Fractal-Regular Surface Characterization Based on Experimental Data From Atomic Force Microscopy of Hard Disks

Engineering surfaces should be characterized as fractal-regular surfaces since they possess both a macroscopic regular shape component and a random fractal component. In the present study, surface topography measurements were conducted for magnetic hard disks with an atomic force microscope (AFM). The power spectral density data obtained reveal a regular shape region and two fractal regions, indicating bifractal-regular behavior. By combining the AFM data with previous profilometer data, a complete description of the power spectral density behavior of the measured surfaces was obtained for a wide range of scales from 2 nm to 5 mm. The fractal dimension was found to be 1.935 and 1.186 for the upper fractal region and lower fractal region, respectively. Good agreement between the AFM data and profilometer data was observed in a range of overlapping scales. A multi-section modified Weierstrass-Mandelbrot function has been proposed to simulate bi-fractal surfaces with a power spectral density trend which matches that of experimental data.