Topography of Metallic Surfaces Subjected to Plastic Strain: Roughness, Spatial Correlations, and Eigenvalue Spectral Entropy

Published

July 19, 2007

Author(s)

Joseph B. Hubbard, Mark R. Stoudt, Lyle E. Levine

Abstract

We employ scanning confocal laser microscopy (SLCM) to obtain topographic images of the surface of an aluminum alloy subjected to various levels of uniaxial strain. These images are discretized into a square array of pixels, each of which is then assigned a numerical value corresponding to the deviation of surface height relative to an averaged background. The result is a set of real, non-Hermitian n x n matrices, which are diagonalized to produce a collection of spectra, each of which consists of n complex eigenvalues. These eigenvalue spectra are observed to change systematically as the degree of plastic strain is varied. Because this approach is based solely on the behavior of the eigenvalue spectra, it eliminates the need for the a priori assumptions about surface character used in conventional topographic analyses. The information contained within an eigenvalue spectrum is distilled into a scalar measure of topographic disorder, referred to as the spectral entropy. The special entropy is observed to decrease monotonically with increasing plastic strain. This behavior is consistent with the observed topographical changes induced by plastic strain. In addition, the spectral entropy can be decomposed into a constant term that is independent of all spatial correlations that occur in the surface roughness, and a term that incorporates these correlations at all levels of complexity.

Citation

Journal of Applied Physics

Pub Type

Journals

Keywords

Eigenvalue spectra, non-Hermitian matrices, random matrices, spatial correlation, spectral entropy, surface roughness

Citation

Hubbard, J. , Stoudt, M. and Levine, L. (2007), Topography of Metallic Surfaces Subjected to Plastic Strain: Roughness, Spatial Correlations, and Eigenvalue Spectral Entropy, Journal of Applied Physics (Accessed May 5, 2026)

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