Scaling Laws for Sintering

Because the surface energy per volume is larger for small particles and because the fundamental driving force for sintering is surface-energy reduction, compacts composed of smaller powders will typically sinter more rapidly. Smaller powders are more difficult to produce and handle therefore, predictions of sintering rate dependence on size are used to make choices of initial particle size. Herring s 

Suppose that two sintering systems, S and B, are identical in all aspects except their size.15 Each length dimension of system B is A times as large as the corresponding dimension of system S. Under identical conditions and provided that the same sintering mechanism is operative, the ratio of sintering rates can be determined from the relative sizes of the specimens. 

The current, 7, is proportional to the diffusion potential gradient, V, and to the cross-sectional area, A, through which this flux flows. Therefore, 

Suppose that the plane A is the bisector between the source of atoms and their sink (i.e.. the sources and sinks listed in Table 16.1). The component of diffusion 

15The systems may be similar powder compacts of the same powder material but, differing particle sizes, or they may be model systems such as those illustrated in Figs. 16.6 and 16.9 but with all corresponding length dimensions scaled similarly. 

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