The derivation of twin laws in non-merohedric twins - Application to the analysis of hybrid twinsReport as inadecuate

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1 CMMMB - Cristallographie et modélisation des matériaux minéraux et biologiques 2 Dipartimento di Scienze Mineralogiche e Petrologiche

Abstract : An algorithm is presented to derive the twin laws in non-merohedric twins through the systematic search for quasi-perpendicular lattice planes-directions. The twin lattice, i.e. the sublattice common to the whole crystalline edifice built by the twinned individuals, is based on a supercell of the individual defined by a pair of quasi-perpendicular lattice elements hkl-uvw. Starting from a real or supposed twin element, hkl or uvw, the set of quasi-perpendicular lattice elements with user-defined limits on the twin index and obliquity is explored. The degree of lattice quasi-restoration is commonly measured by the classical twin index but in some cases, especially for large supercells, this index represents only a first approximation of the degree of lattice quasi-restoration, because more than one pair hkl-uvw may exist, and more than one concurrent sublattices of nodes, based on the same twin element, may be quasi-restored, although within different obliquities. These twins, whose existence has been recently recognized, are termed hybrid twins. In hybrid twins the degree of lattice quasi-restoration is measured by the effective twin index nE, a generalization of the classical twin index. A number of examples previously reported simply as -non-Friedelian- twins are analysed and reinterpreted as hybrid twins. A Fortran program is made available, which derives the twin laws according to this algorithm, and analyses the pseudo-symmetry of the concurrent sublattices defined by each pair hkl-uvw.

Keywords : Geminography hybrid twinning reticular merohedry polyholohedry effective twin index concurrent quasi-restored sublattices

Author: Massimo Nespolo - Giovanni Ferraris -



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