SYMMETRY IN MULTIPLE DIFFRACTION PATTERNS. C.B.R. Parente, V.L. Mazzocchi and S. Metairon, Instituto de Pesquisas Energeticas e Nucleares - Ipen-Cnen/Sp CP 11049-Pinheiros, 05422-970 Sao Paulo, SP, Brazil. J.M. Sasaki and L.P. Cardoso, Instituto de Fisica Gleb Wataghin - Unicamp CP 6165, 13083-970 Campinas, SP, Brazil

It is well known that a multiple diffraction (m.d.) pattern has symmetry mirrors in certain azimuthal positions. In principle, peaks symmetrically positioned around a mirror have same intensity. Nevertheless, for two times in some of our experimental patterns we have unequivocally observed symmetrical peaks with different intensities. Casting about such peaks in experimental m.d. patterns in the literature, we have observed several pairs of them. In this work we make a systematic study about the appearance of such peaks in hexagonal, trigonal and cubic structures. Both experimental and simulated x-ray and neutron m.d. patterns were employed in the study. Plotting the data in circular plots allows immediate observation of the symmetry of the patterns. Two kinds of mirrors are observed: isomorphic mirrors, that produce symmetrical peaks with identical intensities, and anamorphic mirrors, where symmetrical peaks can have different intensities. The number of isomorphic mirrors equals the order n of the symmetry axis normal to the primary reflecting planes. Results show that in the cubic system n-fold axes, produce only isomorphic mirrors, for n even, and anamorphic mirrors intercalated between isomorphic mirrors, for n odd. For [[alpha]]-(trigonal) and ß-quartz (hexagonal) results are opposite to those of cubic system. The 3-fold symmetry of reflection 00.1 from the hexagonal cell of [[alpha]]-quartz produces only isomorphic mirrors. For the 6- fold symmetry of same reflection from, ß-quartz intercalation occurs.

Work partially supported by International Atomic Energy Agency (IAEA) and Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (CNPq).