Sintering models

Figure C2.11.6. The classic two-particle sintering model illustrating material transport and neck growtli at tire particle contacts resulting in coarsening (left) and densification (right) during sintering. Surface diffusion (a), evaporation-condensation (b), and volume diffusion (c) contribute to coarsening, while volume diffusion (d), grain boundary diffusion (e), solution-precipitation (f), and dislocation motion (g) contribute to densification.

W.S. Coblenz, J.M. Dynys, R.M. Cannon, and R.L. Coble. Initial stage solid-state sintering models A critical analysis and assessment. In G. C. Kuczynski, editor, Proceedings of the Fifth International Conference on Sintering and Related Phenomena, pages 141-157, New York, 1980. Plenum Press. 

TABLE 16.6 Intermediate Stage Sintering Models Parameters fiar Simplified Models Represented by the Equation = K[(.y ClD)nR BTmf- t)... 

Generalizing the sintering model discussed in the previous section to a fractal ceramic compact requires that equation 16.46 be used for the shrinkage of each generation of particles. Equation 16.55 can be rewritten as a product of the packing fractions of each generation, i, as a function of sintering time ... 

The complex nature of the sintering process in real powder systems coupled with the drastic simplifications assumed in the models means that quantitative testing of the sintering models is seldom meaningful. Nevertheless, the models clearly indicate the parameters that must be controlled to promote densification. Because of the strong... 

While the observed dependence of the densification rate on particle size, applied pressure, and temperature follows qualitatively the predictions of the sintering models, factors such as particle packing, sintering atmosphere, and heating schedule can have a decisive effect on the sintering process. 

The most commonly used technique for sintering studies of model catalysts, TEM, has two variations (1) a macroscopic mode in which the sample is examined before and after various treatments without attempting to examine the exact same collection of crystallites or (2) a microscopic mode in which the same area of the sanqile is examined befne and after thermal treatments. Examples of TEM micrographs of fresh and oxygen-sintered model Pt/alumina taken in the macroscopic mode are shown in Figure 1, while same area microgr hs for a fresh and... 

The influence of temperature and time on densification can be estimated by using so-called density diagrams (sintering maps) [5.85], which are based on approximate sintering models. Nevertheless, empirical rate equations are used for industrial purposes to calculate the necessary sintering times at different temperatures. 

Figure 10.11 (a) Initial stage of sintering model represented by spheres in tangential... 

Clearly, the sintering kinetics will be different during each of the aforementioned stages. To further complicate matters, in addition to having to treat each stage separately, the kinetics will depend on the specific atomic mechanisms operative. Despite these complications, most, if not all, sintering models share the following common philosophy ... 

Figure 24.10 Data from Kang, S.-J.L. and Jung, Y.-I. (2004) Sintering kinetics at the final stage of sintering Model calculation and map construction, Acta Mater. 52, 4373.

Olevsky EA, Wang X, Maximenko A, Meyers MA (2007) Eabrication of net-shape functionally graded composites by electrophoretic deposition and sintering modeling and experimentation. J Am Ceram Soc 90 3047-3056... 

For the final stage sintering models, the powder system is treated as an array of equalsized tetrakaidecahedra with spherical pores with the same size located at the comers, as shown in Fig. 5.15d. The tetrakaidecahedron has 24 pores, with one at each comer. Because each pore is shared by four tetrakaidecahedra, the pore volume for every one tetrakaidecahedron is Vp = (24/4)(4/3)a r, with r being the radius of the pore. According to Eq. (5.153), the porosity per tetrakaidecahedron is given by... 

Analytical sintering models are based on the idealized models for the three stages of sintering shown in Fig. 8.8. Because the vacancy concentration under the neck surface is not affected by the external stress, Eq. (5.134) is still valid, i.e., there is... 

Johnson DL, Cutler IB (1963) Diffusion sintering. 1. Initial stae sintering models and their application to shrinkage of powder compacts. J Am Ceram Soc 46 541-545... 

The importance of the grain boundary as a source of material for sintering was not recognized when various sintering models were proposed in the... 

According to Coble s final stage sintering model, the rate of pore volume change AVpjAt by lattice diffusion is expressed as... 

Koblenz, W. S., Dynys, J. M., Cannon, R. M. and Coble, R. L., Initial stage solid state sintering models. A critical analysis and assessment, in Sintering Processes, Mater. Sci. Res., Vol. 13, Plenum Press, New York, 141-57, 1980. 

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