Planes in crystals

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... 

The clean siuface of solids sustains not only surface relaxation but also surface reconstruction in which the displacement of surface atoms produces a two-dimensional superlattice overlapped with, but different from, the interior lattice structure. While the lattice planes in crystals are conventionally expressed in terms of Miller indices (e.g. (100) and (110) for low index planes in the face centered cubic lattice), but for the surface of solid crystals, we use an index of the form (1 X 1) to describe a two-dimensional surface lattice which is exactly the same as the interior lattice. An index (5 x 20) is used to express a surface plane in which a surface atom exactly overlaps an interior lattice atom at every five atomic distances in the x direction and at twenty atomic distances in the y direction. 

In a demonstration of the pharmaceutical advantage that can be realized through the use of a cocrystal form of a substance, it was shown that the 1 1 cocrystal of caffeine and methyl gallate exhibited significantly improved powder compaction properties [64], The compression characteristics of the cocrystal were reported to be excellent over the entire pressure range studied, with the tablet tensile strength of the cocrystal being twice that of caffeine at pressures less than 200 MPa. The superior compaction properties of the cocrystal product were attributed to the presence of slip planes in crystal structure. 

Turning from the properties of x-rays, we must now consider the geometry and structure of crystals in order to discover what there is about crystals in general that enables them to diffract x-rays. We must also consider particular crystals of various kinds and how the very large number of crystals found in nature are classified into a relatively small number of groups. Finally, we will examine the ways in which the orientation of lines and planes in crystals can be represented in terms of symbols or in graphical form. 

Laue and X-Ray Diffraction. The suggestion made by von Laue was that the distance between the atom planes in crystals should be of the same order as the wavelength of X-rays, so that it should be possible to use a crystal as a diffraction grating for this particular type of radiation. It was by following up this suggestion and using the apparatus shown in outline in Fig. 4 that his associates, Friedrich and... 

Planes (geometric), italicized, 151 Planes in crystals, 260-261 Planets, capitalization, 87 Plural forms... 

Table 6.1 Comparison of primary glide planes in crystals having the rock-salt...

TABLE 17.2 Comparison of Primary Glide Planes in Crystals Having a Rocksalt Structure... 

Directions and planes in crystals are described using Miller indices, explained in appendix B. 

Miller indices form a notation system in crystallography for directions and planes in crystal lattices. Lattice planes are determined by the three integers h, k, and /, also called Miller indices. In a cubic lattice, these indices coincide with the inverse intercepts along the lattice vectors as shown in Figure 2.14. Thus, (MO simply denotes a plane that intercepts at the three lattice vectors at the points alh, b/k, and cH (or a multiple of those). If one of the indices is zero, the planes are parallel to that axis. 

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