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Introduction In the early 1980s Prof. Bowen at Massachusetts Institute of Technology 1 2 advanced the concept that sintered ceramic bodies could be improved by decreasing the defects in green bodies. In addition, his group advanced the idea that ideal green bodies should be composed of monodisperse particles packed into an ordered array. They used the hydrolysis of metal alkoxides to produce narrow size distribution sol-gel powders (i.e., amorphous). These powders were allowed to settle under the force of gravity into an ordered array which was dried and sintered. Sintering took place at much lower temperatures and at faster rates than traditional ceramic processing (e.g., broad size distributions of crystalline powders). Improvements in strength and toughness of the sintered body were never d e m o n s t r a t e d by Bowen's group for these novel ceramics. Ordered particles have packing faults which lead to ordered domains, as shown in Figure 1, similar to grains in polycrystalline materials. When sintered, the ordered domains shrink separately and pull away from each other as shown in Figure 2. This leads to defects in the sintered body of sizes similar to those of the ordered domains which can encompass as many as 10,000 particles. These ordered domains lead to weakness in the sintered body according to Griffith's theory. The long-range ordering of particles must be p r e v e n t e d to improve the microstructure. Random close packing is therefore desired. By analogy with Lindemann's melting rule, random close packing

where G0 is the initial volume of the compact, K is the densification rate constant given by

Jo

'(/; 7(0*

where f(r) is the particle size distribution usually taken to be log-normal, n is the time dependent factor, m is the size dependent factor, and the proportionality constant, q, is different for various sintering mechanisms given by Chappel et al.4 For example, n = 2, m = 2 and q = 27 z y2/(16 T)2) for viscous diffusion sintering (y = surface free energy, 7) = viscosity, and z = coordination number). The effect of the width of the particle size Figure 2. Partly sintered ordered packing distribution on the densification rate conof monodisperse particles, from F. Lang, stant, K, is shown in Figure 4. Increasing the log normal d i s t r i b u t i o n w i d t h J. Am. Ceram. Soc. (in press). parameter az from O (monisized) to 1.0 (ground powders) decreases the sintering rate from 1.0 to —0.01 when either lattice can be obtained by using particle size distributions where the standard deviation is greater than 10%. There are two reasons for the faster sintering at lower temperatures observed with Bowen's work.2 One reason is the use of sol-gel particles. Sol-gel particles are produced by the aggregation of small —0.01 /xm particles which are in turn composed of aggregates of yet smaller particles as shown in Figure 3. These particles have a classic fractal geometry3 where the fractal dimension, D, is defined as D = 3.0 + In P/ln S where P is the packing fraction of each aggregate and S is the gen