I have to calculate the following:
a) The speed of the acoustic phonons
b) Which phonons(frequency and wavevector) can be observed for scattering angles between 0° and 180° and how much of the Brillouin zone they cover.

The problem statement is as follows: Light from an Argon laser($\lambda=514.5nm$) is scattered by a NaCl crystal(refraction index=1.544). The scattered light is analyzed perpendicular to the beam direction(scattering angle $\theta=90°$). Two pais of lines are observed, the frequency displacement of this lines w.r.t the lasers frequency is $\Delta\nu=19.26GHz$ and $\Delta\nu=10.25GHz$

For part a) I did the following:
because the wavenumber of the incident and scattered radiation is much smaller than the 1BZ the additive reciprocal lattice vector must be zero.
Let k be the phonon wavevector and q the laser wavevector.

From a "scattering diagram" we get the following:


Where $n$ is the refraction index, $\omega$ the angular frequency and $c$ the speed of light.

Using conservation of energy and the Debye approximation$\omega(k)=c_s.k$:

$\Delta \omega=c_s.n.\omega/c.sin(\theta/2)$

$\omega=2.\pi.\nu$ Solve for $c_s$ and plug in the values of $\Delta\omega$

For part b) I really dont know where to start, at first I thought about using the Bragg's condition but I don't see how it can make things easier. Im stuck. I would appreciate some help.



Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.