Determination of Activation Energy of Sintering of ThO 2U 3 O 8 Pellets Using the Master Sintering Curve Approach

ThO2 containing around 2 to 3 % UO2 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.


Introduction
ThO 2 containing around 2 to 3 % U 233 O 2 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 U 238 fertile component by Th 232 [3][4].
ThO 2 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 ThO 2 -U 3 O 8 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.

Theory of Master Sintering Curve
The master sintering curve is derived from the densification rate equation of the combined-stage sintering model [10][11][12][13][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 ___________________________________________________________________________ each other experimentally.The temperature dependent side of the equation can be represented by [14] 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]: where t i is the duration of the isothermal portion of the run.For a constant heating rate, equation ( 1) can be written as: where c is the heating rate used and T o 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.

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.

Experimental
The green ThO 2 -2 % U 3 O 8 pellets for this study were prepared by the conventional powder metallurgy technique.The procedure for the fabrication of ThO 2 -2 % U 3 O 8 green pellets consisted of the following steps: ___________________________________________________________________________ 1. Milling of the as-received ThO 2 powder in a planetary ball to break its platelet morphology, 2. Mixing/milling of the above milled ThO 2 powder with the required quantity of U 3 O 8 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 ThO 2 and U 3 O 8 powders used in this study are given in Tab.I.

Dilatometry
The shrinkage behaviour of pure ThO 2 -2 % U 3 O 8 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.

Characterization
The sintered ThO 2 -UO 2 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 CuK α 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.___________________________________________________________________________ )

Results
Fig. 1 shows the shrinkage behaviour of ThO 2 -2 % U 3 O 8 pellets in air for different heating rates used in this study.Here dl/l 0 is plotted against temperature.The shrinkage data from the above dilatometric runs were converted into % T.D. using the following relation [15]: where ρ and ρ 0 are the density of the sintered and green pellets, respectively and dl/l o 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.

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 ___________________________________________________________________________ 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 (D l ) and the grain boundary diffusion coefficients (D b ) 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][23][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 ThO 2 -U 3 O 8 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.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.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 T m .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 ThO 2 -UO 2 pellets covered under this study showed a uniform grain size of 5 µm, and thus validating the present approach.

Conclusions
High-density ThO 2 -UO 2 pellets have been fabricated by powder metallurgy route using ThO 2 and U 3 O 8 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.

Fig. 1 Fig. 2
Fig. 1 Shrinkage curves for ThO 2 -2 % U 3 O 8 pellets in air for the different heating rates.The dl/l 0 values are plotted against temperature, where l 0 is the initial length.

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.___________________________________________________________________________

Fig. 4
Fig. 4 Mean residual squares for various values of the activation energy.