ISSN 0020-1685, Inorganic Materials, 2008, Vol. 44, No. 3, pp. 272–277. © Pleiades Publishing, Ltd., 2008.
Original Russian Text © V.K. Ivanov, O.S. Polezhaeva, G.P. Kopitsa, A.E. Baranchikov, Yu.D. Tret’yakov, 2008, published in Neorganicheskie Materialy, 2008, Vol. 44, No. 3,
Cerium dioxide (
widely used as ionic conductors, catalysts, sensors, UV
filters, etc. [1–5]. In particular, ceria is the basic com-
ponent of advanced high-temperature solid oxide fuel
cells and three-way catalysts for post-treating exhaust
gases [6, 7].
was also proposed for biomedical
applications: the introduction of trace amounts of ceria
into a retina reduces the adverse effect of UV radiation
on photoreceptor cells . According to Vodungbo
et al. , doped ceria is a magnetic semiconductor pos-
sessing ferromagnetic properties at room temperature.
In most of these applications, use is made of nanoc-
rystalline ceria with controlled particle size, specific
surface, and aggregation, which determine the struc-
ture-sensitive properties of the material. To date, a vari-
ety of approaches have been proposed for size and spe-
cific surface control [10, 11]. At the same time, quan-
titative description of the aggregation behavior of
nanopowders continues to be a challenge, primarily
because there are no generally accepted analysis
Approaches based on fractal geometry are among
the most promising ways of describing ensembles of
aggregated particles [12, 13]. Indeed, the fractal
dimension of clusters measures the degree of filling
of space and, consequently, can be considered an
integral characteristic of the micromorphology of
In view of this, the objective of this work was to
develop a process for the preparation of nanocrystalline
ceria with controlled specific surface and to study the
effect of synthesis and heat-treatment conditions on the
) and related materials are
particle size and fractal dimension of the synthesized
Nanocrystalline ceria was prepared by adding aque-
ous ammonia to water–alcohol solutions of
The starting chemicals used were reagent-grade
, analytical-grade isopropanol, and
3 M aqueous ammonia. 0.08 M cerium(III) nitrate solu-
tions in water–isopropanol mixtures with water : alco-
hol volume ratios of 1 : 1, 1 : 3, 1 : 6, and 1 : 19 were
rapidly added to vigorously stirred aqueous ammonia
taken in fivefold excess. The reaction was then left
standing at room temperature for 2 h. The resultant pre-
cipitates were washed three times with isopropanol,
centrifuged, and dried at
obtained at water : alcohol volume ratios of 1 : 1 and
1 : 6 were then annealed at 200, 300, 400, 500, 600, and
for 2 h.
During synthesis, we took aliquots (0.5 ml) of the
suspensions and measured their transmission
spectra in the UV/VIS spectral region. Since the absor-
bance of the solutions exceeded 1.5, the aliquots were
diluted with distilled water (1 : 40 to 1 : 80).
Transmission spectra were measured on an SF-2000
1010 nm in 0.1-nm steps. The optical slit width was
0.2 nm. As the light source, we used a deuterium lamp
in the range 190 to 394.5 nm and a halogen lamp
between 395 and 1010 nm. The exposure time was
for 2 h. The samples
in the range 190 to
OKB Spektr, Russia.
Fractal Structure of Ceria Nanopowders
V. K. Ivanov , O. S. Polezhaeva
A. E. Baranchikov
, and Yu. D. Tret’yakov
Kurnakov Institute of General and Inorganic Chemistry, Russian Academy
of Sciences, Leninskii pr. 31, Moscow, 119991 Russia
Moscow State University, Vorob’evy gory 1, Moscow, 119899 Russia
Konstantinov Institute of Nuclear Physics, Russian Academy of Sciences,
Orlova Roshcha, Gatchina, Leningrad oblast, 188300 Russia
Received May 22, 2007
, G. P. Kopitsa
studied by UV/VIS spectroscopy, low-temperature nitrogen adsorption measurements, x-ray diffraction, trans-
mission electron microscopy, and thermal analysis, and the effect of high-temperature annealing on the fractal
structure of the CeO
nanopowders has been examined.
—The formation of ceria nanoparticles from water–alcohol solutions of cerium(III) nitrate has been
FRACTAL STRUCTURE OF CERIA NANOPOWDERS273
50 ms. For each sample, the results were averaged over
The band gap of
nanoparticles was determined
using plots of
is the photon energy. The sloping por-
tion of each plot was approximated by a straight line,
and the band gap was determined as the intercept of the
line with the abscissa.
X-ray diffraction (XRD) measurements were per-
formed on a DRON-3M powder diffractometer (Cu
radiation) at a scan rate of
present were identified using JCPDS PDF data. XRD
data were also used to evaluate the size of coherently
scattering domains (CSDs). To this end, we used the
is the absorption
/min. The phases
the 111 diffraction peak from
Microstructures were examined by transmission
electron microscopy (TEM) on a Leo912 AB Omega
operated at 100 kV. Before TEM examination, each
specimen was placed on a polymer-coated copper grid
3.05 mm in diameter.
The specific surface of the
mined by low-temperature nitrogen adsorption mea-
surements with a QuantaChrome Nova 4200B analyzer.
The samples were outgassed in a dry box at
vacuum for 5 h. The sample surface was analyzed by a
multipoint (28 points) Brunauer–Emmett–Teller (BET)
method. The pore size distribution was inferred from
nitrogen desorption isotherms using the Barrett–
Joyner–Halenda method. The fractal characteristics of
surfaces were analyzed by the Neimark–Kiselev
method, in which the surface fractal dimension is cal-
culated using measured adsorption isotherms [14, 15].
Thermal analysis (DTA + TG) was performed in air
during heating to
at a rate of
Perkin-Elmer TG7 analyzer. The sample weight was
is the intrinsic width of
powders was deter-
C/min, using a
RESULTS AND DISCUSSION
UV/VIS spectroscopy data (Fig. 1) demonstrate
that, just after mixing water–isopropanol solutions of
cerium(III) nitrate with aqueous ammonia, the absorp-
tion spectrum shows a band in the range 280–300 nm,
. Thus, the forming cerium(III)
hydroxide oxidizes to cerium(IV) almost instanta-
neously. At the same time, heat-flow calorimetry results
 indicate that, after mixing together such solutions
, heat evolution continues for 100–140 min.
It is, therefore, reasonable to assume that, holding the
suspensions in the mother solution leads to gradual
dehydration of Ce(IV) hydroxy compounds and
Earlier calorimetry data  indicate that this pro-
cess is autocatalytic: hydroxy complexes decompose
predominantly on the surface of the
formed, increasing their size. The same is evidenced by
the UV/VIS spectroscopy data. Indeed, it follows from
the data in Fig. 1 that, with increasing holding time, the
absorption edge systematically shifts to longer wave-
lengths. The shift is due to the decrease in the band gap
particles because of the reduction in the
contribution of the quantum size effect.
Figure 2 shows the band gap of
from UV spectroscopy data, as a function of the hold-
ing time of the suspensions in the mother solution. The
is seen to gradually decrease from 3.35–
350 400 450 500 550 600 650 700
water–isopropanol mixtures at synthesis times of (
) 20, and (
) 40 min.
UV/VIS absorption spectra of CeO
20 3040 50607080 90
solutions with water : isopropanol = (
) 1 : 19.
Band gap of ceria as a function of synthesis time for
) 1 : 1, (
) 1 : 3, (
) 1 : 6,
IVANOV et al.
3.40 to 3.15–3.20 eV. According to Zhang et al. ,
values are characteristic of
5.5–6.1 nm in diameter, while the final values are very
close to the band gap of bulk ceria,
Increasing the isopropanol content in the reaction sys-
tem to 86–95% slightly reduces the growth time of the
XRD results indicate the formation of cubic ceria
(fluorite structure) with trace amounts of an amorphous
phase (presumably, cerium hydroxy compounds). In all
of the samples, the CSD size, evaluated from the width
of the 111 peak, is
nm. Thus, the isopropanol content
in the reaction mixture has little or no effect on the size
of the resulting
particles. The same is evidenced
by TEM data (Fig. 3): the samples prepared from the
solutions with the lowest (50 vol %) and highest (95 vol %)
isopropanol contents have the form of aggregated pow-
ders consisting of nearly monodisperse particles 4–
5 nm in size. Note that the particle size evaluated from
the UV/VIS spectroscopy data differs slightly from
those determined by TEM and XRD, which is most
likely due to aggregation of the
According to the low-temperature nitrogen adsorp-
tion results, our samples range in porosity from 0.10 to
/g, with the largest contribution coming from
micro- and mesopores more than 5 nm in size. The spe-
cific surface of the materials strongly depends on the
solution composition: 220, 133, 124, and 110 m
the samples synthesized from the solutions containing
50, 75, 86, and 95% isopropanol, respectively.
Neimark–Kiselev analysis of the nitrogen adsorption
data indicates that, in the size range from 0.2 to 3.5 nm,
all of the samples prepared by precipitation from
water–alcohol solutions have fractal surfaces. Compar-
ison with the
particle sizes determined by TEM
and XRD leads us to conclude that the fractal properties
are due to the surface of the intergranular pores. Thus,
it is reasonable to assume that fractal structures result
from monomer–cluster or cluster–cluster aggregation
of the nanoparticles.
This assumption is supported by the fact that the
surface fractal dimension
depends on the isopropanol
content of the water–alcohol mixtures (Fig. 4). It can be
seen that, with increasing isopropanol content,
decreases systematically, which correlates well with
the reduction in BET surface area. This attests to the
formation of more compact aggregates, i.e., reducing
the dielectric permittivity of the reaction mixture leads
to a change in aggregation mechanism. Note also that
the present experimental data are in conflict with the
results reported by Chen and Chang , who found
that the surface area of
increasing alcohol content in the reaction mixture. This
is attributable to the effect of precipitation conditions
on the aggregation behavior of nanoparticles.
According to the present thermal analysis data,
obtained during heating in air, the TG curves of the
= 3.19 eV.
powders increased with
solutions with water : isopropanol = (a) 1 : 1 and (b) 1 : 19.
TEM micrographs of ceria samples prepared from
vol % isopropanol
60 70 80 90100
tial isopropanol content.
surface fractal dimension as a function of ini-
FRACTAL STRUCTURE OF CERIA NANOPOWDERS 275
mixtures differ very little. The total weight loss is
15%. In the range 25 to
adsorbed water, which is an endothermic process. As
the temperature is raised to
curves show two reproducible, well-defined exothermic
peaks, which are probably due to the crystallization of
the amorphous component and the oxidation of the
residual Ce(III). At higher temperatures, no thermal
events were detected.
Note that the weight loss continues up to
The TG curves can be divided into two portions: 25 to
to 1150°C. The first portion corre-
sponds to the release of chemically bonded and sorbed
water; the nature of the higher temperature process is
not yet fully clear. The most likely process is the
removal of the residual bonded water, which only
reaches completion at very high temperatures, like in
the case of ZrO2 · H2O dehydration . At the same
time, according to Kim et al. , the surface layer of
ceria nanoparticles is typically oxygen-deficient, and
the deviation from stoichiometry increases markedly as
the temperature is raised from 350 to 475°ë. Therefore,
the weight loss at temperatures from 400 to 1150°C
may also be due in part to oxygen release.
To analyze in detail the processes that take place
during high-temperature heat treatment of CeO2, we
performed thermal analysis of the powders precipitated
from 1 : 1 mixtures of water and isopropanol and then
annealed for 1 h at 200, 400, 600, and 700°ë. The TG
curves of those samples are presented in Fig. 5. Prean-
nealing at 200 and 400°C is seen to systematically
reduce the weight loss in the first step of the process,
corresponding to the removal of chemically bonded and
sorbed water. Under these annealing conditions, dehy-
dration does not reach completion, leading to a signifi-
samples prepared from different water–alcohol
, the samples loose
, the DTA
cant weight loss in the first step (up to 5–10%). The
samples preannealed at 600–700°C are fully dehy-
drated below 160°C. Thus, we are led to conclude that
the observed weight loss (1.5–2%) is due to the removal
of the water adsorbed during storage and that the sam-
ples contained no chemically bonded water.
According to XRD data (Fig. 6), high-temperature
annealing of the CeO2 powders leads to gradual growth
of the nanocrystallites. The particle size of the ceria
samples synthesized at different isopropanol contents
varies little at annealing temperatures below 500°ë and
rises steeply at higher annealing temperatures.
TEM data (Fig. 7) also indicate that the particles
grow insignificantly at low annealing temperatures.
0 200 400600800 10001200
Fig. 5. TG curves of ceria samples prepared via precipita-
tion from solutions with water : isopropanol = 1 : 1 and
annealed at (1) 60, (2) 200, (3) 400, (4) 600, and (5) 700°C.
200300 400500600 700
Fig. 6. CSD size as a function of annealing temperature for
CeO2 samples synthesized from solutions with water : iso-
propanol = (1) 1 : 1 and (2) 1 : 6.
200 300400 500600700 800
Fig. 7. CeO2 surface fractal dimension as a function of
INORGANIC MATERIALS Vol. 44 No. 3 2008
IVANOV et al.
Note that annealing at 300–400°ë leads to the forma-
tion of more regularly shaped particles in comparison
with the unannealed samples, but the particle size dis-
tribution remains very narrow. In contrast, annealing in
the range 500–700°ë leads not only to marked particle
growth (to ~20 nm) but also to a broader particle size
distribution. According to low-temperature nitrogen
adsorption data, the specific surface of the CeO2 sam-
ples remains rather large (>100 m2/g) at annealing tem-
peratures from 200 to 400°C and decreases largely
The particle size evaluated from the adsorption data
under the assumption that the nanoparticles are spheri-
cal in shape is on average 3–5 nm larger than that deter-
mined by TEM and XRD, which is obviously due to
nanoparticle aggregation. dBET is linearly related to
dCSD (R2 = 0.9994), with no inflections. This indicates
that the aggregation behavior of the nanoparticles
remains unchanged over the entire temperature range
According to Neimark–Kiselev analysis results, the
physicochemical processes that take place during heat
treatment of CeO2 nanopowders, including the removal
of chemically bonded and sorbed water and gradual
recrystallization of the nanoparticles, do not lead to dis-
appearance of the fractal structure of the sample sur-
face. The boundaries of the self-similarity range also
remain unchanged (0.2–3.5 nm), but the surface fractal
dimension decreases systematically (Fig. 8). This find-
ing correlates well with the observed effect of high-
temperature annealing on the fractal structure of the
surface of fine iron(III) oxide powders  and with
other results [22, 23]. It is reasonable to assume that the
reduction in fractal dimension on annealing, without
disappearance of the fractal structure, is common to
many systems and can be used to prepare fine-particle
oxide materials of various compositions with con-
trolled surface fractal dimension.
We studied the formation of nanocrystalline CeO2
powders from water–alcohol solutions of cerium(III)
nitrate. The results demonstrate that the solution com-
position has an insignificant effect on the size of the
resulting CeO2 particles but influences their aggrega-
tion behavior, specific surface, and surface fractal
We also studied the effect of annealing at tempera-
tures from 200 to 700°ë on the composition and micro-
morphology of the ceria powders. Our data indicate that
high-temperature annealing can be used to control the
surface fractal dimension of CeO2 powders.
We are grateful to the staff of the TsKP Prosvechiv-
ayushchaya elektronnaya mikroskopiya, Moscow State
University, and especially to S.S. Abramchuk for study-
ing the morphology of CeO2 nanoparticles.
This work was supported by the Russian Foundation
for Basic Research (project no. 08-03-00471), the
Chemistry and Materials Science Division of the Rus-
sian Academy of Sciences (program no. 8), and the Pre-
sidium of the Russian Academy of Sciences (program
1. Fergus, J.W., Electrolytes for Solid Oxide Fuel Cells,
J. Power Sources, 2006, vol. 162, pp. 30–40.
2. Yabe, S. and Sato, T., Cerium Oxide for Sunscreen Cos-
metics, J. Solid State Chem., 2003, vol. 171, pp. 7–11.
3. Izu, N. and Shin, W., Evaluation of Response Character-
istics of Resistive Oxygen Sensors Based on Porous
Cerium Oxide, Sens. Actuators, B, 2006, vol. 113,
4. Panzera, G., Modafferi, V., Candamano, S., et al., CO
Selective Oxidation on Ceria-Supported Au Catalysts for
Fig. 8. TEM micrographs of ceria samples prepared from
solutions with water : isopropanol = 1 : 1 and annealed at
(a) 400 and (b) 600°C.
INORGANIC MATERIALS Vol. 44 No. 3 2008 Download full-text
FRACTAL STRUCTURE OF CERIA NANOPOWDERS 277
Fuel Cell Application, J. Power Sources, 2004, vol. 135,
5. Zerva, C. and Philippopoulos, C.J., Ceria Catalysts for
Water Gas Shift Reaction: Influence of Preparation
Method on Their Activity, Appl. Catal., vol. 67, pp. 105–
6. Muraki, H. and Zhang, G., Design of Advanced Automo-
tive Exhaust Catalysts, Catal. Today, 2000, vol. 63,
7. Gandhi, H.S., Graham, G.W., and McCabe, R.W., Auto-
motive Exhaust Catalysis, J. Catal., 2003, vol. 216,
8. Chen, J., Patil, S., Seal, S., and McGinnis, J.F., Rare
Earth Nanoparticles Prevent Retinal Degeneration
Induced by Intracellular Peroxides, Nature Nanotech-
nol., 2006, vol. 1, pp. 142–150.
9. Vodungbo, B., Zheng, Y., Vidal, F., et al., Room Temper-
ature Ferromagnetism of Co-Doped CeO2 Diluted Mag-
netic Oxide: Effect of Oxygen and Anisotropy, Appl.
Phys. Lett., 2007, vol. 90, pp. 062 510.1–062 510.3.
10. Binary Rare Earth Oxides, Adachi, G. et al., Ed., Dor-
drecht: Kluwer, 2004.
11. Catalysis by Ceria and Related Materials (Catalytic Sci-
ence Series), Trovarelli, A., Ed., Singapore: World Sci-
12. Harrison, A., Fractals in Chemistry, Oxford: Oxford
Univ. Press, 1995.
13. Mandelbrot, B.B., The Fractal Geometry of Nature, New
York: Freeman, 2000.
14. Neimark, A.V., Calculating Surface Fractal Dimension
of Adsorbents, Adsorpt. Sci. Technol., 1990, vol. 7,
15. Neimark, A.V., A Thermodynamic Approach for Calcu-
lating the Surface Fractal Dimension, Pis’ma Zh. Eksp.
Teor. Fiz., 1990, vol. 51, no. 10, pp. 535–538.
16. Ivanov, V.K., Sharikov, F.Yu., Polezhaeva, O.S., and
Tret’yakov, Yu.D., Formation of Nanocrystalline Ceria
from Water–Alcohol Solutions of Cerium(III) Nitrate,
Dokl. Akad. Nauk, Ser. Khim., 2006, vol. 411, no. 4,
17. Zhang, F., Jin, Q., and Chan, S.-W., Ceria Nanoparticles:
Size, Size Distribution, and Shape, J. Appl. Phys., 2004,
vol. 95, pp. 4319–4326.
18. Chen, H.-I. and Chang, H.-Y., Homogeneous Precipita-
tion of Cerium Dioxide Nanoparticles in Alcohol/Water
Mixed Solvents, Colloid. Surf. A: Physicochem. Eng.
Aspects, 2004, vol. 242, pp. 61–69.
19. Tarnopolsky, V.A., Aliev, A.D., Churagulov, B.R., et al.,
Influence of Thermal Treatment on the Ion Transport
Properties of Hydrated Zirconia, Solid State Ionics,
2003, vols. 162–163, pp. 225–229.
20. Kim, S., Merkle, R., and Maier, J., Oxygen Non-stoichi-
ometry of Nanosized Ceria Powder, Surf. Sci., 2004,
vol. 549, pp. 196–202.
21. Ivanov, V.K., Baranov, A.N., Oleinikov, N.N., and
Tret’yakov, Yu.D., Synthesis of Ferric Oxide with Con-
trolled Surface Fractal Dimension, Zh. Neorg. Khim.,
2002, vol. 47, no. 12, pp. 1925–1929.
22. Class, H.J. and de With, G., Fractal Characterization of
the Compaction and Sintering of Ferrites, J. Mater.
Charact., 2001, vol. 47, pp. 27–37.
23. Beurroies, I., Duffours, L., Delord, P., et al., Fractal
Geometry Change Induced by Compression Densifica-
tion, J. Non-Cryst. Solids, 1998, vol. 241, pp. 38–44.