Der gitterfaktor des gaußschen parakristalls

By using so-called “characteristics”, the long-range distortion in Gaussian paracrystals may be described in a way which is independent of the lattice, provided distance and directional fluctuations between neighbouring lattice points are used. By a two-fold Fourier transform — similar to the approach of Warren and Averbach — the lattice factor, describing the interference effect of the Gaussian paracrystal, is found from the convolution of an ideal reciprocal lattice with a lattice-independent profile function. Threadlike “one-dimensional” Gaussian and ideal paracrystals are identical with each other. Making use of the two-fold Fourier transform, Hosemann's K-factor splits into isolated discs (“Scheibchen”) showing Lorentzian profiles. The profile function of two-and three-dimensional Gaussian paracrystals shows a Lorentzian-2/3 or a Lorentzian-2 profile, respectively. The different profiles are experimentally distinguishable when using a position-sensitive detector. Thus, based on experimental results, paracrystalline lattice distortions with Gaussian characteristics are detectable.