# Primitive Translation Vectors

1. Jan 27, 2014

### S_Flaherty

1. The problem statement, all variables and given/known data
The vectors r1 and r2 below represent atomic positions in a crystal.

r1 = (n1 + n3)ax + (n2 + n3)ay + n3az
r2 = (n1 + n3 + 1/2)ax + (n2 + n3 1/2)ay + (n3 + 1/2)az

Assume first that the two vectors above correspond to two different types of atom. Find a set of primitive translation vectors and an appropriate basis to describe this structure. Identify the Bravais lattice type.

2. Relevant equations
No equations were given in class or in the text that I can recognize as being useful for this.

3. The attempt at a solution
I'm not really sure what I'm supposed to be looking for here. My attempt at a solution for the first primitive translation vectors for r1 is:

a1 = n1ax
a2 = n2ay
a3 = n3a(x + y + z)

Am I on the right track? Or am I completely misunderstanding what is being asked?

2. Jan 31, 2014

### ehild

The primitive translation vectors are the shortest independent translation vectors. Their linear combinations are the lattice points.
r2 is not a lattice point, but the position vector of the second atom of the basis.

ehild