Kinetics of the glass-transition and crystallization process of

Fe72−xNbxAl5Ga2P11C6B4 (x = 0,2) metallic glasses

N. Mitrovic, S. Roth, and J. Eckert

Citation: Appl. Phys. Lett. 78, 2145 (2001); doi: 10.1063/1.1361099

View online: http://dx.doi.org/10.1063/1.1361099
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Published by the American Institute of Physics.

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APPLIED PHYSICS LETTERS VOLUME 78, NUMBER 15 9 APRIL 2001

Kinetics of the glass-transition and crystallization process

of Fe72À x Nbx Al5 Ga2 P11C6 B4 „ x Ä0, 2… metallic glasses
N. Mitrovic,a) S. Roth,b) and J. Eckert
Institut für Metallische Werkstoffe, IFW Dresden, PF 270016, D-01171 Dresden, Germany
共Received 21 November 2000; accepted for publication 12 February 2001兲
The kinetics of the glass-transition and the crystallization process of multicomponent ferromagnetic
Fe72⫺x Nbx Al5Ga2P11C6B4 (x⫽0, 2) metallic glasses have been investigated by constant-rate heating
differential scanning calorimetry at different heating rates. The glass-transition temperature T g and
the crystallization peak temperature T p shift to higher temperatures with increasing heating rate. The
apparent activation energy and the frequency factor are evaluated by the Kissinger method, and the
rate constant of the crystallization process is estimated by an Arrhenius law. The kinetics of the
glass-transition process have been analyzed in terms of a Vogel–Fulcher–Tammann equation
describing the heating rate dependence of the glass-transition temperature. The effect of the niobium
addition on the glass-forming ability has been investigated with respect to the glass-transition and
crystallization kinetics, revealing that substitution of Nb for Fe does not improve the glass-forming
ability and it lowers the thermal stability of the material. © 2001 American Institute of Physics.
关DOI: 10.1063/1.1361099兴

In recent years a new class of bulk metallic glasses with Fe72⫺x Nbx Al5Ga2P11C6B4 (x⫽0, 2) metallic glasses and to
promising magnetic properties prepared by different casting compare the apparent activation energy, the frequency factor,
techniques has been intensively investigated. Extensive ef- the rate constants and the fragility parameters for the alloys
forts have been made to improve the glass-forming ability without or with Nb substitution 共x⫽0 or 1兲. The crystalliza-
共GFA兲 and the magnetic properties of ferrous group metal- tion kinetics under nonisothermal conditions are interpreted
based alloys such as Fe–共Al, Ga兲-共P, C, B, Si, Ge兲, Fe– by the Kissinger method.5 The dependence of the glass tran-
共Co, Ni兲–共Zr, Hf, Nb兲–B and Co–Fe–共Zr, Nb, Ta兲–B sys- sition on the heating rate is analyzed using the Vogel–
tems which exhibit promising soft magnetic properties.1–4 Fulcher–Tammann 共VFT兲 equation, which successfully de-
For example, previous work on soft magnetic Fe-based Fe– scribes the viscosity behavior in the glass-transition region
共Al, Ga兲–共P, C, B兲 alloys focused on the replacement of P by for a number of bulk metallic glass-forming alloys, espe-
1–3 at. % Si 共Refs. 2 and 3兲 or on the replacement of Fe by cially for Zr-based multicomponent alloys with high thermal
TM atoms (TM⫽Ti, Hf, V, Ta, W, Mn, Nb, Mo, Cr, Co). 1 stability of the supercooled liquid against crystallization.6,7
Among these alloys, the Nb-containing alloy Multicomponent prealloys with compositions
(Fe70Al5Ga2P11C6B4Nb2) had the largest temperature inter- Fe72⫺x Nbx Al5Ga2P11C6B4 (x⫽0, 2) were prepared by arc
val of the supercooled liquid region before crystallization melting under a Ti-gettered argon atmosphere. From the pre-
⌬T x ⫽65 K, 1 defined by the temperature span between the alloys, rapidly quenched ribbons with a cross section of
onset temperature of the glass transition T g and the onset about 3.5⫻0.03 mm2 were produced by single- roller melt
temperature of crystallization T x (⌬T x ⫽T x – T g ). spinning. It should be noted that the Nb-containing alloy has
In order to better characterize the optimum annealing poorer castability compared to the Nb-free alloy and tends to
treatment of ferromagnetic metallic glasses, it is necessary to become brittle even in the as-spun state. The amorphous na-
study the glass-transition and crystallization kinetics in de- ture of the ribbons was checked by x-ray diffraction using a
tail. There is no detailed work on the glass-transition behav- Philips PW 1820 diffractometer with Co K ␣ radiation. The
ior and crystallization kinetics of soft magnetic Fe-based samples were proven to be fully amorphous in the as-spun
bulk metallic glass 共BMG兲-forming systems up to now. state.
There is only information that the crystallization process of The thermal stability of the ribbons was examined by a
Nb-free Fe70⫺x Al5Ga2P11C6B4Nbx (x⫽0) takes place differential scanning calorimeter 共DSC兲 共Perkin-Elmer
DSC7兲. The experiments were performed up to 873 K under
through a single exothermic reaction associated with simul-
a continuous argon flow at different heating rates ranging
taneous precipitation of ␣-Fe, Fe3B, Fe3P and Fe3C iron-
from 1 to 200 K/min. The samples were first heated to above
metalloid compounds upon crystallizaton.4
T g and cooled to room temperature at 40 K/min in order to
Consequently, the aim of this work is to study the kinet-
achieve a relaxed state for all samples. After that, the mea-
ics of the glass-transition and crystallization process of
surements at different heating rates and an additional scan
with the individual heating rate of a fully crystallized sample
a兲
Permanent address: Joint Laboratory for Advanced Materials of SASA, were done. This additional scan of the fully crystallized ma-
Technical Faculty Cacak, Cacak, Yugoslavia; electronic mail:
terial was used as the baseline and subtracted from the first
mitar@tfc.tfc.kg.ac.yu
b兲
Author to whom correspondence should be addressed; electronic mail: run before data analysis.
s.roth@ifw-dresden.de Figure 1 shows constant-rate DSC traces for the

0003-6951/2001/78(15)/2145/3/$18.00 2145 © 2001 American Institute of Physics

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2146 Appl. Phys. Lett., Vol. 78, No. 15, 9 April 2001 Mitrovic, Roth, and Eckert

TABLE I. Dependence of the crystallization peak temperature T p on the

heating rate ␤ for the Fe72⫺x Nbx Al5Ga2P11C6B4 (x⫽0, 2) alloys.

T p 共K兲
␤
共K/min兲 x⫽0 x⫽2

5 776 771
10 784 779
20 791 786
40 802 794
80 810 804

where Z is the frequency factor, R g is the gas constant and

FIG. 1. DSC traces for Fe72⫺x Nbx Al5Ga2P11C6B4 (x⫽0, 2) amorphous rib- E a is the apparent activation energy. Plotting ln (␤/T2p) as a
bons at 40 K/min. function of 1/T p 共see Fig. 2兲 enables the calculation of E a
from the slope of this plot E a /R g and the frequency factor Z
Fe72⫺x Nbx Al5Ga2P11C6B4 (x⫽0, 2) alloys obtained at a can be determined from the intercept of this line with the
heating rate of 40 K/min. The DSC curves for both alloys ordinate 共see Table I兲, while the rate constant k cr can be
exhibit a distinct glass transition, followed by a wide super- determined from the Arrhenius law,
cooled liquid region before crystallization at higher tempera- k cr共 T 兲 ⫽Z exp共 ⫺E a /R g T 兲 . 共2兲
ture. For our discussion, we used the onset temperature T g as
a chacteristic temperature which can be determined as the The following values are calculated for the crystallization
intersection of the tangents to the scan above and below the process of the different alloys: E cr,a ⫽405 kJ/mol and Z cr
initial change in the baseline slope. The crystallization tem- ⫽8⫻1026 min⫺1 for x⫽0 and E cr,a ⫽422 kJ/mol and Z cr
perature T x is determined as the onset temperature of the ⫽2⫻1028 min⫺1 for x⫽2. Hence, the activation energy for
exothermic event with peak temperature T p . The T g , T x and crystallization is slightly lower for the Nb-free alloy but the
T p values are 736, 801 and 802 K, respectively, for the Nb- frequency factor is two orders lower than for the Nb-
free alloy. Nb addition lowers T g to 729 K, T x to 792 K and containing alloy. The evaluation of the rate constant k cr gives
T p to 794 K. The decrease is larger for T x than for T g , a measure by which to estimate the glass-forming ability to
leading to a slight decrease in ⌬T x from 65 K for x⫽0 to 63 some extent. In general, a metallic glass with smaller crys-
K for x⫽2. Furthermore, the crystallization enthalpy of the tallization rate constant k cr is of better GFA, i.e., the smaller
Nb-free alloy 共131 J/g兲 is higher than that of the Nb- the value of k cr , the larger the supercooled liquid region
containing alloy 共119 J/g兲. ⌬T x . 8 The temperature dependence of the rate constants for
The apparent activation energy, the frequency factor and the two alloys is shown in the inset of Fig. 2. The partial
the rate constant of the crystallization are estimated by the replacement of Fe by Nb atoms causes an increase of the
Kissinger method.5 The dependence of T p on the heating rate crystallization rate constant.
␤ is described in this model by

␤ /T 2p ⫽ 共 ZR g /E a 兲 exp共 ⫺E a /R g T p 兲 , 共1兲

FIG. 3. DSC curves for Fe72⫺x Nbx Al5Ga2P11C6B4 (x⫽0, 2) taken at differ-
FIG. 2. Kissinger plots for Fe72⫺x Nbx Al5Ga2P11C6B4 (x⫽0, 2). The inset ent heating rates 共numbers denote the magnification for better comparison of
shows the temperature dependence of the crystallization rate constants k cr . the signals兲. The insets shows T g vs log ␤.
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Appl. Phys. Lett., Vol. 78, No. 15, 9 April 2001 Mitrovic, Roth, and Eckert 2147

TABLE II. VFT parameters for the best fit of the DSC data according to
Eq. 共5兲.

ln B T 0g
Alloy 共K/s兲 D* 共K兲

x⫽0 16.4 2.98 626

x⫽2 10.3 0.86 679

Figure 3 shows the shift of the glass-transition region

with the heating rate. Some reports have calorimetrically ob-
served a linear increase of T g with the logarithm of the heat-
ing rate,8,9 but these results were limited to heating rates up
to 80 K/min. However, there are also investigations with
heating rates up to 200 K/min for Pd–Ni- and Zr–Be-based
alloys, which reveal the validity of VFT-type functional be-
havior for describing the transition from the amorphous into
the supercooled liquid state.6,7,10 In order to observe the de-
viation from a linear dependence of T g on log ␤ 共see the FIG. 4. Inverse heating rate 1/␤ as a function of T g normalized to T *
g 共T *
g :
onset of the glass transition at 1 K/min兲 for Fe72⫺x Nbx Al5Ga2P11C6B4
insets in Fig. 3兲 we performed DSC measurements with heat- 共x⫽0, 2).
ing rates between 1 and 200 K/min.
The dependence of T g on the heating rate ␤ given by the bulk glass-forming systems such as Mg65Cu25Y10 共D * ⫽23兲
VFT equation can be written in the form,10 or Zr46.75Ti8.25Cu7.5Ni10B27.5 共D * ⫽22.7兲.6,7 The reason for
this difference may be related to the different fitting algo-
␤ 共 T g 兲 ⫽B exp关 A/ 共 T 0g ⫺T g 兲 , 共3兲
rithm performed in Ref. 6 which was based on the evaluation
where A is a constant, T 0g
is the asymptotic value of T g of T 0g from viscosity measurements at different temperatures
usually approximated as the onset of the glass transition followed by fitting of the DSC data to obtain the remaining
within the limit of infinitely slow cooling and heating rate two VFT parameters 共B and D * 兲 with T 0g taken from the
and B has the dimension of a heating rate. The fragility pa- viscosity measurement.
rameter D * can be expressed as6,7 In summary, we examined the effect of Nb addition on
the kinetics of the glass-transition and crystallization process
D * ⫽A/T 0g . 共4兲
for Fe72⫺x Nbx Al5Ga2P11C6B4 共x⫽0, 2兲 alloys. Upon replac-
Fitting of the experimental data has been performed by ing Fe by Nb, T g and T x shift to lower temperatures and
the equation result in a reduction of ⌬T x . The values of the apparent
activation energy, frequency factor, and rate constant of crys-
ln ␤ 共 T g 兲 ⫽ln B⫺D * T 0g / 共 T g ⫺T 0g 兲 , 共5兲
tallization increase by Nb addition. However, the Nb-free
with three simultaneously adjustable VFT parameters B, D * alloy has the lower limit temperature for the glass transition,
and T 0g . The calculated values are given in Table II and the T 0g , and about a four times higher fragility parameter. From
best fits are shown by lines in Fig. 4. all these observations it can be deduced that the GFA is not
The lower limit for the glass transition T 0g is about 50 K improved with Nb addition in the Fe–Al–Ga–P–C–B sys-
higher for the Nb-containing alloy. In the fragility concept a tem.
large heating rate dependence of T g is indicative of strong
glass behavior.11 In Fig. 4 it is shown how the fragility of the One of the authors 共N.M.兲 thanks the German Academic
investigated alloys is deduced from the dependence of the Exchange Service DAAD and the Saxon Ministry for Sci-
inverse heating rate 1/␤ on T g normalized to T g* 共onset of the ence and Art for financial support during his stay at IFW
glass transition observed at the lowest heating rate of 1 Dresden.
K/min兲.6 The fragility parameter of the Nb-free alloy 共D * 1
A. Inoue and J. S. Gook, Mater. Trans., JIM 36, 1282 共1995兲.
⫽2.98兲 is about four times larger than that for th Nb- 2
T. Mizushima, A. Makino, and A. Inoue, J. Appl. Phys. 83, 6329 共1998兲.
containing alloy 共D * ⫽0.86兲, i.e., the Nb-free alloy shows 3
T. Mizushima, A. Makino, S. Yoshida, and A. Inoue, J. Appl. Phys. 85,
better GFA. It should be mentioned that strong glass formers 4418 共1999兲.
exhibit T g much larger than T g* and, consequently, a higher
4
A. Inoue, Mater. Sci. Eng., A 226–228, 357 共1997兲.
5
H. E. Kissinger, Anal. Chem. 29, 1702 共1957兲.
value of the fragility parameter D * . The D * values obtained 6
R. Busch, E. Bakke, and W. L. Johnson, Acta Mater. 46, 4725 共1998兲.
for the different alloys are close to the fragility parameters 7
R. Busch and W. L. Johnson, Appl. Phys. Lett. 72, 2695 共1998兲.
8
extracted from the VFT parameters calculated for Y. X. Zhuang, W. H. Wang, Y. Zhang, M. X. Pan, and D. Q. Zhao, Appl.
Phys. Lett. 75, 2392 共1999兲.
Pd40Ni40P19Si1 共D * ⫽1.04兲, Pd77Si16.5Ag6 共D * ⫽1.34兲 and 9
M. Lasocka, Mater. Sci. Eng. 23, 173 共1976兲.
La55Al25Ni20 共D * ⫽5.92兲.10 However, all these data are 10
R. Brüning and K. Samwer, Phys. Rev. B 46, 11318 共1992兲.
much smaller than the previously reported values for easy 11
C. A. Angell, Science 267, 1924 共1995兲.

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