Lattice Positions, Directions,
and Planes
Lattice positions are expressed through fractions of unit cell
dimensions.
Equivalent positions are connected by the lattice translations,
consisting of integral multiple of lattice constants along
directions parallel to crystallographic axes.
Such as set of directions, which are structurally
equivalent, is called a famil of directions and is
designed by angular brackets, <>.
Lattice planes are expressed through Miller* Indices.
The integers represent the inverse of axial interccepts.
The grenral notation for Miller Indices is (hkl), and it
can be used for any of the seven crystal systems.
Because the hexagonal system can be conviniently
represented by four axes, a four-digit set of MillerBravais Indices.
As for structurally equivalent directions, we can group
structurally equivalent planes as a family of planes
with Miller or Miller-Bravais Indices enclosed in braces
Polymeric Structures
In those regions of the microstructure that are
crystalline, the structure tends to be quite complex.
The complexity of the unit cells of common polymers
is generally beyond the scope.