WDS'09 Proceedings of Contributed Papers, Part III, 208–212, 2009.
ISBN 978-80-7378-103-3 © MATFYZPRESS
Study of the Phase Composition of Fe2O3 Nanoparticles
V. Valeš, J. Poltierová-Vejpravová, A. Mantlíková, and V. Holý
Charles University, Faculty of Mathematics and Physics, Department of Condensed Matter Physics, Prague,
Czech Republic.
P. Brázda
Charles University, Faculty of Science, Department of Inorganic Chemistry, Prague, Czech Republic.
Abstract. The changes of the phase composition of iron oxide samples prepared by
solgel method using single precursor both for nanoparticles and the matrix were studied
by x-ray diffraction. Obtained data were analyzed by an approach using the Debye
formula which is suitable for the size of particles up to about 10 nm. The phase
composition of the nanoparticles was described by a core-shell model corresponding to
the assumed inward movement of the phase interface between two phases. First results
of the phase composition of Fe2O3 nanoparticles have already been obtained.
Introduction
Important physical properties of nanoparticles are determined mainly by their atomic structure,
especially by their phase composition and the presence of structure defects. X-ray diffraction is a good
tool for studying the structure of the nanoparticles, its application for very small particles is however
limited by very small intensity of the scattered wave. For this reason special experimental setups, like
e.g. diffraction with small incidence angle, are used and many experiments have to be done at
synchrotrons. Standard methods of the measured data analysis based on the description of the
diffraction using instrumental functions and functions of physical broadening of the lines fail in the
case of very small particles. An ab-initio calculation method (based on the Debye formula [Cervellino
et al., 2004; Cervellino et al., 2003]) has to be used instead.
In this work the Debye formula is used for the description of the diffraction of iron oxide samples
measured at ANKA synchrotron in Karlsruhe. Using this approach we determine basic parameters of
the particles such as lattice parameters and the size of the particles, as well as the presence of different
phases. During annealing, subsequent phase transitions from γ-Fe2O3 to ε-Fe2O3 and to α-Fe2O3 take
place. New phases nucleate probably at the surface of the nanoparticles and the phase transformation
proceeds towards the particle center ([Woo et al., 2008; Gich et al., 2006]), so that the structure of the
nanoparticles can be described by a core-shell model; this model was used in the Debye-formula based
simulation. From the analysis of the experimental data we determined the kinetic parameters of the
phase transitions and their dependence on the nanoparticle sizes.
Measured samples
The great interest in Fe2O3 nanoparticles is caused mainly by magnetic properties of these
particles, namely extremely high room temperature coercivity of epsilon phase of these iron oxide
nanoparticles. The samples were prepared by ex-situ annealing of organic precursors and then
measured at ANKA synchrotron in Karlsruhe with incidence angle 5º and the wavelength of 0.95007
Å. The primary beam was monochromatized by a 2x111Si monochromator, the diffracted radiation
was measured by a point detector equipped with a narrow entrance slit and a filter suppressing the Fefluorescence. The series of samples was prepared with the final annealing temperature from 900 ºC to
1150 ºC with the step of 50 ºC. To the temperature of 900 ºC all the samples were heated at the speed
1 ºC per minute and stayed at this temperature for 4 hours. As for the sample with the final
temperature 900 ºC this was the whole procedure. The other samples were then with the same speed
heated to their final annealing temperature with the 4-hour waiting each 50 ºC up to their final heating
temperature. This procedure causes the creation of Fe2O3 nanoparticles in the amorphous SiO2 matrix.
From the literature [Brázda et al., 2009] it is known that the particles created at the lowest final
temperature should be in the form of maghemite and with increasing final temperature the phase of
Fe2O3 particles should change to ε and hematite.
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VALEŠ ET AL.: STUDY OF THE PHASE COMPOSITION OF Fe2O3 NANOPARTICLES
Theoretical description
Debye formula in Eq. (1), which has been used for the x-ray data analysis describes the intensity
distribution of the samples consisting of the same randomly oriented particles, knowing the positions
of the atoms in one such a particle.
I (Q ) = ∑ f i f j* ⋅
i, j
sin (Qrij )
,
Qrij
(1)
where the double sum goes over all atoms in the particle, Q is the length of the scattering vector, fi is
the atom form factor of the i-th atom and rij is the distance between i-th and j-th atom. The formula is
valid for any arrangement of atoms in any particle; no lattice is needed; only exact positions of atoms
in the particle are important. The only technical limit of using of this equation is the number of terms
in the double sum. For instance, a particle of Fe2O3 of diameter of 13 nm contains about 105 atoms,
which means that there are 1010 interatomic distances that have to be taken into account for every Q.
For this reason, the distribution function of atomic pairs was calculated and a histogram of all
interatomic distances was created; an example of such histogram is shown in Fig. 1 corresponding to a
spherical particle with the radius of 40 Å, the histogram has been constructed using the step width of
0.01 Å.
Since we introduced the histogram of interatomic distances, we can rewrite the Eq. (1) using
calculated data from the histogram, i.e. we know the multiplicity of each of interval of distances. The
rewritten form of Debye formula in equation (2) enables us to perform calculations for much larger
samples. For the intensity we can write
I (Q ) = ∑ mi f
i
2
sin (Qri )
,
Qri
(2)
where mi is the multiplicity factor for the i-th interval of distances. The expression in Eq. (2) is valid
only for one type of atoms in the particle, which is not our case (because of different atom form
factors). This fact requires only some technical changes, which do not affect the fundamental meaning
of Eq. (2).
The phase transition from one phase to the other is supposed to take place from the particle
surface to its center. For this reason the core-shell model of the particle (particle consisting of two
different phases) has been introduced to the Debye formula program. In order to have a brief look in to
the behavior of the simulated data calculated by our model, diffraction curves for different phases
5
3,0x10
maghemite
Rmaghemite=4nm
ε-Fe2O3
2000
5
2,5x10
1500
5
Intensity (cps)
2,0x10
m
5
1,5x10
5
1,0x10
1000
500
4
5,0x10
0,0
0
0
20
40
60
80
10
20
30
40
50
60
2θ (deg)
°
r[A]
Figure 1. Calculated histogram of interatomic Figure 2. Calculation of diffraction curves for
distances in a spherical Fe2O3 particle of radius different phases of Fe2O3. The full line
of 40 Å. The histogram step is 0.01 Å.
corresponds to the pure maghemite particle of
radius of 50 Å; the dotted one to the pure ε-Fe2O3
particle of the same radius; and the dashed line
represents the diffraction from the particles of
radius 50 Å, which consist of the core (radius
40 Å) of maghemite and the shell of ε-Fe2O3.
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VALEŠ ET AL.: STUDY OF THE PHASE COMPOSITION OF Fe2O3 NANOPARTICLES
were calculated (Fig. 2). From this picture the difference between the maghemite and ε phases of
Fe2O3 can be seen as well as the effect of the core-shell structure of these two phases, which causes
some “mixture” of the diffraction pattern of both phases.
Data analysis
Several samples from the series described above were analysed by the Debye-formula approach
using the core-shell model, assuming that the interface of the two phases moves from the surface to the
center of the particle. The data from the Figs. 3 – 5 (samples A – C) were fitted by hand and the results
are summarized in Table 1; the errors were estimated from this fit too. The background was
approximated ad-hoc by a polynomial of the third power. The broad peak around 13º is caused by the
amorphous SiO2 matrix and for our fitting is not important. The fits describe the measured data well
and the parameters of the core-shell model were obtained. The sample D (Fig. 6) could not have been
fitted because of a too large size of the particles that made the simulation extremely time-consuming.
600
700
d a ta
fit
500
500
400
Intensity (cps)
Intensity (cps)
data
fit
600
300
200
100
400
300
200
100
0
0
10
20
30
40
50
60
10
20
2 θ (d e g )
30
40
50
60
2 θ (deg)
Figure 3. Sample A. Measured data and fit of the Figure 4. Sample B. Measured data and fit of
sample annealed at the 900 ºC as the highest the sample annealed at the 950 ºC as the
temperature.
highest temperature.
800
3000
data
fit
700
2500
600
500
Intensity (cps)
Intensity (cps)
data
400
300
200
2000
1500
1000
500
100
0
0
0
10
20
30
40
50
60
10
2θ (deg)
20
30
40
50
60
2θ (deg)
Figure 5. Sample C. Measured data and fit of the Figure 6. Sample D. Measured data of the
sample annealed at the 1000 ºC as the highest sample annealed at the 1100 ºC as the highest
temperature.
temperature.
Table 1. Results obtained from the measured data fitting. The errors of the rate of both phases are
roughly estimated. The error of the total radius is not mentioned; the value of the total radius means
the lower estimate of the real radius.
Sample
Total radius (Å)
Maghemite (%)
ε-Fe2O3 (%)
A
40
34 ± 6
66 ± 6
B
50
26 ± 4
74 ± 4
C
58
0±8
100 ± 8
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VALEŠ ET AL.: STUDY OF THE PHASE COMPOSITION OF Fe2O3 NANOPARTICLES
Discussion
As we showed in the previous section, the calculated fit describes well the measured data.
However, the question of the uniqueness of the model is still open. For instance, we assumed that the
new phase is being created at the surface of the particle; i.e., that the shell is represented by the “new”
phase while the “old” one is in the core, as we have assumed in our model. If this assumption is not
valid we have to change the phase of the core to the phase of the shell and vice versa. This possibility
has to be taken into account as well as the situation when there is no core-shell structure and for
example some particles consist of one phase and the others of the second one.
The difference between the interchange of core and shell in sample A is shown in the Fig. 7. In
this case there are slight differences which could be observable, but the question is if by the “hand”
fitting we can get better agreement.
In the Fig. 8, where the difference between core-shell particle model and the mixture of particles
consisting of single phase is shown, one can see that the difference between both cases is much
smaller and it is impossible to distinguish between them. Both calculations have been made using the
same ratio of present phases. Since the peak corresponding to certain phase is created only by the
atoms in the particle belonging to this phase, the total size of the whole particle has to be larger for the
core-shell model then for the model consisting of single phase particles. This can be seen from the Fig.
8, where the widths of diffraction peaks for both models are approximately the same and for the
calculation using mixture model, particles were about 30 % smaller then particles used for core-shell
model calculation. It could be possible to determine the size of the particles using other methods
(TEM) and decide which model this size corresponds to. From the work [Bráza et al., 2009] it follows
that the average radius of the particles annealed up to 1000 ºC is 60 Å, what is just in between both
model cases (mixture model, core-shell model; Fig. 8) so it has to be investigated more.
0
0
0
1
200
0
0
2
Intensity (cps)
300
0
0
4
Intensity (cps)
0
0
6
28 A of maghemite in ε
30 A of ε in maghemite
400
mixture of separate phases,
°
radius 50 A
core-shell, ε around maghemite,
°
radius 44.8/70 A
0
0
8
°
Rtot=40 A
500
100
0
60
0
6
50
0
5
40
2θ (deg)
0
4
30
0
3
20
0
2
10
0
1
0
2θ (deg)
Figure 7. Analysis of sample A. The difference
of the diffraction pattern when exchanging the
phase composition in the core and in the shell.
The total radius of the particle is 40 Å.
Figure 8. Analysis of sample B. The difference
of the diffraction pattern between the core-shell
structure model (maghemite in the core, radius
70 Å) and the mixture of one-phase particles
(radius 50 Å) mixed in the same ratio that
corresponds to the ratio in the core-shell model.
Conclusion
From the fitting of the measured data we obtained the total size of analyzed samples (A – C) and
the fraction of the maghemite and ε phase assuming the core-shell model with maghemite as a core. It
can be seen that the size of the particles increase with increasing annealing temperature and that the
fraction of maghemite decreases and it completely vanishes at the temperature of 1000 ºC. This
corresponds to the assumption presented above. As for the sample D, which has not been analysed, the
hematite diffraction peaks appear.
Both he core-shell model of the nanoparticles and the Debye formula are suitable tools for the
analysis of our samples. In the future we have to investigate, whether it is possible to distinguish
between the core and the shell, i.e., whether we can determine which phase is in the core and which
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VALEŠ ET AL.: STUDY OF THE PHASE COMPOSITION OF Fe2O3 NANOPARTICLES
one is in the shell. A method, which would enable us to analyze larger particles, has to be
implemented as well.
References
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Chang-Woo Lee, Sung-Soo Jung and Jai-Sung Lee, Materials Letters 62, 561, 2008.
M. Gich, C. Frontera, A. Roig et al, Chemistry of Materials 18, 3889, 2006.
P. Brázda, D. Nižňanský, J.-L. Rehspringer, J. Poltierová Vejpravová, J. Sol-Gel Sci. Technol., 51, 78-83, 2009.
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