Journal of Non-Crystalline Solids 357 (2011) 2590–2594
Contents lists available at ScienceDirect
Journal of Non-Crystalline Solids
j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / j n o n c r y s o l
Crystallization kinetics in Cu46Zr45Al7Y2 bulk metallic glass by differential scanning
calorimetry (DSC)
J.C. Qiao, J.M. Pelletier ⁎
Université de Lyon, MATEIS, UMR CNRS5510, Bat. B. Pascal, INSA-Lyon, F-69621 Villeurbanne cedex, France
a r t i c l e
i n f o
Article history:
Received 7 September 2010
Received in revised form 10 December 2010
Accepted 22 December 2010
Available online 12 March 2011
Keywords:
Metallic glass;
Cu46Zr45Al7Y2;
Crystallization kinetics;
Kissinger and Johnson–Mehl–Avrami
methods;
Activation energy
a b s t r a c t
Crystallization transformation kinetics in isothermal and non-isothermal (continuous heating) modes were
investigated in Cu46Zr45Al7Y2 bulk metallic glass by differential scanning calorimetry (DSC). In isochronal heating
process, activation energy for crystallization at different crystallized volume fraction is analyzed by Kissinger
method. Average value for crystallization in Cu46Zr45Al7Y2 bulk metallic glass is 361 kJ/mol in isochronal process.
Isothermal transformation kinetics was described by the Johnson–Mehl–Avrami (JMA) model. Avrami exponent
n ranges from 2.4 to 2.8. The average value, around 2.5, indicates that crystallization mechanism is mainly threedimensional diffusion-controlled. Activation energy is 484 kJ/mol in isothermal transformation for Cu46Zr45Al7Y2
bulk metallic glass. These different results were discussed using kinetic models. In addition, average activation
energy of Cu46Zr45Al7Y2 bulk metallic glass calculated using Arrhenius equation is larger than the value calculated
by the Kissinger method in non-isothermal conditions. The reason lies in the nucleation determinant in the nonisothermal mode, since crystallization begins at low temperature. Moreover, both nucleation and growth are
involved with the same significance during isothermal crystallization. Therefore, the energy barrier in isothermal
annealing mode is higher than that of isochronal conditions.
© 2011 Elsevier B.V. All rights reserved.
1. Introduction
Kinetics of phase transformation is an old problem, with many
application fields, especially in metallic alloys. Let us for instance
mention kinetics of precipitation, short or long range ordering.
Recently, a new type of metallic alloy has been developed: bulk
metallic glasses. Compared with crystallized counterparts, bulk
metallic glasses exhibit attractive properties, such as excellent
strength and hardness, good stability and higher mechanical
properties, due to lack of long range order in the atomic assembly
[1–9]. Thus, bulk metallic glasses are potential materials for applications in various engineering fields. However, bulk metallic glasses, as
any amorphous alloy, can evolve towards a more stable state, i.e.
crystalline state, during heating in the super-cooled liquid region.
Recently, many reports have been published on crystallization
kinetics in both isochronal and isothermal situations in bulk metallic
glasses, such as Zr-based [10–16], Cu-based [17–19], Ti-based [20,21]
and Fe-based bulk metallic glasses [22–24]. All these bulk metallic
glasses present excellent resistance with respect to crystallization in
the super-cooled liquid region, leading therefore to a fairly simple
analysis of the phenomenon.
In bulk metallic glasses, many researchers have used differential
scanning calorimetry (DSC) or differential thermal analysis (DTA) to
detect crystallization and to determine pertinent information, such as
⁎ Corresponding author. Tel.: + 33 4 72 43 83 18; fax: + 33 4 72 43 85 28.
E-mail address: jean-marc.pelletier@insa-lyon.fr (J.M. Pelletier).
0022-3093/$ – see front matter © 2011 Elsevier B.V. All rights reserved.
doi:10.1016/j.jnoncrysol.2010.12.071
activation energy, incubation time or mechanisms of nucleation and
growth [25,26].
Crystallization can occur either during a continuous heating from
low temperature (non-isothermal mode) or during annealing at a given
temperature (isothermal mode). Depending on the heating process,
different models have been proposed to describe the results. For nonisothermal crystallization of amorphous materials, Ozawa–Flynn–Wall
method [27], Friedman method [28], Kissinger method [29], Augis–
Bennett method [30], Gao–Wang model [31] and Johnson–Mehl–
Avrami (JMA) [32] were used to investigate the crystallization kinetics
in many kinds of amorphous materials. More recently [33,34], a new
analysis method (various heating rates (VHR)) was introduced to
analyze the crystallization kinetics for non-crystalline solids in nonisothermal mode. In other words, the crystallization kinetic parameters,
such as the apparent activation energy Ea and kinetic exponent n, are
introduced in this model. Kozmidis-Petrović et al. [35] analyzed the noncrystallization parameters of metal-chalcogenide glass using different
methods, such as crystallization mechanism and activation energy. In
fact, all these methods are based on the JMA theory. The starting point is
always the evolution of crystallized fraction in relation to time. Johnson–
Mehl–Avrami (JMA) is usually used to describe the isothermal
crystallization kinetics [36–39]. This model is also used for any kind of
phase transformation, for instance for precipitation in a solid solution.
This model gives good results, mainly in isothermal conditions. For
instance, Prashanth et al. [26] in Zr65Ag5Cu12.5Ni10Al7.5 glassy powder
and Xie et al. [17] in Cu50Zr45Ti5 bulk metallic glass, have shown that the
crystallization process is diffusion-controlled with three-dimensional
J.C. Qiao, J.M. Pelletier / Journal of Non-Crystalline Solids 357 (2011) 2590–2594
2591
growth. In contrast, Wang et al. [40] have used an integral fitting method
to describe the isochronal transformation kinetics in Ti50Cu42Ni8
amorphous alloy and they found that this model is more suitable to
describe the crystallization kinetics.
Cu-based bulk metallic glasses show excellent glass forming
ability, wide super-cooled liquid region and high mechanical
properties [41–43]. However, only few investigations have been
conducted in Cu46Zr45Al7Y2 bulk metallic glass [44], especially
concerning the crystallization phenomenon. Therefore, DSC experiments in this bulk metallic glass are presented and discussed in the
present work to give further information on this phenomenon.
2. Experimental
2.1. Sample preparation
Master ingots of alloys with composition Cu46Zr45Al7Y2 were
kindly provided by Prof. Y. Yokoyama, Institute of Materials Research,
Tohoku University, Sendai, Japan. Cylindrical samples were mechanically cut to prepare DSC samples. In order to remove surface
oxidation prior to experiments, these samples were carefully polished
using diamond paste and finally washed in ethanol in an ultrasonic
cleaning machine.
2.2. Structure characterization
Structure of the specimens in the bulk metallic glasses was
examined by X-ray diffraction at room temperature using the Cu Kα
radiation produced by a commercial device (D8, Bruker AXS Gmbh,
Germany).
2.3. DSC experiments
Thermal properties and phase transformations were investigated
using a standard commercial instrument (Pekin Elmer, DSC-7) under
high purity dry nitrogen at a flow rate of 20 ml min−1. Alumina pans
were used as sample holders. In order to ensure the reliability of the
data in the experiments, temperature and enthalpy calibration were
calibrated with an indium standard specimen (T m = 429.7 K,
ΔH c = 28.48 J/g) and zinc standard specimen with 3.283 mg
(Tm = 692.6 K, ΔHc = 108.37 J/g), giving an accuracy of ±0.2 K and
±0.02 mW, respectively. The baselines of DSC in the present work
were described in Ref. [45].
First isochronal DSC experiments were carried out using different
constant heating rates. Then, isothermal crystallization of the samples
was tested in the super-cooled liquid region (SLR), i.e. above the glass
transition temperature (Tg) and below the temperature corresponding
to the onset of crystallization (Tx). The samples were heated up to the
annealing temperature at a heating rate of 20 K min−1 and then hold at
this temperature to follow the crystallization until completion. Finally,
samples were cooled down to room temperature.
Fig. 1. DSC curves in Cu46Zr45Al7Y2 bulk metallic glass, with various heating rates.
position of which shifts to higher temperatures when the heating rate
is increased. Therefore, crystallization process is simple, in contrast for
instance to what is observed in the classical VIT1 bulk metallic glass
(Zr–Ti–Cu–Ni–Be bulk metallic glass) where a complex double peak is
obtained. This double peak was attributed to the existence of a
decomposition phenomenon which precedes the crystallization
phenomenon itself [46]. This was confirmed by transmission electron
microscopy (TEM) observations [46]. In this alloy, analysis of the
crystallization kinetics is difficult to perform, since the two contributions have to be separated. In the present alloy, a direct analysis is
possible.
From the DSC curves, the crystallized volume fraction for nonisothermal crystallization, α, can be deduced as a function of the
temperature using the following equation [47–49]:
T
α=
∫T ðdHc =dT ÞdT
0
T∞
∫T ðdHc =dT ÞdT
0
=
A0
A∞
ð1Þ
where T0 and T∞ are the temperatures at which crystallization begins
and ends in amorphous materials, dHc/dT is the heat capacity at
constant pressure. In addition, A0 and A∞ are the areas under the DSC
curves, respectively.
The crystallization volume fraction is plotted as a function of
temperature in Fig. 2. All the curves present a sigmoidal dependence
with temperature. The same evolution has been observed in all the
amorphous materials (bulk metallic glasses and polymers) during the
non-isothermal crystallization processes.
3. Results and discussion
3.1. XRD analysis of the as-cast bulk metallic glasses
XRD pattern of the as-prepared Cu46Zr45Al7Y2 bulk metallic glass
presents a typical broad diffuse maximum, without diffraction peak
corresponding to a crystalline phase. Therefore, this alloy exhibits the
typical characteristics of an amorphous structure.
3.2. Non-isothermal crystallization behaviour
DSC curves in Cu46Zr45Al7Y2 bulk metallic glass recorded during
continuous heating with different heating rates are shown in Fig. 1.
Crystallization phenomenon induces a simple exothermic peak, the
Fig. 2. Plots of crystallization volume fraction α as a function of temperature, using
different heating rates.
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J.C. Qiao, J.M. Pelletier / Journal of Non-Crystalline Solids 357 (2011) 2590–2594
Fig. 3. Kissinger plots for different crystallization volume fractions α in Cu46Zr45Al7Y2
bulk metallic glass (ranging from 0.1 to 0.9).
The activation energy Ea can be determined by the Kissinger's
relationship [16,50,51]
ln
Rh
Tθ2
!
=−
Ea
+C
RTθ
ð2Þ
where, Rh is the heating rate during the experiment, Tθ is the
characteristic temperatures such as Tg, Tx, and Tp (crystallization peak
temperature) and C is a constant. Plots of ln(Rh/T2θ )versus 1/T2 for
different crystalline volume fractions α (range from 0.1 to 0.9) are
shown in Fig. 3 and Fig. 4. Results are in good agreement with the
Kissinger's equation, since straight lines are clearly observed. The
activation energy in Cu46Zr45Al7Y2 bulk metallic glass is nearly
independent on crystalline volume fraction. An average value
(361 kJ/mol) can be calculated in non-isothermal heating mode.
3.3. Isothermal behaviours
In isothermal crystallization conditions, evolution of the crystalline volume fraction α, as a function of time is given by [47]:
A
α=
= 0
A
∞
∫t ðdHc = dt Þdt
0
t∞
exothermic peak after a given incubation time (τ). This incubation
time decreases when the annealing temperature is increased, due to a
higher mobility at higher annealing temperature, which facilitates
concentration fluctuations necessary for large-scale crystallization
[52]. These results are in good agreement with previously reported
data in Pd-based bulk metallic glasses [53], Zr-based bulk metallic
glasses [15,40,54] and Cu-based bulk metallic glasses [19].
From these curves, the evolution of the crystalline volume fraction
is shown in Fig. 6, versus the annealing time during isothermal
annealing. All the curves exhibit a typical sigmoidal trend.
3.3.1. Kinetic parameters
Transformation kinetics can be described using the Johnson–
Mehl–Avrami (JMA) equation [11,40,55,56]:
n
αðt Þ = 1−exp −K ðt−τÞ
ð3Þ
0
where dHc/dt is the heat flow. The DSC curves obtained at different
annealing temperatures are shown in Fig. 5. They look like those
recorded in non-isothermal conditions. DSC curves exhibit a single
Fig. 4. Activation energy Ea in Cu46Zr45Al7Y2 bulk metallic glass as a function of
crystallization volume fraction α (α ranging from 0.1 to 0.9) in non-isothermal heating
process.
ð4Þ
where τ is the incubation time, which in fact is a fitting parameter.
Taking the double logarithm of Eq. (4), the following expression is
deduced [40,55]:
ln½−lnð1−αðt ÞÞ = nln K + nlnðt−τÞ
t
∫t ðdHc = dt Þdt
Fig. 5. Isothermal DSC curves at different annealing temperatures in Cu46Zr45Al7Y2 bulk
metallic glass.
ð5Þ
By plotting of ln[− ln(1 − α)] versus ln(t − τ) at various annealing
temperatures with 0.2 ≤ α ≤ 0.8 (Fig. 7), the kinetic exponent n and
the reaction rate constant K can be calculated. Values are given in
Table 1.
Kinetic exponent n varies with annealing temperatures from 2.4 to
2.8. Similar variations have been reported in other bulk metallic
Fig. 6. Crystallization volume fraction α as a function of annealing time for various
annealing temperatures in Cu46Zr45Al7Y2 bulk metallic glass.
J.C. Qiao, J.M. Pelletier / Journal of Non-Crystalline Solids 357 (2011) 2590–2594
2593
Fig. 8. Plots for activation energy determination in Cu46Zr45Al7Y2 bulk metallic glass.
Fig. 7. Avrami plots at various annealing temperature in Cu46Zr45Al7Y2 bulk metallic
glass with 0.2 ≤ α ≤ 0.8.
glasses: Zr65Ag5Cu12.5Ni10Al7.5[40], Zr55.9Cu18.6Ta8Al7.5Ni10[57] and
Zr63.33Ti8.89Cu15.45Ni12.33 [58]. These variations are fairly limited.
According to the diffusion-controlled growth theory [52], n = 1.5
means that growth of particles occurs with a nucleation rate close to
zero; 1.5 b n b 2.5 indicates a growth of particles with decreasing
nucleation rate, n = 2.5 reflects growth of particles with constant
nucleation rate, and n N 2.5 corresponds to the growth of small
particles with an increasing nucleation rate [58,59].
The average kinetic exponent n in Cu46Zr45Al7Y2 bulk metallic glass
is close to 2.5. Similar values of n have been reported in other based
bulk metallic glasses: Ca50Mg22.5Cu27.5 [38] and Cu52.5Ti30Zr11.5Ni6
[19]. So in these various bulk metallic glasses, growth of crystalline
particles occurs with a constant nucleation rate.
3.3.2. Activation energy
The activation energy for the crystallization process in isothermal
model can be determined using the Arrhenius equation [19]:
E
t ðaÞ = t0 exp a
RT
ð6Þ
where t0 is a constant. Plots of ln t(a) versus 1/T during isothermal
annealing are shown in Fig. 8. All the fitting curves are almost straight
lines. Activation energy is nearly constant, with an average value of
484 kJ/mol.
Fig. 9 presents activation energy Ea as a function of crystallization
volume fraction α in Cu46Zr45Al7Y2 bulk metallic glass (α range from
0.1 to 0.9) in isothermal mode. This average activation energy
corresponding to isothermal conditions calculated using Arrhenius
equation is larger than the value calculated by the Kissinger method in
non-isothermal conditions (during a continuous heating). This
phenomenon has also been observed in other bulk metallic glasses:
Cu52.5Ti30Zr11.5Ni6 bulk metallic glass [19] and Zr65Cu27Al8 bulk
metallic glass [60]. Yang et al. [19] suggested that isochronal heating
induces higher temperature compared with isothermal heating
condition and then crystallization transformation from metastable
state to crystalline phases is easier at higher heating temperature.
Thus, the energy barrier in isothermal annealing mode is higher than
that of non-isothermal conditions.
Two phenomena occur during the crystallization process: nucleation
and growth. Generally, it is assumed that nucleation is determinant in
the non-isothermal mode, since crystallization begins at low temperature. On the other hand, during isothermal crystallization, both
nucleation and growth are involved with the same significance.
Therefore, the crystallization mechanism in non-isothermal and
isothermal modes is different. Cu46Zr45Al7Y2 bulk metallic glass has a
higher apparent activation energy than Mg-based [61], Cu-based [62]
and Zr-based [12], but lower than Al33Ni16Zr51 bulk metallic glass [63].
4. Conclusion
Kinetics of crystallization in Cu46Zr45Al7Y2 bulk metallic glass was
studied by DSC in both non-isothermal and isothermal modes. The
main results are as follows:
• Classical models developed in the literature (Kissinger model or JMA
model) are really appropriate to describe the crystallization process.
• During a non-isothermal annealing, the average value of activation
energy, determined using the Kissinger method, is 361 kJ/mol.
• In isothermal annealing conditions, the Johnson–Mehl–Avrami
model applies. Avrami exponent n ranges from 2.4 to 2.8. These
values, close to 2.5, indicate that the crystallization mechanism is
mainly diffusion-controlled. Crystal growth occurs by a threedimensional long range ordering. The average value of activation
energy is 484 kJ/mol.
• Two phenomena occur during the crystallization process: nucleation and growth. Generally, it is assumed that nucleation is
Table 1
Kinetic exponent n, reaction rate constant K and incubation time τ at different
annealing temperatures with 0.2 ≤ α ≤ 0.8 in Cu46Zr45Al7Y2 (Cu-based) BMG.
Annealing temperature (K)
n
τ (min)
K
753
748
743
738
2.5
2.7
2.4
2.4
0.25
0.47
1.23
1.65
0.64
0.38
0.25
0.14
Fig. 9. Activation energy Ea as a function of crystallization volume fraction α for
Cu46Zr45Al7Y2 bulk metallic glass (α range from 0.1 to 0.9) in isothermal mode.
2594
J.C. Qiao, J.M. Pelletier / Journal of Non-Crystalline Solids 357 (2011) 2590–2594
determinant in the non-isothermal mode, since crystallization
begins at low temperature. On the other hand, during isothermal
crystallization, both nucleation and growth are involved with the
same significance. Therefore, the energy barrier in isothermal
annealing mode is higher than that in non-isothermal conditions.
Acknowledgements
One of the authors, J.C. Qiao, wants to express his thanks to Dr. J.M.
Chenal and Dr. S. Cardinal, for valuable discussion and assistance in
XRD and DSC experiments during the course of the work. Prof. Y.
Yokoyama is acknowledged for providing the bulk metallic glasses.
Qiao thanks China Scholarship Council (CSC) for providing the
scholarship.
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