The equilibrium morphologies of the inner grains and the liquid menisci between surface grains for a uniformly intermixed grain-liquid system are analyzed. The driving force of liquid flow into isolated pores during liquid phase sintering is also analyzed from the curvature of the liquid menisci around the pores.
The minimum interface energy configurations of the grainliquid mixture are determined for various dihedral angles and liquid content by a numerical analysis of a model which consists of a rhombic dodecahedron grain in contact with liquid matrix at its curved surfaces along truncated edges and corners. For dihedral angles Φ greater than 90˚ the total interface energy E increases monotonically with the liquid volume fraction $V_ℓ$. For Φ=0˚, E decreases with $V_ℓ$ until the grains become spherical at $V_ℓ = 26%$. For 0˚<Φ≤75˚, E vs $V_ℓ$ curves show the minima which represent the most stable configurations to be obtained when $V_ℓ$ can be freely varied. The slope of E vs $V_ℓ$ curve is shown to be an effective pressure on specimen surface, which represents the driving force for changing the grain shape with a corresponding change of $V_ℓ$ while keeping the grain volume constant.
The menisci curvature required to maintain the contactflattened grain with a limited $V_ℓ$ is calcurated from the condition that the capillary force is balanced against the grain sphering force on the specimen surface. The radius of the menisci at equilibrium increases with $V_ℓ$. Its dependence on the dihedral angles, wetting angles and the ratio of the interfacial energies between the liquid-vapor and solid-liquid phase is also described. The grain-meniscus system maintains a geometrically similar shape with respect to the change of the grain size; hence the meniscus radius increases in proportion to the grain radius. It is proposed that the difference between the capillary force and the sphering force is the meaningful driving force for grain shape accommodation during liquid phase sintering.
Finally, the pore filling process is described with a system containing a spierical pore in which the grain shape is in equilibrium with liquid menisci. When grain growth reaches a critical point, he liquid menisci around the pore becomes spherical and the driving force for filling the pore rapidly increase as liquid flow into it. The critical grain size required for filling a pore increases linearly with pore size. The pore filling behaviors in the real system which contain many pores with irregular shape are discussed quaqlitatively.
