Small-angle X-ray scattering study on the microstructure evolution of zirconia nanoparticles during calcination

Article abstract of DOI:10.1016/j.jssc.2005.12.002

Zirconia nanoparticles have been synthesized from zirconium hydroxide precipitates followed by a supercritical CO₂ extraction. The microstructure evolution of these zirconia nanoparticles during the calcination at the moderate temperature has been investigated. Assisted by the analyses of TEM and XRD, small-angle X-ray scattering (SAXS) study offers possibilities to a comprehensive and quantitative characterization of the structural evolution on the nanometer scales. The as-synthesized zirconia sample exhibits a mass fractal structure constructed by the surface fractal particles. Such a structure can be preserved up to 300 °C. After calcination at 400 °C, considerable structural rearrangement occurs. In the interior of nanoparticles zirconia nanocrystallites emerge. It is the scattering from such zirconia nanoparticles that give rise to the broadened crossover in the ln[J(q)] vs. ln q plot and the scattering peak in the ln[q³J(q)] vs. q² plot. With a further increase in the calcination temperature, the power-law region at large-q in ln J(q) vs. ln q plot expands, and the peak in ln[q³J(q)] vs. q² plot shifts towards lower q values, indicating size increases in both the nanocrystallites and nanoparticles. Besides, the mass fractal structure constructed by zirconia nanoparticles can be largely preserved during the moderate temperature calcination.

Full text of DOI:10.1016/j.jssc.2005.12.002

ARTICLE IN PRESS
Journal of Solid State Chemistry 179 (2006) 959–967
www.elsevier.com/locate/jssc
Small-angle X-ray scattering study on the microstructure evolution
of zirconia nanoparticles during calcination
Ã
Liping Lianga,b,c, Yao Xua, , Xianglin Houa, Dong Wua, Yuhan Suna,
Zhihong Lid, Zhonghua Wud
aState Key Laboratory of Coal Conversion, Institute of Coal Chemistry, Chinese Academy of Sciences, Taiyuan 030001, PR China
bCollege of Material Science and Engineering, Taiyuan University of Science and Technology, Taiyuan 030024, PR China
cGraduate School of Chinese Academy of Sciences, Beijing 100039, PR China
dNational Synchrotron Radiation Laboratory, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100039, PR China
Received 20 September 2005; received in revised form 27 November 2005; accepted 1 December 2005
Available online 3 February 2006
Abstract
Zirconia nanoparticles have been synthesized from zirconium hydroxide precipitates followed by a supercritical CO2 extraction. The
microstructure evolution of these zirconia nanoparticles during the calcination at the moderate temperature has been investigated.
Assisted by the analyses of TEM and XRD, small-angle X-ray scattering (SAXS) study offers possibilities to a comprehensive and
quantitative characterization of the structural evolution on the nanometer scales. The as-synthesized zirconia sample exhibits a mass
fractal structure constructed by the surface fractal particles. Such a structure can be preserved up to 300 1C. After calcination at 400 1C,
considerable structural rearrangement occurs. In the interior of nanoparticles zirconia nanocrystallites emerge. It is the scattering from
such zirconia nanoparticles that give rise to the broadened crossover in the ln[J(q)] vs. ln q plot and the scattering peak in the ln[q3J(q)] vs.
q2 plot. With a further increase in the calcination temperature, the power-law region at large-q in ln J(q) vs. ln q plot expands, and the
peak in ln[q3J(q)] vs. q2 plot shifts towards lower q values, indicating size increases in both the nanocrystallites and nanoparticles.
Besides, the mass fractal structure constructed by zirconia nanoparticles can be largely preserved during the moderate temperature
calcination.
r 2005 Elsevier Inc. All rights reserved.
Keywords: Zirconia oxide; Nanoparticle; Small-angle X-ray scattering; Calcination
1. Introduction
The simplest and most common preparation method begins
with dissolving a soluble zirconium salt in water and
forming zirconium hydroxide gelatinous precipitates by
increasing the pH value. The precipitates are then dried
and calcined to form crystalline polymorphs of zirconia. It
has been demonstrated that the microstructures of zirconia
strongly depend on the calcination conditions, which
partially determine the particle size distribution, phase
construction, crystal size, and so on [5,6]. Hence, it is of
great importance to investigate the microstructure evolu-
tion during calcination of zirconia precipitates.
Recent research progress in zirconia has greatly en-
hanced the prospects for various industrial applications
such as solid electrolytes in solid oxide fuel cells and
sensors, catalyst/catalyst support, optical films, protective
coating, membranes and dispersed phase in composite
materials [1–4]. For practical applications, it will be
advantageous to precisely control the precessing para-
meters to produce zirconia with proper microstructures.
Many excellent studies on the calcination process of
zirconia have been reported, which characterize the
microstructure evolution by means of electron microscopy
Ã
Corresponding author. Fax: +86 351 4041153.
E-mail addresses: lianglipingcn@yahoo.com.cn
(L. Liang), xuyao@sxicc.an.cn (Y. Xu).
0022-4596/$ - see front matter r 2005 Elsevier Inc. All rights reserved.
doi:10.1016/j.jssc.2005.12.002

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(TEM or SEM), X-ray diffraction (XRD), XRD line
broadening analysis, extended X-ray absorption fine
structure (EXAFS) and UV Raman spectroscopy, and
yield much valuable information on the size, shape of the
nanoparticles and the long-range order of the atoms [5–8].
However, due to the complexity of zirconia phase
transformation and the restriction of experimental techni-
ques, the microstructure evolution mechanism during the
calcination of zirconia nanoparticles have not been
completely elucidated.
To probe the structures in the nanometer range, small-
angle X-ray scattering (SAXS) that arises from the spatial
fluctuations of electronic density within a material, has
proved to be a powerful tool. It can provide valuable
information on length scales between approximately 1 and
100 nm. Up to now, SAXS technique has been used to
study the fractal features of materials directly from the
logarithmic form of the scattering intensity curves [9–12].
SAXS can also be employed to study the interfacial
characteristics between two phases or the density fluctua-
tions within the matrix according to a negative or positive
deviation from Porod’s law [13–15]. In analysis of the
particle size distribution in colloidal system or the pore size
distribution in porous materials, SAXS can yield statisti-
cally more evident information about the scatterers’
dimension by giving an average over all particles within
the illuminated sample volume [10,16]. More recently, with
the rapid development in the experimental techniques,
SAXS has been widely used to characterize materials such
as alloys [17], polymers [18], silica [9,11–15], amorphous
zirconia [19–21] and so forth. However, to the best of our
knowledge, the microstructure evolution of zirconia
nanoparticles during calcination has not been studied by
SAXS until now.
temperatures for 2 h. For the sake of clarity, the as-
synthesized and calcined samples were named hereafter
‘‘S050 and SX’’, respectively, where X denotes the
calcination temperature in 1C.
2.2. Characterization
All zirconia samples were examined with a Hitachi H-
800 transmission electron microscope (TEM) to obtain
information on the size and morphology of zirconia
particles. The crystalline phases present in the as-synthe-
sized and calcined powders were determined on a Rigaku
D Max III VC diffractometer equipped with a rotating
anode. Line traces were obtained over 2y values ranging
from 201 to 701. Narrow scan analysis was conducted in the
2y range of 16–331, as it contained the strong lines for the
tetragonal (1 1 1)t phase, the monoclinic (1 1 1)m and
(1 1 1)m phase. These three peaks were curve fitted using a
special peak-fit software equipped on the diffractometer to
obtain the full-width at half-maximum intensity (FWHM).
The average crystallite size of either the monoclinic phase
or the tetragonal phase was then calculated using
Scherrer’s equation [8]. N2 physical adsorption analysis
was carried out on a Tristar 3000 Sorptometer using the
static adsorption procedures. BET surface area was
calculated from the linear part of the BET plot according
to IUPAC recommendations.
The SAXS experiments were carried out with a long-slit
collimation system on 4B9A beamline at the Beijing
Synchrotron Radiation Facility, China. A detailed descrip-
tion of the scattering facility was given elsewhere [22]. The
incident X-ray wavelength l was 0.154 nm, the scattering
angle 2y was approximately 0–31, and the scattering vector
was denoted as q, q ¼ 4p sin y=l. The scattered X-ray
intensities were recorded using the imagery plate technol-
ogy. The background scattering and absorption of the
samples were corrected to obtain J(q)ꢀq curves, where J(q)
is the slit-smeared scattering intensity. And the data
analysis was directly based on the smeared scattering
intensity.
In the present work, zirconia nanoparticles were
synthesized from zirconium hydroxide precipitates fol-
lowed by a supercritical CO2 extraction. The microstruc-
ture evolution of so-prepared zirconia particles was
investigated by SAXS, TEM, XRD, and N2 adsorption
as a function of the calcination temperature up to 600 1C.
2. Experimental section
3. Theoretical background of SAXS
2.1. Sample synthesis
Since the SAXS phenomenon was experimentally ob-
served, rapid progress has been made on both the theory
and the experimental technique. Among the established
theoretical system, three basic theories, namely Porod’s law
[23–25], Debye’s theory [26,27], and Guinier’s theory [28],
have been widely accepted and have become the ground-
work for extracting the structural information by proces-
sing the SAXS data. These basic theories describe the
different aspects of the same object coming from their
different approximation to the real electronic structure.
Porod’s theory describes the asymptotic dependence of the
SAXS intensity on the scattering vector at the large
scattering vector. Debye’s theory reflects the correlation
between the scatterers. And Guinier’s theory mainly
Zirconium hydroxide gelatinous precipitate was ob-
tained by adding the aqueous ammonia dropwise to the
solution of zirconium oxychloride at room temperature
with continuous stirring until pH value reached 10. After
an overnight aging, the precipitate was washed thoroughly
with distilled water until chloride ions could not be
detected, and then washed with anhydrous ethanol to
obtain alcogels. To alleviate the hard agglomeration of
particles during the drying process, the solvent entrapped
in the alcogels was removed by supercritical extraction of
CO2, which was carried out at 50 1C and 15 Mpa. The as-
synthesized zirconia powder was calcined in air at different

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961
focuses on the shape and size distribution of the scatterers.
Thus, the consistency of the results derived from different
theories provides good estimation on the validity of the
SAXS analysis.
Different from the Porod’s law, Debye considered more
about the correlation between the scatterers. For an ideal
two-phase system, according to Debye’s theory, the slit-
smeared scattering intensity is given as [27,32]
Our SAXS data interpretation was mainly based on the
three basic theories. A detailed description of the concern-
ing SAXS theories is as follows.
The general theory about the scattering of a two-phase
system is known as [26]:
JðqÞꢀ2=3 ¼ Aꢀ2=3 þ Aꢀ2=3A2cq2,
(6)
where A is a constant, Ac is the correlation distance. The
parameters, A and Ac can be derived from the slope and
intercept of the linear region of J(q)ꢀ2/3 vs. q2 plot. From
the correlation distance, many valuable structural para-
meters can be calculated such as the specific surface area
Sd, the mean chord length in the solid phase, Ls and that in
the pores, Lp of the porous material. The involved
equations are listed as follows [30]:
Z
1
sinðqrÞ
2
IðqÞ ¼ IehðDrÞ iV
gðrÞ
4pr2dr,
(1)
qr
0
where I(q) is the total scattering intensity, Ie is the
scattering intensity of the single electron, Dr is the electron
density contrast between two phases, V is the irradiated
volume by X-ray, g(r) is the spatial correlation function of
the electron density.
For an ideal two-phase system having sharply defined
phase boundaries and a constant but different electron
density in each phase, the scattering intensity in the region,
where q sufficiently far from zero, will take the form of
Porod’s law [23]
Sd ¼ 4wð1 ꢀ wÞ=Ac,
Lp ¼ Ac=w,
(7)
(8)
(9)
Ls ¼ Ac=ð1 ꢀ wÞ,
where w is the volume fraction of the scatterers as
mentioned previously.
For a practical, non-ideal system, where there is either a
diffuse interface layer or electron density fluctuation within
any phase, the deviation from Porod’s law will be observed
[33–36]. It is the additive scattering derived from the
interface layer or the density fluctuation that makes the
large-q region of the ln[q3J(q)] vs. q2 plot no longer
constant. In this case, the Porod constant, Kp can be
obtained by linearly fitting the large-q region of the
ln[q3J(q)] vs. q2 plot using the following equations
[14,36,37]:
2
q4IðqÞ ¼ Kp0 ¼ Ie2pðDrÞ SpV for pinhole-collimation; and
2
q3JðqÞ ¼ Kp ¼ Iep2ðDrÞ SpV for slit-collimation;
(2)
where Kp is the Porod constant, which is proportional to
the total interfacial area, SpV in the scattering volume.
Obviously, according to Porod’s law, the ln[q3J(q)] vs. q2
plot will tend progressively to be a straight line with slope
of zero at large q value. Moreover, for slit-collimation, the
formula to evaluate the surface area per volume unit, Sp
can be expressed as follows [24,29,30]:
ln½q3JðqÞꢁ ¼ ln KP ꢂ s2q2,
(10)
where s is a parameter related to either the thickness of the
interfacial layer or the electron density inhomogeneity.
Besides the forementioned applications, the SAXS
analysis can also be employed to study the fractal
structures. As all known, the typical property of a fractal
structure is its self-similarity, i.e., irrespective of length
scales or magnification the repetition of disorder within the
structure takes place. To describe such a structural
property, the fractal dimension D is employed, which
quantifies how the mass, M in mass-fractals or the surface
area, A in surface-fractals changes with the radius R. In a
real system, however, the fractal character can only be
observed within a limited range of size. Hence, it is equally
important to determine the corresponding length scale
region. One approach to obtain the fractal dimension and
the corresponding length scales is based on the power-law
regions in the SAXS curves [38]. Generally, in the power-
law regime (qRgc1cqa0, Rg and a0 corresponding to the
radius of gyration of particles and the chemical length of
the monomeric units, respectively), the SAXS intensity J(q)
may show an exponential dependence on q and can be
described as [38]
Sp ¼ 4wð1 ꢀ wÞKp=Q,
(3)
where w is the volume fraction of the scatterers and Q is the
integrated invariant. The evaluation of Q requires carefully
using the Guinier approximation [28] and the Porod’s
approximation [24] for intensity extrapolation at the
unmeasurable small and large angles, respectively. The
corresponding expression is given by [23–25,30]
Z
Z
Z
1
qmin
qmax
Q ¼
qJðqÞdq ¼
1
qJðqÞdq þ
qJðqÞdq
qmin
0
0
Z
þ
qJðqÞdq.
ð4Þ
qmax
The volume fraction w can either be calculated from the
bulk density and skeletal density of the sample or be
estimated from the measurement of the absolute intensity
of the primary beam, I0 according to the following
equation [30,31]:
w ¼ Q=4p2Ie ¼ QL2ðm2c4=e4Þ=4p2I0,
where m and e are the mass and electrical charge of an
electron, respectively, c is the velocity of light, L is the
distance from the sample to the detector.
(5)
JðqÞ ¼ Cqꢀa
,
(11)

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962
where C is a constant. The exponent ꢀa can be estimated
by plotting ln J(q) vs. ln q, which is related to the mass
fractal dimension Dm or the surface fractal dimension Ds as
follows [30,38]:
particle size from ꢃ10 to ꢃ30 nm can be observed.
However, the network structure constructed by nanopar-
ticles can be preserved even in sample after calcination at
600 1C.
1pa þ 1o3 for mass fractal; Dm ¼ a þ 1,
3pa þ 1o4 for surface fractal; Ds ¼ 6 ꢀ ða þ 1Þ,
a þ 1X4 for nonfractal:
(12)
(13)
(14)
4. Results
4.1. TEM analysis
Fig. 1 shows the TEM images of all samples. It is
expected that the sample S050 retain the network structure
of the original alcogel on the whole. Calcination at 300 1C
can hardly bring any perceptible difference in TEM image,
implying no significant changes in size, shape and interac-
tion of particles. As the calcination temperature is
gradually elevated up to 600 1C, a monotonic increase in
Fig. 2. X-ray diffraction of zirconia sample: (a) S050, (b) S300, (c) S400,
(d) S500, (e) S600.
Fig. 1. TEM images of Zirconia samples: (a) S050, (b) S300, (c) S400, (d) S500, (e) S600.

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Table 1
The average crystallite size of the tetragonal and monoclinic phases in
ZrO2 nanoparticles calculated from X-ray diffractiona
(2)–(10), only these structural parameters for S050 and
S300 can be calculated. With no significant deviation from
Porod’s law and Debye’s theory makes it easy to obtain the
Porod constant Kp (Eq. (2) or (10)) and the correlation
distance, Ac (Eq. (6)) from the SAXS curves. The
integrated invariant Q can be calculated from Eq. (4) by
using the Guinier approximation and the Porod’s law. The
volume fraction, w can be deduced from the absolute
intensity of the primary beam I0 according to the Eq. (5).
And then, using Eqs. (3) and (7)–(9), the specific surface
areas Sp and Sd and the mean lengths of the chords in two
phases Ls and Lp can be obtained. The calculation results
are summarized in Table 2. For comparison, the specific
surface area derived from the N2 adsorption is also listed.
As mentioned previously, different from the scattering
charater of S050 and S300, the ln[q3J(q)] vs. q2 plot of the
scattering intensity shows a visible peak in the mid-q range
after the sample is calcined at 400 1C. And a further
increase in the calcination temperature causes a gradual
shift of this peak towards lower q value (Figs. 3(c)–(e)). As
all known, the SAXS originates from the spatial fluctuation
Sample
Dt,
(nm)
D
m;ð111ÞðnmÞ
Dm,
(nm)
(1 1 1)
¯
(1 1 1)
S400
S500
S600
6.4
6.9
5.1
5.8
8.9
5.7
6.8
10.7
10.4
¯
SX denotes the sample calcined at X 1C. Dt, (1 1 1), Dm, ð111Þ and Dm,
(1 1 1) are the average crystallite size calculated from the diffraction lines
¯
of the tetragonal (1 1 1)t phase, monoclinic ð111Þm and (1 1 1)m phase.
aUncertainty on the calculated values is 70.5 nm.
4.2. XRD analysis
Fig. 2 displays the XRD patterns of the samples. Both
S050 and S300 are X-ray amorphous. For S400, the
diffraction peaks of the tetragonal phase (t-ZrO2) are
predominant, while those of the monoclinic phase
(m-ZrO2) are relatively weak. Besides, small fraction of
ZrO2 may still be existed as amorphous phase because the
XRD peaks are somewhat broad. With the further increase
in calcination temperature, the diffraction peaks of t-ZrO2
decline and those of m-ZrO2 increase, corresponding to the
t-m phase transformation. However, some t-ZrO2 phase
still exist even after the powder is calcined at 600 1C. In
addition, heat treatment at the increasing temperature
gives rise to narrower diffraction peaks, indicating an
increase in crystallinity. From the strong lines of the
¯
tetragonal (111)t phase, monoclinic ð111Þm and (111)m
phase, the average crystallite size can be estimated, as
shown in Table 1.
4.3. SAXS analysis
Fig. 3 shows the ln[q3J(q)] vs. q2 plots of all samples. Due
to the fluctuation of the incident X-ray intensity, the
oscillation of the scattering intensity is unavoidable in the
whole q range. For the scattering curves of S050 and S300
(Figs. 3(a) and (b)), no visible deviation from the Porod’s
law can be observed, revealing systems with nearly
homogeneous matrices and sharp interface. However, with
a distinct peak emerging in mid-q range, the ln[q3J(q)] vs. q2
plot gives a thoroughly different appearance after the
powder is calcined at 400–600 1C (Figs. 3(c)–(e)). As
mentioned above, due to the additive scattering, the
scattering character from a non-ideal system may show a
negative or positive deviation from Porod’s law at large q
range. But in our case, the additive scattering occurs in
mid-q region, so it is unreasonable to consider such a
phenomenon to be any of the conventional deviations from
Porod’s law [14,15,34]. Hence, for samples S400, S500 and
S600, it is comparatively difficult from the SAXS data to
obtain some structural information such as the specific
surface area, the correlation distance, or the mean chord
length in the solid particles and in the pores. Through Eqs.
Fig. 3. ln[q3J(q)] vs. q2 plots of the scattering intensity of zirconia samples:
(a) S050, (b) S300, (c) S400, (d) S500, (e) S600. For sake of clarity, curves
(b)–(d) are shifted upwards. The code qmax denotes the upper limit of the q
range corresponding to the scattering peak.
Table 2
Textural parameters of zirconia samples derived from the extended
Porod’s law and Debye’s theory [14,37]a
Sample
w
Ac
Ls
Lp
Sp (m2/
cm3)
Sd (m2/
cm3)
SBET
(m2/g)
(nm) (nm) (nm)
S050
S300
0.29 9.2
0.31 8.6
13.2 30.8
12.6 26.8
75.1
82.1
91.0
101.6
279.6
256.6
S050 and S300 denote the samples as-synthesized and calcined at 300 1C.
w is the volume fraction of the scatterers. Ac is the correlation distance. Ls
and Lp denote the mean length of chords in the solid phase and in the
pores. Sp and Sd denote the specific surface area derived from Porod’s law
and Debye’s theory, respectively. SBET is the specific area determined by
N2 physical adsorption.
aThe upper error limit for all derived values is between 5% and 10%.

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964
of electronic density in the investigated system. Hence,
these considerable changes in SAXS intensity must be
related to significant structure rearrangements. To get a
better understanding of the involved structure changes, it is
necessary to ascertain the position of these peaks. For sake
of clarity, we introduce here qmin and qmax to denote the
lower and upper limits of the q range on which the peak
existed. In Figs. 3(c)–(e), qmax can be readily estimated
from the beginning of the linear trend at high-q region.
When q larger than qmax, the plot of ln[q3J(q)] vs. q2 can be
fitted into a straight line with slope of zero. On the
contrary, extracting qmin from these curves will give more
errors. So we look for another method to ascertain the
(a) The power law appears at high
q
, which corresponds to short
(region I),
qmaxoqoꢃ1.4 nmꢀ1
length scales and shows an exponent of ꢀa1. For
samples S050 and S300, this power-law region is
between approximately 0.4 and 1.4 nmꢀ1. The values
of exponent are found to be ꢀ2.92 and ꢀ2.89, which
correspond to scatterings by surface fractals with Ds as
2.08 and 2.11, respectively. According to the researches
of Vollet [9] and Rieker [10], this power-law region
should correspond to the surface scattering from the
primary scatterers, i.e., zirconia nanoparticles. More-
over, the average size of these nanoparticles can be
roughly estimated as 3.5/qc [9], where qc corresponds to
the approximate situation of the crossover region, and
their maximum size can be estimated as 2p/qmax. Thus,
in sample S050 and S300, zirconia nanoparticles are
surface fractals with an average size of about 13.0 nm
value of qmin
.
The ln[J(q)] vs. ln q plots of the scattering intensity are
shown in Fig. 4. All scattering curves present, in general, two
power-law regions (region I and III), in which the intensity
shows an exponential dependence on q according to Eq. (11),
and a curved crossover region (region II) between them. The
ln[J(q)] vs. ln q plots of S050 and S300 (Figs. 4(a) and (b))
show features of the mass fractal clusters composed of
surface fractals, such as zirconia xerogels [19], silica aerogels
[9], and carbon blacks [10]. After the calcination at
400–600 1C, however, the scattering curves are heavily
distorted with a much broader crossover region and a
suppressed power-law region at large q value (Figs. 4(c)–(e)).
It can be demonstrated that the broadened crossovers have a
one-to-one correspondence to the peaks presented in the
ln[q3J(q)] vs. q2 plots (Figs. 3(c)–(e)) from both their position
and changing tendency with the increase in the calcination
temperature. Thus, the q range corresponding to either the
peak or the curved crossover region, qminoqoqmax, can be
well defined. Using Bragg’s law, the corresponding length
scale is expressed as 2p/qmaxoLo2p/qmin. As to the two
power-law regions, the exponents, ꢀa are extracted by linear
fitting the data over the q-regions shown in Fig. 4. And
the fractal dimensions, Dm and Ds, are obtained through
Eqs. (12)–(14). The fractal dimensions and the involved
characteristic length scales are summarized in Table 3. A
detailed description of the scattering features in Fig. 4 is
as follows:
Fig. 4. ln J(q) vs. ln q plots of the scattering intensity of zirconia samples:
(a) S050, (b) S300, (c) S400, (d) S500, (e) S600. For sake of clarity, curves
(b)–(d) were shifted upwards. The scattering regions: I is the power-law
region at high q, II is the curved crossover region at intermediate q, III is
the power-law region at low q. The code qc corresponds to the
approximate situation of the crossover region. The codes qmin and qmax
denote the lower and upper limits of the q range corresponding to the
extended crossover region.
Table 3
Fractal dimensions and the characteristic length scales in Fig. 5a
Sample
High-q region (I)
Mid-q region (II)
LminꢀLmax (nm)
Low-q region (III)
Ds
DL ¼ LmaxꢀLmin (nm)
Dm
S050
S300
S400
S500
S600
2.08
2.11
20.9–26.2
19.6–25.1
5.5–18.5
6.5–19.6
10.6–31.4
5.3
5.5
2.38
2.40
2.39
2.40
2.32
Nonfractal
Nonfractal
Nonfractal
13.0
13.1
20.8
S050 and SX denote the samples as-synthesized and calcined at X 1C. Ds and Dm are the surface fractal dimension and the mass fractal dimension,
respectively. Lmin is the lower limit of the mid-q region and the maximum size of the primary scatterers. Lmax is the upper limit of the mid-q region and the
minimum size of the mass fractal clusters. Lmin and Lmax are defined as 2p/qmax and 2p/qmin, respectively.
aUncertainty on the value of the fractal exponents is estimated to be 70.05.

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(3.5/0.27 nmꢀ1) and 12.1 nm (3.5/0.29 nmꢀ1). Their
maximum sizes are approximate by 20.9 nm (2p/
0.30 nmꢀ1) and 19.6 nm (2p/0.32 nmꢀ1), respectively.
After calcination at 400–600 1C, this power-law region
is first suppressed and then expanded gradually
towards the small-q region, with qmax of about 1.2,
1.0, and 0.6 nmꢀ1 (Fig. 4). The exponents approximate
to ꢀ4.0, suggesting scattering from non-fractal scat-
terers (Eq. (14)). Using again Bragg’s law, the
maximum size of the primary scatterers for S400,
S500, and S600 can be estimated as 5.5, 6.5, and
10.6 nm, respectively. Obviously, calcination at 400 1C
induces a considerable decrease in the size of the
primary scatterers from ꢃ19.6 to ꢃ5.6 nm. Although it
has been widely accepted that heat-treatment at a
higher temperature may lead to decrease in both the
particle size and surface fractal dimension due to the
nature of the sintering process, such a decrease is too
large to be ascribed to sintering densification. It must
be more convincing to relate it to the emergence of a
new scatterer population during the structural rearran-
gement. Combined with XRD results (Fig. 2 and
Table 1), the new scatterer population with maximum
size of ꢃ5.5 nm is believed to be zirconia nanocrys-
tallites. As the calcination temperature is elevated to
500 and 600 1C, the maximum size of these nanocrys-
tallites increases from 5.5 to 6.5 and 10.6 nm, in good
agreement with the average size of the nanocrystallites
derived from the XRD line broadening analysis
(Table 1).
Fig. 5. The sketched model for the structural evolution as a function of
calcination temperature probed by SAXS: (a) S050 and S300, (b) S400,
(c) S500, (d) S600.
(b) The power law applies at low
q (region III),
ꢃ0.1oqoqmin. This power law corresponds to long
length scales and for all samples, demonstrates an
exponent between ꢀ1.40 and ꢀ1.32, which indicates
scattering from mass fractals with fractal dimension of
2.32oDmo2.40 (Eq. (12)). It is obvious that these
mass fractals are zirconia clusters constructed by
nanoparticles.
circles. The representation is just intended to analyze the
structural evolution during the heat treatments.
SAXS results indicate that the as-synthesized zirconia
sample consists of mass fractal aggregates constructed by
primary particles with nearly uniform interior structure.
Such a structural characteristics might derive from both the
inheritance of the original wet gel and the slight modifica-
tion in drying process. According to the recent research of
Southon [20] and Chen [39], the formation of zirconia wet
gel involved in our case can be generally described as
follows: with the high pH value of ꢃ10 and slow addition
of ammonia, the predominant zirconium coordination
monomers in the present system can be regarded as a
tetragonal bipyramid, in which hydroxyl ions fully occupy
the six acmes of the bipyramid. Based on these monomers,
zirconium tetramers with a short-range structure are
formed, in which four zirconium atoms are arranged in a
two-dimensional square lattice, each connected by double
hydroxyl bridges, giving an ideal stoichiometry of Zr(OH)4.
Moreover, the mean bond length of Zr–OH in the tetramer
is close to that of Zr–O in bulk tetragonal zirconia [20,39].
Hence, further polymerization between these tetramer
precursors mainly forms the netlike ordered tetragonal
precursor structure, as well as some local disorders
probably due to the defects in lattice, any oxo bridges
(c) The curved crossover region appears at intermediate q
(region II). For S400, S500, and S600, the crossover
regions are broadened. The corresponding length scale
is between the maximum size of the nanocrystallites
and the minimum size of the mass fractal clusters, and
is very close to the size of the nanoparticles. Hence, the
scattering occurred at this region can be considered as
the scattering from zirconia nanoparticles.
5. Discussion
The SAXS data, complemented by TEM, XRD, and N2
physical adsorption analysis, provide abundant informa-
tion on the microstructure evolution of zirconia nanopar-
ticles. The set of experimental data can be explained based
on the model sketched in Fig. 5, where the structure is
sketched as a function of the length scale represented by

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L. Liang et al. / Journal of Solid State Chemistry 179 (2006) 959–967
966
and incomplete hydroxyl ions substitution [40]. With the
subsequent liquid CO2 exchange and supercritical CO2
extraction, the boundary of a new particle (primary
particle) is formed. However, different from the conven-
tional drying process, removal of liquid phase at the
supercritical conditions makes it possible for the as-
synthesized powder to largely preserve the structure of
the original wet gel. Such an inheritance might explain the
mass fractal character of the as-synthesized powder.
Besides, the interior of thus-obtained primary particles is
nearly uniform with only slight electronic density fluctua-
tions that might originate from the local disorder in the
original network structure and the imperfect solvent
exchange. The slight interior electronic density fluctuation
gives an additive contribution to the scattering from the
surface boundary of the particles, thus resulting in a little
deviation from the scattering exponent ꢀ3 of Porod’s law,
giving the power-law region with exponent of ꢀ2.92
(Fig. 4(a)), and endowing the particles with surface fractal
characteristics.
From the crossover in Fig. 4(a), the average dimension
of these new-formed particles has been roughly estimated
as ꢃ13.0 nm (3.5/qc), consistent with the mean chord length
in the solid phase Ls of 13.2 nm (in Table 2). And the
fractal dimension of the mass fractal clusters has been
determined as about 2.38. Both the small particle size of
about 13.0 nm and the low mass fractal dimension of 2.38
predict that the as-synthesized powder is a loose-packed
material with high specific area, consistent with the results
(Table 2) from not only SAXS but also N2 adsorption
analysis.
Such a structure can be essentially preserved after
calcination at 300 1C. Indeed, there is no perceptible
changes in TEM diagrams and XRD patterns. And the
fractal characteristics are very similar to those of the as-
synthesized powder (Fig. 4). However, due to the
advantages of SAXS analysis, the information on the
fine structural changes can be detected. As can be seen in
Table 2, calcination at 300 1C leads to a little decrease in
the average chord length Ls and Lp. This fact can be related
to the removal of the small amount of water entrapped in
the gel matrix [20,41].
Calcination at 400 1C will lead to the emergence of a new
scatterer population. Based on the SAXS and XRD results,
this new scatterer population has been assigned to ZrO2
nanocrystallites due to the phase transformation from
amorphous Zr(OH)4 to crystalline ZrO2. And an in-
volved phase transformation can be presented as follows.
During calcination at 400 1C, the ordered tetragonal
precursor structures in the interior of the particles begin
to crystallize into tetragonal phase accompanied by the
small fraction of monoclinic phase, which might directly
come from the locally disordered structure. This phase
transformation may involve several steps, including the
loss of the terminal hydroxyl groups, oxolation of hy-
droxyl bridges to form embryonic oxide nuclei and
growth of the nuclei to form observable crystallites, and
a perfect phase transformation cannot be achieved at such
a low temperature. Therefore, the nanoparticle becomes a
complex of tetragonal nanocrystallites, small fraction of
monoclinic nanocrystallites and amorphous phase. Such a
phase transformation process is supported by our SAXS
results in three aspects. First, after calcination at 400 1C,
zirconia nanocrystallites become the main scatterers at
high-q region. Scattering from the surface of crystallites
(non-fractal) might account for the presence of power-law
region with exponent ꢀa1 approximate to ꢀ4.0 (Fig. 4(c)).
Second, when the scattering from the particles comes into
consideration, the small fraction of monoclinic and
amorphous phase, as well as the grain boundary, may
function as the electronic density fluctuation and give an
additive contribution to the scattering from the surface
boundary of the particles. The electronic density fluctua-
tion in our case occurs at a larger dimension. Thus, instead
of giving rise to the conventional positive deviation from
Porod’s law at large-q value, the additive scattering occurrs
at mid-q region and results in the distinct peak in ln[q3J(q)]
vs. q2 plot (Fig. 3(c)). Finally, the scattering from zirconia
nanoparticles, which comprise the nanocrystallites and
construct the mass fractal clusters, would be responsible
for the broadened crossover region in ln J(q) vs. ln q plot
(Fig. 4(c)).
With a further increase in calcination temperature to
500–600 1C, the average crystallite size increases and t-m
phase transformation occurs (Fig. 2). According to the
researches of Li [6] and Shukla [8], in an agglomerate-free
system such as our case, the metastable tetragonal phase
can exist only when the crystallite size is less than the
critical size, ꢃ6 nm. This is confirmed again by our XRD
line broadening analysis (Table 1). Our SAXS analysis
shows that the maximum size of the new scatterers
increased from 5.5 nm (400 1C) to 6.5 nm (500 1C) and then
10.6 nm (600 1C) (Lmin in Table 3), suggesting again that
the new scatterers are no other than zirconia nanocrys-
tallites. Moreover, it can predicted that, in these cases, the
small fraction of tetragonal phase and the grain boundary
may act as the electronic density fluctuation and give rise to
the peaks in ln[q3J(q)] vs. q2 plot. And the expanding of the
large-q power-law region (region I) in ln J(q) vs. ln q plot
and the peak shifting in ln[q3J(q)] vs. q2 plot towards lower
q values can be correlated with the size increase in both
nanocrystallites and particles, which arises as a conse-
quence of mass transfer process within and between
particles due to the elevated calcination temperature. In
addition, as shown in Table 3, the length scale range related
to the crossover (DL) extends from 13.0 to 20.8 nm as the
calcination temperature increases from 400 to 600 1C,
indicating a gradual increase in the polydispersity of
zirconia nanoparticles.
It is also worth noting that all samples exhibit the
mass fractal behavior at low-q region. This suggests
that the mass fractal structure constructed by nanoparticles
can be largely preserved during the calcination up to
600 1C.

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967
6. Conclusion
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In our study, SAXS technique was employed to
investigate the microstructure evolution of zirconia nano-
particles during the calcination at moderate temperature.
Assisted by the analyses of TEM and XRD, the SAXS
study offers opportunities to a comprehensive and quanti-
tative characterization of the structural evolution on the
nanometer scales. The detailed description of the involved
structural changes is as follows. The as-synthesized zirconia
sample has a typical mass fractal structure with fractal
dimension Dm of 2.38, constructed by the surface fractal
particles with an average size of about 13.2 nm and a
fractal dimension Ds of 2.08. Such a structure can be
largely preserved up to 300 1C. After calcination at 400 1C,
considerable structural rearrangement occurs. In the
interior of zirconia nanoparticles emerge zirconia nano-
crystallites with the maximum size of 5.5 nm. It is the
scattering from such zirconia nanoparticles that give rise to
the broadened crossover in the ln[J(q)] vs. ln q plot and the
scattering peak in the ln[q3J(q)] vs. q2 plot. Further
increasing the calcination temperature to 500 1C and then
600 1C, the maximum size of the nanocrystallites increases
to 6.5 nm and then 10.6 nm. Simultaneously, the maximum
size of the zirconia nanoparticles increases from 18.5 to
19.6 and 31.4 nm due to the mass transfer within and
between particles at the elevated temperature. It is also
noticeable that the mass fractal structure constructed by
zirconia nanoparticles could be largely preserved during
the moderate temperature calcination.
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Acknowledgment
The financial support from the National Key Native
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