Parabola offset

Also in case of Pb(II)-WO the MMCT state does not lead to quenching (see above). In this case the quenching temperature of the emission increases relative to that of the constituents, since the parabola offset of this MMCT state is relatively small [50]. 

Fig. 3. The confieruz ational coordinate diagram. The curves g and e relate to the ground state AQ gives the parabolas offset. (See also text.)...

The Pr " case has an advantage above that of Eu, viz., the higher excited state can emit, so that the Stokes shift can be measured. This gives information on the relaxation and the parabolas offset. It was found that the nonradiative Afbd —> Af transition becomes of importance if the Stokes shift is larger than 3000 cm l. 

Fig. 2.3. Configurational coordinate diagram (see also text). The ground state (g) has the equilibrium distance Ro the vibrational states v = 0, 1,2 are shown. The exeiied stale (e) has the equilibrium distance R(/ the vibrational states v = 0, 1,2 are shown. The parabola offset is AR(= R,> -R j)...

Fig. 3.1. Configurational coordinate diagram (see also Fig. 2.3). The absorption transition g- t is for reasons of clarity drawn as one line only (the transition with maximum intensity). After absorption the system reaches high vibrational levels of the excited state. Subsequently it relaxes to the lowest vibrational level v = 0 from where emission e -> g occurs in a broad band. The parabola offset is given by AR...

Fig. 4.7. Temperature dependence of the luminescence quantum efficiency (q) according to calculations on a model phosphor system. In (a) the eneigy difference between the parabola minima (Ezp) is varied (values in cm ). In b) the vibrational frequency is varied (values in cm ). In (c) the parabola offset (AR) varies it decreases from left to right 6%...

Let us assume a reaction coordinate x running from 0 (reactant) to 1 (product). The energy of the reactant as a function of x is taken as a simple parabola with a force constant of a. The energy of the product is also taken as a parabola with the same force constant, but offset by the reaction energy AEq- The position of the TS (jc ) is taken as the point where the two parabola intersect, as shown in Figure 15.27. The TS position is calculated by equating the two energy expressions. 

Fig. 1. The configurational coordinate diagram. The energy E is plotted versus a configurational coordinate Q. The offset between the parabolae is given by Qb0 - Q 0. The ground state a contains vibrational levels with quantum number n, the excited state b with quantum number ri...

The parameter S measures the interaction between the dopant ion and the vibrating lattice. Equation [5] shows that if S is large, the Stokes shift is also large. Equation [4] shows that S is immediately related to the offset of the parabolas in the configurational coordinate diagram (Fig. 3). This offset, AQ = Q o - Qo), may vary considerably as a function of the dopant ion and as a function of the vibrating lattice, as we will see below. 

In our opinion this shows that the thermal quenching temperature of the luminescence of the closed-shell complexes depends more strongly on the energy difference between the parabolae than on their offset ). In fact only the colourless complexes are able to show luminescence of any importance. 

Fig. 2.5. The optical absorption transition between two parabolas which have an offset relative to each other in the configurational coordinate diagram consists of a broad absorption band, See also text...

In general the temperature dependence of the nonradiative processes is reasonably well understood. However, the magnitude of the nonradiative rate is not, and can also not be calculated with any accuracy except for the weak-coupling case. The rea.son for this is that the temperature dependence stems from the phonon statistics which is known. However, the physical processes are not accurately known. Especially the deviation fiom parabolic behaviour in the configurational coordinate diagram (anhar-monicily) may influence the nonradiative rate with many powers of ten. However, it will be clear that the offset between the two parabolas (AR) is a very important parameter for the nonradiative transition rate. This rate will increase dramatically if AR becomes larger. 

Fig. 4.9. The role of the charge-transfer state (CT) in the quenching of the luminescence of the Ru ion. Only a few parabolas of the configuration have been drawn. In a), the situation for Y2O3 is depicted the CT state feeds the emitting levels. In (b), the CT state has a larger offset. As a consequence the CT state populates, at least partly, the ground state levels, so that the luminescence is. strongly reduced...

Fig. 4.10. Schemaiic configurational coordinate diagram for (4/ ). Drawn parabolas relate to the 4/ configuration the broken parabolas indicate two possible situations for the 4f configuration (1 and II). Excitation into I yields d- /emission from 1 (arrow 1). Excitation into II (with larger offset) yields a nonradiative transition to the 4/ configuration (arrow 2) which may be followed by intraconfigurational 4/ emission...

Fig. 14.2 Configurational coordinate diagrams of bismuth-doped alkali borate glasses a for lower and b for higher content of alkali oxide. Po and 2 states are marked as broken lines because the transitions from Sq to the states are forbidden. Horizontal lines denote the vibrational levels. The blue solid lines refer to the nonradiation relaxations. Upward-directed red solid lines refer to the excitation processes, and downward-directed black solid lines refer to the emission process. AQ indicates the offset of parabolas. Reprinted from Ref. [44] by permission of OSA Publishing...

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