A diffuse interface description of intergranular films in polycrystalline ceramics

The thermodynamic equilibrium between a thin liquid phase and adjoining gra ins of a co-existing solid phase is treated, using a diffuse interface form ulation applied to a multilayer of liquid and solid phases. The analysis le ads to spatial variation in composition, which minimizes the overall free e nergy, The overall energy includes a gradient-energy contribution. For a fi xed overall composition; the equilibrium concentration profile is dependent on the thicknesses of the two phases, relative to the interface width (a c haracteristic-length scale in the analysis). When the thickness of the liqu id phase approaches the characteristic length, its composition can deviate markedly from the bulk liquid-phase composition. In the absence of any stab ilizing 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 f ilm to dissolve. Therefore, the observations of equilibrium film thicknesse s in certain ceramics imply that, in those materials, additional stabilizin g forces must exist between the grains.