Hillock formation by surface drift-diffusion driven by the gradient of elastic dipole interaction energy under compressive stresses in bi-crystalline thin films

Abstract

We investigated surface drift diffusion induced grain boundary (GB) grooving and ridge (hillock) formation and growth, under the combined actions of the capillary forces and applied uniaxial compressive stresses, in bi-crystal thin films with dynamical computer simulations. In the present theory, the generalized driving force for the stress induced surface drift diffusion includes not only the usual gradient of the elastic strain energy density, but also the elastic dipole tensor interaction energy. During the morphological evolution of GB ridge formation and growth, triple junction (TJ) displacement and its velocity are continuously tracked down in order to resolve precisely the crossover time and depth at which velocity sign inversion takes place. An incubation time for the onset of the ridge growth stage coupled to the GB-TJ displacement velocity inversion is defined and its dependence on the stress is investigated. This analysis implies that the ridge growth stage is not controlled by Ziegler’s ‘maximum entropy production principle’ but rather Prigogine’s ‘minimum entropy production hypothesis’ for the stationary non-equilibrium states in complex systems, which are exposed to external applied body forces and surface tractions. Keywords: Surfaces and interfaces; Grain boundary grooving; Non-equilibrium thermodynamics; Surface/grain boundary diffusion; Compressive stresses; Thin films DOI: 10.17350/HJSE19030000010 Full Text: