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Unit cell (UC): (elementary cell :?: )
You can assembly from them the crystal. It is defined with elementary translation vectors.
Basic property of the lattice is periodical repetition of the translation vectors.
Primitive cell (PC):
Unit cell with the lowest bulk. It contains only one lattice point.
diamond structure is two cells with FCC lattice, where one is moved (1/3 of body diagonal) in the orientation of body diagonal. (see attached picture)
properties:
=====SC=====
bulk of UC: a³
bulk of PC: a³
number of lattice points in UC: 8×1/8
=====BCC=====
bulk of UC: a³
bulk of PC: a³/2
number of lattice points in UC: 8×1/8+1=2
=====FCC=====
bulk of UC: a³
bulk of PC: a³/4
number of lattice points in UC: 8×1/8+3=4
=====DIAMOND=====
bulk of UC: a³
bulk of PC: a³/4
number of lattice points in UC: (8×1/8+3)*2=8 :?: number of 8 is correct, but i don't remember how can you get it
The crystal structure of a material is often discussed in terms of its unit cell. The unit cell is a spatial arrangement of atoms which is tiled in three-dimensional space to describe the crystal. The unit cell is given by its lattice parameters, the length of the cell edges and the angles between them, while the positions of the atoms inside the unit cell are described by the set of atomic positions (xi,yi,zi) measured from a lattice point.
For each crystal structure there is a conventional unit cell, which is the smallest unit that has the full symmetry of the crystal (see below). However, the conventional unit cell is not always the smallest possible choice. A primitive unit cell of a particular crystal structure is the smallest possible unit cell one can construct such that, when tiled, it completely fills space. This primitive unit cell does not, however, display all the symmetries inherent in the crystal. A Wigner-Seitz cell is a particular kind of primitive cell which has the same symmetry as the lattice.
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