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Examination was made of ultrasonic attenuation α44 and elastic constant C44 of vanadium single crystals with hydrogen between 4.2 and 220 K, as a function of temperature, hydrogen concentration, frequency, and rates of cooling and heating. Attenuation in the V–H α phase at 210 K increased in proportion to the square of hydrogen concentration, while C44 was linear. At a cooling rate of 3.0 K/min, attenuation of the specimen with 1000 at. ppm H increased below the critical solution temperature and showed a peak. At 0.1 K/min, discontinuous decrease was observed at the temperature. During isothermal annealing below this temperature, attenuation at the higher cooling rate decreased with time in two stages and approached the value for the lower cooling rate. The results are discussed based on ultrasonic double refraction due to the volume array of hydrogens and hydride particles formed under the influence of C44‐mode ultrasonic waves.

The temperature dependence of ultrasonic absorption and nonlinearity parameter has been investigated in the range 80–300 K for LiF and NaF. We have estimated the attenuation of ultrasound in these materials for longitudinal and shear waves along the [100], [110], and [111] directions using Mason’s pure mode formulation [in Physical Acoustics, edited by W. P. Mason and R. N. Thurston (Academic, New York, 1964–65), Vol. 3B, Chap. 6] and also using a computer program recently developed by us which is based on the interaction of the sound wave with a much wider spectrum of the phonon modes and which also incorporates the refinements suggested by Merkulov, Kovalenok, and Konovodchenko [Sov. Phys. Solid State 11, 2241 (1970)] regarding the dependence of Mason’s integral on the cutoff frequency supported by the lattice. The results obtained using our program are in better agreement with the experimental variation of attenuation than those obtained using Mason’s pure mode scheme in most cases. The nonlinearity pa...

The pressure dependence of ultrasonic attenuation in Zr41Ti14Cu12.5Ni10−xBe22.5Cx (x=0,1) bulk metallic glasses has been studied up to 0.5 GPa by using a pulse echo overlap method. The effect of carbon addition on the attenuation is also investigated. Some unique characteristics of the ultrasonic attenuation are found and compared with those of other glasses. The origin of the anomalous attenuation behavior is discussed.

Measurements of the thermal expansion, ultrasonic wave velocity, and ultrasonic attenuation are reported for very dilute Cr‐Mn alloy single crystals. The threshold Mn concentration needed to drive the first‐order antiferromagnetic transition in Cr to second order is found to be smaller than 0.05 at. % Mn. This result is discussed in terms of recent theories. The critical behavior of the sound velocity and ultrasonic attenuation of Cr+0.1 at. % Mn is well described by a power law near TN but not for the thermal expansion.

The new semiconducting noncrystalline solid “tellurite glasses” of the form 0.7 TeO2–(0.3−x)V2O5–xAnOm have been prepared in bulk form with different compositions where AnOm is CeO2 or ZnO and x=0.03,0.05,0.07,0.10 mol %. Longitudinal ultrasonic attenuation in these glasses has been measured at frequencies of 2, 4, 6, and 8 MHz and in the temperature range of 100–300 K. The results showed the presence of a very well defined peak which shifts to higher temperature with increasing frequency, suggesting a kind of relaxation process. The acoustic activation energy, as well as the relaxation frequency, has been calculated and correlated with the relaxation strength for each composition. Correlations between the present low temperature of ultrasonic attenuation and the previous room temperature elastic moduli have been achieved for both glass series.

Measurements are reported of the temperature variation of the sound velocity and ultrasonic attenuation coefficient of Cr‐Al alloy single crystals containing 1.2, 1.9, and 2.6 at % Al. The results close to the Neel temperature are not satisfied by existing theories for the critical behavior of itinerant electron antiferromagnets.

The properties of dense flint glasses relevant to acousto−optic applications have been measured for longitudinal sound waves and He−Ne laser light. Some Schott glasses have proved highly suitable for acousto−optic modulators, others for wide−band optical deflectors. Besides typical acousto−optic properties such as sound velocity, figure of merit, and ultrasonic attenuation, thermal parameters such as the thermal coefficients of sound velocity and refractive index were also measured.

We report some microwave ultrasonic attenuation measurements at 9155 MHz on pure single‐crystal yttrium iron garnet (YIG) which we believe determine the intrinsic attenuation in this material. Previous measurements on YIG by other workers were complicated by spurious effects. Our measurements are compared with current theories of attenuation by phonon‐phonon interactions using the recently measured third‐order elastic constants of YIG. The agreement found is about the same as in many other materials, which suggests that the intrinsic attenuation in YIG is understood and is caused by interactions with thermal phonons.

A matrix inversion procedure is presented for the computation of the grain‐size distribution NV of a solid volume from the image‐size distribution on a photomicrograph of its surface. Averages over the distribution NV are taken to find the average volume to use in ultrasonic scattering formulas. For several metals, NV is adequately expressed in terms of the grain radius R as NV=A (R−R0) exp (−aR) where R0, A, and a are constants for a specimen. NV is zero for R

The attenuation of plane elastic waves in the megacycle region is investigated for several different propagation directions in single crystalline zinc. Results are in qualitative agreement with the losses predicted theoretically due to dislocation damping and thermoelastic effects, and in addition losses not accounted for by the available theory are observed.

In order to study the anomalous ultrasonic attenuation in these compounds, detailed measurements have been performed as a function of temperature, using a variety of frequencies, sound modes, and materials. Their results prove the existence of a selection rule for the interaction mechanism and confirm previous statements of a relaxation process. From symmetry arguments as well as from the observed strong effects of the Ge or Si atoms, respectively, the conclusion was reached that the anomalous attenuation is closely connected to vacancies in the Ge or Si sublattice.

The attenuation of compressional waves traveling in the [100] direction in germanium has been measured in the frequency range from 5 to 300 Mc/sec. Below 20 Mc/sec, the loss was found to be mostly due to diffraction. The remaining attenuation can be described by an expression of the form α=Kfn, where α is the attenuation, f the frequency, n a constant near but somewhat less than two, and K a constant. The attenuation is attributed to the damped forced oscillation of dislocation segments. The value of the damping constant found from the data (about 1.1×10−4 g‐sec−1‐cm−1) is in agreement with the estimate of Leibfried and Nabarro.

Measurements of the temperature dependence of the longitudinal and shear ultrasonic attenuation from 5 to 50 Mc/sec were made in SiO2, GeO2, B2O3, and As2O3 glass. In each case a relaxation loss with a distribution of relaxation times was found. The median activation energy of the relaxation process is about 500 cal/mole in SiO2, 2500 cal/mole in GeO2, 5400 cal/mole in As2O3, and 6300 cal/mole in B2O3. The results are interpreted in terms of a two‐bond‐length model of glass where the relaxation loss is associated with bridging oxygen atoms which have two stress‐sensitive equivalent equilibrium positions. A relationship between the relaxation loss mechanism and the viscosity of these glasses is assumed in this study. A calculation of the activation energies based upon this assumption agrees well with the values determined experimentally.

Ultrasonic attenuation measurements were used to study the thermal part of the dislocation damping factor in copper and lead at frequencies between 10 and 90 MHz in the temperature range 1–180°K. With the assumption that the Granato‐Lucke theory is correct in the limits of small and large dislocation damping, it was found that the Lothe expression for the dislocation damping factor well describes the temperature variation of the measured attenuation. The frequency dependence of the attenuation was found to be in serious disagreement with the Granato‐Lucke prediction.

It has been known for several years that single crystals of chromium display a narrow peak in the ultrasonic attenuation at temperatures near the Neel temperature. There are presented detailed measurements of the attenuation of longitudinal waves which were made to ascertain whether the peak could be explained by a temperature‐dependent relaxation time. The attenuation was found to increase linearly with frequency for temperatures above the peak, and was not a simple function of frequency at lower temperatures. In either case, a simple relaxation mechanism appears not to operate, and a theory developed specifically for chromium seems necessary. The temperature dependence of the attenuation above the peak temperature follows a Gaussian falloff and is probably attributable to inhomogenieties, which smear out the local Neel temperatures.

Ultrasonic attenuation was measured in single‐crystal aluminum oxide (Al2O3) using the pulse technique. Measurements were made at frequencies from 100 to 3000 Mc/sec and at temperatures 4° to 300°K. The observed ultrasonic losses are explained by a scattering from microscopic bubbles in single crystals grown by flame fusion.

The dislocation contribution to the ultrasonic attenuation of high‐purity copper single crystals has been quantitatively determined by forming the difference between the measured attenuation and the nondislocation part of attenuation as measured after heavy irradiation. In this way mainly, the influence of temperature, deformation, γ irradiation, and heat treatment on the dislocation damping has been studied. The measurements were evaluated according to the Granato‐Lucke theory of dislocation resonance. One of the main objectives of the work was to test the applicability of various experimental and theoretical methods for gaining quantitative information on dislocations from ultrasonic attenuation measurements.

Pulse‐echo ultrasonic attenuation measurements were made for longitudinal and transverse waves in the [100], [110], and [111] propagation directions in NaCl specimens cut from a single boule. The attenuation α was proportional to the orientation factor Ω (relating the resolved stress on the slip system of the crystal to the applied stress), and to the square of the frequency f. Under x‐ray irradiation, α decreased for modes with Ω=≠0 but remained constant where Ω=0. Dislocation damping is considered to cause the loss.

In many insulating crystals, the attenuation of sound waves of microwave frequencies is a result of energy transfer from the sound wave to thermal phonons. A simple correlation exists between sound attenuation in such crystals near room temperature and their thermal properties. This correlation is exhibited at 300°K for a number of crystals for which both sound attenuation and thermal measurements have been made. Crystals which have low sound attenuation at microwave frequencies and room temperature appear to be those with light mass atoms, high Debye temperatures, and complex crystal structures. Estimates are made of the sound attenuation to be expected at 300°K in two materials for which thermal data alone are available.

The various mechanisms producing damping of ultrasonic elastic waves in solids are reviewed in this paper. Particular attention is given to the changes in attenuation produced by pinning of dislocation lines. Measurements of ultrasonic attenuation in irradiated single crystals of NaCl are presented and discussed, on the assumption that the dislocation density remains constant while the radiation displaced defects pin the dislocations. The effects on the velocity of propagation are discussed on the basis of the same model.

Microwave ultrasonic attentuation measurements have been made on single crystals of topaz, beryl, and tourmaline, and all are found to exhibit very low losses. The room‐temperature attenuation coefficients are consistent with the Akhiezer mechanism which arises from interactions between the ultrasonic wave and the thermal‐phonon assembly.

Hughes' pulse technique for measuring longitudinal velocities has been adapted and extended to measure attenuation of longitudinal waves in the frequency range from 250 to 1,000 kc. Data for attenuation in nepers per wavelength in six different plastics (Plexiglas, polystyrene, nylon 101, Formica XXN, polyethylene, and Teflon) are given for eight different frequencies ranging from 250 to 1000 kc. The results for Plexiglas and polystyrene are compared with results obtained previously by other methods. Attenuation in nepers per wavelength has been found to decrease when frequency increases for all plastics, except for Teflon, which shows a well‐defined peak at about 700 kc.

The attenuation of 10‐ and 30‐MHz sound waves in deuterated and undeuterated chromium potassium alum have been measured over the temperature range 300–4.2 K. A very large attenuation peak occurs in the temperature range 70–160 K. It is believed that this is associated with phonon‐phonon scattering.

Single crystals of bismuth silicon oxide doped with Al, Ga, or B have been grown by the Czochralski method. Doping with Ga and B reduced the previously observed anomalous ultrasonic attenuation at low temperatures considerably, doping with Al removed it completely. In a similar way the additional optical absorption below the intrinsic absorption edge is affected. Numerical comparison of both results gives values for the defect concentrations involved [(2–6) ×1017 cm−3] and for the deformation potential (about 3 eV).

Ultrasonic attenuation measurements have been made at 12, 30, and 46 Mc/sec and from 1.8°K to room temperature on a cadmium sulfide specimen. The specimen had a dark room temperature conductivity of about 10‐2 (Ω·cm)‐1. A very large attenuation peak was observed in the neighborhood of 15°‐20°K. Conductivity values showed that the peak is undoubtedly due to relaxation effects in the space‐charge bunching caused by the acoustic wave, the mechanism proposed by Hutson and White.

The acoustic attenuation of shear and longitudinal waves propagating along the c axis in LiTaO3 has been measured from 1 to 9 GHz. Measurements were made from 4° to 300°K using the microwave pulse‐echo technique and at 300°K using optical Bragg diffraction. The shear‐ and longitudinal‐wave attenuation in LiTaO3 at 300°K was found to be similar to that of LiNbO3. However, the change in shear‐wave attenuation between 4° and 300°K is much smaller in LiTaO3 than in LiNbO3.

The temperature dependence of the attenuation of 30‐Mc/sec longitudinal ultrasonic waves has been measured from room temperature to 380°C in CdS. The observed attenuation is in good agreement with the theory of Hutson and White and with the temperature dependence of the resistance measured on the same specimen.

The study of ultrasonic attenuation in polycrystalline materials at elevated temperatures is gaining much importance during recent years. Recently, Darbari, Singh, and Verma have devised a new method for such a study. This method is known as the ``shouldered‐specimen pulse‐echo technique''. However, in the theoretical derivation of the expression for the acoustic attenuation α for this experimental method, they have not considered the effects due to spreading of the acoustic beam in the shouldered specimen. In the present short article, the previous theory is modified so as to take into account the effects of this beam spread due to diffraction. The modified theory finds excellent agreement with the experimental results, is applicable for any diameter of the transducer, and gives the correct picture of the propagation of the acoustic pulses in a shouldered specimen.

Recent quantitative measurements of frequency and temperature dependence of the ultrasonic attenuation in the vicinity of the magnetic phase transition for a number of materials (Gd, Tb, Dy, Ho, RbMnF3, MnFr2, Cr) enable us to compare these results critically with a number of recent theories. For each of these materials we know the spin‐phonon coupling mechanism and the coupling strength fairly well. The comparison shows that the anisotropic case (materials with a rather large uniaxial anisotropy) is better understood than the isotropic one. The only case where the spin‐phonon coupling is of the single ion magnetostrictive type, shear wave in Dy, the critical attenuation can be semiquantitatively accounted for by considering higher‐order spin components in the magnetoelastic Hamiltonian.

The attenuation of longitudinal ultrasonic waves in single‐crystal germanium has been measured at several frequencies between 0.15 and 2.84 GHz in the temperature range 10°–60°K. The measured attenuation was the same for propagation in the 〈100〉,〈110〉, and 〈111〉 crystallographic directions, and varied with temperature as T7 at the highest frequencies and lowest temperatures, and as T3 at the lowest frequencies near 60°K. The frequency dependence was less than linear at the lowest temperatures and between linear and quadratic at 60°K.

Measurements of ultrasonic attenuation due to the scattering of longitudinal elastic waves from a distribution of cavities in a solid medium are found to be consistent with theoretical predictions. Under certain conditions such measurements can be utilized to nondestructively characterize the size and number density of such a collection of scatterers.

Ultrasonic propagation in Al2O3 at low temperatures and high frequencies (to 3000 Mc/sec) is discussed in terms of the relations given by Woodruff and Ehrenreich. Phonon relaxation times calculated from thermal conductivity measurements are used. The measured low‐temperature attenuation values at 1315 Mc/sec agree with the calculated values. A comparison of attenuation as a function of frequency is made among Al2O3, Ge, Si, and quartz. On comparing experimental values of attenuation for pure Al2O3 and impure Al2O3 (ruby) it is found that impurities lead to an increase in the attenuation as would be predicted from the corresponding effect of impurities on the thermal phonon relaxation time.

The dependence of ultrasonic attenuation and velocity on plastic deformation in 2S aluminum is compared at two frequencies, five and ten megacycles, and the comparison shows agreement as regards frequency dependence with what one can expect from dislocation damping theory.