1983
DOI: 10.1063/1.445485
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On the nonradiative and radiative decay rates and a modified exponential energy gap law for 4f–4f transitions in rare-earth ions

Abstract: A modified exponential energy gap law for nonradiative decay has been derived for 4f–4f transitions where only a few phonons participate in the transition. Its preexponential factor varies by only a factor of 10 for different host materials and is purely electronic in nature. The modified law is the usual law (giving a factor of 105 variation) modified by using an energy gap which is effectively two (maximum) phonon energies smaller than the energy difference between the initial and the final electronic state.… Show more

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Cited by 435 publications
(184 citation statements)
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“…Empirically, multiphonon non-radiative transfer is a predominant process when energy is less than 5-6 cut-off phonon energy [26]. Following that empirical rule also known as gap law, a dominance of multiphonon relaxation process is predicted for all DE < 3900 cm À1 and 4880 cm À1 for anatase and rutile, respectively.…”
Section: Tiomentioning
confidence: 99%
“…Empirically, multiphonon non-radiative transfer is a predominant process when energy is less than 5-6 cut-off phonon energy [26]. Following that empirical rule also known as gap law, a dominance of multiphonon relaxation process is predicted for all DE < 3900 cm À1 and 4880 cm À1 for anatase and rutile, respectively.…”
Section: Tiomentioning
confidence: 99%
“…A quenching mechanism for luminescent species characterized by a small parabola offset is multiphonon relaxation, where the energy gap is bridged by the simultaneous emission of phonons 8,34 (Figure 5b). The nonradiative multiphonon relaxation rate decreases exponentially with the number of phonons p (with p = ΔE/pω max , where ΔE is the energy gap and pω max is the maximum phonon energy).…”
Section: Articlementioning
confidence: 99%
“…Van Dijk and Schuurmans [163,164] developed a modified energy gap law for nonradiative decay where only a few phonons participate in the transition of the form…”
Section: Multiphonon Relaxationmentioning
confidence: 99%