Shear horizontal modes

The calculated Rayleigh mode (SJ, the lowest lying phonon branch, is in good agreement with the experimental data of Harten et al. for all three metals. Due to symmetry selection rules the shear horizontal mode just below the transverse bulk band edge can not be observed by scattering methods. The mode denoted by Sg is the anomalous acoustic phonon branch discussed above. Jayanthi et al. ascribed this anomalous soft resonance to an increased Coulomb attraction at the surface, reducing the effective ion-ion repulsion of surface atoms. The Coulomb attraction term is similar for all three metals... 

Figure 20. Surface phonon dispersion for Rbl(OOl). The upper panel shows a comparison of the HAS data with a slab dynamics calculation for the unrelaxed surface, while the lower panel is a comparison of the same data with a similar calculation for a relaxed surface. The sagittal plane and shear horizontal modes are labeled by SP and SH, respectively, and the superscripts indicate which ion (Rb or T) is predominantly involved in the motion of the mode. The other labels follow the notation of Figs. 16 and 17. (Reproduced from Fig. 3 of Ref. 68, with permission.)...

In the rx region of the SBZ, no points corresponding to the S2 mode were found. However, the relaxation appears to introduce a sagittal plane mode with perpendicular polarization just below the shear horizontal mode S5, for which a number of data points are rather close. Again, there are some points that appear to be associated with crossing and longitudinal... 

Figure 27. Extended zone plot for MgO(001) showing the data obtained from a number of TOF spectra. The solid curve is the calculated Rayleigh wave dispersion, while the dashed curve in the <110> direction is the S7 shear horizontal mode which lies below the sagittal plane modes for this crystal in this direction. The dot-dashed line is a scan curve at the angles indicated. (Reproduced from Fig. 3 of Ref. 82, with permission.)...

V/e pass now to investigate the effects of the bulk parametrization. In Fig. 12 are presented the surface phonons for Pt by using the (1C) model for a slab formed by 65 atomic planes. The full lines in the A and Z directions refer to modes polarized in the sagittal plane defined by the momentum Q and the normal to the surface. In the Y direction the full lines refer to modes that, on the surface, are polarized in a plane with Miller indices (l,-1,0). The dashed lines in the A and I directions are relative to Shear Horizontal modes. In Fig. 13 are reported the calculations for the (4CA) model. As one can clearly see the use of the (1C) model deeply modify the surface phonon spectrum with respect to the (4CA) model. The band width of all the branches and the relative gaps are, in the (1C) case, too narrow with respect to the experimental values determined from neutron data. Furthermore the shape of the branches is very crytical to the value of the force constant g. In this case the results are strongly model-dependent. We want to stress that the modification in the branches by the use of the (lC) model with respect to the use of the (4CA) model are more pronounced than in the bulk case. This Indicate that it is necessary to have a very good parametrization of the bulk properties in order to study surface dynamics. In Figs. 14, 15, 16 are drawn the surface phonons for noble metals. 

As an optical technique, Brillouin scattering allows the determination of the elastic constants and hence of the bulk moduli through the interaction of light with thermal excitation in a material, in particular acoustic phonons in a crystal. In this technique, the elastic constants Cn and Cgg can be directly obtained from measurement of the phase velocity of the longitudinal mode and of the shear horizontal mode traveling parallel to the crystal surface. The remaining constants,... 

Adler, E.L. (1989) Electromechanical coupling to Lamb and shear-horizontal modes in piezoelectric plates. IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control, 36, 223. 

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...

A piezoelectric mass sensor is a device that measures the amount of material adsorbed on its surface by the effect of the adsorbed material on the propagation of acoustic waves. Piezoelectric devices work by converting electrical energy to mechanical energy. There are a number of different piezoelectric mass sensors. Thickness shear mode sensors measure the resonant frequency of a quartz crystal. Surface acoustic wave mode sensors measure the amplitude or time delay. Flexure mode devices measure the resonant frequency of a thin Si3N4 membrane. In shear horizontal acoustic plate mode sensors, the resonant frequency of a quartz crystal is measured. 

Fig. 12.3. Mercury sensor based on surface acoustic waves (SAW) with shear-horizontal acoustic plate mode. This approach was tested in Ref. [8].

Figure 3.1 Schematic sketches of the four types of acoustic sensors, (a) Thickness-Shear Mode (TSM) resonator (b) Surface-Acoustic-Wave (SAW) sensor, (c) Shear-Horizontal Acoustic-Plate-Mode (SH APM) sensor, and (d) Flexural-Plate-Wave (FPW) sensor.

Figure 3.33 Schematic of an acoustic plate mode (APM) device showing the shear horizontal (SH) displacement of the mode as it propagates between input and output transducers. (Reprinted with permission. See Ref. (54). 1989 Elsevier Publishers.)...

Figure 3.34 Cross-sectional displacement profiles for the four lowest-order shear horizontal plate modes. These profiles are normalized equal power flow per width of the plate. (Reprinted with permission. See Ref. [M). 1989 Elsevier PuMishers.)...

SH-APM shear-horizontal acoustic plate mode (SH-APM) sorption (sorb) ST-cut quartz... 

D Mcallister Biode, Inc. Cape Elizabeth, ME DoE Developing a simple sensor for use in waste, surface, and groundwater using a shear horizontal acoustic plate mode (SHAPM) sensor, a form of piezoelectric sensor... 

Fig. 2 A Schematic cross-section depicting the shear horizontal wave in a QCM device. B Contact mode AFM image of a QCM electrode surface at 0 V and 30 V. The horizontal displacement hy applying voltage can clearly he seen hy the surface scratch. C AFM traces recorded on the siuface at 30 V and 0 V, respectively. These measurements are optimal for quantifying the displacement, which is 3 nm in the given case...

Figure 17. Surface phonon dispersion for KBrfOOl). The data are compared to a Green s function calculation used to determine the bulk bands (shown by the shaded regions with polarizations perpendicular or parallel to the surface as indicated in the figure) and the surface localized modes (shown as solid lines). The predominant polarizations of the modes are indicated by perpendicular and parallel symbols, and the labels of the modes follow the notation in Fig. 16. Note that modes Sy and S5 are polarized shear horizontal and cannot be observed in this scattering arrangement. The data plotted as triangles are obtained from weaker peaks in the TOF spectra than the points represented by open circles. (Reproduced from Fig. 8 of Ref. 49, with permission.)...

Martin F., Newton M. L, McHale G., Melzak K. A., and Gizeli E., Pulse mode shear horizontal-surface acoustic wave (SH-SAW) system for liquid based sensing applications, Biosensors and Bioelectronics, 19, 627-632, 2004. 

Shen C.-Y, Hsu C.-L., Hsu K.-C., and Jeng J.-S., Analysis of shear horizontal surface acoustic wave sensors with the coupling of modes theory, Jpn J. Appl. Phys., 44, 1510-1513, 2005. 

Vibration frequencies and phonon dispersion See Figs. 20 - 23. Table 13. Perpendicular vibration frequencies /zcoi and characteristics of the phonon dispersion curves for the noble gas monolayers. The sound velocities c/ and c, were obtained from the initial slope of the dispersion curves for the longitudinal (L) and shear-horizontal (SH) modes, respectively. Where complete or partial dispersion curves are available, oidy the value at the boundary of the surface Brillouin zone is indicated. Abbreviations used F, M, K high syrtunetry points of the 2D adlayer Brillouin zone (BZ) [001], [110] and [112] crystallographic directions of the substrate surface. All data were obtained using inelastic He-atom scattering. (Ad. = adsorbate) ... 

Notations used R, L Pt(lll) surface Rayleigh wave and longitudinal resonance, respectively S, LA and SH perpendicular, longitudinal and shear horizontal Xe adlayer modes, respectively. The lines are calculations based on McLachlan modified HFD-B2 gas-phase potentials (sohd hues) [OOB]. 

Fig. 23. Phonon dispersion curves for a Xe monolayer on Cu(lOO) along the [100] substrate direction (after [97G]). Notations used R Cu(lOO) surface Rayleigh wave and SH perpendicular and shear horizontal Xe adlayer modes, respectively. The SH mode was first explained by assigning it to the longitudinal branch [97G,99S2], which required a large softening of the inplane Xe-Xe force constant. Later it was suggested [97B1,00B] that it should be assigned to the SH-polarized mode.

Figure 2. Schemes for using piezoelectric quartz crystals. A. Quartz crystal microbalance configuration, standing shear wave between facing Au electrode contacts B. Surface acoustical mode configuration, surface undulation caused by bias between metal fingers C. Horizontal shear plate mode.

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