Section 5.1.1.2.1. Indexing crystal faces

Crystal faces are described by three numbers, the Miller indices, that define the relative positions at which the three axes of the unit cell are intercepted by the crystal face (Blundell & Johnson, 1976; Phillips, 1957). The crystal face that is designated hkl makes intercepts , and with the three axes (a, b and c) of the unit cell. When the Miller indices are negative, because the crystal face intercepts an axis in a negative direction, they are designated or . Most faces of a crystal are, as required by the law of rational indices, represented by small integers. For symmetry reasons, planes in hexagonal crystals are conveniently described by four axes, three in a plane at 120° to each other. This leads to four indices, hkil, where . Crystal faces are designated by round brackets, e.g. (100), as shown in two simple examples in Fig. 5.1.1.1. A set of faces then defines a crystal form. All sets of planes hkl related by symmetry, such as the main faces of an octahedron (111), (), (), (), (), (), () and (), may be represented by the use of curly brackets, e.g. . Square brackets, e.g. [111], are used to indicate a direction in a crystal, [001] being the c axial direction. Thus, information about several faces of a crystal is contained in information about one face if the relevant symmetry of the crystal is known. If the atomic structure of the crystal is known, it is possible to determine which aspects of the macromolecule lie on the various crystal faces.

Figure 5.1.1.1 | top | pdf | Crystal faces. (a) Cube and (b) octahedron. (c) Unit-cell axes.