The theory of sintering

In this section brief description of the theory of sintering and the advantage of sol-gel prepared powders as starting materials are presented. The following sections will be devoted to the representation of sintered ceramics obtained by the sol-gel prepared precursors. 

The theory of bond formation between the crystal particles in plastic fats needs revision. Recently, it has been proposed that a process of sintering —the formation of solid bridges between fat crystals—occurs during... 

V.V. Skorohod, Development of the ideas of Ya. I. Frenkel in the contemporary rheological theory of sintering, Powder Metall. Metal Ceram., 34, 521-527 (1995). 

The shrinkage rate due to power-law creep, 8creep can be evaluated based on the continuum theory of sintering, which deals with the dependences of normalized shear and bulk viscosity modules on porosity, 9, along with the effective sintering. 

Since the development of the classical model and theory, almost all of the phenomena and kinetics of liquid phase sintering have been explained and analysed in terms of the three-stage model and theory. In particular, the theory of the second stage, contact flattening theory, has been the standard theory of liquid phase sintering for decades, despite doubts raised by some research-ergi3,i5,i6,i05,i06 validity of the basic assumptions. Modified contact... 

The theory of coalescence required two stages the first was an agglomeration step which was driven by drying of the latex film, allowing the particles to be pushed together into close-packed adhesive contact, but with small adhesion because of the presence of water the second was a sintering step in which the work of adhesion increased as the last water was removed and elastic deformation occurred with shrinkage. 

A comprehensive theory of sintering should be capable of describing the entire sintering process as well as the evolution of the microstructure (i.e., grain size, pore size, and the distribution of the grain and pore sizes). However, in view of the complex nature of the process, it is unlikely that such a theory will be developed. A more realistic approach, which is adopted in this book, is to first develop an understanding of the densification and coarsening phenomena separately and then explore the consequences of their interaction. 

Figure 11.20 Comparison of the predictions of Scherer s theory of sintering with rigid inclusions with the predictions of the rule of mixtures. The linear strain rate of the composite normalized by the strain rate from the rule of mixtures [Eq. (11.7)] is plotted versus the relative density of the matrix for the indicated volume fraction of inclusions Vf. The dashed curves represent the composite sphere model [Eq. (11.33)], and solid curves, the self-consistent model [Eq. (11.35)]. (From Ref. 33.)...

Mass transport processes in ceramics are of interest due to their importance in materials preparation techniques. The phenomenon of sintering by diffusion is reasonably well understood for metallic systems.For 2-component ionic systems two additional features must be considered. (i) In order to produce an overall transfer of material a net flux of each component will occur, the components having in general unequal mobilities. These fluxes are interdependent since, locally, certain concentration ratios must be maintained. (ii) The concentration of defects will vary with distance from the free surface. As an example of the incorporation of these effects we may consider the changes in morphology of a nearly planar surface to which Mullins theory of mass transport may be applied. For the two component case, eg. NaCl, the equation describing the surface evolution by volume diffusion processes may be written as( )... 

Theory of Sintering of Crystalline Materials describes models based on transport by diffusion. The low initial density of gels and the strong tendency toward grain growth make it difficult to sinter to full density. 

Very little information is available on the kinetics of sintering of gel fdms. The data of Brinker and Mukherjee [75], shown in Fig. 32, indicate that a film densifies faster than a bulk gel made from the same preparation, even though the film has lower surface area. This is contrary to the theory illustrated in Fig. 14, which predicts that a film will sinter more slowly than an unconstrained gel, since a film can shrink only in the direction perpendicular to the substrate. The experimental results suggest that the films... 

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