Sol-gel derived (Li, Ta, Sb) modified sodium potassium niobate ceramics: Processing and piezoelectric properties

Article abstract of DOI:10.1016/j.jallcom.2010.09.134

Nano-scaled lead-free perovskite powders (50-100 nm) with a composition of (Na_0.52K_0.4425)(Nb_0.8825Sb_0.08) O₃-0.0375LiTaO₃ (NKNS-3.75LT) have been synthesized via a modified low-cost citrate sol-gel route, in which Nb₂O₅ and Ta₂O₅ were transformed into stable and soluble chelate complexes to replace costly metal alkoxides. The thermal decomposition process and structural transformation behavior of the as-prepared xerogel was investigated by means of thermo-gravitometry and differential scanning calorimetry, X-ray diffractometry and Fourier-transform infrared spectrometry. The results indicated that the ideal crystallization of the NKNS-3.75LT powder with a single perovskite structure occurs at 500-600 °C, significantly lower than that for a conventional mixed-oxide route. Transmission electron microscopy observation showed that the crystalline powder has particle sizes in the range of 30-100 nm and exhibits polyhedron-like morphology, probably resulting in a specific grain growth behavior upon densification. The sol-gel derived NKNS-3.75LT ceramics sintered at 1090 °C exhibit excellent piezoelectric properties of d₃₃ ～418 pC/N and k_p ～0.54 for NKN based random ceramics.

Full text of DOI:10.1016/j.jallcom.2010.09.134

Journal of Alloys and Compounds 509 (2011) 936–941
Contents lists available at ScienceDirect
Journal of Alloys and Compounds
journal homepage: www.elsevier.com/locate/jallcom
Sol–gel derived (Li, Ta, Sb) modified sodium potassium niobate ceramics:
Processing and piezoelectric properties
Hongqiang Wang, Ruzhong Zuo∗, Jian Fu, Yi Liu
Institute of Electro Ceramics & Devices, School of Materials Science and Engineering, Hefei University of Technology, Hefei 230009, PR China
a r t i c l e i n f o
a b s t r a c t
Article history:
Nano-scaled
lead-free
perovskite
powders
(50–100 nm)
with
a
composition
of
Received 11 August 2010
Received in revised form
10 September 2010
Accepted 18 September 2010
Available online 29 September 2010
(Na0.52K0.4425)(Nb0.8825Sb0.08)O3-0.0375LiTaO3 (NKNS-3.75LT) have been synthesized via
a
modi-
fied low-cost citrate sol–gel route, in which Nb2O5 and Ta2O5 were transformed into stable and soluble
chelate complexes to replace costly metal alkoxides. The thermal decomposition process and structural
transformation behavior of the as-prepared xerogel was investigated by means of thermo-gravitometry
and differential scanning calorimetry, X-ray diffractometry and Fourier-transform infrared spectrometry.
The results indicated that the ideal crystallization of the NKNS-3.75LT powder with a single perovskite
structure occurs at 500–600 ◦C, significantly lower than that for a conventional mixed-oxide route.
Transmission electron microscopy observation showed that the crystalline powder has particle sizes in
the range of 30–100 nm and exhibits polyhedron-like morphology, probably resulting in a specific grain
growth behavior upon densification. The sol–gel derived NKNS-3.75LT ceramics sintered at 1090 ◦C
exhibit excellent piezoelectric properties of d33 ∼418 pC/N and kp ∼0.54 for NKN based random ceramics.
Keywords:
Sol–gel
Ceramics
Ferroelectrics
Piezoelectricity
© 2010 Elsevier B.V. All rights reserved.
1. Introduction
By comparison, soft-chemical routes exhibit outstanding advan-
tages and have been widely used to prepare superfine powders
Lead-free piezoelectric ceramics have attracted a lot of atten-
tion in the last few years mainly owing to increasing concerns to
the environment. As one important member of lead-free family,
the (Na,K)NbO3 (NKN) based lead-free compositions were exten-
sively investigated [1–4] and have been considered as one of the
most potential candidate materials based on their large piezoelec-
tric constant d33 of >300 pC/N. Particularly, the (Li, Ta, Sb)-modified
NKN ceramics were reported to have comparable piezoelectric
properties to those of some commercial PZT ceramics [5–8]. The
piezoelectric and electromechanical properties have been so far
obviously modified through a lot of attempts to optimize the com-
position and processing [7–9], and to improve the thermal stability
[4,9]. It can be found that most of these researches were focused on
conventional solid-state reaction methods for making random NKN
based piezoelectric ceramics. This traditional synthesis method
usually needs relatively high calcination temperatures and sinter-
ing temperatures at which the evaporation of Na2O and K2O could
become more serious. Moreover, complex compositions are dif-
ficult to get homogeneously distributed in a solid state reaction
method [10,11], probably inducing difficulties of controlling the
microstructure and chemical stoichiometry.
and thin films. Some merits like accurate chemical stoichiometry,
good composition homogeneity and low crystallization temper-
ature can be achieved owing to the mixing of various liquid
precursors on a molecular level. Such chemical methods as cit-
rate method [12], conventional sol–gel method [13], hydrothermal
method [14,15], mechanochemical synthesis [16] and sol–gel auto-
combustion method [17,18] have been applied in recent years for
sodium bismuth titanate based lead-free ceramics, leading to the
improved densification behavior and electrical properties. Unfor-
tunately, the soft-chemical route has not been extensively applied
in NKN based ceramics, although it was occasionally used to make
niobate based thin films [19–21], probably because metal alkoxides
(CnH2n+1O)5Nb have made this processing costly in the preparation
of the powders [22]. Only few attempts have been made to make
Li-doped NKN powders by a sol–gel process using Nb2O5 as Nb
source [23,24], in which the problem of easier hydrolysis of niobium
alkoxides could be avoided. Unfortunately, this attempt has never
been extended to the preparation of more complex compositions
based on NKN as concluded from the literature survey. More notice-
ably, the processing and electrical properties of sol–gel derived (Li,
Ta and Sb) modified NKN bulk ceramics have never been reported
either.
The purpose of this study is thus to explore a modified citrate
sol–gel process using Nb2O5 and Ta2O5 as niobium and tanta-
lum sources to prepare typical lead-free piezoelectric ceramics
∗
Corresponding author. Tel.: +86 551 2905285; fax: +86 551 2905285.
E-mail address: piezolab@hfut.edu.cn (R. Zuo).
0925-8388/$ – see front matter © 2010 Elsevier B.V. All rights reserved.
doi:10.1016/j.jallcom.2010.09.134

H. Wang et al. / Journal of Alloys and Compounds 509 (2011) 936–941
937
556 oC
Nb(OH)5
Ta(OH)5
(C2H3O2)3Sb
KNO3
NaNO3
Citrate: Met.= 2:1
Glycol
LiNO3
20
15
10
5
3.5%
90
60
30
Oxalic acid
Citrate: Met.= 2:1
Solution A
44.7%
SolutionB
Ammonia to pH=7.5
291 oC
TransparentSol
Solvent evaporation T=70-80oC
17.1%
0
TransparentGel
150
300
450
600
750
Temperature (oC)
Fig. 1. Flow chart of preparing NKNS-3.75LT gel via a citrate sol–gel method.
Fig. 2. Thermo-gravitometry and differential scanning calorimetry analysis of the
of (Na0.52K0.4425)(Nb0.8825Sb0.08)O3-0.0375LiTaO3 (NKNS-3.75LT),
which have been previously prepared by a mixed-oxide solid state
method and exhibited excellent piezoelectric properties of d33
∼395 pC/N and kp ∼64% [8]. A special attention was focused on the
chemical reaction condition and structural transformation behav-
ior of the as-prepared xerogel by means of kinds of characterization
techniques. Moreover, the sintering, microstructure and piezoelec-
tric properties of the sol–gel derived NKNS-3.75LT ceramics have
been discussed. The results are expected to extend the applica-
tion of sol–gel routes to high-performance NKN-based lead-free
ceramics with complex compositions.
NKNS-3.75LT gel.
of the ceramics sintered at different temperatures was observed using a scanning
electron microscope (SEM, SSX-550, Shimadzu, Japan). The sample density was eval-
uated by the Archimedes method. The dielectric properties (dielectric constant ε3T3
and loss tanı) were measured with changing temperature by an LCR meter (Agilent
E4980A, USA). The piezoelectric constant d33 was measured directly on a quasi-static
d33 meter (YE2730A, Sinocera, China). The electromechanical coupling coefficient
kp was measured by a high precision impedance analyzer (PV70A, Beijing Band ERA
Co., Ltd. China). The remnant polarization (Pr) was characterized by measuring polar-
ization versus electric field hysteresis loops using a ferroelectric measuring system
(Precision LC, Radiant Technologies, Inc., USA).
2. Experimental procedure
3. Results and discussion
The raw materials used in this study are Nb2O5 (≥99.5%), Ta2O5 (≥99.5%), K2CO3
(≥99.0%), NaNO3 (≥99.0%), KNO3 (≥99.0%), LiNO3 (≥99.0%), glycol (≥99.0%), HNO3
(65.0–68.0%), Sb(CH3COO)2 (≥99.9%), citric acid (≥99.5%), oxalic acid (≥99.5%) and
ammonia (25–28%). Firstly, Nb2O5 and K2CO3 were mixed and calcined at 900 ◦C for
2 h to form a soluble potassium tantalate according to their phase diagram [25]. Then,
the as-prepared potassium tantalate was dissolved in distilled water and titrated by
nitric acid to obtain a precipitate of tantalum hydroxide by adjusting the pH value of
the solution. Finally, the precipitate of tantalum hydroxide was washed and filtered
over 10 times so as to make sure that K ions were totally removed. The relevant
chemical reactions [26] can be written as follows:
The TG and DSC curves of the NKNS-3.75LT gel are shown in
Fig. 2. A small weight loss of 3.5% at temperatures up to ∼150 ◦C
is due to the evaporation of remaining water, glycol and ammonia.
The exothermic peaks at ∼291 ◦C could be attributed to the thermal
decomposition of citrate complexes, corresponding to a weight loss
of 44.7%. The strong exothermic peak at 556 ◦C would be related
to the combustion of residual organic components, accompanied
by a weight loss of 17.1%. No further weight loss or peaks can be
seen thereafter in TG and DSC curves, indicating that the thermal
decomposition of the NKNS-3.75LT gel or the removal of organic
substances has been completed before 600 ◦C.
Ta2O5 + 3K2CO3 = 2K3TaO4 + 3CO2
6K3TaO4 + 5H2O = 18K+ + Ta6O198− + 10OH−
Ta6O198− + 8H+ + 11H2O = 6Ta(OH)5↓
The thermal decomposition process of the xerogel can be ana-
lyzed in more details by room-temperature FT-IR spectra as shown
in Fig. 3. The samples were prepared by calcining the xerogel at
A similar preparation procedure was used to make niobium hydroxide. Both niobium
precursor and tantalum precursors were chelated with citric acid. The NKNS-3.75LT
gel was prepared following the procedure as indicated in Fig. 1. The molar ratio of
citric acid to metal cations was 2:1. The niobium hydroxide and tantalum hydroxide
were firstly dissolved in oxalic acid solution and then added with citric acid as chelat-
ing agent to form chelate complex with niobium ions and tantalum ions (solution
A). According to the required stoichiometry, KNO3, NaNO3, LiNO3 and Sb(CH3COO)2
were introduced into glycol (solution B). Subsequently, solution A and solution B
were mixed to form a stable sol by adjusting the pH value to ∼7.5. Citric acid is a
polydentate ligand with three carboxyls and a hydroxyl and can easily form stable
and soluble chelate complexes with metal cations in an alkalescent solution. Gly-
col with double hydroxyl groups can form ester groups and network structures by
increasing molecular weight of precursors, and further enhance the stability of solu-
tion. The as-prepared sol was heated at 70–80 ◦C to remove redundant solvent and to
form gel. In the end the xerogel was calcined at 200–800 ◦C for 3 h to obtain crystal-
lite powders. The powder compact was then sintered in air within the temperature
range of 1050–1130 ◦C at a heating rate of 5 ◦C/min.
Thermo-gravitometry (TG) and differential scanning calorimetry (DSC) analy-
sis of the as-prepared gel was carried out using a simultaneous thermal analyzer
(STA409C, Netzsch, Germany). The structure evolution of the gel after heat treat-
ment was analyzed by a Fourier-transform infrared (FT-IR) spectrometer (Spectrum
400, PerkinElmer, USA). The powders calcined at different temperatures were char-
acterized by an X-ray diffractometer (XRD, D/MAX2500 VL/PC, Rigaku, Japan), and
a Raman spectrometer (LabRAM HR800, HJY, France). The morphology of the as-
synthesized crystallite particles was analyzed by means of a transmission electron
microscope (TEM, Model H-800, Hitachi, Japan). The microstructure on the surface
700 oC
600 oC
500 oC
1380
400 oC
1640
1640
300 oC
200 oC
gel
1380
1640 1380
1740
1740
1380
1640 1080
1040
1202
3300
1080
1408
1740
1332
1040
4000
3000
2000
1000
Wavenumber (cm-1)
Fig. 3. Fourier-transform infrared spectra of the NKNS-3.75LT gel and as-calcined
powders at different temperatures as indicated.

938
H. Wang et al. / Journal of Alloys and Compounds 509 (2011) 936–941
ν5
Perovskite
Li2K3Ta5O15
# KSb3O5
O
O
(110)
ν1
(100)
O
*
ν2
800 oC
ν4
ν3
ν1+ν5
K LiNb O
^
3
6
17
(200)
O
(211)
O
700oC
600oC
(210)
O
(111)
O
#
#
800 oC
^
^
^
700 oC
500oC
400oC
600 oC
500 oC
300 oC
400 oC
300 oC
200
400
600
800
1000
*
Raman shift (cm-1)
20
30
40
50
60
Fig. 5. Raman spectrum of the NKNS-3.75LT powders obtained by heat-treating the
gel at different temperatures as indicated.
2θ (degree)
Fig. 4. X-ray diffraction patterns of the NKNS-3.75LT gel powders calcined at dif-
ferent temperatures as indicated.
Combined with TG-DSC analysis and IR spectra, it can be recog-
nized that the sol–gel derived powders can be well synthesized at
600 ◦C, approximately 200–300 ◦C lower than those prepared by a
conventional mixed-oxide method [2–4]. The homogeneous mix-
ing of chelate complexes and metal cations at a molecular level
provides the possibility for obviously reduced migration distance
of various ions.
In order to deeply explore the phase structural transforma-
tion of the gel powders undergoing the heat treatment, Raman
spectra of these powders at room temperature are shown in
Fig. 5. As a main unit of a perovskite structure, the vibra-
tions of the NbO6 octahedra are usually considered to consist
of 1A1g(␯1) + 1Eg(␯2) + 2F1u(␯3 + ␯4) + F2g(␯5) + F2u(␯6) [30], among
which 1A1g(␯1) + 1Eg(␯2) + F1u(␯3) belong to stretching modes and
the other belong to bending modes. As shown in Fig. 5, the stretch-
ing and bending modes of NbO6 octahedra start to appear in the
sample which was heat treated at 400 ◦C, indicating the formation
of perovskite structure. This is in good agreement with the XRD
results (Fig. 4). However, owing to its low crystallinity, the inten-
sity of Raman spectrum is low for the sample calcined at 400 ◦C.
It can be seen that the intensity of Raman spectrum increases
with an increase of the calcination temperature. Furthermore, the
different temperatures. Peaks were assigned with reference to stan-
dard texts [27]. The broad absorption peak around 3300 cm−1 is
typical of O–H stretching from H2O. In the gel sample, the peaks
at 1040 cm−1 and 1080 cm−1 are attributed to C–O stretching from
remains of glycol. The peak at 1202 cm−1 is due to the vibration
of –C–O–C– bonds between the acid and hydroxyl groups in citric
acid and glycerol, which offers an evidence for the esterification
during processing [28]. The peaks at 1332 cm−1 and 1408 cm−1 are
ascribed to the symmetric vibration of –COO− from metal carboxy-
lates, indicating that the chelation of metal ions exists [29]. It is
thus concluded that in this study citric acid as a chelating agent
was chelated with metal ions to form a stable network structure.
After heat treatment, obvious changes happen in FI-IR spectra. The
peaks at 1380 cm−1 can be assigned to CH3 symmetric bending
[22] related to inorganic carbonates or bicarbonates (HCO3−), indi-
cating that citrate complexes decompose into carbonates between
200 ◦C and 300 ◦C. This reaction could be the reason for the exother-
mic peak at ∼291 ◦C in the DSC curve. In addition, the presence of
peaks at 1640 cm−1 and 1740 cm−1 can be attributed to the C
C
and C O stretching, respectively, suggesting the thermal decom-
position of organic matters occurs. Before 500 ◦C, the absorption
peaks are nearly the same, except that the absorption strength
becomes weak with increasing temperature. Starting from 600 ◦C,
there is no indication of organic residues from IR spectra but a weak
absorbance in the O–H stretching (3300 cm−1), assuming that all
organic substances have been decomposed after 600 ◦C.
The crystallization behavior of the NKNS-3.75LT gel undergo-
ing the treatment at different temperatures was characterized, as
shown in Fig. 4. The powders exhibit typical patterns of amorphous
phases below 300 ◦C. As the calcination temperature rises to 400 ◦C,
the characteristic diffraction peaks of a perovskite structure begin
to appear apart from a small amount of secondary phases (indexed
as Li2K3Ta5O15). A single perovskite structure can be obtained till
the gel was calcined at 500 ◦C. Between 500 ◦C and 700 ◦C, noth-
ing happened except for slight changes in the crystal symmetry
as seen from the splitting of (200) diffraction peaks. This could
be attributed to the degree of grain growth and the particle size
effect. That is to say, there exists a grain size induced phase tran-
sition from pseudocubic to orthorhombic phases, leading to the
change of the phase content. However, powders calcined at 800 ◦C
obviously contain secondary phases (indexed as K3LiNb6O17 and
KSb3O5), probably because of the volatilization of Na2O and K2O.
wavenumber of the ␯ mode representing a double-degenerate
1
symmetric O–Nb–O stretching vibration moves towards to higher
value with increasing the calcination temperature. The same
change trend is observed in the ␯5 mode representing a triply
degenerate symmetric O–Nb–O bending vibration. Similar to the
XRD results, these changes could be related to the variation of crys-
tallinity (Fig. 4) and grain size (see infra), which tends to induce a
change of NbO6 octahedra. A reduction in the intensity of Raman
spectrum can be observed in the sample calcined at 800 ◦C, proba-
bly because of the presence of the secondary phase.
The particle morphology of the NKNS-3.75LT gel powders cal-
cined at 500–800 ◦C for 3 h is shown in Fig. 6. It can be seen that
the average particle size is about 30 nm for the powder calcined
at 500 ◦C. However, the polyhedral particles clustered into the
agglomeration, resulting from some residual organic substances
between them. The existence of residual organic matters can be
confirmedbythe above-mentionedDSC-TG analysis. As the calcina-
tion temperature rises to 600 ◦C, most of particles are well dispersed
with only a slight degree of soft agglomeration. The particle mor-
phology is still polyhedral but the average particle size reaches
100 nm. The particles were obviously coarsened as the calcina-
tion temperature was further increased (∼150 nm and ∼200 nm for
700 ◦C and 800 ◦C, respectively). However, the rapid grain growth

H. Wang et al. / Journal of Alloys and Compounds 509 (2011) 936–941
939
Fig. 6. Transmission electron microscopy micrographs of the NKNS-3.75LT powders obtained by heat-treating the gel at different temperatures: (a) 500 ◦C, (b) 600 ◦C, (c)
700 ◦C and (d) 800 ◦C.
is accompanied by a reduced degree of agglomeration. Consider-
ing the balance between the particle growth and agglomeration, it
would be appropriate to calcine the gel powder at 600 ◦C in this
study.
particles at higher sintering temperatures. As the sintering tem-
perature is relatively low (density is also low), the liquid phases
formed only at locally existed particle contacts leads to the rapid
growth of a small amount of particles (AGG). As the sintering tem-
perature increases, the number of particle contact becomes much
more such that the formed liquid phase tends to be more uni-
formly distributed, and thereby more grains could nucleate and
then normally grow simultaneously. This mechanism of forming
liquid phases correlated to locally higher contact pressure could be
as a supplement to the existing explanation about AGG, although
more supports from experiments are needed in future. On the other
hand, it can be seen that the samples look still porous as sintered
at 1050 ◦C but the grain size has reached the submicron scale. The
fast grain growth tends to weaken the driving force of densification,
which often happens in a conventional pressure-less sintering of
nano-scaled powders with high surface free energies. The optimal
temperature of 1090 ◦C, at which the highest density of 4.63 g/cm3
can be obtained, was only slightly decreased compared to that in
previous works [8], which could be correlated with the existing
soft agglomeration of powders and even the shaping method of
green compacts. The study on whether it can be improved using
cold-isostatic pressing is still in progress.
The physical and various electrical properties of sol–gel derived
and conventionally processed NKNS-3.75LT ceramics were sum-
marized in Table 1 for comparison. It is obvious that the optimum
sintering temperature and the corresponding grain size in this
study were slightly reduced compared to those of samples by a
mixed oxide method. The sol–gel derived NKNS-3.75LT ceram-
ics sintered at 1070 ◦C have huge grains (5 ␮m) and small grains
(1 ␮m), typical of the abnormal grain growth. The normal grain
growth starts to disappear with further increasing temperature
and then the average grain size is ∼2 ␮m. The sol–gel derived
The SEM images of the sol–gel derived NKNS-3.75LT ceramics
sintered at various temperatures are shown in Fig. 7. Noticeably, the
sample density obviously increases with increasing the sintering
temperature but the phenomenon of abnormal grain growth (AGG)
can be observed as the sintering temperature rises to 1070 ◦C. With
a further increase of sintering temperature, the sample becomes
denser and the grain size tends to become more and more homo-
geneous such that a bimodal distribution of the grain size slowly
dies away, indicating that normal grain growth (NGG) starts. Simul-
taneously the average grain size becomes large with increasing
the sintering temperature as expected. When the sintering tem-
perature increases to 1130 ◦C, the grain size looks uniform and
but gets significantly coarsened, leading to a slight reduction of
the density. The special grain growth behavior with an increase
of sintering temperature has been recognized in some NKN-based
ceramics manufactured by solid state reaction methods [30,31].
For perovskites, AGG has been explained by faceting, in connection
with attachment sites for growth such as dislocations or polytype
stacking faults favoring a small number of grains in an otherwise
blocked matrix of small grains [32,33]. This explanation fits to the
faceted grain morphology of NKNS-3.75LT particles (see Fig. 6).
Moreover, both Park and Shen suggested that the change of grain
growth behavior from AGG to NGG be correlated with the exis-
tence of liquid phases owing to the volatilization of Na2O [31] or
the excess of Na2O [34]. However, yet the formation mechanism
of liquid phases seems to be not very clear. We thought that the
specific particle morphology of polyhedron could also facilitate
the formation of liquid phases at sharp-angled contacts between

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H. Wang et al. / Journal of Alloys and Compounds 509 (2011) 936–941
Fig. 7. Scanning electron microscopy micrographs of sol–gel derived NKNS-3.75LT ceramics sintered at different temperatures: (a) 1050 ◦C, (b) 1070 ◦C, (c) 1080 ◦C, (d)
1090 ◦C, (e) 1110 ◦C and (f) 1130 ◦C.
Table 1
Sintering behavior and electrical properties of NKNS-3.75LT ceramics prepared by different processing methods.
Processing
Sintering
temperature
(◦C)
Density
(g/cm3)
Average
grain size
(␮m)
Pr (␮C/cm2)
d33 (pC/N)
kp
εT33
tanı
Tc (◦C)
Mixed oxide method [8]
Modified sol–gel
method [this study]
1100
1070
1090
1110
4.62
4.39
4.63
4.56
2.5
1 or 5
2
20.8
–
25.6
24.1
395
323
418
332
0.52
0.46
0.54
0.48
2390
1992
2413
2296
0.04
251
258
257
261
0.039
0.037
0.045
2.7
NKN-3.75LT, (Na0.52K0.4425)(Nb0.8825Sb0.08)O3-0.0375LiTaO3.

H. Wang et al. / Journal of Alloys and Compounds 509 (2011) 936–941
941
ceramics sintered at 1090 ◦C exhibit improved densification
and attractive dielectric, ferroelectric and piezoelectric proper-
ties of ꢀ = 4.63 g/cm3, ε3T3 = 2413, tanı = 0.037, Pr = 25.6 ␮C/cm2,
d33 = 418 pC/N and kp = 0.54 in addition to similar Tc values (257 ◦C),
compared to those prepared by mixed oxide methods, demon-
strating that the citrate sol–gel method could be advantageous
for making high-performance lead-free piezoelectric ceramics. The
high chemical homogeneity and relatively high sintering activity
would be helpful for systems with complex compositions and dif-
ficulties in sintering.
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Acknowledgements
This work was financially supported by Key Project of Natural
Science Research of Universities in Anhui Province (KJ2009A089),
a
project of Natural Science Foundation of Anhui Province
(090414179), National Natural Science Foundation of China
(50972035), and a Program for New Century Excellent Talents in
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