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Twin laws explained by partitions of space
Author(s) -
Follner H.
Publication year - 1987
Publication title -
crystal research and technology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.377
H-Index - 64
eISSN - 1521-4079
pISSN - 0232-1300
DOI - 10.1002/crat.2170220412
Subject(s) - reciprocal lattice , monoclinic crystal system , reciprocal , crystallography , crystal structure , crystal twinning , lattice (music) , octahedron , fourier transform , crystal (programming language) , space (punctuation) , chemistry , condensed matter physics , mathematics , physics , diffraction , optics , mathematical analysis , linguistics , philosophy , programming language , computer science , acoustics , microstructure
Twin laws of monoclinic potassium feldspars, potassium sulphate, cerussite and hexabromobenzene can be explained by partitions of space. The face indices of the crystals denote points of a lattice in the reciprocal space. A Fourier transform leads to the morphological lattice. The reciprocal crystal is the Dirichlet domain of the morphological lattice and the structural content consisting of groups of atoms or molecules is the morphological unit. The bond strength between neighbouring morphological units is proportional to the area of the common face of the reciprocal crystals. The reciprocal crystal represents the energetical structure of a crystal. Twins can be explained by continuation of the energetical structures across the twin boundaries. The symmetry operations result from pseudosymmetries of the reciprocal crystals. It is possible to predict planes favoured for the formation of twins or parallel grown individuals.