Constrained sintering of a sphere with radial density gradient: Viscous model
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I.
INTRODUCTION
SINTERING is both a traditional craft and an important subject in ceramic science. In advanced ceramics, a primary objective in ceramic sintering is the densification of a ceramic to yield a homogeneous microstructure to allow reproducible and high value properties. The overall driving force for sintering is a reduction of the Gibbs free energy of a powder compact brought about by the transfer of material, such that the total pore surface and therefore the overall volume of the powder compact are reduced. Both densification and grain growth result in an overall decrease in Gibbs free energy during sintering. The fast firing or rapid sintering technique has been developed to achieve maximum density and minimize grain growth.[1] In general, the enthalpy associated with the densification is higher than that associated with grain growth. The principle underlying fast sintering is that the green body is heated rapidly to surpass the temperature range at which high rates of grain growth take place, while still maintaining a relatively low densification rate, and to reach as quickly as possible the temperature range where the densification rate is higher than the grain growth rate. With fast fire sintering, full density can be achieved in a short time with only limited grain growth. However, a quite different phenomenon was observed when the technique was applied to densify nanocrystalline ZrO2-3 mol pct Y2O3;[2] in this case, densification could not be taken to completion by means of a very high heating rate. In addition, it was found that a density gradient occurred even in small samples (0.2 g in weight). The surface layer was shown to be dense, but the center of the sample hardly densified. As the sample size increases, then this phenomenon, generated by the high heating rate, becomes more serious. A second important phenomenon was found to occur during densification of large pieces of ZrO2 ceramics. Experimental results on the sintering of 3Y-TZP showed that JIE LUO, Research Fellow, and R. STEVENS, Professor and Head, Department of Materials Science and Engineering, are with the University of Bath, Bath, United Kingdom BA2 7AY. YUHE REN, formerly Research Fellow, School of Mathematical Science, University of Bath, United Kingdom, is Research Associate, Dept. of Computing, Imperial College of Science, Technology & Medicine, London, United Kingdom, SW7 2BZ. Manuscript submitted March 25, 1997. METALLURGICAL AND MATERIALS TRANSACTIONS B
large samples required a higher temperature and a longer dwell time to densify.[3] A similar phenomenon has been observed in our laboratory when firing large components of fine ZrO2 ceramics.[4] A significant density gradient was generated in the zirconia bodies; the outside layer was found to have a high density and center regions to have a lower density (Figure 1 shows an example). ZrO2 ceramics have low thermal conductivity, and most importantly, the fine powder compact has a thermal conductivity less than 1/10 that of the bulk ceramic under discussion.[4] The ther
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