Pole figures inverse

ORIENTATION MEASURED FROM INVERSE POLE FIGURES... 

The presence of phase transitions at 19 and 30°C provides an opportunity to test the proposed deformation model. Below 19°C the lattice contracts into a triclinic structure witli strong intermolecular interaction. 5,26 sjamplcs deformed below 19°C should develop off-c-axis orientation while samples deformed above 30°C should not. Figures 1.12 and 1.13 show inverse pole figures for samples deformed at 2 and 70°C. The observed orientation agrees with our proposed model. - With tlris set of experiments, it is possible to activate the oblique slip process or, alternatively, to deactivate it in the high-temperature phase above 30°C. 

Fig. 15 Inverse pole figure summarizing reactivity and orientation stability data for titania.

Fig. 12.9. Electron backscatter diffraction (EBSD) map showing the grain structure of a poly-Si film on glass prepared by the ALILE process (left) and the corresponding inverse pole figure showing the preferential (100) orientation of the poly-Si surface (right). The region used for the definition of the preferential (100) orientation -R(ioo) is indicated by a dashed line (20° tilt with respect to the perfect (100) orientation). The sample was annealed at 425°C for 16 h. Afterwards the Al(+Si) top layer was removed by CMP. The area under investigation was 80 x 80 pm2. Red, green and blue correspond to (100), (110) and (111), respectively, (from [39])...

A pole figure shows the distribution of a selected crystallographic direction relative to certain directions in the specimen. Texture data may also be presented in the form of an inverse pole figure, which shows the distribution of a selected direction in the specimen relative to the crystal axes. The projection plane for an inverse pole figure is therefore a standard projection of the crystal, of which only the unit stereographic triangle need be shown. Both wire and sheet textures may be represented. 

Figure 9-24(a) is an inverse pole figure for the inside texture of an extruded aluminum rod, showing the density distribution of the rod axis on a times-random basis. It was derived by a trial-and-error method [9.36] from pole density curves, as in Fig. 9-22, for the ((X)l), (111), and (113) poles. We note concentrations of the rod axis at [001] and [111], indicating a double fiber texture the volume fractions of the [001] and [ill] components were estimated as 0.53 and 0.47, respectively. Note that an inverse pole figure shows immediately the crystallographic direction of the.scatter. In this double texture, there is a larger scatter of each component toward one another than toward [011]. 

Sheet textures may also be represented by inverse pole figures. Here three separate projections are needed to show the distribution of the sheet normal, rolling direction, and transverse direction. Figure 9-24(b) is such a projection for the normal direction of the steel sheet whose (110) pole figure was given in Fig. 9-20 it was calculated from the crystal orientation distribution mentioned in Sec. 9-8. The distribution of the normal direction is also shown in (c), for the same material. This distribution was measured directly in the following way. A powder pattern is made of the sheet in a diffractometer by the usual method, with the sheet equally... 

Fig. 9-24 Inverse pole figures, (a) Distribution of axis of aluminum rod, extruded at 450°F to a reduction in area of 92 percent and a final diameter of 23 mm. letter, McHargue, and Williams [9.36]. (b) and (c) show the distribution of the sheet normal for the steel sheet of Fig. 9-20. Bunge and Roberts [9.18].

The inverse pole figures of Figs. 9-24(b) and (c) both show a high density of (111) poles parallel to the sheet normal and are therefore consistent with the [111] quasi-fiber texture mentioned in Sec. 9-8. 

The inverse pole figure is the best way to represent a fiber texture, but it offers no advantage over a direct pole figure in the description of a sheet texture. Inverse or direct, a pole figure is a two-dimensional plot that fixes, at a point, only a direction in space, be it crystal space or specimen space. Only the three-dimensional plot afforded by the crystal orientation distribution (Sec. 9-8) can completely describe the orientations present, and this approach, being quite general, is just as applicable to fiber textures as it is to sheet. 

When higher accuracy is desired one can resort to using inverse pole figures. The term inverse is used since in constructing such a figure, one converts the orientation distribution of the poles of specific planes (determined with respect to some reference axis) to an orientation distribution of the reference axis with respect to a fixed position of the... 

Orientation Measured from Inverse Pole Figures. 12... 

Inverse-pole-figure methods of orientation representation were introduced in 1964-1965 by Roe and Krigbaum (73,74). They expressed orientation distribution in terms of expansions of associated Legendre polynomials this effort was expanded later by Nomura and Kawai (75,76), who also showed that fluorescence measurements of orientation correspond to mixed fourth- and second-order terms. 

Fig. 5-22. Inverse pole figures from HRT core tank Zircaloy-2 before and after refabrication. Solid lines as-received, dotted lines after refabrication.

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