Number of longitudinal normals and degenerate directions for triclinic and monoclinic media

We solved the problem of finding longitudinal acoustic directions of monoclinic media using the eliminant method. By extending Khatkevich's approach and using the Bezout theorem, we proved that the number of longitudinal normals for mechanically stable monoclinic media can not be larger than 13. Both longitudinal normals (n ₁, n ₂, n ₃) lying in and out of plane perpendicular to the two-fold axis (n ₃ ≠ 0) of monoclinic media are considered. Closed-form equations for ratios x = n ₁/n ₃ y = n ₂/n ₃ are derived and exactly solved by the eliminant method. With the help of this method, we show that in the case of the CDP (CsH₂PO₄) crystal, the number of longitudinal normals equals three. Their components are given. For media of higher symmetries (rhombic, trigonal, tetragonal, hexagonal and cubic), our approach yields well-known results obtained mainly by Borgnis and Khatkevich. For triclinic elastic media, we proved that the number of degenerate directions can not be greater than 132. Received 24 August 2002 Published online 14 February 2003 RID="a" ID="a"e-mail: ardud@ift.uni.wroc.pl     

Surface shear horizontal waves associated with a periodic array of wires deposited on a substrate

The vibrational and electronic spectra of a semi-infinite crystal with a planar surface are modified by the presence of surface inhomogeneities or roughness such as ridges or grooves, quantum wires or tips. We develop a Green's function formalism to investigate the localized and resonant acoustic modes of shear horizontal polarization associated with the surface of a substrate supporting a single and a periodic array of wires. Each material is assumed to be an isotropic elastic medium. The calculation can be applied to an arbitrary choice of the shape and elastic parameters of the wires. The surface modes are obtained as well-defined peaks of the densities of states (DOS). In this paper, we calculate the variation of the density of states associated with the adsorption of a single wire, and the dispersion curves of the surface modes for a periodic array of wires on the flat surface of a substrate. We discuss their behaviors as a function of the elastic parameters and the relationship between resonant modes of the single wire and dispersion curves of the surface modes for a periodic structure. Received 6 December 2000