Science of Sintering, 41 (2009) 103-115 ________________________________________________________________________ doi: 10.2298/SOS0902103K UDK 622.785:661.884 Densification Strain Rate in Sintering of ThO2 and ThO2-0.25%Nb2O5 Pellets T.R.G. Kutty*), K.B. Khan, A. Kumar, H.S. Kamath# Radiometallurgy Division, # Nuclear Fuels Group, Bhabha Atomic Research Centre, Trombay, Mumbai 400 085, India Abstract: The densification behaviour of ThO2 and ThO2 containing 0.25%Nb2O5 powder compacts was studied with the help of a high temperature push-rod type dilatometer. From the temperature versus density plots, densification strain rate, (1/ρ)(dρ/dt), were calculated. It was observed that the addition of Nb2O5 to ThO2 has caused a drastic increase in densification strain rate in the density range of 76 to 82% of T.D. A five-fold increase in the values of strain rate for ThO2-0.25%Nb2O5 in comparison to pure ThO2 was observed in the temperature range of 1300 to 1350oC. The decrease in the densification strain rate for ThO2- 0.25% Nb2O5 (composition in wt%) at high densities may be attributed to the grain size effect. Keywords: Sintering, Densification strain rate, Dilatometer, Thoria 1. Introduction Large scale production of nuclear fuel pellets is carried out by processes involving milling, pre-compaction and granulation followed by cold compaction and high temperature sintering in reducing atmosphere at around 1650°C. Sintering is a diffusion controlled process by which bonding of particles in a mass of powder in the solid state occurs by atomic or molecular attraction through the application of heat. The densification is due to the decrease in the surface area and therefore a reduction in the free energy of the system. Instead of solid – gas interfaces, solid – solid boundaries of lower energy are formed during the sintering. Sintering is traditionally viewed in terms of three distinct stages (initial, intermediate and final) and most of the models have focused on a specific stage [1-6]. The combined-stage sintering model, proposed by Hansen et al. , describes the densification through the entire stages of sintering. By observing the similarities in the three stages of sintering, a single equation was derived which describes the densification through all stages of sintering. In this model the microstructure is characterized by two separate parameters representing geometry and the average grain size. The instantaneous linear shrinkage rate is given as: -dl/ldt = (γΩ/kT) [(ΓvDv/G3)+(ΓbδxDb/G4)] (1) where dl/ldt is the normalized linear shrinkage rate, γ is the surface energy, Ω is the atomic _____________________________ *) Corresponding author: firstname.lastname@example.org. 104 T.R.G. Kutty et al. /Science of Sintering, 41 (2009) 103-115 ___________________________________________________________________________ volume, k is the Boltzmann constant, T is the absolute temperature, G is the mean grain diameter, Dv and Db are the coefficients of volume and grain boundary diffusion, respectively, δ is the width of the grain boundary and Γv and Γb are the collections of microstructure scaling parameters for volume and grain boundary diffusion, respectively. If there exists only one dominant diffusion mechanism in the sintering process, it is possible to separate terms related to the microstructural and materials properties and terms related to heating schedule [8-9]. Assuming that only one of the diffusion mechanisms (either volume or grain boundary diffusion) dominates the sintering process, we can rewrite equation (1) as : (1/ρ)(dρ/dt) = 3(γΩD0/k) (Γ(ρ)/(G(ρ))n) (exp(-Q/RT)/T) (2) where ρ is the density, Q is the activation energy, D0 is the pre-exponential factor and R is the gas constant. The densification rate is conventionally represented by dρ/dt. It may be noted that dρ/ρ gives an idea of densification. The densification is accompanied by shrinkage and shrinkage, dl/lo, is nothing but strain. Hence, (1/ρ)(dρ/dt), namely densification strain rate, will be more meaningful and therefore, we have used this term throughout the text. It is therefore possible to separate terms related to the microstructural and materials properties and terms related to heating schedule in Eq. (2) as follows [6,10]: • (1/ρ)(dρ/dt) = ρ i = A* F(ρ)* θ(T) (3) • Here i ρ i s defined as the densification strain rate, A includes all constants, F(ρ) is equal to Γ(ρ)/G(ρ)n and is function only of density and θ(T) is function only of temperature. Thus, F(ρ) is considered to be dependent on microstructural geometry . Many parameters of green sample have a great influence on densification strain rate (ρi), such as green density, particle size distribution, heterogeneity like aggregates and the . fabrication history of the powder . ρi curves are expected to be a good help to choose raw . materials and to control the microstructural evolution. It has been reported that the densification strain rate in sintering is analogous to constant stress creep rate. It is observed in a number of ceramics that the ratio of densification strain rate to constant stress creep rate remains constant [11-12]. Therefore, it may be possible to predict creep rate from the experimentally determined values of ρi. Hence a study was undertaken to evaluate the densification behaviour of ThO2 bearing ceramics using a high temperature dilatometer. In this study, densification strain rate curves as a function of density and temperature were investigated for ThO2 and ThO2-0.25%Nb2O5 (composition in wt%) compacts from the beginning to the end of sintering process. 2. Experimental 2.1. Fabrication of green pellets The green ThO2 and ThO2-0.25% Nb2O5 pellets for this study were prepared by the conventional powder metallurgy technique. The characteristics of the starting ThO2 powders used in this study are given in Tab.I. ThO2-0.25% Nb2O5 pellets are prepared using ThO2 and Nb2O5 powders as the starting material. The procedure for the fabrication of ThO2-0.25% Nb2O5 green pellets consists of the following steps: a) milling of the as-received ThO2 powder in a planetary ball mill to break its platelet morphology, T.R.g. Kutty et al./Science of Sintering, 41 (2009) 103-115 105 ___________________________________________________________________________ b) mixing/milling of the above milled ThO2 powder with the required quantity of Nb2O5 powder for 4 h in a planetary ball mill with tungsten carbide balls, c) double precompaction of the above prepared mixtures at 150 MPa, d) granulation of the precompacts, and e) final cold compaction of the granulated powder at 300 MPa into green pellets. Tab.I Characteristics of pure ThO2 powder Property Value Oxygen to metal ratio 2.00 Apparent density (g/cm3) 0.70 Total impurities (ppm) <1200 Theoretical density, ρ (g/cm3) 10.00 Specific surface area, S (m2/g) 1.50 Green density of the compacts of ThO2 and ThO2-0.25% Nb2O5 made by the powder route was around 66±1% of the theoretical density (T.D.). 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 mm in diameter and around 7 mm in length. 2.2. Dilatometry The shrinkage behaviour of pellets of mentioned above was studied using a high temperature horizontal dilatometer (Netzsch, model 402E). The dilatometry was carried out under the following condition: • Force on the sample 0.2 N • gas flow 12 l/h • heating rate 6°C/min The length changes were transmitted through the frictionless push rod to an LVDT transducer. The accuracy of the measurement of change in length was within ± 0.1μm. Tab. II Metallic impurities in the sintered ThO2 pellet Element Impurity (ppm) Na 12 Al 8 Mg 5 Si <100 Fe 12 Cr <1 Co <5 Ni <1 Mo <5 W <50 Cu 1.0 B <0.6 106 T.R.G. Kutty et al. /Science of Sintering, 41 (2009) 103-115 ___________________________________________________________________________ A calibrated thermocouple was placed just above the sample to record the sample temperature. The dilatometric experiments were carried out in air. Tab. II gives the typical impurity contents of a sintered pellet. 2.3. Characterization The ThO2 powder used in this study was characterized by the following techniques: • Surface area measurement (BET) • Particle size (XRD, Laser analysis) • Microstructure (SEM) The particle size was determined using laser based particle size analyzer which employs the time of transit theory. The specific surface area of the powder was measured using the Brunauer-Emmett-Teller (BET) method with helium as the adsorbate gas. The particle shape was determined by SEM. The ThO2 and ThO2-0.25% Nb2O5 pellets were characterized by their density, O/M ratio, phases, microstructures and homogeneity. The O/M ratio 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 using CuKα radiation and graphite monochromator. The green density was measured geometrically and sintered density was determined following the Archimedes method. For metallography, the pellets were mounted in Araldite and ground using successive grades of emery paper. The final polishing was done using diamond paste and then etched thermally by holding the pellets at 1250oC for 4 h in air. The grain size was determined by the intercept method. 3. Results The shrinkage versus temperature plots for the various pellets employed in this study are shown in Fig. 1. Here -dl/lo is plotted against temperature, where lo is the initial length of the pellet in the axial direction and dl is its increment. It shows the shrinkage behaviour of pure ThO2 and ThO2 containing 0.25 wt% of Nb2O5 as dopant in air. The effect of dopants on shrinkage has been clearly brought out in this figure. The onset of sintering shifts towards the lower temperature on the addition of a dopant. For pure ThO2, the sintering commences only at temperatures above 960oC, while it starts about 850oC for the ThO2-0.25%Nb2O5. The onset temperature of shrinkage was determined from the dilatometric curves by determining the point at which it deviates from its horizontal path. For this, a line is drawn along the linear part of curve. The deviation from linear path is taken as the onset point. It is possible to compute the shrinkage levels at two different temperatures from Fig. 1 and also the effect of additives on the shrinkage at a particular temperature. At 1400oC, the shrinkage was 3% for pure ThO2 and was 11% for ThO2-0.25%Nb2O5, respectively. The effect of Nb2O5 was found to be very significant especially in the temperature range of 1300 to 1400oC. For the above composition, at temperatures greater than 1400oC, the rate of shrinkage decreases drastically with increase in temperature. It can be seen from Fig. 1 that even at 1650oC, the shrinkage for pure ThO2 in air was found to be less than 8.5%. The shrinkage values of the dilatometric data were converted into percent of theoretical density using the relation : ρs = [1/(1-dl/lo)]3 ρ0 (4) T.R.g. Kutty et al./Science of Sintering, 41 (2009) 103-115 107 ___________________________________________________________________________ where, ρs and ρ0 are the density of the sintered and green pellets, respectively and lo is the initial length. Fig. 2 shows the relative density versus temperature plot for the above pellets. At the highest temperature of 1650oC, a density of around 95% of T.D. was obtained for ThO2-0.25%Nb2O5 when sintered in air. But for pure ThO2, density was only about 87%. -0,02 0,00 0,02 0,04 - dl/l0 0,06 ThO2 0,08 0,10 ThO2+0.25%Nb2O5 0,12 0,14 400 600 800 1000 1200 1400 1600 1800 o Temperature ( C) Fig. 1 Shrinkage curves for ThO2 and ThO2-0.25%Nb2O5 pellets in air. The dl/lo values are plotted against temperature, where lo is the initial length. The densification strain rate, (1/ρ)(dρ/dt), derived from the slope of Fig. 2, is plotted against density (ρ) for the above compositions. The plot is shown in Fig. 3 suggests that densification strain rate increases with relative density for ThO2 and ThO2-0.25%Nb2O5 and reaches a maximum and then decreases. The maximum densification strain rate was at around 77 and 82% T.D. for ThO2 and ThO2-0.25%Nb2O5, respectively. The effect of dopant on densification strain rate is very well demonstrated in this figure. On addition of Nb2O5, ρi drastically increases in the density range of 76 to 82% T.D. 1,00 100 0,95 95 ThO2+0.25%Nb2O5 0,90 90 0,85 85 Relative density ThO2 0,80 80 % T.D. 0,75 75 0,70 70 0,65 65 0,60 60 0,55 55 200 400 600 800 1000 1200 1400 1600 1800 2000 o Temperature ( C) Fig. 2 Shrinkage curves of Fig.1 is replotted as relative density versus temperature for ThO2 and ThO2-0.25%Nb2O5 pellets. 108 T.R.G. Kutty et al. /Science of Sintering, 41 (2009) 103-115 ___________________________________________________________________________ % T.D. 70 75 80 85 90 95 100 0,0005 Atmosphere: air Heating rate: 6K/min 0,0004 ThO2-0.25% Nb2O5 0,0003 dρ/ρdt (s ) -1 0,0002 ThO2 0,0001 0,0000 0,70 0,75 0,80 0,85 0,90 0,95 1,00 Relative density Fig. 3 Densification strain rate versus density plot for ThO2 and ThO2-0.25%Nb2O5 pellets in air. Fig. 4 shows a plot of densification strain rate, (1/ρ)(dρ/dt), versus temperature for ThO2 and ThO2-0.25%Nb2O5 when sintered in air. It is evident from the above that the densification starts only at around 1000oC for the compositions mentioned above. A maximum in ρi occurs at about 1475oC for ThO2 and at 1350oC for ThO2-0.25% Nb2O5. But the striking feature of the Fig. 4 is the five-fold increase in the values of densification strain . rate for ThO2-0.25%Nb2O5 in comparison to pure ThO2 in the temperature range of 1300 to 1350oC. 0,0005 Sintering atmosphere: air Heating rate: 6K/min ThO2-0.25% Nb2O5 0,0004 dρ/ρdt, (s ) -1 0,0003 0,0002 0,0001 ThO2 0,0000 600 800 1000 1200 1400 1600 1800 o Temperature, ( C) Fig. 4 Densification strain rate is plotted against temperature for ThO2 and ThO2-0.25%Nb2O5 pellets. The sintering atmosphere is air. The particle distribution and the volume cumulative graphs for the ThO2 and Nb2O5 powders are shown in Fig. 5 (a) and 5 (b), respectively. ThO2 powder showed a bimodal distribution centering around 0.47 and 3.80 µm, respectively. T.R.g. Kutty et al./Science of Sintering, 41 (2009) 103-115 109 ___________________________________________________________________________ 10 100 8 80 V olum e (% ) 6 60 4 40 2 20 0 0 0.01 0.1 1 10 100 1000 3000 P artic le S iz e (µm ) a) 12 100 10 80 V olum e (% ) 8 60 6 4 40 2 20 0 0 0.01 0.1 1 10 100 1000 3000 P artic le S ize (µm ) b) Fig. 5 Particle size and the volume cumulative graphs for ThO2 (Fig.5a) and Nb2O5 (Fig.5b) powders. From the Fig. 5 (a), it may be noted that about 20% particles are below 1 µm. Nb2O5 powder showed a peak at 3.90 µm, as shown in Fig. 5 (b). The surface area values for ThO2 powders were 1.50 m2/g. A close examination on the shape of the above mentioned powder was carried by SEM. The ThO2 particles exhibited irregular surfaces with angular appearance. X-ray diffraction patterns for ThO2 and ThO2-0.25% Nb2O5 confirm that the compounds are fcc single phased. The lattice parameters were calculated from this high angle scan by least squares method. The lattice parameters of pure ThO2 and ThO2-0.25%Nb2O5 were found to be almost same (0.5591 nm). The grain sizes determined by intercept method were found to be 5 and 12 μm for ThO2 and ThO2-0.25%Nb2O5, respectively. 5 a) b) Fig. 6 Microstructure of ThO2 (Fig.6a) and ThO2-0.25%Nb2O5 (Fig.6b) pellets. These pellets were sintered in air and etched thermally. The typical microstructures of ThO2 and ThO2-0.25%Nb2O5 pellet are given in Fig. 6 110 T.R.G. Kutty et al. /Science of Sintering, 41 (2009) 103-115 ___________________________________________________________________________ 4. Discussion The density of the ThO2 depends up on the following factors: 1. type and the amount of the additives used, 2. fabrication route followed and, 3. sintering atmosphere employed. The importance of densification strain rate of ThO2 and ThO2-0.25%Nb2O5 has been clearly brought out in the Figs 3 to 4. Let us see its significance in understanding the sintering phenomenon. Densification strain rate curves as a function of relative density are sensitive to microstructure and heating schedule. In the first part of densification, ρi increases linearly . with two slopes if the green sample is agglomerated and with one slope if it is agglomerate- free . Many authors have shown that the drop in ρi takes place when the pores break away from the boundary, so that they could only be eliminated by the slower diffusion process . . Several studies [16-17] showed that the number of pores per unit volume has a major influence on the densification kinetics. Therefore, increasing the number of pores per unit volume would enhance densification strain rate at constant ρ and G, and narrowing the pore size distribution would inhibit grain growth and increase the ρi indirectly. In addition, Mayo  showed that densification strain rate is inversely proportional to the pore size for nanocrystalline zirconia. The effect of heating rate on densification strain rate has been reported . The ρi densification strain rate increases almost linearly with the heating rate at a given temperature. Also, the densification strain rate is inversely proportional to the particle size at any temperature . It was observed that materials with a wide particle size distribution sintered easily [12,20]. . A deep understanding of the defect structure and oxygen nonstoichiometry of doped thoria is of crucial importance for its practical use as both an O ion conductor and nuclear fuel . Since the oxygen diffusion and thermo-physical performances depend up on the defect . structures, these properties must be known. In addition, the atmosphere used for sintering itself can influence the effectiveness of formed defects . The addition of a lower valency additive like MgO/CaO to ThO2 is expected to create vacant oxygen sites in ThO2 lattice. The same effect may also be achieved by providing a reducing atmosphere. Similarly, the addition of a higher valency additive like Nb2O5 is expected to create oxygen interstitials in ThO2. The same effect may also be achieved by providing oxidizing atmosphere. Thus either a lower valency additive in a reducing atmosphere or a higher valency additive in an oxidizing atmosphere may be expected to cause activated sintering . Thus the effects of additive and atmosphere reinforce when niobia-added thoria is sintered in air. Two possibilities exist when Nb2O5 is dissolved substitutionally in ThO2. We can have an oxygen interstitial model or thorium vacancy model [22,24-25]. For oxygen interstitial model, using the notation of Kroger and Vink, we have: Nb2O5 ⎯ThO2 → 2 Nb ⋅ + 4Oo + Oi, , ⎯ ⎯ (5) Th the unit cell corresponding to this model is Th3NbO8.5. For thorium vacancy model, we have the following relation: 2 Nb2O5 ⎯ 4 Nb ⋅ + 10Oo + Oi,,,, ⎯→ (6) Th ,,,, the unit cell corresponding to this model is Th2.75NbO8. Here, VTh denotes Th vacancy having charge -4 with respect to the lattice. T.R.g. Kutty et al./Science of Sintering, 41 (2009) 103-115 111 ___________________________________________________________________________ Thus, doping of ThO2 by higher-valency additive may result either in oxygen interstitials or vacant thorium sites. The same defects, namely Oi and VTh, can also be created by an oxidative environment: . ,, 1 / 2O2 ( g ) → Oi + 2 h (7) . ,,,, O2 ( g ) → VTh + 4 h + 2Oo (8) . where h indicates the effective positive charge that is created in accommodating neutral atmospheric oxygen into ionic lattice. Since both Frenkel and Schottky defects are present simultaneously, the formation of oxygen interstitials should decrease the concentration of oxygen vacancies, thereby increasing the concentration of thorium vacancies through Schottky equilibrium . The increase in the concentration of thorium vacancies leads to the increase in thorium diffusion coefficient and thus enhances grain growth. With this background in mind, we will analyze the densification strain rate behaviour of ThO2 bearing compacts. 4.1. Effect of additives The densification strain rate of pure ThO2 shows a gradual increase with density to a maximum value and then shows a decrease (Fig. 3). The smooth increase in the ρi indicates . that the green compacts were free of agglomerates. The presence of agglomerates slows down densification and leads to a densification strain rate curve with two slopes . On addition of 0.25% Nb2O5, the densification strain rate increases gradually up to 76% and then shows a steep increase to a maximum at about 82%T.D. and then decreases and reaches a minimum at 93% T.D. Lange  studied the sintering of alumina powder compacts at constant heating rates of 2.5 to 20oC/min up to 1550oC. He reported that maximum shrinkage rates occurred at the same relative density of 77%, whatever the heating rate. This is in good agreement with the present work, where the maximum in the densification strain rates occur for the samples . covered in this study in the density range of 77-82%. A large increase in the ρi was noticed for ThO2-0.25%Nb2O5 in comparison to pure ThO2 in the temperature range of 1300 to 1350oC. Let us try to find the cause for this phenomenon from the electrical conductivity data. The electrical conductivity generally increases with temperature. The electrical conductivity of ThO2 was measured by Subbharao et al.  and reported that the conductivity values are higher than that of Nb2O5 doped ThO2 at all temperatures. Also, the electrical conductivity of MgO-doped ThO2 was reported to be higher than that of pure ThO2 [30,31]. The variation of electrical conductivity (σ) with respect to absolute temperature (T) can be expressed by the following equation: σT = A exp (-E/kT) (9) where A is the pre-exponential factor and E is the activation energy. Fig. 7 shows the electrical conductivity data for ThO2 and Nb2O5 doped ThO2. Bransky and Tallan  have measured the electrical conductivity of ThO2 as a function of temperature at different oxygen pressures. They reported that the upper limit of oxygen pressure at which ThO2, is stoichiometric is seen to be about 10-6 atm. If the oxygen pressure in the sintering furnace is greater than 10-6 atm, it may be considered as an oxidative atmosphere which would tend to 112 T.R.G. Kutty et al. /Science of Sintering, 41 (2009) 103-115 ___________________________________________________________________________ generate oxygen interstitials in thorium oxide. In the oxidizing region, the increase in electrical conductivity occurred in both low and high temperatures. However, in the reducing atmosphere the increase in electrical conductivity was observed only at higher temperatures. Thus at low temperatures the combination of higher valency additive and oxidizing atmosphere leads to give a higher defect concentration than does the combination of lower valency additive and reducing atmosphere[32,33]. o T ( C) 700 800 900 1000 1100 1200 1300 1400 4 3 σT (Ω cm K) -1 2 -1 ThO2 1 ThO2+Nb2O5 0 1050 1200 1350 1500 1650 T (K) Fig. 7 Electrical conductivity of ThO2 and Nb2O5 doped ThO2 plotted against temperature[29,31]. Matsui and Naito  stated that the electrical conductivity of UO2+x is increased by doping with cations of lower valency than uranium ions, since the lower-valent cations substituted for uranium ions can act effectively as hole donors. Conversely, the electrical conductivity of UO2+x is decreased by doping with cations of higher valency, which act effectively as electron donors. Similarly, the oxygen potentials, ΔGO2 of UO2+x doped with higher valent cations are decreased and the decrease of the oxygen potential is probably due to the decrease of the mean uranium valence by adding niobium ions with higher valence. ThO2 is isostructural with UO2. Incorporation Mg2+ or Nb5+ in the ThO2 lattice generates oxygen vacancies or oxygen interstitials, respectively. The electrical conductivity of ThO2 is decreased by doping with cations of higher valency like Nb5+. This has been clearly brought out in Fig. 7. When one Th+4 ion is substituted by one Nb+5 ion in the ThO2 lattice, the effective positive charge of +1 is imparted on the lattice. Hence the addition of Nb2O5 to ThO2 causes to form significantly high concentrations of oxygen interstitial ions. Metal vacancies will also be formed at the same time but in very low concentrations. An increase in thorium lattice vacancy, increases its diffusion coefficient. In view of the above, it can be expected that the effects of addition of Nb2O5 to ThO2 would be to enhance the diffusion of thorium in ThO2 and to decrease the electrical conductivity. This is verified by the work carried out by Matzke [35,36]. He determined the ratio of the diffusion coefficient of tracer uranium in doped ThO2 to the diffusion coefficient in undoped ThO2 at different temperatures. At 1400°C the ratio was 340 for Nb2O5-doped ThO2 and <0.25 for Y2O3-doped ThO2. From Fig. 7, it is clear that the electrical conductivities of ThO2 and Nb2O5-doped ThO2 pellets diverge at high temperatures. Above 1050°C, the differences in the electrical conductivities values of the above are increasing with the temperature. At 1300°C, the T.R.g. Kutty et al./Science of Sintering, 41 (2009) 103-115 113 ___________________________________________________________________________ electrical conductivity of Nb2O5-doped ThO2 is about 3 times lower than that of ThO2. As mentioned earlier, the maximum densification rate in Nb2O5-doped ThO2 occurs at around 1300°C. The large difference in the electrical conductivity values indicates that the diffusion takes much faster in Nb2O5-doped ThO2 resulting in higher density and larger grain size. From Fig. 3, it can be seen that a drastic decrease in the densification rate has been observed for ThO2-0.25% Nb2O5 pellet when the density was above 84%T.D. As mentioned earlier, for oxide ceramics, diffusion is expected to be the dominant mass transport mechanism during sintering. A theoretical model for densification by diffusional mass transport predicts an equation of the form  (m+1)/2 ε d = (1/3ρ) (dρ/dt) = ADΣ[φ * ]/(GmkT) (10) Where A is a constant, D is the diffusion coefficient for the rate controlled densification mechanism, Σ is the sintering stress or sintering potential, φ is the stress intensification factor and m is the exponent that depends on the mechanism of densification (m = 3 for grain boundary diffusion and m = 2 for lattice diffusion). From equation (10), two main factors which are responsible for the reduction of densification strain rate in ceramics are : 1. The reduction in diffusion coefficient for densification 2. An increase in diffusion distance or grain size Let us see the effect of grain size on densification strain rate. Recently, Lim et al. studied the microstructural evolution during sintering of agglomerate-free alumina powder compacts. They observed that grain growth is significant when density is approximately above 80%. Lance et al.  have shown that in the last part of densification after maximum ρi, coarsening mechanism is promoted. Here, grain size increases significantly leading to a decrease in the densification. The grain size of ThO2-0.25% Nb2O5 pellet was about 12 µm while that of ThO2 sample was only 5 µm, respectively. Therefore the grains have grown . appreciably for ThO2-0.25% Nb2O5 pellet. Therefore the large reduction in densification strain rate above 85%T.D. is due to the grain size effect. 5. Conclusions The densification behaviour of ThO2, and ThO2-0.25% Nb2O5 powder compacts were carried out in a high temperature push-rod type dilatometer. The following conclusions are drawn from the above study: a) The addition of Nb2O5 to ThO2 has caused drastic increase in densification strain rate in the density range of 76 to 82% of T.D. b) The increase in the densification strain rate for ThO2-0.25% Nb2O5 can be explained in terms of its lower electrical conductivity values. c) The decrease in the densification strain rate for ThO2-0.25% Nb2O5 at high densities may be attributed to the grain size effect. d) For ThO2-0.25% Nb2O5, the combination of higher valency additive and oxidizing atmosphere led to a higher defect concentration leading to higher density and larger grain size. 114 T.R.G. Kutty et al. /Science of Sintering, 41 (2009) 103-115 ___________________________________________________________________________ References 1. R.L. Coble, J. Appl. Phys. 32 (1961) 787. 2. D.L. Johnson and T.M. Clarke, Acta Met. 12 (1964) 1173. 3. R.L. Coble, J. Am. Ceram. Soc. 41 (1958) 55. 4. W.S. Young, I.B. Cutler, J. Am. Ceram. 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Примећено је да додатак Nb2O5 довео до драстичног увећања брзине згушњавања у опсегу густине од 76 до 82% теоријске густине. Петоструко увећање вредности брзине за ThO2-0.25%Nb2O5 у поређењу са чистим ThO2 је примећен у температурном опсегу између 1300 и 1350оС. Смањење брзине згушњавања за ThO2-0.25% Nb2O5 на већим густинама се може припиисати ефекту промене величине зрна. Кључне речи: Синтеровање, брзина згушњавања, дилатометар, торијум.
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