# Primitive cell

1. Jan 16, 2008

### ehrenfest

[SOLVED] primitive cell

1. The problem statement, all variables and given/known data
http://en.wikipedia.org/wiki/Primitive_cell
Could someone give me a mathematically rigorous of a primitive cell? I have read like 4 different definitions and none of them seem mathematically rigorous.
I think Wikipedia's definition is particularly ambiguous: "a minimum cell corresponding to a single lattice point" ?
In what sense is minimum being used? In what sense is cell being used?

EDIT: this should probably be in the Advanced Physics section but I cannot delete it or move it

2. Relevant equations

3. The attempt at a solution

2. Jan 16, 2008

### ehrenfest

In the picture in the Crystal Structure section of http://en.wikipedia.org/wiki/NaCl, what is the primitive cell AND WHY?

Last edited: Jan 16, 2008
3. Jan 16, 2008

### ehrenfest

I think I understand now. Go to http://www.neutron.anl.gov/hyper-physics/bravais.html [Broken].

The primitive cell of the cubic face-centered structure of the NaCl lattice IS NOT THE CUBE. The cube is the CONVENTIONAL cell for the primitive face-centered cubic structure (e.g. NaCl) but IT CANNOT BE THE PRIMITIVE CELL BECAUSE IT CONTAINS 4 LATTICE POINTS WHICH IS MORE THAN 1.

The primitive cell of the the fcc crystal is actually a rhombohedron.

Last edited by a moderator: May 3, 2017
4. Jan 17, 2008

### malawi_glenn

You got the idea :) Crystal structure is quite hard in the beginning, many new things to learn.