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Help with theoretical density

  1. Aug 21, 2012 #1

    perplexabot

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    I posted this in the engineering section but no replies : ( ... Let us see if the physicists can help.

    1. The problem statement, all variables and given/known data
    Given: Density (D) of Si is 2.328 g/cm^3. Si has diamond crystal structure.
    Find: Theoretical density of a single crystal of Si.


    2. Relevant equations
    Theoretical density = m/V


    3. The attempt at a solution
    I know mass = (number of atoms) x (mass of atom), in a diamond crystal structure there are: [(1/8) x 8] + [(1/2) x 6] + [(1) x 4] = 8 Si atoms/crystal structure

    Now calculating volume is my issue, do I need the lattice constant? If so, how does one calculate it?

    Or is it just V = (m x 8)/D = (m x 8)/2.328, where m = 28.1 amu converted to grams?
    However, if I do that, I think I'll end up with the given density. What is the difference between the given density and theoretical density? Please help.

    Thank you.
     
  2. jcsd
  3. Aug 21, 2012 #2

    Simon Bridge

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    If the theory is very good - nothing. (Usually the "given" density will be some empirically determined value.)

    For the lattice constant: what is the Si-Si bond length?
     
  4. Aug 22, 2012 #3

    perplexabot

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    Hmm, that makes sense. Thank you for clearing that out.

    Well using google the lattice constant for silicon is 5.43095 Angstroms at 300K. Should this constant be given in the problem? So the volume would be (5.43095 * 10^-8)^3 cm^3 ?
     
  5. Aug 22, 2012 #4

    Simon Bridge

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    That is what it means all right.

    Just looking up the lattice constant is a valid alternative to applying some theory to predict it ;)
     
  6. Aug 22, 2012 #5

    perplexabot

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    Haha. Thank you. Finally, someone was able to help me out.
     
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