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Powder Technology 253 (2014) 553–560
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Powder Technology
journal homepage: www.elsevier.com/locate/powtec
Kinetic analysis of thermite reaction in Al–Ti–Fe2O3 system to produce
(Fe,Ti)3Al–Al2O3 nanocomposite
M. Raﬁei a,⁎, M.H. Enayati b, F. Karimzadeh b
a
b
Young Researchers and Elite Club, Najafabad Branch, Islamic Azad University, Najafabad, Isfahan, Iran
Department of Materials Engineering, Isfahan University of Technology, Isfahan 84156-83111, Iran
a r t i c l e
i n f o
Article history:
Received 16 August 2013
Received in revised form 12 November 2013
Accepted 14 December 2013
Available online 21 December 2013
Keywords:
Mechanical alloying
(Fe,Ti)3Al–Al2O3 nanocomposite
Kinetic
DTA
a b s t r a c t
In this study, (Fe,Ti)3Al–Al2O3 nanocomposite was synthesized by mechanical alloying (MA) of Al–Ti–Fe2O3
powder mixture. Structural evolution and thermal analysis of powder particles during MA were studied by Xray diffractometry (XRD) and differential thermal analysis (DTA). Kinetic analysis of Fe2O3–Al reaction was conducted using free model methods. The (Fe,Ti)3Al–Al2O3 nanocomposite was formed during MA via Fe2O3–Al
thermite reaction. The Fe2O3–Al reaction appeared to occur in combustion mode and the formation of (Fe,
Ti)3Al–Al2O3 nanocomposite occurred in two consecutive stages. In the ﬁrst stage, Al2O3 and in the second
stage, (Fe,Ti)3Al phases were formed. Kinetic analysis revealed that for ball milled powders the reaction of
Fe2O3 with Al can take place below Al melting temperature with a different reaction path.
© 2013 Elsevier B.V. All rights reserved.
1. Introduction
Fe3Al based intermetallics have attractive properties like high hardness, high melting point and excellent oxidation and corrosion resistance [1] making them useful for several structural applications
including gas metal ﬁlters, heating element, heat treatment ﬁxtures,
high temperature dies and molds and cutting tools [2,3]. Addition of a
third alloying element such as Ti, Cr, … to Fe3Al intermetallic compound
can improve mechanical properties in particular ductility at room
temperature by mechanisms such as solid solution and/or precipitation
hardening as well as grain boundary modiﬁcation [4–6]. It has also been
shown that the dispersion of hard second phase particles (e.g., Al2O3) in
the matrix can enhance the mechanical properties [7]. Intermetallic
based composites reinforced by alumina exhibit high strength, good
wear resistance and improved fracture toughness [8,9]. In situ formation of Al2O3 in Fe3Al matrix can be readily achieved by ball milling of
Fe2O3 with Al powder mixture via the solid-state displacement reaction
of 2Al + Fe2O3 = 2Fe + Al2O3. There are several methods for estimating kinetic parameters of solid-state reactions based on differential
thermal analysis (DTA) and differential scanning calorimeter (DSC)
data. Among these free model methods, the Kissinger–Akahira–Sunose
(KAS), Flynn–Wall–Ozawa (FWO), Tang and Starink are the most
reliable methods for calculating activation energy of thermally activated
reactions [10]. Patankar and Fores [11] studied the formation of Nb3Sn
compound by MA of Nb and Sn elemental powders. They reported that
after 3 h MA a Nb(Sn), solid solution is formed. Through Kissinger–
Akahira–Sunose and Flynn–Wall–Ozawa methods, the activation energy
⁎ Corresponding author. Tel./fax: +98 312 5219109.
E-mail address: raﬁ[email protected] (M. Raﬁei).
0032-5910/$ – see front matter © 2013 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.powtec.2013.12.028
was calculated to be about 312 kJ·mol−1. Fan et al. [12] studied the
kinetics of thermite reaction in 8Al–3Fe2O3 system. Their results showed
that thermite reaction during DSC run occurred after melting of Al. Also,
an activation energy of 145 kJ·mol−1 was reported for thermite reaction in this system, indicating that the diffusion of Al in FeAl2O4 compound controls the thermite reaction. Mostaan et al. [13] studied the
kinetics of formation of Al2O3/Nb composite by four isoconversional
methods (KAS, FWO, Tang and Starink). Their results showed that all
methods lead to a similar value of activation energy. In our previous
work, the (Fe,Ti)3Al–Al2O3 nanocomposite was synthesized by mechanical alloying (MA) starting from Fe–Al and TiO2 powder mixture [14]. In
the present work (Fe,Ti)3Al–Al2O3 nanocomposite was synthesized by
MA of Al–Ti and Fe2O3 powder mixture. The kinetics of thermite reaction
were studied to gain further insight into the formation mechanism of
(Fe,Ti)3Al–Al2O3 nanocomposite by MA route.
2. Experimental methods
Fe, Al, Ti and Fe2O3 powders with a purity higher than 99% were used
as starting materials. Al particles were irregular in shape with size distribution of about 50–100 μm. Ti particles had an irregular shape with
porous structure and size distribution of about 400–500 μm. Fe2O3 powder had irregular particles with size distribution of about 0.5–4 μm. Al,
Ti and Fe2O3 powders were mixed according to reaction (4). MA was
carried out in a high energy planetary ball mill, nominally at room temperature and under Ar atmosphere. The details of MA conditions are
reported elsewhere [15]. Samples were taken at selected time intervals
and characterized by X-ray diffraction (XRD) in a Philips X'PERT
MPD diffractometer using ﬁltered Cu Kα radiation (λ = 0.1542 nm).
Annealing of powder particles was carried out to study the thermal
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M. Raﬁei et al. / Powder Technology 253 (2014) 553–560
behavior of milled powders. A small amount of powder was sealed and
annealed up to 900 and 1200 °C in a conventional furnace with a
heating rate of 5 °C/min and then cooled in air. The structural transitions occurring during annealing were determined by XRD. The crystallite size and internal strain of powders were estimated using the
Williamson–Hall method [16]. The kinetic parameters were obtained
by DTA in Perkin-Elmer DSC-7 analyzer, in 25–1200 °C temperature
range, under Ar atmosphere and in three different heating rates of 5,
15 and 20 °C/min. The baseline for DTA traces was calculated by software provided in the Perkin-Elmer DSC-7 analyzer.
3. Results and discussion
3.1. Thermodynamic aspects of Fe2O3–Al reaction
Reaction of Fe2O3 with Al producing Fe and Al2O3 phases is as
follows:
2Al þ Fe2 O3 ¼ 2Fe þ Al2 O3
−1
298
ΔG0
¼ −840 kJ mol
−1
298
ΔH0
¼ −852 kJ mol :
ð1Þ
ΔG0 298 and ΔH0 298 values for this reaction were calculated according
to relations (2) and (3) and thermodynamic data given in references
[17]. Reaction (1) is extremely exothermic (ΔH0 298 ≪ 0) and can thermodynamically occur at ambient temperature as its ΔG0 298 is negative.
ΔG0
X
298
¼
298
¼ ΔH0
ΔH 0
ΔH 0
298
298
ðProductÞ−
−TΔS0
298
X
kJ mol
ΔH0
−1
:
298
−1
ðReactantÞ kJ mol
ð2Þ
ð3Þ
Adiabatic temperature, Tab, for this reaction was calculated to be
about 2690 °C. As a result, reaction (1) occurs in combustion mode
during MA. In the current study, extra Al (1 mol) and Ti (1 mol) powders were added to the powder mixture to produce (Fe,Ti)3Al matrix.
The excess Al and Ti elements act as diluting agents and reduce Tab to
2152 °C, indicating that reaction (1) could occur in combustion mode
during MA even in the presence of diluents.
3.2. Structural evolution
(Fe,Ti)3Al–45 vol.% Al2O3 nanocomposite was synthesized according
to the following reaction:
3Al þ Ti þ Fe2 O3 ¼ ðFe; TiÞ3 Al þ Al2 O3 :
ð4Þ
Fig. 1 shows the XRD patterns of 3Al–Ti–Fe2O3 powder mixture asreceived and after different milling times. As can be seen, in asreceived powder, only Al, Ti and Fe2O3 peaks are seen. By increasing
milling time to 2 h, the intensity of Al, Ti and Fe2O3 diffraction peaks
decreased and their width increased due to the internal strain induced
by lattice defects and reﬁnement of crystallite size.
The XRD pattern of the 5 h milled sample revealed that Al reacted
with Fe2O3 forming (Fe,Ti)3Al and Al2O3 phases. Further milling led to
the broadening and decreasing of (Fe,Ti)3Al and Al2O3 peaks. Crystallite
size and internal strain of (Fe,Ti)3Al and Al2O3 phases after 100 h of MA
were calculated to be about 10 ± 3 nm, 0.95 ± 0.1%, 20 ± 5 nm and
3 ± 0.2%, respectively. Therefore, XRD results accord well with the
thermodynamic prediction and conﬁrm that the reaction of Al with
Fe2O3 occurs in a manner similar to self-propagating high temperature
synthesis (SHS) mode. It has been reported that in Fe–Al–TiO2 system,
the (Fe,Ti)3Al intermetallic compound is completely formed after 40 h
of MA, while in Al–Ti–Fe2O3 system, the intermetallic compound was
rapidly formed after 5 h of MA [14]. This is because in Al–Ti–Fe2O3
powder mixture, the reaction between Al and Fe2O3 occurred in
combustion mode and the heat released by this reaction accelerated
(Fe,Ti)3Al formation. This implies that reaction (4) during MA includes
two consecutive stages according to the following reactions:
2Al þ Fe2 O3 ¼ 2Fe þ Al2 O3
ð5Þ
2Fe þ Al þ Ti ¼ ðFe; TiÞ3 Al:
ð6Þ
3.3. Thermal analysis of powders
DTA of powder particles was conducted to determine the effect of
milling on kinetics of Fe2O3–Al reaction. For this purpose, powders
milled for 2 and 4 h (before thermite reaction) were selected. As seen
Fig. 1. XRD patterns of 3Al–Ti–Fe2O3 powder mixture at different milling times.
M. Raﬁei et al. / Powder Technology 253 (2014) 553–560
in Fig. 2 the XRD pattern of the sample milled for 4 h includes only the
peaks of initial powder mixture. Results of DTA for samples milled for 2
and 4 h are presented in Fig. 3.
The sample milled for 2 h showed two exothermic peaks at 870 and
1110 °C and one endothermic peak at 659 °C. The endothermic peak
was related to Al melting. In order to determine the nature of exothermic peaks, samples heated to 900 and 1200 °C were analyzed by XRD.
The results are presented in Fig. 4. As can be seen, after heating up to
900 °C, Al2O3, Fe, Ti and Al peaks are presented in the XRD pattern, indicating that the ﬁrst exothermic peak on the DTA curve is related to the
reaction between Al and Fe2O3 (reaction (5)). Fig. 4b indicates the
XRD patterns after heating up to 1200 °C. As it is clear, only (Fe,Ti)3Al
and Al2O3 peaks exist on the XRD pattern, indicating that the second
exothermic peak on the DTA curve is related to the formation of (Fe,
Ti)3Al intermetallic compound according to reaction (6). These results
conﬁrm that reaction (4) occurs in two consecutive stages during
heating. Comparison of DTA curves of two samples (Fig. 3) indicates
that in the sample milled for a longer time (4 h), Fe2O3–Al reaction
takes place before Al melting and two exothermic peaks become
closer. This indicates that with increasing milling time, the formation
of (Fe,Ti)3Al intermetallic compound occurs immediately after the
reduction of Fe2O3 by Al (Fig. 3b). It may be concluded that during
MA, a similar reaction sequence occurs although the formation of
(Fe,Ti)3Al–Al2O3 structure appears to take place as a single stage on
XRD.
where A is the pre-exponential factor (s−1), E is the activation energy
(kJ·mol−1), and R is the universal gas constant. This equation can be
integrated by the separation of variables:
Zα
0
dα
A
¼
f ðα Þ β
ZT
T0
ZT
E
AE
expð−Y Þ
exp −
dY:
dT≅
RT
βR
Y2
ð9Þ
0
The right-hand integral, usually called temperature integral, P(Y),
does not have any analytical solution.
Z∞
P ðY Þ ¼
Yf
expð−Y Þ
dY:
Y2
ð10Þ
Temperature integral can be solved using several approximations
which lead to the isoconversion method, as expressed below:
β
E
Ln k ¼ C− :
RT
T
ð11Þ
Different methods have been introduced for calculating activation
energy. Among them, the most popular ones are:
1. Kissinger–Akahira–Sunose (KAS) method [18–20], that is expressed
as follows:
3.4. Kinetic analysis
Transformation rate of a given solid-state reaction in isothermal
conditions is related to the temperature (T) and degree of conversion
(α) according to the following relationship:
555
β
Ln 2i
T αi
!
¼ C k ðα Þ−
Eα
RT αi
ð12Þ
where the Ck(α) is calculated by:
dα
¼ kðT Þ f ðα Þ
dt
ð7Þ
where k(t) is the reaction rate constant, f(α) is the reaction model, and α
is the extent of transformation. Under non-isothermal conditions, with
constant heating rate of β = dT / dt, the kinetic relation can be
expressed by the following equation:
dα A
E
¼ exp −
f ðα Þ
dT β
RT
ð8Þ
AR
:
C k ðα Þ ¼ Ln
Eα
ð13Þ
2. Flynn–Wall–Ozawa (FWO) method, which was independently
suggested by Flynn and Wall [21] and Ozawa [22]:
Lnðβi Þ ¼ C w ðα Þ−1:0518
Fig. 2. XRD patterns of 3Al–Ti–Fe2O3 powder mixture after 4 h MA.
Eα
:
RT αi
ð14Þ
556
M. Raﬁei et al. / Powder Technology 253 (2014) 553–560
Fig. 3. DTA curves of (a) 2 h milled sample and (b) 4 h milled sample.
3. Tang method [23], that is given by:
βi
E
¼ C T ðα Þ−1:0014 α :
Ln
RT αi
T αi 1:89
ð15Þ
4. Starink method [24,25], which is expressed as follows:
βi
E
¼ C s ðα Þ−1:0008 α :
Ln
RT αi
T αi 1:92
ð16Þ
3.4.1. Kinetic studies of Fe2O3 reduction by Al in Al–Ti–Fe2O3 system
As previously mentioned, the reaction of Fe2O3 with Al in Al–Ti–
Fe2O3 system during MA occurred after 4.5 h. Therefore, samples milled
for 2 and 4 h were highly activated. Fig. 5 shows DTA curves of the
sample milled for 2 h heated with different rates. As can be seen, by
increasing the heating rate up to 15 °C/min, the ﬁrst exothermic peak
displaced to the higher temperatures, whereas the second exothermic
peak disappeared. It is due to the displacement of the second peak to
temperatures higher than 1200 °C. By increasing the heating rate up
to 20 °C/min, the ﬁrst exothermic peak, which was related to Fe2O3–
Al reaction, was displaced to 1040 °C. Also, with increasing heating
rate, the peak height was increased.
Fig. 4. XRD patterns of 3Al–Ti–Fe2O3 powder mixture (a) after 2 h MA and subsequent heating up to 900 °C with the heating rate of 5 °C/min and (b) after 2 h MA and heating up to
1200 °C with the heating rate of 5 °C/min.
M. Raﬁei et al. / Powder Technology 253 (2014) 553–560
557
Fig. 5. DTA curves of 3Al–Ti–Fe2O3 powder mixture after 2 h MA at different heating rates.
The activation energy of Fe2O3–Al reaction for the sample milled for
2 h at α = 0.5 (apparent activation energy) was calculated by different
methods given in Section 3.4. The curves plotted for calculating the
apparent activation energy (Ea) are presented in Fig. 6. The results are
presented in Table 1. The values of apparent activation energy obtained
by four methods are similar. Fan et al. [12] studied the kinetics of Fe2O3–
Al reaction after 30 min MA using the Starink method. They reported
that the activation energy was about 145 kJ·mol−1. However, in the
present study, the apparent activation energy for Fe2O3–Al reaction
was measured to be about 83.1 kJ·mol−1 using the same method. This
difference in Ea values is probably due to the longer milling times and
the presence of Ti in the powder mixture.
Fig. 7 shows the activation energy (Ea) versus the degree of transformation (α) calculated by the Kissinger method. As can be seen, Ea is
independent of α suggesting that the mechanism of reaction remains
unchanged with time. This shows that reaction kinetics is controlled
by a single-step mechanism. Generally, the change in Ea with α occurs
for reactions with multi-step mechanism [26].
Fig. 6. The curves plotted for calculating the apparent activation energy (Ea) by (a) Tang, (b) Starink, (c) Flynn–Wall–Ozawa and (d) Kissinger–Akahira–Sunose methods.
Table 1
The calculated apparent activation energy by different methods for thermite reaction.
Method
Kissinger–Akahira–Sunose
Flynn–Wall–Ozawa
Tang
Starink
Apparent activation energy (kJ·mol−1)
82.3 ± 4%
97 ± 3%
83.3 ± 3%
83.1 ± 4%
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M. Raﬁei et al. / Powder Technology 253 (2014) 553–560
Fig. 7. The activation energy changes for thermite reaction versus the degree of conversion.
In some cases, the change in the reaction mechanism changes the
pre-exponential factor rather than the activation energy [27]. The
results showed that the pre-exponential factor is almost constant
(2.1 × 105–4.9 × 105 s−1).
The change of α as a function of temperature for Fe2O3–Al reaction is
presented in Fig. 8. As can be seen, α–T curves for all three heating rates
have an S shape indicating that with increasing heating rate, the reaction mechanism is constant and the free model methods can be applied.
Fig. 8. Degree of conversion versus temperature for Fe2O3–Al reaction at different heating rates.
Fig. 9. DTA curves of 3Al–Ti–Fe2O3 powder mixture after 4 h MA at different heating rates.
M. Raﬁei et al. / Powder Technology 253 (2014) 553–560
559
Fig. 10. The curve plotted for calculating the apparent activation energy by the Kissinger method.
Fig. 9 shows DTA curves of samples milled for 4 h at three different
heating rates. On each curve, two close exothermic peaks exist. As previously mentioned, the ﬁrst exothermic peak is caused by the reaction of
Fe2O3 with Al, while the second one is related to (Fe,Ti)3Al formation.
By increasing milling time from 2 to 4 h, the onset temperature of
Fe2O3–Al reaction decreased to a temperature lower than Al melting.
The change in the onset temperature of the reaction can be attributed
to the MA process, which increases the stored energy due to the increasing surface area and crystal defect density [27]. Comparison of Figs. 5
and 9 shows that with increasing milling time, the width of ﬁrst exothermic peak is decreased. This shows that MA process decreases the
temperature range of reactions. The activation energy of Fe2O3–Al reaction for the sample milled for 4 h was calculated by the Kissinger method as presented in Fig. 10. The apparent activation energy and preexponential factor were calculated to be about 253 kJ·mol− 1 and
2.2 × 1014 s−1 respectively which are higher than 82.3 kJ·mol−1 and
3.7 × 105 s− 1 obtained for the sample milled for 2 h. It is expected
that increasing milling time decreases the activation energy. In fact,
in most cases, the activation energy changes due to the MA process
are caused by the change in reaction path and reaction mechanism.
As pointed out, for the 2 h milled sample, the reaction of Fe 2 O 3
with Al occurred as soon as Al melts, while after 4 h milling this reaction occurs in solid-state without Al melting. These results indicate
that the reaction mode and path are different for powders activated
by ball milling.
4. Conclusions
(Fe,Ti)3Al–Al2O3 nanocomposite powder was successfully synthesized by MA of the Al–Ti–Fe2O3 powder mixture. Kinetics of Fe2O3–Al
reaction in this system was analyzed by free model methods and the
following results were obtained:
1. MA of Al–Ti–Fe2O3 powder mixture led to in-situ formation of (Fe,
Ti)3Al–Al2O3 nanocomposite via the reaction of Fe2O3 with Al. This
reaction occurred in combustion mode and ordered (Fe,Ti)3Al intermetallic compound and crystalline Al2O3 phase were formed. By
increasing milling time up to 100 h, the ordered DO3 structure was
transformed to the disordered structure.
2. The (Fe,Ti)3Al–Al2O3 nanocomposite formed in two steps. In the ﬁrst
stage, the reaction of Fe2O3 with Al produces Fe and Al2O3 phases.
This is followed with alloying of Fe, Ti and the remaining Al to form
(Fe,Ti)3Al phase.
3. Increasing the milling time from 2 to 4 h reduced the onset temperature of Fe2O3–Al reaction to a temperature below Al melting
temperature.
4. Changing the reaction path and mechanism in Al–Ti–Fe2O3 system
with milling time increases the activation energy of Fe2O3–Al
reaction.
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