Hexagonal paracrystals

Spatially interacting Gaussian random variables arranged on a hexagonal lattice are used to construct examples of hexagonal paracrystals. As for previously described paracrystals on a square lattice the distributions may be specified by a variance, σ_L², defining the magnitude of the displacement away from the underlying perfect lattice together with parameters defining transverse and longitudinal correlations (ρ_T and ρ_L) between neighbouring displacements. A strong longitudinal correlation indicates a small variation from cell to cell in the length of the cell edge whereas a strong transverse correlation indicates a small variation in the cell edge direction. For values of σ_L>~0.30 of the unit cell spacing the diffraction patterns contain diffuse peaks only with no evidence of Bragg peaks arising from the underlying regular lattice.