A diffuse interface description of intergranular films in polycrystalline ceramics

The thermodynamic equilibrium between a thin liquid phase and adjoining grains of a co-existing solid phase is treated, using a diffuse interface formulation applied to a multilayer of liquid and solid phases. The analysis leads to spatial variation in composition, which minimizes the overall free energy, The overall energy includes a gradient-energy contribution. For a fixed overall composition; the equilibrium concentration profile is dependent on the thicknesses of the two phases, relative to the interface width (a characteristic-length scale in the analysis). When the thickness of the liquid phase approaches the characteristic length, its composition can deviate markedly from the bulk liquid-phase composition. In the absence of any stabilizing interactions, such as repulsive structural and electrostatic forces, the analysis indicates that there is a driving force for thinning of the film and a minimum thickness exists at which it becomes favorable for the film to dissolve. Therefore, the observations of equilibrium film thicknesses in certain ceramics imply that, in those materials, additional stabilizing forces must exist between the grains.