THE ELEMENTS OF SYMMETRY
Crystals
are built up of atoms which constitute the internal structure of the crystals.
The unit cells within the crystal repeat themselves in a regular pattern
causing most crystals to appear symmetrical.
Symmetry
is defined as the degree of regular positions of common features (faces, edges,
nodes, etc.) on a crystal. The degree of
symmetry varies from one crystal to another and this variation has been used to
classify crystals into systems and classes.
The
three important symmetry elements are:
-
Center of symmetry
-
Axis of symmetry and
-
Plane of symmetry
1) Center
of symmetry: It is an imaginary point within a crystal
around which like features (faces, edges, nodes, etc.) on the crystal are
arranged on opposite sides and are equidistant from it.
In crystals that have centers of
symmetry, it is assumed that each feature on the crystal has a corresponding
feature on the opposite side of an imaginary point in the middle called the
center of symmetry. Such features can be
linked by a line passing through this point.
Most crystals especially those of the cubic system
have centers of symmetry.
F1-F
indicates Faces,
E1-E
indicates Edges,
N1-N
indicates Nodes which are on opposite sides and Equidistant from the point O which is the center of symmetry.
|
2) Plane
of symmetry:It is an imaginary line
or position through which a crystal can be cut or divided into two equal and
similarly placed halves such that one half is a mirror image of the other. In regularly formed crystals, the planes of
symmetry are either axial or diagonal.
For
example, a cube has 9 planes of symmetry (3 axial and 6 diagonal).
3) Axis
of symmetry: it is an imaginary line passing through a
crystal about which a crystal can be rotated through 360o (a
complete turn) so that the same features (faces, edges, or nodes) come to
occupy the same position in space more than once.
The degree of regularity of a feature
in space during one complete rotation is known as the fold. Fold of an axis of
symmetry is the number of times any feature of a crystal occupies the same
position in a complete rotation.
That
is 360o/n (where n ≠
1). n
represents the degree of the axis.
There
are 4 axes of symmetry:
Fold
|
Other
name
|
Symbol
|
n value
|
|
1.
|
Two fold
|
Diad
|
 |
n = 2
The same view occurs
every 180o on rotation
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2.
|
Three fold
|
Triad
|
n = 3
The same view occurs
every 120o on rotation
|
|
3.
|
Four fold
|
Tetrad
|
n = 4
The same view occurs
every 90o on rotation
|
|
4.
|
Six fold
|
Hexad
|
n = 6
The
same view occurs every 60o on rotation
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|
5.
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The symmetry
elements are very important because they have been used to classify crystals
into systems and systems into classes.
All together there are 32 symmetry classes and 7 symmetry systems.
7 Systems
|
32 Classes
|
The class in a system that has the highest symmetry elements
is known as the Holosymmetry class. For example; Galena falls under the Cubic
system and has 32 symmetry elements.
Each system
has a characeristic symmetry element which is a diagnostic property to that
system while the other elements simply define the classes of that system.
The
following table shows the different systems and their diagnostic symmetry
elements:
System
|
Number
of classes
|
||
1.
|
The Cubic System
|
5
|
4iii
|
2.
|
The Tetragonal System
|
7
|
1iv
|
3.
|
The Hexagonal System
|
7
|
1vi
|
4.
|
The Trigonal System
|
5
|
1iii
|
5.
|
The Orthorhombic
System
|
3
|
3ii
|
6.
|
The Monoclinic System
|
3
|
1ii
|
7.
|
The Triclinic System
|
2
|
None
|
50%
of all known crystals belong to the monoclinic system
10%
belong to the triclinic system
25%
belong to the orthorhombic system.
Of
the remaining 4 systems, the Cubic system is the most abundant followed by the
Tetragonal, Trigonal and finally the Hexagonal system.
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