A. Surface EnergySurface energies are the major factors determining behavior during liquid phase sintering. The minimum criteria for successful liquid phase sintering are i) a low temperature liquid, ii) solubility of the solid in the liquid, and iii) liquid wetting of the solid grains (1). These conditions result in a reduction in surface energy with liquid spreading. At high volume fractions of solid, the elimination of porosity and its associated surface energy requires shape accommodation on the part of the solid grains, which IS dependent on solubility of the solid in the liquid. Furthermore the rate of microstructural coarsening during liquid phase sintering, as seen by the grain growth rate, increases with the solid-liquid surface energy. These factors lead to the conclusion that surface energy is the major driving force for densification.The surface energy is the work needed to expand a surface normal to itself. Inherently, surface energy is traced to interatomic forces. Consequently, material parameters like the heat of vaporization, hardness, elastic modulus, and melting temperature provide a rough gauge of the surface energy (2).To better understand surface energies, contrast the interior and exterior regions of a solid. The interior is uniform with homogeneous bonding. Thus, the time averaged net force on an atom is zero. In contrast, the exterior surface represents an unbalanced force situation. The bonding is not homogeneous and the time averaged net force is directed towards the interior. As a consequence, the exterior regions move toward a minimized surface area with a lower surface energy. For a fluid, the liquid-vapor surface energy is uniform in all directions. Thus, for simple liquids, surface energy is characterized by a single value which decreases with increasing temperature. The liquid-vapor surface energy lLV dependence on temperature T is given as follows (3,4): (3. 1) 43 R. M. German, Liquid Phase Sintering
