Primitive Cell

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Primitive Cell

The primitive cell is a Fundamental Domain with respect to translational symmetry only. In the case of additional symmetries a fundamental domain is smaller.

A Crystal can be categorized by its lattice and the atoms that lie in a primitive cell (the ''basis''). A cell will fill all the lattice space without leaving gaps by repetition of crystal translation operations.

''Primitive translation vectors'' are used to define a crystal translation vector,

ec T

, and also gives a lattice cell of smallest volume for a particular lattice. The ''lattice'' and translation vectors

ec a_1

,

ec a_2

, and

ec a_3

are ''primitive'' if the atoms look the same from any lattice points using integers

u_1

,

u_2

, and

u_3

.

:

ec T = u_1ec a_1 + u_2ec a_2 + u_3ec a_3

The primitive cell is defined by the primitive axes (vectors)

ec a_1

,

ec a_2

, and

ec a_3

. The volume,

ec V_c

, of the primitive cell is given by the parallelepiped from the above axes as,