Cubic crystals, stereographic projection

Fig. 3.6 (a) Stereographic projection map of a (001) oriented cubic crystal. The facet sizes reflect approximately those of the field ion image of a fee crystal. 

Locating the hkl pole in the standard stereographic projection of a cubic crystal... 

FIGURE 2.14. Some of the various shapes (hahits) of crystals that can result from a crystal structure with a cubic unit cell, (a) Models of a cube, octahedron, and rhombic dodecahedron, composed of cubic unit cells, (b) Tetrahedron, (c) cube, (d) octahedron, (e) rhombic dodecahedron, (f) tetrahexahedron, (g) icositetrahedron, and (h) irregular dodecahedron (pyritohedron). The corresponding stereographic projections are also shown, with filled circles for the northern hemisphere and open circles for the southern hemisphere (see Figure 2.13). (Models courtesy Amy Kaufman). 

The lattice reorientation caused by twinning can be clearly shown on the stereographic projection. In Fig. 2-40 the open symbols are the 100 poles of a cubic crystal projected on the (001) plane. If this crystal is FCC, then one of its possible twin planes is (TT1), represented on the projection both by its pole and its trace. The cube poles of the twin formed by reflection in this plane are shown as solid symbols these poles are located by rotating the projection on a Wulff net until the pole of the twin plane lies on the equator, after which the cube poles of the crystal can be moved along latitude circles of the net to their final position. 

A transmission Laue pattern is made of a cubic crystal in the orientation of Prob. 3-1. By means of a stereographic projection similar to Fig. 3-8, show that the beams diffracted by the planes (2T0), (2T3), and (211), all of which belong to the zone [l20], lie on the surface of a cone whose axis is the zone axis. What is the angle between the zone axis and the transmitted beam ... 

Stereographic projections of low-index planes in a cubic crystal and in a hep crystal are given in Fig. 5. Only one side of the projection is visible thus it must not be forgotten that below ... 

Figure 5 (a) Standard (001) stereographic projection of poles and zones circles for cubic crystals (after E A. Wood, Crystal Orientation Manual, Columbia Univ. Press, New York, 1963). 

In the Figure 2.49 the standard stereographic projection of the cubic crystal is considered oriented so that the direction [001] (thus along Oz) includes the North Pole of the sphere of projection. Only the information indicated in the northern hemisphere projection are required, those of the southern hemisphere being the duplicate with the opposite sign. 

FIGURE 2.49 The standard projection ofa cubic crystal detail for the 001 plan projection (left) and of other planes and directions (right) after Stereographic Projection (2003). 

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