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Debye temperature for Na

  1. Dec 17, 2015 #1

    MMS

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    1. The problem statement, all variables and given/known data
    Na has a bcc structure with molecular mass of 22.99 gr/mol, mass density of 0.971 gr/cm^3.
    The average speed of sound in Na (at room temperature=300K) is 3200 m/s.
    Calculate the Debye temperature for Na

    2. Relevant equations
    I worked out this equation to calculate the Debye temperature (If needed I can show how)
    XzxlsHT.png
    3. The attempt at a solution
    I plugged in all the numbers in the above equation with the correct units and I get that the Debye temperature is 280.3K. However, in literature I found that it is approximately 150K.
    Is there something wrong with my calculations? Am I missing out on something here?

    Thank you!
     
  2. jcsd
  3. Dec 18, 2015 #2

    SteamKing

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    Please provide your calculations.
     
  4. Dec 18, 2015 #3

    MMS

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    BnOvrQ7.png
     
  5. Dec 18, 2015 #4

    SteamKing

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    No, I meant your numbers.
     
  6. Dec 18, 2015 #5

    MMS

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    ShjbCQo.png
     
  7. Dec 19, 2015 #6

    MMS

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    Anyone?
     
  8. Dec 19, 2015 #7

    SteamKing

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    Your calculations are arithmetically correct, as far as I can see.

    It's not clear that NA ⋅ ρ / MW is an accurate substitute for the N / V which is used in other Debye Temperature derivations I have seen. Your expression doesn't seem to account for the fact that since sodium is bcc, there are two atoms per cell, rather than one. It makes a difference in calculating the edge length of the cell.

    I think for calculating a reasonable approximation to the Debye Temp., this is the issue which must be resolved. In some articles I have seen, the authors try to use the properties of the material measured close to the Debye Temp., like the speed of sound and the density, to come up with a more accurate calculation.
     
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