Application of Chaos Theory to Design for Precise and Fine Surfaces

1.Chaotic Characteristics of Mirror-Finished Surface Produced by Ultra-Precision TurningMirror-like surfaces obtained by the ultra-precision turning using diamond tools are smooth to the eye，but rough under a microscope。Although a lot of work has been done on the roughness of the mirror-finished surface，its inhomogeneous static structure is not yet well analyzed。This has led to attempt to discuss quantitatively whether the surface texture was indeed chaotic or not。In this study，the trajectory on the attractor reconstructed in phase space from a measured surface profile was characterized by the Lyapunov exponent and the finite correlation dimension and hence it has the chaotic characteristics.Further，the mirror-finished surface produced by the ultra-precision turning becomes more chaotic as the feed rate and the cutting speed decrease.2。Fractal Characteristics of Si Surface Produced by Anisotropic EtchingThe roughness of Si(100)surfaces etched in aqueous KOH，especially the roughness of the surface with low or no micropyramid formations，was studied using fractal analysis。The etched surfaces exhibited the fractal characteristics，and their fractal dimensions and their root-mean square roughness were found to be dependent on the etching time and the temperature.The simulation of the surface growth using noise reduced Eden model proved that the selective dissolution of Si atoms by random attacks of H I D22齐埃D2O and OH on the Si-Si bond caused the roughening phenomenon that was observed experimentally。

1. Chaotic Characteristics of Mirror-Finished Surface Produced by Ultra-Precision TurningMirror-like surfaces obtained by the ultra-precision turning using diamond tools are smooth to the eye, but rough under a microscope. Although a lot of work has been done on the roughness of the mirror-finished surface, its inhomogeneous static structure is not yet well analyzed. This has led to attempt to discuss quantitatively whether the surface texture was indeed chaotic or not. In this study, the trajectory on the attractor reconstructed in phase space from a measured surface profile was characterized by the Lyapunov exponent and the finite correlation dimension and hence it has the chaotic characteristics. Further, the mirror-finished surface produced by the ultra-precision turning becomes more chaotic as the feed rate and the cutting speed decrease.2. Fractal Characteristics of Si Surface Produced by Anisotropic EtchingThe roughness of Si (100) surfaces etched in aqueous KOH, especially the roughness of the surface with low or no micropyramid formations, was studied using fractal analysis. The etched surfaces exhibited the fractal characteristics, and their fractal dimensions and their root-mean square roughness were found to be dependent on the etching time and the temperature. The simulation of the surface growth using noise reduced Eden model proved that the selective dissolution of Si atoms by random attacks of HィイD22ィエD2O and OH on the Si-Si bond caused the roughening phenomenon that was observed experimentally.