Diffraction theory of nanotwin superlattices with low symmetry phase

A nanotwin diffraction theory is developed. It predicts an adaptive diffraction phenomenon, where the Bragg reflection peaks are determined by coherent superposition of scattered waves from individual twin-related nanocrystals and adaptively shift along the twin peak splitting vectors in response to a change in the twin variant volume fraction. Application of this theory to tetragonal phase explains the intrinsic lattice parameter relationships of monoclinic M-C phase recently discovered in ferroelectric Pb[(Mg1/3Nb2/3)(1-x)Ti-x]O-3 and Pb[(Zn1/3Nb2/3)(1-x)Ti-x]O-3.