Phonon Assisted Relaxation in Phosphors

Because the energy gaps for many of the trivalent rare earths are often no more than 2000 cm-i and many of the Stark States are as close as 200 

Examine the diagram, given as 6.8.40 above, showing calculated free-ion energy levels again. For the most part, the energy levels are rather closely spaced. When an upper ener level of a rare earth ion in a crystal is excited, it may decay to a lower state by  

2) Energy transfer to another site by a multipole process 

When we say phonon-emission, we are actually stating that infra-red photons matching the phonon spectrum of the lattice are emitted and that lattice absorption then occurs- this is equivalent to virtual photon emission since the emitted photons never appear outside of the lattice). The last process has been studied extensively and we shall summarize the results herein. The rare earths are unique in that, for energy gaps of several thousands of wavenumbers, several simultaiieous phonon emission processes may be involved. 

Multiphonon relaxation processes are usually studied by determining both the transition rates for the process, and the phonon spectrum of the host crystal. Total transition rates (reciprocals of fluorescent lifetimes) are measured and multiphonon (MP) decay rates are extracted from these. In practice, one does not observe the MP transition rate between two energy levels, but that between two J- manifolds, i.e.- the sets of Stark States The decay rate, W, obeys the relation  

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