M. A. Breazeale

Interaction of ultrasonic waves incident at the Rayleigh angle onto a liquid‐solid interface

The behavior of a Gaussian ultrasonic beam incident on a liquid‐solid interface at the Rayleigh angle, the angle at which surface waves are excited on the interface, has been studied in some detail. The reflected beam is displaced in the manner predicted by Schoch; however, the ’’Schoch displacement’’ in general is too large. Good agreement is obtained between experimental results and the theory of Bertoni and Tamir, which assumes that the incident beam couples resonantly into a leaky surface wave at the Rayleigh angle and that the energy reradiated from this leaky surface wave interferes with specularly reflected energy. The propagation distance of the ultrasonic beam is explicitly included in describing the ultrasonic wave reflection at the Rayleigh angle.

Ultrasonic nonlinearity parameters and third‐order elastic constants of copper between 300 and 3 °K

The ultrasonic harmonic generation technique has been used to extend measurement of the nonlinearity parameters of copper to 3 °K. Comparison of these data and combinations of truly adiabatic third‐order elastic (TOE) constants with predictions of simplified models show that a central force, nearest neighbor model accounts reasonably well for the behavior of copper in the regions of 45 and 200 °K and less well at other regions. The central force, nearest neighbor model also gives a good qualitative explanation for the temperature dependence of the combinations of TOE constants that are measured in this investigation.

Reflection of a Gaussian ultrasonic beam from a liquid‐solid interface

A Gaussian distribution of amplitudes in an ultrasonic beam reflected from liquid‐solid interfaces is used in the reexamination of the concept of “beam displacement” which occurs at the angle of excitation of surface waves on the interface. Experimental results show that the energy of the reflected beam is redistributed into two or more beams at (or near) this angle. The theory of Brekhovskikh has been extended to include both a Gaussian input beam and the second derivative of the phase shift upon reflection. Reasonable agreement is obtained between theory and experiment for water‐aluminum and water‐brass interfaces. For water‐beryllium and water‐stainless steel the agreement is fair.

Adiabatic third‐order elastic constants of fused silica

Results of ultrasonic harmonic generation are combined with those of ultrasonic beam mixing [R. W. Dunham and H. B. Huntington], to obtain a complete set of truly adiabatic third‐order elastic constants of a strain‐free sample of G.E. type 151 fused silica: C111+64.8±0.5×1011 dyn/cm2; C144=+5.4±0.3×1011 dyn/cm2; and C456=−1.32±0.08×1011 dyn/cm2. Differences among values of the third‐order elastic constants for different samples are great enough that care in sample selection is necessary for consistent results.

Generation of Fractional Harmonics in a Resonant Ultrasonic Wave System

The problem of a fluid‐filled cavity caused to resonate by an ultrasonic wave is described as a parametric phenomenon. Variation of the cavity resonance frequency as a result of the periodic change of length produces the condition for parametric resonance. As a result, fractional harmonics of the driver transducer frequency are generated. The wave equation describing the system is transformed into an ordinary differential equation with periodic coefficients. The solution of this differential equation (Mathieus equation) predicts frequency doublets which have been observed experimentally. A threshold condition of parametric excitation is derived from the region of unstable solutions of Mathieus equation. This threshold condition relates the amplitude and frequency of the driver transducer to the cavity length and to the absorption per wavelength of the medium. Reasonable agreement between theory and experiment is obtained.

Third‐order elastic constants and Grüneisen parameters of silicon and germanium between 3 and 300 °K

We present a method to determine all six independent third‐order elastic (TOE) constants of diamond‐like solids as a function of temperature from measured values of the ultrasonic nonlinearity parameters. Ultrasonic harmonic generation experiments along the three principal directions of a cubic crystal lead to the determination of the nonlinearity parameters, which contain three linear combinations of TOE constants. These data are sufficient to determine the three anharmonic first and second neighbor force constants in the Keating model for diamond‐like solids. Ultrasonic velocity data are used to determine the two harmonic force constants in this model. Since our experiments have given data on silicon and germanium between liquid helium temperature and room temperature, we are able to evaluate and plot the Keating model force constants and hence all the six third‐order elastic constants between 3 and 300 °K. Most of the TOE constants of silicon and germanium are smoothly varying functions of temperature;...

Reply to ’’Radiation pattern of partially electroded piezoelectric transducers’’

The radiation pattern of transducers excited by a strip electrode and a ground plane closely approximates a Gaussian function, and hence is a single beam if the ratio of the electrode width to the transducer thickness is between 2 and 4. We calculate the electric fringing at the surface of the transducer and show the extent to which electric fringing accounts for the radiation pattern.

Temperature variation of some combinations of third‐order elastic constants of silicon between 300 and 3 °K

The ultrasonic harmonic generation technique has been used to determine the nonlinearity parameters of silicon between room temperature and 3 °K. By measuring the amplitude of the second harmonic of an initially sinusoidal longitudinal ultrasonic wave propagating along the three principal directions, the temperature dependence of three linear combinations of third‐order elastic (TOE) constants of silicon have been studied. Between room temperature and 77 °K, the magnitude of the TOE constants does not vary much as a function of temperature. Between 77 and 3 °K, C111 changes by 3.5%, C112+4C166 changes by 11.7%, and C123+6C144+8C456 changes by −207%. All these combinations are negative at room temperature as well as at low temperatures except C123+6C144+8C456 which is positive below 8 °K. Room‐temperature values of the strain generalized Gruneisen parameters of silicon have been calculated from measured nonlinearity parameters and are compared with existing values. Complete sets of third‐order elastic cons...

Parametric Phenomena in Physics

Parametric excitation of a resonant system is a self-excitation caused by a periodic variation of some parameter of the system. A brief history of parametric phenomena is given from Faraday and Lord Rayleigh through modern day physics. The general characteristics of “parametric generators” are viewed through a specific example from acoustics, which is treated in detail.

Temperature variation of elastic nonlinearity of NaCl

The second harmonic generation technique has been used to evaluate combinations of third‐order elastic constants (TOEC) of NaCl between room temperature and liquid‐nitrogen temperature. TOEC data at room temperature are compared both with theory and other experimental results. The temperature variation of C111 is somewhat larger than predicted by theory. The temperature behavior suggests that a noncentral force and other exchange interactions predominate at 0 K.