Phonon Radiation Research Articles

Phonon emission of two-dimensional plasmons

The author considers the acoustic phonon radiation by the plasma waves of quasi-two-dimensional inversion electron layers. The electron-phonon interaction is taken into account using the phenomenological deformation potential in the jellium model.

Kapitza conductance of crystals cleaved under He II

The Kapitza conductance of LiF and KBr single crystals has been measured immediately after cleaving under superfluid helium. Heating techniques were used to evaluate the conductance and it approached the phonon radiation limit for these materials. Cleaving LiF under He ll reduced the Kapitza conductance compared to an aged, cleaved surface by only a few percent. Despite the very good cleaved surface obtained with LiF crystals, the results suggest that sufficient microfracturing of the surface occurs upon cleaving to significantly increase the Kapitza conductance over the acoustic mismatch theory values. These results are in contradiction to results obtained by phonon reflection techniques.

Sine-Gordon kinks on a discrete lattice. I. Hamiltonian formalism

We derive a complete Hamiltonian formalism for a kink on a one-dimensional discrete lattice in which the position of the center of the kink appears as one of the canonical variables. Our method is a generalization to the discrete lattice of the method used in field theory to introduce the soliton as a canonical degree of freedom. The derivation is valid for a particle chain in a periodic potential when there exists a solitary-wave solution in the continuum limit. We show that the discrete lattice is responsible for an adiabatic dressing of the kink and for spontaneous emission of phonons. In the limit where the effective length of the kink is much larger than the interparticle spacing the kink experiences the well-known periodic Peierls-Nabarro potential. In the case of a short kink, the discrete lattice causes the continuum kink configuration to be adiabatically dressed, leading to a renormalization of the Peierls-Nabarro potential and in turn to an enhancement of corresponding small-amplitude oscillatory frequency. In addition, we formally derive an equation that describes the radiation of phonons by the moving kink, an effect of the lattice discreteness.

Sine-Gordon kinks on a discrete lattice. II. Static properties.

The differences in the static properties between the discrete and continuum kink solutions of the one-dimensional sine-Gordon equation are found with use of a discretized Hamiltonian formalism which we have developed previously. The difference in the kink profile is treated as a static dressing of the continuum soliton. We point out some of the salient features of the static dressing and their dependence on the kink-size parameter ${l}_{0}$. We find that the dressing has important effects on dynamical quantities such as the kink pinning frequency and the depth of the Peierls-Nabarro potential. When the static dressing is included, the actual depth and curvature of the potential are found to be approximately twice the value obtained using the continuum approximation. Hence, the square of the pinning frequency is doubled. We also find that for short kinks (small ${l}_{0}$) the static dressing develops some spatial structure which we believe will have important consequences in the dynamics, namely in the spontaneous radiation of phonons by the moving kink. We show that our analytic results agree closely with results obtained from molecular-dynamics simulations. The agreement with the simulations provides strong evidence for the reliability of our formalism to predict manifestations of discreteness and their ramifications.

Ballistic-phonon pulses in a solid-liquid He-II interface

Results are presented on the transmission of ballistic longitudinal (L) and transverse (T) phonon pulses from sapphire into liquid He-II at a temperature T<or=0.25K. Fast response time thin film transducers are used and broad-band (Planck type) phonon radiation is employed. The conversion of L- and T-mode pulses at the interface into He-II is resolved using time-of-flight detection, with a detector located at some distance from the surface in bulk He-II. The ballistic part of the transmitted energy flux is measured as a function of generator power and hydrostatic He-II pressure. The transmission probability for T-mode phonons is found to be higher than for the L-mode. The data also indicate a strong frequency down conversion at the interface, larger for the L-mode than for the T-mode.

Resonance interaction of electronic two‐level states and short‐wave phonon radiation in ruby

AbstractThe resonance interaction of 874 GHz phonons with the electronic (Ē, 2Ā)‐two‐level‐states in optically pumped ruby is studied. In a resonance volume containing the two‐level states phonon pulses are generated by optical pumping. The occupation number of these phonons is determined and also their escape time from the resonance volume for a large range of concentrations of two‐level states. A simple diffusion model for the phonon propagation in the resonance volume cannot explain the results. It is suggested that the resonant electron–phonon interaction is dominated by a process of spectral and spatial phonon diffusion.

?-quartz as a substrate in thermal phonon radiation

Using the mechanical strong anisotropicα-quartz, measurements of radiation temperature as a function of phonon radiation power were performed for gold and copper radiators evaporated on theX- orZ-crystal face, respectively. The comparison with theoretical model calculations of phonon transmission across the interface yields agreement with the isotropic/anisotropic acoustic mismatch model. A strong increase in radiation temperature in comparison to linear emission models is observed at temperatures above about 40 K. We suppose that this effect is due to phonon back-scattering which leads to a back-heating of the metal film.

Theory of one-dimensional ionic and solitary-wave conduction in potassium hollandite

It is argued that ions moving in hollandite crystals should not be significantly scattered by impurities. This could lead to large conductivities for low ionic concentrations. Ionic conduction for high concentration of ions occurs by motion of solitary-wave-like defects whose motion is damped by phonon radiation. An expression for the electrical conductivity is found using models for the motion of such solitary waves which were previously applied to the study of dislocation motion under an applied stress. Comparison is made with experiments on hollandite with the aid of an interrupted-strand model.

Time delay in formation of a γ-phase electron-hole drop in germanium

An explanation is given for the long time delay in the formation of gamma phase EHD in germanium. The Cerenkov radiation of phonons by moving alpha drops at velocity mach 0.2–0.3 is calculated to be the controlling process in the time delay.

Superconducting tunnel junctions as quantitative detector of intense thermal phonon radiation

Thermal phonons are emitted from a pulse-heated constantan film into an a-cut sapphire (kept at 1.2 K) and are detected quantitatively by recording the current-voltage characteristic of the tunnel junction during the relatively strong phonon irradiation. These measurements are made with the maximum of the Planck distribution of the emitted phonons varied in the frequency range from 0.3 to 1.5 THz. These momentary diode characteristics coincide within experimental error withd c-characteristics at higher substrate temperatures. Assuming thermal equilibrium between electrons and phonons in the tin film and assuming the validity of the acoustic-mismatch model, a comparison can be made between observed phonon power and theoretically expected phonon power. Good agreement is achieved if the influence of the acoustic cut-off frequencies of the tin detector material is taken into account.

Probability of a new radiation in 10 7−10 9 Hz region

The crystal field is written in the exact form and from that a range of force is derived. It is found that the crystal field cannot extend beyond three to four times the unit-cell distance. The electron paramagnetic resonance line is re-interpreted as a zero-phonon line. A new radiation occurring as a result of cross terms between the Zeeman-like radio frequency interaction and the orbit-lattice coupling is proposed to manifest itself as new sidebands in the paramagnetic resonance phenomenon. The separation between the paramagnetic resonance line and the new lines provides a method to study the lowest energy region of the phonon radiation spectrum.

Kapitza resistance?A universal curve

It is shown that when all unquestionable data on Kapitza resistance are plotted as reduced thermal boundary resistivity versusTϑD, then a universal curve results. The curve shows that for smallTϑD they are close to the acoustic mismatch theory, and for largeTϑD they are close to the phonon radiation limit. The parameterTϑD extends over three orders of magnitude, which compares with the usual factor of two in most measurements. The universality has several implications: First, it shows that Kapitza resistance is to first approximation a bulk effect; next, the curve can be used to test theories of Kapitza resistance (an example is given); finally, the value for an unmeasured solid-liquid helium interface can be estimated with some reasonable confidence.

Radiation temperature and radiation power of thermal phonon radiators using diamond as transmission medium

Thermal phonon radiators allow short pulses of incoherent thermal phonon beams to generate in a simple manner and the center frequency of the broad frequency distribution of the emitted phonons to vary up to the acoustic cutoff frequencies. This paper reports experimental investigations of the connection between radiation temperature and radiation power using films of several metals (copper, nickel, gold, and lead) as phonon radiators on diamond. The measured dependencies of the radiation temperature on the radiation power show that the radiation process is by far better described by assuming acoustic mismatch between radiator and transmission medium than using the model of perfect match. Some metals on diamond give a phonon radiation power of several kilowatts per square millimeter radiator area. With a diamond substrate held at liquid-helium temperature, a radiation temperature of a few hundred degrees Kelvin was achieved. If the phonon radiator deposited on diamond is immersed in liquid helium, the transport of heat to the liquid helium becomes important at radiation temperature below 30 °K and is dominant below 20 °K. This effect can be explained by assuming a thin vapor layer between the hot radiator and the liquid helium, and a gas kinetic energy transfer.

Asymptotic Eigenvalue Distribution for the Wave Equation in a Cylinder of Arbitrary Cross Section

The asymptotic distribution of the eigenvalues ${k}_{n}$ of the scalar wave equation $\ensuremath{\Delta}u+{k}^{2}u=0$ is calculated for a three-dimensional finite domain of general cylindrical shape with Dirichlet and Neumann boundary conditions. In the limit of large $k$, the number $\overline{N}(k)$ of modes not exceeding $k$, smoothed in order to eliminate its fluctuating part, is determined. Four terms of the expansion of $\overline{N}(k)$ are obtained. The boundary effects for the thermal phonon radiation of thin films are discussed as an application. The respective results for the electromagnetic vector waves in a lossless closed cavity (blackbody radiation) are presented as well. Here the constant term in the expansion is independent of the shape of the domain and does not account for corners or connectivity. $E$- and $H$-type resonances have to be observed separately in order to yield the complete shape dependence of $\overline{N}(k)$. The edge- and curvature-dependent corrections of the Planck, Wien, and Stefan-Boltzmann radiation formulas are given.

Kapitza conductance due to helium atoms interacting with a surface

A calculation has been made of the Kapitza conductance between a solid and helium as a result of the interaction between independent helium atoms and the solid. In the low temperature limit the expression for the conductance due to transitions between unbound states is the same as that for phonon radiation into the gas, that is, the Khalatnikov model with appropriate minor modifications. At higher temperatures it increases above this limit suggesting that the neglect of the attractive potential is a significant defect of the Khalatnikov model. The conductance due to transitions between bound and unbound states has also been calculated. Because of the neglect of interactions between helium atoms the model only becomes realistic for this process at the higher temperatures when the conductance is less than that due to transitions between continuum states.

THE KAPITZA RESISTANCE AND HEAT TRANSFER AT LOW TEMPERATURES

— A brief review is given of some important heat transfer problems at 1 °K and below. Included are discussions of the thermal contact resistance between solid-solid and solid-liquid helium II boundaries (Kapitza resistance). The results are compared to available theoretical models, with particular interest placed on the upper limit, the phonon radiation model.

SEMICLASSICAL THEORY OF PHONON RADIATION PROCESSES

For the various forms of the spin-lattice coupling in paramagnetic salts of the iron group ions, derived in a previous paper, a semiclassical phonon radiation theory is developed. The phonon fields are analyzed in terms of phonon multipole fields, and the phonon multipole moments are expressed in terms of the effective spin variable. The phonon multipole fields are all monopole fields in the sense that the corresponding static fields fall off at large distances as R−2, but they are monopole, dipole, and quadrupole fields as far as the angular dependence is concerned. As a result, the rates of emission by the different phonon multipoles are all of the same order of magnitude. The equation of motion of a dressed spin is derived, and the phonon radiation damping is shown to depend on the third time derivative of the phonon multipole moments. As an application, the classical theory of the resulting spin-lattice relaxation is discussed briefly.

THEORY OF THE SPIN-LATTICE INTERACTION IN PARAMAGNETIC SALTS OF IRON-GROUP IONS

The form of the spin-lattice coupling in hydrated salts of the iron-group ions is derived in terms of the lattice vibrational coordinates and the effective spin variable, using general symmetry arguments. The most important coupling terms for octahedral and spherical symmetry are given, and the role of the breathing and rotational modes is discussed, as well as the concept of adiabatic and non-adiabatic coupling. This work forms the basis of the semiclassical theory of phonon radiation processes and phonon multipole fields and interactions to be presented in a subsequent paper. Finally, explicit expressions for the coupling constants in terms of the electronic structure of the ions are also derived, for the case of a nondegenerate ground orbital level.

Transport of Heat from Metals to Insulators at Low Temperatures

The thermal relaxation times of thin indium and lead films evaporated on sapphire and quartz single-crystal substrates have been measured. These times are compared with the predictions of two models for the heat-loss process. The first assumes perfect thermal contact between the two materials and corresponds to perfect black-body phonon radiation from the film into the insulator. The second, which predicts a somewhat reduced rate of heat loss (up to \ensuremath{\sim}40% less), corresponds to an acoustic-mismatch model in which the reflection of phonons at the interface is considered. The possible relevance of these two models to the experimental situation in which a metal film is involved is discussed. Experimentally it is found that the results for the indium films approach the predictions for the perfect-thermal-contact model, while the results for the lead films show a slower rate of heat loss than either model predicts. Comparison to other experimental results is also made.

Phonon Radiation by Uniformly Moving Charged Particles in Piezoelectric Solids

The rate of emission and the radiation pattern of coherent phonon radiation were obtained for a charged particle traveling along the symmetry axis of a piezoelectric crystal of hexagonal symmetry. The phonon power per unit frequency radiated by a charged particle is proportional to frequency. Macroscopic equations used in the derivation permit solution of a phonon radiation problem which otherwise would be quite complicated.