Analysis of stacking order and disorder by continuous Fourier transformation of diffracted intensities. Example: β'₁ Cu–Al martensite

The continuous Fourier transformation of I(h₃) (h₃ = 0,1) is proposed as a method for the analysis of the stacking sequence in close-packed structures. By this method, the diffraction pattern is directly translated into autocorrelation parameters P⁰_n, P⁺_n, P⁻_n of the stacking sequence. It applies to periodic stacking sequences, for which the Fourier coefficients can be analysed in terms of the Zdhanov symbol, as well as to faulted stacking sequences, where the Fourier coefficients can be analysed in terms of faulting probabilities. In the work reported, the method proposed is applied to powder diffraction data from β′₁ Cu–Al martensite. The stacking sequence in the martensite investigated can be dealt with as statistical, with Reichweites = 3, and faulting parameters α = 0.18, β = 0.54. There is reasonably good agreement between the experimentally measured Fourier coefficients and the Fourier coefficients calculated from the above mentioned α and β values.