On the Equilibrium Thickness of Intergranular Glass Phases in Ceramic Materials

The fundamental question as to whether thin intergranular films can adopt an equilibrium thickness in polycrystalline ceramics is addressed. Two continuum approaches are presented, one based on interfacial energies and the other on the force balance normal to the boundary. These indicate that there will exist a stable thickness for the intergranular film and that it will be of the order of 1 nm. The origin of an equilibrium thickness is shown to be the result of two competing interactions, an attractive van der Waals-disperson interaction between the grains on either side of the boundary acting to thin the film and a repulsive term, due to the structure of the intergranular liquid, opposing this attraction. As both of these interactions are of short range (<lo nm), it is a natural consequence that the equilibrium thickness is of the order of 1 nm, a value commensurate with that observed experimentally in a wide range of ceramics. Two further consequences of importance are indicated. The first is that thin intergranular liquid phases can support a normal stress. The second is that the dielectric constants of the adjacent grains play an important role in determining the thicknesses of the intergranular phase. This leads to the conclusion, consistent with observations, that the thickness of the intergranular phase in polyphase ceramics is expected to be different at boundaries between dissimilar phases than that between like phases.