Excitation models

Dissociation at a surface appears to be analogous to dissociation in the gas phase. The impinging electron causes a Franck-Condon transition to an electronic state which subsequently dissociates. This one-dimensional Franck-Condon excitation model is illustrated schematically in Fig. 31. The cross section for the electronic transition is probably comparable to gas phase excitation processes. After excitation the particle, which is now in a repulsive state, begins to move away from the surface. If it has sufficient energy it may escape from the surface. If not the fragments remain adsorbed. Moreover, radiationless de-excitation may occur... 

The measurements were carried out using polarized-light from synchrotron radiation. The angle-resolved UPS spectra were recorded for specific directions of photon incidence, photon polarization, and electron exit, chosen in order to resolve the momentum dependence of the 7t-electron energy bands which could be observed in this experiment. Details are available elsewhere63. The UPS results are analysed not only with the help of the valence effective Hamiltonian (VEH) method, but also with the help of new quantum-chemical calculations based upon the excitation model method64. The full VEH band structure is shown in Fig. 7.32. 

The VEH results (Fig. 7.35) indicate that, below the dispersed 7t2-band there is a band of less dispersion, corresponding to a ff-band involving the triple bonds in the back bone, and a flat (non-dispersed) band corresponding to the C=0 groups in the 4-BCMU side chains. In the excitation model results (Fig. 7.36), below the 7t2-band there... 

Fig. 7.36 The ARUPS peak energies plotted versus the excitation model n-band structure.

Fig. 15. (a) Schematic Er excitation model, showing the electronic band structure of Si nanocrystall-doped Si02 and the Er 4f energy levels. An optically generated exciton (dotted line) confined in the nanocrystal can recombine and excite Er3+. (b) Schematic representation of SiC>2 containing Er (crosses) and nanocrystals (circles). The nanocrystals that couple to Er (filled circles) show no exciton luminescence (redraw after (Kik and Polman, 2001)). 

A molecular fluorescence model is presented which is particularly appropriate for short pulse excitation. The frozen excitation model treats the two rotational levels which are directly excited by the laser as an isolated system with constant total number density. Consider the four level molecular model illustrated in Fig. 1. The four level model was solved by Berg and Shackleford (5 ) for the case where steady state is established throughout all molecular levels. Levels le and 2e are the single... 

Using the frozen excitation model to analyze the data shown in Fig. 3, and calibrating the system via Rayleigh scattering (8J, a total OH number density of 4 x 1C>16 cm 3 was calculated for an assumed flame temperature of 2000 K in the methane-air torch. Nt was not compared directly with the results of absorption studies future flat flame burner studies will involve direct comparison of absorption and fluorescence. 

Figure 12. Excitation of the singular mode Ns as a function of the external pump parameter (phonon flux

Raman spectra for the sample were conducted in a compression-decompression cycle. In this experiment, the crystalline diffraction began to disappear above 7-8 GPa during compression, and pressure-induced amorphization was indicated by the Raman spectra above 13 GPa (Fig. 14). The resultant HDA Si exhibits the Raman spectrum that differs from the spectrum of normal -Si (LDA Si). Rather, the characteristics of the spectrum for HDA Si resemble those of the (3-tin crystal, which indicates that HDA Si has a (locally) analogous structure to the (3-tin structure. The synthesis of the HDA form of Si by Deb et al. [263] has a strong resemblance to that of water (ice) by Mishima et al. [149, 196]. Whereas compression induced amorphization that was almost completed at 13-15 GPa, decompression induced an HDA-LDA transition below 10 GPa, which is clearly shown in the Raman spectra (Fig. 14). This is the first direct observation of an amorphous-amorphous transition in Si. The spectrum at 0 GPa after the pressure release exhibits the characteristic bands of tetrahedrally coordinated -Si (LDA Si). Based on their experimental findings Deb et al. [263] discussed the possible existence of liquid-liquid transition in Si by invoking a bond-excitation model [258, 259]. They have predicted a first-order transition between high-density liquid (HDL) and low-density liquid... 

Christiansen O, Koch H, Jprgensen P (1995) Response functions in the CC3 iterative triple excitation model. J Chem Phys 103 7429-7441. 

Bar-Nun and Lifshitz suggest the vibrational excitation model, previously employed by Bauer and Ossa is applicable. In this model the energy required for the process is not in translational modes, but rather in vibrational. Once the critical vibrational level is reached by collisional excitation a very rapid four-... 

D. Watts and R.. Bartlett,/. Chem. Phys., 93, 6104 (1990). The Coupled-Cluster Single, Double, and Triple Excitation Model for Open-Shell Single Reference Functions. 

O. Christiansen, H. Koch, and P. Jorgensen, J. Chem. Phys., 103, 7429 (1995). Response Functions in the CC3 Iterative Triple Excitation Model. 

It is well known that, in order to obtain reasonable predictions for spectra, a Cl treatment is preferable to the simple one-particle excitation model (see Sect. 5.3). However, allowing for horizontal correlation through Cl with n orbitals is not sufficient to restore agreement with experiment (for a discussion, see 28>). We come back to this point at the end of this section. 

A more direct evidence of the surface localized excitation mechanism has been obtained by a polarization dependence study. For K/Pt(lll) at 0.36 ML, it has been demonstrated that the coherent excitation of the K—Pt stretching mode occurs with p-polarized excitation and not with s-polarized exdtation. Since the s-polarization absorptance is about one fourth of that with p-polarization under the experimental conditions (2.19 eV photon energy, 70° angle of inddence), the coherent amplitude should be detectable with s-polarization if the substrate-mediated process operates. Therefore, the negligible oscillatory component with s-polarization is inconsistent with the substrate-mediated excitation model and it is indicated that some electronic transitions involving K-induced surface states are responsible for the coherent excitations. 

To this group belong several models of very different kinds such as the image model (RE-IE), the charge transfer (RE-CT) model, the electron-hole excitation model (RE-EH), and the Raman reflectivity model (RE-RF). These models have very little in common except that they all lead to enhancements by virtue of a resonance scattering mechanism. The validity of the last statement is not always realized by people, but it will be shown below to hold true. 

Examples of stable filament solutions of the excitable model (7.33), obtained numerically for the flow of the filament model of Sect. 2.7.1, are shown in Fig. 7.13 (Neufeld et al., 2002c Hernandez-Garcfa et ah, 2003). At Da = Dac 12.5 the stable filament solution collide with the unstable pulse (7.29) in a saddle-node bifurcation, so that no... 

Fig. 2.10. Relation between mean system frequency v and driving frequency i/ (top) and number of locked cycles Ni ck (bottom) of the excitable model as a function of driving frequency v. Lines show dependence as solutions of eqs. (2.36) and (2.37). The + symbols present results from simulations of the discrete system and circles correspond to data from simulations of the FHN system. Parameters for the FHN system eq. (2.11) ao = 0.405, ai = 0.5, = 0.001, D = 10 , Sx(t) = 0, Sy t) = A with A = 0.015. Parameters for the two state model (theory and simulations) from simulations of the interspike interval distribution density (cf. Fig. 2.6) T ss 2620, ro 0.0087 and n 8.3 10- . [15]...

The tris-(2-aminomethylpyridine)iron(II) halides, [Fe(2-NH2pic)3]X2 (X=C1, Br, I), also show a spin crossover [5]. In this instance the halide anions have a very strong effect on the equilibrium, as shown by the magnetic moment versus temperature plot in Fig. 8.2. No interpretation can be formulated using a simple thermal excitation model. The chloride gives Mossbauer spectra indicating T2 at room temperature, Ai at 4-2 K, and both states in coexistence at 77 K, with no detectable interconversion within the observation time-scale. 

The driving mechanisms for the island vertical correlation have been the subject of extensive studies over the past years. Because the buried islands produce a nonuniform strain field at the surface of the spacer layer, i.e. the regions above the islands are tensely strained while the regions in between islands remain compressed, exciting models have treated the island distribution at the spacer layer surface by considering the effect of such a strain field on surface diffusion [4] or on island nucleation [3]. Recent calculations have taken into account the effect of the elastic anisotropy of the materials [16], the surface energy [18] or the elastic interaction between the buried islands with newly deposited ones [19]. However, in all of the above models it was assumed that the surface of the spacer layer becomes perfectly flat before the deposition of a new layer. From the experimental point of view, this... 

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