M. AMINZARE Department of Materials and Metallurgical Engineering, Iran University of Science and Technology Tehran, Iran

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1 2 nd International Conference on Ultrafine Grained and Nanostructured Materials Center of Excellence For High Performance Materials School of Metallurgy and Materials Engineering University College of Engineering, University of Tehran Tehran, Iran Nov An Investigation on Sintering Behavior of Ultra Fine Al 2 O 3 Powder by Master Sintering Curve Method M. AMINZARE Department of Materials and Metallurgical Engineering, Iran University of Science and Technology Tehran, Iran masoudaminzare@yahoo.com M. MAZAHERI Institute of Physics of Complex Matter, Swiss Federal Institute of Technology Lausanne (EPFL) 1015 Lausanne, Switzerland mehdi.mazaheri@epfl.com F. GOLESTANI-FARD Department of Materials and Metallurgical Engineering, Iran University of Science and Technology Tehran, Iran golestanifard@iust.ac.ir H.R. REZAYI Department of Materials and Metallurgical Engineering, Iran University of Science and Technology Tehran, Iran hrezaie@iust.ac.ir Received Day Month Day Revised Day Month Day The Master sintering curve (MSC) has been developed to study the sintering characteristics of powder compacts. In the present study, master sintering curve was constructed to analyze the densification behavior of ultra fine alumina powder (~ 150 nm). The green bodies were prepared by pressure filtration (PF) with green density of 65%. After that a sensitive dilatometer was used to record the shrinkage/ shrinkage rate of the specimens up to 1400 C. The effect of heating rate on densification was also investigated under non-isothermal sintering in three different heating rates of 2, 10 and 25 o C/min. The apparent activation energy for densification of 605±15 kj.mol -1 was calculated using dilatometry data applied into combined-stage sintering model. In the microscopic Corresponding author. Tel: addresses: golestanifard@iust.ac.ir (F. GOLESTAN-IFARD) 1

2 2 M. AminZare, M. Mazaheri, F. Golestani-fard, H. R. Rezayi point of view, heating rate not only was affected on sintering behavior but also by increasing the heating rate the shrinkage of the samples increased from 875 (for 25 C min -1 ) to 443 nm (for Y C min -1 ). Keywords: Master sintering curve, Ultra fine alumina, Densification behavior. 1. Introduction Sintering as a complicated process involves densification of powder and microstructure evolution through the action of different transport mechanisms. It is recognized that the sintering behavior depends on many characteristics of powders and sintering conditions. For instance composition of raw materials, particle size and size distribution and last but not last shaping methods. 1-4 Sintering methods have been widely investigated due to their technological importance. In sintering stage, it is important to predict what is/are the mechanism(s) controlling the microstructure evolution and densification. Since past decades, many research attempts have been paid to modeling of the sintering by computer simulations. 5, 6 However, these models are limited to a single matter transportation process and only one of the stages of sintering and therefore have little success. Master sintering curve (MSC) is one of the promising and practical approaches to predict and control sintering which presented by Su and Johnson 7 for first time, based on the combined stage sintering model. 8 The MSC model describes the sintering behavior for a given powder regardless of the sintering regime. It also can be used to compare the sinter ability of different powders 9-11 and to estimate the apparent activation energy for sintering. 12 In the MSC theory two equal functions are introduced; Φ(ρ) which is function of density and Θ(t,T(t)), which is as a function of temperature and time. This relationship is given by: where Q is the apparent activation energy for sintering, R the gas constant, T the absolute temperature, t the time. Θ(t,T(t)) includes only temperature, time, and an apparent activation energy (Q) and is a function of thermal history. The relationship between density (ρ) and Θ function is defined as the master sintering curve 12. In this model, a unique MSC can be obtained if only one diffusion mechanism dominant in sintering and the microstructure is a function only of density. In the present work, sintering behavior of an ultra fine Al 2 O 3 powder with mean particle size of 150 nm was studied. The apparent activation energy for sintering calculated and the master sintering curve has been plotted. Furthermore, effect of heating rate on densification and final grain size was studied. 2. Experimental procedure Φ( ρ) = Θ( t, T ( t)) 1 Q exp( ) dt T RT An ultra pure Al 2 O 3 powder as raw material (Taimei Chemicals Co. Ltd., Tokyo, Japan) with a particle size D 50 of 0.15µm was used. The microstructure of samples was characterized by scanning electron microscopy after polishing using diamond pastes (10, t 0 (1)

3 An Investigation on Sintering Behavior of Ultra Fine Al 2O 3 Powder by Master Sintering Curve Method 5, 1 and 0.05 µm) and thermal etching. (SEM, Philips XL30). The theoretical density, surface area and primary particle size of powder as reported by supplier is 3.96 g.cm -3, 14.5 m 2.g -1, 0.1 µm, respectively. The powder was stabilized by a polyelectrolyte (Dolapix CE64, zschimmer-schwarz, lahnstein, Germany) in aqueous slurry with 53vol% alumina for pressure filtration. The pressure filtration of slurries on an organic membrane with 0.2 µm pore size at a pressure of 40 MPa was preceded in a cylindrical steel die. Detail of pressure filtration method was presented elsewhere 13. The green density was 62.4% ±0.2 theoretical density (TD) by using measuring weight of the specimen. Non-isothermal sintering was performed at different heating rates of 2, 10 and 25 C.min -1 by using a sinter-dilatometer (TAM 801, NETZCG, Germany). The relative densities of the sintered specimens were calculated using the following equation 14 : 3 ρ = s (1 dl / L + α T T dr R + α T T 2 0 ( 0))(1 / 0 ( 0)) 1 ρ g (2) where dl/l 0 and dr/r 0 are instantaneous linear and radial shrinkage which obtained by the dilatometer test, previously; L 0 is the initial length and R 0 is the initial diameter of the specimen, ρ g is the green density, T 0 is the room temperature and α is the coefficient of thermal expansion. 3. Result and discussion SEM micrograph of the as received powder is shown at Fig. 1. As seen, The powders of spherical particles have narrow distribution and no hard agglomeration can be observed. The average grain size of this powder is about 150 nm. Fig.1 Scanning electron microscopy of ultra pure alumina powder.

4 4 M. AminZare, M. Mazaheri, F. Golestani-fard, H. R. Rezayi Free strain and strain rate of powder compacts during nonisothermal sintering at three different heating rates of 2, 10 and 25 C.min -1 up to 1400 o C are shown in Fig. 2 a and b. Free strain was estimated as ε free = (ε z + 2ε r )/3 where ε z is the longitudinal and ε r is the radial true strains. 13 As is observable in Fig. 2 b, at any heating rate, the strain rate increased to a maximum and then decreased. Additionally, the maximum of strain rate occurs at the range of 80-85% TD. Hilli et al. 15 has reported similar results for monodoped and mixture doped alumina powders.. Fig. 2 Effect of heating rate on the free strain (a) and strain rate (b) of alumina compact at three different heating rates. Fig. 3 shows the densification rate of compact bodies with different heating rates. It is observed that the maximum values of densification rate for are a function of the heating rates. For instance, these values were changed from 1259 to 1332 by increasing the heating rate from 2 to 25 C.min -1. It means that, the maximum densification were dependent on heating rate of sintering regime. Such a behavior has been previously referred by Bernard-Granger and Guizard for pure alumina 16 and 3Y-TZP. 17 Fig. 3 Densification rate of the alumina compact as a function of temperature which different heating rates used.

5 An Investigation on Sintering Behavior of Ultra Fine Al 2O 3 Powder by Master Sintering Curve Method Fig. 4 shows the linear relationship between the density and heating rate (in log-log scale) at intermediate sintering stage (approximately ) which might be an indicator of suppressed grain growth. 18, 19 Mazaheri et. al. recently has been reported the same behavior for 3Y-TZP system Fig. 4. Density versus heating rate at various temperatures in log-scale. According to Eq. 1. construction of MSC required the value of activation energy. For 7, 12 this purpose, the apparent activation energy estimated by the least square method. Therefore, the activation energy was founded to be 605kJ.mol -1 with the accuracy about ±15KJ/mol. The activation energy of densification is known as the main characteristic of sintering which can explain the fundamental diffusion mechanism during the sintering process. It is not easy to determine the diffusion mechanism which is responsible for different stages of densification. MSC assumes that only one diffusion mechanism govern in sintering. 7 Although, sintering of most materials is combination of different diffusion paths such as volume, surface and grain boundary diffusion mechnisms 21, 22, the value of activation energy which determined by MSC for sintering mostly can show deviation from grain boundary or volume diffusion activation energy and relates to mixture of different mechanisms that dominant during sintering. 23 In the other words, when one of the diffusion mechanisms is the demonstrated mechanism in the sintering stages, the other ones were being the limiting steps. Hence, it seems that the present value (605±15 kj.mol -1 ) is not exactly activation energy for grain boundary diffusion or volume diffusion but also it should be apparent activation energy and can be assumed as contribution value between different diffusion mechanisms from beginning to end of the sintering process.

6 6 M. AminZare, M. Mazaheri, F. Golestani-fard, H. R. Rezayi Using the abovementioned activation energy value for sintering, MSC has been constructed (Fig. 5). This indicates that there should have been a general curve, MSC, which is use as a practical approach to predict densification under sintering condition. Fig.5. Master sintering curve for alumina powder prepared by pressure filtration. The MSC curve can be used as a useful tool for designing the best heating profile for getting the desired final density. Table 1. summarized the prediction datas of the sintering time in seconds required for alumina samples to reach a particular density at a constant temperature 24 which extracted from MSC curve. For instance, in order to have a 97% relative density, the samples is sintered for 12 minutes at 1400 o C, or 45 minutes at 1350 o C, or 3 hours at 1300 o C; while it is not acceptable at 1200 o C due to long time sintering (approximately 3days). Table 1. The predictions data for sintering time in seconds for ultra fine alumina green bodies processed via pressure filtration Relative density (%) Temperature ( o C) 80% 85% 90% 95% 97% Fig. 6 demonstrate, show the final microstructure of alumina sample which sintered at 1400 C with different heating rates. The microstructure observation shows that the heating rate has an important affect on the final grain size of samples. For example, the mean grain size was founded to be about 875 nm at 2 o C.min -1, 650 nm at 10 o C.min -1 and

7 An Investigation on Sintering Behavior of Ultra Fine Al 2O 3 Powder by Master Sintering Curve Method 443 nm at o C.min -1. In addition, samples were composed of polygonal grains, which support the evidence of solid-state sintering. 7 Fig. 6. SEM micrographs of polished and thermally etched surfaces of alumina samples sintered until 1400 o C with heating rate of 2 (a), 10 (b) and 25 o C.min -1 (c). 4. Conclusion In this study construction of the Master Sintering Curve theory for non-isothermal sintering of alumina were done. Non-isothermal sintering of alumina was carried out in a sensitive dilatometer at three different heating rates. It was concluded that the densification process took place by the conventional solid-state diffusion mechanism which started at 1000 C and completed at above 1350 C. A MSC curve was constructed for densification data and also the activation energy for sintering was estimated about at 605±15 kj.mol -1 which shows that it should be apparent activation energy and can be assumed as contribution value between different diffusion mechanisms from beginning to end of the sintering process. References 1. A. Krell, and P. Blank, Journal of the European Ceramic Society, 16, (1996). 2. C. Legras, C. Carry, P. Bowen, H. Hofmann, Journal of the European Ceramic Society, 19, (1999). 3. M. Azar, P. Palmero, M. Lamnardi, V. Garnier, L. Montanaro, G. Fantazzi, J. Chevalier, Journal of the European Ceramic Society, 28, (2008). 4. A. Krell, and J. Klimke, Journal of the American Ceramic Society, 89, (2006). 5. R. L. Cobel, Journal of Applied Physics, (1961). 6. G. N. Hassold, I. W. Chen, D. J. Srolovit, Journal of the American Ceramic Society, 73, (1990). 7. H. Su, D. L. Johnson, Journal of the American Ceramic Society, 79, (1996). 8. J. Hansen, R. P. Rusin, M. Teng, D. L. Johnson, Journal of the American Ceramic Society, (1992). 9. K.G. Ewsuk, D.T. Ellerby, C.B Diantanio, Journal of the American Ceramic Society, 89, (2006). 10. M.S. Nikalic, V.P. Pavavic, N. Labus, B. Materials Science Forum, 494, (2005). 11. C.B. Diantanio, K.G Ewsuk, Ceramic Transaction, (2005).

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