Miller bravais indices

  1. Dec 4, 2013 #1
    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. jcsd
  3. Dec 5, 2013 #2

    DrDu

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    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.
     
  4. Dec 5, 2013 #3
    The redundancy in coordinate implies the relationship
     
  5. Dec 5, 2013 #4
    How do you define these basis vectors? Is a3 in the same plane as a1 and a2?
     
  6. Dec 5, 2013 #5
    Yes they are are all with a 60 degree angle relative to each other.
     
  7. Dec 5, 2013 #6
    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.
     
  8. Dec 5, 2013 #7
    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.
     
  9. Dec 5, 2013 #8
    yes exactly, 3 vectors in the hexagonal plane, one in the c-direction
     
  10. Dec 5, 2013 #9
    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).
     
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