The morphological stability of continuous intergranular phases: Thermodynamic considerations

A thermodynamic analysis of the morphological stability of continuous intergranular phases, incorporating the number of bounding grains n, and dihedral angle psi as variables is presented. For each n, the minimum thermodynamically unstable wavelength of an infinitesimal amplitude perturbation coincides with the Rayleigh result (2 pi R,) for psi = 180 degrees For n = 2, the ratio lambda(min)/2 pi rR, decreases with psi, approaching a limit of (0.7)(1/2) as psi -> 0 degrees. For n >= 3, lambda(min)/2 pi R-c increases with decreasing psi and tends to infinity as psi + pi - (2 pi/n), or equivalently as the interface curvature vanishes. For fixed psi, the stability increases with n. Several applications and implications of the analysis are discussed.