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Miller index

  1. How we can calculate the Miller's index? :rofl:
    Thanks
     
  2. jcsd
  3. Gokul43201

    Gokul43201 11,141
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  4. 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

    turin 2,326
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    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

    Gokul43201 11,141
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    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. 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

    turin 2,326
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    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

    Gokul43201 11,141
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    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]
     

  10. 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.
     
  11. Dr Transport

    Dr Transport 1,503
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    (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

    Gokul43201 11,141
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    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) ?
     
  13. Dr Transport

    Dr Transport 1,503
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    correct, (220) instead of (020)...........
     
  14. 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

    Dr Transport 1,503
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    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. 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

    Gokul43201 11,141
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    Could you clarify what those numbers are, and what is pm ? Is it picometer (10^-12 m) ?
     

  18. 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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