# Miller bravais indices

1. ### aaaa202

There are four miller indices (hklj) for the hexagonal lattice, the third being redudant:

l=-(h+k) (1)

Given the basis vectors a1,a2,a3 I can certainly see that:

a3=-(a1+a2)

But how does this immidiatly lead me to the relation (1) between the miller indices?

2. ### DrDu

4,514
Spontaneously, I don't know the answer, but I think it is relatively easy to work out. Have you tried?
If you really encounter problems, we all are willing to help you.

3. ### Woopydalan

743
The redundancy in coordinate implies the relationship

4. ### nasu

How do you define these basis vectors? Is a3 in the same plane as a1 and a2?

5. ### aaaa202

Yes they are are all with a 60 degree angle relative to each other.

6. ### aaaa202

The problem is how exactly to relate the miller indices given (-a1+a2)=a3. After all miller indices for a plane are obtained as inverses of the coordinates for the intersection of the lattice vectors with the plabe.

7. ### nasu

Oh, so these are the a1,a2,a3 in the system with four indices. You have and a4 as well. Right?
Sorry, I was confused.

8. ### aaaa202

yes exactly, 3 vectors in the hexagonal plane, one in the c-direction

9. ### M Quack

856
Hint: Miller indices refer to a point in reciprocal space, hence you have to construct the reciprocal space basis vectors.

G = H a* + K b* + L c*(for the "normal" 3 Miller indices).