Title: Theory / Unimportant / Experimental / Chemistry / Symmetry
Tags: fromMath mathToDef mathToSee complex

Name: A symmetry of \(O\)
Definition: Some operation which can be carried out on \(O\), such that \(O\) is unchanged once the operation is completed.
Page: 869
Chapter: III
Variables: \(O\) an object

Name: A point symmetry of \(O\)
Definition: A symmetry of \(O\) which leaves exactly one point unchanged.
Page: 869
Chapter: III
Variables: \(O\) an object

The point symetry are:
-Rotations around an axis,
-reflection across a plane,
-inversion through a point and
-rotation around an axis, followed by inversion through a point on the axis.
Page: 869
Chapter: III

Name: An \(n\)-fold rotation axis
Definition: A rotation through an angle \(360^\circ/n\).
Page: 869
Chapter: III
Variables: \(n\) an integer

Name: Mirror plane
Definition: The symmetry element of a reflection symmetry.
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Chapter: III
Name2: Plane of symmetry

Name: Center of symmetry
Definition: The fixed-point of a point-symmetry.
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Chapter: III

Name: An \(n\)-fold rotatory inversion axis
Definition: An \(n\)-fold rotation followed by inversion through a partical point on the axis.
Page: 869
Chapter: III
Variables: \(n\in\mathbb N\)
Context: Chemistry

Q: \(S\) admits [...] and [...].
A: a point, common to all of its axis, mirror plane and conter of symmetry; is a group
Page: 869
Chapter: III
Variables: \(m\) a molecule
\(S\) its set of symmetry

Name: Translation symmetry
Definition: A translation of the cristal by a vector displacement equal to any of the three crystal axes, or any combination of integral multiples of the axes.
Page: 871
Chapter: III
Variables: \(m\) a crystal

Q: \(l\) has [...] at [...].
A: centers of symmetry; the lattice points
Page: 873
Chapter: III
Variables: \(l\) a lattice

Q: \(l\) may have:
-[...]
-[...].
A: mirror symmetry; 1-,2-,3-,4- and 6-fold rotation
Page: 873
Chapter: III
Variables: \(l\) a lattice

Name: Crystallographic point groups
Definition: The group of symmetry of lattices.
Page: 873
Chapter: III
Name2: The crystal classes

A symmetry point group is represented using:
-2,3,4, and 6 for the multiplicity of their rotation axes
-\(\overline 2, \overline 3, \overline 4, \overline 6\) for the rotary inversion axes
-\(\overline 1\) for a center of symmetry
-m for a mirror
Page: 873
Chapter: III

Name: The principal axis
Definition: The rotation or rotatory inversion axis of highest multiplicity.
Page: 873
Chapter: III
Variables: \(m\) a lattice

Q: The order of the description in a crystallographic point groups:
-[...]
-[...]
-[...]
A: principal axis; secondary axis; miror plane
Page: 873
Chapter: III

Definition: A miror plane parallel to a \(n\) principal axis.
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Chapter: III
Variables: \(n\) be 2, 3, 4, or 6
Notation: \(n\)m

Definition: A miror plane perpendicular to a \(n\) principal axis.
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Chapter: III
Variables: \(n\) be 2, 3, 4, or 6
Notation: \(n\)/m

Question: The secondary axis possible are:
Answer: 2-fold axes, apart for the cubic group.
Page: 874
Chapter: III