Читать книгу Earth Materials - John O'Brien - Страница 94

Three other symmetry operations exist. However, unlike those discussed so far, they are compound symmetry operations that combine two simple symmetry operations. Glide reflection (g) is a symmetry operation that combines translation (t) parallel to a mirror plane (m) with reflection across the mirror plane to produce a glide plane (Figure 4.6).

Rotoinversion (n^–) is an operation that combines rotation about an axis with inversion through a center to produce an axis of rotoinversion (Figure 4.7). Figure 4.7b illustrates an axis of fourfold rotoinversion ( ) in which the motif is repeated after 90° rotation followed by inversion through a center so that it is repeated four times by rotoinversion during a 360° rotation. Axes of twofold rotoinversion ( ) are unique symmetry operations, whereas axes of threefold rotoinversion ( ) are equivalent to a threefold axis of rotation and a center of inversion (3i), and axes of sixfold rotoinversion ( ) are equivalent to a threefold axis of rotation perpendicular to a mirror plane (3/m).

Screw rotation (n_a) is a symmetry operation that combines translation parallel to an axis with rotation about the axis. This is similar to what occurs when a screw is inserted into a wall (Figure 4.7c). Much more detailed treatments of the various types of compound symmetry operations can be found in Klein and Dutrow (2007), Wenk and Bulakh (2016) or Nesse (2016).

Figure 4.7 (a) An axis of fourfold rotation (4). This contrasts with (b) an axis of fourfold rotoinversion () that combines rotation with inversion every 90°, and (c) a fourfold screw axis (4₁) that combines translation with 90° rotations every one‐fourth translation.

Source: Wenk and Bulakh (2004). © Cambridge University Press.