Phonon Dispersion Interpretation

[sghosh]

Dear friends of physics forum
I have calculated the phonon dispersion of an fcc phase using PHONON software. the fcc phase I am talking about is a metastable phase of Zr. Zr, as we all know exists in hcp and bcc phases.
I wanted to calculate the heat capacity at constant volume using the phonon dispersion.
I get three acoustic branches in the phonon dispersion. I would like to know where and how can we explain such dispersions.

My second question related to the calculation of heat capacity at constant pressure. How can we calculate Cp using Cv for a metastable fcc phase.

Thanks
Suddhasattwa

 

[eljose79]

Dear Suddhasattwa,

Thank you for sharing your research on the phonon dispersion of the fcc phase of Zr. It is always exciting to see new developments in the field of materials science. To answer your first question, the three acoustic branches in the phonon dispersion can be explained by the different modes of vibrations in the crystal lattice. The acoustic branches correspond to the longitudinal and transverse acoustic modes, which are related to the compression and shear of the lattice, respectively. The third acoustic branch is due to the optical mode, which involves the motion of the ions in the lattice as a whole.

As for your second question, the calculation of heat capacity at constant pressure (Cp) using heat capacity at constant volume (Cv) can be done using the relationship Cp = Cv + V*(alpha^2)*T, where V is the volume, alpha is the thermal expansion coefficient, and T is the temperature. This relationship assumes that the thermal expansion of the material is negligible. However, for a metastable fcc phase, there may be significant thermal expansion, so this equation may not be accurate. In this case, it would be best to directly measure the heat capacity at constant pressure using experimental techniques.

I hope this helps answer your questions. Keep up the great work in your research!