Three-dimensional orientation distribution functions of the crystallites in copper sheets, cold rolled to different degrees of reduction, have been determined using neutron diffraction pole figures. The main features of the textures may be represented by the orientation 'tube' already described in prior publications. Two ranges of rolling reduction can be distinguished, a lower one (30 to 50 %) and a higher one (70 to 95 %) the texture changes of which correspond to those calculated after the Taylor theory. In an intermediate range (50 to 70 %) a different deformation mechanism occurs which leads to an intermediate (001) [110] texture component. It is supposed that anisotropic hardening may have occured in this range.
Neutron diffraction proves advantageous as compared to X-ray diffraction in texture analysis because of the lower absorption coefficient for a broad variety of materials especially metals. The spherical sample method is recommended because it yields the most reliable results and it does not require great preparational efforts. The fundamental difference between the spherical sample method in X-ray and in neutron diffraction is discussed.
X-RAY AND NEUTRON DIFFRACTION
A new heterocyclic compound, cyclo-tris(2,6-pyridylformamidine), was synthesized as a highly crystalline powder-like substance from which very small whiskers were produced by a sublimation technique. By rotatingcrystal and powder diffraction measurements, a set of structural data were obtained which were ®tted mathematically to a structural model. The ®tting procedure included geometry optimization by ab initio calculations, crystal structure and X-ray diffraction pattern simulation as well as structure re®nement based on the newly developed Rietveld algorithm BGMN 1 under force-®eld constraints. A single-crystal structure re®nement could not be carried out because of the small size of the whiskers. In order to obtain the atomic coordinates a new procedure incorporating a powder diffraction pattern re®nement was used. Cyclo-tris(2,6pyridylformamidine) crystallizes in a monoclinic unit cell with a = 28.18 (1), b = 14.67 (1), c = 4.428 (1) A Ê , = 90.10 (2) . The symmetry was determined as P2 1 /a. The expected threefold symmetry of the cyclic compound was disturbed in the crystallized state, in agreement with solid-state NMR investigations. The best approximation was obtained when water molecules were additionally packed into the unit cell. ² Present address: HU È LS Silicone GmbH, Friedrich-von-Heyden-Platz 1, D-01610 Nu È nchritz, Germany.Fig. 1. One of the boundary structures of an isolated trimer molecule (note that positions numbered 12, 14, 32, 34, 52 and 54 are each occupied by an H atom).
Three‐dimensional orientation distribution functions were calculated from (111), (200), (220) and (311) pole figures for α‐copper–zinc alloys in the concentration range from 0 to about 30% zinc. The pole figures were measured by neutron diffraction. The main feature of the texture transition is a continuous shortening or cut off of the tube of preferred orientations present in the copper texture beginning with the end orientation ~(12) [11]. This orientation has nearly completely disappeared at about 5% zinc. Simultaneously its twin orientation (011) [100] appears. A second feature is the continuous decrease of maximum density of all texture components over the whole concentration range. The results support Wassermann's theory of mechanical twinning as the reason for the texture transition.
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