Dear all,
I want to calculate the in-plane speed of sound from the phonons spectrum of a 2D materials, let say graphene, which can be calculated from the slope of w(k) of acoustic LA mode. I did a linear fit and found the slope. I used the relation f = c/lambda, where c= speed of light and lambda is the slope in meters (changed from cm). Then, this value of f is multiplied by 2pi. The resultant unit became radian/sec. I have two questions, 1) how to convert rad/s to m/s? and 2) Is this procedure correct? If not, what will be the correct way of calculation in-plane speed of sound from phonons dispersion?
Thank you very much.
Hello Saif,
if the funktion w(k) is given than you calculate the first derivative of w(k). This gives you the group velocity of sound for the corresponding k. If you have the slope, than you have the velocity of sound.
The function w(k) is nothing more than f = v/lambda. F is the frequency, lambda the wavelength and v the velocity of sound, not the velocity of light!
But happen: the slope gives the group velocity and w/k the phase velocity.
Due to w = 2pi*f and k = 2pi/lambda a recalculation with the factor 2pi is not necessary.
You need to have the phonons dispersion curves (k vector vs. w(k) diagram).
Then you can calculare the sound velocity (which is the same as the group velocity of phonons) for a particular set of modes , i.e. for an Acoustic (transverse or longitudinal) modes on a specific direction in your solid.
as vel = dw(k)/dk on that direction
- Badges
- Science topic
- Similar topics
- Physical Sciences
- Materials Science
- Materials
- Carbon Materials
- Graphite
- Graphene