Intermediate Stage Contact Flattening

Under these conditions, a compressive pressure is exerted between the two particles due to the capillary pressure and the surface tension of the liquid. (See Section 14.2.) Because of this compressive pressure at the contact area, the chemical potential of atoms at the contact area is higher than elsewhere (i.e. at the surface of the neck region). Therefore, the solid at the contact area dissolves and the dissolved material is transported to the surface of the neck. As a result of this material transport, the contact area increases and the grain shape is accommodated (contact flattening). At the same time, the pore shrinks continuously and the compact is densified. Kingery considered the pressure 

The material transport by diffusion through a thin liquid film at the contact area is similar to that in Coble s intermediate stage model.Therefore, 

This equation suggests that the shrinkage is proportional to one-third of the sintering time. 

The rate of material transport controlled by interface reaction was considered to be proportional to a reaction constant and the contact area. Then, 

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