Phonon Attenuation Research Articles

The interpretation of hypersonic and ultrasonic 'velocities' in fluids

It is suggested that the conventional view of Brillouin light scattering and ultrasonic excitation in fluids in terms of phonon phase velocity and attenuation can be misleading and leads to spurious anomalies. A simple comparison is made of the two types of experiments from a fundamental point of view. The analysis of an ultrasonic experiment from first principles is given and is illustrated by an explicit example, the classical hydrodynamic fluid. It is pointed out that an important parameter is usually overlooked in the conventional ultrasonic experiment.

The attenuation of phonons in liquid helium at very low temperatures

A theory is developed to describe the attenuation of high-frequency phonons in liquid helium at low temperatures, assuming a model excitation spectrum due to Jackle and Kehr (1971). At very low temperatures the attenuation is negligible when the dispersion is normal, but significant when dispersion is anomalous. The recent measurements of Narayanamurti et al. (1973) are interpreted as the decay of a broad-band phonon system.

Improved calculations of Kapitza resistance: Combined effects of phonon attenuation and impedance matching on Kapitza resistance

We calculate the Kapitza resistance ${R}_{K}(T)$ for a Cu-${\mathrm{He}}^{4}$ interface using the acoustic mismatch theory of Khalatnikov and of Mazo and Onsager. Included in the calculation are the effects of: phonon attenuation in the Cu as well as impedance matching due to the increased He density near the interface. We calculate ${R}_{K}(T)$ for several values of attenuation in the Cu; detailed calculations are displayed for the case of equal attenuations for longitudinal and transverse waves in the solid. Also considered are different attenuation profiles in the Cu. We use a density profile calculated from compressibility data and the Van der Waals attractive force between He and the Cu substrate. Our model includes the effects of a solid layer of He at the Cu surface, i.e., in such a He layer both longitudinal and transverse waves are allowed. Included in our calculations are the effects of different density profiles for the He. The calculations indicate that for suitable choices of the physical parameters, the theoretical results for ${R}_{K}(T)$ agree in magnitude as well as $T$ dependence with the experimental data. Unfortunately, the important physical properties have not yet been experimentally determined and definitive test of this theory must await such data.

The combined effects of phonon attenuation and impedance matching on Kapitza resistance

The Kapitza resistance for Cu-HeII has been calculated using an acoustic mismatch theory which includes the effects of transverse waves in the dense helium region at the liquid-solid interface and phonon attenuation in the copper. The impedance matching becomes significant above 0.1 K.

The effect of phonon lifetimes on the Kapitza resistance

The effect of attenuation of phonons in the solid on the Kapitza resistance at a solid- 4He boundary is discussed using a transfer Hamiltonian formalism. It is explicitly shown why the attenuation of Rayleigh waves is a dominant mechanism for the thermal boundary conductance.

The attenuation of high frequency phonons in metals

Measurements of the attenuation of high frequency ( approximately 100 GHz) phonons in copper and in superconducting aluminium are described. The phonons are generated and detected by means of superconducting tunnel junctions; a brief analysis of this novel experimental technique is included. The attenuation lengths observed are of the same order as, but rather less than, values calculated using free electron theory. The role played by elastic phonon scattering in determining the attenuation length is considered, and some measurements of the phonon propagation through granular copper presented. These can be explained in terms of the interaction of elastic and inelastic phonon scattering.

Microwave phonon attenuation in X-cut LiNbO 3

The attenuation of 9.4 GHz longitudinal (L) and shear (S) hypersonic waves has been measured as a function of temperature in X-cut LiNbO 3 by means of a pulse-echo method. It is found that α S( T∝( T) 3 and α( T) 5, 20 < T (K) < 60.

Acoustic-mismatch model of the Kaptiza resistance

The Kapitza resistance theory of Khalatnikov is modified so as to include the effects of phonon attenuation in the solid. The modified theory agrees well with many features noted in low temperature measurements on CuHe interfaces.

The transport of heat between solids at low temperature

It has been demonstrated experimentally that the acoustic mismatch theory provides the correct physical description of the nonelectronic thermal conductance across the interface between two solids. The theory has been modified so as to include the effect of phonon attenuation in the solids.

Attenuation of Hypersound by Collinear Phonon Interactions in Quartz

Low-temperature measurements of the attenuation of microwave phonons of longitudinal polarization along the $x$ axis and of transverse polarization along the $\mathrm{ac}$ axis of natural quartz at 1.25 and 2.1 GHz are compared with calculations for a dispersive anisotropic continuum. By separating the analysis of the data into two temperature zones whose extent is determined by the relative magnitudes of $\ensuremath{\Omega}\ensuremath{\tau}$ and of the dispersion factor $\ensuremath{\beta}=\frac{v}{c}$, it was possible to obtain, respectively, estimates for the generalized Gr\"uneisen parameters when ${(1+\ensuremath{\beta})}^{\ensuremath{-}1}&lt;\ensuremath{\Omega}\ensuremath{\tau}&lt;{(1\ensuremath{-}\ensuremath{\beta})}^{\ensuremath{-}1}$ and for the strength of the thermal-phonon interactions at low temperatures when $\ensuremath{\Omega}\ensuremath{\tau}&gt;{(1\ensuremath{-}\ensuremath{\beta})}^{\ensuremath{-}1}$. Very good agreement is obtained for the temperature and frequency dependence of the absorption coefficient by assuming that the transverse-wave attenuation is due to collisions with collinear transverse phonons. For longitudinal waves, evidence is in accordance with the assumption that the main contribution to the attenuation is from collisions with longitudinal and transverse thermal phonons. We find however, that the former process becomes increasingly predominant as the temperature is reduced. The experimental and theoretical Gr\"uneisen parameters agree to better than a factor of 5. For large $\ensuremath{\Omega}\ensuremath{\tau}$ calculations predict a reduction in the temperature dependence of the absorption with moderate concentration of point impurities.

Brillouin Spectra of Ethyl Ether and Carbon Disulfide

Brillouin spectra of ethyl ether and carbon disulfide (at 20.0°C) were investigated for scattering angles of 20°–145°. A single-mode laser was used for excitation; scattered light was collected in a solid angle of 1.5×10−4 sr; and the total instrumental width was ∼100 Mc/sec. Linewidths of 10±5 to 215±10 Mc/sec were measured and velocities determined to an accuracy of ±0.5%. In ethyl ether the phonon velocity and attenuation were constant in the frequency range 0.8–4.1 Gc/sec, and the values agreed with acoustic measurements at 100 Mc/sec. In CS2 a considerable decrease in attenuation was observed in the range 1.7–6.1 Gc/sec, with the value at high frequency approaching the classical attenuation attributed to shear viscosity. This variation in attenuation is in good agreement with the theory of a single relaxation time for the total vibrational specific heat, as established by acoustic measurements in the frequency range 2–200 Mc/sec.

Microwave Phonon Attenuation Measurements inn-Type Silicon

Microwave phonon attenuation at 9.3 GHz in $n$-type silicon has been measured between 2 and 100 K. The excess attenuation observed in impure samples is attributed to conduction electrons. The intervalley relaxation time is determined from these results for Sb- and As-doped silicon with impurity concentration between 3 \ifmmode\times\else\texttimes\fi{} ${10}^{17}$ and 2 \ifmmode\times\else\texttimes\fi{} ${10}^{19}$ ${\mathrm{cm}}^{\ensuremath{-}3}$. A large excess attenuation, not accounted for by any existing theories, is observed at low temperatures in nondegenerate samples. The discrepancy between experiment and theory is thought to arise from electrons in impurity states. It is suggested that hopping conduction may explain our results at low temperatures. No specific influence of impurity band formation on attenuation is found experimentally.

Acoustic Two-Magnon Processes in an Antiferromagnet

The attenuation of acoustic phonons due to linear processes involving any pair of magnons (nuclear and electronic) is calculated for some antiferromagnets. Numerical estimates of the intensities from such processes are made for RbMn${\mathrm{F}}_{3}$ and for Mn${\mathrm{F}}_{2}$. It is predicted that, in certain favorable cases, such effects may be observable with present-day sensitivities at frequencies which are not near any of the single-spin-wave resonant frequencies.

A simple magnetic thermometer for use below 1 K

Results are presented of the Kapitza conductance between annealed and electropolished ‘clean” copper samples and liquid He4 in the temperature range 0.3 K to 1.3 K. A description is given of the apparatus and techniques developed to enable in situ high vacuum treatment of the sample surface, without an excessive heat load on the He3 refrigerator during measurements of the Kapitza conductance. The experimental results of this work are in excellent agreement with previous results, measured at higher temperatures, for similarly prepared surfaces. The temperature dependence of the measured heat transfer coefficient shows a clear maximum at 1 K. This new result is in qualitative agreement with the theoretical treatment of the Kapitza conductance in terms of acoustic theory, modified to include phonon attenuation and impedance matching. However the large magnitude of the heat transfer coefficient, suggests that some alternative mechanism may dominate the Kapitza conductance, even to ‘clean’ surfaces.

Performance and applications of microwave photon-phonon double-quantum detection in MgO

Microwave phonons at 3.1, 4.7, and 9.3 GHz were generated with CdS thin-film transducers, propagated through Fe 2+-doped MgO at 1.5 K, and detected with a photon-phonon double-quantum detector. In comparing double-quantum detection with the conventional piezoelectric method, it was found that the energy detecting properties of the former yielded exponential decays even when the latter did not. The field, frequency, and angular dependencies of the double-quantum detector were measured and interpreted. A shift from the double-quantum absorption to a slowly decaying saturation signal of opposite sign was observed as the phonon frequency approached that of the photons. The better precision made possible by the exponential echo pattern of the double-quantum detector was used to obtain accurate values for phonon attenuation. The frequency dependence of attenuation in MgO at 1.5°K was measured for the first time. This dependence could be fitted to a term proportional to frequency (of about 0.3dB/cm-GHz) which indicated the presence of scattering from dislocations, and a frequency-independent term (of about 0.4 dB/cm) attributed to boundary scattering. Double-quantum detection was also used to detect the scattered phonons observed between the echoes, and to demonstrate that they represented elastically scattered phonons. Longitudinal to-transverse mode conversion in one sample correlated with the presence of small-angle grain boundaries, as indicated by X-ray diffraction and laser ultramicroscope observations.

Hypersonic attenuation in niobium in the mixed state

The hypersonic attenuation of longitudinal and transverse modes in niobium is observed throughout the mixed state. The field dependence of the attenuation is shown not to be directly dependent on the normal state volume in the mixed state. The transverse and longitudinal attenuation have similar field dependences with the longitudinal mode coupling more strongly than the transverse mode to the vortices. The frequency and conductivity dependence of the phonon attenuation in the Meissner state exhibits features which are not strictly similar to the behavior of the attenuation in insulators, and might be associated with the coupling of the pair states to the lattice.

Third-Order Elastic Constants of Ge at Room and Liquid-Nitrogen Temperatures

Keating's theory is applied to explain the recent experimental data of the third-order elastic moduli for Ge at room and liquid-nitrogen temperatures. The agreement between theory and experiment obtained for the new data at 293°K is better than that obtained by Keating. Also, the theory explains the experimental data at 77°K in an excellent way. It is found that unlike the other anharmonic interactions, the nearest-neighbor central one is further enhanced with the lowering of the temperature. The important parameter in Akhiezer's theory for microwave phonon attenuation in solids, called the nonlinearity constant D, has also been calculated for the said temperatures for 〈100〉 and 〈111〉 directions of ultrasonic longitudinal wave propagation, and in both the cases, it is found to be temperature dependent. The present work represents the first experimental support for our previous prediction, derived on the phonon conductivity data for Si, that D is temperature dependent and decreases at low temperatures.

Interaction of Microwave Phonons with Donor Electrons in Ge and Si

It has been found that small concentrations of shallow donors in Ge and Si produce relatively large amounts of attenuation of microwave phonons at low temperatures (about 1 part per million produces about 10 dB/cm attenuation at 9 GHz). A theory is given which explains the various observed temperature, polarization, and frequency dependences of the attenuation in terms of ultrasonically induced relaxation of electrons bound to the donors. It is pointed out that such measurements can give information on the energy-level seperations, symmetries, and relaxation times of bound electrons.

Magnetic Field Dependence of the Ultrasonic Attenuation by Neutral Donors in Germanium

Magnetic field dependence has been calculated in detail for the attenuation of microwave phonons by neutral donors in Ge. Magnetic fields give rise to a considerable change in the attenuation. The aspect of the change depends on whether the product of the phonon angular frequency (ω q t ) and the relaxation time (τ) is larger or smaller than 1: roughly speaking, the attenuation increases with magnetic fields when ω q t τ≫1, while it decreases when \(\omega_{qt}\tau{\lesssim}1\). The magnitude of the change depends on the strength and the direction of magnetic fields and also on the level width of triplet states when \(\omega_{qt}\tau{\lesssim}1\). Besides the ultrasonic spin resonance, a resonant absorption of phonons in the triplet states can occur when the energy splitting of triplet states becomes equal to the phonon energy and the splitting becomes larger than the level width of triplet states.

Coupled Electronic Spins, Nuclear Spins, and Phonons in a Cubic Antiferromagnet

The spin response functions for the electronic and nuclear spins in a cubic antiferromagnet are obtained in the random-phase approximation. These response functions are then used to investigate the coupled electronic-spin-nuclear-spin-phonon system. Predicted changes in phonon velocity and attenuation in RbMn${\mathrm{F}}_{3}$ due to interaction with electronic and nuclear spin waves are obtained. Some of these predictions agree with previous experiments and theory, and others can be checked by further experiments.