Crystallography
A crystal is a
solid object with a geometric shape that reflects a “long-range” regular
internal structure.
Space lattice: The
regular internal structure of a crystal is manifested by the existence of a
space lattice, which is "an array of
points in space that can be repeated indefinitely".
Unit cell: A unit cell is the smallest number of "points"
which completely define the space lattice. The repetition of those points or
unit cells in a space lattice is performed by certain operations which build the space lattice.
The selection of unit cells:
Ø The
smallest sized unit that retains the characteristics of the space lattice.
Ø Edges
of the cell should coincide with symmetry axes.
Ø Edges
of the cell related to each other by the symmetry of the lattice.
The Crystal Systems
The crystal classes are grouped
into seven crystal systems based on the following criteria:
1)
Relative lengths of the crystallographic axes
2)
Number of crystallographic axes
3)
Values of the inter-axial angles
4)
Some essential element of symmetry
The seven crystal systems are:
(1) The Cubic system:
Three crystallographic axes, a = b = c, = = = 90. Essential element of
symmetry is a three-fold rotary or rotary inversion axis.
(2) The Tetragonal system:
Three crystallographic axes, a = b c, = = = 90. Essential element of
symmetry is a four-fold rotary or rotary inversion axis.
(3) The Rhombohedral system:
Four crystallographic axes, three of which are equal and coplanar and at angles
of 120°, fourth axis "c" is perpendicular to the other three axes,
and is characterized by commonly being a three fold axis of symmetry.
(4) The Hexagonal system:
Four crystallographic axes, three of which are equal and coplanar (a1,
a2, a3) and at angles of 120°, fourth axis (c) is
perpendicular to the other three axes, and is characterized by being a six fold
axis of symmetry.
(5) The Orthorhombic system:
a b c, = = = 90. Essential element of
symmetry is a two-fold rotary axis.
(6) The Monoclinic system:
a b c, = = 90, > 90. Essential element of
symmetry is a two fold rotary axis or a plane. The 2-fold rotational axis or
the direction perpendicular to the mirror plane is usually taken as the b axis,
the a axis is inclined to the front (b > 90°), and c is
vertical.
(7) The Triclinic system:
a b c, . No essential element of
symmetry. Additional criteria: As much as possible, b and a
should be both > 90°. The most pronounced zone should be vertical.
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Article By
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Mr.Ibhrahim
Assistant Professor
H&S Department
LAQSHYA Institute of Technology & Sciences
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