High-Speed Scanning of Piezo-Probes for Nano-fabrication

Low scanning speed of piezo-probes has been a fundamental limitation of scanning probe based nano-fabrication techniques. Typical scan-rates achieved are limited, by structural vibrations of the piezo-probe, to about 1/10th the fundamental vibrational frequency of the piezo-probe. Faster scanning of piezo-probes is achieved here (experimental results are presented) by using inversion of the piezo-dynamics—this approach uses a feedforward input voltage, applied to piezo-probe, to compensate for piezo vibrations.

Axisymmetric Free Vibration of Shallow Spherical Shells With a Circular Rigid Insert

A general solution for the third-order partial differential equations for the axisymmetric free vibration of thin isotropic shallow spherical shells with a rigid insert is presented in this paper. The frequency equation in terms of Bessel functions as well as modified Bessel functions is solved for the fundamental vibrational frequency and mode shape. Both linear and non-linear boundary conditions are applied and the results are compared. The relationship between the vibrational frequency, mode shape and the size of the rigid insert is discussed.

Localized vibrations of H – and D – ions in the alkaline earth fluorides

Measurements of the absorption spectra associated with the vibrations of H - and D - ions in CaF 2 , SrF 2 and BaF 2 have been made in the region 1 to 17 μm . The most detailed investigation has been made in CaF 2 , where, in addition to the fundamental vibrational frequency, a second harmonic and two third harmonics of the fundamental frequency have been observed. The spectra have been assigned to the localized vibrations of isolated light ions on fluorine sites. The harmonics are seen because of anharmonic effects; to a good approximation the light ions can be considered to oscillate in an anharmonic tetrahedral potential well produced by a nearly static host lattice. W eak satellite lines are observed in the immediate vicinity of the fundamental vibrational lines due to the presence of small concentrations of H – and D – ions in other lattice configurations. Broad bands occur at displacements greater than about 100 cm-1 to higher and lower frequencies from the localized vibrational lines due to combined excitation of the localized mode and lattice band modes. The temperature-dependent intensity, shift and width of the localized vibrational lines have been measured. The presence of the broad side bands and the temperature-dependent effects arise from anharmonic interactions with the band modes of lattice vibration. A simple model of the band modes leads to very satisfactory agreement between theory and observed anharmonic effects for reasonable values of the anharmonic force constants which are regarded as parameters.