In geometry, biology, mineralogy, and solid state physics, a unit cell is a repeating unit formed by the vectors spanning the points of a lattice. The geometry of the unit cell is defined as a parallelotope in n dimensions.
The concept is used particularly in describing crystal structure in two and three dimensions, though it makes sense in all dimensions. A lattice can be characterized by the geometry of its unit cell. The unit cell is a section of the tiling (a parallelogram or parallelepiped) that generates the whole tiling using only translations, and is as small as possible.
There are two special cases of the unit cell: the primitive cell and the conventional cell. The primitive cell is a unit cell corresponding to a single lattice point. In some cases, the full symmetry of a crystal structure is not obvious from the primitive cell, in which cases a conventional cell may be used. A conventional cell (which may or may not be primitive) is the smallest unit cell with the full symmetry of the lattice and may include more than one lattice point.
Let's suppose we have a Phonon gas in 1-D then:
- density of states g(k)=A/ \frac{ d\omega (k)}{dk} (i don't remember the value of constant A sorry.. :-p :-p )
- The Schroedinguer equation (NO interaction) would be:
H_TOTAL =\Sum_{i}\frac{P^{2} _{i}}{2M}+ \sum_{i}B\omega ^{2}(k)...
How would I go about finding the APF for a simple hexagonal unit cell. Which is a rectangle. I know one length is a0(HCP) but I cannot figure out the other side of the rectangle. Also, wouldn't the height be the c?