Twin domain model

Although these NMR data clearly support a dynamical model for disorder in P-cristobalite, they are not sensitive to whether the motions of adjacent oxygens are correlated (as required for a model of re-orienting twin domains), or, whether the motion is continuous or a hopping between discrete positions they indicate only that the path of each oxygen traces a pattern with 3-fold or higher symmetry over times of the order 4.7-10 s. Thus, these results cannot discriminate between models based on RUMs or dynamical twin domains, and place only a lower limit on the timescale of the motions. A tighter restriction... 

Figure 8. Idealized models of junction between twinning domains.

Fig. 12. YBa2Cu307 (a) [001] image of quasi-perpendicular twinning domains (b) idealized model of the...

Several models for the structure of the twin walls have been proposed (30, and ref. therein). The simplest of these is illustrated in Figure 4. The twin wall is formed by three consecutive diagonals. The copper atoms located on the central one have two-fold coordination with corresponding oxygen stoichiometry of x = 6.0. Those located on the two neighboring rows on each side of the central diagonal have three-fold coordination and oxygen stoichiometry x = 6.5. Within each domain, away from the boundary, the composition is x = 7.0 and copper has the usual four-fold planar coordination of... 

Rehling P, Model K, Brandner K, Kovermann P, Sickmann A, Meyer HE, Kuhlbrandt W, Wagner R, Truscott KN, Pfanner N (2003) Protein insertion into the mitochondrial inner membrane by a twin-pore translocase. Science 299 1747-1751 Richards TA, Cavalier-Smith T (2005) Myosin domain evolution and the primary divergence of eukaryotes. Nature 436 1113-1118... 

Fig. 9.4. El ongated cyclic penta-tetrahedral twin model of gold nanorods, taken from [45], (a) Idealized 3-D morphology showing 111 end faces and 100 side faces. The common five-fold axis of elongation is [110], (b) Cross-section of nanorod structure showing arrangement of twins T1 to T5, and possible orientations of domains with respect to the...

Figure 13. Model of self-reversal in the ilmenite-hematite solid solution (after Hoffman 1992). Boxes represent (001) cation layers (viewed down the c-axis), shaded according to their Fe-occupancy (Fe = dark, Ti = light). Two ordered ferrimagnetic domains are shown (left and right) separated by a twin wall (central) with a canted antiferromagnetic stmeture. (a) The twin wall orders first with its parasitic moment parallel to the external field. The ferrimagnetic domains order perpendicular to external field and antiparallel to each other, (b) The domain moments tilt away from the wall moment at lower temperatnres, creating a large reverse component of magnetization.

Figure 11. Simulated spectra for the outer [+(3/2,5/2)] satellite transitions for Al in ALPO4 P-cristobalite for a model of re-orienting twin- and anti-phase domains of a-like symmetry. Spectral width for the ordered domains (bottom,...

All in all, the WPPM approach can provide a simultaneous structure and microstructure refinement, based on physical models of the phases under study, without using any arbitrary profile function. Considering the terms of Equation (26), refinement parameters to be optimized in a least-squares analysis are relatively few, namely, mean (p) and variance (cr) of a suitable distribution of coherent domain sizes, dislocation density (p), effective outer cut-off radius (R ) and character (/e, effective fraction of edge dislocations), twin fault (P), deformation fault (a) and APB (y) probabilities. 

Our theoretical analysis of the twin structure of LSGMO allows to correlate each twin law with a transformation matrix connected to the orthorhombic or trigonal basis vectors of neighbouring domains. Using twin models and the analytical geometry approach, the relationship of the basis vectors was obtained for all symmetry allowed domain pairs of the trigonal... 

Figure 3. Model of the "chevron-like" twin structure of the trigonal phase formed by W-type domain walls (Oil), (110) and (121).

Usually the second domain is weaker and is often not as well centred in the beam. These additional data are thus of poorer quality and often do not improve the model. Secondly they would be treated as independent data, but are of course not independent of reflections of the first domain with the same indices, which would tend to falsify the standard uncertainties. In the higher symmetry trigonal Laue group these two twin laws are equivalent. 

This can be explained by obverse/reverse twinning. Only the reflections with I = 3n have a contribution from the second domain, and thus a measured intensity higher than one would calculate for the model. Closer inspection of the systematic absences for the lattice centring (see above) and reciprocal space plots (see Figure 7.12) confirmthis hypothesis in all layers with / = 3n, the reflections withyt 3n are absent. So only one third of the reflections are observed. For the layers with I 7 3n, one third are absent, only the reflections with —h + k + l 3n and with h — k + I 3n. 

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