PHONON FOCUSING AND THE SHAPE OF THE RAY SURFACE IN CUBIC CRYSTALS

A systematic study has been carried out on the dependence of the phonon ray surface of cubic crystals on elastic constants. The correspondence between folds in this surface and the presence of caustics in the flux of phonons emanating from a localised heat source is explored. The line, cusp, butterfly and hyperbolic umbilic elementary catastrophes as well as some remarkable types of structural instability are shown to occur in these caustics. A method is demonstrated for portraying the ray surface which provides an immediate indication of the number of separate components a ballistic heat pulse will split up into on propagating in various directions, and what the relative intensities and the spacings of these components will be

Laser thermoelastic generation in metals above melt threshold

We have established the detailed spatio-temporal evolution of heat conduction of the irradiated sample due to the incidence of a laser pulse, including the temperature rise of the solid phase preceding the melting, and the appearance, subsequent growth and then contraction and disappearance of the melt pool due to re-solidification. With these we have identified three regimes of stress evolution: (1) presence of lateral compressive stress in solid that has undergone mild heating without melting, (2) absence of lateral stress in the molten metal, (3) presence of lateral tensile stress in re-solidified and cooling solid. The gradient of the lateral stress, integrated over depth, represents the evolving radial force distribution, which can be regarded as acting at the surface. From the radial surface, stress distributions the radial and normal surface forces were computed. Then we convolved surface force distributions with plate’s Green’sfunctions. We have also performed FEM calculations of the epicentral displacement response to surface forces and find very good agreement with Green’s functions calculations

Measurement of the Elastic Properties of Solids by Brillouin Spectroscopy

Brillouin Light Scattering (BLS) is a non-contact measurement technique that exploits light scattering to probe the properties of ultrasonic waves, either bulk waves propagating in transparent solids or liquids, or surface acoustic waves (SAWs) propagating at the surface of homogeneous solids or of thin layers, either supported or free standing. In BLS the scattering geometry selects a specific wavevector and probes the ‘thermal noise’ at that wavevector, therefore performing a sampling of the dispersion relation of waves. This is done by illuminating the surface with a laser beam and examining the spectrum of the scattered light.. From the spectrum of the ‘inelastically’ scattered light and the scattering geometry, one can derive the dispersion relation for the ultrasonic waves, and then infer the elastic properties of the material. How this is done is the subject matter of this chapter. The light scattering nature of BLS measurements has three main consequences. First, mechanical contact with the sample is not needed: only optical access is required. Second, scattering occurs locally, in a volume of the order of tens of micrometers. Third, in BLS it is the acoustic wavelength that is determined by the experimental conditions. With visible light the explored acoustic wavelengths are sub-micrometric, meaning that with typical surface and bulk acoustic modes the probed frequencies range from a few GHz up to several tens of GHz. Such small wavelengths give a peculiar sensitivity to thin and ultra-thin. Brillouin scattering techniques also have drawbacks. First, thermally excited fluctuations have small amplitude, requiring time consuming measurements; second, the probed wavelengths are small and span a limited range. Therefore, Brillouin scattering techniques are the preferred technique for materials such as thin films and whenever the contactless nature of measurements makes BLS the only, or almost the only, available choice, as it happens in extreme conditions like thye diamond anvil cell. This chapter is a review of the application of BLS for the evaluation of the elastic properties of materials in the above two main areas—thin coatings and solids under extreme conditions. It should be mentioned that BLS is also actively exploited for the characterization of magnetic materials through the detection of magnons or spin waves. However, this is a different field that deserves a review by itself and will not be considered here