Surface vibration lattice vibrations

To study the reaction of molecules on surfaces in detail, it is important to consider the different degrees of freedom the system has. The reacting molecule s rotational, vibrational and translational degrees of freedom will affect its interaction as it hits the surface. In addition, the surface has lattice vibrations (phonons) and electronic degrees of freedom. Both the lattice vibrations and the electrons can act as efficient energy absorbers or energy sources in a chemical reaction. 

The special points method depends upon retention of the translational periodicity of a lattice, which is lost if we consider defects, surfaces, or lattice vibrations. (Even the special vibrational mode with frequency listed in Table 8-1 entailed a halving of the translational symmetry.) It is therefore extremely desirable to seek an approximate description in terms of bond orbitals, so that the energy can be summed bond by bond as discussed in Chapter 3. We proceed to that now. 

Dynamic models for ionic lattices recognize explicitly the force constants between ions and their polarization. In shell models, the ions are represented as a shell and a core, coupled by a spring (see Refs. 57-59), and parameters are evaluated by matching bulk elastic and dielectric properties. Application of these models to the surface region has allowed calculation of surface vibrational modes [60] and LEED patterns [61-63] (see Section VIII-2). 

The Mossbauer effect can only be detected in the solid state because the absorption and emission events must occur without energy losses due to recoil effects. The fraction of the absorption and emission events without exchange of recoil energy is called the recoilless fraction, f. It depends on temperature and on the energy of the lattice vibrations /is high for a rigid lattice, but low for surface atoms. 

The infrared spectra for various aluminum oxides and hydroxides are shown in Figure 3. Figure 3a is a-alumina (Harshaw A13980), ground to a fine powder with a surface area of 4 m /g. The absorption between 550 and 900 cm is due to two overlapping lattice modes, and the low frequency band at 400 cm is due to another set of lattice vibrations. These results are similar to those obtained by reflection measurements, except that the powder does not show as... 

The results presented here for silicas and aluminas illustrate that there is a wealth of structural information in the infrared spectra that has not previously been recognized. In particular, it was found that adsorbed water affects the lattice vibrations of silica, and that particle-particle Interactions affect the vibrations of surface species. In the case of alumina, it was found that aluminum oxides and hydroxides could be distinguished by their infrared spectra. The absence of spectral windows for photoacoustic spectroscopy allowed more complete band identification of adsorbed surface species, making distinctions between different structures easier. The ability to perform structural analyses by infrared spectroscopy clearly indicates the utility of photoacoustic spectroscopy. 

Lanz and Com [51] proposed a 20-nm thick space charge layer on the Ti02 surface. When the fourth-order response with our TMA-covered surface is generated in the space charge layer, the broad width of the 826-cm band is understood as a depth-dependent wavenumber of the lattice vibration. 

As shown in Figure 6.6, the raw SH intensity and modulated component were almost identical to what was observed on the TMA-covered surface. A slight bump appeared at 570 cm in addition to the four major bands of lattice vibrations. 

LEED intensities also depend on the lattice vibrations at the surface of the crystal. A high Debye temperature of the surface results in intense LEED spots. In fact, measurement of spot intensities as a function of primary electron energy provides a way to determine the surface Debye temperature [20]. 

As noted in the introduction, vibrations in molecules can be excited by interaction with waves and with particles. In electron energy loss spectroscopy (EELS, sometimes HREELS for high resolution EELS) a beam of monochromatic, low energy electrons falls on the surface, where it excites lattice vibrations of the substrate, molecular vibrations of adsorbed species and even electronic transitions. An energy spectrum of the scattered electrons reveals how much energy the electrons have lost to vibrations, according to the formula ... 

In situ characterization. Catalysts should preferably be investigated under the conditions under which they are active in the reaction. Various reasons exist why this may not be possible, however. For example, lattice vibrations often impede the use of EXAFS, XRD and Mossbauer spectroscopy at reaction temperatures the mean free path of electrons and ions dictates that XPS, SIMS and LEIS are carried out in vacuum, etc. Nevertheless, one should strive to choose the conditions as close as possible to those of the catalytic reaction. This means that the catalyst is kept under reaction gases or inert atmosphere at low temperature to be studied by EXAFS and Mossbauer spectroscopy or that it is transferred to the vacuum spectrometers under conditions preserving the chemical state of the surface. 

Vibrations in the surface plane, however, will be rather similar to those in the bulk because the coordination in this plane is complete, at least for fee (111) and (100), hep (001) and bcc (110) surfaces. Thus the Debye temperature of a surface is lower than that of the bulk, because the perpendicular lattice vibrations are softer at the surface. A rule of thumb is that the surface Debye temperature varies between about 1/3 and 2/3 of the bulk value (see Table A.2). Also included in this table is the displacement ratio, the ratio of the mean squared displacements of surface and bulk atoms due to the lattice vibrations [1]. 

The vector / j specifies the position of the atom in a two-dimensional lattice in a plane parallel to the surface and the value of identifies the lattice plane with respect to the surface (1 = 1 for the surface l er. u is the displacement of the vibrating atom from its equilibrium position Rq. The total kinetic energy of the vibrating lattice is... 

Lewis, D.G. Cardde, C.M. (1989) Hydrolysis of Fe(III) solution to hydrous iron oxides. Aust. J. Soil Res. 27 103-115 Lewis, D.G. Farmer,V.C. (1986) Infrared absorption of surface hydroxyl groups and lattice vibrations in lepidocrodte (y-FeOOH) and boehmite (y-Al-OOH). Clay Min. 21 93-100... 

Onari, S. Arai,T. Kudo, K. (1977) Infrared lattice vibrations and dielectronic dispersion in a- Fe203. Phys. Rev. B16 1717 Onoda, G.Y. de Bruyn, P.L. (1966) Proton adsorption ot the ferric oxide/aqueous solution interface. I. A kinetic study of adsorption. Surface Sd. 4 48—63... 

Dynamic smdies of the alloy system in CO and H2 demonstrate that the morphology and chemical surfaces differ in the different gases and they influence chemisorption properties. Subnanometre layers of Pd observed in CO and in the synthesis gas have been confirmed by EDX analyses. The surfaces are primarily Pd-rich (100) surfaces generated during the syngas reaction and may be active structures in the methanol synthesis. Diffuse scattering is observed in perfect B2 catalyst particles. This is attributed to directional lattice vibrations, with the diffuse streaks resulting primarily from the intersections of 111 reciprocal lattice (rel) walls and (110) rel rods with the Ewald sphere. 

The extinction curves for magnesium oxide particles (Fig. 11.2) and aluminum particles (Fig. 11.4) show the dominance of surface modes. The strong extinction by MgO particles near 0.07 eV( - 17 ju.m) is a surface mode associated with lattice vibrations. Even more striking is the extinction feature in aluminum that dominates the ultraviolet region near 8 eV no corresponding feature exists in the bulk solid. Magnesium oxide and aluminum particles will be treated in more detail, both theoretically and experimentally, in this chapter. 

We shall call the frequency at which t = —2em and t" — 0 the Frohlich frequency coF the corresponding normal mode—the mode of uniform polarization—is sometimes called the Frohlich mode. In his excellent book on dielectrics, Frohlich (1949) obtained an expression for the frequency of polarization oscillation due to lattice vibrations in small dielectric crystals. His expression, based on a one-oscillator Lorentz model, is similar to (12.20). The frequency that Frohlich derived occurs where t = —2tm. Although he did not explicitly point out this condition, the frequency at which (12.6) is satisfied has generally become known as the Frohlich frequency. The oscillation mode associated with it, which is in fact the lowest-order surface mode, has likewise become known as the Frohlich mode. Whether or not Frohlich s name should be attached to these quantities could be debated we shall not do so, however. It is sufficient for us to have convenient labels without worrying about completely justifying them. 

Ions in the lattice of a solid can also partake in a collective oscillation which, when quantized, is called a phonon. Again, as with plasmons, the presence of a boundary can modify the characteristics of such lattice vibrations. Thus, the infrared surface modes that we discussed previously are sometimes called surface phonons. Such surface phonons in ionic crystals have been clearly discussed in a landmark paper by Ruppin and Englman (1970), who distinguish between polariton and pure phonon modes. In the classical language of Chapter 4 a polariton mode is merely a normal mode where no restriction is made on the size of the sphere pure phonon modes come about when the sphere is sufficiently small that retardation effects can be neglected. In the language of elementary excitations a polariton is a kind of hybrid excitation that exhibits mixed photon and phonon behavior. 

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