What Is the Bravais Lattice Type and Miller Indices of This Crystal?

[lovephy85]

Homework Statement

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 what is miller indices? and what are the volumes of the primitive and conventional unit cells?

Homework Equations

Primitive unit cell volume V = a . (b x c) but in this state a not perpendicular with b,c

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 is that it's Hexagonal. However that also requires that , 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!?
and miller indices 112

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

 

[jdwood983]

You have asked this in another thread, you shouldn't repost the same question
https://www.physicsforums.com/showthread.php?t=348243

Primitive unit cells contain only one lattice point, conventional unit cells do not. If you have the primitive unit cell volume, then the conventional unit cell volume is $$n$$ times bigger, where $$n$$ is the number of lattice points in the conventional unit cell.