Acoustic breathing mode frequencies in cylinders, cylindrical shells and composite cylinders of general anisotropic crystals: Application to nanowires

We present here a study of the acoustic breathing modes for infinitely long cylinders, cylindrical shells and composite cylinders of general anisotropic crystals. We assume cylindrical anisotropy for the systems studied. We obtain expressions in closed form for their frequencies in the case of cylinders and cylindrical shells, valid for any anisotropic material, thus including up to 21 independent elastic constants. In the case of the lowest breathing mode of a thin cylindrical shell we obtain a simple analytical formula. This can be used to obtain a first estimate of the breathing mode frequency in nanotubes for any material. In the case of core–shell and composite cylinders we obtain the expressions for the secular determinant. We calculate the frequencies of the lowest acoustic breathing mode of Au, CdSe, InAs, GaAs, Ag and Bi nanowires obtained recently by different experimental groups. We also present results for the acoustic breathing modes of Au/Ag and ZnS/SiO2 core–shell nanowires produced recently.