1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Thermal phonons @ low temperatures

  1. Nov 13, 2012 #1
    1. The problem statement, all variables and given/known data

    a) estimate the number of phonons in a 1mm cube of a crystal at 10K, taking a sound speed of 1000m/s.

    b) estimate the frequency ω for which you will find the highest phonon nrg content in the range of ω to ω+dω. (Again, assume low temps). Give your solution in the form hω = αkBT, finding the value of α.

    c) show that the dominant phonon wavelength λ, assuming simple cubic lattice, can be written λ = βaθD/T with a being the lattice constant. Find β.


    Problem i'm having is am I supposed to find an exact value as he has not stated. (Haven't been able to see my prof)



    3. The attempt at a solution

    Only thing i can think of for part a is

    Nph = ∫dωD(ω)n

    where n is the planck distribution and D is the density of states. Only problem is that this equation only uses the temperature

    debeye frequency is ω3 = 6πv3N/V

    I'm assuming N is the number of phonons which is no help.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?



Similar Discussions: Thermal phonons @ low temperatures
  1. Thermal conductivity (Replies: 0)

  2. Thermal average (Replies: 0)

Loading...