Crystal Symmetry

By Tirumala Prasad

Symmetry in crystals is due to the orderly arrangement of atoms. Such an arrangement of atoms is known as the lattice. In crystals there is a three dimensional arrangement of atoms. Such an arrangement is known as the space lattice. The imaginary lines drawn through the crystal lattice are known as the crystallographic axis. The arrangement of lattice points does determine the angular relationships and also the possibility of the development of the crystal faces. In a perfectly ordered lattice, the angular relationships among the crystal faces would be constant and is known as the law of the constancy of inter facial angles. The repetition of the orderly unit cells at regular intervals is known as the translational symmetry.

Centre of symmetry, axis of symmetry, planes of symmetry, etc are known as the symmetry elements. A point or a line about which the symmetry operations are carried out is known as the symmetry element. A non-translational movement of an object that produces a new orientation which is indistinguishable from the original one.

A centre of symmetry is a point in a crystal, along which if lines are drawn, they will meet the faces at equal distances from such a point. A crystal can have as many axis of symmetry and planes of symmetry but it can have only one centre of symmetry. An axis of symmetry is an axis along which if a crystal is rotated for 360 degrees, similar faces will appear. Such repetition is known as self coincidence or invariance. For instance, the minerals belonging to cubic system do possess thirteen axis of symmetry. A plane of symmetry is a plane along which if a crystal is cut in to two halves, one half is the mirror image of the other. For instance, minerals belonging to cubic system do possess nine planes of symmetry.

Roto inversion operation involves both rotation and inversion operations. Translational glide involves reflection and translation operations. Inversion is also an important symmetry operation.

The study of symmetry is important to identify the crystals, to understand their atomic structure, and also physical properties related to mechanics, optics, electricity, magnetism, etc.

The orientation of the crystallographic axis is variable in several crystallographic systems. There are primarily six crystallographic systems as cubic, tetragonal, hexagonal, orthorhombic, monoclinic, and triclinic. The cubic system does have three axis of equal length. All the three axis are separated from each other by ninety degrees. The vertical axis is longer than the remaining two axis in tetragonal system but all are separated from each other by ninety degrees. There are four crystallographic axes in the hexagonal system. Three of them are of equal length but the vertical one is longer axes. The orthorhombic axes resemble a match box. One axes is inclined in the monoclinic system. All the three axes are inclined in the triclinc system.

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