Stereographic triangle

Figure 4,2, Medal struck in Austria to commemorate the 50th anniversary of the discovery of the critical shear stress law by Erich Schmid. The image represents a stereographic triangle with "isobars showing crystal orientations of constant resolved shear stress (courtesy H.P. Stiiwe).

Fig. 5.1. The unit stereographic triangle for fee showing the location and Miller indices of various faces...

Fig. 2. Stereographic triangle indicating various crystallographic orientations of fee solid surfaces using Miller index notations.

On cutting a crystal surface in the middle of the stereographic triangle, a surface structure that exhibits a large density of kinks in the steps will be produced. One of these high-kink-density surfaces is shown schematically in Fig. 3c. 

Fig. 6. A stereographic triangle of a platinum crystal depicting the various high Miller index surfaces of platinum that were studied.

How many different <210> directions are there in a cubic crystal How many stereographic triangles does each <210 direction share ... 

The stereographic projection or stereographic triangle shown in Fig. 4.4 serves as a visual framework for considering all the surfaces that can be cleaved from a face centered cubic lattice. All points in or on the stereographic triangle uniquely... 

R-3-Methylcyclohexanone desorption reveals the same types of easily assigned desorption features on many of the other chiral and achiral surfaces in the stereographic triangle [23]. 

Similarly, the orientation of a single-crystal wire or rod may be described in terms of the location of its axis in the unit stereographic triangle. Note that this method does not completely describe the orientation of the crystal, since it allows... 

Fig. 8-8 Use of the unit stereographic triangle to describe crystal orientation. The point inside the triangle is the normal to the single crystal plate whose orientation is shown in Fig. 8-7.

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 10. Unit stereographic triangle for the fee structure with the (100) face at the center of the projection, (a) Regions which correspond to different bond orders (Ref. 17) ...

Figure 40. C(E) curves for iodide adsorption on gold faces distributed on the three main zones of the projected unit stereographic triangle (concentration = 100 mM KI, frequency = 80 Hz, and sweep rate = 3mVs" ) (a) (lll)-(llO) zone (b) (Ill)-(IOO) zone (c) from (110) to (210) on the (lOO)-(llO) zone and (d) from (210) to (100) on the (lOO)-(llO) zone. ...

For faces distributed on the three main zones of the projected unit stereographic triangle (see Section III.2), systematic changes of the CO exist they were described by the TLK model (see Section... 

Fig. 16.11 Unit stereographic triangle of polyhedral nanocrystals bounded by different crystal...

In analogy with the stereographic triangle where the three basal planes are located at the vertices, an intrinsic triangle can be made which coordinates the crystal surface index and the shape of fee metal nanocrystals as shown in Fig. 16.11 [83, 84]. The three vertices represent the coordinates of polyhedral nanociystals bounded by basal facets, i.e., cube covered by 100], octahedron by 111, and rhombic dodecahedron by 110 faces. 

In this chapter the special features of surfaces and internal boundaries in single-phase crystalline systems are described. The orientation dependence of the surface functions will be discussed and the use of Wulff plots and stereographic triangles to present the orientation dependence of surface energy will be demonstrated. The various types of internal boundaries (grain boundaries, twin boundaries, etc.) and their thermodynamic properties will be discussed. 

Figure 4.3 A stereographic triangle for a cubic crystal showing selected poles . Values of the surface free energy for Cu from Reference [4] for selected orientations are superposed on the triangle.

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