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# Miller index

1. ### Petit Einstein

8
How we can calculate the Miller's index? :rofl:
Thanks

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3. ### Gokul43201

11,141
Staff Emeritus
4. ### Petit Einstein

8
Yes i know about this, but i want ask u: what is the different between (102) et (012)? how to obtain(102) ?are there the methode to take this?Thank.

5. ### turin

2,326
It's a convention. There is something about the four different delimiters: (),[],{}, and <>. When you surround the numbers with (), then (102) is the same as (012), unless you are worried about the orientation. For the orientation's sake, you should have a right-handed permutation (conventionally) or you should specify.

6. ### Gokul43201

11,141
Staff Emeritus
If I remember the conventions correctly {xyz} refers to the familiy of planes with indices x,y,z. (x,y,z) refers to the specific plane.

Similarly [] and <> are for a line and a family of lines.

If you have a polycrystalline material, you don't really care about a specific plane, and only wish to specify the family (this specifies plane spacing, and hence diffraction angles, etc.). However, for a single crystal, the specific plane within a family could be important.

7. ### Petit Einstein

8
So we can not calculate directly all this index?
In Bragg relation, if we know the angle incident, so we can calculat the distance inter_reticular, suppose that we know about wave lenght.From heer, do we can calculate the Miller index? if yes , how to do?
Thank for respons.

8. ### turin

2,326
I don't think you can do it at just one orientation. I think you have to probe (in principle) all angles of incidence from all directions to extract the orientation of the lattice in the laboratory. I haven't really worked formally with this stuff in the lab though.

9. ### Gokul43201

11,141
Staff Emeritus
From the Bragg angle and the wavelength, you can get the inter-plane spacing, d.

$$n \lambda = 2d sin \theta~~$$

From the value of d, and the knowledge of the material (which tells you the lattice parameter, a) you can calculate the Miller Indices of the reflecting planes

$$d = \frac {a} {\sqrt{h^2+k^2+l^2}}$$

10. ### Petit Einstein

8

{h^2+k^2+l^2} is equal to 8 so we will get the Miller index for example:
h=2; k=2 and l=0 or we write (220). if we want get (202) or (022) , are there possible?

11. ### Dr Transport

1,503
(020) and (022) are different planes of the same family
{220} = (220),(202),(022),(-220),(2-20),(-202),(20-2),(-2-20),(-20-2),(-20-2) etc.....

12. ### Gokul43201

11,141
Staff Emeritus
Like I said before, the plane spacing only specifies the family, not a particular plane. So you should really be talking about the family of planes {220} which Dr Transport has listed above.

PS : Dr Transport - there's an error in your first line. Perhaps you meant to write (220) instead of (020) ?

1,503

14. ### Petit Einstein

8
yes i understand here, but how to obtain:
{220} = (220),(202),(022),(-220),(2-20),(-202),(20-2),(-2-20),(-20-2),(-20-2) etc.?with the calculat?

15. ### Dr Transport

1,503
each has an equivalent distance d, in a cubic material all of these are the same plane. In a tetragonal material, there would not be as many equivalent planes because different axes are not the same.

16. ### Petit Einstein

8
if i have: (degré) a (pm)
11,6 665,4
13,5 661,8
19,6 651,3
23,9 660,5
28,4 649,7
and wave lengh = 154,5pm .
How we can calculat the Miller index?
Thak for the friend who will want give me the respons.

17. ### Gokul43201

11,141
Staff Emeritus
Could you clarify what those numbers are, and what is pm ? Is it picometer (10^-12 m) ?

18. ### Petit Einstein

8

Now I have one question to ask u:
for example, I have the value of Bragg angle and of latice constant:
(degré) a (pm)
11,6 665,4
13,5 661,8
19,6 651,3
23,9 660,5
28,4 649,7
and i have the vawe lengh used = 154,5pm.
How can we calculat the Miller index?
Thank for the response to me.