SOME SYMMETRY EXAMPLES
variety - AMETHYST
Minerals usually form distinct crystals.
The shape of the crystals has
been found to play an important role in the identification of minerals.
The study of crystals is called crystallography and is an important field
of study. Not only do scientists in this field study natural crystals but
also the crystals formed by metal alloys, chemicals, and other synthetic
materials. Often it is the use of crystallographic tools, such as an x-ray
spectrometer, that find and distinguish new minerals as well as verify
or correct the identification of specimens. It is through the use of these
tools that the structure of a crystal can be gleaned.
How can crystallography help an ordinary rockhound to identify minerals?
A mineral's crystalline structure, the arrangement of its component atoms
and/or ions, is responsible for the outward shape of the crystal (see crystal
and crystal forms).
Rarely does one mineral form crystals that are completely unique to itself.
Rather, a mineral will form crystals that are consistent with the symmetry
class that the mineral falls into, based on its own structure. Also, symmetry
affects a number of other properties such as cleavage,
hardness and at times
what symmetry class a mineral belongs to is very helpful in identifying
There are several symmetry operations that help define the crystal's
outward symmetry. These operations represent the way a crystal can repeat
the facets or faces on their crystal's surface.
One way to repeat a face is with a mirror plane that can reflect
a face from one side of the crystal to the other. Consequent to being reflected
by a mirror plane, the reflected face must be identical but reversed in
orientation. In other words, if the original face has any right handed
characteristics, then the reflected face must have the same characteristics
but with a left handed slant to them.
A rotational axis is a line imaginarily drawn through the crystal
that acts as an axis just like the axis for a tire. A face can be repeated
on a crystal when the crystal is rotated around this axis and a new face
is left at various intervals during the rotation. Consequent to being rotated
is that the face must be identical to the original face when the face is
viewed head on. In other words, if the face has a right handed slant and
is rotated, the rotated faces must keep the right handed slant.
The interval for dropping a face is determined by a division of the
full turn into equal segments. For example, to drop four faces on a crystal
the rotation requires a stop at every 90 degrees and this type of rotation
is called a four fold rotational axis. Rotational axes can have rotations
of 1, 2, 3, 4 and 6 fold. Thus the 1 fold axis rotates the crystal in 360
degree intervals, the 2 fold interval is 180 degrees, the 3 fold interval
is 120 degrees, the 4 fold interval is 90 degrees and the 6 fold interval
is 60 degrees.
A rotoinversion axis goes one step further, by after rotating
once and before dropping a face, it inverts the face through the crystal's
center to the other side. The resulting face is completely flipped, i.e.,
up is down and right is left. The rotoinversion continues until it returns
to the original starting face. Rotoinversion is constrained by the same
rules for the simple rotational axes with the same folds or turns and degrees.
Finally a symmetry operation called a center is all that is left
of symmetry operations to discuss. A center is simply, or perhaps not so
simply, an operation that takes a face on one side of a crystal and inverts
it through the center of the crystal. This has the same effect as the inversion
in a rotoinversion operation in that the face is completely flipped up
to down and right to left. Every point in a crystal is inverted to the
other side of the crystal. Usually, a center is one operation that is all
but ignored in most crystals because it is often caused by the juxtaposition
of other symmetry operations. However in the triclinic system it is the
only possible symmetry operation except for a one fold rotational axis,
which is actually just returning a crystal face to its original position.
Other axes mentioned are crystallographic axes that are used by crystallographers
like geometric axes to plot the faces and symmetry elements and their orientations
within the crystal. These axes may or may not be part of the symmetry of
the crystals. But they usually are since crystallographers will often orient
the crystallographic axes along the planes and axes of symmetry.
Below is a list of links to the seven crystallographic systems and their
member classes. Listed with the systems are the minimal requirements for
a mineral to belong to that particular group. All crystalline solids can
be classified as belonging to one of these systems based on its structure
and inherent symmetry. Substances that are non-crystalline are called amorphous
(without form) and are thus not classified.
THESE ARE THE SEVEN CRYSTALLOGRAPHIC SYSTEMS:
4 three fold axis of rotation.
1 four fold axis of rotation.
1 six fold axis of rotation.
1 three fold axis of rotation.
either 3 two fold axis of rotation or 1 two fold axis of rotation and two
either 1 two fold axis of rotation or 1 mirror plane.
either a center or only translational symmetry.
AMORPHOUS; no symmetry is present and it is therefore not a crystallographic system.
MORE SYMMETRY EXAMPLES
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