Different Types of Symmetry in Cubic Lattices
Category : JEE Main & Advanced
(1) Centre of symmetry : An imaginary point within the crystal such that any line drawn through it intersects the surface of the crystal at equal distances in both directions.
(2) Plane of symmetry : It is an imaginary plane which passes through the centre of a crystal and divides it into two equal portions such that one part is exactly the mirror image of the other.
A cubical crystal possesses six diagonal plane of symmetry and three rectangular plane of symmetry.
(3) Axis of symmetry : It is an imaginary straight line about which, if the crystal is rotated, it will present the same appearance more than once during the complete revolution. In general, if the same appearance of a crystal is repeated on rotating through an angle \[\frac{{{360}^{o}}}{n}\], around an imaginary axis, the axis is called an n-fold axis.
A cubical crystal possesses in all 13 axis of symmetry
| Axis of four-fold symmetry = 3 (Because of six faces) | Axis of three-fold symmetry = 4 (Because of eight corners) | Axis of two-fold symmetry = 6 (Because of twelve edges) |
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(4) Elements of symmetry : The total number of planes, axes and centre of symmetry possessed by a crystal are termed as elements of symmetry. A cubic crystal possesses a total of 23 elements of symmetry.
Planes of symmetry\[=(3+6)=9\],
Axes of symmetry\[=(3+4+6)=13\],
Centre of symmetry = 1.
Total number of symmetry elements = 23
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