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Miller bravais indices 
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#1
Dec413, 01:33 PM

P: 1,005

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
Dec513, 01:44 AM

Sci Advisor
P: 3,630

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
Dec513, 02:25 AM

P: 746

The redundancy in coordinate implies the relationship



#4
Dec513, 09:56 AM

P: 1,988

Miller bravais indices



#5
Dec513, 10:10 AM

P: 1,005

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



#6
Dec513, 10:11 AM

P: 1,005

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
Dec513, 11:01 AM

P: 1,988

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
Dec513, 11:59 AM

P: 1,005

yes exactly, 3 vectors in the hexagonal plane, one in the cdirection



#9
Dec513, 01:09 PM

P: 673

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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