Reduction of iron oxide catalysts: the investigation of kinetic parameters using rate perturbation and linear heating thermoanalytical techniques

Article abstract of DOI:10.1021/jp003189+

The mechanisms and kinetics of the reduction of powdered Fe₂O₃ and Fe₃O₄ samples have been investigated under nonisothermal conditions to provide a detailed insight into the processes occurring. Both conventional linear heating temperature-programmed reduction (TPR) and constant rate temperature-programmed reduction (CR-TPR) techniques were utilized. Fe₂O₃ was found to reduce to Fe in a two-step process via Fe₃O₄. The mechanism of the prereduction step of Fe₂O₃ to Fe₃O₄ was found to follow an nth order expression where nucleation or diffusion was not the rate-controlling factor while the main reduction step to metal was described by a model involving the random formation and growth of nuclei. A CR-TPR rate perturbation method, 'rate-jump', was applied to the measurement of variations in apparent activation energy throughout the reduction processes, under near-equilibrium conditions and the activation energy measurements are compared with those obtained under conventional linear heating conditions.

Full text of DOI:10.1021/jp003189+

220
J. Phys. Chem. B 2001, 105, 220-228
Reduction of Iron Oxide Catalysts: The Investigation of Kinetic Parameters Using Rate
Perturbation and Linear Heating Thermoanalytical Techniques
†
Michael. J. Tiernan, Philip. A. Barnes,* and Gareth. M. B. Parkes
Centre for Applied Catalysis, Materials Research DiVision, UniVersity of Huddersfield,
Queensgate, HD1 3DH, U.K.
ReceiVed: September 5, 2000; In Final Form: NoVember 1, 2000
2 3 3 4
The mechanisms and kinetics of the reduction of powdered Fe O and Fe O samples have been investigated
under nonisothermal conditions to provide a detailed insight into the processes occurring. Both conventional
linear heating temperature-programmed reduction (TPR) and constant rate temperature-programmed reduction
(
CR-TPR) techniques were utilized. Fe
O
2 3
was found to reduce to Fe in a two-step process via Fe
3 4
O . The
mechanism of the prereduction step of Fe
2
O
3
to Fe was found to follow an nth order expression where
3 4
O
nucleation or diffusion was not the rate-controlling factor while the main reduction step to metal was described
by a model involving the random formation and growth of nuclei. A CR-TPR rate perturbation method,
“rate-jump”, was applied to the measurement of variations in apparent activation energy throughout the reduction
processes, under near-equilibrium conditions and the activation energy measurements are compared with
those obtained under conventional linear heating conditions.
1
. Introduction
boundary) models of reduction (discussed in detail below).12
The reductions of Fe2O3 and Fe3O4 to Fe have been reported to
1
.1. Reduction of Iron Oxide. The reduction of iron oxides
follow all of these models, with variations attributed to
experimental factors such as sample particle size or the
by both hydrogen and carbon monoxide has been investigated
very extensively because of its relevance for iron production
and the preparation of ammonia synthesis catalysts.
has three oxides, namely hematite (Fe2O3), magnetite (Fe3O4),
and w u¨ stite (FeO). The latter is unstable below 570 °C when it
1
,2,5,8
conditions chosen for analysis.
been reported to reduce via a phase boundary mechanism
topochemical mode of reaction) while smaller particles tend
Larger particle sizes have
1
,2-11
Iron
(
to show sigmoidal reduction isotherms associated with a
formation and growth of nuclei model (uniform internal
9
decomposes to R-Fe and Fe3O4. The literature suggests that
the reduction of Fe2O3 to Fe metal, at temperatures below 570
1
reduction) particularly at lower temperatures. An auto-catalytic
°
C, proceeds in two steps via Fe3O4 intermediate as follows:
role of freshly formed Fe particles in the presence of certain
levels of water vapor (2-7.5 v/v% in the reducing mixture)
has also been proposed involving transport of active hydrogen
from metal sites to the oxide through “portholes” of water vapor
3
Fe O + H f 2Fe O + H O Step 1
2
3
2
3
4
2
Fe O + 4H f 3Fe + 4H O Step 2
3
4
2
2
3,4
trapped between the metal and oxide phases. However, in
general the addition of H2O is reported to retard the reduction
rate particularly for the Fe3O4 f Fe step.
Step 1 is exothermic, while reduction to the metal in step 2 is
endothermic. Discrepancies exist in the kinetic model(s) which
1
3
Conventionally, reduction kinetics of metal oxides, such as
Fe2O3 or Fe3O4, have been studied under isothermal conditions
where the extent of reduction, R, is measured as a function of
time. In recent years, nonisothermal techniques for the inves-
tigation of kinetic parameters have become popular because of
their less cumbersome and tedious nature when compared with
a series of isothermal experiments at different temperatures.13
In particular, temperature-programmed reduction (TPR) experi-
ments have been performed using linear heating rates to
investigate the reduction of metal oxides and metal salts as a
function of temperature. The inherent simplicity and high
sensitivity of linear heating TPR make it a very important
analytical method which has provided extremely valuable
information in a range of areas including the characterization
have been reported for the reduction steps. Such inconsistencies
may be attributed to variations in the type of sample specimen
used (powder, pellet, or ore) and the experimental conditions
1,2,8
employed (temperature, pressure, isothermal, nonisothermal).
In particular, differences are found in the literature in the
conditions of reduction temperature, H2O pressure, and particle/
crystallite size. Comparisons are further complicated because
not only do different oxides exist but also the presence of
8
impurities (e.g., Ca, Mn, and Mg in ores) and dopant materials
1
1
(
e.g., K in ammonia synthesis catalysts) may significantly
2,3
affect the reduction process. In the case of reduction of either
hematite or magnetite at temperatures above 600 °C, the
1
0
formation of a stable w u¨ stite phase must also be considered.
.2. Kinetic Studies of Iron Oxide Reduction. Kinetic data
1
1
2
and preparation of catalysts. Unfortunately, the use of linear
heating rates in thermal analysis techniques results in nonuni-
form reaction conditions throughout the sample leading to
for the reduction of metal oxides are generally interpreted in
terms of nucleation, auto-catalytic, or contracting sphere (phase
14-16
relatively poor resolution and kinetic data.
Further difficul-
*
Corresponding author. E-mail: p.a.barnes2@hud.ac.uk.
Current address: School of Chemical Sciences, Dublin City University,
†
ties arise in TPR, because variations in sample mass, heating
rate or gas flow rate lead to different H2 consumption rates.
Dublin 9, Ireland
1
0.1021/jp003189+ CCC: $20.00 © 2001 American Chemical Society
Published on Web 12/13/2000

Reduction of Iron Oxide Catalysts
J. Phys. Chem. B, Vol. 105, No. 1, 2001 221
For these reasons, TPR profiles are known to be remarkably
dependent on the experimental conditions employed which can
affect both the shape and resolution of reduction steps as well
as peak temperatures.1
The most frequently cited kinetic models can be categorized
into three groups which describe diffusion-controlled processes,
boundary-controlled (nth-order processes), and processes involv-
2,14,15-17
1,23-25
ing random nucleation and subsequent growth of nuclei.
Such limitations of linear heating TPR can be illustrated by
examples of the reduction of Fe2O3 taken from the literature.
Satisfactory resolution of the two steps involved in the reduction
of Fe2O3 has been found to be difficult to achieve under linear
Algebraic expressions (f(R)) for each of these models can be
1
,22,23
found in the literature.
For diffusion-controlled processes,
gas diffusion through the product layer is the rate-determining
step. Phase boundary-controlled models are geometrically
defined as shrinking/unreacted core or contracting sphere models
with the reaction proceeding topochemically and in which the
chemical reaction is the rate-determining step. In terms of the
reduction of metal oxides, nucleation-controlled processes
involve uniform internal reduction and occur by the initial
random removal of lattice oxygen atoms until a critical
concentration of vacancies is reached. The vacancies are then
annihilated by lattice rearrangement to produce metal nuclei.
The nuclei then grow and, as they expand, the reduction process
accelerates due to the increasing metal-metal oxide interface
which is further increased by the formation of new nuclei.
Eventually, merging of product nuclei causes a decrease in
sample-product interfacial area and the reduction decelerates.
Autocatalytic mechanisms, where the product metal dissociates
hydrogen molecules thereby increasing the rate of reduction of
remaining metal oxide, must also be considered when studying
1
heating rate TPR conditions. Combined with a lack of sensitiv-
ity, this can limit ability to gain a detailed insight into step 1 of
1
the hematite reduction process. Prudent choice of experimental
conditions, such as H2 and H2O pressure, is also essential. The
level of H2O in the reducing mixture has been shown to affect
both the rate and the mechanism of reduction.1,3,4 The H2 partial
pressure employed has also been shown to affect both peak
temperatures and resolution.6 Comparison of previous litera-
ture studies using unsupported iron oxides has shown that the
use of integral conditions with respect to H2 and H2O pressures
may result in strongly deformed and broadened peaks when
compared with profiles obtained under differential conditions,
emphasising the care required when performing linear heating
,16
1
,2
rate experiments.
To provide more optimal conditions for kinetic analysis of
TPR profiles we have recently described an apparatus developed
to perform reduction under constant rate thermal analysis
1
,12
solid-gas reductions.
18
(CRTA) conditions as well as conventional linear heating rates.
It is well-known that a number of experimental factors, such
as geometric considerations, are important in solid-state reactions
and can produce significant deviations in f(R) and the measured
The advantages of CRTA, where the reaction is forced to
proceed at a low and constant rate, are well documented for
1
8-21
27
the study of decomposition and reduction reactions.
In
values of A and E for a given reaction. In such circumstances,
comparison with linear heating rate methods, CRTA reduces
temperature and pressure gradients across the sample bed and
allows reactant and product gases to be maintained at a constant
concentration level. In this manner, CRTA provides superior
control of mass and thermal transfer effects while application
of a “rate-jump” method allows the apparent activation energy
it is not appropriate to interpret E in terms of the usual energy
barrier model of homogeneous chemical reaction kinetics and,
for this reason, the term apparent activation energy is often
2
2
applied.
2.2. Apparent Activation Energy Measurements. Kinetic
analysis of linear heating rate and CRTA “rate-jump” experi-
ments can be achieved using methods based on the general
kinetic eq 1 above. The methods used in the current study are
outlined below.
of reaction to be determined under near-equilibrium condi-
tions.1
8,22
CR-TPR can also provide enhanced resolution for
overlapping reduction events while the shape of the temperature
profile obtained gives an insight into reduction mechanisms of
1
2.2.1. Linear Heating Rate Methods. Wimmers et al. have
18
supported and unsupported samples.
proposed a method, based on eq 1, which allows the apparent
activation energy, Ea, for the reduction of iron oxide under linear
heating conditions to be determined using the following
equation:
In the present study, CR-TPR is used to investigate kinetic
aspects of the reduction of iron oxides (hematite and magnetite)
under experimental conditions designed to optimize resolution
of the reduction events and provide a mechanistic insight into
each event. Results are compared to those obtained under linear
heating conditions.
-E
RTm
â
a
AR
Ea
ln
)
+ ln
+ constant
(2)
2
(
)
(
)
Tm
2. Theory
where â is the heating rate.
When ln(â/T ) is plotted versus 1/Tm a straight line is
obtained with a slope of -Ea/R.
2
.1. Kinetic Model. Gas-solid reactions such as reductions
2
m
are typified by complex kinetics which frequently cannot be
described by a single nth-order expression over the entire
1,18
No prior knowledge of the
kinetic model describing the reduction mechanism is required
in order to calculate Ea. This method assumes that any changes
in reduction mechanism and the extent of reduction (R) at Tm,
caused by changes in the heating rate employed, are negligible.
1,18
reaction range. Kinetic interpretation of thermal analysis data
is normally carried out using equations based on the general
kinetic equation:
1
Wimmers and coauthors noted that eq 2 is generally applicable
-E/RT
rate ) dR/dt ) A f(R) exp
(1)
for the determination of activation energy from conventional
TPR measurements.
where A is the preexponential factor, T is the absolute temper-
ature, t is the time, R is the fraction of sample reacted, E is the
activation energy, R is the gas constant (8.314 J mol K ),
and f(R) is a function which represents the reaction mechanism.
The aim is to determine the kinetic model (f(R)) which gives
the best description of the studied reaction and allows the
calculation of meaningful parameters E and A.
2.2.2. CRTA “Rate-Jump” Method. The underlying principles
and exact measurement procedures associated with the use of
the CRTA “rate-jump” method for the determination of model-
free activation energy values have been previously described
for gas-solid reduction and solid-state decomposition reac-
tions. In this technique, the rate of reaction is made to alternate
between two pre-selected target rates by appropriate control of
-
1
-1
18
22

222 J. Phys. Chem. B, Vol. 105, No. 1, 2001
Tiernan et al.
2
0
the temperature or, for certain systems, the concentration of a
TABLE 1: Experimental Conditions Employed for CRTA
2
8
“Rate-Jump” Experiments for the Reduction of Fe O and
reactant gas. In the former case, provided equilibrium of the
reaction rate is achieved at the two successive rates, the
corresponding temperature measurements can be used to
calculate a value of Ea for the reaction using the following form
of the Arrhenius equation:
2
3
Fe
3
O
4
Samples
sample
mass
sample (mg) (mg H
a
b
C
2
1
C
2
2
no. of
“rate-jumps”
O min-1) (mg H
O min-1
)
-
-
3
-3
Fe
Fe
2
O
O
3
30.0
30.0
3.6 × 10
3.6 × 10
4.4 × 10
4.4 × 10
132
116
3
-3
3
4
T2
C1
Ea ) RT
1
ln
(3)
a
1 2
C C ) higher water
) lower water evolution rate target. b
(
)
T1 - T2 C2
evolution rate target.
where T1 and T2 are the temperature measurements correspond-
ing to the two pre-set reaction rates C1 and C2, at the same
value of R (extent of reaction).21 To ensure that T1 and T2 values
for each jump correspond to the same extent of reaction, an
extrapolation procedure is performed using best-fit curves drawn
through the higher and lower levels of successive “jumps” for
both temperature and reduction rate as detailed in a previous
paper.22
The use of the “rate-jump” method to provide measurements
of thermally activated reactions has been recommended since
the results obtained are less dependent on experimental param-
2
1,26,29
eters than those obtained with conventional techniques
as the effects of heat and mass transfer can be minimized.
2
0
This can be most successfully achieved if the target reduction
rates, C1 and C2, as well as the difference between the selected
rates, be maintained as low as possible in order to minimize
heat and mass transfer effects throughout the reduction process
as well as changes in reactant and/or product concentration
during each jump. The method assumes that any changes in
f(R), as well as R, during each “rate-jump” are negligible,
emphasising the requirement that the execution time for each
jump be small in comparison with the duration of the reaction.
Furthermore, by making a large number of “rate-jump” mea-
surements, any variation in Ea throughout the reaction can be
Figure 1. X-ray diffraction powder patterns of Fe O (a) and Fe O
4
(b) samples.
2
3
3
described previously.18 Important features of the apparatus
include direct sample temperature measurement, a fast response
furnace, and a highly sensitive specific detector. Rapid computer
control of the furnace heating or cooling rates allows regulation
of the reaction rate, at pre-set values, via a feedback loop for
CRTA experiments.
1
8,22
quantified.
The use of low overall reaction rates ensures that near-
equilibrium conditions are reached. While each experiment may
therefore last for many hours there is no need for the series of
runs at different temperatures (for isothermal work) or at various
heating rates (for linear heating experiments). Not only does
this save time but it also removes uncertainties which can arise
in a series of experiments due to the inevitable slight variations
in the sample and experimental conditions.
It should be noted that in the CRTA “rate-jump” method,
the resolution of two consecutive events is often more clearly
seen from the temperature curve.18 In an ideal experiment, the
reaction rate curve would show no discontinuity between two
such processes which would be revealed only by reference to
the temperature trace.
For all experiments the reduction atmosphere consisted of
5% hydrogen in helium at a flow rate of 52 cm3 min .
Conventional TPR experiments were performed using a variety
-1
-1
of linear heating rates in the range of 2 to 15 °C min . Equation
2 was then used to yield values for the apparent activation
energy of the reduction. A sample mass of 2.0 ( 0.1 mg was
employed in all linear heating rate experiments.
Details of the experimental conditions employed for CRTA
“rate-jump” experiments are shown in Table 1. Experiments
were performed using maximum heating and cooling rates of 5
-
1
and 10 °C min , respectively. The heating rate was varied
between these two limits in order to alternate between two pre-
selected target reduction rates, C and C . Equation 3 was then
3
. Experimental Section
.1. Materials. Fe2O3 (99.98%, Aldrich) and Fe3O4 (99.997%,
1
2
used to calculate the activation energy for each jump.
3
Alfa Chemicals) were used. Samples were sieved through a 250
µm mesh prior to all experiments.
4
. Results and Discussion
3
.2. Materials Characterization. X-ray diffraction (XRD)
4.1. Materials Characterization. XRD patterns are shown
spectra of Fe2O3 and Fe3O4 samples were obtained using Cu
in Figure 1 which confirm the structure of Fe2O3 and Fe3O4
samples with the main peak for Fe2O3 present at a 2θ angle of
33.0° (Figure 1a) and for Fe3O4 at 2θ angle of 35.2° (Figure
KR (λ ) 1.5418 Å) radiation. Scanning electron micrography
(SEM) images were obtained using a S-3000N Hitachi instru-
3
,30
ment. The surface area of each sample was estimated using the
BET method based on the adsorption of N2 at -195 °C using
a Micromeritics Gemini Analyzer instrument and pore size
analysis was performed using a Coulter SA 3100 instrument.
1b).
Representative SEM images of the two samples are
shown in Figure 2 at low (Figure 2b,d) and high (Figure 2a,c)
magnification. The Fe2O3 sample (Figure 2a,b) consists of
chipped particles of various shapes with flat sharp-edged
surfaces. By contrast, the Fe3O4 sample (Figure 2c,d) is seen to
consist of much smaller particles with a more lustrous and less
3
.3. TPR Conditions. The TPR apparatus, which uses a
hygrometer to detect H2O evolved during reduction, has been

Reduction of Iron Oxide Catalysts
J. Phys. Chem. B, Vol. 105, No. 1, 2001 223
2 3 3 4
Figure 2. Typical SEM photographs of Fe O (a,b) and Fe O (c,d) samples.
2 3
Figure 3. TPR profile of Fe O under linear heating rate conditions.
3 4
Figure 4. TPR profile of Fe O under linear heating rate conditions.
2
-1
2
-1
-1
defined surface. BET surface areas of 160 m g and 2 m g
3
-1
3
and total pore volumes of 0.185 cm g and 0.005 cm g
were measured for Fe2O3 and Fe3O4, respectively.
showed two overlapping peaks indicating a two-step reduction
process. Depending on the heating rate employed, the peak
maximum ranged from 327 to 383 °C for the minor peak and
from 389 to 522 °C for the major peak (see Table 2).
4
.2. Comparison of CRTA and Linear Heating Tech-
niques. Figures3 and 4 illustrate TPR results obtained under
linear heating conditions for the Fe2O3 and Fe3O4 samples.
Figure 3 shows a typical TPR profile for Fe2O3 obtained using
2
Shimokawabe et al. reported peak temperatures of 350 °C and
550 °C in the TPR profile of an Fe2O3 sample prepared by
decomposition of Fe(OH)(CH3COO)2 in air at 500 °C and
-1
a linear heating rate of 10 °C min . The maximum rate of H2O
-
2
-1
-1
production was ca. 4.35 × 10 mg min for the major peak.
reduced under a linear heating rate of 4.5 °C min . Meaningful
Under all linear heating rates employed the reduction of Fe2O3
comparison of exact peak temperatures with other studies is

224 J. Phys. Chem. B, Vol. 105, No. 1, 2001
Tiernan et al.
TABLE 2: Variation of T
m
with Linear Heating Rate (â) for
set reaction rates throughout each step. The target reaction rates
were maintained over a temperature range of 250-270 °C for
the first reduction step while the majority of the second step
occurs at the pre-selected rates over the temperature range of
245-295 °C. This shows that the reduction steps can be
achieved at a much lower temperature than indicated in Figure
Fe
2
O
3
Reduction
â
T
m
(°C) (°C)
T
m
(
°C min-1)
peak [1]
peak [2]
2
5
0
5
327
353
373
383
389
438
491
522
1
1
3
under conventional linear heating conditions. It also shows
that a large proportion of the second step in the reduction
occurred within the same temperature range as the first
temperature step even though the steps are consecutive in
occurrence. This is associated with a difference in the mecha-
nism of the two steps which is not apparent from linear heating
rate profiles and is discussed in more detail below.
TABLE 3: Variation of T
Fe Reduction
m
with Linear Heating Rate (â) for
3
O
4
â (°C min-1
)
T
m
(°C)
2
5
0
5
410
458
503
531
1
1
Figure 6 shows the CRTA “rate-jump” profile obtained for
the reduction of Fe3O4. The reduction is seen to proceed in a
single step across a temperature range of 260-345 °C, as judged
by a lack of discontinuity in the temperature trace.
difficult because of the different experimental and pretreatment
conditions employed by the various workers.12 However, most
literature agrees that the reduction of powdered hematite to
4
.3. Mechanism and Apparent Activation Energy of
Reduction. Figure 7 shows the R versus temperature profile
for the linear heating rate experiment (Figure 7a) and the CRTA
metallic iron involves two stages via the formation of magnetite
steps 1 and 2, discussed above).1-3 Boot et al. reported only
6
(
“
rate-jump” experiment (Figure 7b) for the reduction of Fe2O3,
one unresolved reduction peak for Fe2O3 in a physical mixture
3 wt % Fe) with ZrO2. However, this could be attributable to
the latter form of presentation being valuable for quantitative
comparisons. From both curves, it is seen that the first reduction
step accounts for approximately 11% of the overall reduction
process. A value of 11.1% corresponds to the formation of
Fe3O4, with 88.9% of the H2O production associated with
subsequent reduction to Fe. It is apparent from Figure 7 that
the resolution of the two events is greater under CRTA
conditions than using conventional linear heating with the R
profile in Figure 7b confirming that the prereduction step to
Fe3O4 is complete prior to the onset of the main reduction step
to metallic iron. This agrees with previous literature studies on
powder Fe2O3 samples which generally report that the reduction
(
the high concentration of H2 (70% in Ar) employed for linear
heating TPR which would be expected to result in poor
resolution of overlapping events.
Figure 4 shows the TPR profile obtained for Fe3O4 under
-
1
linear heating conditions of 10 °C min . A single peak is
observed over a temperature range of ca. 370-610 °C with a
maximum at 502 °C. The maximum rate of H2O production is
-
2
-1
ca. 3.69 × 10 mg min . Peak temperatures at other heating
rates employed are shown in Table 3. Comparison of Tables 2
and 3 shows that at all heating rates employed the peak
temperature for Fe3O4 f Fe reduction was higher during
reduction of Fe3O4 starting material relative to the peak
temperature for the second step in the reduction of Fe2O3 sample.
Differences in reducibility might be associated with the higher
surface area of the Fe2O3 sample providing a greater number
of reactive sites at which reduction can start.2
1
,2,3
Sastri and co-workers3
proceeds in two consecutive steps.
reported that findings from X-ray diffractometry, M o¨ ssbauer
spectroscopy and photomicrography studies showed that the
reduction proceeds in a stepwise manner with only two phases,
either Fe2O3 and Fe3O4 or Fe3O4 and Fe, existing at any stage
throughout isothermal reduction below 570 °C. Jung and
,31
Figure 5 shows the reduction profile of Fe2O3 under CRTA
5
“
rate-jump” conditions. The reduction takes place in two
Thompson showed using a dynamic X-ray diffraction (DXRD)
consecutive steps as can be seen by the discontinuity in the
temperature curve. The temperature profile shows how the
computer control system attempts to alternate between the pre-
technique that the isothermal reduction of Al2O3-supported
Fe2O3 (31.8 wt % Fe) to Fe at 400 °C proceeded via Fe3O4 and
that it was only after complete reduction of hematite to magnetite
2 3
Figure 5. TPR profile of Fe O under CRTA “rate-jump” conditions.

Reduction of Iron Oxide Catalysts
J. Phys. Chem. B, Vol. 105, No. 1, 2001 225
3 4
Figure 6. TPR profile of Fe O under CRTA “rate-jump” conditions.
throughout the reduction step. This causes the R versus
temperature profile to characteristically curve back on itself
1
8,24,31
during the reduction process.
This can be explained as
follows. The temperature increases at first until the initial
formation of nuclei after which the temperature decreases in
order to maintain a constant reduction rate as the metal-metal
oxide interfacial area expands. Toward the later stages of
reduction, the expanding nuclei start to overlap and the area of
the sample-product interface starts to decrease so the temperature
has to rise again to prevent deceleration of the reaction. In some
cases, metal nuclei formed are believed to dissociate and activate
dihydrogen molecules leading to autocatalysis which could also
result in a similar R versus temperature profile to that obtained
for the main reduction step in Figure 7b. The shape of the R
versus temperature plot obtained for the prereduction step of
Fe2O3 indicates that a different kinetic model was in operation
for this step as a continual rise in temperature was required to
maintain the desired reduction rate. This profile shape is
associated with an “nth-order” type of kinetic model where
nucleation or diffusion are not the rate-controlling factors.2
Although the second step is initiated at a higher temperature
than the prereduction step it can be seen from Figure 7b that a
large proportion of the main reduction step proceeded within
the same temperature range as the prereduction to Fe3O4 under
CRTA experiments. Although the initial formation of nuclei in
the reduction of Fe3O4 requires a higher temperature than is
required for the prereduction step, once the nuclei formed begin
to grow the reaction accelerates and a lower temperature is then
capable of maintaining the constant pre-selected rate of reduction
throughout a large proportion of the main reduction step to Fe.
The temperature then increases again toward the end of the
reduction during the deceleration stage when nuclei begin to
overlap and cause a decrease in the reaction interface.
Figure 7. Extent of reaction (R) versus temperature plot for the TPR
of Fe under (a) linear heating and (b) CRTA ‘”rate-jump” conditions.
2 3
O
2,24
that the latter was then further reduced to iron. Shimokawabe
2
et al. also reported that the reduction of R-Fe2O3 samples,
prepared by decomposition of iron salts at temperatures below
7
00 °C, proceeded via a two-step mechanism with the Fe2O3
f Fe3O4 step being completed before the onset of the Fe3O4
-
1
f Fe step under linear heating rate conditions of 4.5 °C min .
However, for samples prepared by decomposition of salts at
temperatures above 900 °C, steps 1 and 2 occurred simulta-
2
neously under the reduction conditions employed. Wimmers
1
et al. reported that the Fe2O3 f Fe3O4 step was either advanced
significantly or completed before onset of the Fe3O4 f Fe
reduction step in linear heating rate experiments under various
conditions. Discrepancies were attributed to variations in the
samples of Fe2O3 as well as the experimental conditions
employed. In the present study, the CRTA profile in Figure 7b
shows that if the reduction is forced to proceed at a slow rate
then the prereduction to Fe3O4 is completed prior to subsequent
reduction to Fe.
Figure 8 shows R versus temperature plots obtained for the
reduction of Fe3O4 starting material under linear heating rate
(Figure 8a) and CRTA “rate-jump” (Figure 8b) conditions. The
reduction is seen to occur in a single step and the shape of the
CRTA plot again indicates that the reduction to metal proceeds
via a nucleation or autocatalytic process.
The shape of R versus temperature profiles in CRTA
experiments can reveal information on the mechanism of solid-
1
8,22,24
state reactions.
The form of the R profile for the main
Apparent activation energies were calculated from both linear
reduction step in Figure 7b indicates that the Fe3O4 f Fe
heating rate and CRTA “rate-jump” profiles. Using the linear
2
m
reduction follows a nucleation or autocatalytic mechanism
heating rate results shown in Table 2, a plot of ln(â/T ) versus
(discussed above) with a rise, fall, and then rise again in
1/Tm was found to be a straight line for both peaks associated
temperature required to maintain a constant reaction rate
with the reduction of Fe2O3 sample. Using the equations of these

226 J. Phys. Chem. B, Vol. 105, No. 1, 2001
Tiernan et al.
Figure 9. Apparent activation energy (E
function of the extent of reduction (R), measured from CRTA “rate-
jump” experiments for (a) Fe to Fe reduction step in the reduction
of Fe starting material and (b) reduction of Fe starting material.
a 3 4
) for Fe O reduction as a
3 4
O
Figure 8. Extent of reaction (R) versus temperature plot for the TPR
of Fe under (a) linear heating and (b) CRTA “rate-jump” conditions.
2
O
3
3 4
O
3 4
O
of Ea exist for the growth stage of the process relative to those
required for the initial nucleation stage.
lines, the apparent activation energy for each step was calculated
using eq 2. A value of 105.3 kJ mol-1 was calculated for the
prereduction of Fe2O3 to Fe3O4 (equation of line; Y )
4
.4. Comparison with Literature Kinetic Studies. In
general, the reduction of Fe3O4, at lower temperatures and with
smaller particle sizes, has been reported to show sigmoidal
isothermal reduction curves characteristic of an induction period
attributed to a nucleation process as the rate-determining step
-
12674.0X + 9.2, correlation coefficient ) 0.998) and a value
-1
of 53.6 kJ mol was found for the main reduction step of Fe3O4
to Fe (equation of line; Y ) -6446.4X -2.5, correlation
coefficient ) 0.996).
1
,8
and involving uniform internal reduction. With increasing
particle size or reduction temperature, the literature indicates
that this induction period becomes less pronounced with a shift
in mechanism to one associated with a topochemical mode of
reaction where chemical reaction at the oxide/Fe interface and/
or diffusion through a porous Fe product layer (>7 mm particle
In the same manner, the results in Table 3 were used to
calculate the apparent activation energy for the reduction of the
2
m
Fe3O4 sample to Fe. A plot of ln(â/T ) versus 1/Tm was found
to be a straight line described by the equation Y ) -7730.0X
-
1.0 (correlation coefficient ) 0.998). Using eq 2, Ea was
-
1
calculated to be 64.3 kJ mol . The higher apparent activation
energy, relative to that for the reduction of Fe3O4 formed from
Fe2O3 starting material, may be associated with the different
1,8
sizes) becomes rate-determining.
Table 4 summarizes the findings of the current and previous
studies on the mechanism and activation energy of the reduction
of powdered Fe2O3 and Fe3O4 samples. From this table, it is
clear that even for the study of powdered samples, which would
all be expected to have relatively small particle sizes, discrep-
ancies do exist with respect to the mechanism of reduction
2
textural characteristics of the two starting materials.
We have previously reported that the use of a CRTA “rate-
jump” method to calculate apparent activation energies for metal
oxide reduction can allow a more meaningful insight into
variations of Ea throughout the reduction process when com-
1
reported. Wimmers et al. studied the reduction of extremely
18
pared with linear heating rate methods. As discussed above,
the temperature profiles shown in Figures 5 and 6 show how
the sample temperature was varied in order to alternate between
the two pre-selected reaction rates throughout the reduction
process(es) involved. Ea was calculated for each individual jump
using eq 3. For the reduction of Fe2O3 to Fe3O4, Ea was found
to be independent of R in that, while there was some scatter,
there was no obvious trend recognized. The average value of
small Fe2O3 particles (0.3 µm average diameter) under linear
heating conditions. In dry H /Ar, step 2 of the reduction process
2
occurred via a nucleation mechanism in agreement with that
found in the current study. Evaluation of the mechanism of
hematite to magnetite (step 1) was not possible due to a lack of
resolution under the linear heating rate reduction conditions
1
employed in the study. In direct contrast to the findings of the
2
current work, Shimokawabe et al. reported that the Fe O f
3
4
-
1
Ea for this prereduction step was 96 kJ mol . Although only a
small number of “rate-jumps” were achieved for this step, an
extrapolation technique22 was used to help ensure that the
temperature measurements, T1 and T2, for the target reduction
rates, C1 and C2, were made at the same value of R for each
jump. For the reduction of Fe3O4 to Fe, results showed that the
apparent activation energy decreased over the course of the
reduction as illustrated in Figure 9 which is consistent with an
autocatalytic effect.18 Similar results have been reported for the
reduction of CuO where Ea has been found to decrease with
Fe main reduction step was reported to proceed via a phase
boundary mechanism while the prereduction step of Fe O f
2
3
Fe O involved formation and random growth of nuclei under
3
4
2
3
isothermal conditions. Sastri et al. also reported a two-step
mechanism via magnetite for the reduction of hematite under
isothermal conditions and concluded that the overall rate of
reaction was phase-boundary controlled with the topochemical
reduction of Fe3O4 to Fe proceeding via formation and
nucleation of metallic iron.
Table 4 also shows that discrepancies exist within the
literature with regard to the measured activation energies for
the reduction of powdered iron oxides. Such variations may be
associated with differences between the samples studied and/
3
2,33
extent of reduction under both isothermal
and CRTA “rate-
jump” conditions.18 The reduction of CuO is reported to follow
a similar type of mechanism, involving formation and growth
of nuclei or autocatalytic effects, to that presently found for
the reduction of Fe3O4 and one possibility1 is that lower values
or the conditions employed for sample pretreatment and/or
8
1-3
For example, Shimokawabe et al.2 prepared
reduction.

Reduction of Iron Oxide Catalysts
J. Phys. Chem. B, Vol. 105, No. 1, 2001 227
TABLE 4: Comparison of Kinetic Models and Activation Energies for the Reduction of Fe
2 3
O Found in This Work and in the
Literature
source
reduction step
reduction mechanism
E (kJ mol-1)
method
Wimmers et al.1
Fe
2
Fe
3
Fe
2
Fe
3
Fe
2
Fe
2
Fe
3
Fe
2
Fe
3
O
O
O
O
O
O
O
O
O
f Fe
f Fe
f Fe
f Fe
f Fe
f Fe
f Fe
f Fe
f Fe
O
n/dc
n/dc
111
linear heating rate
linear heating rate
linear heating rate
linear heating rate
isothermal
linear heating rate
linear heating rate
CRTA “rate-jump”
CRTA “rate-jump”
3
4
3
4
3
3
4
3
4
3
4
random nucleation
random nucleation
phase boundary
phase boundary
n/dc
Shimokawabe et al.2
O
3 4
74-117
a
a
60-73
Sastri et al.3
this work
57-73a
106
3
O
4
4
n/dc
54
this work
3
O
phase boundary
random nucleation
96
59-69b
a
depending on heating conditions employed for pretreatment prior to reduction. b depending on the extent of reduction. c n/d - not determined.
R-Fe2O3 by the decomposition of iron salts in air at temperatures
of between 500 °C and 1200 °C and found that samples prepared
by decomposition at higher temperatures had greater activation
energies for the reduction than those prepared at lower tem-
peratures. This was associated with a higher reactivity of smaller
particles for samples prepared at lower temperatures and was
more particularly pronounced for the prereduction step of Fe2O3
Fe3O4 starting material to Fe also showed this reduction process
to involve nucleation and/or autocatalysis.
CRTA “rate-jump” profiles allowed the measurement of
apparent activation energies as a function of the extent of
reaction for the different reduction processes. For the reduction
-1
of Fe2O3, Ea was found to be 96 kJ mol for the initial reduction
to Fe3O4. For the main reduction step to Fe, Ea decreased from
3
-1
to Fe3O4 than for the main reduction to Fe. Sastri et al. reported
69 to 59 kJ mol as the reduction proceeded. Similarly, for
that pretreatment at 850 °C of R-Fe2O3 resulted in an increase
the reduction of Fe3O4 starting material, Ea decreased from 75
to 61 kJ mol as the reaction progressed from start to finish.
-
1
-1
in activation energy to 73 kJ mol relative to a value of 57 kJ
-1
mol for a sample that had undergone no heat treatment. Thus,
Ea is strongly sample dependent.
The differences between these two sets of values is thought to
reflect the effects of sample morphology in the apparent
activation energy of the reduction process.
It should be noted that the kinetics of the reduction reactions
are expected to be strongly sample-dependent and further
studies, using the advantages of the CRTA “rate-jump” method
may elucidate the effects of parameters such as particle size
and the presence of various impurities or promoters in the iron
oxide phase on the reduction processes.
In the present study differences, albeit fairly small, exist (see
Table 4) between the activation energies measured under linear
heating rate conditions relative to those obtained using the
CRTA “rate-jump” method. Of course, the latter technique also
reveals changes in the energy of activation throughout the
reduction of Fe3O4 to Fe (see Figure 9). Use of the CRTA “rate-
jump” method for the measurement of Ea values for solid-state
reactions has been recommended because heat and mass transfer
effects are minimized1
8,26,29
while the ability to completely
Acknowledgment. The authors gratefully acknowledge the
generous support of the Engineering and Physical Sciences
Research Council (EPSRC) in funding this program of work
(Grant No. GR/L19539).
resolve individual processes ensures that the values obtained
are strictly associated with a given process. Hence, it is
contended that the values obtained using this method (rather
than linear heating rate experiments) more closely approximate
to the true activation energy for the reduction of the iron oxide
powders studied. This is particularly so for the Fe3O4 to Fe
reduction whereas measurement of Ea under CRTA “rate-jump”
conditions for the prereduction of Fe2O3 to Fe3O4 may be
slightly less accurate due to the smaller number of jumps
achieved.
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