Crystallographic symmetry is an important concept in X-ray crystallography. A crystal is said to possess symmetry when the arrangement of atoms in the crystal is repeated in a regular pattern. This means that the crystal can be rotated, translated or reflected in a particular way and still appear the same. Crystallographic symmetry is classified into two types: translational symmetry and rotational symmetry.
Translational symmetry refers to the regular arrangement of atoms in a crystal lattice in three dimensions. This means that the atoms are arranged in a repeating pattern that can be translated along three axes to produce the crystal lattice.
Rotational symmetry refers to the arrangement of atoms in a crystal lattice that is the same when the crystal is rotated around an axis. This can be either a one-fold (no symmetry), two-fold, three-fold, four-fold, six-fold or higher order axis.
The presence of symmetry in a crystal is important for X-ray crystallography because it produces a diffraction pattern that is highly ordered and predictable. When X-rays encounter a crystal, they diffract off the atoms in the crystal in a regular pattern. The diffraction pattern is a result of the interference of the X-rays that have been diffracted by the atoms in the crystal lattice. The angles and intensities of the diffraction spots in the pattern provide information about the arrangement of atoms in the crystal.
The symmetry of the crystal affects the diffraction pattern by determining the positions and intensities of the diffraction spots. For example, a crystal with a high degree of symmetry will produce a diffraction pattern with fewer spots that are highly ordered, while a crystal with a lower degree of symmetry will produce a more complex and disordered diffraction pattern.
Overall, crystallographic symmetry and diffraction play a crucial role in X-ray crystallography, as they provide the basis for determining the 3D structure of biological macromolecules, such as proteins and nucleic acids.