Sintering of Particles by Diffusion Mechanisms

The simplest example of diffusion-controlled sintering is the fusion of two spherical liquid droplets under the action of molecular attractions. This was considered by Frenkel in his famous theoiy published in 1945 and later discussed by Kuczynski.  

Frenkel imagined two spherical liquid droplets meeting slowly so that the surfaces became drawn together by the molecular surface attractions, as in Fig. 9.30(a). The liquid surfaces should leap into contact as a result of such attractions, but the growth of the contact spot must then be limited by the viscous resistance to flow of the liquid spheres. At short times, the movement of the spheres towards each other should be proportional to time t and inversely related to the viscosity r, as indicated in Fig. 9.30(b), giving the contact spot diameter d in the equation 

From Equation (9.25) it is evident that the droplets move towards each other as the viscous coalescence occurs. The linear shrinkage of a cubic packing of such droplets would therefore be given by 

There are two problems of sintering which are not explained by the equations such as (9.26) above. The first is that sintering should proceed in proportion to time, but instead stops prematurely the second is that the expected shrinkage rate should be larger for smaller diameter particles but often is not. Both these problems are connected to the fact that powder compacts contain agglomerates, which get stronger and more numerous as the particles get finer. 

Agglomerates compacted together as in Fig. 9.32 sinter like larger particles of diameter D and so shrink more slowly than expected from the primary particle size. Additionally, agglomerates can act like foreign inclusions which inhibit 

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