Reduction kinetics of mechanically activated hematite concentrate with hydrogen gas using nonisothermal methods

Article abstract of DOI:10.1016/j.tca.2006.12.023

The reduction kinetics of both non-activated and mechanically activated hematite concentrate in a vibratory mill for different grinding periods have been studied using themogravimetry (TG). Changes in the structure of hematite were studied using X-ray diffraction analysis. The isoconversional method of Kissinger-Akahira-Sunose (KAS) was used to determine the activation energy of the different reactions. The Vyazovkin model-free kinetic method was also used for prediction of kinetic behavior of the samples for a given temperature. Fe₂O₃ was found to reduce to Fe in a two-step via Fe₃O₄. Intensive grinding resulted in improved resolution of overlapping reduction events. It was also established that the mechanical activation had a positive effect on the first step of reduction. With increasing the grinding time, the activation energy at lower extent of conversion (α ≤ 0.11) decreased from 166 to 106 kJ mol^-1 range in the initial sample to about 102-70 kJ mol^-1 in the sample ground for 9 h. The complexity of the reduction of hematite to magnetite and magnetite to iron was illustrated by the dependence of E on the extent of conversion, α(0.02 ≤ α ≤ 0.95). The values of E decreased sharply with α for 0.02 ≤ α ≤ 0.11 range in the initial sample and mechanically activated samples, followed by a slight decrease in the values of E during further reduction by α ≤ 0.85 in the ground samples up to 3 h. A slight increasing dependence of E on α for mechanically activated sample within 9 h in the second step of reduction was observed due to the finely agglomerated particles during intensive milling and subsequently the formation of a dense layer during the reduction processes. In addition, the dependence of ln A_α on α was detected and it was found that the ln A_α shows the same dependence on α as the apparent activation energies.

Full text of DOI:10.1016/j.tca.2006.12.023

Thermochimica Acta 454 (2007) 69–77
Reduction kinetics of mechanically activated hematite concentrate with
hydrogen gas using nonisothermal methods
Parviz Pourghahramani∗, Eric Forssberg
Division of Mineral Processing, Lulea˚ University of Technology, SE-971 87 Lulea˚, Sweden
Received 10 August 2006; received in revised form 22 December 2006; accepted 22 December 2006
Available online 9 January 2007
Abstract
The reduction kinetics of both non-activated and mechanically activated hematite concentrate in a vibratory mill for different grinding periods have
been studied using themogravimetry (TG). Changes in the structure of hematite were studied using X-ray diffraction analysis. The isoconversional
method of Kissinger–Akahira–Sunose (KAS) was used to determine the activation energy of the different reactions. The Vyazovkin model-free
kinetic method was also used for prediction of kinetic behavior of the samples for a given temperature.
Fe2O3 was found to reduce to Fe in a two-step via Fe3O4. Intensive grinding resulted in improved resolution of overlapping reduction events.
It was also established that the mechanical activation had a positive effect on the first step of reduction. With increasing the grinding time, the
activation energy at lower extent of conversion (α ≤ 0.11) decreased from 166 to 106 kJ mol−1 range in the initial sample to about 102–70 kJ mol−1
in the sample ground for 9 h. The complexity of the reduction of hematite to magnetite and magnetite to iron was illustrated by the dependence
of E on the extent of conversion, α(0.02 ≤ α ≤ 0.95). The values of E decreased sharply with α for 0.02 ≤ α ≤ 0.11 range in the initial sample and
mechanically activated samples, followed by a slight decrease in the values of E during further reduction by α ≤ 0.85 in the ground samples up to
3 h. A slight increasing dependence of E on α for mechanically activated sample within 9 h in the second step of reduction was observed due to the
finely agglomerated particles during intensive milling and subsequently the formation of a dense layer during the reduction processes. In addition,
the dependence of ln Aα on α was detected and it was found that the ln Aα shows the same dependence on α as the apparent activation energies.
© 2007 Elsevier B.V. All rights reserved.
Keywords: Mechanical activation; Iron oxide; Reduction kinetics; Themogravimetry; Nonisothermal
1. Introduction
Fe3O4 + 4H2 → 3Fe + 4H2O
step2
(2)
Step 1 is exothermic, whilst reduction to the metal in step
2 is endothermic [2]. Excellent agreements were achieved in
the rate-controlling reactions. Kinetics data for the reduction
of iron oxides are generally described in terms of nucleation/
autocatalytic, diffusion and phase boundary models. However,
discrepancies exist among the reported kinetics models for the
reduction steps. Such inconsistencies may be attributed to the
starting raw material characteristics, sample specimen used
(powder, pellet, or ore), nature of reducing gas, temperature
range, reduction step, presence of water, gas impurities, physical
shape, etc. [3,4]. It is generally agreed that the rate of reduction
by H2 is significantly faster than that by CO [5]. However, dur-
ing the final stage of reduction, the rate with hydrogen decreases
compared with CO. In the reduction of iron ores with hydrogen,
a dense iron shell forms around the particles (magnetite and/or
The reduction of iron oxides by hydrogen has been investi-
gatedextensivelybecauseofitsrelevancetoironproduction. The
existence of a series of three successive reactions from hematite
¨
(Fe2O3) to iron through magnetite and wustite (Fe1−xO) is of
interest from an academic point of view, regarding the possi-
bility of coupling between two steps and the consequences of
each step upon the following one. The literature [1,2] suggests
that the reduction of Fe2O3 to iron metal, at lower temperature
below 570 ◦C, proceeds in two steps via Fe3O4 intermediate as
follows:
3Fe2O3 + H2 → 2Fe3O4 + H2O
step1
(1)
∗
¨
wustite grains) and subsequently inhibits gaseous transport dur-
Corresponding author. Tel.: +46 920 491313; fax: +46 92097364.
E-mail address: Parviz.Pourghahramani@ltu.se (P. Pourghahramani).
ing reaction [1,6,7]. Several investigations have been reported
0040-6031/$ – see front matter © 2007 Elsevier B.V. All rights reserved.
doi:10.1016/j.tca.2006.12.023

70
P. Pourghahramani, E. Forssberg / Thermochimica Acta 454 (2007) 69–77
Table 1
that the reduction of Fe2O3 is catalyzed by metal additives in
the presence of water vapor (2–7.5%, v/v in reducing mixture).
This enhancement is ascribed to “hydrogen spill over” effect
which provides the necessary active hydrogen at the reduction
centers [2,8]. However, the addition of H2O retards generally
the reduction rate, especially for Fe3O4 → Fe step [3].
Milling conditions in the vibratory mill
Milling conditions
Vibratory milling
Media filling (%)
Mass of media (kg)
Milling time (h)
Ball to powder weight ratio
Speed (RPM)
70
33.16
1, 3, 9
67.68:1
1000
8
The concept of high-energy milling has attracted consid-
erable scientific and technical interests in recent years as a
consequence of higher reactivity and properties developed by
this process. Mechanical activation has found a wide range
of application potential such as the intensification of thermal
reactivity of minerals [9]. Mechanical activation has usually a
positive influence on the leaching reaction kinetics. In addition,
the mechanical activation of minerals makes it possible to reduce
their reaction temperature and/or their decomposition tempera-
ture or causes such a degree of disordering. Thermal behavior
of mechanically activated galena and pyrite has been investi-
gated by Hu et al. [10–12]. It has been found that mechanically
activated pyrite and galena are more easily decomposed during
thermal treatments than non-activated pyrite and galena. More-
over, theactivationenergyofthethermaldecompositionofpyrite
decreases as a consequence of mechanical activation. Mechani-
cally activated sphalerite also oxidizes easily than non-activated
sphalerite [13]. Milling of manganese ore with graphite led to
enhanced reduction at decreased temperatures [14]. Mechani-
cal activation of hematite concentrate can result in reduction of
hematite to maghemite (␥-Fe2O3), magnetite and subsequently
to FeO [15,16]. Since oxygen bonds on the hematite surface
are broken, oxygen is released during high energy milling of
hematite particles in air. However, the transformation of all
hematite by milling process occurs after relatively long period of
time. It is thought that the mechanical activation with a low tem-
perature heat treatment can be successfully applied for reduction
of hematite to magnetite.
Amplitude (mm)
Milling experiments were made in air atmosphere under closed
milling condition, i.e., the door of mill was kept closed during
the whole milling process periods. The grinding conditions are
summarized in Table 1. The samples were sealed into plastic
tubes and kept in a freezer for further measurements.
2.3. Characterization
Thermogravimetric analyses (TG) were conducted with a
NETZSCH STA 409C instrument at three heating rates of 10,
15 and 20 ◦C min−1 from room temperature to 850 ◦C. The high
temperature furnace was heated by graphite heating elements,
whichwereprotectedbyinjectionofinertargongas. Thetemper-
ature of furnace was controlled by a tungsten thermocouple. The
heating was performed under highly pure hydrogen as reduction
gas with a flow rate of 100 ml min−1. The mass of samples was
almost 95 mg.
The morphological characterization of the samples was per-
formed using a Philips XL 30 scanning electron microscope
(SEM) equipped with a LaB6 emission source and running at
20 kV. After drying, the samples were gold coated using gold
sputtering prior to SEM investigation.
The XRD patterns were obtained using a Siemens D5000
powder diffractometer with Bragg-Brentano geometry equipped
with a curved graphite monochromator in the diffracted beam
arm and using Cu K␣ radiation (λ = 0.15406 nm). The XRD
patterns of the samples were recorded using a step size of 0.02◦
and a counting time of 5 s per step.
The goal of this paper is to study the reduction kinetics of both
non-activated hematite and mechanically activated hematite in
a vibratory mill for various grinding times.
2. Experimental
3. Kinetic analysis
2.1. Material
Several methods have been applied for kinetics studies of
solid state reactions [17]. The methods of kinetics analysis can
be classified based on experimental conditions selected and the
mathematical analysis performed. The mathematical methods
are divided into model fitting and isoconversional (model-free)
methods. Modelistic methods have been criticized in nonisother-
mal studies because (1) they assume a constant kinetic triplet
(A, E and model), (2) they involve fitting three parameters (A, E
and model), which are simultaneously determined from a single
curve, (3) they involve a single heating rate, which is not always
sufficient to determine reaction kinetics and (4) the selection of
the best model is a challenging task based on a statistical param-
eter (r2) [18–22]. Model fitting methods were the most popular
methods in the analysis of solid state kinetics. The popularities
of these models have recently declined in favor of isoconver-
sional methods which can compute kinetics parameters without
The high-purity hematite concentrate used in this study
was kindly supplied by the LKAB (Luossavaara Kiirunavaara
Aktiebolag) company in Sweden. The chemical analysis showed
that the initial hematite powder contained about 97.91% Fe2O3,
0.73% Al2O3, 0.73% SiO2, 0.26% TiO2, 0.20% MgO, 0.022%
MnO, and 0.088% P2O5. Other components such as K2O, CaO
and Na2O comprise 0.051%. The X-ray diffraction analysis rep-
resented only the hematite diffraction peaks.
2.2. Mechanical activation
The dry grinding tests were carried out using a vibratory ball
millwithdimensionsofL320 mm × Ø185 mm. Amixtureofball
steel media with dimensions between 6 and 22.2 mm and with
apparent density of 4875 kg m−3 was used as grinding media.

P. Pourghahramani, E. Forssberg / Thermochimica Acta 454 (2007) 69–77
71
modelistic assumptions [22,23]. On the other hand, a successful
kinetics analysis can be performed using several experiments
at the same degree of conversion if careful experiments will be
applied considering the suggestions by Ortega [24]. The basic
assumption of isoconversional methods is that the reaction rate
at a constant conversion is only a function of temperature, and
the reaction model is independent of temperature of heating rate
[25–28]. Thus, constant E values may be expected in the case of
single-state decomposition, while a multi-step reaction E varies
with conversion degree due to the variation in the relative contri-
butions of the single step to the overall reaction rates. The goal
of the model-free kinetics analysis is to use this variation, as
an additional source of information on the reaction mechanism
[29,30]. The main disadvantage of isoconversional approach is
that they do not suggest direct evaluation of the pre-exponential
factor without kinetic model. To use the isoconversional meth-
ods, a series of experiments has to be conducted at different
heating rates [31].
factor from the slope and intercept of the curve with a single
heating rate, respectively. All integral functions in Appendix A
can be tested and the best method can be selected with regard to
a statistical parameter such as correlation coefficient (r).
On the other hand, the isoconversional methods calculate the
kinetics parameters at a progressive degree of conversion (α)
without the modelistic assumptions. Among the isoconversional
methods, Kissinger–Akahira–Sunose(KAS)[34,35]methodhas
been widely used to estimate activation energy regardless of the
rate expressions of reactions as follows:
ꢀ
ꢁ
β
T2
AE
E
ln
= ln
−
(7)
g(α)R
RT
For α = const., the plot ln β/T2 versus 1/T obtained from curves
recorded at several heating rates, should be a straight line whose
slopecanbeusedtocalculatetheactivationenergy. Inthepresent
paper, the above mentioned methods were used for calculation of
the kinetic parameters of the reduction of mechanically activated
and non-activated hematite samples to iron.
The isoconversional method provides a model-free way of
making kinetic predictions. Furthermore, model-free kinetics
doesnotneedtheexperimentalvaluesof A, andg(a)orf(a)forthe
practical purposes of kinetic predictions. The respective predic-
tive equation [37,38] was given in the following form assuming
the partial kinetic triplets remain the same over the temperature
region related to a given conversion:
In the kinetic analysis, a reaction progress expresses con-
ventionally in terms of conversion fraction or extent of reaction
as:
wi − w
α =
(3)
wi − wf
where wi, w and wf are the initial, actual and final weight of the
sample, respectively.
The rate of a solid state reaction can be described by:
ꢅ
ꢀ
ꢁ
Tα
0
dα
dt
dα
dT
−E
exp(−Eα/RT)dT
= β
= k(T)f(α) = A exp
f(α)
(4)
tα =
(8)
RT
β exp(−Eα/RT0)
where k(T) is the rate constant at temperature T, f(α) is a function
of α which represents the reaction mechanism, α the extent of
reaction, tisthetimeand β istheheatingrate. AandEcorrespond
to the pre-exponential and activation energy, respectively. Eq.
(4), can be expressed in the form of its integral, g(α), with Eq.
(5).
This enables the time, tα, at which a given conversion will be
reached at an arbitrary temperature, T0, to be computed. Tα is an
experimental value of the temperature corresponding to a given
conversion at the heating rate β and Eα is the activation energy
at a given conversion.
ꢀ
ꢁ
ꢂ
ꢂ
AE
α
T
4. Results and discussion
d(α)
f(α)
A
β
−E
g(α) =
=
exp
dT;
RT
0
0
4.1. X-ray diffraction analysis
ꢂ
ꢂ
∞
∞
E
If
e−x
AE
βR
= x ⇒ g(α) =
dx =
x2
p(x)dx
RT
βR
The XRD patterns of non-activated and activated samples
are given in Fig. 1. Considering the peaks of non-activated and
activated hematite, the X-ray patterns of the milled samples only
show the Bragg reflections of hematite, suggesting that the start-
ing material did not undergo significant reactions either during
milling or after prolonged milling. With the increased grind-
ing time, a continuous broadening of the diffraction peaks and
decreased intensity of diffraction peaks were observed. These
indicate an increase in the degree of lattice disorder and a
decrease in the crystallite size, thereby reducing the symme-
try of the unit cell until some fraction of the material becomes
amorphous. ComparingtheXRDpatternsindicatesthatthemax-
imum line broadening and minimum intensity are obtained for
hematite sample ground for longer time. In literature [9,11],
it was reported that the mechanical activation resulted in the
amorphization of minerals, development of large numbers of
dislocation and their associated strain fields, decrease of crys-
x
x
(5)
where p(x) is the temperature integral. The Eqs. (4) and (5)
underlie most of the methods of kinetics processing. Several
reaction models used in the analysis of solid state kinetics are
listed in Appendix A in terms of g(α) and f(α). The p(x) has no
analytic solution, but several approximations have been made.
One of the most widely used approximations has been given by
Coats and Redfern [32,33] for exponential p(x):
ꢀ
ꢃ
ꢀ
ꢁꢄꢁ
AR
βE
g(α)
T2
AR
βE
2RTexp
E
ln
= ln
1 −
−
E
RT
ꢀ
ꢁ
ꢀ
ꢁ
2RT
g(a)
T2
E
If :
ꢀ 1 ⇒ ln
= ln
−
(6)
E
RT
where Texp is the mean experimental temperature. A plot of
ln g(α)/T2 versus1/Tgivesactivationenergyandpre-exponential

72
P. Pourghahramani, E. Forssberg / Thermochimica Acta 454 (2007) 69–77
Fig. 3. XRDpatternsofthereductionproductsoftheinitialsample. Theproducts
obtained under heating rate of 10 ◦C/min.
(Fig. 3). The XRD pattern of the reduction product of the ini-
tial sample heated to 450 ◦C with heating rate of 10 ◦C min−1
represents both magnetite and hematite phases. The weight loss
was calculated at about 2.87% up to 450 ◦C, which is still lower
than the weight loss value corresponding to the complete con-
version of hematite to magnetite (3.33%). The reduction of the
initial hematite to 500 ◦C produces reflection peaks of mag-
netite and iron phases in the XRD powder pattern. As a result,
the reduction proceeds stepwise (Fe2O3 → Fe3O4 → Fe). This
agrees with previous literature studies on powder Fe2O3 sample
which generally report that the reduction proceeds in two con-
secutive steps [1,2]. Sastri et al. [2] reported that the findings
Fig. 1. X-ray diffraction patterns of non-activated and activated hematite. Here-
after, 0 h refers to the initial sample or non-activated sample.
tallite size and change of the lattice parameters which might
lead to an overall decrease in long range lattice periodicity. This
may be interpreted as the formation of a metastable “amorphous
phase”, because line broadening and the reduction of diffrac-
tion peaks intensity take place on X-ray pattern after prolonged
milling.
4.2. Reduction behavior
¨
from X-ray diffractometry, Mossbauer spectroscopy and pho-
tomicrography studies showed that the reduction precedes in a
stepwise manner with only two phases, either Fe2O3 and Fe3O4
or Fe3O4 and Fe, existing at any stages throughout isothermal
reduction below 570 ◦C. It should be noted that the absence of
Conventionally, reduction kinetics of iron oxides, such as
hematite or magnetite, has been studied in terms of the extent
of reaction (α). Fig. 2 shows changes in the degree of conver-
sion with three different heating rates for the reduction of the
initial sample by H2 as a function of temperature. A close look
on the curves indicates slight changes of slopes at different tem-
peratures, the changes are more prominent at lower and higher
temperature ranges. These are indicative of sequential reactions.
The changes in the slope of the curves at α = 0.11 correspond to
the quantitative conversion of hematite to magnetite. The pro-
duction of 89% H2O associated with the subsequent reduction to
Fe. The investigation of onset temperatures from the TG curves
confirmed that the prereduction step to Fe3O4 is complete prior
to the onset of the main reduction step to metal iron. This view
is also supported by X-ray analysis of the reduction products
¨
wustite in the XRD patterns of the reduction product does not
¨
mean that wustite does not exist during the reduction because
the dismutation reaction Fe (1−x) O can give Fe and magnetite.
According to Fig. 4, the slope of the curves corresponding to
the activated samples changes when reaction progress reaches
around 0.11. This indicates that the two steps of the reaction
are resolved well as a result of mechanical activation. For non-
activated hematite, the use of higher heating rates do not allow
the complete conversion of hematite to iron metal at the same
temperature ranges as it occurs for the samples ground by the
mill. The maximum degree of conversion for all mechanically
Fig. 2. Changes in the degree of conversion with three heating rates during the
reduction of the initial sample as a function of temperature.
Fig. 4. Changes in the degree of conversion with three heating rates during the
reduction of the sample ground for 9 h in the mill as a function of temperature.

P. Pourghahramani, E. Forssberg / Thermochimica Acta 454 (2007) 69–77
73
Fig. 5. TG curves of the initial sample and the samples ground for various
grinding periods by the mill as a function of temperature.
activated samples is calculated close to unity, corresponding to
the complete conversion of hematite to magnetite. It is clear that
the reduction in the activated samples starts notably at lower
temperatures (higher reactivity) than that in the initial sample.
The beginning temperature of reaction decreases from 400 ◦C
in the initial sample to about 250 ◦C in the sample ground for
9 h. Many workers have reported higher reaction rate at tem-
peratures just below 600 ◦C than higher temperatures. Several
reasons have been proposed for the occurrence of rate minimum
[6,7]. These include sintering of the iron product which reduces
diffusion of the reductant and the product gas to form the reac-
tion interface. The rate minimum phenomenon is clear in the
curve as shown in Fig. 4 at higher temperature for mechanically
activated hematite.
The DTG curves corresponding to the heating rate of
10 ◦C min−1 for the initial sample and the samples ground for
different periods are shown in Fig. 5 as a function of tempera-
ture. The TG curves also represent a two-step weight loss which
can be easily identified from the changes in the slope and the
peaks of the curves. The first step of weight loss, corresponding
to the reduction of hematite to magnetite, occurs at the lower
temperatures. The second step (main step) of weight loss, the
reduction of magnetite to iron, extends toward higher tempera-
ture sides up to 780 ◦C. Interestingly, the first step of weight loss
is more pronounced for mechanically activated samples com-
pared with the initial sample. In addition, a plateau between the
two steps of reduction process can be observed. It is apparent
that the resolution of the two events is greater for mechanically
activated samples than for the initial sample. This is a conse-
quence of the reduction of the energy required to reorganize the
crystalline structure of hematite. The energy supplied by milling
causes structural disorder through the distortion or breakage of
the crystalline network. This was evident from the reduction of
the intensities of XRD peaks reported in Fig. 1. Once more, this
emphasizes that the mechanical activation results in improved
resolution of overlapping reduction events. Moreover, the area of
peak in the second step of reduction decreases concomitantly as
the area of peak in the first weight loss step centered approx-
imately between 300 and 450 ◦C increases, depending upon
grinding time. For the non-activated hematite, the first step of
reduction initiates and terminates at a certain temperature range.
This is an expected property for crystalline hematite. However,
activated hematite exhibits different starting and finishing tem-
Fig. 6. Dependence of E on α characteristic of the reduction of non-activated
hematite and mechanically activated hematite for various grinding times; a large
scale of the curves for the range of 0.25 ≤ α ≤ 0.85 are shown in inset.
peratures of reduction in the first step of reduction, depending on
grinding times and consequently the structural changes induced
during milling.
4.3. Kinetic results
The application of the isoconversional methods requires the
determination of the absolute temperature at which a fixed extent
of reduction from the several TG curves recorded at different
heating rates. The degree of conversion between 0.02 and 0.95
is investigated. The basic parameters such as conversion degree,
heating rate and temperature were inserted into Eq. (7). The cor-
relation coefficients for the linear regressions were higher than
0.94. The dependence of the activation energy E on α charac-
teristic for hydrogen reduction of non-activated hematite and
mechanically activated hematite for different periods is shown
in Fig. 6.
The overall decreasing dependence of the activation energy
on α indicates that the overall reaction contains at least two steps.
A decrease in the activation energy is most likely caused by
transition of the limiting step from the higher activation energy
reaction to the lower activation energy reaction. The curves cor-
responding to the initial sample and the mechanically activated
samples show that E decreases with extent of conversion (α)
by α ≤ 0.11, corresponding the reduction of hematite to mag-
netite, with increasing the grinding time. After this range, the
activation energy continues to decrease for the initial sample
and mechanically activated samples up to 3 h as opposed with
the activation energy for mechanically activated sample within
9 h in which the activation energy tends to increase slightly and
then decreases by α ≤ 0.85. The activation energy of the initial
sample and ground sample for 1 h decrease drastically when the
conversion degree exceeds 0.85 as opposed with the reduction
of the activated samples for more than 1 h. Since the reduction
of the initial sample and activated sample for 1 h extends up to
900 ◦C at higher heating rates, the decreases of the activation
energy can probably be due to the phase transition of α-Fe to
γ-Fe (906 ◦C) [36].

74
P. Pourghahramani, E. Forssberg / Thermochimica Acta 454 (2007) 69–77
Fig. 7. SEM micrographs of the reduction products of the initial sample (a) and the sample ground for 9 h (b).
decreases to about 102–70 kJ mol−1 in the sample ground for
9 h. The disordering of structure in mechanically activated sam-
ples brings about an increase in the rate of reduction process and
a decrease in the activation energy [9]. For the second step of
reduction, the ground sample up to 1 h exhibits no significant
difference in activation energy by conversion degree of 0.85.
Grinding for 3 h result in a slightly smaller activation energy
compared with the initial sample; while prolonged milling for
9 h leads to higher activation energy than the initial sample. This
can be attributed to the agglomeration of finely ground particles
during intensive milling and subsequently to the formation of a
dense layer as a result of the partial sintering at higher tempera-
tures. As a result, the effect of disordering of hematite structure
overlapped by the formation of the dense layer. Therefore, the
reduction is retarded [5]. It can be concluded that mechanical
activation has a positive effect on the prereduction step in terms
of activation energy and small positive effect on the second step
of reduction in the samples ground up to 3 h.
Furthermore, the dependence of the apparent activation
energy (E) on the extent of conversion (α) is a source of addi-
tional kinetic information of process [41]. The obtained results
reveal that the dependence of the apparent activation energy (E)
on the extent of conversion (α) helps not only to disclose the
complexity of reduction processes, but also to identify its kinetic
scheme. A decreasing dependence of E on α is often encountered
in solid decompositions which follow: solid → solid + gas [38].
The curves obtained for non-activated sample and mechanically
activated samples up to 3 h reveal a typical reversible reaction
according to Vyazovkin et al. [38,42–44]. Vyazovkin and Lin-
ert [42] have been shown that the decreasing dependence of E
In the lower degree of conversion (lower temperature region),
the reduction of non-activated hematite is much more sensitive
to the extent of reaction. The first step of reduction, correspond-
ing to α ≤ 0.11, in the initial sample describes with activation
energy of about 166–106 kJ mol−1, while the calculated value
for the second reduction step, corresponding to 0.11 ≤ α ≤ 0.95,
is about 72–9 kJ mol−1. Comparison with literature data shows
that discrepancies exist among the measured activation energies
for the reduction of powdered iron oxides. Such variations may
be associated with differences between the samples studied and
or the conditions employed for sample reduction. For exam-
ple, Munteanu et al. [39] reported the activation energies of 162
and 104 kJ mol−1 for the first and second steps of the reduc-
tion using temperature-programmed method between 450 and
700 ◦C, where the precursor of Fe2O3 was ferrihydrite. Sastri et
al. [2] reported that pretreatment at 850 ◦C of α-Fe2O3 resulted
in an increase in activation energy to 73 kJ mol−1 relative to a
value of 57 kJ mol−1 for a sample that had undergone no heat
treatment. Thus, the activation energy is strongly sample depen-
dent and conditions employed for the reduction. The decreasing
trend of activation energy in the two steps of the reduction can be
explained in the terms of a nucleation and growth the model of
reduction in which the activation energy required during nucle-
ation is higher than that needed in the growth stage (autocatalytic
effects). Similar trends have been reported for the reduction of
iron oxides where E has been found to decrease with extent of
reduction using CR-TPR “rate Jump” technique [40].
For activated hematite, the activation energy for the range of
α ≤ 0.11 decreases with increasing grinding time. The activa-
tion energy from 166 to 106 kJ mol−1 range in the initial sample
Fig. 8. The artificial isokinetic relationship (ln A vs. E) using Coats–Redfern method at heating rate of 10 ◦C/min for the initial sample in the range of 0.02 ≤ α ≤ 0.1
(a), and 0.1 < α < 0.95 (b).

P. Pourghahramani, E. Forssberg / Thermochimica Acta 454 (2007) 69–77
75
on α corresponds to the kinetic scheme of a reversible reaction
followed by an irreversible one. For such process E is limited
by the sum of the activation energy of the irreversible reaction
and the enthalpy of the reversible reaction at low conversions.
At high values of conversions, E is limited only by the activa-
tion energy of the irreversible reaction at high α [41]. In our
case, the reduction of hematite to magnetite probably proceeds
through the exothermic stage at low conversion degrees, which
is characterized by a high value of the apparent activation energy
between166and70 kJ mol−1 dependingonthesample. Thehigh
values of the effective activation energy represent the sum of the
enthalpy of the reversible process and of the apparent activation
of the irreversible process. On the other hand, lower value of
the activation energy at higher conversions is a characteristic of
the process proceeding through a reversible endothermic pro-
cess. For mechanically activated sample for 9 h, the decreasing
dependence of the activation energy is followed by increasing
and then decreasing the activation energy for α ≥ 0.11; indicat-
ing increasing difficulty in the progress of reaction. The second
step is probably involving competiting between the reduction of
magnetite to iron and sintering process which may account for
the increasing dependence of E on α.
and samples. It was found that each TG curve could be equally
well described by several kinetic models resulting in correlation
coefficients close to unity. Therefore, the Arrhenius parameters
derived were highly variable, exhibiting a strong dependence
on the reaction function chosen and a weak dependence on the
heating rate. This extra flexibility in the fitting procedure intro-
duces errors in the functional form of the reaction model. This
can be offset by making compensation errors in the Arrhenius
parameters. Vyazovkin et al. [38,47,48] explored widely artifi-
cial isokinetic relationship (IKR) that occurs on fitting various
reaction models to the same set of nonisothermal kinetic data.
Originally, this procedure was suggested [48] for estimating the
pre-exponential factor in the isoconversional method as applied
to a single-step process. However, the procedure can be applied
to isolate the ln A on α dependence for multi-step processes [38].
Use of the so-called artificial isokinetic relationship may be used
to evaluate the pre-exponential factors for the model-free anal-
Fig. 7 exhibits the morphological aspects of the reduction
products using SEM studies at the initial and activated samples.
Unlike the initial sample, the partial sintering can be clearly
observed in the mechanically activated hematite. The partial
sintering leads to the formation of rounded particles in the acti-
vated sample as a consequence of mass transport process by
moving mass from particle surface and internal mass sources
[45]. It seems that the agglomeration of the finely ground parti-
cles during extended dry milling facilitates the sintering process.
The clusters of the partially sintered material can be further
observed due to the formation of massive and compact agglom-
erates which was identified and reported during intensive dry
grinding process elsewhere [46].
4.3.1. The evaluation of pre-exponential factor
The Coats–Redfern analysis of the thermogravimetric data
recorded at a single heating rate has been carried out by insert-
ing various g(α) in Appendix A into Eq. (6) that results in a set of
Arrhenius parameters determined from the plot ln g(α)/T2 ver-
sus 1/T. Similar calculations were made for other heating rates
Fig. 10. Prediction at different temperatures using heating rate of 10 ◦C/min for
the initial sample (a) and mechanically activated samples for 1(b), 3 (c) and 9
(d) hours.
Fig. 9. Dependence of ln Aα on extent of conversion, α, estimated from Eq. (9)
for different samples.

76
P. Pourghahramani, E. Forssberg / Thermochimica Acta 454 (2007) 69–77
ysis. It is observed that the values of the activation energy and
pre-exponential factor, obtained for different function of g(α),
are correlated through the following relation of compensation:
with our nonisothermal experiments where the onset of reaction
for the initial sample is calculated about 420 ◦C. It follows from
the figure that a conversion of 0.1 is attainable for 70, 26, 14 and
10 min at T = 450 ◦C in the initial sample and ground samples
for 1, 3 and 9 h, respectively. With increasing temperature, the
difference between the samples for achieving a given conversion
at an identical temperature reduces. Achieving a conversion of
0.7 at T = 650 in the initial sample and activated samples for 1,3
and 9 h, respectively, takes about 67, 65, 65.2 and 58 min that
samples are maintained under reducing program. The results
reveal that the mechanical activation has large positive effect on
the reduction of hematite at lower temperatures compared with
reduction at higher temperatures.
lnAi = aEi + b
(9)
where the subscript i refers to the one of the possible models
considered (g(α) in Appendix A) to describe the process. This
reveals that the rate of process can be fairly described by Eq. (6)
with practically any model g(α) and fitting k(T) which compen-
sates the error of reaction model choice. An example of artificial
isokinetic relationship for the initial sample is given in Fig. 8.
All of the plots represent excellent fit where the correlation
coefficient exceeds 0.97.
Once the correlation coefficients of the artificial isokinetic
relationships have been evaluated, the Ea values from the iso-
conversional methods are substituted for Ea in the compensation
effect Eq. (9) [38] for the studied systems to estimate the corre-
sponding ln Aa values and obtaining the dependence of ln Aa on
α. The results are summarized in Fig. 9. Clearly, the ln Aa shows
the same dependence on α as the apparent activation energies
(E).
5. Conclusion
The reduction of Fe2O3 to Fe was found to occur in a two step
process via Fe3O4. The TG and DTG analysis showed that the
two reduction steps took place consecutively. The mechanical
activation promoted partial amorphous solids along with some
structural distortions in hematite. This pretreatment resulted in
improved resolution of overlapping reduction events. The pre-
reduction step in the activated samples initiated and completed
at lower temperatures than that in non-activated samples. The
activation energy of the first step of reduction decreased with
increasing the grinding time. Intensive milling increased slightly
the average activation energy of the second reduction step due
to the present of finely agglomerated particles and intensive
sintering of the particles in higher temperature ranges.
Our study shows that the activation energy of the two steps
of the reduction depends greatly on the extent of conversion,
implicating that the reduction of hematite to magnetite and mag-
netite to iron features multi-step characteristics. The decreasing
trend of activation energy in the two steps of the reduction
can be explained in the terms of a nucleation and growth the
4.3.2. Predictions
Predictions are among the most important practical feature of
kinetic analysis [42]. They are widely used to evaluate the kinetic
behavior of materials beyond the temperature region of exper-
imental measurements. By using Eq. (8), with nonisothermal
kinetic data, the prediction of samples behavior in isothermal
conditions is possible. Fig. 10 presents conversion curves of the
reduction of the initial sample and ground samples in the mill
as a function of time, for different temperatures. On the basis of
the curves obtained for the samples, one may state that the con-
version time decreases as a function of temperature. It is evident
from the graph that the initial sample does not reduce at 350 ◦C
as opposed with mechanically activated hematite. This agrees
Table A.1
Solid state rate expressions for different reaction models
1 dα
Model
Differential form f(α) =
Integral form g(α) = kt
k
dt
Nucleation models
Power law (P2)
Power law (P3)
2α(1/2)
3α(2/3)
α(1/2)
α(1/3)
Avarami-Erofe’ev (A1.5)
Avarami-Erofe’ev (A2)
Avarami-Erofe’ev (A3)
Avarami-Erofe’ev (A4)
Geometrical contraction models
Contracting area (R2)
Contracting volume (R3)
Diffusion models
1D Diffusion (D1)
2D Diffusion (D2)
3D Diffusion–Jander Eq. (D3)
Ginstling–Brounshtein (D4)
Reaction-order models
Zero-order (F0/R1)
3(1 − α)[−ln(1 − α)]1/3/2
2(1 − α)[−ln(1 − α)]1/2
3(1 − α)[−ln(1 − α)]2/3
4(1 − α)[−ln(1 − α)]3/4
[−ln(1 − α)]2/3
[−ln(1 − α)]1/2
[−ln(1 − α)]1/3
[−ln(1 − α)]1/4
2(1 − α)1/2
[1 − (1 − α)1/2
]
]
3(1 − α)2/3
[1 − (1 − α)1/3
1/(2α)
α2
[−ln(1 − α)]−1
[(1 − α)ln(1 − α)] + α
(3/2)(1 − α)2/3[1 − (1 − α)1/3
(3/2)(1 − α)−1/3 − 1)−1
]
[1 − (1 − α)1/3
]
−1
2
(1 − 2α/3) − (1 − α)2/3
1
α
First-order (F1)
Second-order (F2)
Third-order (F3)
(1 − α)
(1 − α)2
(1 − α)3
−ln(1 − α)
(1 − α)−1 − 1
0.5[(1 − α)−2 − 1]

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77
model of reduction in which the activation energy required dur-
ing nucleation is higher than that needed in the growth stage
(autocatalytic effects). The prediction of reduction behavior of
the samples revealed that with increasing temperature, the dif-
ference between the samples for achieving a given conversion
reduces at an identical temperature.
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Appendix A
See Table A.1 for solid state rate expressions for different
reaction models.
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