Pseudo-surface wave

Fig. 11.4. Velocities of bulk and surface waves in an (001) plane the angle of propagation in the plane is relative to a [100] direction, (a) Zirconia, anisotropy factor Aan = 0.36 (b) gallium arsenide, anisotropy factor Aan = 1.83 material constants taken from Table 11.3. Bulk polarizations L, longitudinal SV, shear vertical, polarized normal to the (001) plane SH, shear horizontal, polarized in the (001) plane. Surface modes R, Rayleigh, slower than any bulk wave in that propagation direction PS, pseudo-surface wave, faster than one polarization of bulk shear wave propagating in...

Fig. 11.8. Rayleigh and pseudo-surface wave velocities measured on GaAs(OOl), indicated by +. The solid lines are the calculated curves of Fig. 11.4(b) (without the longitudinal wave curve), plotted on the enlarged vertical scale used for the experimental...

As shown in Fig. 4.19, in anisotropic medium, a surface acoustic wave represents a combined longitudinal (4.19a) and shear (4.19b) motion of the lattice in the y-(0)-z plane this is the saggital plane. In anisotropic media, in certain multilayer structures and at some interfaces, the surface wave velocity exceeds the velocity of the shear wave and the energy continuously leaks from the surface to the bulk of the material. In such cases, we talk about pseudo- or leaky waves. Various energy-loss... 

The 3d ab initio simulations [4] for Na3 are based, in a similar way, on three ab initio potential-energy surfaces for Na3(X), Na3(B), and Na3(X), with 3d ab initio dipole coupling between Na3(X) and Na3(B) evaluated by V. Bonacic-Koutecky et al. [5] plus Condon-type coupling between Na3(B) and Na3(X). Additional potential-energy surfaces interfere at the conical intersections of the pseudo-Jahn-Teller distorted Na3(B) state (see Ref. 6), but we have tested carefully [4] that these interferences are negligible in the frequency domains of the experimental femtosecond/picosecond laser pulse experiments [7] as well as in the continuous-wave experiments [8]. 

Apparently, the current in the ascending part of the wave and the pseudo-limiting current are mostly determined by transport-independent, kinetic factors. The limiting current of the second wave, obtained after correction for the IR voltage drop, satisfies the Levich relation (Chapter 1, Equation 1.15) and is hence determined by the transport rate of hydrogen peroxide to the electrode surface. This wave will not be further discussed since it is of no use for the aim of this investigation. 

Worthy of speoial mention is the use of laser for phonon detection, as in Brillouin speotrosoopy which is especially suitable for deteoting surface acoustic waves (SAWs). Generalized SAWs can be used to obtain Brillouin speotra with a 5-pass Fabry-Perot interferometer [29] on the other hand, pseudo-SAWs, which are weaker than the previous ones, require a tandem (3 -r 3)-pass Fabry-Perot interferometer system [30]. 

Solution of the Kohn-Sham equations as outlined above are done within the static limit, i.e. use of the Born-Oppenheimer approximation, which implies that the motions of the nuclei and electrons are solved separately. It should however in many cases be of interest to include the dynamics of, for example, the reaction of molecules with clusters or surfaces. A combined ab initio method for solving both the geometric and electronic problem simultaneously is the Car-Parrinello method, which is a DFT dynamics method [52]. This method uses a plane wave expansion for the density, and the inner ions are replaced by pseudo-potentials [53]. Today this method has been extensively used for studies of dynamic problems in solids, clusters, fullerenes etc [54-61]. We have recently in a co-operation project with Andreoni at IBM used this technique for studying the existence of different isomers of transition metal clusters [62,63]. 

Figure 6 shows schematically the physiochemical processes involved in the HMX/GAP pseudo-propellant combustion. A physical model for RDX/GAP pseudo-propellant combustion is available in Ref. 38. The entire combustion-wave structure is segmented into three regions solid phase, near-surface... 

Since both bulk and surface states are molecular in character, the wave functions of atoms in both types of position can be calculated by the same method. Appelbaum and Hamann [70] assume two-dimensional periodicity along the surface and make the same Fourier expansion of the pseudo-wave function as for the bulk, except that at each of a set of discrete surface normal co-ordinates a different set of expansion coefficients is used. These sets can be integrated from outside the surface into the bulk. Well inside the bulk, these wave functions are matched to bulk states of similar lateral symmetry and the matching condition determines energies and wave functions. 

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