Crystal symmetry

CRYSTAL SYMMETRY

✓ Crystals possess different external symmetries which are described by certain mental operation. 

✓ A symmetry operation is one that takes the crystal into a configuration identical to the initial configuration.

✓ The crystal is said to posses a symmetry element corresponding to an operation, if after performing the particular operation the crystal goes into a position indistinguishable from the initial position.

✓ Thus, a crystal possesses definite symmetry in the arrangement of its external faces.

✓ The symmetry of a crystal is that characteristic of a crystal which indicates that if the parts of an ideal crystal are interchanged, the result produced is just like the original crystal.

✓ The different ways in which the symmetry of a crystal can be specified and combined together is known as 'symmetry class'. 

✓ Importance: The crystal symmetry and its study help the crystallographers to classify crystals into crystal system by a systematic scheme. The type of symmetry possessed by a crystal is also important for studying the physical behaviour of the crystals.

1. Symmetry Elements

In describing the symmetry of crystals, three separate and distinct symmetry elements required to be understood. They are: 

1. Centre of symmetry,

2. Axis of symmetry, and 

3. Plane of symmetry.

1. Centre of symmetry

✓ A centre of symmetry is such a point in the crystal that any straight line drawn through this point intersects the crystal surface at equal distances in both directions and joins identical points (particles) in the crystal. It is also called the centre of inversion.

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✓ Example: The centre of a cube is the centre of symmetry while a tetrahedron does not have a centre of symmetry.

2. Axis of symmetry

✔ An axis of symmetry is a line about which the crystal may be rotated such that after a definite angular rotation about this axis the crystal comes into congruent position.

✔ It is found that crystalline solids can have 2, 3, 4, 6 - fold axes of symmetry corresponding to 180°, 120°, 90°, 60° rotations respectively.

✓ Example: The principal axis of a cube are 4-fold symmetry axis and a hexagonal crystal unit has a 6-fold symmetry axis. 

3. Plane of symmetry

✔ It is the plane drawn in a crystal, which divides a crystal into two similar halves where one half of the crystal is the reflection of the other half.

✔ It is actually a mirror plane. The plane of symmetry of a crystal lo 100 also contains its centre.

✔ Example: A cube have six diagonal planes of symmetry.