The symmetry of crystals. Representation
of Bravais
lattices
The
repetition modes by translation in crystals must be compatible with the
possible crystallographic point groups (the 32 crystal classes),
and
this is why we find only 14 types
of translational lattices which are
compatible with the crystal classes.
These types of lattices (translational repetiton modes) are known as
the Bravais
lattices...
The lattice points (black and gray points) do not represent atoms. They
represent places in space that are indistinguishable from each other.
An observer at any of these points would not be able to distinguish in
which of them he is located.
Symbols P
C I
F R refer to the
different lattice types:
- P
=
primitive, there is only 1 reticular point inside the cell. It has
1 point
in each of the 8 corners, but only 1/8 of point inside the cell, that
is, 8/8=1 complete lattice point in the cell.
- C
= centered on the two faces perpendicular to the c
axis of the unit cell. It has 2 complete lattice points
within
the cell, that is, 1 complete point corresponding to the 8/8 of
vertices and 2/2 that correspond to the faces perpendicular to the c
axis. In total: 8/8 + 2/2 = 2.
- I =
centered in the body of the cell. It has 2 complete reticular points
within the cell, 1 complete in the center of the body, and the usual
8/8.
- F =
centered in all faces of the cell. It has 4 complete lattice
points within the cell, 6/2 corresponding to the centers of the faces
and the usual 8/8.
- R
=
primitive, identical cell axes and cell angles, or hexagonal two times
body centered containing 3 complete lattice points, that is, 2 on a
diagonal of the cell body and the usual 8/8.
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