Point Symmetry Operations in Crystallography

These flashcards cover key vocabulary and concepts related to point symmetry operations in crystallography, aiming to assist students in understanding fundamental terms and principles as outlined in the lecture notes.

Symmetry

The property of an object that remains unchanged under certain transformations such as rotation or reflection.

Transformation

An operation that alters the position, size, or shape of an object, while preserving its fundamental properties.

Point Symmetry Operation

A symmetry operation that is specified with respect to a point in space that does not move during the operation.

Stereographic Projection

A method of projecting three-dimensional objects onto a two-dimensional plane while preserving angles.

Translational Symmetry

A form of symmetry where an object can be translated along certain directions and remain unchanged.

Active Operator

An operator that moves all points and position vectors while keeping the reference axes fixed.

Passive Operator

An operator that moves the reference axes without altering the positions of the points.

Rotation Matrix

A matrix that represents a rotation operation in the coordinate system.

Improper Rotation

A transformation that involves a rotation followed by a reflection, which changes the handedness of the object.

Centrosymmetry

A form of symmetry where each point has a corresponding point at an equal distance on the opposite side of a center.

Mirror Reflection

A symmetry operation where points are reflected across a mirror plane, effectively producing a mirror image.

Schönflies Notation

A system of symbols used to describe molecular and crystal symmetries.

Hermann-Mauguin Notation

An international notation used to specify symmetry in crystals using alphanumeric symbols.

Center of Inversion

A symmetry element where for every point in an object, there exists an equivalent point directly opposite through a center.