Miller bravais indices

  • Thread starter aaaa202
  • Start date
  • #1
aaaa202
1,170
3
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?
 

Answers and Replies

  • #2
DrDu
Science Advisor
6,256
906
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
The redundancy in coordinate implies the relationship
 
  • #4
nasu
3,957
583
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?

How do you define these basis vectors? Is a3 in the same plane as a1 and a2?
 
  • #5
aaaa202
1,170
3
Yes they are are all with a 60 degree angle relative to each other.
 
  • #6
aaaa202
1,170
3
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
3,957
583
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
1,170
3
yes exactly, 3 vectors in the hexagonal plane, one in the c-direction
 
  • #9
M Quack
899
67
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).
 

Suggested for: Miller bravais indices

  • Last Post
Replies
1
Views
911
Replies
3
Views
2K
  • Last Post
Replies
1
Views
1K
Replies
1
Views
1K
  • Last Post
Replies
8
Views
2K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
18
Views
3K
  • Last Post
Replies
6
Views
4K
Replies
4
Views
4K
Top