Kinetics analysis of mechano-chemically and thermally synthesized Cu by Johnson-Mehl-Avrami model

Article abstract of DOI:10.1016/j.jallcom.2007.01.133

In this paper, the isothermal reduction process kinetics of Cu₂O with carbon under high vacuum for a non-activated sample and mechanically activated samples has been studied. The influence of milling time on the apparent activation energy was analyzed using Johnson-Mehl-Avrami (JMA) model. In order to gain a deeper insight into the possible mechanisms that govern mechanochemical solid-state reduction of Cu₂O, the kinetic of the process was investigated using a similar model. It was found that in temperature range of 550-650 °C, the rate determining step of the thermal reduction is chemical reaction. But in the range of 650-750 °C, the rate determining step seems to be diffusion. Analyzing the relevant experimental results and comparison of the thermal and mechanochemical reduction kinetics showed that the mechanical activation induced by milling may decrease the required reaction activation energy by increasing defect sites. However, it appears that the thermal and mechanical activation induce different transformation rates, but the transformation paths are the same.

Full text of DOI:10.1016/j.jallcom.2007.01.133

Journal of Alloys and Compounds 455 (2008) 447–453
Kinetics analysis of mechano-chemically and thermally
synthesized Cu by Johnson–Mehl–Avrami model
S. Sheibani∗, A. Ataie, S. Heshmati-Manesh
School of Metallurgy and Materials Engineering, University of Tehran, Tehran, Iran
Received 23 December 2006; received in revised form 24 January 2007; accepted 24 January 2007
Available online 30 January 2007
Abstract
In this paper, the isothermal reduction process kinetics of Cu2O with carbon under high vacuum for a non-activated sample and mechanically
activated samples has been studied. The influence of milling time on the apparent activation energy was analyzed using Johnson–Mehl–Avrami
(JMA) model. In order to gain a deeper insight into the possible mechanisms that govern mechanochemical solid-state reduction of Cu2O, the
kinetic of the process was investigated using a similar model. It was found that in temperature range of 550–650 ◦C, the rate determining step of
the thermal reduction is chemical reaction. But in the range of 650–750 ◦C, the rate determining step seems to be diffusion. Analyzing the relevant
experimental results and comparison of the thermal and mechanochemical reduction kinetics showed that the mechanical activation induced by
milling may decrease the required reaction activation energy by increasing defect sites. However, it appears that the thermal and mechanical
activation induce different transformation rates, but the transformation paths are the same.
© 2007 Elsevier B.V. All rights reserved.
Keywords: Kinetics; Mechanochemical; Reaction mechanism; JMA model
1. Introduction
Although the mechanochemical synthesis is known as a very
useful technique, it suffers from theoretical principles. One of
the most important limitations is the ambiguity of the mech-
anism and evaluation of mechanical activation as well as a
suitable characterisation of transformation paths [2]. Therefore,
the transformation kinetics in the intermediate stages of milling
continue to gather extensive attention in the field of solid state
chemistry and materials science and has been the target of some
investigations.
In the solid state reactions, determination of kinetics equa-
tion, rate controlling steps and kinetics parameters such as
activation energy will provide a valuable insight in the mecha-
nism of the process [3]. Many research works have been carried
out on mechanical alloying and mechanical activation kinet-
ics and the way which mechanical energy affects the reaction
rate. There are studies on the kinetics of thermal decomposition
of mechanically activated compounds [2,4,5], chemical leach-
ing of mechanically activated minerals [6–8] and formation of
solid solution and/or amorphous alloys by mechanical alloy-
ing, and crystallization of the as-milled amorphous powders
[9–14]. However, the activation energies and mechanisms of
displacement reactions as a function of milling time need more
investigation. The possibility of mechanochemical reduction
Mechanical alloying and mechanochemistry are novel solid
state processing routes for producing metals, alloys and inter-
metallics in the nanocrystalline scale. The mechanochemistry
includes exchange reactions, reduction/oxidation reactions,
decomposition of compounds and phase transformations. Solid
state reactions involve the formation of a product phase at the
interfaces of the reactants. Subsequently, further growth of the
product phase involves diffusion of the reactant atoms through
the product phase, which constitutes a barrier layer prevent-
ing further diffusion. Hence, high temperature is required for
the reaction to occur at a reasonable rate. Mechanical milling
increases the reaction kinetics due to the generation of clean
and fresh surfaces, increased defect density and reduction of
particles size [1].
∗
Corresponding author at: School of Metallurgy and Materials Engineering,
University of Tehran, P.O. Box 14395-553, Tehran, Iran. Tel.: +98 912 1958219;
fax: +98 21 88006076.
E-mail address: Sheibani s@engmail.ut.ac.ir (S. Sheibani).
0925-8388/$ – see front matter © 2007 Elsevier B.V. All rights reserved.
doi:10.1016/j.jallcom.2007.01.133

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S. Sheibani et al. / Journal of Alloys and Compounds 455 (2008) 447–453
of cuprite (Cu2O) with graphite has been already investigated
[15], but the kinetics of mechanochemical reduction and thermal
reduction of mechanically activated powder mixtures have not
been studied thoroughly.
This paper presents detailed descriptions of the effects
of mechanochemical activation on the Cu2O reduction with
graphite and production of Cu. Furthermore, comparison of the
reduction kinetics in thermal and mechanochemical production
ofCuwas employed tounderstand themechanismof the reaction
in both routes.
example, the reaction conversion after 60 min thermal reduction
at 600 ◦C for unmilled sample is 0.11, whereas at 700 ◦C this
value increases to 0.69.
In the present work, it was found appropriate to use the
Johnson–Mehl–Avrami (JMA) equation to determine the kinet-
ics of the reaction. This equation describes a wide variety of
isothermal solid state transformations and generally it is used
to determine the mechanisms which govern the nucleation and
growth [10,14]. This equation has general form of:
α(t) = 1 − exp[−(Kt)n]
(5)
2. Experimental procedure
where α(t) is the extent of the reduction after time t, n is the
Avrami exponent, which depends on the growth mechanism and
the dimensionality [10]. K is the reaction rate constant whose
temperature dependence is usually given by an Arrhenius equa-
tion in terms of the apparent activation energy. Large values of
K imply rapid transformations. The values of n and K provide a
clue to the type of reaction mechanisms which dominate during
the reaction and also show how fast these mechanisms work [12].
For analyzing the results, Eq. (5) may be rewritten in the form
of following equation:
High purity Cu2O (99%, 5–30 ␮m) and graphite (99.9%, 10–50 ␮m) were
used as precursors and milling was performed in a high-energy Fritsch P5 plan-
etary ball mill, with a speed of 300 rpm for various milling times. Ball to powder
weight ratio was adjusted to 35. Cu2O with 40 mol% of extra carbon was reduced
according to the reaction (1):
2Cu2O + C → 4Cu + CO2↑
(1)
Phase identification was examined by X-ray diffraction (XRD) analysis
(Philips PW-1730) using Cu K␣ radiation. According to the literature, the degree
of structure disorder, F, is defined as below [2]:
ln(−ln(1 − α)) = n ln K + n ln t
(6)
(IB)t
F =
(2)
(IB)0
The constants values of K and n can be calculated by plotting
a linear plot of ln(−ln(1 − α)) as a function of ln t, Avrami plot.
Fig. 2(a)–(e) shows the Avrami plots for samples at 550, 600,
650, 700 and 750 ◦C, respectively.
As seen from Fig. 2 in all the cases a good linear fit is
observed. It shows that the JMA model accurately describes the
isothermal Cu formation from the unmilled and milled Cu2O–C
mixtures. The kinetics parameters, n and K, can be extracted
from the slopes and intercepts of the plots. Table 1 gives these
parameters for these mixtures. In all the cases a good linear fit
was observed because correlation coefficients, r, are greater than
0.99.
In Table 1 it can be seen that in every constant temperature,
n and K increase with milling time. But, mechanical activation
increases K at low temperature more significantly. For exam-
ple, activation of the mixtures for 6 h increase the reaction rate
constant in order of 109 at 550 ◦C, but it is only 2.5 at 700 ◦C.
Additionally, higher values of n for much activated samples indi-
cate that mechanical activation induces a promoting nucleation
effect. This is due to the fact that the structure refining to the
nanoscale during milling, introduces various defects which are
convenient nucleation sites.
where (IB)t is the integral width corresponding to the disordered sample after
milling time t and (IB)0 is the integral width corresponding to the non-disordered
sample. Meanwhile, IB can be calculated from the following equation:
A
IB =
(3)
Imax
where A is the area under the diffraction peak whose maximum intensity is Imax
.
Unmilled sample and three samples milled for 2, 4 and 6 h were used for
isothermal reduction experiments. Three grams of each sample was pressed in a
cylindrical mould to obtain a density of about 1.50 g cm−3. The pressed samples
were dried at 110 ◦C for 2 h in a vacuum tube furnace. The dried samples were
gradually heated at a rate of 40 K min−1 using a programmable vacuum tube
furnace equipped with thermogravimetric system, at 100 Pa. These samples were
heat treated at 550, 600, 650, 700 and 750 ◦C, for 5–120 min. The changes of
weight in each sample were measured continuously. The extent of the reaction,
α, in each sample was calculated using the following equation [5]:
w0 − wt
α =
(4)
fw0
where w0 and wt are the weights of the initial sample and the one milled for time
t, respectively. f is the fraction of weight loss for complete reduction of Cu2O
according to the reaction (1).
3. Results and discussion
The activation energy for the reaction may be obtained using
the Arrhenius equation in the following form:
3.1. Kinetics modeling of isothermal reduction at the high
temperature annealing
Ea
ln K = ln A −
(7)
RT
Fig. 1(a)–(e) shows the variation of extent of reduction versus
time for unmilled and 2, 4 and 6 h milled samples heated at 550,
600, 650, 700 and 750 ◦C. A remarkable effect of milling on the
kinetics of reduction can be seen between unmilled and milled
samples, especially at 550 and 600 ◦C. Furthermore, prolonged
milling and mechanical activation resulted in much higher cop-
per production and reduction rates. The results illustrate that
temperature significantly affected the reduction rate, as well. For
where A is the pre-exponential factor, Ea is the activation energy,
R is the gases constant and T is the absolute temperature. Fig. 3
shows the lines fitted on ln K versus T−1 plot for each acti-
vated samples. Ea can be obtained from slope of lines in each
temperature range.
The Arrhenius plots in Fig. 3 indicate a change in reac-
tion mechanism at T = 650 ◦C which is manifested by the slope

S. Sheibani et al. / Journal of Alloys and Compounds 455 (2008) 447–453
449
Fig. 1. Extent of the reaction for different samples heated at (a) 550 ◦C, (b) 600 ◦C, (c) 650 ◦C, (d) 700 ◦C and (e) 750 ◦C as a function of annealing time.
change for unmilled and mechanically activated samples for 2
and 4 h. Therefore, the reduction mechanism probably changes
from chemical controlled at low temperature to diffusion con-
trolled at high temperature [16]. Table 2 shows the apparent
activation energy values obtained for reduction reaction in var-
ious conditions. Since the correlation coefficient is very close
to 1 (r > 0.99), the optimized values were calculated with the
best-fit lines.
trolled, at 650–750 ◦C is diffusion controlled. The reason is that
at low temperatures the rate of chemical reaction is so slow that it
is much less than the rate of diffusion. At high temperatures, the
rateofchemicalreactionacceleratedwithriseintemperatureand
it becomes much faster than the rate of diffusion, i.e., it becomes
diffusion controlled [16]. Rapid formation of dense Cu layer at
high temperature surrounding the unreacted Cu2O core could be
another reason for change in mechanism by increasing temper-
ature. Therefore, carbon and CO2 have to diffuse through this
layer. Thus, the process becomes diffusion controlled, although
It is found that although the reduction kinetics at 550–650 ◦C
for unmilled, 2 and 4 h milled mixtures is surface chemical con-

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S. Sheibani et al. / Journal of Alloys and Compounds 455 (2008) 447–453
Fig. 2. The Avrami plot of ln(−ln(1 − α)) vs. ln t for samples heated at (a) 550 ◦C, (b) 600 ◦C, (c) 650 ◦C, (d) 700 ◦C and (e) 750 ◦C.
it is chemically controlled at low temperatures. In this process
both reasons are plausible.
ples. This effect may be attributed to enhanced reactivity by
increasing surface area, SA, and the degree of structural disor-
der, F. Structural disorder means changes in lattice strain and
in crystallite size increased with milling time. The changes in
F with milling time can be plotted using Eq. (2). In Fig. 4 it
can be seen that up to 6 h of milling, the degree of F increases
by 5.6 times. These results are consistent with literature for the
rate of thermal decomposition reactions in minerals [2]. The
influence of SA and F has been expressed by an empirical coef-
ficient in the form of SAF by means of the following relation
[2]:
In Table 2 it can also be seen that increasing the milling
time decreases the activation energies for both determining steps
(surface chemical and diffusion steps), i.e., promotes the reac-
tion kinetics. This may be explained by the shorter diffusion
paths provided by reduced particle sizes and defects formation
in the particles by mechanical activation. On the other hand,
it can be found that from apparent activation energy for 6 h
milled sample, the rate determining step in temperature range
of 550–750 ◦C is diffusion. It means that the mechanical activa-
tion shifts the mechanism change temperature (Arrhenius plot
break) to lower temperature, when compared with other sam-
K = a + bSAF
(8)

S. Sheibani et al. / Journal of Alloys and Compounds 455 (2008) 447–453
451
Table 1
Kinetics parameters for unmilled and milled mixtures extracted from Avrami
plots at different temperatures
Milling time (h)
n
K (min−1
)
r
T = 550 ◦C
0
2
4
6
0.1184
0.1237
0.1363
0.1401
6.56 × 10−12
6.43 × 10−8
2.75 × 10−5
6.74 × 10−3
0.996
0.991
0.995
0.998
T = 600 ◦C
0
2
4
6
0.1318
0.1347
0.1386
0.1426
1.36 × 10−7
2.90 × 10−5
1.51 × 10−3
21.23 × 10−3
0.997
0.994
0.992
0.996
T = 650 ◦C
0
2
4
6
0.3034
0.3051
0.3086
0.3183
4.29 × 10−3
10.98 × 10−3
22.07 × 10−3
39.04 × 10−3
0.992
0.996
0.994
0.998
Fig. 4. Influence of milling time on structural disorder of the Cu2O.
where a and b are constant values. Hence, increment of F results
in an increase in K. Moreover, thermal reduction of Cu2O is
a heterogeneous reaction, the rate of which increases with the
surface area of the sample.
T = 700 ◦C
0
2
4
6
0.2950
0.3223
0.3453
0.3685
30.25 × 10−3
46.72 × 10−3
61.40 × 10−3
75.66 × 10−3
0.995
0.993
0.997
0.994
3.2. Kinetics modeling of mechanochemical reduction
during the room temperature milling
T = 750 ◦C
0
2
4
6
0.3206
0.3466
0.3683
0.3787
40.71 × 10−3
67.53 × 10−3
78.29 × 10−3
91.23 × 10−3
0.996
0.995
0.998
0.997
Fig. 5 shows XRD patterns of the samples milled for various
times, revealing the structural evolution as milling progressed
in the powder mixture. With an increase in the milling time, the
peaks of Cu2O were gradually broadened and their intensities
decreased. The asymmetry of the second peak of the 6-h pat-
tern clearly suggests the presence of some Cu. Further milling
increased the Cu peaks intensities, and single phase Cu was
obtained after 30 h of milling.
Fig. 6 shows the progress of the reduction reaction during
milling (shown by experimental data), measured by the ratio of
the areas under the largest XRD peaks of Cu and Cu2O. As it
was pointed out previously [15], the Cu formation curve in Fig. 6
indicates that the mechanochemical reduction of Cu2O and Cu
Fig. 3. Arrhenius plots for thermal reduction of Cu2O with carbon at tempera-
ture = 550–750 ◦C.
Table 2
The apparent activation energy values of unmilled and mechanically activated
samples
Milling time (h)
E (kJ mol−1
)
T = 550–650 ◦C
T = 650–750 ◦C
0
2
4
6
1387.47, r = 0.996
795.24, r = 0.994
359.51, r = 0.996
291.76, r = 0.998
216.19, r = 0.997
152.77, r = 0.995
94.98, r = 0.997
Fig. 5. XRD patterns of the samples milled for various milling times.

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S. Sheibani et al. / Journal of Alloys and Compounds 455 (2008) 447–453
tified as a good description of kinetics for mechanochemical
synthesis of Cu. It should be noted that, the deviations are
probably related to the extraction of experimental data from
XRD results, especially up to 6 h. Considering an average value
of n = 1.815 and using Avrami plot the reaction rate constant,
K = 9.994 × 10−4 min−1 is calculated for this process. There-
fore, the kinetics equation for mechanochemical reduction of
Cu2O to Cu under mentioned conditions may be written as
below:
α(t) = 1 − exp[−(9.994 × 10−4t)1.815
]
(9)
where t is milling time in minutes and α is the fraction of pro-
duced Cu.
Fig. 6. Relative fraction of copper produced as a function of the milling time at
room temperature in compared with JMA model corresponding to the average
Avrami exponent of 1.815.
3.3. Comparison between kinetics modeling of high
temperature thermal and mechanochemical reduction
formation occurs via a nucleation and growth mechanism. The
above figure shows an incubation time of nearly 6 h after which
the reduction reaction starts with a sharply rising rate. The rate
of the reaction diminishes slowly with prolonged milling. This
suggests that the process occurs via a nucleation and growth
mechanism [17]. Moreover, the initial incubation period prob-
ably corresponds to grain refinement and mixing. It should be
mentioned that the real incubation time might be less than 6 h
and tiny amounts of Cu may be produced earlier than 6 h. How-
ever, the related peaks could not be detected probably due to
the minor amount of Cu and limitation of the XRD resolution.
Furthermore, within the first 15 h of milling, most of the Cu2O
(70%) reacts withcarbon withahighreaction rateafterwhichthe
reaction rate decreases with further milling. Consequently, the
JMA model is used for kinetics analysis of this process as well.
Fig. 7 shows the Avrami plot for mechanochemical synthesis
of Cu, where α was determined from Fig. 6 and t is milling time
in hour. In view of the fact that α value was assumed to be zero
until 6 h of milling, Avrami plot began at this time. The average
Avrami exponent, nav, was calculated as 1.815 from the slope
of fitted line.
Since solid state reactions occur at the reactant–product inter-
face, the reaction rate is proportional to the surface area of the
unreacted part of the material as well as nucleation process. The
lower Avrami exponents of the high temperature thermal reduc-
tion indicate that the surface of each particle is covered by a
layer of the final product in the initial stages and the reaction
proceeds by diffusion-controlled growth in three dimensions,
where nucleation cannot take place during the process. On the
other hand, for mechanochemical reduction, the refining of grain
size during mechanical milling introduces a large percentage
of grain and interphase boundaries and various defects, all of
which could promote the accelerated reduction reaction. Under
the above conditions, the number of the nucleation sites and
diffusion paths increased progressively as compared with the
high temperature thermal reduction. Additionally, milling can
remove the product layer from the surface of each particle con-
tinuously. These lead to the extremely higher value of Avrami
exponent [12,13].
It appears from the modeling results that although different
activation factors induce different transformation rates, the pro-
cess does not proceed through different transformation paths,
since the JMA model describes both reduction paths accurately,
and both thermal and mechanical activation increase Avrami
exponent and decrease diffusion barriers. Thus, the inference of
different reaction pathways may depend on the different periods
which activation factors can overcome on the barriers. For exam-
ple, mechanical activation can create suitable nucleation sites
much faster than thermal activation, but thermal activation can
remove chemical interface reaction barrier much more conve-
nient than mechanical activation. In thermal activation diffusion
coefficient varies exponentially with temperature and increas-
ing the temperature results in removing diffusion barrier. On
the other hand, mechanical activation provides short diffusion
paths due to the formation of defects and removing product
layer between reactants. It may be concluded that, although the
activation mechanisms are different in thermal and mechanical
activation, the mechanism of the Cu2O reduction seems to be
similar in both rates.
For comparison, α is plotted corresponding to the nav (see
Fig. 6). According to this figure, the JMA model can be iden-
Fig. 7. The Avrami plot of ln(−ln(1 − α)) vs. ln t for mechanochemical forma-
tion of Cu.

S. Sheibani et al. / Journal of Alloys and Compounds 455 (2008) 447–453
453
4. Conclusions
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thermal and mechanochemicalCu formation from Cu2O–C mix-
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indicates a change in reduction mechanism for unmilled, 2 and
4 h milled mixtures involving a transition from surface chemical
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addition to activated fresh surface areas during milling, which
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Acknowledgement
The financial support of this work by the Iranian Nanotech-
nology initiative is gratefully acknowledged. Also, the authors
would like to express their thanks to Mr. Khayati for useful help
and discussions.