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Hexagonal Miller-Bravais indices

Since a subsidiary axis is assumed in addition to the and axes in the hexagonal system (and in the hexagonal expression of the trigonal system), the index is expressed by four indices for a general face (hktl). This is called the Miller-Bravais index. For example, in Fig. A.3.1(b) a face ACB cuts the + and + axes at 1 (= OA, OB), and the - axis at 0C = 0D = OB/2. Therefore this face is indexed as (1120). From geometry, h(l) + k(l) = i(2). [Pg.284]

The Miller-Bravais index system for identifying planes and directions in hexagonal crystals is similar to the Miller index system except that it uses four axes rather than three. The advantage of the four-index system is that the symmetry is more apparent. Three of the axes, ai, a2, and a3, he in the hexagonal (basal) plane at 120° to one another and the fourth or c-axis is perpendicular to then, as shown in Figure 3.1. [Pg.21]

The Miller indices of planes in crystals with a hexagonal unit cell can be ambiguous. In order to eliminate this ambiguity, four indices, (hkil), are often used. These are called Miller-Bravais indices and are only used in the hexagonal system. The index i is given by... [Pg.451]

For hexagonal crystal planes, a slightly different indexing nomenclature is used relative to cubic crystals. To index a plane in the hexagonal system, four axes are used, called Miller-Bravais indices. In addition to both a and b axes, another axis... [Pg.30]

Index the lattice planes drawn in the figure below using Miller - Bravais (hkil) and Miller indices (hid). The lattice is hexagonal with the c-axis is normal to the plane of the page and hence the index l is 0 in all cases. [Pg.40]

FIGURE 5.6 Indices of planes (using Miller-Bravais notation) and directions (using three-index Miller notation) in the hexagonal unit cell. [Pg.76]

However, there should be noted that, in terms of directions, many crystal-lographers prefer not to make the transformation within Miller-Bravais axes system, while working with the Miller system for directions and with Miller-Bravais only for the planes indexing of the hexagonal system. [Pg.152]

Here, uppercase U, V, and W indices are associated with the three-index scheme (instead of u, V, and w as previously), whereas lowercase u, v, f, and w correlate with the Miller-Bravais four-index system. For example, using these equations, the [010] direction becomes [1210]. Several directions have been drawn in the hexagonal unit cell of Figure 3.9. [Pg.70]

For crystals having hexagonal symmetry, it is desirable that equivalent planes have the same indices as with directions, this is accomplished by the Miller-Bravais system shown in Figure 3.8. This eonvention leads to the four-index (hkil) scheme, which is favored in most instances because it more clearly identifies the orientation of a plane in a hexagonal crystal. There is some redimdaney in that i is determined by the sum of h and k through... [Pg.79]

Convert the [110] and [001] directions into the four-index Miller-Bravais scheme for hexagonal unit cells. [Pg.100]

Figure 4.2 Shows the Miller indexing scheme for crystal planes and directions in a simple cubic crystal. Similar indexing methods are used in other Bravais lattices, although the basis vectors are not necessarily parallel to Cartesian coordinate axes. In hexagonal lattices an alternate labeling scheme employing four in ws in which only three of the four are independent is often used. Notice that the two (111) planes marked are adjacent and parallel to one another. Figure 4.2 Shows the Miller indexing scheme for crystal planes and directions in a simple cubic crystal. Similar indexing methods are used in other Bravais lattices, although the basis vectors are not necessarily parallel to Cartesian coordinate axes. In hexagonal lattices an alternate labeling scheme employing four in ws in which only three of the four are independent is often used. Notice that the two (111) planes marked are adjacent and parallel to one another.

See other pages where Hexagonal Miller-Bravais indices is mentioned: [Pg.240]    [Pg.151]    [Pg.22]    [Pg.44]    [Pg.32]    [Pg.75]    [Pg.94]    [Pg.32]    [Pg.75]    [Pg.94]    [Pg.288]    [Pg.33]   
See also in sourсe #XX -- [ Pg.462 ]




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Bravais indices

Hexagonal

Hexagonal crystals and Miller-Bravais indices

Hexagonal lattices and Miller-Bravais indices

Hexagons

Miller

Miller-Bravais Indices for Hexagonal Coordinate Systems

Miller-Bravais indices

Miller-Bravais indices for hexagonal

Miller-Bravais indices for hexagonal crystals

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