The diffraction behaviours of imperfect nanotwin superlattices were considered and the effects of random variations in nanotwin layer thicknesses and variant volume fractions on the diffraction peak intensity profiles investigated. Imperfect nanotwin superlattices exhibit a pronounced adaptive diffraction phenomenon when the Brillouin zone-dependent condition, Tγ|s•K| < 8π, was met, where T was the twin-related bilayer thickness, γ was the twinning shear strain magnitude, s was the twinning shear direction unit vector, and K was the reciprocal lattice vector of the constituent crystal denoting the fundamental reflection spots and Brillouin zones in reciprocal space. Nano-twin layer thickness variations had little effect upon the diffraction intensity distributions of adaptive Bragg reflection peaks, whereas variant volume fraction variations significantly reduce the height and broaden the width of adaptive peaks, but only affected their integrated intensities slightly and did not change their positions. In spite of imperfections, an extraordinary peak still appeared at position k along the twin peak splitting vector ΔK, as determined by a lever rule according to the average twin variant volume fraction. Imperfect nanotwin superlattices exhibited a certain degree of diffuse reflection around the adaptive peaks, with strong Lorentzian shape characteristics; adaptive peaks exhibited anisotropic broadening, i.e. the peak was broader in the direction perpendicular to the twin plane, and sharper parallel to the twin plane. The width of the adaptive peak did not provide direct information of nano-domain size, but the Brillouin zone-dependent diffraction behavior could be used to determine the nano-domain sizes.

Diffraction Theory of Nanotwin Superlattices with Low Symmetry Phase - Adaptive Diffraction of Imperfect Nanotwin Superlattices. W.F.Rao, Y.U.Wang: Philosophical Magazine, 2010, 90[1-4], 197-217