Stability analysis of solid morphology incorporating surface elasticity and surface tension

This paper is primarily focused on exploring the morphological instability conditions inherent in nanostructured solid surfaces. Employing the constitutive equations of Gurtin–Murdoch model, we examine how surface elasticity and surface tension exert their influence on surface relief formation. Within this framework, we posit that the surface instability of the solid surface is instigated by surface diffusion processes propelled by the nuanced interplay of surface and bulk energy across the undulated surface. To distinguish the strain field along the undulated surface, we navigate the solution space of the plane elasticity problem, accounting for plane strain conditions. Our investigation tracks the linearized evolution of the surface, capturing the change in the amplitude of surface perturbations with time. Thus, the presented linear stability analysis sheds light on the precise conditions that initiate the early-stage increase in surface relief amplitude. This nuanced exploration provides not only a theoretical foundation, but also practical insights into the intricate mechanisms governing the morphological stability of nanostructured solid surfaces.