Some essential processes during liquid phase sintering have been analyzed theoretically. Equilibrium grain shape and the liquid pressure, with liquid content in fully densified specimen, have been calculated. And the relation between the interparticle forces and the liquid pressure due to capillary action has been established. The elimination of isolated pores by liquid flow has been interpreted in terms of liquid pressure.
A model for equilibrium grain shape has been proposed and its surface energy has been calculated with varying liquid content and dihedral angle. The liquid content for the minimum surface energy of a grain was found to be about 26, 19 and 11 vol.% for dihedral angle of 0˚, 30˚ and 45˚respectively. As the liquid content decreases, the increasing rate of surface energy of a grain becomes higher.
An analysis of the relation between interparticle force and liquid pressure based on a model of three dimensional close-placked paticles show that the inter particle force increase with decreasing liquid pressure. This result agree qualitatively with that obtained earlier by using two particle model proposed by Kingery. This three dimensionally close-packed model, however is closer to the real system than the two particle model.
The equilibrium pressure has been calculated from the relation that the mechanical work done to deform a particle would have been equal to the surface energy increase of the particle. This equilibrium liquid pressure corresponds to the liquid pressure in a fully densified specimen with close-packed particles of equal size. The equilibrium liquid pressure increases with increasing the dihedral angles the liquid volume fraction and particle size. When the actual liquid pressure in a specimen is lower than the equilibrium value the polyhedral grains deforms more, but when it is higher than the equilibrium value, the polyhedral grain recovers its shape.
The change of liquid pressure around the spherical pores before and after complete wetting of the particle around the pores by liquid has been calculated. When the wetting angle is higher than 0˚, the liquid pressure diminishes discontinuously by complete wetting. When the wetting angle is 0˚, the liquid pressure diminishes continuously. The driving force of liquid flow into pore will be this liquid pressure drop around the pores. If a pore is larger than the pore of critical size in equilibrium with the liquid pressure, it will not be filled by liquid flow until the liquid pressure reaches the pressure which is in equilibrium with the pore. The critical pore size increase with particle size and wetting angle.
