• Septim

#### Septim

Greetings everyone,

I am taking a course on elementary condensed matter physics and our textbook is "Introduction to Solid State Physics" by Charles Kittel. I have read the crystal structure from 4 books; however, I am still confused about the definitions such as unit cell, primitive vector and primitive basis vectors. Is the unit cell only consists of the lattice or the lattice + basis? I have made a searched and it seems that the latter is more appropriate. Are there such things as non-primitive basis vectors and primitive basis? These terms confuse me a lot. I would be glad if you can come up with an explanation or guide me to references.

The unit cell can be primitive or non-primitive (sometimes called "conventional unit cell").
For the same lattice you can use either one. And unit (lattice) vectors can be defined for both types of unit cell.

To fully describe the unit cell you need the lattice and the basis.

The choice of the unit cell is not unique - even for the primitive unit cell you can have many choices.

The conventional unit cell usually contains more than one primitive unit cell. It is chosen because it better reflects the symmetry of the lattice.

Take the face-centered cubic cell, for example. The conventional, cube-shaped cell contains 4 primitive cells. a possible choice for the primitive cell is lattice vectors (0, 1/2, 1/2), (1/2, 0, 1/2) and (1/2, 1/2, 0). If you draw a 3D model of this primitive cell, then the cubic symmetry is far from obvious.