Journal of Modern Physics, 2011, 2, 416-420
doi:10.4236/jmp.2011.25051 Published Online May 2011 (
Copyright © 2011 SciRes. JMP
Sintering Kinetics of Soft-Doped PZT (54/46) Systems
M. D. Durruthy-Rodríguez1,2, F. Calderón-Piñar3, C. Malf a tt i 4, L. D. Pérez-Fernández5
1Applied Physics Department, Cybernetic, Mathematic and Physics Institute, Vedado,
Havana City, Havana, Cuba
2CINVESTAV-Unidad Querétaro, IPN, Li bramiento Norponiente No. 2000, Fracc.
Real de Juriquilla, Querétaro, Querétaro, México
3Magnetism Laboratory, Science and Materials Technology Institutes, Havana University, San Lázaro y L,
Vedado, Havana City, Cuba
4Metalurgy Deparme nt, Engeneering School, Rio Grande do Sul Federal University, Porto Alegre, RS - Brasil
5Applied Physics Department, Cybernetic, Mathematic and Physics Institute Vedado,
Havana City, Havana, Cuba
Received February 9, 2011; revised April 13, 2011; accepted April 16, 2011
The influence of dopant concentration on PZT (54/46) systems doped with lanthanum and/or niobium is
studied. The sintering kinetics is presented for 1 wt% of the dopant used to find the main mechanism which
drives this process. The results were compared with a phenomenological model for viscous sintering and
solid state sintering. The exponent obtained for viscous sintering in PZTN, PLZT and PLZTN were 0.05,
0.01, and 0.23 respectively, which indicate that the process is reactive liquid in all cases. In the other hand,
the exponent obtained for solid state sintering were 6.61, 5.68, and 1.23 respectively, and prevalence Ost-
wald ripening and coalescence process together. Both dopants inhibit the grain growth and accelerate the
sintering process, which increases with dopant concentration and the combination of both dopants. Shoro-
hod-Olevsky model was applied for explain grain growth evolution, but does not coincide strictly with the
applied model, which suggests that the process is very complex.
Keywords: Sintering Kinetics, Porosity, Dopant Concentration
1. Introduction
Because doped PZT (54/46) piezoceramics are polycrys-
talline, their microstructural characterist ics (grain size an d
orientation distribution, phase distribution, phase and
domain morphology) as well as their defects (atomic
structures of domain walls, native defects, impurities)
play crucial roles in determining their properties [1].
Usually, some of these factors act simultaneously, mak-
ing the polarization switching phenomena very intricate.
The local densification effect [2] is one of the most im-
portant technological problems related to sintering, as a
strong densification may occur in some parts of a porous
body while large pores appear in others. This shows the
instability caused b y initially-small heterogeneities in the
spatial distribution of pores, and may lead to various
microstructural defects nucleation producing macro-
scopic lattice and damage. A non-uniform density distri-
bution provoked by sintering instability may cause poor
mechanical properties of the final product. Sintering is
generally incapable of compensating defects introduced
in earlier processing steps. Understanding the influence
of such defects is a fundamental challenge.
Some of the possible reactions when obtaining the
perovskite ABO3 are: replacing Pb2+ by La3+ with va-
cancy V compensating in site A (Pb1-3x/2LaxVx/2
(Zr0.54Ti0.46)O3) or B (P b1-3x/2LaxVx/2(Zr0.54Ti0.46)1-x/4Vx/4O3),
and replacing Ti4+(Zr4+) by Nb5+ compensating in A
(Pb(Zr0.54Ti0.46)1-5y/4NyVy/4O3) or
B(Pb1- y/2Vy/2(Zr0.54Ti0.46)1-yNbyO3). The positions with
increasing vacancies will generate pores. Here, the in-
fluence of dopant concentration on the densification
process during sintering is studied.
2. Experiment
The samples were prepared for Pb(Zr0.54Ti0.46)O3 + x wt%
D, where dopant D is Nb2O5 (PZTN) or La2O3 (PLZT),
Copyright © 2011 SciRes. JMP
and x = 0.02, 0.04, 0.06, 0.08, 0.10; and Pb1-3x/2LaxVPbx/2
(Zr0.54Ti0.46) 1-5y/4NyVZrTiy/4O3 (PLZTN) for simultaneous
doping with x = y = 0.04, 0.08, 0.1. Reagent purities are:
PbCO3 98%, BDH; ZrO2 99%, Merck; TiO2 99%, Riedel
of Haën; Nb2O5 spectrally pure, JMC; and La2O3 spec-
trally pure, Merck. The components were mixed via hu-
mid milling with ethylic alcohol in an agate mortar mill
during 90 min, and the calcinations were made at 960˚C
during 90 min in a covered alumina crucible. The sam-
ples were sintered in lead atmosphere at 1200˚C and
1250˚C during dif f erent times.
3. Results and Discussion
3.1. Characterization of the Sintering Process
Mainly, two approaches are used to explain the sintering
process: the mesoscopic microstructural model, and the
continuum phenomenological model. Here, we use Olev-
sky’s model [3], which corresponds to the second approach
and is based on the p lasticity and the viscou s theory of lin-
ear deformation of porous bodies [2,4,5]. In this work, the
relative density rel
, the sintering rate *
, and the volu-
metric shrinkage are used as control parameters[6].
The isothermal rate of grain growth can be expressed
by phenomenological kineti cs grain growth equat ion [7,8] :
GG KtQRT (1)
where G is the average size at time t, G0 is the initial
grain size, n is the kinetic grain growth exponent value,
K0 is a constant, Q is apparent activation energy, R is the
gas co nten t, and T is the absolu te te mpe ra ture. When ev er
G0 is significantly smaller than G, then G0 can be ne-
glected and Equation 1 simplifies to
and this equation can b e transformed into
ln1 ln1 lnexpGntnK QRT  (3)
The n value can be calculated from slope of lnG versus
lnt line plot, the grain growth kinetic exponent is readily
Initial and final densities were obtained from the di-
mensions and mass of the samples by measuring with a
micrometer (± 0.01 mm) and a Sartorius balance (± 10–4
g). SEM was applied with a JSM-5800 microscope
(MAG, ×1000; ×2000; ×3500; ×10 000; ACCV 10 kV
and 15 kV) to describe the samples microstructures and
3.2. Densification Process
PLZT and PZTN samples attained sintering state at 60
and 100 min respectively with rel
90% - 95% T
with T
as the theoretical density, and exhibited similar
behaviors for x > 0.6. For PZTN and PLZTN samples
with low niobium concentrations, rel
dependence is
observed. In all cases, the loss of mass is smaller than
2%. Both, *
ratify rel
behavior. rel
confirm typical ceramic behavior with viscous sin-
tering [1-3]. Independent substitutions in A and B have
equal influence in the sintering parameters for equal
dopant concentrations (x = 0.06, 0.08, 0.10). This substi-
tution type causes a decreasing *
and increasing rel
. A strong dependence of the sintering parameters
on dopant concentration is evident. The experimental
results for the three composition s do not adjust strictly to
the Skorohod-Olevsky Model (SOM)[9] for *
1), the best results were for PLZT and PLZTN samples,
Figure 1. Experimental and the SOM results for the sintering rate *
 . None of the three cases coincides with the model,
only PZTN follows the values of the model for the initial and final instants.
Copyright © 2011 SciRes. JMP
as work compositions do not exhibit a unique grain size
and the grains are not spherical. The density reached by
all PLZTN samples is low. The importance of achieving
sintering in the smallest possible time avoiding the lead
loss is recognized [10]. In general, the best results corre-
spond to x = 0.06, 0.08, 0.10 and times of 60 - 100 min.
The mechanisms that govern the densification process
are the decreasing superficial area and free energy via the
elimination of the interface solid-vapor, and the fact that
in the sintering process the interaction of grain and po-
rosity is in both directions [12-14]. Samples porosity
 [14] show the influence of the dopant Nb
and La + Nb concentrations for which the p0 decreases
(Figure 2(a)). For PZTN samples, p0 varies from 23% -
10% in the initial states, to 17% - 3% at the end of the
process. For PLZTN samples, the variation is smaller
(12% at the beginning and 10% at the end). As expected,
p0 also decreases with the sintering time, mainly for
PZTN, due to the viscous sintering process, from 31% -
34% to 3% - 10% (Figure 2(b)). For the PLZT, the
variation of p0 does not exhibit a defined tendency nei-
ther with La concentration nor sintering time. But the
porosity have strong depends on the grain size, having a
biggest growth for the PLZT samples (Figure 2(c)).
3.3. SEM Analysis
The grain sizes obtained of the microphotographs SEM
of each one of the samples carrying out a statistical
analysis of the measurement obtained, Figure 3 show the
grain size ev olution with dopant concen tration for PLZT,
(a) (b) (c)
Figure 2. Behavior of the porosity p0 with the dopant concentration, sintering time and the grain size of PLZT, PZTN and
PLZTN ceramic samples sintered at 1250˚C. The porosity increased with the grain size in all cases.
0.4 0.8 1.0
m 5
m 10
m 10
m 5
Figure 3. Behavior of grain size with dopant concentration. Only appear 0.4, 0.8 and 1.0 wt% of PLZTN and PZTN, and 0.6,
0.8 and 1.0 wt% for PLZT ceramics sintering at 1250˚C during 100 minutes.
Copyright © 2011 SciRes. JMP
Increasing dopant concentration implies that grain size
decreases with narrower distribution (Table 1). The
largest decrement is obtained for PLZTN with 0.8 and
1.0 wt%. The double substitution shows a notable inhib-
iting effect of grain growth. It is evident that inhibiting
the grain growth is the fundamental cause of the low
obtained by PLZTN samples. Moreover, it is not
possible to eliminate the porosity as in the other compo-
sitions. The SEM analysis reveals the existence of a
strong dependence between the dopant concentration, the
grain size and its distribution (Figure 2(c)), independ-
ently of the sintering time. The sintering kinetics of the
dopant used for 1 wt% allows determining the mecha-
nism that prevails in the process. The results are com-
pared with the phenomenological model proposed by
Kingery[1] for viscous sintering, which provides a rela-
tionship between volumetric shrinkage and time via
t , where K is a parameter involving the viscosity,
the superficial tension and th e radius of the particles, and
n = 2/5, 2/3, 1/3, 1 stand for processes with diffusion in
the grain boundary, evaporation-condensation, a reactive
liquid, and vitrification, respectively. The exponents ob-
tained for PZTN, PLZT and PLZTN were 0.05, 0.01 and
0.23, respectively, which indicates that a reactive liquid
process occurs in the three cases (Figure 4). La3+ and
Nb5+ dopants inhibit the grain growth strongly, so the
behavior of the *
and grain growth of the obtained
materials does not coincide strictly with the applied sin-
tering model, as the actual grains are not spherical and
the density reached by some samples is low.
On the other hand, the average grain size increases
with sintering temperatures as well as for longer sintering
Table 1. Dependence of the grain size on the sintering ma-
terials at 1250˚C with dopant concentration.
Dopant wt %
Grain size interval
grain size
0.6 1 - 9 3 ± 0.05
0.8 1 - 7 2 ± 0.05 La
1.0 1 - 2 1 ± 0.05
0.2 14 - 36 25 ± 0.05
0.4 6 - 20 13 ± 0.05
0.6 2 - 10 6 ± 0.05
0.8 1 - 5 2 ± 0.04
1.0 1 - 6 3 ± 0.05
0.4 - 0.4 1 - 4 2 ± 0.2
0.8 - 0.8 0.25 - 4 1 ± 0.2
1.0 - 1.0 1 - 3 1 ± 0.2
Figure 4. Analysis of the volumetric shrinkage
with the
sintering time for PLZT, PZTN and PLZTN at 1.0/54/46.
times [3,10]. Figure 5 illustrates the isothermal grain
growth results for PLZT 54/46, PZTN 54/46 and PLZTN
54/46 sintered at 1250˚C. The results For PLZT are 0.5,
1.66, 3 and 5 hours; for PZTN 0.5, 1, 1.66, 2.5 and 5
hours, and for PLZTN 1, 1.5, 2 and 2.5 hours. In the
form of Equation 3, the exponents obtained (n) were 6.61,
5.68, and 1.23 for PLZT, PZTN and PLZTN, respec-
Usually, the n value for ceramics was 2, and the rate
determining step of the growth process was the d iffusion .
And when the n value was 3, the rate d etermining step of
the growth process was the Ostwald ripening process or
lattice diffusion from the grain boundary, but for grain
boundary diffusion the n value was 4, and for the leaded
process by diffusion cross dislocation the n value was 5.
In some cases, the n value is possibly found higher (5 -
11), because there are grain growths by coalescence
In this study the n values were 6.61 and 5.68 for PLZT
and PZTN, suggesting that the rate determining steps
were coalescence in both cases, and for PLZTN n = 1.23
Figure 5. Grain growth of PLZT, PZTN and PLZTN at
1.0/54/46 ceramics.
Copyright © 2011 SciRes. JMP
suggesting that the rate determining step was viscous
The n value was influenced by the particle size, the
agglomeration shape and impurities type and content.
The Consideration of all this results suggests that per-
haps a grain growth mechanism occurs at critical impuri-
ties content and the mixing of dopants modified very
much the sintering kinetics.
4. Conclusions
From the point of view of the sintering, the same dopant
concentrations in A and B, the results for rel
, *
are similar. For the combination A + B, the sintered
state was not obtained. Both dopants inhibit the grain
growth and accelerate the sintering process. This effect
increases with the dopant concentration and with the
combination of both dopants. The phenomenological
model for viscous sintering suggests, in all the cases, that
sintering is governed by a reactive liquid process. The
phenomenological model for solid state sintering sug-
gests for PLZT and PZTN that the sintering rate deter-
mining step was coalescence and for PLZTN the rate
determining step was viscous flow. As the actual grains
are not identical in size and shape, the theoretical results
differs form the experimental ones to the Skorohod-
Olevsky Model.
5. Acknowledgments
The authors gratefu lly acknowledge the support from the
project PNCB 10/04, Cuba, and Prof. Dr. Jose Antonio
Eiras, Head of Department of Physics, Science and
Technology Center, UFSCar, Brazil, for providing SEM
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