Symmetry in crystallography pdf

  • What are the elements of symmetry?

    A symmetry element is a geometrical entity about which a symmetry operation is performed.
    A symmetry element can be a point, axis, or plane.
    A symmetry operation is the movement of a body (molecule) such that after the movement the molecule appears the same as before..

  • What are the essential symmetry of crystals?

    In crystals, the symmetry axes (rotation axes) can only be two-fold (2), three-fold (3), four-fold (4) or six-fold (6), depending on the number of times (order of rotation) that a motif can be repeated by a rotation operation, being transformed into a new state indistinguishable from its starting state..

  • Although objects themselves may appear to have 5-fold, 7-fold, 8-fold, or 12-fold rotation axes, these are not possible in crystals.
The unique symmetry operation in an orthorhombic system is The unique symmetry operation in an orthorhombic system is 2/m 2/m 2/m – Three twofold axis of 

What is a special class of symmetries in crystallography?

However, a special class of symmetries in crystallography is represented by proper or improper rotations followed by a non-lattice translation

The rotational part of a roto-translation operator must leave either a line or a plane invariant


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