Bulk phonons

The application of infrared photoacoustic spectroscopy to characterize silica and alumina samples is reported. High quality infrared photoacoustic spectra illuminate structural changes between different forms of silica and alumina, as well as permit adsorbate structure to be probed. Adsorption studies on aerosil suggest adsorbed species shield the electric fields due to particle-particle interactions and induce changes in the vibrational spectra of the adsorbates as well as in the bulk phonon band. It is shown that different forms of aluminum oxides and hydroxides could be distinguished by the infrared spectra. 

The infrared photoacoustic spectra presented here complement and extend previous results from transmission infrared studies. As an extension of previous studies of silica the photoacoustic results presented here have identified features in the infrared spectra that coincide with bulk phonon modes between 1000 and 1200 cm and below 500 cm . The photoacoustic spectra of water adsorbed on aerosil... 

Bulk phonon modes are absent in wave numbers near 357 cm , the center-frequency of the second band. According to electron energy loss studies done in a vacuum [52, 53], TMA-free TiO2(110) surfaces exhibit surface optical phonons at 370-353 cm . The 357-cm band is related to the surface optical phonons. 

Fig. 17. Bulk phonon dispersion of longitudinal modes in Cu and Ni crystals, along the (110) and (100) directions. After Ref. 37.)...

Fig. 18. Longitudinal bulk phonon density of states projected on bulk (top) and surface layers (bottom). After Ref. 36.)...

A dramatic hybridization splitting around the crossing between the dispersionless adlayer mode and the substrate Rayleigh wave (and a less dramatic one around the crossing with the co = CiQg line - due to the Van Hove singularity in the projected bulk phonon density of states). 

A substantial linewidth broadening of the adlayer modes in the whole region near T where they overlap the bulk phonon bands of the substrate the excited adlayer modes may decay by emitting phonons into the substrate they become leaky modes. These anomalies were expected to extend up to trilayers even if more pronounced for bi- and in particular for monolayers. 

Figure 5 shows a typical IET spectrum obtained from an undosed Al/Al-oxide/Pb junction where the oxide layer was formed by exposing the A1 base electrode to an oxygen plasma at a partial pressure of nominally 100 mTorr for approximately 1-2 min. The sample was not removed from the vacuum chamber during fabrication. No surface contamination is evident the peaks at 945, and 3620 cm-1 are due to Al—O bulk phonon modes, and the stretching of surface hydroxyls, respectively. 

To explain the observed width, it is necessary to look for strong surface-to-bulk interactions, i.e. large magnitudes of surface-exciton wave vectors. Such states, in our experimental conditions, may arise from virtual interactions with the surface polariton branch, which contains the whole branch of K vectors. We propose the following indirect mechanism for the surface-to-bulk transfer The surface exciton, K = 0, is scattered, with creation of a virtual surface phonon, to a surface polariton (K / 0). For K 0, the dipole sums for the interaction between surface and bulk layers may be very important (a few hundred reciprocal centimeters). Through this interaction the surface exciton penetrates deeply into the bulk, where the energy relaxes by the creation of bulk phonons. The probability of such a process is determined by the diagram... 

However, very soon it became clear that the situation is more complex (e.g. [9, 10]). The obvious problem arises with the fact that the red-yellow PL from PS is relatively slow with a decay time in the range of tens of microseconds, which, together with some further experimental observations [11] and theoretical calculations [9,10,12], is considered as strong evidence for an indirect band gap. However, as pointed out by Hybertsen [13], the electron and hole wave functions in small crystallites are spread in k space so that it is no longer meaningful to debate whether the gap is direct or indirect. Detailed calculations show that the phonon assisted transitions dominate in crystallites larger than about 1.5 nm, where an important part of the phonon contribution comes from scattering at the surface of the crystallites and a part from the bulk phonons. 

This is an appropriate place to mention that besides the low-frequency bands associated with some adsorbed species, there are several other Raman features which are related to the (rough) metal itself. Macomber and Furtak have reported weak and broad features at 160 and 110 cm which they associated with silver bulk phonon scattering. These bands, and, in addition, one at 73 cm have been seen earlier by Pockrand and Otto, in an UHV system. 

Figure 7. Bulk phonon dispersion curves for KBr and RbCl in their <100> and <111> high-symmetry directions. Both crystals have fee lattices and rocksalt structures. Note that the transverse branches, labeled TA (transverse acoustic) and TO (transverse optical), are doubly degenerate in these directions. (Adapted from Fig. 3 of Ref. 32.)...

The situation at surfaces is more complicated, and richer in information. The altered chemical environment at the surface modifies the dynamics to give rise to new vibrational modes which have amplitudes that decay rapidly into the bulk and so are localized at the surface [33]. Hence, the displacements of the atoms at the surface are due both to surface phonons and to bulk phonons projected onto the surface. Since the crystalline symmetry at the surface is reduced from three dimensions to the two dimensions in the plane parallel to the surface, the wavevector characterizing the states becomes the two-dimensional vector Q = qy). (We follow the conventional notation using uppercase letters for surface projections of three-dimensional vectors and take the positive sense for the z-direction as outward normal to the surface.) Thus, for a given Q there is a whole band of bulk vibrational frequencies which appear at the surface, corresponding to all the bulk phonons with different values of (which effectively form a continuum) along with the isolated frequencies from the surface localized modes. 

The dynamical model employed in the theoretical calculations is the Shell Model, of which there are several variants [6, 9]. It is designed to approximate the physical situation of the ions in the crystalline environment more realistically than does the Bom-von Karman treatment with harmonic force constants between neighboring atoms as discussed in Section II, but its handling of the forces is not so very different. The Shell Model was developed for these materials to account for the bulk phonon dispersion that was measured by neutron scattering experiments as well as for their dielectric... 

For Nal, the large group of points in the center of the bulk band in FX near the F point are probably due to phonon-assisted bound state resonances which were also found for NaCl and for LiF [58, 61, 63]. In the case of NaCl, the bound state energies had been determined by other scattering experiments [75, 76] so that the peaks in the TOF spectra due to bulk phonon resonances could be reliably removed from the phonon dispersion diagram in Fig. 24. For Nal the values of the bound states still need to be established. 

The effects of relaxation on the calculated surface phonon dispersion in Rbl have apparently been verified, particularly by the observation of a surface optical mode which lies above the bulk phonon optical bands. Except for the mysterious acoustic band mode in Rbl, the Shell model calculations have generally been quite accurate in predicting surface vibrational mode energies in both high-symmetry directions of the alkali halide (001) surfaces. 

Figure 32. Surface phonon dispersion for Nb(OOl). The data are the solid points which were taken at 900 K. Panels a and b correspond to slab dynamics calculations with two different force constant models the calculation in panel b uses the force constants from the bulk phonon fits. The solid lines represent the surface phonons and resonances polarized mainly longitudinally (or parallel), the lines with long dashes represent phonons polarized mainly perpendicularly, and those with short dashes are shear horizontal. (Reproduced from Fig. 6 of Ref. 107, with permission.)...

Figure 34. Surface phonon dispersion for 2H-TaSe2. The HAS data are shown as solid circles except for weak points which appear in the TOP spectra as hybridized longitudinal modes that are shown as crosses. All the data were obtained at 60 K, well into the low-temperature phase. The calculated striped and shaded regions, corresponding to transverse and longitudinal polarizations respectively, are the slab-adapted bulk phonon bands, while the solid line is a calculation for the Rayleigh wave based on the Dispersive Linear Chain Model (shown schematically in Fig. 35). The open circles at g = 0 are from Raman scattering experiments. (This figure has been corrected from Fig. 23 in Ref. 54.)...

A bulk phonon contribution to the time-of-flight spectrum has recently been identified by subtracting out all the other contributions. See Ref. 41. 

Eq. (14) would give the shape of a spectrum typical for a low-viscosity liquid, consisting of a central peak due to entropy fluctuations and frequency-shifted Stokes and anti-Stokes lines related to density fluctuations resulting in a bulk phonon. 

Fig. 41. Schematic plot of the dispersion of a Rayleigh surface phonon (sohd line) and of a bulk phonon band (hatched area). Atoms or molecules adsorbed on the surface can change the surface phonon dispersion, visible as an increase or decrease of the corresponding frequencies relative to those of the clean surface. These shifts are equivalent to a...

Fig. 5.2-58 Surface phonon dispersion curves for Si(lll) 2x1 measured by HATOF. Energies at symmetry points X, 10.2 and 11.1 meV S, 10.5 and ll.bmeV. The flat phonon mode at 10.5 meV is associated with the 2 x 1 reconstruction. The surface mode couples with transverse bulk phonons near the center of the SBZ, giving rise to considerable broadening. The shaded area corresponds to the width ofthe 10.5 meV peak [2.90], The energy of the optical mode (not shown in the figure) is 56.0 meV [2.91]...

The bulk phonons are evaluated within a microscopic approach based on a force constants parametrization. We include central and angular forces in order to simulate the anisotropy of the electron gas produced by the presence of d levels. The surface phonons are evaluated, with these force constants, for a sufficiently thick slab in order to avoid interference effects between the modes of the -two surfaces. 

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