Symmetry and Crystallographic axis

Symmetry and Crystallographic axis

i) Symmetry

ii)  Crystallographic axis

Symmetry:

Symmetry is understood a sort of regularity in the arrangement of faces on the body of a crystal. Symmetry is a property of fundamental importance for a crystal. It can be studied with reference to three different characters, commonly called elements of symmetry. These are:

A plane of symmetry An axis of symmetry Centre of symmetry

A plane of symmetry

Any imaginary plane passing through the centre of a crystal in such a way that it divides the crystal in two exactly similar halves is called plane of symmetry. In other words, a plane of symmetry is said to exist in a crystal when for each face, edge or solid angle there is another similar face, edge or solid angle occupying identical position on the opposite side of this plane.

An axis of symmetry:

It is defined as an imaginary line in a crystal passing through its centre in such a way that when a crystal is given a complete rotation along this line a certain cryatl face comes to occupy the same position at least twice. The nature of the axis of the symmetry into one of four types:

Axis of Binary or twofold symmetry

This requires that a crystal must be rotated by an angle of 180^o to bring the reference face occupy the same position.

Axis of Trigonal or threefold symmetry

It is that axis on which a crystal must be rotated by an angle of 120^o for a reference face to occupy the same position again in space.

Axis of tetragonal or fourfold symmetry

It is that axis on which the crystal must be rotated by an angle of 90⁰ to bring a reference face in the same position in space.

Axis of hexagonal or six fold symmetry:

In which a rotation of 60⁰ is required to fulfil the condition of repetition of reference face.

Centre of symmetry

A crystal said to possess a centre of symmetry if on passing an imaginary line from some definite face, edge or corner on one side of the crystal through its centre another exactly similar face or edge or corner is found on the other side at an equal distance from the centre.

ii) CRYSTALLOGRAPHIC AXES

These are also termed as axes of reference and are simply certain imaginary lines arbitrarily selected in such a way that all of them pass though centre of an ideal crystal. The concept of axes of reference is based on the fact that exact mathematical relations exist between all the faces on a given crystal with reference to its centre.

In crystallography following general assumptions have been universally agreed upon regarding these crystallographic lines:

a)     Three Straight Lines, essentially passing though a common centre and varying in mutual relationships with respect to their lengths and angular inclinations from: all equal, Interchangable and it right to all unequal and inclined with each other.

b)   Four straight lines, essentially passing through a common centre; one vertical, being unequal to the other three but at right angles to them. The three horizontal axes are separated

from each other at 120⁰

The concept of crystallographic axis has been the basis of classifying all, the crystalline substances into six crystal systems.