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Interplanar distance

  1. Jan 1, 2016 #1
    i am trying to find the formula for the inter-planar distance for the cubic .
    i do know that it's :d (h,k,l)= a /√ (h² +k²+l²), i am only able to get to : 2π/(√a*²(h²+k²+l²)) , with a* being the parameter of the reciprocal lattice , the explanation given to how to go from a* to a , is that for all cubic lattices : a* = 2π/a , and this is what i don t understand , a = a* , only in the case of the simple cube , for body centered cube for example : we find a* = (2π/a)( j+k )with a*, j,k vectors ,a : parameter of the elementary lattice ; so calculating the modulus we find a*= √2 2π/a ;
    and i am feeling frustrated , i know i am missing something but i don t know what .
     
    Last edited: Jan 1, 2016
  2. jcsd
  3. Jan 1, 2016 #2

    mathman

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    It looks like you need to clarify the definitions of a and a*.
     
  4. Jan 1, 2016 #3
    a refers to the parameter of the elementary lattice , as a, b, c , of the simple cubic lattice .
    lattice_parameters.gif
    a* is the parameter of the reciprocal lattice , as in a* , b* , c* .
    crystal-structure-analysis-46-638.jpg
    a* , b* , c* are deduced from the parameters of the primitive lattice, a1 , a2 and a3 .
    in the second pic a* is b1 , b*is b2 , c* is b3 , .
    you can see that the modulus of a* = b 1 , is not 2π/a .
     
  5. Jan 1, 2016 #4
    after a lot of searching , i noticed something , they do not actually mention the modulus of the vectors themselves but the lattice constant , i don t exactly understand what the difference is .
    lattice constant is defined as the physical dimension of unit cells in a crystal lattice. so how is that different from the modulus of the lattice vector ?
     
  6. Jan 2, 2016 #5
    i think i finally understood what is going on : you see i have always assumed that they were talking about the primitive vectors , for example to calculate the reciprocal vectors in the case of body centered we had to look for the primitive lattice ( which is a simple cube ) , but doing that means we re calculating the primitive reciprocal vectors . not just the reciprocal vectors .
    and so if we actually try to calculate the reciprocal vectors of the actual body centered lattice,without going through the primitive lattice , we find 2π/a , and that is true for all cubic lattices .
    uhhhh finally . all because of one word : primitive .
     
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