2D Fourier Analysis and its Application to Study of Scaling Properties and Fractal Dimensions of ε-Martensite Distribution in γ-Matrix of Fe-Mn-Si Alloy

Abstract
2D Fourier analysis is proposed to obtain quantitative information on the structural amplitudes in reciprocal space for different heterophase systems. An original technique for profound computer processing of optical images transformed into an appropriate digital form is developed. Correlation Fourier analysis is applied to study a spatial distribution of γ → ε martensitic transformation product in Fe-Mn-Si shape memory alloy. An evident spatial self-similarity and scaling behavior is observed, indicating a fractal-like distribution of ε-phase in 7-matrix. The structural factor versus wave number dependence shows three scaling invariant regions with different scaling dimensions and crossover regions between them. A simple fractal model is proposed to interpret experimental results.