In Up-conversion measurements, the energy transfer from Tb3+ to Yb3+ is due to multiphonon relaxation, i.e phonon-assisted energy transfer. For this, I need to know the phonon energy associated with the host so that the number of phonon's emitted during energy trasfer can be estimated.
Phonon energy can be calculated theoretically by the lattice dynamical studies. The dispersion relation can give phonon energy as a function of wave vector. Experimentally phonon dispersions can be studied by inelastic scattering of photons or neutrons by long wavelength phonons . Raman scattering studies could also be useful, as these involve multi-phonon processes. These are only principles. For details for a specific system, you should refer to relevant research articles.
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