## Treatise on materials science and technology, Volume 3 |

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Page 134

The same year, Rollins, Taylor, and Todd (213) performed experiments using

specimens of fused silica, polycrystalline aluminum, and polycrystalline

magnesium in which they confirm certain three-

associated with the nonlinear interaction of ultrasonic beams. They successfully

verified all five three-

demonstrated that a third beam of reasonable intensity was generated at the

volume of interaction of ...

The same year, Rollins, Taylor, and Todd (213) performed experiments using

specimens of fused silica, polycrystalline aluminum, and polycrystalline

magnesium in which they confirm certain three-

**phonon**interaction effectsassociated with the nonlinear interaction of ultrasonic beams. They successfully

verified all five three-

**phonon**interaction cases predicted theoretically (161). Theydemonstrated that a third beam of reasonable intensity was generated at the

volume of interaction of ...

Page 140

Carr (179) investigated experimentally the second-harmonic generation of

microwave

fundamental to the second harmonic is completely reversed after longitudinal

waves are reflected from a stress-free surface or from a half- wavelength-thick

transducer; therefore the second harmonic in an almost lossless medium

vanishes upon arrival at ...

Carr (179) investigated experimentally the second-harmonic generation of

microwave

**phonons**. He showed that for z-cut quartz and sapphire, where the**phonon**-**phonon**volume interaction dominates, the original energy flow from thefundamental to the second harmonic is completely reversed after longitudinal

waves are reflected from a stress-free surface or from a half- wavelength-thick

transducer; therefore the second harmonic in an almost lossless medium

vanishes upon arrival at ...

Page 151

scattered by collisions with the thermal

occurs determines the ultrasonic attenuation. In the second approach, the

ultrasonic beam is treated macroscopically and is considered to disturb the

equilibrium of the thermal

solid. Collisions between the thermal

state and the attenuation is computed from the entropy increase associated with

these collisions.

scattered by collisions with the thermal

**phonons**; the rate at which this scatteringoccurs determines the ultrasonic attenuation. In the second approach, the

ultrasonic beam is treated macroscopically and is considered to disturb the

equilibrium of the thermal

**phonon**system as a result of its passage through thesolid. Collisions between the thermal

**phonons**re-establishes the equilibriumstate and the attenuation is computed from the entropy increase associated with

these collisions.

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Alers aluminum Andreatch anisotropic Appl axis calculated compressive stress copper crystallographic orientation cubic crystals determine direction cosines displacement gradients displacements along 001 elastic moduli elastic wave propagation energy-flux vector equation of motion experimental germanium given by Eq hydrostatic pressure hydrostatic pressure longitudinal hydrostatic pressure transverse ideal orientation interaction isotropic solid linear elastic wave longitudinal wave longitudinal wave propagating materials mode transverse wave nonlinear elastic wave obtain Papadakis particle displacements phonons Phys plane wave pressure longitudinal wave pressure transverse wave pure mode longitudinal pure mode transverse quasitransverse waves rolling direction rolling plane second harmonic second-order elastic constants shear wave single crystals six third-order elastic stress along 001 stress along 110 Substituting Eqs symmetry test specimen texture third-order elastic constants Thurston and Brugger transducer transverse wave ultrasonic beam ultrasonic pulse uniaxial stress values wave along 100 wave normal wave speeds wave velocity Young's modulus