Vacancy sharing

In Cu(FexCr2-x)04 series gradual substitution of Fe " for Cr introduces Cu at O sites. When the amount of Cu " at O sites is lower, one can expect that most of the anionic vacancies formed during the reduction of Cu " to Cu is shared between Cu(I) and Cr (III) or Fe (III) ions. With increase in the amount of Cu " at O sites, reduction produces BMV shared between Cu(I) and Cu(I) in addition to BMV shared between Cu(I) and Cr(III) or Fe(III). In CF5 and CF6 which are having higher amount of CU at O sites than CF4, the probability for BMV shared between Cu(I) and Cu(I) is more. The similarity in activity of all the three catalysts shows that the BMV associated with Cu(I) and Cu(I) is less active than those vacancies shared between Cu(I) and Cr(III) or Fe(III). This indicates that the second cation is also involved in the structure of the catalytic site by sharing anionic vacancies with cuprous ions. 

A powerful but short-lived color center laser is based on theFj center. As indicated in Fig. l,theFj center consists of two adjacent anion vacancies sharing one trapped electron. In contrast to the Fa,b(II) centers, the FJ relaxation... 

Figure 11. C> vacancy sharing probabilities W for various collision systems involving Ni, Br, and 1 projectiles as a function of the scaling parameters X from Eq. (35). The solid line follows from Eq. (32) with f = 2X. From Meyerhof. ...

Meyerhof was the first to apply the formula (32) to iC-vacancy sharing and to verify its scaling ability. The results are shown in Figure 11. The experimental sharing probabilities are deduced from W = < hI(o h + Cl), where cross sections for K excitation of the heavier and lighter collision partner, respectively. The experimental data compare well with the universal curve following from Eq. (32) by means of the scaling parameter... 

Several subsequent studies have confirmed Meyerhof s analysis. In particular, precision measurements using the method of Auger spectroscopy have shown that Eq. (32) is able to predict X-vacancy sharing probabilities with accuracies of typically 10%. This is seen in Figure 12, where Auger data from different laboratories " are summarized. The experimental results are in excellent agreement with the Meyerhof-Demkov formula (32). Only the relatively light system B + C shows remarkable discrepancies from the theoretical curve. 

Screening effects from the inner shell have been examined also in the work devoted to double X-vacancy sharing. For the system S + Ar McDonald et alP have detected a 20% difference in the one-electron probability for transitions into the 2o- MO with one and two vacancies. However, for most heavier systems such effects have not been observed. The experimental results for double X-vacancy sharing have been shown to be in accordance with statistical rules for nonrelaxed orbitals such as those given in Eq. (28). Hence, as expected, the screening effects from inner shells diminish for heavier collision partners. 

It is emphasized that this cancellation does not occur for L-vacancy sharing. With set II in Table 1, one obtains = 1.82Xj. from Eq. (36) where the index refers to the L shell. This exponent is in good agreement with the observation by Lennard et who studied extensively vacancy... 

Figure 14. Probability Wl for L-vacancy sharing as a function of the scaling parameter...

Finally, the coupled equations (9) for adiabatic states are integrated to determine probabilities for vacancy exchange. In the following sections, results are discussed for systems with three and four states. Prior to this study, the possibility is examined of applying the two-state models in the description of KL- and LX-vacancy sharing. 

In the application of two-state models to XL- and LX-vacancy sharing, controversial results are encountered. It is found that the Demkov-Meyerhof... 

It seems that Demkov s model is not well suited for the treatment of asymmetric collision systems. Thus, following the suggestion by Meyerhof et various studies of KL- and LX-vacancy sharing have been performed in terms of Nikitin s model, " which has a greater flexibility in describing the orbital energies. Often, the model parameters have been extracted from the fit of the 3<7--4energy difference obtained from independent molecular orbital calculations. 

Figure 19. Schematic plot of inner-shell MO s involved in -vacancy sharing (b), CL-vacancy sharing (c), and LK-vacancy sharing (d). For comparison, valence orbitals V and V2 are also shown (a). Notation as in Figure 1. (From Ref. 11.)...

To deduce radial coupling matrix elements, Eq. (14) is applied. It is expected that KL-vacancy sharing is primarily determined by the 3o--4radial coupling matrix element shown in Figure 23. The model results compare well with the data from the more elaborate three-state calcula-... 

Figure 29. Vacancy sharing probabilities for the K and L shells in the systems B + Ar, C + Ar, N + Ar, and O + Ar as a function of the inverse projectile velocity. The data refer to the excitation of the lower-lying levels, i.e., the Ar i-shell orbitals for B -I- Ar and the K-shell orbitals of the lighter particle in the other systems. The dots refer to experimental results by Reed et al and the solid lines follow from three-state model calculations on the basis of the SHM matrix elements (18). The dashed line represents two-state calculations for O H- Ar by means of Nikitin s model." ...

In Figure 29, significant discrepancies between the SHM calculations and experiment are still observed. These discrepancies are partially understood. The transition probability in the LK systems is relatively small in the range of small incident velocities, so that, there, mechanisms other than vacancy sharing become important. Unilateral screening effects due to double vacancy production in the 4a- MO and/or two-electron transitions filling the double hole states are expected to be important. 

The model calculations of LK-vacancy sharing yield probabilities seperately for the excitation of 2s and 2p states. These data may be used to gain information about diabatic correlation rules. For LK systems two different rules have been proposed with respect to the diabatic state 3 da which corresponds to the 4or MO. Barat and Lichten proposed the correlation of the 3 da state with the 2p level, whereas Eichler et suggested the correlation with the 2s level. 

Figure 34 shows also experimental results obtained by Schneider et using the method of Auger spectroscopy. For the system S + Ar it is seen that the RAD(cr) process provides the major contribution to the Ar L excitation. However, for Si + Ar the RAD((r) process becomes less important. In this case an additional process different from vacancy sharing has to be considered. This process, analyzed by Wille, is attributed to the lS-2ir-4or rotational coupling mechanism (Figure 31). As expected the respective cross sections from this process, labeled ROT in Figure 34, are practically the same for the systems S + Ar and Si + Ar. On the contrary, with increasing asymmetry of the system the RAD(o-) process loses importance, since the energy gap between the L shells of the collision partners increases (Figure 31). Hence, it is concluded that pure L-vacancy sharing may be studied only in rather symmetric collision systems.

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