# Bravais lattices

1. Apr 30, 2008

### raintrek

1. The problem statement, all variables and given/known data

A crystal has a basis of one atom per lattice point and a set of primitive translation vectors of

a = 3i, b = 3j, c = 1.5(i+j+k)

where i,j,k are unit vectors in the x,y,z directions of a Cartesian coordinate system. What is the Bravais lattice type of this crystal and what are the volumes of the primitive and conventional unit cells?

2. Relevant equations

Primitive unit cell volume V = a . (b x c)

3. The attempt at a solution

I'm slightly unsure about these Bravais lattices given the multiple permutations they can seem to take.

My assumption, as $$a=b\neq c$$ is that it's Hexagonal. However that also requires that $$\alpha=\beta=90^{o},\gamma=120^{o}$$, where gamma is the angle between a,b, alpha between b,c, beta between c,a. But that seems to contradict that the a,b vectors are in i,j directions, ie at 90 degrees. Am I missing something here!?

I've worked out the primitive unit cell volume to be 13.5, however I'm also at a loss how to calculate the conventional unit cell volume...

Any help would be hugely appreciated