|
|
|
|
Bravais Crystal Lattice @ Jewel Info 4 U
By:Ritika
Bravais crystal lattice in
crystallography is used to explain
the geometrical symmetry of a
crystal in details. The other term
used to refer to bravais crystal
lattice is space lattice.
There are about fourteen distinct
bravais crystal lattices. A crystal
structure is one of the
characteristics of minerals which
form the base for bravais crystal
lattice in crystallography. Those
are the 14 bravais lattices used to
describe crystal structures. A
bravais lattice is the period
arrangement of points that through
repeated translation of the lattice
vectors will fill space. All
crystals could be defined in detail
by any of these fourteen bravais
crystal lattices. Bravais lattice
took its name after Auguste Bravais.
Lattice Type and Lattice
Centering
The kinds of lattice centering used
by bravais lattice system are:
* Primitive Centering: In this,
lattice points lie on the corner of
the cells alone.
* Body Centered: In the body
centered lattice centering, there
are lattice points lying on the
corner of the cells along with one
more lattice point placed on the
centre of the cell.
* Face Centered: In the face
centered style, there are lattice
points lying on the corner of the
cells along with a lattice point
placed at centre of each of the
faces of the cell.
* Centered on a Single Face: In
this, as the name implies, there is
one additional lattice point at the
center of one of the cell faces.
The seven crystal systems are
combined with the various possible
lattice centering defined as above
which results in bravais crystal
lattice in crystallography. The two
dimensional centering is simple
since a parallelogram has only one
face whereas the three dimensional
ones have more options which leads
to six different centering
arrangements.
Fourteen Bravais Crystal
Lattices
The bravis crystal lattice has
fourteen bravais lattices which all
occupy the three-dimensional space.
These fourteen bravais lattices are
defined based on the seven crystal
systems. There are 230 space groups
with 32 crystallographic point
groups. Except quasi crystals, all
other crystalline materials lie in
one of the fourteen bravais crystal
lattices. The fourteen bravais
crystal lattices or space lattices
are:
* Triclinic Bravais Crystal Lattice
* Simple Monoclinic Bravais Crystal
Lattice
* Base Centered Monoclinic Bravais
Crystal Lattice
* Simple Orthorhombic Bravais
Crystal Lattice
* Base-Centered Orthorhombic Bravais
Crystal Lattice
* Body-Centered Orthorhombic Bravais
Crystal Lattice
* Face-Centered Orthorhombic Bravais
Crystal Lattice
* Hexagonal Bravais Crystal Lattice
* Rhombohedral or Trigonal Bravais
Crystal Lattice
* Simple Tetragonal Bravais Crystal
Lattice
* Body-Centered Tetragonal Bravais
Crystal Lattice
* Simple Cubic or Isometric Bravais
Crystal Lattice
* Body-Centered Cubic Bravais
Crystal Lattice
* Face-Centered Cubic Bravais
Crystal Lattice
Let's know a little about each of
the above fourteen bravais crystal
lattices.
* Triclinic Bravais Crystal Lattice:
In the triclinic bravais crystal
lattice, vectors of unequal length
are used for defining the crystal
system. In addition, in this crystal
lattice, the three vectors used are
not mutually orthogonal.
* Simple Monoclinic Bravais Crystal
Lattice and Base Centered Monoclinic
Bravais Crystal Lattice: The
monoclinic bravais lattice also is
defined by using vectors of unequal
length. The resulting structure is a
rectangular prism with base having
the shape of a parallelogram. In
this bravais crystal lattice, two
pairs of perpendicular vectors are
used with third pair having an angle
other than 90 degrees.
* Simple Orthorhombic Bravais
Crystal Lattice , Base-Centered
Orthorhombic Bravais Crystal Lattice
, Body-Centered Orthorhombic Bravais
Crystal Lattice and Face-Centered
Orthorhombic Bravais Crystal
Lattice: If a cubic lattice is
stretched along two lattice vectors
it results in a rectangular prism
with base having the shape of
rectangle and this is termed as
orthorhombic lattices. In the
orthorhombic lattices all the three
bases intersect at 90 degrees with
also the three vectors being
mutually orthogonal.
* Hexagonal Bravais Crystal Lattice:
In the hexagonal crystal lattice,
the symmetry is equal as the right
prism has a hexagonal base. An
example of this is graphite.
* Rhombohedral or Trigonal Bravais
Crystal Lattice: The rhombohedral
bravais crystal lattice is also
termed as Trigonal bravais crystal
which is well defined by using
vectors of equal length. In
addition, it is also important to
note that all the three vectors used
to define the rhombohedral bravais
crystal lattice are not mutually
orthogonal. The rhombohedral bravais
crystal lattice is similar to the
cubic system being stretched along
diagonally across the body.
* Simple Tetragonal Bravais Crystal
Lattice and Body-Centered Tetragonal
Bravais Crystal Lattice: Tetragonal
crystal lattice is obtained by using
a cubic lattice and stretching the
same along a lattice vector. The
tetragonal crystal lattice is
similar to a rectangular prism
having the base as the shape of
square.
* Simple Cubic or Isometric Bravais
Crystal Lattice: Each corner of a
cube is defined with a lattice point
in the case of cubic crystal system.
Also, each lattice point shares
equal spacing between eight adjacent
cubes
* Body-Centered Cubic Bravais
Crystal Lattice: In the case of
body-centered cubic crystal system,
there are eight corner points
defined with a lattice point in each
of these right corner points. In
addition to this one, more lattice
point is used to define the center
of the unit cell.
* Face-Centered Cubic Bravais
Crystal Lattice: In the
face-centered cubic crystal system,
the lattice points are placed on the
faces of the cube.
Bravais lattices in Two
Dimensional Space
There are five Bravais lattices in
two dimensional spaces. They are:
* Oblique
* Rectangular
* Centered Rectangular
* Hexagonal and
* Square
Bravais lattices in Four
Dimensional Space
There are fifty two bravais lattices
in four dimensional space. Of these
fifty two bravais lattices, twenty
one are primitive and thirty one are
centered.
The point group of the bravais
lattice is the set of all point
operations that leave the lattice
invariant. Also, the bravais
lattices associated with the same
space group are considered the same
type, although they are not
equivalent. That is, the bravais
lattices associated with the same
point group as classified as the
same crystal system. It is vital to
note that a two-dimensional
honeycomb do not form a bravais
lattice. A bravais lattice is a
lattice in which every lattice
points have exactly the same
environment. That is, the bravais
lattice can be spanned by primitive
vectors.
Related Links :
|
 |
Belly Button Piercing
The Egyptians, the Indians and many other cultures pierced this humble button to show the significance of the person sporting a pierced navel - Royalty, Warriors, exceptional Beauty. |
|
|
|
|
|
|
|
