Diffraction theory of nanotwin superlattices with low symmetry phase:: Application to rhombohedral nanotwins and monoclinic MA and MB phases

The Brillouin zone-dependent conditions for coherent and adaptive diffractions are formulated. Adaptive diffraction phenomenon of nanotwins is analyzed. Extraordinary Bragg reflection peaks appear and adaptively shift along the conventional twin peak splitting vectors, whose positions are determined by lever rule according to twin variant volume fractions. Analysis of rhombohedral nanotwins shows that the nanotwin superlattices of rhombohedral phase with {001} and {110} twin planes diffract incident waves just like monoclinic M-A and M-B phases, respectively, whose lattice parameters are intrinsically related to that of rhombohedral phase. Crystallographic analysis of rhombohedral nanotwins by nanodomain averaging gives the same monoclinic M-A and M-B phases.