ˇRp(x) =

(A

ˇ

)I(E, T) (2)

here T0 is the initial temperature of non-isothermal experi-ent, g(˛) is the integral form of the model function, and p(x)

s the temperature integral, for x = E/RT, which does not havenalytical solution. Several approximations were introduced toolve the temperature integral in Eq. (2). In general, all of thesepproximations lead to a direct isoconversional method. The mostopular isoconversional methods used for calculation of the acti-ation energy are Kissinger–Akahira–Sunose, Ozawa–Flynn–Wallre popular isoconversional methods for calculating the activationnergy [11]. However, the systematic error is unavoidable in thesewo methods. By contrast, Vyazovkin isoconversional method [12]s a non-isothermal method that utilizes an accurate, non-linear,enum–Yang approximation [13] of the temperature integral, lead-ng to an accurate estimation of E. Therefore, the Vyazovkin method

as adopted to calculate the activation energy in present work,hich gives:

=

∣∣∣∣∣∣n∑

i=1

n∑j /= i

I(E˛,T˛i)ˇj

I(E˛, T˛j)ˇi

∣∣∣∣∣∣ (3)

here n is the number of heating rates, i and j denote different heat-ng rates. The activation energy can be determined at any particularalue of by finding the value of E˛ which minimizes the objectiveunction ˚.where the integral temperature I(E, T) is given by:

(E, T) =∫ T˛

T˛−�˛

exp(

− E

RT

)dT (4)

The temperature integral I(E, T) was evaluated using the fourthational approximation of Senum–Yang [13]. The minimizationrocedure is repeated for each value of to find the dependencef E˛ on ˛. Uncertainties were calculated according to the fact thathe variance to the minimal variance ratio follows the F-distributionassuming a 90% confidence range) [14].

.2. Isokinetic (model-fitting) method

For non-isothermal experiments, model-fitting methodsnvolve fitting different kinetic models to the conversion-emperature curves and simultaneously determining the activationnergy E and the pre-exponential factor A. Among a lot of non-sothermal model-fitting methods, the Coats–Redfern method15,16] is one of the most popular one. This method is based onhe equation:

n(

g(˛)T2

)= ln

(AR

ˇE

[1 −

(2RT∗

E

)])− E

RT(5)

here T* is the mean experimental temperature.From the slope and intercept of a straight line of ln (g(˛)/T2)

ersus 1/T, E˛ and A can be calculated for a particular reactionodel.

.3. Compensation effect

Using the Coats–Redfern method (Eq. (6)), for each heating ratend for each reaction model g(a), a pair of kinetic parameters ln Ajnd E˛j are established. The compensation effect always existshen the reaction model changes. The compensation parameters

Acta 570 (2013) 27– 32

a� and b� , which represents the compensation effect relation, aredetermined in accordance with Eq. (7) [17,18]:

ln Aj = a� + b�E˛j (6)

where Aj and E˛j are the corresponding values of the kinetic param-eters. They are attributed to the j-th reaction model that listed inRef. [19] for a given heating rate ˇ. a is an artificial isokinetic rateconstant (a� = ln Kiso) and constant b is given by (b� = 1/RTiso) whereKiso is an artificial isokinetic rate constant and Tiso is an artificialisokinetic temperature [20–22].

2.4. Invariant kinetic parameters method (IKP)

The straight lines ln Aj vs. E˛j for several heating rates shouldintersect in a point which corresponds to the true values of ln A andE˛. These were called the invariant activation parameters (ln Ainv,E˛,inv) by Lesnikovich and Levchik [23,24] as they are independentof the conversion, the model and the heating rate. The evaluation ofthe invariant activation parameters is performed from the super-correlation relation:

a� = ln Ainv − b�E˛,inv (7)

Thus, the straight line av vs. bv allows us to determine theinvariant kinetic parameters (ln Ainv, E˛,inv), from the slope and theintercept.

2.5. Master plots

The master plots have been widely used to determined thekinetic model function g(˛). By comparing the theoretical masterplots, which are obtained for a wide range of ideal kinetic models,with the experimental master plot, the appropriate kinetic modelfor the crystallization reaction investigated is selected. Using thereference point at a = 0.50, the following integral master equationcan be derived from Eq. (2):

g(˛)g(0.50)

= p(x)p(x0.50)

(8)

where p(x0.50) is the temperature integral at the value of a = 0.50. Inthis paper, the fourth rational approximation of Senum–Yang [13]is used for p(x).

3. Experimental

Ingot of (Zr46Cu42Al7Y5)95Be5 (nominal composition, at.%)metallic glass was prepared by arc melting pure metal elements:Zr (99.99%), Cu (99.99%), Al (99.99%), Y (99.99%) and Be (99.97%)in a Ti-gettered argon atmosphere. Each ingot was melted atleast five times to ensure the homogeneity. The alloy ingot wasremelted in a fused glass tube under a vacuum level of about5 × 103 Pa and then injection cast with ultrahigh purity argon intoa copper mold to prepare cylindrical rods of 3 mm diameter and100 mm length. X-ray diffraction (XRD) with Cu K˛1 (� = 1.5404 A)radiation for phase identification was performed on the as-castsamples via 20◦–80◦ scans. A scan speed of 2◦/min and a chartspeed of 1 cm/min were maintained. The X-ray diffraction tracesof (Zr46Cu42Al7Y5)95Be5 metallic glass are shown in Fig. 1. Onlya broad diffraction peak at the position of about 2� = 37 ◦can beobserved and no appreciable diffraction peaks corresponding to

crystalline phases are detected, indicating a fully amorphous singlephase in the metallic glass. The crystallization kinetics of the metal-lic glass was studied by DSC in argon atmosphere using a NetzschSTA 449C device.

X.C. Lu et al. / Thermochimica Acta 570 (2013) 27– 32 29

4

(1cst(iTrorTwtcl

wtvf[(cactr2cctecv

F2

Fig. 1. X-ray pattern of (Zr46Cu42Al7Y5)95Be5 metallic glass.

. Results and discussion

The typical DSC curves of crystallization process ofZr46Cu42Al7Y5)95Be5 metallic glass at the heating rates of0, 20, 30 and 40 K/min are shown in Fig. 2. It can be seen that allurves exhibit a distinct glass transition, followed by an obviousupercooled liquid region, and then crystallization. There arehree exothermic peaks clearly separated in the DSC curves ofZr46Cu42Al7Y5)95Be5 metallic glass at all heating rates, whichndicates three stages of the crystallization. The temperaturesg, Tx, and Tp, which are marked by arrows in the DSC curves,epresent the glass transition temperature, the onset temperaturef crystallization and the peak temperature of crystallization,espectively. It is evident that the crystallization temperatures Tp1,p2 and Tp3 for all three stages shift to higher temperature sideith increasing heating rates. This indicates that the crystallization

emperatures exhibit a dependence on the heating rate during theontinuous heating. A similar behavior has been reported in manyiteratures [25,26].

From DSC data for each heating rate, the Vyazovkin methodas used to investigate the variation of the activation energy with

ransformed fraction ˛. The model-free method allows the acti-ation energy to be estimated as a function of the transformedraction without making any assumptions about the reaction model27,28]. Fig. 3 shows the variation of E˛ as a function of forZr46Cu42Al7Y5)95Be5 metallic glass. As can be seen, at the loweronversions (up to = 0.35), the value of E˛ show a little vari-tion with an average value of 284.09 ± 5.31 kJ/mol for the firstrystallization peak, which indicates that crystallization occurshrough a single mechanism. After = 0.35, in the conversionange of 0.40 ≤ ≤ 0.95, E˛ value shows a dramatic decrease from67.76 ± 7.39 kJ/mol to 173.43 ± 8.58 kJ/mol in the E˛ value. Thehange of E˛ with increasing reveals for 0.35 ≤ ≤ 0.95 that therystallization reaction changes to a multiple-step mechanism. For

he second crystallization peak, the value of E˛ increases mod-rately from 246.48 ± 13.14 kJ/mol to 303.04 ± 8.35 kJ/mol in theonversion range of 0.05 ≤ ≤ 0.30. It was found that in the con-ersion range of 0.35 ≤ ≤ 0.95, the E˛ value is almost stable, and

ig. 2. DSC curves of (Zr46Cu42Al7Y5)95Be5 metallic glass at the heating rates of 10,0, 30 and 40 K/min.

Fig. 3. The variation of E˛ as a function of for (Zr46Cu42Al7Y5)95Be5 metallic glass.

the value of E˛ can be taken as a constant. For a given conversionrange, the average values of E˛ estimated are 316.43 ± 6.93 kJ/mol.The value of E˛ relatively constant with respect to conversiondegree in the range of 0.05 ≤ ≤ 0.70 for the third crystallizationpeak. It was found that the average value of E˛ in the range of0.05 ≤ ≤ 0.70 is equal to 287.28 ± 11.38 kJ/mol. In addition, for

≥ 0.70, we can detect a sharp decreases from 279.05 ± 7.06 kJ/molto 248.52 ± 3.88 kJ/mol in the E˛ value.

As reported by Chen et al. [29], the first crystallization peakmay correspond to partial crystallization of amorphous phase intothe CuZr phase as the primary phase at the initial stage, and thenthe significant decrease in the E˛ value is associated with theprecipitation of a mixture of CuZr and Cu10Zr7 as binary eutec-tic. It can be point out that the obtained average value of E˛

(284.09 ± 5.31 kJ/mol) is in agreement with the value reported byKim et al. [30] (281 kJ/mol) for Cu43Zr43Al7Be7. However, CuZrphase, which is a metastable phase with B2 structure, tends todecompose into Cu10Zr7 and CuZr2 at low temperatures (<988 K).Stasi et al. [31] argue that the decomposition of CuZr phase maybe the cause of the appearance of the second endothermic peak inthe DSC traces. According to the study of Park et al. [3], it can beconcluded that the appearance of the third endothermic peak inthe DSC traces may be related to the precipitation of Be-containingcompound.

It is shown in Fig. 3 that E˛ is independent of the transformedfraction in the range of 0.05–0.35 for the first crystallization peak,0.35–0.95 for the second crystallization peak and 0.05–0.70 thethird crystallization peak. Model-fitting and IKP have been appliedacross those intervals.

The kinetic parameters ln Aj and E˛j for the crystallization pro-cess of (Zr46Cu42Al7Y5)95Be5 metallic glass can be obtained usingthe Coats–Redfern method for each heating rate and for each reac-tion model (the figure not shown). According to the compensationeffect, the values of ln Aj and E˛j of different reaction models arerelated linearly at a given heating rate and the results are shown inFig. 4. The values of the compensation parameters a, b, Kiso, and Tisofor (Zr46Cu42Al7Y5)95Be5 metallic glass are given in Table 1. As can

be seen, the values of isokinetic parameters Kiso and Tiso increasewith increasing of the heating rate. The values of Tiso may lie outof the region of the experimental temperatures when a reactionmodel was not properly assumed [18,19]. Besides, the isokinetic

30 X.C. Lu et al. / Thermochimica Acta 570 (2013) 27– 32

Table 1The values of a, b, Kiso , and Tiso for the crystallization process of (Zr46Cu42Al7Y5)95Be5 metallic glass at different heating rates.

Crystallization peaks (K/min) a� (min−1) b� (×10−4 mol/kJ) Kiso (min−1) Tiso (K) Rca

First peak 10 0.4345 ± 0.3481 1.6161 ± 0.0017 1.5442 744.25 0.999820 1.0904 ± 0.3409 1.5930 ± 0.0016 2.9754 755.05 0.999830 1.3457 ± 0.5217 1.5835 ± 0.0025 3.8408 759.58 0.999540 1.7924 ± 0.3413 1.5682 ± 0.0018 6.0041 766.98 0.9998

Second peak 10 −2.1772 ± 0.3819 1.4295 ± 0.0080 0.1134 841.42 0.999420 −1.5551 ± 0.3638 1.4092 ± 0.0073 0.2112 853.56 0.999530 −1.2266 ± 0.3615 1.3991 ± 0.0077 0.2933 859.71 0.999440 −0.8875 ± 0.3594 1.3884 ± 0.0071 0.4117 866.31 0.9995

Third peak 10 −0.9890 ± 0.4511 1.3136 ± 0.0053 0.3720 915.67 0.999720 −0.2291 ± 0.4125 1.2880 ± 0.0047 0.7953 933.82 0.999730 0.1901 ± 0.4132 1.2728 ± 0.0045 1.2094 945.01 0.9998

1.2654 ± 0.0046 1.5085 950.52 0.9997

tp

itEtflfi3of

tc˛isott

F(

40 0.4111 ± 0.4134

a Rc represents the coefficients of linear correlations.

emperatures Tiso lies within the region of the experimental tem-eratures, indicating the reaction model g(˛) is a properly chosen.

Using the super correlation relation (Eq. (6)), the correspond-ng values of the invariant kinetic parameters (ln Ainv, E˛,inv) forhe three crystallization processes were calculated. The results are˛,inv = 282.76 ± 2.30 kJ/mol, ln Ainv = 46.13 ± 0.37 for the first crys-allization peak, E˛,inv = 314.10 ± 3.08 kJ/mol, ln Ainv = 42.72 ± 0.43or the second crystallization peak and E˛,inv = 289.70 ± 3.42 kJ/mol,n Ainv = 37.07 ± 0.44 for the third crystallization peak. It can beound that the values of the invariant kinetic parameter E˛,invs approximately the average values of E˛ (284.09 ± 5.31 kJ/mol,16.43 ± 6.93 kJ/mol, and 287.28 ± 11.38 kJ/mol) which werebtained using the Vyazovkin method in the considered intervalor the three crystallization peaks, respectively.

Once the correlation parameters a and b have been evaluated,he values of E˛ are substituted for E˛j in Eq. (7) to estimate theorresponding ln A values and obtaining the dependence of ln A on. This procedure could be applied for multi-step reactions that

nvolving several processes, as it is originally applied to a single-tep process [18,32]. Fig. 5 shows the variation of ln A as a functionf the ˛, for (Zr Cu Al Y ) Be metallic glass. It is clear from

46 42 7 5 95 5his figure that this dependence (ln A versus ˛) is typically same ashat of E˛ on due to the linear dependence between ln A and E˛

ig. 4. The isokinetic relationships (ln Aj vs. E˛j) for the crystallization process ofZr46Cu42Al7Y5)95Be5 metallic glass at different heating rates.

Fig. 5. The variation of ln A as a function of for (Zr46Cu42Al7Y5)95Be5 metallic glass.

(Eq. (6)). After determining the experimental values of E˛ and ln Aone can determine the reaction model numerically.

It is helpful to verify function of reaction mechanism whichwill properly describe the investigated crystallization processes inthe sake of applying the integral master plot method at the differ-

ent heating rates for each crystallization peak. Figs. 6–8 show theexperimental master plot for the three crystallization processes of(Zr46Cu42Al7Y5)95Be5 metallic glass at the different heating rates,

Fig. 6. The experimental master curve for the first crystallization processes of(Zr46Cu42Al7Y5)95Be5 metallic glass at the different heating rates (the solid line wascalculated from the theoretical models).

X.C. Lu et al. / Thermochimica Acta 570 (2013) 27– 32 31

Table 2The values of SD of the possible reaction models for the first and second crystallization kinetic process of (Zr46Cu42Al7Y5)95Be5 metallic glass.

SD P1 P2 P3 R2 A2 A3 A4 A3/2

First crystallization peak 0.3017 0.2737 0.2295

Third crystallization peak 0.1933

F(

reFca(gt(oghtiomcamtttpm

F(c

ig. 7. The experimental master curve for the second crystallization processes ofZr46Cu42Al7Y5)95Be5 metallic glass at the different heating rates.

espectively. The solid lines were calculated according to the mod-ls in the Ref. [19]. For the first crystallization peak, as shown inig. 6, it can be inferred that the behavior of the crystallization pro-ess can be characterized predominantly by the random nucleationnd growth of nuclei model, know as the Avrami-Eroféev modelAm, m(1 − ˛)[−ln (1 − ˛)](1 − (1/m)), m stands for integer values ran-ing from 1 to 4 when the growth rate of nuclei is proportional tohe interphase area, but it would also stand for non-integer values1/2, 3/2 or 5/2) for some cases of diffusion controlled rate of growthf nuclei). The experimental points at lower conversions ( < 0.50)enerally lie on the A4 master curve for all heating rates and atigher conversions ( > 0.50), the experimental points lie betweenhe A3 and A3/2 master curves. For higher conversions, it would benteresting that the experimental master curves tend to lie moren the A3 master curve at the heating rate of 10 K/min, on the A2aster curve at the heating rate of 20 K/min, on the A3/2 master

urve at the heating rate of 30 K/min and 40 K/min. This may given indication that as the heating rate increases, the crystallizationechanism changes to a lower exponent n, which might ascribed

o the relative contribution from nucleation and crystal growth. Inhe initial stage, model A4 is observed because of nucleation and

hree-dimensional crystal growth. However, as the crystallizationroceeds, nucleation may become increasingly unimportant, anday eventually stop. Therefore, the overall crystallization kinetics

ig. 8. The experimental master curve for the third crystallization processes ofZr46Cu42Al7Y5)95Be5 metallic glass at the different heating rates (the solid line wasalculated from the theoretical models).

0.1759 0.0951 0.1561 0.2061 0.11240.0388 0.0324

may transform from A4 to A3 (or lower) when nucleation ceases.Close to the end of crystallization, spheroidal crystals may impingeon their neighbors or on the walls of the container, resulting inloss of one or two dimensions of growth. Therefore, the dimensionof crystal growth may be reduced near the end. This explanationis supported by the microscopic observation of Chen et al. [29].To choose an acceptable reaction model, a method based on thestandard deviation between the theoretical master data and theexperimental ones was used. The criterion for selecting acceptablemodels can also be taken as follows [5]

SD =

√√√√∑∑[gk(˛i)gk(0.5) − pj(xi)

pj(x0.5)

]2

(n − 1)(m − 1)(9)

where m and n are numbers of points and heating rates, respec-tively. The value of SD is the average square of the deviationbetween p(x)/p(x0.5) calculated on the base of experiment andgk(x)/gk(0.5), in which k denotes the serial number of model func-tions listed in Ref. [19]. If a model describes the experimental resultsaccurately, it is possible to find a minimum for SD.

The values of SD of the possible reaction models are listed inTable 2, in which models A2 shows minimum of SD. This indicatesthe first crystallization kinetic process of (Zr46Cu42Al7Y5)95Be5metallic glass could probably be described by an Avrami-Eroféevmodel A2 (g(x) = [−ln (1 − ˛)]1/2).

For the second crystallization peak, as can be seen in Fig. 7,the experimental master plot of the different heating rates arepractically identical, indicating that there is no change in mech-anism with a change in the heating rate. It might be becausethe decomposition of CuZr phase regard the pre-existing Cu10Zr7particle as the nucleus and only crystal growth is observed. Thecomparisons of the experimental master plot with theoreticalones indicates that the second crystallization kinetic process of(Zr46Cu42Al7Y5)95Be5 metallic glass agree with the A3/2 mastercurve very well. This suggests the best reaction model chosen forthe second crystallization kinetic process of (Zr46Cu42Al7Y5)95Be5metallic glass is A3/2 (Avrami-Eroféev with the power exponent1.5, i.e. g(x) = [−ln (1 − ˛)]2/3) for the whole range at all heatingrates.

For the third crystallization peak, from Fig. 8, the experimentalmaster plots of the different heating rates are also practically iden-tical, but none of theoretical master plots matches the experimentalones perfectly. It can be seen the experimental points at lower con-versions ( < 0.50) generally lie on the A2 master plot for all heatingrates and at higher conversions ( > 0.50) lie between the A2 andA3/2 master plots. The values of SD of the possible reaction modelsare also listed in Table 2. As can be seen the A3/2 reaction modelcould perfectly describe the third crystallization kinetic process of(Zr46Cu42Al7Y5)95Be5 metallic glass.

5. Conclusion

In present work, the crystallization processes of three clearlyseparated crystallization peaks of (Zr46Cu42Al7Y5)95Be5 metallic

glass, under non-isothermal condition, are studied using differ-ential scanning calorimetry (DSC) technique. From DSC data, theactivation energy (E˛), pre-exponential frequency A(˛) and kineticmodel function g(˛) was estimated using the isoconversional,

3 imica

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[

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[

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[

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metallic glasses, Journal of Optoelectronics and Advanced Materials 10 (2008)

2 X.C. Lu et al. / Thermoch

sokinetic and master plots methods. It was found that the crystal-ization processes of (Zr46Cu42Al7Y5)95Be5 metallic glass representhe complex processes, where there are conversion regions with aonstant value of the activation energy (E˛). The pre-exponentialrequency A(˛) was determined from the linear relation, knowns the kinetic compensation effect. The invariant kinetic param-ters (ln Ainv, E˛,inv) for the three crystallization processes werealculated, which is approximately the average values obtained byhe Vyazovkin method in the considered interval. The best reac-ion models chosen for describing the three crystallization kineticrocesses are A2, A3/2 and A3/2, respectively.

cknowledgement

The authors like to acknowledge the collaboration and stimu-ating discussions with Liu Jiaojiao.

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