Topological Data Analysis of Nanoscale Roughness in Brass Samples

Area of Science:

• Surface Science and Engineering
• Materials Characterization
• Nanotechnology

Background:

• Surface topography is complex and cannot be defined by a single roughness parameter.
• The choice of roughness parameters is application-dependent.
• Surface features exhibit orderliness and scale-dependency, influenced by sampling length and resolution.

Purpose of the Study:

• To investigate nanoscale surface roughness using multi-parameter analysis.
• To explore topological features in high-dimensional dataspaces for surface characterization.
• To compare various roughness parameters derived from atomic force microscopy (AFM) data.

Main Methods:

• Analysis of nanoscale surface roughness using atomic force microscopy (AFM) images.
• Utilized 3x3, 4x4, and 5x5 pixel patches from AFM images of sonochemically treated brass samples.
• Calculated roughness parameters, correlation length, extremum point distribution, persistence diagrams, and barcodes.

Main Results:

• Demonstrated that nanoscale surface roughness is characterized by multiple interdependent parameters.
• Identified scale-dependent topological features in the surface topography.
• Provided a comparative analysis of calculated roughness parameters.

Conclusions:

• A single parameter is insufficient for characterizing complex nanoscale surface roughness.
• Topological features and multi-parameter analysis offer a more comprehensive understanding of surface topography.
• The study highlights the importance of selecting appropriate parameters based on experimental scale and application.