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In the 2D lattice below is is possible to pick any
parallelogram to be the unit cell. In practice it is best to choose
the smallest unit cell or the unit cell which provides the most symmetry.
All the parallelograms represent valid unit cells
For some lattice patterns, the smallest unit cell doesn't
describe the present symmetry. It is then desirable to pick a larger
unit cell which does describe the symmetry. If the unit cell contains
another lattice point it is called non-primitive, otherwise it
is primitive.
The smallest unit cell doesn't reflect the symmetry within
the structure
In the special case where there is an angle of 120°
between the lattice directions, it is best to use a hexagonal
unit cell. This unit cell is primitive and, when repeated, leads
to 6-fold symmetry.
This idea holds for 3D lattices though it is more complicated
to demonstrate. Below is a simple example that shows two different units
cells for a cubic close packed lattice. (Crystal packing will
be discussed later in this TLP)
Shown is a rotating cubic close packed structure
This idea holds for 3D lattices though it is more complicated
to demonstrate. Below is a simple example that shows two different units
cells for a cubic close packed lattice. (Crystal packing will
be discussed later in this TLP)
The parallepiped shows one possible unit cell
This idea holds for 3D lattices though it is more complicated
to demonstrate. Below is a simple example that shows two different units
cells for a cubic close packed lattice. (Crystal packing will
be discussed later in this TLP)
The cube shows another possible unit cell. This is the
preferred unit cell for cubic close packed structures because
it contains the most symmetry