Journal of Non-Crystalline Solids 404 (2014) 7–12

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Journal of Non-Crystalline Solids

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Crystallization kinetics of Cu38Zr46Ag8Al8 bulk metallic glass in differentheating conditions

J. Cui a, J.S. Li a, J. Wang a,⁎, H.C. Kou a, J.C. Qiao b, S. Gravier c, J.J. Blandin c

a State Key Laboratory of Solidification Processing, Northwestern Polytechnical University, Xi'an 710072, Shaanxi Province, PR Chinab Université de Lyon, CNRS, INSA-Lyon, MATEIS UMR5510, F-69621 Villeurbanne, Francec SIMAP, INP Grenoble/CNRS/UJF, 38402, Saint-Martin d'Hères, Cedex, France

⁎ Corresponding author. Tel.: +86 29 8846 0568; fax: +E-mail address: nwpuwj@nwpu.edu.cn (J. Wang).

http://dx.doi.org/10.1016/j.jnoncrysol.2014.07.0290022-3093/© 2014 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 16 April 2014Received in revised form 17 July 2014Available online 10 August 2014

Keywords:Bulk metallic glass;Crystallization kinetics;Activation energy;Kissinger and Johnson–Mehl–Avrami;Local Avrami exponent

The crystallization kinetics of Cu38Zr46Ag8Al8 bulk metallic glass in non-isothermal mode and isothermal modeare investigated by differential scanning calorimetry. In non-isothermal conditions, the average value ofactivation energy is determined by Kissinger equation, and the value is around 310 kJ/mol. The crystallizationenthalpy is about 28.69 J/g. In addition, the local Avrami exponent is adopted to describe the crystallizationprocess. In isothermal route, the average value of activation energy for crystallization is calculatedby theArrheniusequation, and the value is about 451 kJ/mol. The crystallization enthalpy is about 1.63 J/g. And the Avramiexponent n ranges from 4.10 to 4.74, which indicates that the crystallization mechanism is mainly governed byconstant nucleation rate. The created phases in the two conditions are different which can be confirmed by theX-ray diffraction test, this result is in accordance with the different crystallization enthalpies, but it's differentwith other investigations.

© 2014 Elsevier B.V. All rights reserved.

1. Introduction

Compared with their crystalline counterparts, bulk metallic glasses(BMGs) have a series of special combination of structural and functionalproperties, such as higher strength, larger elasticity, lower elasticmodulus andexcellent corrosion resistance due to the lackof translationalor orientational long-range order [1,2]. Namely, there are no conventional“defects” in bulk metallic glasses [3–8], such as grain boundary anddislocations. Therefore, bulk metallic glasses are potential materialswhich can be applied on structural and functional materials.

In recent years, Cu-based bulk metallic glasses have been widelyinvestigated due to their excellent glass forming ability, good thermalstability, wide supercooled liquid region (SLR) and high mechanicalproperties at room temperature, as well as the containing of relativelylow cost elements [9–11]. Therefore, it is an ideal candidate which canbe applied in near shape fabri cation of precise and complex-shapedcomponents by means of the thermal plastic forming (TPF) method.During the process of TPF, crystallization of BMGs must be avoided,since crystallization or partial crystallization of BMGs will lead to adrastic degradation of mechanical properties at room-temperature[12]. In other words, crystallization makes BMG parts unsafe. Based onthis discussion, if we want to avoid crystallization effectively, it'smeaningful to understand the crystallization kinetics of BMG.

86 29 8846 0294.

However, BMGs tend to transfer from amorphous state to crystallinestate by thermal annealing. Moreover, thermal stability always links tothe mechanical properties in BMGs. Thus, it is very necessary toinvestigate the thermal stability and crystallization behavior in bulkmetallic glasses. In general, differential scanning calorimetry (DSC) ordifferential thermal analysis (DTA) is widely used to research thermalstability and crystallization behavior in amorphous materials [13–18].The properties for amorphous materials, such as glass transitiontemperature (Tg), temperature corresponding to the onset of crystal-lization (Tx), crystallization peak temperature (Tp) and crystallizationenthalpy could be obtained from theDSC curves. Furthermore, apparentactivation energy could be calculated by relevant models from the DSCdata. In effect, thermal stability and crystallization behavior restrict theapplications of bulk metallic glasses.

It is well-known that there are two steps leading crystallizationduring the process of TPF: continuous heating from low temperature(non-isothermal mode) and annealing at a given temperature (isother-mal mode). For these twomodes of crystallization, all we are concernedabout are the activation energy of crystallization and the description ofwhole crystallization process. There are different methods that canbe employed to describe activation energy of crystallization, suchas Kissinger method [19]and Friedman method [20] and many subjectmatters are modeled to analyze the thermoanalytical kinetic patterns[21,22]. It should be noted that Johnson–Mehl–Avrami (JMA) model isalways used to describe the crystallization process and gives goodresults [23–27], for example, Xie et al. [28] adopted this method in

8 J. Cui et al. / Journal of Non-Crystalline Solids 404 (2014) 7–12

Cu50Zr45Ti5 BMG. Moreover, this method also can be used for any kindof phase transformation.

Therefore, themain purpose of this work is to investigate crystalliza-tion transformation kinetics in the non-isothermal and isothermalmodes of Cu38Zr46Ag8Al8 bulk metallic glass by DSC. In addition,the research can provide some new insight to further understandcrystallization transformation kinetics, relevant thermal stabilityand physical properties in bulk metallic glasses.

2. Experimental procedure

2.1. Sample preparation

The pre-alloyed ingot of Cu38Zr46Ag8Al8 (at%) BMG was preparedby arc melting under a purified argon atmosphere in a water-cooledcopper crucible and in situ suction casting into a water-cooledcopper mold, then the rods of BMG with a diameter around 3 mmwere fabricated. Purity of the elements was above 99.9%. The ingotwas re-melted several times in order to ensure the homogeneity.The DSC samples were mechanically cut from as-cast rods, and thesurfaces of samples were carefully polished and finally washed inethanol by an ultrasonic cleaning machine in order to remove thesurface oxidation before the DSC experiments. The amorphicity ofCu38Zr46Ag8Al8 BMG was detected by means of X-ray diffraction(XRD, DX-2700).

2.2. DSC experiments

The information of thermal properties and phase transformationwere determined by differential scanning calorimetry (DSC, PerkinElmer, Diamond) under a high purity flowing argon gas atmospherewith the flowing rate of 20 ml/min and alumina pans were used assample holders, and the temperature accuracy is ±0.01 K.

The non-isothermal DSC experiments were carried out by usingdifferent steadyheating rates from2.5 K/min to 20 K/min. The isothermalcrystallization experiments were performed in the supercooled liquidregion (SLR) of Cu38Zr46Ag8Al8 BMG. The samples were heated up tothe annealing temperature at a heating rate of 20 K/min, then holdingat the selected temperatures until the crystallization completed, afterthat, samples were cooled down to room temperature.

3. Results and discussion

3.1. Non-isothermal crystallization behavior

The crystallization peaks of DSC curves in Cu38Zr46Ag8Al8 BMGperformed at different heating rates are shown in Fig. 1. The heating

Fig. 1. The crystallization part of DSC curves in Cu38Zr46Ag8Al8 bulk metallic glass withvarious heating rates.

rates are chosen as 2.5 K/min, 5 K/min, 10 K/min and 20 K/min, respec-tively. As can be seen from Fig. 1, crystallization only induces a singlepronounced exothermic peak at each heating rate, and the position ofpeak shifts to higher temperature with the increase of heating rate.Therefore, the crystallization process in this alloy is simple, and thecrystallization kinetics can be analyzed directly. By contrast with thesingle exothermic peak, there are also complex exothermic peaks thatexist in other kinds of BMGs. For example, double exothermic peakscan be obtained in classical VIT1 BMG [29], and three exothermicpeaks can be obtained in Cu52.5Ti30Zr11.5Ni6 BMG [30], all of thesepeaks correspond to the multiplestage crystallization modes. For thesealloys, the crystallization kinetics is difficult to analyze, since all thecontributions have to be discussed separately. The XRD patterns of thecrystallized BMG are shown in Fig. 2, from which we can see thatthere are two created phases in non-isothermal condition: CuZr phaseand AlAg phase, and three created phases in isothermal condition:CuZr phase, AlAg phase and AgZr phase. The different created phasesin the two heating conditions can also be confirmed by the differentcrystallization enthalpy, which have been done in the following sections.And the result is different with the former research by Wei, et al. [31].

If wewant to analyze the crystallization kinetics during thewholeprocess, the activation energy of the BMG in different crystallizationvolume fraction must be obtained. Before that, the crystallizationvolume fraction for non-isothermal crystallization, α, should beobtained, which can be deduced as a function of temperature fromDSC curves by using the following equation [32–35]:

α ¼

Z T

T0

dHc=dTð ÞdTZ T∞

T0

dHc=dTð ÞdT¼ A0

A∞ð1Þ

where T0 and T∞ are the temperatures at which crystallization beginsand ends in amorphous materials, dHc/dT is the heat capacity in aconstant pressure, and A0 and A∞ are the areas under the DSC curves.The relationship between crystallization fraction and temperature atdifferent heating rates is shown in Fig. 3, all the curves exhibit typicalS-shaped type in different heating rates. Finally, the samples frommetastable state transfer to a more stable state.

The crystallization quantity in non-isothermal condition can beidentified by calculating the area of crystallization enthalpy by usingthe following equation:

ΔH ¼ 1Rh

Z T∞

T0

W Tð ÞdT ð2Þ

whereΔH is crystallization enthalpy,W(T) is heatflow, and Rh is heatingrate. From this equation, the crystallization enthalpy can be calculated;

Fig. 2. XRD patterns of crystallized Cu38Zr46Ag8Al8 bulk metallic glass in differentconditions.

Fig. 3. Relationship between crystallization fractionα and temperature at different heatingrates as a guide to the eyes.

Fig. 5. Relationship between ln[−ln(1−α)] and 1000/T of Cu38Zr46Ag8Al8 bulk metallicglass at different heating rates as a guide to the eyes.

9J. Cui et al. / Journal of Non-Crystalline Solids 404 (2014) 7–12

the crystallization enthalpy is 25.92 J/g at a heating rate of 2.5 K/min,27.24 J/g at 5 K/min, 28.8 J/g at 10 K/min and 32.79 J/g at 20 K/min.The result indicates that the crystallization enthalpy is independent ofheating rate, and it almost maintains the same level, which also meansthat the created phases are the same at these heating rates.

3.1.1. Activation energyThe apparent activation energy, Ea, for glass transition or crystalliza-

tion of amorphous materials under continuous heating conditions canbe determined by the Kissinger equation [36–38]:

lnRh

Tp2

!¼ − Ea

RTpþ C ð3Þ

where Tp is the temperature corresponding to the maximum ofcrystallization peak (in here, it indicates the maximum temperaturevalue of each curve in Fig. 1), and the approximate straight line couldbe obtained by using Kissinger method to fit the experimental values,the result is shown in Fig. 4. From the slope of this line, we can calculatethe activation energy; the value is about 310 kJ/mol in non-isothermalheating conditions.

3.1.2. Crystallization mechanismFor non-isothermal conditions, the Avrami exponent n can be

obtained by plotting ln[−ln(1−α)] vs. 1/T, which can be fitted by astraight line with a slope nEc/R, then the value of Avrami exponent, n,can be calculated. Fig. 5 shows the curves of ln[−ln(1−α)] vs. 1000/T

Fig. 4. Kissinger plot of Cu38Zr46Ag8Al8 bulk metallic glass in non-isothermal condition.The peak temperatures in 4 heating rates are: 758 K, 768 K, 778 K and 790 K. The fit hasR2 value of 0.998. The solid line is fitted by Eq. (3), and the activation energy is about310 kJ/mol.

at heating rate of 2.5, 5, 10, and 20 K/min, respectively. It can be seenthat in the whole process, the Avrami exponent is different with manydistinct stages. So the local Avrami exponent n(α) should be introduced.In order to calculate the local Avrami exponent for non-isothermalcrystallization, we adopt the equation as follows [39]:

n αð Þ ¼ −R∂ ln − ln 1−αð Þ½ �Ea∂ 1=Tð Þ : ð4Þ

Based on this equation, the local Avrami exponents at heating ratesfrom 2.5 K/min to 20 K/min are calculated, the results are shown inFig. 6. It can be seen that the Avrami exponents at different heatingrates display the same tendency and they vary with the increase ofcrystallization fraction during the whole process. Initially, when α isbetween 20% and 80% the n(α) is larger than 4, which means that thenucleation rate increases with time, and the crystallization quantityincreases rapidly. When the α reaches 80%, the n(α) value is back to3–4, it means that the crystallization progresses with a decreasingcrystallization rate, the main reason is due to the lack of solvend.

3.2. Isothermal crystallization behavior

Isothermal crystallization of the metallic glass is carried out in theSLR, i.e. above the glass transition temperature (Tg) and below thetemperature corresponding to the onset of crystallization (Tx). Thesamples are heated up to the annealing temperature with the heatingrate of 20 K/min and then held until the crystallization is completed.Finally, samples are cooled down to room temperature.

Fig. 6. Relationship between local Avrami exponent n(α) and crystallization volumefraction at different heating rates as a guide to the eyes.

Fig. 8. The crystallization part of DSC curves in Cu38Zr46Ag8Al8 bulk metallic glass atdifferent annealing temperatures.

10 J. Cui et al. / Journal of Non-Crystalline Solids 404 (2014) 7–12

In isothermal crystallization condition, the annealing temperaturesare selected in the SLR of Cu38Zr46Ag8Al8 BMG due to the TPF methodas always performed in the SLR. As shown in Fig. 7, we can obtain theTg = 695 K and Tx = 785 K, so the annealing temperatures are chosenas 755 K, 761 K, 767 K, 773 K and 779 K. The crystallization peaks ofeach annealing temperature in DSC curves of Cu38Zr46Ag8Al8 BMG areshown in Fig. 8, the same with the plots in non-isothermal condition.The DSC curves only exhibit a single pronounced exothermic peakafter passing a certain incubation period, τ, which decreases with theincrease of annealing temperature. This phenomenon can be ascribedto the higher atomic mobility at higher annealing temperature, whichcan cause concentrationfluctuation necessary for large-scale crystalliza-tion to set in [39]. The same phenomenon can be found in previousreports in Zr-based BMGs [40–42] and Cu-based BMGs [30,43].

The crystallization volume fraction for isothermal crystallization, α,can be deduced as a function of annealing time from DSC curves byequation which is given by [32]:

α ¼

Z t

t0

dHc=dtð ÞdtZ t∞

t0

dHc=dtð Þdt¼ A0

A∞ð5Þ

where t0 and t∞ are the time when crystallization begins and ends inamorphous materials, dHc/dt is heat flow, and A0, A∞ are also the areasunder DSC curves. Fig. 9 exhibits the relationship between crystalliza-tion fraction and annealing time. The plots all display an S-shapedtrend, and the crystallization process becomes slow with the decreaseof annealing temperature.

Almost the similar with non-isothermal condition, the crystalliza-tion quantity in isothermal condition can be identified by calculatingthe area of crystallization enthalpy using the following equation:

ΔH ¼ 1Rh

Z t∞

t0

W tð Þdt: ð6Þ

The crystallization enthalpy can be calculated by using this equation,the results are 1.68 J/g at annealing temperature of 755 K, 1.47 J/g at761 K, 1.68 J/g at 767 K, 1.62 J/g at 773 K and 1.71 J/g at 779 K. Thecrystallization enthalpy maintains similar value in the isothermalcondition; the created phases are also the same.

3.2.1. Activation energyIn isothermal crystallization condition, the Arrhenius equation is

often utilized to evaluate the activation energy, Ea[29]:

t αð Þ ¼ t0 expEaRT

� �ð7Þ

Fig. 7. DSC curve of Cu38Zr46Ag8Al8 bulk metallic glass (heating rate: 20 K/min). Glasstransition temperature (Tg) and onset crystallization temperature (Tx) are defined.

where t0 is a constant andR is the gas constant. The plots of ln(t(α))versus 1/T at different crystallization volume fractions (from 0.1 to0.9) are shown in Fig. 10, and the approximate straight lines can beobtained by fitting the experimental values using Arrhenius equation.The activation energy can be obtained from the slope of fitting curvesas shown in Fig. 11, the average value is about 451 ± 23 kJ/mol inisothermal heating condition. However, from the results we can seethat the activation energy decreases with the increase of crystallizationfraction. This tendency is due to the energy that consists of two compo-nents: one term corresponding to the nucleation and the other to thegrowth. When crystallization progresses, the energy required fornucleation can progressively disappear and then Ea decreases. Comparedwith isothermal annealing condition, the sample in continuous heatingcondition will be crystallized at a relative higher temperature, whichmeans that crystallization transformation from metastable state tocrystalline phases is easier at higher heating temperature.

3.2.2. Crystallization mechanismThe isothermal annealing time and the crystallization volume

fraction can be modeled by the Johnson–Mehl–Avrami (JMA) equationto describe the transformation kinetics as follows [41,44–46]:

α tð Þ ¼ 1− exp −K t−τð Þn� � ð8Þ

where τ is incubation time for nucleation. Taking the double logarithmof Eq. (8), we can deduce the following equation [40,44]:

ln − ln 1−α tð Þð Þ½ � ¼ n lnK þ n ln t−τð Þ: ð9Þ

Fig. 9. Relationship between crystallization volume fraction and annealing time at differ-ent annealing temperatures in Cu38Zr46Ag8Al8 bulk metallic glass as a guide to the eyes.

Fig. 10. Plots of Cu38Zr46Ag8Al8 bulk metallic glass for activation energy in isothermalconditions. The fits have R2 values all above 0.99.

Fig. 12. Avrami plots of Cu38Zr46Ag8Al8 bulk metallic glass at different annealingtemperatures. The Avrami exponents in different annealing temperatures are: 4.74 in755 K, 4.24 in 761 K, 4.09 in 767 K, 4.54 in 773 K and 4.72 in 779 K, the average value is4.47. The fits all have the same R2 value of 0.999.

11J. Cui et al. / Journal of Non-Crystalline Solids 404 (2014) 7–12

The JMA plots of ln[− ln(1 − α)] versus ln(t − τ) are shown inFig. 12 fromwhich the experimental points can be fitted to give a nearlystraight linewith the slope of n in different annealing temperatures, thecrystallization volume fractions are chosen from 0.2 to 0.8. Based onthis, the kinetic parameters of the Cu38Zr46Ag8Al8 BMG at differentannealing temperatures in isothermal crystallization conditions can becalculated, and the values are given in Table 1.

The Avrami exponents vary from 4.10 to 4.74 for different annealingtemperatures and values are listed in Table 1. Considering the averageAvrami exponent n in Cu38Zr46Ag8Al8 BMG is about 4.47 ± 0.33,suggesting that the crystallization is mainly governed by a constantnucleation rate [47], similar values have been reported in other BMGs:Zr55.9Cu18.6Ta8Al7.5Ni10[48], Al89La6Ni5[49] and Ti50Ni25Cu25[50].

3.2.3. Local Avrami exponentFor amorphousmaterials, the nucleation and growth rates of crystals

do not remain a constant value during thewhole crystallization process.Therefore, the relationship between the local Avrami exponent and thecrystallization volume fractionα should be introduced. Based on Eq. (9),the local Avrami exponent is defined as [51]:

n αð Þ ¼ ∂ ln − ln 1−αð Þ½ �∂ ln t−τð Þ : ð10Þ

Fig. 13 shows the relationship between the local Avrami exponentand the crystallization volume fraction at five different annealingtemperatures, the five curves display the consistent tendency. Accordingto the fact that when α is between 10% and 20%, n(α) = 3.0–4.0, whichmeans that the crystallization progresses with a decreasing crystalliza-tion rate, but the crystallization quantity is increasing in this stage.

Fig. 11. Activation energy of Cu38Zr46Ag8Al8 bulkmetallic glass for different crystallizationvolume fractions in isothermal heating conditions by fitting the experimental points inFig. 10. The average activation energy is 451 ± 23 kJ/mol.

After this stage, the local Avrami exponent is larger than 4.0 whichmeans that the nucleation rate increases with time. Meanwhile, thecrystallization quantity increased rapidly and the n(α) value almostmaintains a stable state until the α reaches 80%, after that the n(α)value is back to 4.0, which means that the nucleation rate decreased toa constant small value; the main reason is due to the lack of solvend.After this stage,with the increase of crystallization fraction, thenucleationrate decreases until the crystallization process is completed. Similarphenomenon has been reported by Sun et al. [52] in the work ofFe33Zr67 metallic glass.

4. Conclusion

The crystallization kinetics of Cu38Zr46Ag8Al8 BMG is investigated byDSC in both non-isothermal and isothermal conditions. Themain resultsof this work are shown as follows:

• In non-isothermal condition, the average crystallization enthalpy isabout 29.36 ± 3.44 J/g, and the average activation energy is about310 kJ/mol.

• In non-isothermal condition, when the crystallization fraction isbetween 20% and 80% the Avrami exponent is larger than 4, whichmeans that the nucleation rate increased with time, and the crystalli-zation quantity increased rapidly. When the crystallization fractionreaches 80%, the Avrami exponent value is back to 3–4, whichmeans that the crystallization progresses with a decreasing crystalli-zation rate, the main reason is due to the lack of solvend.

• In isothermal condition, the average crystallization enthalpy is about1.63 ± 0.12 J/g, and the average value of activation energy is about451 ± 23 kJ/mol.

• In isothermal condition, the Avrami exponent n ranges from 4.10 to4.74, the crystallization mechanism is mainly governed by constantnucleation rate.

Table 1TheAvrami exponent n, reaction rate constantK and incubation time τ at different annealingtemperatures in Cu38Zr46Ag8Al8 bulk metallic glass. The Avrami exponent and reaction rateconstant K are obtained by fitting Fig. 12, and the fits all have the same R2 value of 0.999.

Annealing temperature (K) n τ (min) K

755 4.74 3.12 0.19761 4.24 2.48 0.35767 4.09 1.15 0.50773 4.54 0.55 0.77779 4.72 0.12 1.21

Fig. 13. Relationship between local Avrami exponent n(α) and crystallization volumefraction at different annealing temperatures as a guide to the eyes.

12 J. Cui et al. / Journal of Non-Crystalline Solids 404 (2014) 7–12

Acknowledgments

This work was supported by the Fundamental Research Fund ofNorthwestern Polytechnical University (JC20120203) and the Programof Introducing Talents of Discipline to Universities (B08040). One ofthe authors J. Cui wants to acknowledge China Scholarship Council(CSC) (2011629115) for the financial support.

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