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Homework Help: Solid State Chemistry : please illustrate counting of octahedral, tetrahedral voids

  1. Jul 13, 2007 #1
    1. The problem statement, all variables and given/known data

    Chapter name: Solid state
    Topic: close packed structures in crystalline solids
    Sub-topic: close packing in 3D
    In my Chemistry book I read:
    Now let us suppose there is 1 sphere only. Can anybody explain to me where the one octahedral void and two tetrahedral voids are? I cannot understand how they deduced the above formula. There is no explanation given in the book. It just says: "It is found that such and such thing happens". No illustration is provided. I thought that I could find the answer to my problem on this forum.

    2. Relevant equations

    If N is the number of spheres, then
    number of octahedral voids=N
    number of tetrahedral voids=2N

    3. The attempt at a solution

    No clue. If possible, please answer with pictures/graphics.


    Eagerly waiting!
    Mr V
    Last edited: Jul 13, 2007
  2. jcsd
  3. Jul 13, 2007 #2


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    Staff Emeritus
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    Gold Member

    You can't do that. The ratio of the number of octahedral and tetrahedral voids to the number of lattice sites is accurate only for large N. With a single lattice site, it is meaningless to even speak of an interstitial.

    For visualization: http://www.iucr.org/iucr-top/comm/cteach/pamphlets/5/node1.html

    PS: Next time, please include the name of the source (your Chemistry book), and the location within it, where the quoted text comes from.
  4. Jul 14, 2007 #3
    I don't know if this book is available outside my country.
    Name: Chemistry Part 1 Textbook for class XII NCERT
    Page number: 15

    This is what I found on the link you gave me:
    So, N is actually the number of spheres present in a crystal lattice. An isolated sphere cannot have any voids, but if we consider a single sphere in a lattice, then it makes two tetrahedral voids (by covering the triangles of the above and below layer). As regards to the single octahedral void, I am a little confused. I know that if three spheres are arranged in such a way that they form a triangular void pointing north, and another three spheres form a void pointing south, then if we put one set of three spheres on top of the other set, such that the individual void of each set is not covered, then we say that the two-triangle void is an octahedral void.
    Maybe the logic involved is this: suppose the upper layer has only 2 spheres (the lower layer contains its 3 spheres). Now until and unless the third sphere is also there in the first layer, the octahedral void cannot be formed. So each sphere in the lattice helps in completing an octahedral void. Perhaps this is why it is said that a single sphere generates a single octahedral void. Am I right?

    Anyway, thanks a lot for your reply and for clearing my confusion!! :smile:

    warm regards
    Mr V
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