Microstructural evolution of zirconia nanoparticles caused by rare-earth modification and heat treatment

Article abstract of DOI:10.1006/jcat.1997.1833

High-surface-area zirconias are widely used as catalytic support of noble metals or oxygen sensor electrolytes in automobile exhaust-emission-control systems. Doping zirconia with small amounts of rare-earth (RE) elements may tailor its properties for better catalytic performance. The microstructure in terms of primary-particle size, surface area, porosity, and fractal aggregates of 10 mol% RE-doped zirconias (RE = Nd and Ce) and pure ZrO₂ were characterized by nitrogen adsorption isotherm and small-angle neutron scattering measurements. The crystal phases of these powders were examined by neutron powder diffraction method. Fresh pure zirconia prepared by a hydrolysis method at low temperature consists of small (～4 nm) particles and micropores. Subsequent heat treatments induce a transformation from microporosity to mesoporosity thereby an increase of particle size and a reduction of surface area. In the case of pure ZrO₂ a crossover from a mass-fractal aggregate of rough particles to clustering of smooth particles at a heat-treatment temperature of 600°C was observed. The Nd-modified zirconias prepared by a coprecipitation method, on the other hand, show high resistance to sintering and retain a small particle size and the mass-fractal aggregate after heat treatment at 600°C. Because of the different oxidation states and ionic sizes of Nd³⁺ and Ce⁴⁺ ions, Nd_0.1Zr_0.9O_1.95 and Ce_0.1Zr_0.9O₂ powders exhibit different crystal phases, particle size distributions, and pore structure.

Full text of DOI:10.1006/jcat.1997.1833

JOURNAL OF CATALYSIS 171, 498–505 (1997)
ARTICLE NO. CA971833
Microstructural Evolution of Zirconia Nanoparticles Caused
by Rare-Earth Modification and Heat Treatment
,1
ꢀ
ꢀ
ꢀ
C.-K. Loong, P. Thiyagarajan, J. W. Richardson Jr., M. Ozawa,† and S. Suzuki†
ꢀ
Argonne National Laboratory, Argonne, Illinois 60439-4814; †Nagoya Institute of Technology, Tajimi, Gifu, 507, Japan
Received May 7, 1997; revised July 9, 1997; accepted July 21, 1997
(e.g., Nd3+ or Ce4+ versus Zr4+), ionic charge compensation
may lead to oxygen vacancies in the crystalline solid solu-
tion. The diffusion of oxygen ions via vacancy sites under
an oxygen pressure gradient can provide an additional han-
dle in tailoring the electronic response of an oxygen sensor
and the oxygen storage capacity of an air-purification cata-
lyst. In particular, CeO2 is thought to promote the oxida-
tion reaction of carbon monoxide (CO) and hydrocarbons
(HC) as well as the deoxidization reaction of nitric oxide
(NOx) via a dynamic change of the Ce oxidation states dur-
ing a catalytic cycle (2–5). In general, rare-earth impurities
modify the interfacial energies, diffusion coefficients, and
crystalline anisotropy in a complex manner. As a result, the
porosity, particle-size distribution, and resistance to sinter-
ing vary depending on the dopant element, the preparation
method, and processing. Clearly, a complete understanding
of these phenomena requires systematic investigations by
many different methods.
In a previous study of RE2O3-ZrO2 powders of RE com-
positions up to 50 mol% , the effects of heat treatment on
the crystal morphology and thermal stability were charac-
terized over the 600–1200ꢂC temperature range (6). Here
we concentrate on a detailed study of the microstructure
of pure ZrO2 and Ce- and Nd-doped zirconias at lower an-
nealing temperatures that are typical to the operation of
three-way catalytic converters. A relatively low RE doping
(10 mol% ) is chosen in this first study so that the materi-
als will not be complicated by the formation of interme-
diate phases (7). We have applied the methods of small-
angle neutron scattering (SANS) and nitrogen adsorption
to characterize the microstructure ofa pure zirconia powder
prepared by a hydrolysis method and two RE-modified zir-
conia powders, Nd0.1Zr0.9O1.05 and Ce0.1Zr0.9O2, prepared
by a coprecipitation method. The crystal structures were
examined by neutron powder diffraction (NPD). The pow-
ders were subjected to ex situ and in situ heat treatments
up to 800ꢂC during the investigation. We report the crystal
phases, surface areas, pore and particle size distributions,
and self-similar behavior of these powders as a function of
heat-treatment temperatures.
High-surface-area zirconias are widely used as catalytic support
of noble metals or oxygen sensor electrolytes in automobile exhaust-
emission-control systems. Doping zirconia with small amounts of
rare-earth (RE)elementsmaytailor itspropertiesfor better catalytic
performance. The microstructure in terms of primary-particle size,
surface area, porosity, and fractal aggregates of 10 mol% RE-doped
zirconias (RE = Nd and Ce) and pure ZrO2 were characterized by
nitrogen adsorption isotherm and small-angle neutron scattering
measurements. The crystal phases of these powders were exam-
ined by neutron powder diffraction method. Fresh pure zirconia
prepared by a hydrolysis method at low temperature consists of
small (ꢁ4 nm) particles and micropores. Subsequent heat treat-
ments induce a transformation from microporosity to mesoporosity
thereby an increase of particle size and a reduction of surface area.
In the case of pure ZrO2 a crossover from a mass-fractal aggre-
gate of rough particles to clustering of smooth particles at a heat-
treatment temperature of 600ꢂC was observed. The Nd-modified
zirconias prepared by a coprecipitation method, on the other hand,
show high resistance to sintering and retain a small particle size
and the mass-fractal aggregate after heat treatment at 600ꢂC. Be-
cause of the different oxidation states and ionic sizes of Nd3+ and
Ce4+ ions, Nd0.1Zr0.9O1.95 and Ce0.1Zr0.9O2 powders exhibit differ-
ent crystal phases, particle size distributions, and pore structure.
c
ꢃ 1997 Academic Press
I. INTRODUCTION
The present study is motivated by the need of better sup-
port materials for noble metals in three-way catalytic con-
verters for automobiles. High-surface-area zirconia is one
of the commonly used materials for this purpose. Doping
rare-earth elements (RE) in zirconia helps stabilize the cu-
bic and tetragonal phases over a wide range of temperatures
thereby removing the disruptive phase transformations in
pure zirconia (1). The resulting RE-Zr oxide system shows
a robust thermal stability that is desirable for catalytic ap-
plications. Depending on the valency of the dopant RE ions
1 Person to whom correspondence should be mailed. E-mail: ckloong@
anl.gov.
498
0021-9517/97 $25.00
c
Copyright ꢃ 1997 by Academic Press
All rights of reproduction in any form reserved.

EVOLUTION OF ZIRCONIA NANOPARTICLES
II. EXPERIMENTAL DETAILS
1. Sample Preparation
499
The scattered neutron intensities as a function of position
and time were recorded by using a gas-filled area detector
and time-of-flight techniques. The sample was enclosed in
a Suprasil cell (sample thickness 2 mm) and controlled at a
temperature between ambient temperature and 500ꢂC. The
data were corrected for background and empty-cell scatter-
ing, as well as detector nonlinearity, and were normalized
by using the known scattering cross section of a silica gel
standard. A good Q-resolution (root-mean-square devia-
The pure zirconia powder was synthesized from hydrol-
ysis of a 0.3 mol% ZrOCl2 aqueous solution at 100ꢂC for
91 h. The sediment obtained from filtration was washed
and freeze-dried. The powder was subsequently heated at
290ꢂC in air for 3 h. An X-ray diffraction study qualitatively
confirmed the monoclinic structure of fine ZrO2 crystalline
particles. The fresh powder was divided into two batches.
One batch wasused for in situ SANSexperiments. The other
batch was subjected to sequential heat treatments at 400,
500, 600, 700, and 800ꢂC in air, each for about 3 h. After
each heat treatment a sample was taken out for NPD and
SANS measurements at room temperature.
ꢄ1
˚
tion varying from about 0.001 to 0.012 A over the ob-
served Q-range of 0.007–0.03 Aꢄ1) was achieved without
˚
altering the sample-to-detector configuration. We find no
noticeable effect of instrumental resolution on the inter-
pretation of the present data. Details about the small-angle
diffractometers were given elsewhere(8).
The 10 mol% RE-modified zirconia (RE = Nd and Ce)
powders were prepared by a coprecipitation technique.
Mixtures of hydrous zirconium and rare earth were co-
precipitated from an agitated aqueous solution of ZrOCl2
and RECl3 (total concentration of 0.8 molꢄ1 at the final pH
value of 10) with excess of 10 wt% NH4OH solution. The
products were filtered and washed with distilled water and
then dried by a supercritical technique. The dried mixtures
were calcined at 600ꢂC in air for 3 h. Details concerning
the preparation and characterization of the RE-modified
zirconias have been given elsewhere (6).
3. Nitrogen Adsorption Isotherm Measurements
The adsorption–desorption isotherms of nitrogen at
77 K were measured with the apparatus Autosorb (Quan-
tachrome, USA) as a function of relative pressure P/P0 over
the range of 0.01–0.99. Prior to the a measurement, the sam-
ple was outgassed at ꢁ150ꢂC under vacuum for 8 h. Pore
volume was estimated from nitrogen uptake at P/P0 ꢆ 0.99.
III. EXPERIMENTAL RESULTS
1. Powder Diffraction
2. Neutron Powder Diffraction and Small-Angle Scattering
Pure ZrO2 has three polymorphs: a cubic fluorite struc-
Neutron powder diffraction experiments were carried ture (space group Fm3m) above 2640 K, a tetragonal struc-
out using the General Purpose Powder Diffractometer ture (P42/nmc) between 1400 and 2640 K, and a mono-
(GPPD) at the Intense Pulsed Neutron Source (IPNS) clinic structure (P21/c) below 1400 K. A small amount of
of Argonne National Laboratory. A powder sample was rare-earth solutes in zirconia can stabilize the tetragonal
enclosed in a thin-wall vanadium can (11-mm diameter, and cubic phases over a wide range of temperatures (1, 6).
50-mm long) for room-temperature measurements. A reso- Figure 1 displays a portion of the observed, background-
lution of 1d/d = 0.25% (where d is the atomic spacing) can subtracted, and fitted powder patterns of the Nd0.1Zr0.9O1.95
be achieved from a backscattering geometry at a mean scat- and Ce0.1Zr0.9O2 that were heat treated at 600ꢂC. First,
tering angle (2 ꢀ) of ꢅ148ꢂ. For the present zirconia samples the NPD patterns clearly show different crystal structures
with small grains, resolution effect is not a limiting factor for the two samples: a mixture of cubic and tetragonal
to data analysis.
phases in the Nd0.1Zr0.9O1.95 and a tetragonal structure
While conventional powder diffraction yields informa- in Ce0.1Zr0.9O2. Second, the broad Bragg peaks indicate
tion regarding the average structure of atomic organiza- a small average crystallite size in both materials. Third,
tion over a length scale of typically a crystalline unit-cell the oscillatory residual intensities in Nd0.1Zr0.9O1.95 and
dimension, small-angle scattering provides a characteriza- the anomalous peak profiles in Ce0.1Zr0.9O2 underscore the
tion of inhomogeneity up to ꢁ100 nm. The scattering at low short-range defect structures in RE-modified ZrO2.
wavevector, Q = 4 ꢁ sin ꢀ/ꢂ (where ꢀ is the scattering angle
The NPD profiles of the pure zirconia after annealing at
and ꢂ is the neutron wavelength) arises from fluctuations 290 (as prepared), 400, 500, 600, and 700ꢂC are shown in
of neutron-scattering cross section in the sample. In the Fig. 2. First, all the patterns show the monoclinic crystal
present case the scattering contrast comes from the zirco- structure as expected for ZrO2. Second, the peaks sharpen
nia particles versus the pores. The SANS experiments were progressively with increasing annealing temperature, indi-
carried out using the small-angle diffractometers, SAD, and cating a continuing grain growth and relaxation of inter-
SAND at IPNS. Incident neutrons with wavelengths in the nal microstrain. Third, a broad Lorentzian-like component
range of 0.05–1.4 nm were used and the sample-to-detector in the peak profiles similar to that in Ce0.1Zr0.9O2 was ob-
distance of 1.54 m was fixed throughout the experiment. served. The observed peaks in the sample heat treated at

500
LOONG ET AL.
˚
FIG. 1. Rietveld profile fits in the 0.6 to 1.1-A region of d-spacing for
(a) Nd0.1Zr0.9O1.95 and (b) Ce0.1Zr0.9O2 powdersthat were subjected to heat
treatment at 600ꢂC. The dots are the observed, background-subtracted
intensities. The solid line represents the calculated crystalline intensities.
Tick marks indicate the positions of the Bragg reflections: in (a) cubic (top
row) and tetragonal (bottom row) phases, and in (b) tetragonal phase.
The residual intensities before Fourier filtering are shown at the bottom
of each panel where oscillatory deviations are evident in Nd0.1Zr0.9O1.95
.
˚
FIG. 2. Rietveld profile fits in the 0.5 to 2.7-A region of d-spacing for
700ꢂC are still much wider than the corresponding ones in
a commercial ZrO2 powder prepared by high-temperature
(>900ꢂC) techniques. Therefore, one expects continuing
grain growth at higher annealing temperatures.
pure ZrO2 samples at selected heat-treatment temperatures: (a) 290, (b)
500, and (c) 700ꢂC. The dots and solid lines represent the observed, back-
ground subtracted intensities, and the calculated crystalline intensities,
respectively.
2. Small-Angle Scattering
Figure 3 shows the SANS data in terms of log-intensity
versus log-Q profiles taken at ambient temperature for
Nd0.1Zr0.9O1.95, Ce0.1Zr0.9O2, and ZrO2 that were heat-
treated at 600ꢂC. First, the intensity profiles of the three
samples show distinct Q-dependence, which implies RE-
dopant specific microstructural changes induced by the
modification. Second, each profile shows a break at a cer-
tain Q (denoted by an arrow in Fig. 3) which roughly marks
a change of slope in the curve. The position of this break-
ing point shifts progressively to lower Q for Nd0.1Zr0.9O1.95
,
Ce0.1Zr0.9O2, and ZrO2, which implies a corresponding in-
creasing mean particle size (see the next section). Figure 4
shows the evolution of the SANS profiles of pure ZrO2 sub-
jected to ex situ heat treatments from 290 to 800ꢂC. Again,
a progressive change in the particle size and porosity result-
ing from annealing was observed.
FIG. 3. The log–log plot of SANS intensity versus Q for Nd0.1Zr0.9
O1.95, Ce0.1Zr0.9O2, and ZrO2 that were heat-treated at 60ꢄ01ꢂC. Typical er-
3. Nitrogen Adsorption Isotherms
˚
rors are of the size of the symbols, except for Q > 0.1 A where errors
The isotherms of both Ce0.1Zr0.9O2 and Nd0.1Zr0.9O1.95
exhibit a shape of Type IV with a Type A hysteresis loop,
are large. The solid lines represent the fits of the data to the fractal model.
Limiting slopes for power-law behavior are given by the dotted lines (see
as shown in Fig. 5. This is characteristic of mesoporosity text).

EVOLUTION OF ZIRCONIA NANOPARTICLES
501
FIG. 6. The pore-volume ln radius distribution function of the heat-
treated Nd0.1Zr0.9O1.95, Ce0.1Zr0.9O2 obtained from a t-plot analysis.
ꢁ0.75 for Ce0.1Zr0.9O2 and Nd0.1Zr0.9O1.95, respectively) in
the isotherms signifies multilayer condensation of nitrogen
in the mesopores. At low pressure, the isotherms display
the characteristic of monolayer adsorption on micropores
which are formed between tightly bound crystalline grains.
This behavior is common to zirconia powders prepared us-
ing aqueous solutions and subsequently dried at a low tem-
perature (10–12). A t-plot analysis of the pore-size distribu-
tion, as shown in Fig. 6, reveals that the rare-earth modified
powders consist of principally mesopores which are present
within aggregates of primary and secondary particles.
The isotherms of pure ZrO2 heat treated at 290ꢂC (as
prepared) and 600ꢂC, as shown in Fig. 7, exhibit Type II
behavior (9). The effect of heat treatment on the porosity
of the powders can be seen from the curves of pore-size dis-
tribution as shown in Fig. 8. While the as-prepared sample
contains a considerable amount of micropores in addition
to macropores, the heat-treated sample is devoid of micro-
porosity. Consequently, the 600ꢂC-heat-treated pure ZrO2
powder show a considerably smaller surface area and larger
pore volume than those of the as prepared powder.
FIG. 4. The log–log plot of SANS data for pure ZrO2. All data were
collected using the SAD instrument except for the data sets for 500 and
800ꢂC annealing which were obtained from the SAND instrument. The
SAND diffractometer equipped with an area detector larger than that of
SAD thereby providing data over a wider Q-range. The solid lines for
annealing temperatures equal to or below 500ꢂC are fits of the data using
the fractal model whereas those for other temperatures are fits using the
Ornstein–Zernike model. The dashed line represents power-law behavior
of slope ꢄ4. The plots on the right display the particle size distributions
corresponding to different annealing temperatures.
with principally open-ended cylindrical pores (9). The hys-
teresis loop of Ce0.1Zr0.9O2 occurs at higher relative pres-
sures than those of Nd0.1Zr0.9O1.95, which is indicative of a
larger average pore radius in Ce0.1Zr0.9O2. The uptake of
adsorption at a characteristic relative pressure (ꢁ0.6 and
FIG. 5. Nitrogen adsorption–desorption isotherms at 77 K for
Nd0.1Zr0.9O1.95, Ce0.1Zr0.9O2 that were heat treated at 600ꢂC.
FIG. 7. Nitrogen adsorption–desorption isotherms at 77 K for pure
ZrO2 that were heat treated at 290 and 600ꢂC.

502
LOONG ET AL.
can be modeled by adjustable parameters (14). Short-range
atomic disorder such as defects, compositional fluctuations,
atomic displacements from lattice sites, on the other hand,
give rise to another type of coherent scattering which may
be manifest as a diffuse, variant component superimposed
on the Bragg scattering. Some features of the short-range
order structures may be revealed in terms of a real-space
correlation function which can be extracted from a Fourier
filtering analysis. However, if several substructures coex-
ist, as in the present zirconia samples, interpretation of the
diffraction results should be treated with caution.
While the crystal structure of heat-treated pure ZrO2
remains monoclinic, the Ce0.1Zr0.9O2 and Nd0.1Zr0.9O1.95
powders exhibit crystal structures characteristic of sta-
bilized high-temperature phases of pure zirconia, i.e., a
mixture of cubic (58.7% mole fraction) and tetragonal
(41.3% ) in the Nd0.1Zr0.9O1.95 and a tetragonal structure in
Ce0.1Zr0.9O2. This can be seen from the satisfactory refine-
ments (weighted R-factors 4–10% ) shown in Figs. 1 and 2.
In the analysis of the peak profiles we find an adequate rep-
resentation of all the data by assuming a superposition of a
Gaussian and a Lorentzian component from which the aver-
age crystalline grain size and microstrains were estimated,
respectively. The results are listed in Table 1. As expected,
the particle size of pure ZrO2 increases with increasing
heat-treatment temperature. As the particles coarsen, the
strain in the crystalline lattice is released considerably.
In Nd0.1Zr0.9O1.95 ionic charge compensation for the dif-
ferent oxidation states of Nd(III) and Zr(IV) cations in the
lattice results in oxygen vacancies. The data were analyzed
by assuming a random substitution of Zr with Nd and
FIG. 8. The pore-volume ln radius distribution function of the pure
ZrO2 powders obtained from a t-plot analysis.
IV. DISCUSSION
Experimental results from neutron scattering and N2 ad-
sorption studies show evidence of different crystal phases
and microstructures of zirconia powders that are subjected
to rare-earth modification and heat treatment. We now
present a quantitative analysisofthe data. The NPD profiles
were analyzed by the Rietveld profile refinement method
(13). In general, Bragg diffraction arises from coherent
scattering of neutrons by long-range atomic order in the
crystalline grains averaged over the sample. Incoherence
among the crystalline grains, such as distribution of grain
sizes, grain boundaries, and microstrains, causes deviations
in the observed Bragg-peak intensities from those expected
for an idealpowder. Within the Rietveld refinement some of
these effects such as the average grain size and mircrostrain
TABLE 1
Parameters Characteristic of the Crystal Phases and Microstructures of Rare-Earth-Modified and Pure Zirconia Powdersa
Nd0.1Zr0.9O1.95
h.t. 600ꢂC
Ce0.1Zr0.9O2
h.t. 600ꢂC
ZrO2
h.t. 290ꢂC
ZrO2
h.t. 400ꢂC
ZrO2
h.t. 500ꢂC
ZrO2
h.t. 600ꢂC
ZrO2
h.t. 700ꢂC
ZrO2
h.t. 800ꢂC
Parameters
Preparation method Coprecipitation
Coprecipitation Hydrolysis
Monoclinic
Hydrolysis
Monoclinic Monoclinic Monoclinic
10.5(12)
Hydrolysis
Hydrolysis
Hydrolysis
Monoclinic Monoclinic
27.4(11)
Hydrolysis
Crystal structure
Crystalline grain
size (nm)
Cubic/tetragonal Tetragonal
20.2(7)/8.8(2)
39.1(11)
6.3(2)
15.5(7)
20.8(8)
Microstrain (% )
Weighted R (% )
0.43(4)/0.67(4)
5.6
0.53(1)
6.6
2.16(7)
3.9
2.16(11)
9.4
1.35(3)
7.7
0.90(2)
8.1
0.66(3)
8.2
Primary-particle
size (nm)
Size distribution
r.m.s. deviation
Fractal cutoff (nm)
Fractal dimension
6.56(1)
20.6(1)
3.62(3)
5.68(2)
11.2(4)
22.8(8)
40.1(9)
68.4(25)
1.57(2)
1.17(2)
1.44(2)
1.05(2)
1.12(2)
1.32(2)
1.49(2)
1.50(2)
575(15)
2.97(2)
500(20)
2.92(2)
26.1(4)
2.31(4)
26.4(3)
2.84(1)
22.0(2)
2.82(2)
Surface area (m2/g)
Pore volume (ml/g)
Pore radius (nm)
72.3
0.163
ꢁ3
26.1
0.130
ꢁ5
135.4
0.856
Microporous
35.1
2.51
Macroporous
a
The mean crystalline grain size and microstrain were estimated from the Gaussian and Lorentzian components of the fitted diffraction peak
profiles, respectively. The primary-particle size and its distribution were obtained from fitting the small-angle scattering data with the fractal model
(Nd0.1Zr0.9O1.95, Ce0.1Zr0.9O2, and ZrO2 h.t. ꢇ 500ꢂC) and with the Orenstein–Zernike model (ZrO2 h.t. ꢈ 600ꢂC). The specific area and porosity were
obtained from BET and t-plot analysis of the N2 adsorption data.

EVOLUTION OF ZIRCONIA NANOPARTICLES
503
an oxygen deficiency of 5 mol% . Although all the Bragg loidal systems (25, 29). By definition a mass fractal having
peaks are accounted for by the two-phase crystal struc- a fractal dimension D, namely, the total mass inside a dis-
ture, a broad, oscillatory deviation from the calculated crys- tance r scales as M ∝ r D, a pair-correlation function can be
talline profile is evident in the residual profile in Fig. 1a. constructed as
This oscillatory component was fitted by a smooth, long
D
4ꢁ RD
1
g(r) =
r Dꢄ3 exp(ꢄr/ꢄ) + 1,
[3]
period background function (related to the real space cor-
relation function) thereby filtering out the sharp features
due to crystalline contributions. Interpretation of coeffi-
cients in the background function corresponding to short-
range interatomic spacings, revealed evidence of static,
oxygen vacancy-induced atomic displacements along the
pseudocubic h111i and other directions. Similar results
were also found in a 10 mol% lanthanum doped sample,
La0.1Zr0.9O1.95 (15). Such a procedure led to significant im-
provement of the fit. The same Fourier filtering analysis was
performed on the Ce(IV)-doped zirconia spectra but no ob-
vious spatial correlations due to atomic displacements were
found. The fit was made according to a fully stoichiometric
oxygen occupancy.
The structure of ramified objects formed by aggregates of
small particles has been studied extensively by a variety of
experimental methods including small-angle scattering (10,
16–27). The present study focuses on the characterization of
the crystalline powders rather than the sol-gels since nomi-
nally anhydrous polycrystalline materials are employed for
catalytic applications as support components. A character-
ization of the size distribution of the constituent particles
and the porous structure according to sample preparation
routes and processing conditions (e.g., heat treatments) is
of crucial importance. SANS permits a measurement of the
local density of an aggregate as a function of length scale.
The observed intensity can be expressed as a product of
the form factor of the particles, P(Q), and the interparticle
structure factor, S(Q),
where ꢄ is a cutoff distance beyond which the density of
the fractal object approaches the macroscopic density. The
structure factor then becomes (25, 29)
1
D0(D ꢄ 1)
S(Q) = 1 +
sin[(D ꢄ 1) arctan(Qꢄ)],
ꢂ
ꢃ
(QR)D
(Dꢄ1)/2
1
1 +
Q2ꢄ2
[4]
where 0(x) is a gamma function. One of the goals is to esti-
mate the mean particle size (ꢁ2R) and the size distribution
in the zirconia powders. Therefore, the expression in Eq. [1]
was integrated over a log-normal distribution of sizes with
a geometric standard deviation ꢅ (30). ꢅ is a dimension-
less variable equal to the ratio of the particle size at 15.87%
probabilityto the geometricmean particle size at 50% prob-
ability. Hence ꢅ = 1 implies a distribution of uniform size
(monodispersity). The SANS data were fitted using Eqs. [1],
[2], and [4] which contain six adjustable parameters: R, ꢅ, ꢄ,
D, a prefactor in Eq. [1], and a Q-independent background.
As can be seen in Fig. 3 the distinct SANS profiles of heat-
treated Nd0.1Zr0.9O1.95 and Ce0.1Zr0.9O2 and pure ZrO2 at
600ꢂC can be described adequately by the fractal model. In
general, the position of the broad maximum is mainly de-
termined by the particle form factor from which the mean
particle size (2R) and size distribution (in terms of ꢅ) can be
extracted reliably. The best fits of the data suggest values
of (2R, ꢅ) for the Nd-doped, Ce-doped, and pure zirco-
nia to be (6.56, 1.17), (20.6, 1.44), and (22.8, 1.49), respec-
tively. This result indicates that doping Nd(III) ions in ZrO2
is more effective in preserving the small particle size and
the large surface area of the powder. This in part is due
to the larger ionic radius of Nd3+ (0.098 nm) than that of
Ce4+ (0.080 nm) and Zr4+ (0.072 nm) (31, 32) which hinders
diffusion of atoms from sintering into larger particles. The
mass-fractal dimension and cutoff distance (D, ꢄ), on the
I (Q) ∝ P(Q)S(Q).
[1]
Our method of analysis of the SANS data was governed
by the following criteria: (1) quantitative information re-
garding the particle size and its distribution, as well as the
nature of the aggregate in terms of interparticle correlation
can be obtained; (2) the models employed can be applied
to interpret the data over the entire Q-range; and (3) intro-
duction of adjustable parameters which do not significantly
affect the quality of the fits is avoided. We used the form
factor for a spherical particle of radius R, volume V, and
scattering-length density ꢃ, as evidenced in electron micro-
scopic studies (6, 28),
other hand, depend mainly on the shape and slope of the
curve in the Guinier region (QR 1). For samples having
ꢁ
=
identical particle size the initial slopes of the curves in a
log-I versus log-Q plot may be used to estimate the fractal
dimensions. However, for samples having different particle
size and polydispersity, as in the present case, such a method
of determination of the fractal dimension is not warranted.
The fractal dimension and cutoff distance (D, ꢄ) for the
Nd-doped, Ce-doped, and pure zirconia were found to be
ꢀ
ꢁ
2
sin(QR) ꢄ QR cos(QR)
(QR)3
P(Q) = V2(ꢃ ꢄ ꢃ0)2
3
.
[2]
For the structure factor, which is related to the spatial pair- (2.97, 575 nm), (2.92, 500 nm), and (2.64, 21.2 nm), respec-
correlation function ofthe particlesthrough a Fourier trans- tively. A fundamental property of fractal objects is self-
form, we adopted the S(Q) for a mass fractal as was used affinity over the characteristic fractal length scale. This im-
in previous studies of porous materials, aggregates, and col- plies ꢄ ꢉ R. This behavior is confirmed in the Nd-doped

504
LOONG ET AL.
and Ce-doped zirconia, but not in the pure zirconia that
are heat treated at 600ꢂC. Therefore, although the fractal
model provides a good fit to the ZrO2 data, the fractal in-
terpretation is not a physical one. In fact, we find that a
crossover from a mass-fractal assembly to clusters of solid
particles occurs in pure zirconia at a heat-treatment tem-
perature about 600ꢂC (see below). The final parameters and
estimated uncertainties from the fits are given in Table 1.
The fractal model describes very well the data of pure
ZrO2 up to the heat-treatment temperature of 500ꢂC (see
Fig. 4). Asthe sampleswere annealed from 290to 500ꢂC, the
mean particle size increased from ꢁ3.62 nm to ꢁ11.2 nm,
and the size distribution expanded from ꢅ = 1.05 to ꢅ =
1.32. The fractal dimension did not change significantly
but the fractal cutoff distance decreased from 26.1 nm to
22.0 nm. The result reflects the microstructural change of
the powders due to sintering at elevated temperatures. At
higher temperatures, although the fractal model provided
a good fit to the data and confirmed the trend of particle
coarsening, the fractal dimensions and cutoff distances no
longer made physical sense. This suggests that the parti-
cles have grown in size to an extent that self-affinity behav-
ior cannot be sustained over an increasing length scale. In-
stead, the assembly is better described as a random packing
of solid particles with intertwining macroporosity. We find
that an excellent description of the high-temperature data
was achieved by using the Ornstein–Zernike-type model
FIG. 9. The mean particle size of ZrO2 deduced from in situ SANS
measurements during heating. Each data set was collected over a 30-min
interval.
the data to a power law does not warrant an accurate de-
termination of the slopes. It can be seen from Figs. 3 and 4
that the slopes for the three powders heat-treated at or be-
low 600ꢂC vary between ꢄ3 and ꢄ4. This suggests a certain
degree of surface roughness of particles within the micro-
and mesoporous microstructure. A slope approaching ꢄ4
over a larger Q-range for pure zirconia heat-treated above
600ꢂC (see Fig. 4), on the other hand, suggests the formation
of larger and smoother particles resulted from sintering.
Finally, we tried to study the kinetics of particle coarsen-
ing over the temperature range of 350 to 500ꢂC by in situ
annealing. SANS data were collected in 30-min intervals
as a fresh pure ZrO2 powder was heated to 350, 400, 450,
and 500ꢂC. The mean particle size obtained from fits to the
(33, 34),
ꢆ
S(Q) = 1 +
,
[5]
1 + Q2ꢄ0 2
where ꢆ is a parameter related to osmotic compressibil- fractal model is displayed in Fig. 9. It shows qualitatively
ity in the case of liquids system and ꢄ0 is the correlation a slow growth of particle size between 400 and 450ꢂC and
length of the clusters. It can be seen from Fig. 4 that this a faster growth at 500ꢂC. The observed sizes in the in situ
model fits the data above 500ꢂC annealing temperature heating are less than those from accumulative ex situ heat
very well. The particle size and polydispersity, (2R, ꢅ) for treatments (see Table 1). This suggests that particle growth
600, 700, and 800ꢂC heat-treated samples are (22.8, 1.49), over a 15-h-period did not reach the equilibrium stage.
(40.1, 1.50), and (68.4, 1.57), respectively, and are similar
In general, the SANS data are corroborated by the re-
to those obtained from fitting the fractal model. However, sults of adsorption isotherm and NPD measurements. On
the Ornstein–Zernike model failed to provide an adequate the other hand, different experimental techniques probe
fit of the data for pure zirconia of annealing temperatures different aspects of the microstructure and the resulting pa-
below 600ꢂC and for the rare-earth modified zirconias. The rameters need not be identical. For example, the crystalline
complete results are given in Table 1. We also attempted to grain size obtained from NPD represents the coherency
fit the high-temperature data using other models, such as of atomic long-range order of a global crystal structure
the Debye–Anderson–Brumberger expression (35, 36) and whereas the particle size obtained from SANS represents
the hard-sphere approximation (37, 38). They either fit the the average size of the primary particles in the aggregate.
data poorly or necessitate the use additional parameters of It can been seen from Table 1 that below the annealing
little physical significance.
temperature of 600ꢂC the crystalline grains are larger than
The slope of the curve over the Porod regime (QR ꢉ 1) the primary particles which were nucleated from the hy-
in a log-I versus log-Q plot provides a measure of the sur- drolyzed solution. Bleier and Cannon (39) reported that the
face roughness of the constituent particles in an aggre- effects of hydrated Stern layers associated with complexa-
gate. A slope of ꢄ4 indicates a smooth surface and a value tion of zirconyl chloride tetramers may retard the growth of
between ꢄ3 and ꢄ4 implies a rough fractal-like surface the primary particles, resulting in crystallite alignment dur-
(18, 29). Because of the varying and limited Q-range among ing precipitation. Our NPD results suggest the presence
data sets in the high-Q region, we find that a simple fit of of orientational coherency among the crystalline primary

EVOLUTION OF ZIRCONIA NANOPARTICLES
505
particles. BET analysis of nitrogen adsorption measure-
ments indicate that the high surface area of the as prepared
pure ZrO2 powders (135.4 m2/g) is mainly due to internal
surfaces of micropores within the aggregate of very small
particles. As annealing temperature increases up to about
500ꢂC, microporosity evolves to mesoporosity as particles
grow in size and in size distribution. Above 500ꢂC a more
abrupt change of the microstructure occurs which leads to
a crossover from a mass-fractal-like aggregate to a random
packing of solid particles featuring reduced surface area
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Klippert, T. E., and Wozniak, D. G., J. Appl. Cryst. 30, 208 (1997).
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2nd ed. Academic Press, London, 1982.
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of Porous Solids II” (F. Rodriguez-Reinoso, J. Rouquerol, K. S. W.
Sing, and K. K. Unger, Eds.), p. 257. Elsevier Science, Amsterdam,
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growth doesnot lead to substantialcrystalline grain-growth,
as can be seen from the smaller grain sizes obtained from
NPD results (Table 1). Doping Nd(III) ions in zirconia im-
11. Lecloux, A. J., Blacher, S., Kessels, P.-Y., Marchot, P., Merlo, J.-L.,
prove the ability of preserving the relatively small particle
size, the mesoporosity, and high surface area at high (600ꢂC)
annealing temperature (see Fig. 5). Because of the differ-
ent charge-compensation effects and ionic size between
Nd3+ and Ce4+ ions in the host lattice, Nd0.1Zr0.9O1.95 and
Ce0.1Zr0.9O2 exhibit distinct crystal phases and microstruc-
ture, as evidenced also from the NPD data (Fig. 1).
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V. CONCLUSION
Neutron powder diffraction, small-angle neutron scat-
tering, and N2 adsorption isotherm measurements were
carried out to characterize the crystal phases and mi-
crostructural changes of zirconia nanopowders subject to
Nd- and Ce-doping and heat treatments. As-prepared pure
ZrO2 samples dried at 290ꢂC exhibit microporosity and
high surface area. Subsequent heat treatment rapidly con-
verts microporous structure to mesoporosity. Below a heat-
treatment temperature of 600ꢂC the nature of the aggregate
can be understood quantitativelyasa mass-fractal. At about
600ꢂC, however, the aggregate transforms from fractal-like
to random packing of well-grown, relatively smooth parti-
cles which resulted in a large reduction of surface area due
to the collapse of mesopores to a macroporous structure.
The Nd- and Ce-modified zirconia, on the other hand, re-
tain the fractal geometry and mesoporosity after annealing
at 600ꢂC. Substituting Zr with ꢁ10 mol% of Nd to form a
solid solution of rare-earth oxide and zirconia retards parti-
cle sintering and preserves the large surface area and ther-
mal stability needed for catalytic functions.
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Gelation” (F. Family and D. P. Landau, Eds.), p. 87. Elsevier Science,
Amsterdam, 1984.
26. Nicolai, T., Durand, D., and Gimel, J.-C., in “Light Scattering”
(W. Brown, Ed.), p. 201. Oxford Univ. Press, Oxford, 1996.
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O. Kratky, Eds.), p. 17. Academic Press, New York, 1982.
29. Teixeira, J., in “On Growth and Form, Factal and Non-fractal Patters
in Physics” (H. E. Stanley and N. Ostrowsky, Eds.), p. 145. Nijhoff,
Dordrecht, 1986.
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ACKNOWLEDGMENT
34. Kaler, E. W., in “Modern Aspects of Small-Angle Scattering”
(H. Brumberger, Ed.), p. 329. Kluwer Academic, Dordrecht, 1993.
35. Debye, P., and Bueche, A. M., J. Appl. Phys. 20, 518 (1949).
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Proc. 376, 353 (1995).
We thank J. Nipko and D. G. Wozniak for their assistance in the SANS
experiments. CKL is indebted to S. K. Sinha for many useful discussions.
Work performed at Argonne National Laboratory is supported by the U.S.
DOE, Basic Energy Sciences under Contract W-31-109-ENG-38.
37. Gradzielski, M., and Hoffmann, H., in “The Structure, Dynamics
and Equilibrium Properties of Colloidal Systems” (D. M. Bloor and
E. Wyn-Jones, Eds.), p. 427. Kluwer, Amsterdam, 1990.
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