Symmetry Operations

Important factors in determining crystal structure

Lattice Arrangement

Crystal axes a, b and c

Type of basis

Set of symmetry operation

Crystal Symetry

Crystal have inherent symmetry

It is powerful tool for study the internal structure of crystals

An operation that change the position of a lattice point. However, there is another lattice point at the same position as before the operation.

Types of symmetry operation

Translation

Point Operation

"Combination" Operation

an operation that satisfies eqn:
T = n1a+n2b+n3c

an operation that consists of a rotation about an axis, reflection on a plane and an inverse on a point

a combine
operation of translation and point operation

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There are 4 kinds of operations which is Identity, n-Fold Rotations, Reflection and Inversion.

Identity

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n-Fold Rotations

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Reflection/Mirror

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Inversion

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Point Symmetry Operation

An operation on a fixed point in space

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Inversion Center

A center of symmetry: A point at the center of the molecule.
(x,y,z) --> (-x,-y,-z)

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Reflection Plane

A plane in a cell such that when a mirror reflection in this plane is performed, the cell remains invariant

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