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Crystallographic Axes and its Symmetry Operations @ Jewel Info 4 U
By:Ritika
Symmetry operations are used to
describe the crystal's outward
symmetry. Symmetry operations help
to define the manner in which a
crystal can repeat the facets or
faces on their crystal's surface.
Mirror Plane
The plane that is used to reflect a
face from one side of the crystal to
the other is termed as mirror plane.
It is important to note that while
being reflected using the concept of
mirror plane, the face of reflection
that is maintained is identical but
reversed in orientation. That is,
for example if the original face has
any right handed characteristics,
then the reflected face should
represent all the same attributes as
the original face with a left handed
attribute.
Center Symmetry Operation
Another symmetry operation that is
worth knowing is called 'center'.
The center symmetry operation refers
to an operation which would invert
the original face of a crystal
through the center of the crystal.
In fact, the resulting effect stands
similar to the operation named as
roto inversion axis which is
explained in detail below. That is,
by this operation, every point of
the crystal is inverted to the other
side of the crystal. The center
operation is mostly applied in
triclinic system which follows a
single fold rotational axis by which
with just a single rotation the
crystal face returns to the original
face of rotation.
Rotational Axis
Rotational axis is an imaginary line
which acts an axis and is drawn on a
crystal. By rotating the crystal
along the axis, it is possible to
repeat a crystal face. Thus it is
possible to generate new crystal
faces at consistent intervals of
rotation done as explained above. It
is also vital to note that the
resulting face should be identical
to the original face only if the
orientation is reversed. The next
point of consideration is the
determination of interval for
rotation of crystal face. The
determination of interval for
rotation of crystal face is done by
dividing the full turn into equal
segment intervals. That is, for
instance 360 degrees is divided into
a segment of four 90 degrees that
results in four fold rotational
axis. Thus the numbers of folds the
rotational axes can have are one,
two, three, four or six. This means
that a singe fold axis of rotational
axis of rotation would rotate the
crystal in 360 degree intervals. The
two fold interval of rotational axis
of rotation would rotate the crystal
in 180 degrees, three fold in 120
degrees each, four fold in 90
degrees as explained before and six
fold of rotational axis of rotation
would rotate the crystal in 60
degrees.
Rotoinversion Axis
Rotoinversion does the functionality
of both rotational axis and
inversion along with this. That is,
the rotoinversion axis after
performing the functionality of
rotation once would invert the face
of crystal along the center of
crystal to the opposite side. Thus,
the out coming face would be totally
flipped. For instance, if the
original face is up, the resulting
face would be down and if the
original face is right the resulting
face would be left. This operation
of rotoinverion axis is done until
the operation returns to the
original face. Apart from this, the
rules, determination of interval for
rotation namely folds explained
above for rotational axis all holds
good even for rotoinversion axis.
Crystallographic Axes
The crystallographic axes are used
mainly by crystallographers. These
axes are similar to the geometric
axes and are used for plotting the
orientations of faces and symmetry
elements in crystals. It is
important to know that it is not
vital that the crystallographic axes
should be part of symmetry of the
crystals. It can also be present or
not within the symmetry of the
crystals. Generally, it would be
present in the symmetry of crystal
because crystallographers would try
the orientation mostly along the
planes and axes of symmetry to study
the operations and orientations of
crystals in depth.
The seven system of crystallography
along with the folds required for
the axis of rotation are given
below:
* ISOMETRIC: The isometric crystal
system requires four three fold axes
of rotation. Instances of minerals
and crystals in this system are
spinel, lazurite, analcime, galena,
gold, fluorite, almandine, halite,
cobaltite, diamond, tetrahedrite,
bixbyite and so on.
* TETRAGONAL: The tetragonal crystal
system requires a single four fold
axis of rotation. Instances of
minerals and crystals in this system
are zircon, carletonite, rutile,
scapolite, anatase, vesuvianite,
narsarsukite, autunite, xenotime,
thorite, zeunerite and so on.
* HEXAGONAL: This crystal system
need a single six fold axis of
rotation. Instances of minerals and
crystals in hexagonal system are
aquamarine, gmelinite, pyrrhotite,
apatite, ettringite, molybdenite,
hanksite, thaumasite, vanadinite and
so on.
* TRIGONAL: This crystal system need
a single three fold axis of
rotation. Instances of minerals and
crystals in trigonal system are
sapphire, ankerite, ruby, sturmanite,
magnesite, pyrargyrite,
hematite,rhodochrosite,
cinnabar,elbaite and so on.
* ORTHORHOMBIC: The orthorhombic
crystal system should possess three
two fold axes of rotation or one two
fold axis of rotation with two
mirror planes along with this.
Instances of minerals and crystals
in this system are topaz, staurolite,
barite, anhydrite, chrysoberyl,
olivine, celestite and so on.
* MONOCLINIC: The monoclinic crystal
system requires either a single two
fold axis of rotation or a single
mirror plane. Instances of minerals
and crystals in this system are
brazilianite, aegirine, azurite,
borax, catapleiite, muscovite,
huebnerite, crocoite and so on.
* TRICLINIC: This crystal system
should possess either a center
operation of symmetry or
translational symmetry. Instances of
minerals and crystals in triclinic
system are babingtonite, inesite,
bytownite, kyanite, turquoise,
albite, rhodonite, oligoclase and so
on.
Generally the substances that are
non-crystalline are amorphous. They
do not have any symmetry and so
could not be classified under any
crystallographic system.
The symmetry of the lattice is thus
used for determining the angular
relationships between crystal faces.
The measurements of the angles
between crystal face is used for
calculating the relative lengths of
the crystallographic axes or unit
cell edges. The crystallographic
axes help to define a coordinate
system within the crystal.
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