Analysis of twinning using Fourier and wavelet transforms

In previous research on twinning, Finite Element Methods were used to examine the relationship between twinning microstructure, boundary conditions imposed on the twinning model, and a measure of the success of twinning; the Young measure. Minimizing sequences of deformations for the energy functional were used to approximate twinning microstructure. Since twinned material has a banded microstructure and the uniformity of the bands is related to successful twinning, we investigate a method of measuring twinning quality using Fourier and wavelet transforms. Fourier transforms detect global qualities, such as the frequency of twinning bands in this case, while wavelet transforms capture local qualities well, such as phase changes in twinning bands. We produce a measure of twinning quality from statistical analysis of data obtained from Fourier and wavelet transforms. The quality number distinguishes between twinning with uniform banded patterns and twinning without uniform banded patterns.