Fractal surfaces of ZrO2, WO3, and CeO2 powders

Article abstract of DOI:10.1023/A:1021315219423

The surface fractal properties of ZrO₂, WO₃, and CeO₂ powders prepared by the thermal decomposition of ZrO(NO ₃)₂, (NH₄)₄W₅O ₁₇, and (NH₄)₂Ce(NO₃)₆, respectively, were studied by mercury porosimetry. The results demonstrate that these oxides may, in principle, have fractal surfaces owing to topochemical processes of the type A(s) → B(s) + C(g). The surface fractal dimension of individual crystallites and their aggregates are determined.

Full text of DOI:10.1023/A:1021315219423

Inorganic Materials, Vol. 38, No. 12, 2002, pp. 1224–1227. Translated from Neorganicheskie Materialy, Vol. 38, No. 12, 2002, pp. 1444–1447.
Original Russian Text Copyright © 2002 by Ivanov, Baranov, Oleinikov, Tret’yakov.
Fractal Surfaces of ZrO , WO , and CeO Powders
2
3
2
V. K. Ivanov, A. N. Baranov, N. N. Oleinikov, and Yu. D. Tret’yakov
Kurnakov Institute of General and Inorganic Chemistry, Russian Academy of Sciences,
Leninskii pr. 31, Moscow, 119991 Russia
e-mail: van@igic.ras.ru
Received July 11, 2002; in final form, July 16, 2002
Abstract—The surface fractal properties of ZrO , WO , and CeO powders prepared by the thermal decom-
2
3
2
position of ZrO(NO ) , (NH ) W O , and (NH ) Ce(NO ) , respectively, were studied by mercury porosim-
3
2
4 4
5
17
4 2
3 6
etry. The results demonstrate that these oxides may, in principle, have fractal surfaces owing to topochemical
processes of the type A(s)
B(s) + C(g). The surface fractal dimension of individual crystallites and their
aggregates are determined.
INTRODUCTION
intrusion curve under the assumption that the pores had
a cylindrical shape. The contact angle between mercury
and the material was assumed to be 130°.
Earlier results on the surface structure of Fe O
2
3
powders differing in thermal history suggest that, when
conducted under relatively mild conditions to avoid
defect annealing and grain growth, the decomposition WO
The fractal dimension D of the ZrO , CeO , and
2
2
powders was extracted from Hg porosimetry data
3
of metal salts accompanied by gas release may yield using the Neimark formula [2]
oxide powders with fractal surfaces [1]. To verify this
V
assumption, we studied the surface fractal structure of


D = 2 + d log pdV /d(log p)
ZrO , CeO , and WO powders prepared by decompos-
2
2
3
∫
0
(
1)


ing ZrO(NO ) , (NH ) W O , and (NH ) Ce(NO ) ,
3
2
4 4
5
17
4 2
3 6
respectively.
=
2 + d(log f (p))/d(log p),
where V is the Hg intrusion volume, p is the applied
EXPERIMENTAL
V
pressure, and f(p) = p dV.
∫
0
ZrO samples were prepared by heating crystalline,
2
reagent-grade ZrO(NO ) to 315°C at 5°C/min, fol-
3
2
lowed by isothermal holding for 3 h.
RESULTS AND DISCUSSION
WO samples were prepared by heating crystalline,
3
According to XRD and Hg porosimetry data, the
thermal decomposition of zirconyl nitrate and ammo-
nium cerium nitrate at 315°C yields single-phase ZrO2
and CeO powders characterized by a high porosity and
specific surface (table; Figs. 1b, 1c). The WO powders
reagent-grade (NH ) W O to 580°C at 5°C/min, fol-
4
4
5
17
lowed by isothermal holding for 3 h.
CeO samples were prepared by heating crystalline,
2
2
reagent-grade (NH ) Ce(NO ) to 315°C at 5°C/min,
4
2
3 6
3
followed by isothermal holding for 3 h.
The powders were characterized by x-ray diffrac- smaller specific surface and a lower percentage of small
tion (XRD) on a DRON-3M diffractometer (CuK radi- (d < 0.03 µm) pores (Fig. 1a). Clearly, high-tempera-
ation) at a scan rate of 1–2°/min. The results were ana-
lyzed using JCPDS Powder Diffraction File (PDF2)
data.
obtained at a higher temperature (580°C) have a
α
ture defect annealing has a profound effect on the
microstructure of the materials.
An analysis of the Hg intrusion curves with the use
of the Neimark equation indicates that the WO powder
Microstructures were examined by scanning elec-
3
tron microscopy (SEM) on a JEOL JEM-2000FXII has a fractal surface with a fractal dimension D = 3.00 ±
instrument (accelerating voltage, 200 kV; magnifica- 0.02 (Fig. 2a), which is characteristic of the pore struc-
tions, up to ×20000).
ture of loose aggregates consisting of weakly bonded
oxide particles [1]. The same is evidenced by the limits
of the self-similarity range: 0.11 to 1.15 µm.
The porosity of preevacuated (1.3 Pa) samples was
determined by Hg intrusion porosimetry at pressures
from 0.3 to 220 MPa (Micromeritics PoreSizer 9300).
Fractal analysis of the curves obtained for zirconia
Cumulative and differential pore size distributions and powders reveals two distinct linear portions (d = 0.14–
specific surface areas were found by analyzing the 0.77 and 0.02–0.14 µm) with slopes corresponding to
0
020-1685/02/3812-1224$27.00 © 2002 MAIK “Nauka/Interperiodica”

FRACTAL SURFACES OF ZrO , WO , AND CeO POWDERS
1225
2
3
2
3
V , cm /g
logf(p)
sp
0
0
0
.024
.016
.008
0
4.5
(a)
(
a)
4
3
3
2
2
.0
.5
.0
.5
.0
0.4
0.4
0.4
0.8
0.8
0.8
1.2
1.2
1.2
1.6
0
0.4
0.8
1.2
4
4
4
3
3
.4
.2
.0
.8
.6
(b)
0
0
0
.15
.10
.05
0
(b)
3.4
1.6
0
0.3
0.6
0.9
1.2
4
4
3
3
3
.5
.2
.9
.6
.3
(c)
0
0
0
0
.4
.3
.2
.1
0
(
c)
1.6
0
0.2
0.4
0.6
0.8
1.0
1.2
d, µm
logp [MPa]
Fig. 1. Pore size distributions of (a) WO , (b) ZrO , and
Fig. 2. Log–log plots of the Neimark function for (a) WO3,
(b) ZrO , and (c) CeO samples.
3
2
(
c) CeO samples.
2
2
2
fractal dimensions of 3.03 ± 0.04 and 2.31 ± 0.02 of the ZrO powders (Fig. 3), which demonstrate that
2
(
Fig. 2b). As in the case of WO , the former portion the particles range in size from 0.2 to 3 µm.
3
corresponds to the fractal dimension of the pore struc-
ture of zirconia aggregates, while the latter character-
izes the topology of the pore structure of the particles, exhibits surface fractal properties only in a relatively
which has a smaller fractal dimension. These conclu- narrow range of pore sizes, from 0.16 to 0.6 µm, which
sions are supported indirectly by the SEM micrographs corresponds, according to SEM data (Fig. 4), to inter-
The CeO powder, prepared by the thermal decom-
position of crystalline ammonium cerium nitrate,
2
Mercury porosimetry data for ZrO , WO , and CeO powders
2
3
2
3
2
Sample
CeO2
V , cm /g
S , m /g
∆d, µm
Self-similarity range, µm
D
sp
sp
2.0
0.9
33.3
52.0
0.03–0.9
0.16–0.6
2.84 ± 0.01
2.31 ± 0.02
3.03 ± 0.04
3.00 ± 0.02
2.42 ± 0.04
3.01 ± 0.03
ZrO2
0.0088–1.3
0.02–0.14
0
.14–0.77
WO3
0.1
2.1
8.8
–
0.016–1.15
0.02–2.3
0.11–1.15
0.02–0.19
Fe O [1]
2
3
0
.19–2.3
Note: Vsp is the specific pore volume, Ssp is the specific surface area, ∆d is the spread of pore sizes, and D is the fractal dimension.
INORGANIC MATERIALS Vol. 38 No. 12 2002

1
226
IVANOV et al.
4
µm
1
µm
(
a)
(a)
1
µm
2
00 nm
(b)
(b)
Fig. 3. SEM micrographs of zirconia powders: (a) ×5000,
b) ×20000.
Fig. 4. SEM micrographs of ceria powders: (a) ×10000,
(b) ×50000.
(
aggregate pores. The fractal dimension of the pore sur- aggregates of primary crystallites and their agglomer-
faces is 2.84 ± 0.01 (Fig. 2c). The log–log plot of the ates. The interaggregate pores are close in size to the
Neimark function is nonlinear at high pressures (above aggregates (0.2 to 2 µm and larger).
1
0 MPa), indicating that the surface of individual CeO2
Note that, at the first level of this hierarchy, the frac-
tal dimension of the pore structure depends on the syn-
thesis and sintering conditions and varies from ~2.6 to
particles has a nonfractal topology.
Comparison of the surface fractal properties of
ZrO , CeO , and WO powders with those of Fe O [1]
indicates that all these powders have morphologically
inhomogeneous structures. In view of this, it is reason-
able to distinguish two levels of microstructural organi-
zation, similarly to the classification proposed earlier
2
2
3
2
3
2
(absence of fractal properties owing to annealing pro-
cesses). In a number of samples, the fractal dimension
of the pore structure of aggregates is D = 3, which
points to the maximum morphological inhomogeneity.
If the synthesis conditions are such that the dimension
[
3, 4]. The first level corresponds to primary oxide crys-
tallites. The porosity at this level is due to intercrystal- of the pore structure of aggregates is between 2 and 3,
line pores (d < 0.1 µm) comparable in size to the pri- subsequent high-temperature sintering leads to a sys-
mary crystallites. The second level corresponds to tematic increase in D, which gradually approaches 3.
INORGANIC MATERIALS Vol. 38 No. 12 2002

FRACTAL SURFACES OF ZrO , WO , AND CeO POWDERS
1227
2
3
2
CONCLUSION
REFERENCES
1
. Ivanov, V.K., Baranov, A.N., Kapustin, D.V., and
Tret’yakov, Yu.D., Formation of Surface Fractal Struc-
ture in Fe O Powders, Neorg. Mater., 1997, vol. 33,
no. 7, pp. 830–834 [Inorg. Mater. (Engl. Transl.),
vol. 33, no. 7, pp. 699–702].
It is found that the thermal decomposition of
ZrO(NO ) , (NH ) W O , and (NH ) Ce(NO ) under
3
2
4 4
5
17
4 2
3 6
2
3
conditions that prevent defect annealing and crystallite
sintering, yields ZrO , WO , and CeO powders with
2
3
2
fractal surfaces. Such powders are characterized by two
levels of microstructural organization. The surface frac-
tal dimension of the pore structure of aggregates nota-
bly exceeds the fractal dimension of intercrystalline
pores and occasionally attains D = 3, a value character-
istic of very rough surfaces.
2
3
. Neimark, A.V., Thermodynamic Calculation of the Sur-
face Fractal Dimension, Pis’ma Zh. Eksp. Teor. Fiz.,
1990, vol. 51, no. 10, pp. 535–538.
. Ishchenko, V.V., Shlyakhtin, O.A., and Oleinikov, N.N.,
Microstructure of Oxide Powders Prepared by Thermal
Decomposition of Mohr’s Salt, Neorg. Mater., 1997,
vol. 33, no. 9, pp. 1100–1105 [Inorg. Mater. (Engl.
Transl.), vol. 33, no. 9. pp. 931–935].
ACKNOWLEDGMENTS
4. Ishchenko, V.V., Shlyakhtin, O.A., Oleinikov, N.N.,
et al., Grain Growth in Fe O -Based Ceramics during
2
3
This work was supported by the Leading Scientific
Schools Program, grant no. 00-15-97435.
Sintering, Dokl. Akad. Nauk, 1997, vol. 356, no. 5,
pp. 645–648.
INORGANIC MATERIALS Vol. 38 No. 12 2002