Section 2.2.16.1. Cell choices

One edge of the cell, i.e. one crystal axis, is always chosen along the monoclinic symmetry direction. The other two edges are located in the plane perpendicular to this direction and coincide with translation vectors in this `monoclinic plane'. It is sensible and common practice (see below) to choose these two basis vectors from the shortest three translation vectors in that plane. They are shown in Fig. 2.2.16.1 and labelled e, f and g, in order of increasing length.<sup>11</sup> The two shorter vectors span the `reduced mesh', here e and f; for this mesh, the monoclinic angle is , whereas for the other two primitive meshes larger angles are possible.

Figure 2.2.16.1| top | pdf | The three primitive two-dimensional cells which are spanned by the shortest three translation vectors e, f, g in the monoclinic plane. For the present discussion, the glide vector is considered to be along e and the projection of the centring vector along f.

Other choices of the basis vectors in the monoclinic plane are possible, provided they span a primitive mesh. It turns out, however, that the space-group symbol for any of these (non-reduced) meshes already occurs among the symbols for the three meshes formed by e, f, g in Fig. 2.2.16.1; hence only these cases need be considered. They are designated in this volume as `cell choice 1, 2 or 3' and are depicted in Fig. 2.2.6.4. The transformation matrices for the three cell choices are listed in Table 5.1.3.1 .