Advances in Engineering Mechanics and Materials
Activation Energies for Initial and Intermediate
Stage Sintering of Li2TiO3 Determined by a
Two-Stage Master Sintering Curve Approach
Ahmad Reza Abbasian, Mohammad Reza Rahimipour, and Zohreh Hamnabard
industry to predict the densification behavior from the
sintering data that are readily available [7]. The ability to
predict sintering behavior has been one of the long term
objectives of sintering studies for many decades. Manifold
attempts at simulation and modeling for the prediction of
sintering have been reviewed in published literatures by
previous authors [8]. One of the promising methods how to
describe and predict sintering is the concept of а Master
Sintering Curve (MSC) developed by Su and Johnson [9]. The
MSC can be used to predict the densification behavior of a
given powder and estimates its minimum sintering activation
energy, as well as the understanding of sintering kinetics. The
MSC has been successfully applied to several sintering
systems such as ThO2 [7], BaTi0.975Sn0.025O3/BaTi0.85Sn0.15O3
[10], ZnO [9]-[11], Gd-doped CeO2 [12], TiO2 [13], Al2O3
[9]-[14]-[15], BaTiO3 [16], 3Y-TZP [17], Al2O3 + 5% ZrO2
[9], nickel and stainless steel powders [18]. However, the
application of MSC to sintering of the Li2TiO3 has not been
reported. The present work, therefore, aims to establish MSC
for the Li2TiO3 based on non-isothermal sintering and
systematically analysis of the sintering of the Li2TiO3 ceramic.
Abstract— Lithium meta titanate (Li2TiO3) is considered as one
of the most promising breeder materials for the fusion power. In this
study, the activation energy and sintering kinetics of the Li2TiO3 is
determined with the help of the master sintering curve (MSC). It was
found that a better representation of the sintering behavior could be
achieved by constructing MSC over two consecutive densification
stages with the relative density of 66% set as the boundary. From the
activation energy values of the two stages obtained, lattice diffusion
enhanced with surface diffusion and solely lattice diffusion
mechanisms were identified for the dominant sintering mechanism at
initial and intermediate stages of the Li2TiO3 sintering, respectively.
Keywords— Fusion reactor, Li2TiO3, Tritium breeding, Sintering,
Activation energy.
I. INTRODUCTION
T
he breeding blanket is a key component of the fusion
reactor because it directly involves tritium breeding and
energy extraction, both of which are critical to the
development of fusion power [1]. In the development of
tritium breeding blankets, the lithium meta titanate (Li2TiO3)
ceramic has interested multitude researchers' attention for its
distinguished properties as one of the most promising solid
breeder materials, such as reasonable lithium atom density,
low activation characteristic, high chemical stability, good
compatibility with structural materials, acceptable mechanical
strength and considerably good tritium release characteristics
at low temperatures [2]-[3]-[4]-[5]. Several methods are
available for fabrication of a breeder ceramic material [6].
However, sintering is always the final and critical step for the
fabrication of the ceramics, in which a preformed particulate
body achieves its final shape and properties. In the
conventional sintering procedure, the parameters such as time
and temperature of the sintering are arbitrarily decided on the
‘trial and error’ basis. It could be beneficial for the nuclear
II. THEORY
Formulation of MSC was derived from the combined stage
sintering model [9]-[19] including volume or grain boundary
diffusion mechanism. For the construction of MSC the
parameters of sintering are separated in those related to time
and temperature dependence and the ones associated with the
microstructure. In MSC theory, Φ(ρ), a function of density,
can be given as the function of temperature and time:
t
1
Q
exp(−
)dt
T
RT
0
Φ ( ρ ) = Θ(t , T (t )) ≡ ∫
Where Q is the apparent activation energy for sintering, R is
the gas constant, T is the absolute temperature, and t is the
time. In this case, if the sintering process is dominated by only
unique diffusion mechanism (either volume or grain boundary
diffusion) and the microstructure is a function only of density,
a unique MSC can be obtained. The relationship between
density (ρ) and log[Θ(t,T(t))], i.e. an S-shape curve, is the
master sintering curve. For more details, the assumptions and
limitations of the MSC have been well discussed in the
original MSC papers by Su and Johnson [9]. For the
This work was supported by the NSTRI, and the Materials and Energy
Research Center (no. 389052).
A. R. Abbasian is with Ceramic Department, Materials and Energy
Research Center, Karaj, 31787-316, Iran (corresponding author to provide
phone: 98-263 628 0040; e-mail: abbasian@merc. ac.ir).
M. R. Rahimipour is with Ceramic Department, Materials and Energy
Research Center, Karaj, 31787-316, Iran (e-mail: [email protected]).
Z. Hamnabard is with the Lasers and Optics Research School, NSTRI,
Tehran, 11365-8486, Iran (e-mail: [email protected]).
ISBN: 978-1-61804-241-5
(1)
291
Advances in Engineering Mechanics and Materials
construction of MSC, the integral of Eq. (1) and the
experimental density should be known. The dilatometry can be
conveniently used to determine the density since the
instantaneous density at all times can be obtained from the
dilatometry data [20]. For the calculation of Θ, the activation
energy for the sintering process must be known. If the
activation energy is unknown, it can be estimated with good
precision from Θ versus density ( ρ ) data [9].
III. EXPERIMENTAL
A. Fabrication of Green Pellet
A Li2TiO3 powder (−325 mesh, 40 0939, Sigma-Aldrich,
Germany) was used in this investigation. Images of scanning
electron microscopy (SEM) (Philips XL-30, Netherland) of the
powder at two different magnifications are shown in Fig. 1.
Fig. 1 (a) exhibits the particle shape is polygonal and Fig. 1 (b)
indicates severe agglomeration with different sizes occurred
between the particles. Fig. 2 shows the hard agglomerate size
distribution of the powder was determined with a laser particle
size analyzer (Fritch, Analysette 22, Germany). The mean hard
agglomerate size of the powder was determined at
approximately 23 µm.
Fig. 2 The hard agglomerate size distribution of the Li2TiO3 powder.
B. Sample preparation
The as-received powder was pressed on a hydraulic press
under pressure of about 300±3 MPa at room temperature using
stainless steel die to create bars of ~5×5×50 mm3. Before
proceeding to sintering, to ensure the absence of any moisture,
the compact powder was dried. The green density was
measured by the geometric method. The green density of
Li2TiO3 powder compacts was 2.15±0.03 g/cm3. The value of
3.43 g/cm3 was used as the theoretical density.
C. Shrinkage Measurements
An optical non-contact dilatometer (Misura ODLT, Expert
System, ITALY) was used for monitoring the in situ
dimensional changes of the powder compact during sintering
in air at different heating rates. Two beams of light illuminate
both the ends of a specimen 50 mm long placed horizontally
into the furnace and two digital cameras capture the images of
the last few hundreds microns of each tip. The specimen,
completely free to expand or contract, is measured by the
image that it projects on a Charge-Coupled Device (CCD).
This instrument consists of a kiln equipped with an automatic
temperature controller, which can reach a heating rate of 30 K
per minute. The temperature increases from room temperature
(RT) to 1200°C at the preset heating rate with no holding time.
As a final result, the dimensional changes (expansion or
shrinkage with respect to the initial size) of a material are
plotted in percentage on a graph as a function of the
temperature. Assuming isotropy in densification of all the
specimens, the relative density of the sintered specimen ( ρ s )
Fig. 1 (a and b) SEM analysis of Li2TiO3 powder at two different
magnifications.
was calculated using the following equation [21]:
3


1
ρs = 
 ρg
1 − dL / L0 + α (T − T0 ) 
(2)
dL / L is instantaneous linear shrinkage obtained by
the dilatometer test, L0 is the initial length of the specimen, T
is the measured temperature, T0 is the room temperature ρ g
Where
is the green density, and α is the coefficient of thermal
ISBN: 978-1-61804-241-5
292
Advances in Engineering Mechanics and Materials
expansion.
An average value α as a function of temperature, T, by the
following estimation equations was determined from the
cooling steps of the dilatometer runs performed with the
different heating rate adopted during our investigations.
α ( K −1 ) = 1.4635 ×10−5 + 9.5499 ×10−9 T
− 4.3946 × 10−12T 2 (25 < T < 1360)
α ( K −1 ) = 1.9820×10−5 (T ≥ 1360 K )
(4)
(5)
The final densities after the dilatometer experiments as
calculated in this way were in admissible agreement with those
measured by the Archimedes technique.
IV. RESULTS AND DISCUSSION
A. Dilatometry
Based on a theoretical density 3.43 g/cm3 for the Li2TiO3,
the average green density of the Li2TiO3 powder compacts was
determined to be 62.78% theoretical density after pressing.
The original shrinkage–temperature relation has been
converted into the relative density dependence on temperature
using Eq. (2). The final densities after the dilatometer
experiments as calculated in this way were in admissible
agreement with those measured by the Archimedes technique.
Fig. 3 shows the dependence of density and densification rate
on temperature of the Li2TiO3 at five different heating rates of
2, 3.5, 10, 20 and 30 K min-1. It can be observed that the
density–temperature curves displayed the classical sigmoidal
shape and generally shifted to higher temperatures with
increasing heating rate. It can be noted that the achieved
sintered densities at any temperature showed a modest but
systematic dependence on the heating rate. At some
temperature, the density starts to increase slowly, then enters a
second region where the density increases markedly, and after
reaching value of 70-74% of the theoretical value, a third
region is reached where the increase in density is slows and
finally stops. The maximum density was found to depend upon
the heating rate, the higher the heating rate the lower the
sintered density. This behavior has also have reported for
zirconia [22], alumina [15], cerium oxide [23], and magnesium
aluminate spinel [24] systems. It is well documented that, at a
lower heating rate, the compact is exposed to sintering for a
longer time during heating period; hence, the amount of
relative density is higher. This is ascribed to a prolonged time
scale for mass transport and diffusion when a slower heating
rate is used to reach the same temperature. It can be seen from
Fig. 3 that with increase in heating rate, the height of the peaks
increased and curves shifted to a higher temperature. Wang
and Raj [25] demonstrated that a higher peak temperature and
a greater height of the peak imply a larger activation energy.
Therefore, position and height of the peak in densification rate
(
Fig. 3 Density evolution and densification rate as function of
temperature at different heating rates.
B. Construction of MSC
As mentioned earlier, one of the essential data for obtaining
the master sintering curve is the activation energy. The
standard statistical approach to evaluating the scatter of
experimental data is the minimization of mean residual squares
(MRS). This criterion was used in many recent papers [9][14]-[17]-[26] to determine the sintering activation energy and
construction of MSC and is described, for example, in [26] by
the following formula:
MRS =
ρf
∫
ρg
∑
N
i =1
((Θi / Θ ave ) − 1)2
N
dρ
(5)
Where Θavg is the average of all Θi at a given density, N is
the number of heating profiles used, and ρg or ρf are green or
final densities of the sample.
Unfortunately, the calculation for minimization of MRS
needs repeated numerical calculations which are userunfriendly (complicated and time-consuming). Therefore, in
this work we used simple software developed by Pouchly and
Maca [27]. This newly developed software calculates the MSC
and finds the optimal activation energy of a given material.
Following the above discussion, the MSC was calculated for
the Li2TiO3 samples with using five different heating rates. A
relative density range of 62%–70% was used to construct the
MSC. This selected range of the relative density contributes to
initial and intermediate stage of sintering. Fig. 4 shows the
resulting master sintering curve for the Li2TiO3 powder
compact. The inset shows the dependence of MRS on the
activation energy. The minimum of the MRS, which is 0.3169,
has been found for Q=360 kJ/mol. However, it is difficult to
establish a good fitting. The unsatisfactory construction of
dρ
) give an immediate indication of the activation energy.
dT
ISBN: 978-1-61804-241-5
1
ρ f − ρg
293
Advances in Engineering Mechanics and Materials
MSC most likely revealed that different probable mechanisms
dominate sintering over the entire relative density range
studied.
Fig. 6 The constructed MSC for sintering of Li2TiO3 powder during
intermediate stage (66%-70% of the theoretical density); the
minimum of mean residual square is given at energy of Q= 320
KJ/mol.
Fig. 4 The constructed MSC for sintering of Li2TiO3 powder using an
activation energy of Q= 360 KJ/mol for the whole stage; inset figure
shows the mean residual square as a function of an activation energy.
During the initial stage of sintering, the activation energy
value of Li2TiO3 is determined to be 380 kJ/mol, which is in
good agreement with value of Q=377±10 kJ/mol that
calculated by present authors at previous paper [31]. Wang
and Raj [25]-[32] have derived the sintering-rate equation of
Eq. (6) used for estimation of the activation energy at
intermediate sintering stage by constant rates of heating
techniques, noting that the sintering-rate equation in general
can be separated into temperature-dependent, grain-sizedependent, and density-dependent quantities:
As suggested, a precise MSC can be constructed over
several consecutive stages, based on either temperature [28] or
density range [22]-[29]. Song and co-workers constructed
MSC over two consecutive densification stage [30]. In the
current study, we have divided sintering (in the range of 62%–
70% relative density) into the initial and intermediate stages,
with about 66% relative density as the boundary. Superior
respective MSCs for the two stages are constructed separately
and are shown in Figs. 5 and 6. For the initial stage, an
activation energy value of Q=380 kJ/mol was obtained via the
best fitted ρ-log[Θ(t,T(t))], curve. In the intermediate stage, the
minimum was given at Q=320 kJ/mol. The MRS yielded from
the sigmoidal fitting are 0.3166 and 0.3171, respectively.
Obviously, the constructed MSC based on two consecutive
stages provide a better representation of the sintering behavior
than using a single Q value alone for the whole sintering
process chosen.
ln(T
dT dρ
Q
)=−
+ ln[ f ( ρ )] + ln A − n ln dG
dt dT
RT
(6)
Here, Q is activation energy, T is the absolute temperature, t
is the time, R is the gas constant, f(ρ) is a function of density,
G is the grain size (i.e., diameter), n is the grain size powerlaw exponent (i.e, n=4 for grain boundary diffusion, n=3 for
lattice diffusion), and A is a material parameter (i.e., a
constant) that is insensitive to G, T, and ρ. Using shrinkage
data measured at different heating rates, the Q value can be
determined from the slope of the Arrhenius-type plot of
ln(T
dT dρ
1
at the same density, under a
) versus
dt dT
T
constant grain size. The Q value determined corresponds to an
activation energy either for grain boundary diffusion or for
lattice diffusion, because it is very difficult to determine the
diffusion mechanism experimentally from Eq. (6). According
above discussion, the activation energy for densification in the
Li2TiO3 was determined from the slope an Arrhenius plot of
the sintering data over a density range of 66%–70% relative
density that related to intermediate sintering stage (Fig. 7).
Fig. 5 The constructed MSC for sintering of Li2TiO3 powder during
initial stage (62%-66% of the theoretical density); the minimum of
mean residual square is given at energy of Q= 380 KJ/mol.
ISBN: 978-1-61804-241-5
294
Advances in Engineering Mechanics and Materials
powders at lower temperatures. As explained above, while the
roles of the diffusion mechanism changes, the effectiveness of
MSC based on constant activation energy will be impaired.
Therefore, the densification process was divided into two
consecutive stages according to the extent of densification, the
MSCs of which were generated separately. The boundary
between the first and second stage was assigned to be 66% of
the theoretical density. Although somewhat arbitrary, it did
reflect different temperature sensitivity for solid-state sintering
during the low and intermediate density range. The two-stage
MSC approach has been proved to provide a better
representation of the sintering behavior (Figs. 5 and 6), and the
activation energy is obtained via the best fitted MSC.
During the first stage of sintering, the activation energy of
Li2TiO3 is determined to be 380 kJ/mol, which is in good
agreement with that calculated by present authors [31]. On the
other hand, present authors attributed the dominant sintering
mechanism of the Li2TiO3 to lattice diffusion that may be
enhanced with surface diffusion mechanism [31]. It has
revealed that for the Li2TiO3 sample used, there is a little
difference in the activation energy between the first and
second stage of sintering. A little decrease (60 kJ/mol) of the
activation energy indicates that no change in the dominant
sintering mechanism has occurred. It has been pointed out that
surface diffusion usually increases the apparent activation
energy for densification, yet does not facilitate densification
[18]. Surface diffusion may have contributed to the higher
apparent activation energy. During the second stage, the value
of activation energy obtained is comparable to value reported
for volume diffusion [31]. Therefore, the dominant sintering
mechanism is most appropriately assigned to lattice diffusion.
Fig. 7 Determination of the activation energy for densification via the
constant rate of heating method.
The average activation energy for densification over the
entire density range studied was then calculated from the
activation energies determined at each density. An average
activation energy for densification of Q=330 kJ/mol was
determined, and the standard deviation in Q over the density
range examined was 12 kJ/mol. The good linear fit to the data
for each specific density in Fig. 10 establishes reasonably good
confidence that a representative value of Q can be calculated
for the Li2TiO3 from the Arrhenius plots. Additionally, the
average activation energy of Q=330±12 kJ/mol determined in
this study is consistent with the activation energy of 320
kJ/mol determined using the two stage MSC theory for
intermediate stage of sintering. The consistency of slope with
density in Fig. 10, along with the relatively small standard
deviation in Q with density, indicate that a single value of Q,
and a correspondingly single dominant mechanism (i.e., grain
boundary diffusion or lattice diffusion), controls densification
in the Li2TiO3 from 66% to 70% theoretical density.
Prevalently, sintering mechanisms of ceramic materials are a
diffusion-controlled process and the diffusion of the slowest
moving atoms/ions along the fastest diffusion path determines
the rate of sintering. The activation energy for densification is
a characteristic parameter reflecting the dependence of
densification kinetics on temperature, and it is commonly used
to identify the fundamental mass transport mechanism during
the sintering process. In a practical case, several mechanisms
(volume diffusion, grain-boundary diffusion, etc.) often
operate simultaneous during solid-stage sintering. Therefore,
the resultant activation energy may not be contributed from
one specific sintering mechanism. It is most likely a weighted
value contributed by multiple sintering mechanisms. In the
present work, a single mechanism dominating the whole
densification process was initially assumed by using constant
activation energy to construct the MSC. However, a good
fitting was not able to be achieved. It is probably that the MSC
approach could not represent sufficiently the sintering
behavior at the lower density range. One major complication
arises from surface diffusion, which usually occurs in fine
ISBN: 978-1-61804-241-5
V. CONCLUSIONS
The activation energy of the Li2TiO3 was determined with
the help of MSC. A better representation of the sintering
behavior was obtained by applying the two-stage MSC
approach.
REFERENCES
[1]
[2]
[3]
[4]
[5]
[6]
[7]
295
C.E. Johnson, “Ceramic breeder materials,” Ceramics International, 17
(1991) 253-258.
J.P. Kopasz, J.M. Miller, C.E. Johnson, “Tritium release from lithium
titanate, a low-activation tritium breeding material,” Journal of Nuclear
Materials, 212-215 (1994) 927-931.
J.M. Miller, H.B. Hamilton, J.D. Sullivan, “Testing of lithium titanate
as an alternate blanket material,” Journal of Nuclear Materials, 212-215
(1994) 877-880.
H. Kleykamp, “Chemical reactivity of SiC fibre-reinforced SiC with
beryllium and lithium ceramic breeder materials,” Journal of Nuclear
Materials, 283-287 (2000) 1385-1389.
C. Alvani, S. Casadio, V. Contini, A. Di Bartolomeo, J.D. Lulewicz, N.
Roux, “Li2TiO3 pebbles reprocessing, recovery of 6Li as Li2CO3,”
Journal of Nuclear Materials, 307-311 (2002) 837-841.
X. Wu, Z. Wen, X. Xu, J. Han, B. Lin, “Fabrication and improvement of
the density of Li2TiO3 pebbles by the optimization of a sol-gel method,”
Journal of Nuclear Materials, 393 (2009) 186-191.
T.R.G. Kutty, K.B. Khan, P.V. Hegde, J. Banerjee, A.K. Sengupta, S.
Majumdar, H.S. Kamath, “Development of a master sintering curve for
ThO2,” Journal of Nuclear Materials, 327 (2004) 211-219.
Advances in Engineering Mechanics and Materials
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
[18]
[19]
[20]
[21]
[22]
[23]
[24]
[25]
[26]
[27]
[28]
[29] D.C. Blaine, S.-J. Park, R.M. German, “Linearization of Master
Sintering Curve,” Journal of the American Ceramic Society, 92 (2009)
1403-1409.
[30] X. Song, J. Lu, T. Zhang, J. Ma, “Two-Stage Master Sintering Curve
Approach to Sintering Kinetics of Undoped and Al2O3-Doped 8 Mol%
Yttria-Stabilized Cubic Zirconia,” Journal of the American Ceramic
Society, 94 (2011) 1053-1059.
[31] A. R. Abbasian, M. R. Rahimipour, Z. Hamnabard, “Initial Sintering
Kinetics of Lithim Meta Titanate at Constant Rates of Heating,”
Iranian Journal of Materials Science & Engineering, 10 (2013) 44-53.
[32] J. Wang, R. Raj, “Activation Energy for the Sintering of Two-Phase
Alumina/Zirconia Ceramics,” Journal of the American Ceramic Society,
74 (1991) 1959-1963.
M.W. Reiterer, K.G. Ewsuk, “An Analysis of Four Different
Approaches to Predict and Control Sintering,” Journal of the American
Ceramic Society, 92 (2009) 1419-1427.
H. Su, D.L. Johnson, “Master Sintering Curve: A Practical Approach to
Sintering,” Journal of the American Ceramic Society, 79 (1996) 32113217.
S. Marković, D. Uskoković, “The master sintering curves for
BaTi0.975Sn0.025O3/BaTi0.85Sn0.15O3 functionally graded materials,”
Journal of the European Ceramic Society, 29 (2009) 2309-2316.
K.G. Ewsuk, D.T. Ellerby, C.B. DiAntonio, “Analysis of
Nanocrystalline and Microcrystalline ZnO Sintering Using Master
Sintering Curves,” Journal of the American Ceramic Society, 89 (2006)
2003-2009.
D.Z. Florio, V. Esposito, E. Traversa, R. Muccillo, F.C. Fonseca,
“Master sintering curve for Gd-doped CeO2 solid electrolytes,” Journal
of Thermal Analysis and Calorimetry, 97 (2009) 143-147.
D. Li, S. Chen, W. Shao, X. Ge, Y. Zhang, S. Zhang, “Densification
evolution of TiO2 ceramics during sintering based on the master
sintering curve theory,” Materials Letters, 62 (2008) 849-851.
W.Q. Shao, S.O. Chen, D.Li, H.S.Cao, Y.C.Zhang, S.S. Zhang,
“Prediction of Densification and Microstructure Evolution for α-Al2O3
During Pressureless Sintering at Low Heating Rates Based on the
Master Sintering Curve Theory,” Science of Sintering, 40 (2008) 251261.
[15] M. Aminzare, F. Golestani-fard, O. Guillon, M. Mazaheri, H.R.
Rezaie, “Sintering behavior of an ultrafine alumina powder shaped by
pressure filtration and dry pressing,” Materials Science and
Engineering: A, 527 (2010) 3807-3812.
[16] M.V. Nikolić, V.P. Pavlović, V.B. Pavlović, N. Labus, B.
Stojanović, “Application of the Master Sintering Curve Theory to NonIsothermal Sintering of BaTiO3 Ceramics ” Materials Science Forum
494 (2005) 417-422.
[17] M. Mazaheri, A. Simchi, M. Dourandish, F. Golestani-Fard,
“Master sintering curves of a nanoscale 3Y-TZP powder compacts,”
Ceramics International, 35 (2009) 547-554.
[18] G. Sethi, S.J. Park, J.L. Johnson, R.M. German, “Linking
homogenization and densification in W–Ni–Cu alloys through master
sintering curve (MSC) concepts,” International Journal of Refractory
Metals and Hard Materials, 27 (2009) 688-695.
[19] J.D. Hansen, R.P. Rusin, M.-H. Teng, D.L. Johnson, “CombinedStage Sintering Model,” Journal of the American Ceramic Society, 75
(1992) 1129-1135.
[20] T.R.G. Kutty, P.V. Hegde, K.B. Khan, U. Basak, S.N. Pillai, A.K.
Sengupta, G.C. Jain, S. Majumdar, H.S. Kamath, D.S.C. Purushotham,
“Densification behaviour of UO2 in six different atmospheres,” Journal
of Nuclear Materials, 305 (2002) 159-168.
[21] S. Ran, L. Winnubst, W. Wiratha, D.H.A. Blank, “Sintering
Behavior of 0.8 mol%-CuO-Doped 3Y-TZP Ceramics,” Journal of the
American Ceramic Society, 89 (2006) 151-155.
[22] G. Bernard-Granger, C. Guizard, “Apparent Activation Energy for
the Densification of a Commercially Available Granulated Zirconia
Powder,” Journal of the American Ceramic Society, 90 (2007) 12461250.
[23] Y. Kinemuchi, K. Watari, “Dilatometer analysis of sintering
behavior of nano-CeO2 particles,” Journal of the European Ceramic
Society, 28 (2008) 2019-2024.
[24] K. Rozenburg, I.E. Reimanis, H.-J. Kleebe, R.L. Cook, “Sintering
Kinetics of a MgAl2O4 Spinel Doped with LiF,” Journal of the
American Ceramic Society, 91 (2008) 444-450.
J. Wang, R. Raj, “Estimate of the Activation Energies for Boundary
Diffusion from Rate-Controlled Sintering of Pure Alumina, and
Alumina Doped with Zirconia or Titania,” Journal of the American
Ceramic Society, 73 (1990) 1172-1175.
S.J. Park, R.M. German, “Master curves based on time integration of
thermal work in particulate materials,” International Journal of
Materials and Structural Integrity, 1 (2007) 128-147.
V. Pouchly, K. Maca, “Master Sintering Curve – A Practical Approach
to its Construction,” Science of Sintering, 42 (2010) 25-32.
S. Kiani, J. Pan, J.A. Yeomans, “A New Scheme of Finding the Master
Sintering Curve,” Journal of the American Ceramic Society, 89 (2006)
3393-3396.
ISBN: 978-1-61804-241-5
296