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
There are 4 kinds of operations which is Identity, n-Fold Rotations, Reflection and Inversion.
Identity
n-Fold Rotations
Reflection/Mirror
Inversion
Point Symmetry Operation
An operation on a fixed point in space
Inversion Center
A center of symmetry: A point at the center of the molecule.
(x,y,z) --> (-x,-y,-z)
Reflection Plane
A plane in a cell such that when a mirror reflection in this plane is performed, the cell remains invariant