Topological Data Analysis of Nanoscale Roughness in Brass Samples

Rough surfaces possess complex topographies, which cannot be characterized by a single parameter. The selection of appropriate roughness parameters depends on a particular application. Large datasets representing surface topography possess orderliness, which can be expressed in terms of topological features in high-dimensional dataspaces reflecting properties such as anisotropy and the number of lay directions. The features are scale-dependent because both sampling length and resolution affect them. We study nanoscale surface roughness using 3 X 3, 4 X 4, and 5 X 5 pixel patches obtained from atomic force microscopy (AFM) images of brass (Cu Zn alloy) samples roughened by a sonochemical treatment. We calculate roughness parameters, correlation length, extremum point distribution, persistence diagrams, and barcodes. These parameters of interest are discussed and compared.

Automated summary

For studying surface roughness, appropriate roughness parameters should be selected based on specific applications. Large datasets representing surface topography exhibit orderliness, which can be expressed in terms of topological features in high-dimensional dataspaces reflecting properties such as anisotropy and the number of lay directions. These features are scale-dependent, impacted by both the sampling length and resolution.