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

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Page 35

These authors propagated 25 MHz ultrasonic beams in a quartz crystal with

dimensions 16 mm along the x

beam was directed along the x

beam ...

These authors propagated 25 MHz ultrasonic beams in a quartz crystal with

dimensions 16 mm along the x

**axis**and 32 mm along the y and z axes. The lightbeam was directed along the x

**axis**in all cases. Figure 12 shows the ultrasonicbeam ...

Page 36

with this

mode wave propagates with no deviation of the energy flux from the wave normal

(specimen

with this

**axis**is such that longitudinal wave propagation is istropic, i.e., a puremode wave propagates with no deviation of the energy flux from the wave normal

(specimen

**axis**). Figure 13 shows the ultrasonic beam associated with ...Page 92

(254) The subscripts L and a denote longitudinal wave along the a

compressive stress along the a

expressions for a and /? from Eqs. (252) into Eq. (253) and rearrange we obtain

p0VL ...

(254) The subscripts L and a denote longitudinal wave along the a

**axis**andcompressive stress along the a

**axis**, respectively. Finally, if we substitute theexpressions for a and /? from Eqs. (252) into Eq. (253) and rearrange we obtain

p0VL ...

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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