Evolution of a Surface-Roughness Spectrum Caused by Stress in Nanometer-Scale Chemical Etching

Abstract

It is reported that a flat free surface of a stressed solid is configurationally unstable under chemical etching and the surface roughness grows with different rates for different spatial frequencies. The theory described in this Letter predicts that with a shallow chemical etching the roughness with spatial frequency below a critical value grows while the roughness of higher frequency decays. The theory was verified via an atomic force microscope experiment with aluminum. This study provides a simple experimental method to measure stress in metals and ceramics.

Phase field modelling of stress corrosion

“…The strain energy and the chemical energy provide driving forces for dissolution and transport of molecules. The observation is an evolving surface waviness that has been explained theoretically by [3][4][5]. The spectrum of the waves depends on the strain energy of the body surface and the surface energy.…”

The effect of elastic strain on the microstructure of free surfaces of stressed minerals in contact with an aqueous solution

“…Differences in elastic strain energy are commonly assumed not to play a significant role as a driving force for stress-induced solution mass transfer (pressure solution, PS) or for dynamic recrystallisation [e.g., Paterson, 1973;Lehner, 1990]. PS and dynamic recrystallisation are commonly assumed to be driven by differences in grain boundary surface normal stress (rr,•) and/or differences in crystal plastic strain energy, and it can easily be shown that the potential energy drop associated with differences in rr,• or differences in crystal plastic strain is 2 to 3 orders of magnitude larger than the potential energy drop associated with differences in elastic strain energy, at otherwise similar conditions [e.g., Paterson, 1973].…”

Evolution of anodic stress corrosion cracking in a coated material

“…The tendency for a material to change the shape of its reference configuration is represented by the chemical potential, cf. Kim et al (1999):…”

“…With a linearized theory assuming that the amplitude of the height variation of the body surface is small, it leads to symmetric growth in the sense that the growth rate of hills, as an average, is the same as at valleys, and a critical wavelength can be found, cf. (Kim et al 1999;Asaro and Tiller 1972):…”

“…The phenomenon is theoretically explained by Asaro and Tiller (1972), Grinfeld (1986) and Srolovitz (1989). Mass transportation through etching is considered by Kim et al (1999). The wave spectrum of the developing surface roughness depends on the stress in the body surface and the surface energy.…”