# Miller index

by Petit Einstein
Tags: index, miller
 P: 8 How we can calculate the Miller's index? Thanks
 PF Patron Sci Advisor Emeritus P: 11,137
 P: 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.
HW Helper
P: 2,328

## Miller index

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.
 PF Patron Sci Advisor Emeritus P: 11,137 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.
P: 8
 Quote by 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.
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.
 HW Helper P: 2,328 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.
 PF Patron Sci Advisor Emeritus P: 11,137 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 $$d = \frac {a} {\sqrt{h^2+k^2+l^2}}$$
P: 8
 Quote by Gokul43201 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 $$d = \frac {a} {\sqrt{h^2+k^2+l^2}}$$

{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?
 PF Patron Sci Advisor P: 1,447 (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.....
 PF Patron Sci Advisor Emeritus P: 11,137 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) ?
P: 8
 Quote by 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.....
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?
 PF Patron Sci Advisor P: 1,447 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.
 P: 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.
 PF Patron Sci Advisor Emeritus P: 11,137 Could you clarify what those numbers are, and what is pm ? Is it picometer (10^-12 m) ?
P: 8
 Quote by Petit Einstein Ok i agree with u about this, but for exemple, the value of {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? Thank for your response.

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.

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