Sintering scaling laws

The values of m given above conform to Hemng s scaling law (1950) which states that since the driving force for sintering, the transport length, the area over which uansport occurs and the volume of matter to be transported are proportional to a, and respectively, the times for equivalent change in two powder samples of initial particle size ai q and 2,0 are... 

If sintering occurs by grain-boundary diffusion, the ratio of rates will be the same as for the surface-diffusion case, A-4. A A-1 scaling law can be derived for viscous flow and a A-2 law applies for vapor transport [32],... 

The sintering rate due to boundary diffusion and crystal diffusion will be proportional to Db and DXL, respectively. The scaling laws show that the sintering rate due to boundary diffusion will decrease by the factor A 4 when the particle size is increased by the factor A. The corresponding factor for sintering by crystal... 

Show that a A 4 scaling law holds for the sintering of a bundle of parallel wires by means of grain-boundary diffusion, which was analyzed in Section 16.1.2. 

The exponent a in the scaling law can also be deduced from the sintering equations in Table 4.2 without following Herring s derivation. The sintering... 

Derive the scaling law of sintering by lattice diffusion. Under an applied external pressure Pappi. 5 2y/r), how should the scaling law be modified ... 

To establish the scaling laws of densification and growth at the final stage of sintering, the interaction between the two phenomena has therefore to be considered. For simplicity, we may make the following assumptions ... 

The scaling laws do not assume a specific geometrical model. Instead, the main assumptions in the model are that during sintering (1) the particle size of... 

An important application of the scaling laws is the determination of how the relative rates of sintering by the different mechanisms depend on the particle size of the powder system. This type of information is useful, for example, in the fabrication of ceramics with controlled microstructure. As we observed earlia-, some mechanisms lead to densification while others do not, so the achievement of high density requires that the rates of the densifying mechanisms be enhanced over those for the nondensifying mechanisms. 

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