Miller index

1. Jun 25, 2004

Petit Einstein

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

2. Jun 25, 2004

Gokul43201

Staff Emeritus
3. Jun 30, 2004

Petit Einstein

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.

4. Jun 30, 2004

turin

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.

5. Jun 30, 2004

Gokul43201

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.

6. Jul 1, 2004

Petit Einstein

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.

7. Jul 1, 2004

turin

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.

8. Jul 1, 2004

Gokul43201

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

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

9. Jul 2, 2004

Petit Einstein

{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?

10. Jul 2, 2004

Dr Transport

(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.....

11. Jul 2, 2004

Gokul43201

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) ?

12. Jul 4, 2004

Dr Transport

13. Jul 5, 2004

Petit Einstein

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?

14. Jul 5, 2004

Dr Transport

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.

15. Jul 9, 2004

Petit Einstein

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.

16. Jul 9, 2004

Gokul43201

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

17. Jul 12, 2004

Petit Einstein

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.