And if there was a difference if the propagational mode of the electric field in the crystal is longitudinal or transverse.

  • $\begingroup$ Two different questions. The second one is a bit difficult to interpret. Sounds like homework without enough context. $\endgroup$ – Pieter Sep 10 '18 at 18:36
  • $\begingroup$ It's not homework but I'm studying for an exam and I found this assertion but the cause is not explicit. I asked also about the transverse and longitudinal waves because I saw that when the dielectric constant is 0, the frequency corresponds to the longitudinal waves one, when it is ∞ instead, the frequency of the electric field is known to be that of the longitudinal propagation. It's not done clearly $\endgroup$ – Costantino Sep 10 '18 at 18:56

Why does a ionic crystal polarize more at low frequencies rather than at high ones?

Ionic polarization involves displacement of ions, which have some mass and therefore require some time to change their position. So, as the frequency of the applied electric field increases, the response of the ions deceases and, with it, the degree of polarization.

And if there was a difference if the propagation mode of the electric field in the crystal is longitudinal or transverse.

In free space, EM waves are always transverse. When confined, they may acquire a longitudinal component, but it would depend, among other things, on the geometry, so more information (and more expertise in this field) would be required to answer this part of the question.

  • $\begingroup$ As I read your answer, I remembered how, with a harmonic oscillator modellization of the dielectric atoms (and other approximations) we have that the displacement polarizability is inversely proportional to the reduced mass of the ions in the lattice cell. And now I also know that the longitudinal contribute of the electric field is due to the lattice geometry. Thank you! $\endgroup$ – Costantino Sep 11 '18 at 10:27
  • $\begingroup$ @Costantino Glad to help. $\endgroup$ – V.F. Sep 11 '18 at 11:39

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