1. Crystal Structure and Notation
Definition of a Bravais Lattice:
Infinite array of points with an arrangement and orientation that appears exactly the same viewed from any of the points.
In 3-dimensions, all points with R=ha+kb+lc
a,b,c 3 non-coplanar vectors. (primitive or basis vectors that generate or span the lattice). h, k, l are integers.
Example:
a=ax
b=by

2. Primitive Unit Cell
Volume of spact that, when translated through all vectors in a Bravais lattice just fills all space. (many possible choices).
1 lattice point/primitive unit cell.
The Wigner-Seitz primitive unit cell has the full symmetry of the lattice, commonly used. It is the region of space that is closer to the chosen lattice point than to any other lattice point.