摘要:

If the longitudinal stress is linear in the extension, then theexactequation of one‐dimensional motion, in a material (“Lagrangian”) description, is the linear wave equation. This result provides a rational basis for defining a hypotheticallinearsolid or fluid medium. Such a medium has nonzero higher‐order elastic constants. The expected consequences of linearity of the equation of motion are noted. These include distortionless propagation of finite‐amplitude waves, the absence of interaction of waves with each other, stress independence of the travel time or resonance frequency, and the absence of acoustic radiation pressure. The idea of distortionless propagation of traveling waves is treated in detail in both the material and spatial descriptions, and it is emphasized that distortion of longitudinal mechanical waves isnota necessary consequence of kinematics. In a spatial (“Eulerian”) description, the linear medium has anonlinearequation of motion, but this nonlinear equation has distortionless traveling wave solutions of the formf(t±x/V). Some examples are given of three dimensional constitutive equations that yield the described linear behavior in one dimension. The equation of state of the hypothetical linear medium is highly unrealistic, but is of interest because nonlinear phenomena can be ascribed to departures from it. [An appendix discusses the momentum in a plane progressive wave. Consistent with the absence of radiation pressure, the instantaneous momentum in a plane progressive wave in a semi‐infinite linear medium that was initially at rest is simply proportional to the displacement of the face. The still persistent idea that every wave train of intensityJpropagated with speedWhas momentumJ/W2per unit volume is shown to be an unwarranted generalization. Such a wave train can be set up in the semi‐infinite linear medium if the prescribed velocity at the face is the sum of a sinusoidal part and a properly chosen constant term. A special equation of state is found for which power and momentum are related as above in the initially formed simple (purely progressive) wave resulting from a sinusoidal velocity of the face that starts at time zero.]

ISSN:0001-4966    

DOI:10.1121/1.1911609

出版商:Acoustical Society of America    

年代:1969

数据来源: AIP

摘要:

A sensitive instrument for measuring and recording the amplitude ratio of two video pulses from an ultrasonic echo train is described. The instrument has been designed primarily for ultrasonic attenuation studies using pulse‐echo techniques but may also be used for through transmission, and/or single echo measurements. The unit selects two pulses from the echo train, peak detects them, and measures their amplitude difference in a differential logarithmic voltmeter calibrated in decibels. The resultant output may also be applied to an external recorder. Provisions for zero suppression are included to permit the use of the most sensitive meter range (0.01‐dB resolution) when small changes in attenuation are to be measured against a large background attenuation. Automatic gain control, operating from the first selected echo, has been incorporated in order to maintain operation in the linear portion of the receiver dynamic range.

ISSN:0001-4966    

DOI:10.1121/1.1911610

出版商:Acoustical Society of America    

年代:1969

数据来源: AIP

摘要:

Results are presented for the temperature and frequency dependence of the attenuation of two piezoelectrically active ultrasonic waves in ZnO: (1) compressional waves propagated along thecaxis, and (2) shear waves propagated normal to thecaxis and polarized along thecaxis. Measurements of the phonon phonon attenuation were made over the frequency range 60 MHz to 3.97 GHz and the temperature range 4.2° to 300°K. The frequency dependence at 40°K is of the 1.0 and 0.7 power for the shear and compressional modes, respectively; at 300°K. the frequency dependence is ∼1.6 for both modes. The temperature dependence ranges from at leastT4at low temperatures to essentiallyT0; at 300°K for the shear mode; the temperature dependence for compressional waves at frequencies below 2.0 GHz does not appear to reach aT4dependence for temperatures down to ∼20°K.

ISSN:0001-4966    

DOI:10.1121/1.1911611

出版商:Acoustical Society of America    

年代:1969

数据来源: AIP

摘要:

The damping constantBfor the viscous drag on dislocations was measured for NaCl and LiF. A novel technique was employed to improve the accuracy of the measurements, and many specimens were used to check the reproducibility of the results. Measurements of both the attenuation and velocity changes resulting from dislocation pinning by cobalt‐60 gamma irradiation were made. The values obtained areB=2.4 and 1.6×10−4in cgs units for LiF and NaCl, respectively. These values compare favorably both with theoretical estimates and with values determined from direct measurements at higher stresses by etch‐pit techniques. From the ultrasonic measurements, it is deduced that the viscous drag force is linear in the velocity and that relativistic velocities cannot be achieved in LiF and NaCl at room temperature at the yield stress of soft crystals. The results found demonstrate that relatively precise values for the dislocation drag can be obtained ultrasonically, that values for the dislocation densities in specimens can be determined from nondestructive ultrasonic measurements, and that the ultrasonically determined dislocation velocities are directly related to those determined by etch‐pit measurements at higher stresses.

ISSN:0001-4966    

DOI:10.1121/1.1911612

出版商:Acoustical Society of America    

年代:1969

数据来源: AIP

摘要:

General consideration is given to the analogies that exist between the propagation of light waves and the propagation of ultrasonic waves in anisotropic media. A historical survey is given of prior work in this area, followed by a comparison of present views of the analogies with those of other investigators. The inability to obtain a direct one‐to‐one analogy for all phenomena is discussed.

ISSN:0001-4966    

DOI:10.1121/1.1911613

出版商:Acoustical Society of America    

年代:1969

数据来源: AIP

摘要:

The ultrasonic attenuation in zinc single crystals has been measured between 5 and 105 MHz for all pure modes possible in this metal. By comparing the results with the orientation factors of the Granato‐Lücke theory of dislocation resonance damping, the contribution of dislocations on {112̄2} planes to the attenuation has been quantitatively determined. The participation of nonbasal dislocations has also been proved by measurements of dislocation pinning due to γ irradiation and recovery thereafter. The recovery of the attenuation has been measured between 77° and 350°K. Recovery steps have been found at about 105° and 160°K. Measurements of the recovery after plastic deformation in the temperature range from 230° to 300°K yield an activation energy of 0.56 eV.

ISSN:0001-4966    

DOI:10.1121/1.1911614

出版商:Acoustical Society of America    

年代:1969

数据来源: AIP

摘要:

The ultrasonic attenuation at 31 MHz and 60 MHz has been measured in an iron single crystal from room temperature to 625°C, using zinc sulfide vacuum‐evaporated, thin‐film transducers. Longitudinal waves propagating along the [110] direction were used, and the attenuation was measured in both the “carbon‐free” condition (wet‐hydrogen‐treated) and the carburized condition. We have apparently observed the carbon Snoek peaks in the carburized specimen. Assuming that the Snoek peak occurs only via octahedral site to octahedral site jumps, we obtain a diffusion coefficient of carbon in a α iron, at 408 ±5°C, ofDc = 4.52 × 10−9 cm2/sec, and at 430°±5°C, ofDc = 8.85 × 10−9 cm2/sec. These values fall in a region previously devoid of diffusion data. The new values connect, in a relatively smooth manner, the low temperature Snoek‐effect‐determined diffusion coefficients with the high temperature mass‐flow‐determined coefficients. It must be mentioned, however, that in the case of the diffusion of carbon in α‐iron, the extraction of the diffusion coefficient from the Snoek damping data is by no means obvious. This point is discussed.

ISSN:0001-4966    

DOI:10.1121/1.1911615

出版商:Acoustical Society of America    

年代:1969

数据来源: AIP

摘要:

The temperature dependence of the attenuation of longitudinal waves propagating along thecaxis of aluminum oxide and ruby has been measured at frequencies of 0.4 GHz, 1.23 GHz, 2.32 GHz, and 2.94 GHz in the temperature range 20° to 100°K. The ruby samples contained 0.025, 0.08, 0.2, and 0.9% chromium by weight. respectively. In undoped aluminum oxide, in the temperature range 40° to 50°K, the attenuation is frequency independent and varies asT9. At higher temperatures, the attenuation is frequency dependent and varies less rapidly with temperature. The effect of chromium impurities is to increase the attenuation at low temperatures and to decrease it at high temperatures. The measurements are interpreted in terms of collisions between the low‐energy phonons, constituting the sound wave, and the thermal phonons. Evidence is presented that the main contribution to the attenuation is from collisions of the sound‐wave phonons with transverse thermal phonons. The dependence of the attenuation on temperature, frequency, and chromium concentration found experimentally is in good agreement with that theoretically predicted for this type of collision mechanism.

ISSN:0001-4966    

DOI:10.1121/1.1911616

出版商:Acoustical Society of America    

年代:1969

数据来源: AIP

摘要:

The electromagnetic generation of pure shear and quasicompressional sound waves in metals for propagation, respectively, parallel to and perpendicular to a static magnetic field is investigated for a wide temperature range. Using a semiclassical model of a free electron gas moving against a positive ion background carrying the sound wave, the magnitude of the ionic displacements in the helicon geometry is calculated, together with the propagation constants. In the long‐wavelength limit, the excited mode that propagates differs only slightly from a normal acoustic shear mode. Satisfactory agreement is obtained when these calculations are compared with our experimental results at room temperature, 77° and 4.2°K in static magnetic fields of up to 100 kG.

ISSN:0001-4966    

DOI:10.1121/1.1911617

出版商:Acoustical Society of America    

年代:1969

数据来源: AIP

摘要:

For the purpose of developing a theory of thermally assisted amplitude dependent damping, the equilibrium configurations and activation energies of pinned dislocations are calculated. The model is of a dislocation pinned by an arbitrary number of equidistant pinning points of equal strength. New features not found for a simple double loop are obtained, but most of the important physical processes for the general case are already obtained for a triple loop. The more important of these features are: (i) There are intermediate energy minima between the pinned state and the broken‐away state; (ii) for a given stress more than one reaction path between the pinned state and the broken‐away state may exist; (iii) multiple‐pin breakaway can occur by a single activation; (iv) thermal breakaway can occur at smaller loop lengths or at smaller stresses than is the case for a single pin. A discussion is given of the possible reaction paths of the dislocation in the general (N‐loop) problem. It is shown which equilibrium configurations lie along the lowest reaction path. For the case of long loops, expressions are obtained for the activation energies for both breakaway and repinning along this reaction path.

ISSN:0001-4966    

DOI:10.1121/1.1911618

出版商:Acoustical Society of America    

年代:1969

数据来源: AIP