Science of Sintering, 35 (2003) 125-132
___________________________________________________________________________
UDK 622.785: 661.884: 661.879
Determination of Activation Energy of Sintering of
ThO2-U3O8 Pellets Using the Master Sintering Curve Approach
T. R. G. Kutty1*, K. B. Khan1, P. V. Hegde1,
A. K. Sengupta1, S. Majumdar1 and H. S. Kamath2
1
Radiometallurgy Division, Bhabha Atomic Research Centre, Trombay,
Mumbai 400 085, India
2
Nuclear Fuels Group, Bhabha Atomic Research Centre, Trombay,
Mumbai 400 085, India
Abstract: ThO2 containing around 2 to 3 % U233O2 is considered as fuel for the forthcoming
Indian Advanced Heavy Water Reactor (AHWR). High-density ThO2-UO2 pellets have been
fabricated by powder metallurgy route using ThO2 and U3O8 powders as the starting materials.
U3O8 decomposes to UO2 during high temperature sintering and forms a solid solution with
ThO2. The densification behaviour and sintering kinetics of the above were evaluated using a
high temperature dilatometer using constant heating rate experiments. To evaluate the
activation energy of sintering, a master sintering curve approach has been used. The
activation energy for sintering for the above composition in air was found to be 500 kJ/mol.
Keywords: Sintering; Kinetics; Activation Energy, Dilatometer; Thoria.
Резюме: Исследован оксид ThO2 с добавкой около 2-3 % U233O2 в качестве топлива для
будущего Индийского современного реактора на тяжелой воде. Прессовки ThO2-UO2
высокой плотности получены методом порошковой металлургии с использованием
порошков ThO2 и U3O8 в качестве исходных материалов. В ходе процесса
высокотемпературного спекания происходит разложение U3O8 до UO2, который с ThO2
образует твёрдый раствор. Поведение образцов в процессе уплотнения и кинетика
спекания исследованы при помощи высокотемпературного дилатометра с постоянной
скоростью нагрева. Для оценки энергии активации спекания использован "master sintering
curve". Установлено, что для спекания данной системы на воздухе энергия активации
составляет 500 кдж/моь.
Ключевые слова: Спекание; кинетика; энергия активации; дилатометр; торий.
Садржај: Оксид ThO2 са око 2-3 % U233O2 разматран је као потенцијално гориво за
будући Индијски реактор са тешком водом. Испресци ThO2-UO2 високе густине
направљени су методом металургије праха коришћењем прахова ThO2 и U3O8 као
полазних материјала. Током високотемпературног синтеровања одвија се декомпозиција
U3O8 до UO2, који са ThO2 образује чврсти раствор. Понашање узорака током
згушњавања и кинетика синтеровања проучавани су у високотемпературном
дилатометру у експериментима са константном брзином загревања. За процену енергије
*
Corresponding author: [email protected]
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активације синтеровања коришћена је метода "master sintering curve". Утврђено је да
енергија активације потребна за синтеровање овог система у ваздуху износи
500 kJ/mol.
Кључне речи: Синтеровање; кинетика; енергија активације; дилатометар; торијум.
1. Introduction
ThO2 containing around 2 to 3 % U233O2 is considered as fuel for the forthcoming
Indian Advanced Heavy Water Reactor (AHWR), which is being developed with the specific
aim of utilizing thorium for power generation since India has vast reserves of thorium. The
recent revival of interest in thorium-based fuel cycles is motivated by its potential to address
concerns related to proliferation potential and waste disposal [1-2]. The main source of
proliferation potential and radiotoxicity is plutonium (Pu) generated during the burnup of
standard light water reactor (LWR) fuel. A significant reduction in quantity and “quality” of
Pu may be achieved by replacing the U238 fertile component by Th232 [3-4].
ThO2 pellets are usually fabricated by the conventional powder metallurgy technique.
Large-scale production of these pellets is carried out by processes involving milling, precompaction and granulation followed by cold compaction and high temperature sintering.
Sintering is driven by the reduction in interfacial free energy (sum of surface free energies,
grain boundary free energies, and interphase boundary free energies). The factors that
influence sintering are temperature, annealing time, green density, and bulk composition
[5-6]. One of the ways to increase sintering rates is by decreasing the mean particle size.
Decreasing the particle size will decrease the effective diffusion distances necessary to
achieve the same microstructural changes [7]. The sintering process is a diffusion controlled
process whose rate is controlled by the slower moving metal atoms [8-9]. To determine the
underlying physical mechanisms of sintering for a given material system, one must know the
kinetic mechanisms by which densification and grain growth occur during sintering.
Historically, this has been done experimentally by determining the activation energy for
sintering and then comparing that measured value to values reported elsewhere for each
possible mass transport mechanism. In this study, the activation energy for sintering was
determined using the master sintering curve concept. For this, dilatometric runs were carried
out on ThO2-U3O8 compacts in air with different heating rates viz. 6, 12 and 20ºC/min. The
output of this result was used to generate the activation energy for sintering.
2. Theory of Master Sintering Curve
The master sintering curve is derived from the densification rate equation of the
combined-stage sintering model [10-14]. It is possible to rearrange some elements of the basic
equation, so as to bring all the factors of temperature and time in one side. These elements can
be determined by trial runs, making it possible to predict the densities for other times and
temperatures.
As mentioned earlier, the parameters in the sintering rate equations are separated into
two parts: (a) those related to the microstructure and (b) those related to time and temperature
terms [10]. These parts, which are on the opposite sides of the equation, are then related to
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each other experimentally. The temperature dependent side of the equation can be represented
by [14]
t
Θ=
1

Q 
∫ T exp − RT dt ,
(1)
0
where Q is the sintering activation energy, R is the gas constant, t is the instantaneous time
and T the absolute temperature. Equation (1) can be simplified for the isothermal portion of
the sintering runs to [10]:
Θ=
ti
 Q 
exp −
,
T
 RT 
(2)
where ti is the duration of the isothermal portion of the run. For a constant heating rate,
equation (1) can be written as:
T
Θ=
1 1
 Q 
exp −
dT ,
cT T
RT 

0
∫
(3)
where c is the heating rate used and To is the temperature below which no sintering takes
place.
The relationship between density (ρ) and Θ is defined as the master sintering curve
[14]. For the construction of MSC, the integral of equation (1) and density should be known.
3. Determination of the Activation Energy of Sintering
The activation energy for densification is a characteristic quantity that elucidates the
fundamental diffusion mechanisms during the sintering process. Traditionally, it is obtained
from the shrinkage rate data from either isothermal heating or constant heating rate
experiments. It can be estimated with good precision from the concept of the master sintering
curve [10, 14]. Dilatometry can be conveniently used to determine density since instantaneous
density at all times can be obtained from dilatometric data. The activation energy for sintering
is then calculated in the following way.
First, a particular value of activation energy is chosen and ρ-Θ curves are constructed
for each heating rate. If the curves fail to converge, a new value of activation energy is chosen
and the calculations are repeated. This procedure continues until all curves converge and the
corresponding activation energy is the true activation energy for sintering. If the correct value
of Q is chosen, all of the data converge to a single curve [10]. A curve can be then fitted
through all the data points, and then convergence of data to the fitted line can be quantified
through the sum of residual squares of the points with respect to the fitted line [14]. The best
estimate of Q will be the value of the minimum in the plot of mean residual squares versus
activation energy.
4. Experimental
The green ThO2 –2 % U3O8 pellets for this study were prepared by the conventional
powder metallurgy technique. The procedure for the fabrication of ThO2 – 2 % U3O8 green
pellets consisted of the following steps:
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1. Milling of the as-received ThO2 powder in a planetary ball to break its platelet morphology,
2. Mixing/milling of the above milled ThO2 powder with the required quantity of U3O8
powder for 4 h in a planetary ball mill with tungsten carbide balls,
3. Double precompaction of the above prepared mixtures at 150 MPa,
4. Granulation of the precompacts,
5. Final cold compaction of the granulated powder at 300 MPa into green pellets.
Green density of the compacts was around 67 % of the theoretical density. To facilitate
compaction and to impart handling strength to the green pellets, 1 wt.% zinc behenate was
added as lubricant/binder during the last 1 h of the mixing/milling procedure. The green pellets
were about 8.15 mm in diameter and around 7 mm in length. The characteristics of the starting
ThO2 and U3O8 powders used in this study are given in Tab. I.
Tab. I Characteristics of ThO2 and U3O8 powders.
Property
ThO2
U3O8
2.00
2.66
Apparent density (g/cm )
0.70
1.2
Total impurities (ppm)
< 1200
< 800
1.53
2.15
Theoretical density (g/cm )
10.00
8.34
Molecular weight (g/mol)
264
842
Volume relative to ThO2
1.000
1.273
Oxygen to metal ratio
3
2
Specific surface area (m /g)
3
4.1. Dilatometry
The shrinkage behaviour of pure ThO2 – 2 % U3O8 was followed in a high temperature
dilatometer. The dilatometric studies were carried out using a Netzsch (model 402E)
horizontal dilatometer. The shrinkage of a standard sample (POCO graphite, NIST) was
measured under identical conditions in order to correct for the differences in shrinkage between
the sample holder and the sample. The heating rate used for this study was 6, 12 and 20ºC/min
and gas flow rate was 18 l/h. The sintering kinetics of pellets was evaluated in air.
4.2. Characterization
The sintered ThO2-UO2 pellets were characterized by the following techniques:
thermogravimetry, XRD, density and metallography.
The O/M ratio of the sintered pellets was measured thermogravimetrically and the phase
content was estimated using X-ray diffractometry and metallography. The X-ray diffraction
patterns of the pellets were obtained by CuKα radiation and a graphite monochromator. For
metallography, the sintered pellet was mounted in Bakelite and ground using successive grades
of emery paper. Final polishing was done using diamond paste. Etching was performed
thermally by holding the sample at 1600ºC for 4 hours in air atmosphere. The grain size was
determined by the intercept method. The green density was measured geometrically, while the
sintered density was determined following the Archimedes method.
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5. Results
Fig. 1 shows the shrinkage behaviour of ThO2 – 2 % U3O8 pellets in air for different
heating rates used in this study. Here dl/l0 is plotted against temperature. The shrinkage data
from the above dilatometric runs were converted into % T.D. using the following relation
[15]:
3


1
 ,
 1 + dl / l0 ) 
ρ = ρ0 
(
(4)
where ρ and ρ0 are the density of the sintered and green pellets, respectively and dl/lo is the
shrinkage. The curves (Fig. 2) have the familiar sigmoidal shape and generally shifted to higher
temperatures with increasing heating rate. It can be noted that sintered densities obtained at any
temperature showed a modest but systematic dependence on heating rates. Density was found to
increase at 1300ºC and goes to a maximum value of greater than 90 % of T.D. The maximum
density was found to depend on the heating rate, the higher the heating rate the lower the
sintered density. Slower heating rates lead to densification at lower temperatures since more
time for mass transport and diffusion is available until a given temperature is reached.
100
0.02
ThO2-2%U3O8
6 C/min
o
12 C/min
o
20 C/min
90
Density, %T. D.
-0.02
dl/lo
-0.04
-0.06
o
6 C/min.
o
12 C/min.
o
20 C/min.
-0.08
ThO2-2%U3O8
o
95
0.00
85
80
75
70
-0.10
65
-0.12
400
600
800
1000
1200
1400
1600
1800
o
Temperature ( C)
Fig. 1 Shrinkage curves for ThO2 – 2 % U3O8
pellets in air for the different heating rates. The dl/l0
values are plotted against temperature, where l0 is
the initial length.
60
400
600
800
1000
1200
1400
1600
1800
o
Temperature, C
Fig. 2 Shrinkage curves of Fig. 1 are replotted as
percent of theoretical density (% T.D.) versus
temperature for ThO2 – 2 % U3O8 pellets. The dl/l0
values were converted into % T.D. using Eq. (4).
6. Discussion
Sintering processes have been intensively studied for almost half a century and many
models have been proposed to explain the fundamentals of sintering. One of the main purpose
of these studies is to evaluate the activation energy of sintering for distinguishing the rate
controlling mechanisms and determining the rate-limiting species. Although most sintering
models can be used to evaluate the value of the activation energy of sintering, an Arrhenius
plot of ln strain rate (ε) versus the reciprocal of the absolute temperature is usually used for
the evaluation. However, many times the obtained values of the activation energy are
scattered even for the same material. Bruch [16] obtained very significantly different
activation energies of sintering for compacts with different green densities. Young and Cutler
[17] concluded from their study that non-isothermal sintering could not be used to identify the
mechanism of diffusion because of the wide variation of the evaluated activation energies.
According to the sintering theory, the activation energy of sintering should be consistent with
130
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that of the apparent diffusion coefficient of the rate-limiting species of sintering [18]. In
sintering polycrystalline ceramics, it is commonly observed that both grain boundary and
lattice diffusion of the rate-limiting species can simultaneously contribute to densification.
Some reports [18-19] have suggested that the change of the relative contribution of lattice
diffusion (Dl) and the grain boundary diffusion coefficients (Db) due to the difference of the
impurity level or grain size can affect not only the pre-exponential factor but also the
activation energy of the apparent diffusion coefficient. In this study, we have undertaken an
all-together different approach i.e., master sintering curve, for the evaluation of the activation
energy of sintering.
Sintering is a diffusion controlled process whose rate is controlled by the slower
moving metal atoms. The observed shrinkage depends on the morphology of the powder and
the intrinsic parameters like dislocation density and also on extrinsic parameters such as the
pressure, heating rate, sintering temperature and atmosphere [20-21]. The driving force for
sintering is the reduction in surface energy. Sintering depends on diffusion of atoms, which in
turn, depends on concentration of structural imperfections such as vacancies. The
concentration of structural imperfections is a function of temperature, atmosphere and
dopants. Solid state sintering is a complex process divided into three stages in which different
mechanisms may be operative [22-24]. In the initial stage concave necks are formed at the
contact points of particles. In the intermediate stage neck growth results in a body with
continuous network of tubular pores. This results in a three-dimensional channel network of
pores and a skeleton of solid particles. Shrinkage occurs mainly in this stage. Finally the
continuity of pore channels is broken into individual pores, which are located at the grain
boundaries or inside the grains.
One of the essential data for obtaining the master sintering curve is the activation
energy. For this, the density data for ThO2-U3O8 compacts obtained from the dilatometric
data, and Θ values obtained from the equation (1) are employed. A ρ-Θ curve is then
constructed for all the heating profiles for a chosen value of activation energy (300 kJ/mol) as
shown in Fig. 3a.
Q=300 kJ/mol
95
85
o
6 C/min
12
20
90
6 C/min
12
20
Relative Density, %TD
Relative Density, %TD
95
o
90
80
75
70
65
Q=700 kJ/mol
85
80
75
70
65
-34
-32
-30
-28
-26
-24
-22
-20
-70
-68
Theta Parameter
-66
-64
-62
-60
-58
-56
-54
-52
-50
Theta Parameter
a)
b)
95
Q=500 kJ/mol
o
6 C/min
12
20
Relative Density, %TD
90
85
80
75
70
65
-54
-52
-50
-48
-46
-44
-42
-40
-38
-36
Theta Parameter
c)
Fig. 3 Estimation of activation energy from the master sintering curve. Construction of a ρ-Θ curve for
the different heating profiles for a chosen value of activation energy: (a) 300, (b) 700, (c) 500 kJ/mol.
131
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It can be seen that the curves for different heating rates are not converging. Now a
new value of activation energy is chosen and the calculation is repeated. The curve at
700 kJ/mol is shown in Fig. 3b. Convergence occurs the best at around 500 kJ/mol (Fig. 3c).
Fig. 4 gives the mean residual squares for the various values of activation energy and the
minimum has been found to be for 500 kJ/mol.
0.40
Residual square
0.35
0.30
0.25
0.20
0.15
Q=500 kJ/mol
0.10
350
400
450
500
550
600
650
700
750
Activation energy, kJ/mol
Fig. 4 Mean residual squares for various values of the activation energy.
For evaluating the validity of this approach, the following factors are to be considered.
Since this approach is basically a statistical analysis, the accuracy of this method depends upon
the number of data points. A few data points may lead to wrong results. In this experiment,
length measurement was made in situ under dynamic conditions. As the sample is heated, its
temperature and length values are measured continuously with the help of a thermocouple and
LVDT transducer, respectively, and the output is acquired by a PC. Hence, a large number of
data has collected for each run, which resulted in an over-all large database. Secondly, the
effect of surface diffusion should be minimized. Since the experiments are conducted under
constant heating rate, the contribution from surface diffusion will be minimum [25-26].
Surface diffusion is usually predominant at low temperatures below 0.3 Tm. During the early
stages of sintering, and particularly at low temperatures, surface diffusion inhibits sintering.
In constant heating rate experiments, contribution from surface diffusion is minimized since
the time of surface diffusion regime is comparatively small unless one uses extremely low
constant hearing rates. Thirdly, when exaggerated grain growth takes place in some materials,
sintering data points do not converge very well and hence should be discarded. The
microstructure of ThO2-UO2 pellets covered under this study showed a uniform grain size of
5 µm, and thus validating the present approach.
7. Conclusions
High-density ThO2-UO2 pellets have been fabricated by powder metallurgy route using
ThO2 and U3O8 powders as the starting materials. The densification behaviour and kinetics of
sintering of the above was evaluated using high temperature dilatometry with constant heating
rate experiments. To evaluate the activation energy of sintering, a master sintering curve
approach has been used. The activation energy for sintering for the above composition in air
was found to be 500 kJ/mol.
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