Miller index

Petit Einstein

How we can calculate the Miller's index?
Thanks

Gokul43201

http://onsager.bd.psu.edu/~jircitano/Miller.html

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.

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.

Gokul43201

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.

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.

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.

Gokul43201

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

[tex]n \lambda = 2d sin \theta~~ [/tex]

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

[tex] d = \frac {a} {\sqrt{h^2+k^2+l^2}} [/tex]

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.

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.....

Gokul43201

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) ?

Dr Transport

correct, (220) instead of (020)...........

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?

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.

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.

Gokul43201

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

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.