Phonon-assisted energy transfer between lanthanides

[HAYAO]

Dear all,

I am not understanding well the "phonon-assisted" energy transfer between lanthanide ions and I need some clarifications.

There is a theoretical work by Miyakawa and Dexter (doi:10.1143/JPSJ.32.1577) which explains how phonon plays a role in transferring energy from one (4f-state of) lanthanide to another (4f-state) lanthanide with energy mismatch. Now if I understand correctly, the "phonon" itself spans throughout the entire crystal that the lanthanide ion is doped in. Thus if there is any electron-phonon interactions (where electron refers to the electronic 4f-states of the lanthanides), then all of the lanthanide must be interacting with the same phonon.

However, phonon-assisted energy transfer between lanthanides has been reported for glass material (amorphous material), where a phonon may be localized around to a particular lanthanide ion instead of spanning throughout the entire material. It seems to me, intuitively, that this is a conflicting result with what is written in the above paragraph.

I believe I am making some mistake in terms of understanding specific points discussed above. Either:
1) I am not correctly understanding electron-phonon interaction in general
2) I am correctly understanding 1) but incorrectly understanding phonon-assisted energy transfer
3) I am incorrectly understanding 1) and 2)
4) or I am correctly understanding both, and that above two paragraph is indeed an inconsistency that needs to be resolved.

Does phonon-asssited energy transfer require a phonon mode to span throughout the entire crystal? Or is it fine with a localized phonon? What am I not understanding correctly?

Thank you,
HAYAO

 

[DrDu]

I don't have access to the paper, but I think the phonons act principally by lowering the symmetry of the crystal field thus weakening the selection rules. Furthermore, the change of the cystal field changes the energy. This is a local effect, so the extent of the phonon should not be relevant. Of course you could think about a coherent effect on both of the atoms which are exchanging energy although I would guess this to be of minor importance. I suppose the energy transfer mechanism is some Förster type mechanism, which decays with a high power of the atomic separation distance. Then the question arises whether the localisation length of the phonon is larger or smaller than the range of the energy transfer.

 

[HAYAO]

I don't have access to the paper, but I think the phonons act principally by lowering the symmetry of the crystal field thus weakening the selection rules. Furthermore, the change of the cystal field changes the energy. This is a local effect, so the extent of the phonon should not be relevant. Of course you could think about a coherent effect on both of the atoms which are exchanging energy although I would guess this to be of minor importance. I suppose the energy transfer mechanism is some Förster type mechanism, which decays with a high power of the atomic separation distance. Then the question arises whether the localisation length of the phonon is larger or smaller than the range of the energy transfer.

Thank you DrDu.

Generally, the "phonon-assist" refers to assist from phonon energy. Meanwhile, change in the crystal field and resulting rise of the energy is relevant if the energy is in the order of extremely small scale (1 to 50 cm^-1), because 4f-states of lanthanides barely changes in energy by crystal field. Most sources claim that it actually involves energy scale of a phonon itself (depending on the host, 100 to, in some rare cases, up to 2000 cm^-1).

I believe that the weakening of the selection rules is not relevant to the phonon-assisted energy transfer at least in the paper above, although I think you are absolutely right that phonon would change the selection rule and will thus also change the energy transfer rate.

Yes, it may be about the coherent effect on the atoms that are exchanging energy. The paper itself does not specify whether the extent of phonons should be larger or smaller than the range of energy transfer (in the case of lanthanide-to-lanthanide separation of more than 4 angstroms, dipole-dipole, dipole-quadrupole, quadrupole-quadrupole interactions). But I am really not understanding what I am looking at.

 

[DrDu]

I believe that the weakening of the selection rules is not relevant to the phonon-assisted energy transfer at least in the paper above

From the abstract: "...which produces the highest intensity in vibronic sidebands contributes dominantly to the phonon-assisted process."
To me, that points rather to an effect of the changed selection rules. So if one atom falls from the excited state + phonon to the ground state without phonon, the selection rules are different than without a phonon.
I just checked the article by Myiakawa and Dexter which is cited in the abstract. This confirms this view. Furthermore, in the derivation of the transfer probability, they assume that the two ions interact with different phonons. So localization or not shouldn't be an issue.

 

[HAYAO]

From the abstract: "...which produces the highest intensity in vibronic sidebands contributes dominantly to the phonon-assisted process."
To me, that points rather to an effect of the changed selection rules. So if one atom falls from the excited state + phonon to the ground state without phonon, the selection rules are different than without a phonon.
I just checked the article by Myiakawa and Dexter which is cited in the abstract. This confirms this view. Furthermore, in the derivation of the transfer probability, they assume that the two ions interact with different phonons. So localization or not shouldn't be an issue.

Okay, thank you very much. That really helped me out!