(509e) Rippling Instabilities on the Surface of Stressed Crystalline Solids

Morphological instabilities on surfaces of stressed solids and the resulting pattern formation are of major fundamental and technological significance toward improving materials function and reliability and developing innovative directed assembly processes for nanotechnology. Such a well-known phenomenon is the Asaro–Tiller/Grinfeld (ATG) instability, which leads to the formation of a regular pattern of crack-like grooves emanating from the surface of a stressed elastic solid and deepening by surface diffusion.

We have carried out a systematic analysis of morphological evolution of stressed solid surfaces under the action of an electric field, or a temperature gradient, or the simultaneous action of both and reported that sufficiently strong external fields can inhibit the ATG instability and prevent surface cracking; a linear stability theory predicted fairly accurately the current-induced stabilization of surface morphology in stressed elastic solids. However, complex aspects of surface morphological evolution and pattern formation are not accounted for by the linear theory.

Using self-consistent dynamical simulations according to a well-tested fully nonlinear model of surface morphological evolution, we have studied the surface morphological response of stressed solids both in the absence of and under the simultaneous action of external fields focusing on low-amplitude long-wavelength perturbations from the planar surface morphology. We find that in addition to the ATG instability, a long-wavelength tip-splitting instability may be triggered forming a pattern of secondary ripples on the surface; rippling occurs in the absence of external field application, as well as for weaker-than-critical applied external fields. We have developed a nonlinear wavelength selection theory to analyze the formation of such secondary surface ripples. We have also carried out a comprehensive simulation study to characterize the ripple formation, identify the critical wave-length for rippling, and determine the dependence of the critical wave number for the onset of rippling on the applied external field strength.. Finally, we have examined the effect of the Arrhenius temperature dependence of the surface diffusivity, the strongest temperature dependence of all the relevant material properties, on surface rippling under the action of an externally applied temperature gradient.