Читать книгу Crystallography and Crystal Defects - Anthony Kelly - Страница 19

A centre of symmetry is a point where inversion through that point produces an identical arrangement. The operation of inversion moves the point with coordinates (x, y, z) to the position (−x, −y, −z). For instance, in Figure 1.3 (see also Figure 3.17), if we stood at the centre of the unit cell (coordinates , , ) and looked in any direction [uvw], we would find an identical outlook if we looked in the direction . Clearly, in a lattice, all lattice points are centres of symmetry of the lattice. This follows from Eq. (1.21), since u, v, w can be positive or negative. Of course, since the origin of a set of lattice points can be arbitrarily chosen in a given crystal structure, we must not assume that, in a given crystal with a centre of symmetry, the centres of symmetry necessarily lie where we have chosen to place the lattice points.