Example 6 Find the total number of symmetry elements that exist in a monoclinic
unit cell.
Solution: Looking at Fig. 6.9, we find that there exist:
(i) 2-fold axis parallel to c-axis and passing through the center of the unit cell.
There is only one such axis.
(ii) Two mirror planes intersecting at 90° whose axis is parallel to c-axis. There
are two such planes.
(iii) One center of symmetry at the center of the unit cell.
Thus, there are:
1-diad + 2 surface planes + 1 center of symmetry = 4
Therefore, the total number of symmetry elements in a monoclinic unit cell = 4.
Example 7 Find the total number of symmetry elements that exist in an
orthorhombic unit cell.
Fig. 6.8 Three-dimensional view of ~ 1 and ~ 2
Fig. 6.9 Primitive
Monoclinic
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6 Unit Cell Symmeteries and Their Representations
unit cell.
Solution: Looking at Fig. 6.9, we find that there exist:
(i) 2-fold axis parallel to c-axis and passing through the center of the unit cell.
There is only one such axis.
(ii) Two mirror planes intersecting at 90° whose axis is parallel to c-axis. There
are two such planes.
(iii) One center of symmetry at the center of the unit cell.
Thus, there are:
1-diad + 2 surface planes + 1 center of symmetry = 4
Therefore, the total number of symmetry elements in a monoclinic unit cell = 4.
Example 7 Find the total number of symmetry elements that exist in an
orthorhombic unit cell.
Fig. 6.8 Three-dimensional view of ~ 1 and ~ 2
Fig. 6.9 Primitive
Monoclinic
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6 Unit Cell Symmeteries and Their Representations