Earth Materials. John O'Brien. Читать онлайн. Newlib. NEWLIB.NET

Автор: John O'Brien
Издательство: John Wiley & Sons Limited
Серия:
Жанр произведения: География
Год издания: 0
isbn: 9781119512219
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by the length and direction of ta or t1. Translation in the second direction is represented by the length and direction of tb or t2. The pattern generated depends on the length of the two unit translation vectors and the angles between their directions. The result of any two‐dimensional translation is a plane lattice or plane mesh. A plane lattice is a two‐dimensional array of motifs or nodes in which every node has an environment similar to every other node in the array (Figure 4.2a, b).

Image described by caption. Schematic illustration of five major types of rotational symmetry operations, viewed looking down rotational axes marked by blue symbols in the center of each circle.

       Rotation

Type Symbolic notation Description
Onefold axis of rotation (1 or A1) Any axis of rotation about which the motif is repeated only once during a 360° rotation (Figure 4.3 (1))
Twofold axis of rotation (2 or A2) Motifs repeated every 180° or twice during a 360° rotation (Figure 4.3 (2))
Threefold axis of rotation (3 or A3) Motifs repeated every 120° or three times during a complete rotation (Figure 4.3 (3))
Fourfold axis of rotation (4 or A4) Motifs repeated every 90° or four times during a complete rotation (Figure 4.3 (4))
Sixfold axis of rotation (6 or A6) Motifs repeated every 60° or six times during a complete rotation (Figure 4.3 (5))

       Reflection

Schematic illustration of two- and three-dimensional motifs that illustrate the concept of reflection across a plane of mirror symmetry (m).

      Source: Image from butterflywebsite.com. © Mikula Web Solutions.

      One test for the existence of a mirror plane of symmetry is that all components of the motifs on one side of the plane are repeated at equal distances on the other side of the plane along projection lines perpendicular to the plane. If this is not true, the plane is not a plane of mirror symmetry.

       Inversion