Nonradiative Transitions in Rare Earth Ions The Energy-Gap Law

3 NONRADIATIVE TRANSITIONS IN RARE EARTH IONS THE ENERGY-GAP LAW 

The nonradiative rate. Am, from a (RE) + ion level is also strongly related to the corresponding energy gap. Systematic studies performed over different (RE) + ions in different host crystals have experimentally shown that the rate of phonon emission, or multiphonon emission rate, from a given energy level decreases exponentially with the corresponding energy gap. This behavior can be expressed as follows  

EXAMPLE 6.2 Determine the nonradiative rates from the following energy levels of different ions in lanthanum chloride 5/2 (Er )fPo (Pr +) and 2 5/2 (Yif+). 

The experimentally obtained energy-gap law for LaCls has been represented in Eigure 6.5. Erom this figure, one can obtain that the best fit of the experimental data(theblackpoints)to expression (6.l)corresponds too = 0.015 cm and Anr(O) = 4.22 x 10 ° s. Thus, we can write the energy-gap law for the LaCls crystal as follows  

From this expression, we can estimate the multiphonon emission nonradiative rate, from any particular energy level by simply knowing the energy distance to the next lower energy level (the energy gap), AE. 

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