What Are the Primitive Translation Vectors and Bravais Lattice Type?

[S_Flaherty]

Homework Statement

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.

Homework Equations

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

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?

 

[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