Phonon focusing in quartz and sapphire imaged by electron beam scanning

Anisotropic phonon propagation and phonon focusing in single-crystalline -quartz and sapphire has been investigated using electron beam scanning for imaging the ballistic phonon propagation. The samples were circular disks of 20 mm diameter and 2.0 mm thickness. The phonons generated at the upper flat sample surface by the electron beam were detected with a small-size (43 m×41m) bolometer at the center of the opposite surface. The experiments were performed using a scanning electron microscope with a low-termperature stage. During electron irradiation of the upper sample surface the bottom of the sample was in direct contact with the liquid-He bath. For -quartz, also time-resolved imaging of the phonon intensity has been performed in addition to imaging of the time-integrated bolometer signal. Our results agree remarkably well with calculations by Rösch and Weis.Supported by a grant of the Deutsche Forschungsgemeinschaft     

Dispersive anisotropic ballistic phonon propagation in [100] GaAs

We report experimental observations of the phonon focusing pattern in [100] GaAs using low temperature electron beam scanning for phonon generation. The typical dispersive effects for high-frequency phonons expected from the calculations by Tamura have clearly been observed using PbIn tunnel junctions for phonon detection. The quantitative comparison of our experimental results with the frequency dependent calculations by Tamura allowed to determine the dominant phonon frequencies contributing to the detector signal in our different experiments. Above the temperature of the -point the dominant phonon frequencies appear to be shifted considerably to lower values, which could be explained by a heating effect in the liquid-He layer adjacent to the tunnel junction detector. By comparing the observed magnitude of the detector signal with different theoretical treatments of the detector response, we have found satisfactory agreement for a model where the perturbation due to the high-frequency phonons is restricted to the base electrode of the detector reached first by the phonons following their passage through the crystal.     

Low-temperature transport properties of UCu5

The electrical resistivity (T) and the thermal conductivity (T) have been measured for UCu₅ in the temperature range between 0.02 and 20 K. Two distinct anomalies in (T) are due to previously established phase transitions at approximately 15 and 1 K, respectively. They indicate considerable changes in the electronic structure of this compound, implying sizeable truncations of the Fermi surface with decreasing temperature at both transitions. In almost the entire covered temperature range the thermal conductivity is dominated by phonon contributions. Its temperature dependence is fairly well reproduced by a calculation considering phonon scattering by electrons and by point defects. At very low temperatures, asT approaches 0 K, the Wiedemann-Franz law _e L ₀ T, where _e is the electronic part of (T) andL ₀ is the Lorenz number, is almost perfectly fulfilled.     

Jauch-Piron system of imprimitivities for phonons. I. Localizability in discrete space

This paper is devoted to a discussion of the notion of localizability for phonons, i.e., quasiparticles arising from the harmonic vibrations of a system ofn atoms bound to one another by elastic forces. The natural tools for the analysis of localizability are the projection operatorsÊ() acting on the Hilbert space of one-phonon states, where is an arbitrary subset of the set that consists ofn vectors specifying the equilibrium positions ofn atoms. The expectation value ofÊ() is the probability that the phonon belongs to the atoms whose equilibrium positions are characterized by the elements of . For a strongly localizable phonon all of the projection operatorsÊ() commute with one another, whereas in the case of a weakly localizable phonon the operatorsÊ(₁) andÊ(₂) do not commute when ₁ and ₂ overlap. With the aid of the Jauch-Piron quantum theory of localization in space, the present paper describes the method of obtainingÊ() and also shows that if in the system ofn atoms there exist normal modes of zero frequency, then the phonon is only weakly localizable. Given the explicit expression forÊ(), one can define the number-of-phonons operator as well as the quasiparticle analogue (given in a companion paper) of the Wigner distribution function.     

Electrical and thermal properties of chalcogenide glass system Se75Ge25−x Sb x

The dc and thermal conductivities of five different compositions of the chalcogenide glass system Se₇₅Ge_25–x Sb _x have been studied in a temperature range below T _g. The dc conductivity results indicate that each composition has a single activation energy in the considered temperature range. The coefficient of thermal conductivity increased linearly with temperature below T _g for the compositions investigated. The increase of Sb content in the chalcogenide glass system leads to an increased coefficient of electrical conductivity , an increased coefficient of thermal conductivity , and to a decreased activation energy E and pre-exponential factor ₀. The observed compositional dependencies of and E have been correlated with the increase of weak bond density and the decrease of covalent bond density in the structure of the compositions investigated with increasing Sb content at the expense of Ge content. The decrease in ₀ and the increase in has been, respectively, correlated with the decrease in mobility and the increase in phonon velocity.     

Low temperature thermal properties of crystalline quartz after electron irradiation

Measurements of the temperature specific heat (between 0.12K and 8K) and thermal conductivity (between 0.5K and 20K) of crystalline -quartz after electron irradiation are reported. In the temperature region below 1K the specific heat is larger than in the unirradiated sample. This can be attributed to low energy excitations which are created during irradiation and which are associated with Al impurities. The thermal conductivity is reduced after irradiation. Below 4K the additional thermal resistivity varies asT ^–1.5. The phonon scattering by radiation-induced excitations in -quartz is weak compared to phonon scattering by two level systems (TLS) in vitreous silica.     

Conductivity of a superlattice during electron scattering by optical phonons

The conductivity is calculated for a semiconductor with a superlattice with simultaneous actions of constant (E) and varying (E_o cos t) electric fields, considered quasiclassically. It is shown that in calculating the current-voltage characteristics (CVC) at low temperatures (k_oT h _o, _o being the optical phonon frequency) and e_o = 0 it is necessary to consider electrons as both absorbing and nonabsorbing optical phonons. The frequently used approximation of constant relaxation time is valid only for k_oTh_o, when scattering by optical phonons dominantes.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 81–84, January, 1982.     

Tunneling conductance of a Bi2Sr2CaCu2O8-SnO2 junction along the c-axis

fine structure was observed in the conductance curve of a tunneling junction composed of a single crystalline Bi2212 and an evaporated SnO₂ film. It is similar to those of Bi2212-GaAs mechanical junctions and there is a certain correspondence between the structure and the phonon density of states. Thus the previous conclusion that the structure is due to phonons has been complemented by this work. The energy gap 2 was 57 meV at 13 K and T _c was 78 K. 2(0)/k _B T _c is then 8.3. (T) showed the BCS-like temperature dependence.     

Determination of the far infrared optical constants of η-doped bulk CdxHg1?xTe (CMT) by dispersive fourier transform spectroscopy

Far infrared phase and amplitude reflectivity measurements have been made on two bulk Cd_xHg_1–xTe mixed crystals with composition x=0.29 and x=0.22 by dispersive Fourier transform spectroscopy (DFTS). The results have been used to calculate the real and imaginary parts of the dielectric function (, ) from the Fresnel relations. A plasma contribution is observed in the spectra in addition to the phonon response. For both samples a broad but weak reflection band around 95–105 cm^–1 is observed as well as the expected two-oscillator response from the HgTe-like and CdTe-like optical phonons. This feature is attributed to absorption due to phonon combination bands, but it is too broad to enable assignments to be made. There is no evidence of additional features in the CdTe region due to clustering.     

Some differences in the exponential tail behaviour of the fundamental absorption edge in amorphous and crystalline materials

Some characteristics of optical absorption in the fundamental absorption tail are studied using the parameter which describes the shape of the optical absorption edge of crystalline and amorphous materials. It follows from the experimental data that depends on the morphological state of material. Further, very pronounced linear temperature dependence of was found for crystalline materials whereas only a weak dependence was found for amorphous materials. A unique point of intersection has been observed for all the=f(T) lines pertinent to various crystalline materials in unpolarized light.Lumumbova 1, Praha 8, Czechoslovakia.The author thanks Dr. A. Vako for his attention paid to this work.     

Ground state of a spin-phonon system. I. Variational estimates

A study is made of the ground-state energy of a spin-one-half particle in a fieldB and interacting with a phonon bath. The infrared-sensitive case of acoustic phonons with point coupling in three dimensions is characterized by two parameters, a coupling constant andB. Units are used where the high-momentum phonon cutoff is unity. There is a curve (B) separating a symmetry-breaking region with a long-range phonon field from a normal region. Two simple, well-known, approximations are compared. The source theory yields discontinuities in the first derivatives of the energy with respect toB and whenB>e ^–1 and an infinite-order transition whenB<e ^–1, but is trivial in the large- region. The classical theory yields discontinuities in the second derivatives but is trivial in the small- region. An improved variationally fixed ground-state wave function is analyzed. It gives a new (B) curve with an infinite-order transition with continuous energy derivatives whenB<e/(e ²–1/4) and with discontinuous derivatives whenB is larger than this value. It is nontrivial in the entire (B) plane. The crossover to classical behavior occurs near =1/2 forB1. But the wave function does not describe quantum fluctuations in the large- phase. A second way of combining source and classical effects is described. It yields a second-order transition (near =1/2 forB1) everywhere. These theories are special cases of a symmetry-breaking transformation together with a one-mode treatment of quantum fluctuations. The transition is viewed in terms of a single mode with a variable length, coupled dynamically to the spin.     

Interaction of conduction electrons with local excitations. The infrared divergencies

Using the renormalization group method the higher orders of perturbation theory in the interaction of conduction electrons in metals with local paulions (pseudospins), e.g. two-level systems, crystal-field excitations, and bosons, e.g. phonons, are considered. For the paulions, the lowest order logarithmic singularities in the electron self-energy at =E–E _F±, being the splitting, become weaker, at least in the commutative model. It is shown that the singularities of the type ln are absent. This justifies the applicability of the second order perturbation theory resultm ^{* –1} for the electron effective mass even atm ^*m. For the phonons, the singularities at ±₀, ₀ being the phonon frequency, may become stronger or weaker depending on the conduction band filling and the anharmonic contribution to the deformation potential. The singular contributions to the local excitation Green's function are calculated. They result in the change of the line shape of the local level (the orthogonality catastrophe). The singular terms in the ground state energy and average pseudospin are considered.     

Simultaneous measurement of thermal diffusivity,thermal conductivity and specific heat by impulse-response photopyroelectric spectrometry

A novel photothermal technique is developed, which enables the simultaneous measurement of the thermal diffusivity , thermal conductivity , and the specific heat C of a sample. The technique is based on frequency-modulated time-delay photopyroelectric spectrometry (FM-TDPS), which consists of chirped laser excitation of the sample and detection of the thermal impulse response by a thin-film pyroelectric detector. No calibration is required for the measurements; absolute values for , , and C may be obtained without having to employ a reference sample. Results on superconducting YBa₂Cu₃O_7–x are reported for the temperature range 50–300 K; the values obtained compare favorably with reported measurements of , , and C for YBa₂Cu₃O_7–x , which previously required separate experiments for their determination.     

Comment on Eliashberg's free energy of a strong-coupling metal

We derive in the Migdal-Eliashberg approximation new formulas for the free energy, entropy, and specific heat of conduction electrons coupled to phonons. Analytic results in terms of standard functions are obtained for Einstein phonons, and the calculation for realistic phonon spectra is reduced to simple, weighted integrals over Eliashberg's spectral function ² F(). Our derivation requires a careful analysis of the range of validity of the Midgal-Eliashberg approximation which leads to some insight into the problem of lattice instabilities induced by a strong electron-phonon coupling.     

Thermal fluctuations and ac response of weakly pinned charge density waves

The Fukuyama-Lee theory for the ac response () of weakly pinned charge density waves is extended to include thermal fluctuations. The equation of motion for the local phase includes an extrinsic damping and a distinction is made between static and dynamic parameters in it. It is split into static, thermally fluctuating and response contributions to the phase, respectively. The static problem is treated using a result from Feigel'man's theory which provides a revised value for the weak pinning constant. The impurity averaging of the response equation is performed using the simplifying statistical properties of the stochastic pinning force following Bleher's recent work. The main emphasis is on the treatment of the thermal fluctuations via a thermal field _th. The non-linear Langevin equation for _th is linearized and further simplified by an RPA type approximation which eliminates the impurity fluctuations from _th. The resulting equation is solved exactly. It is shown that the correlation function of the thermal field decays initially with a short time constant. This allows to treat the thermal fluctuations on an equal footing with the impurity fluctuations in the self-consistent Born approximation. The main contribution of the thermal fluctuations results in powers of a thermal factor exp(- _th ² /2) to the first and second order self energies of the phason Green's function. Numerical results due to these modifications are given for (,T). It is found that the absorption peak in Re () broadens and shifts to lower frequencies when the temperature is raised. The corresponding treatment for three spatial dimensional is indicated. The thermal factor is evaluated for this case and differences to Maki's result are noted. The questions of analyticity and conductivity sum rule are also dealt with.Dedicated to Professor Helmut Reik on the occasion of his 60th birthday     

Current controlled negative resistance phenomenon in SbPbSe system

Thin film Al/Sb₂Pb₁Se₇/Al metal-glass-metal sandwiched structures prepared using thermal evaporation technique have been studied. The I–V measurements showed that the devices switched from high resistance OFF state to a low resistance ON state when a particular voltage appeared across it. The OFF state I–V characteristics showed non-ohmic behaviour while in the ON state the devices displayed purely linear characteristics. The switching voltage (V _th) was found to depend on film thickness and temperature of the device. A linear relation between V_th and temperature was observed.     

Anomaly of the soft-mode damping function near phase-transition points due to interaction with acoustic phonons

An expression is derived for the anomalous part (T, ) of the soft-mode damping function due to third-order interaction between critical optical phonons and acoustic phonons. It is shown that in crystals with a large elastic viscosity the damping function of critical phonons can have stronger temperature anomalies near phase-transition points. The frequency dispersion of () is investigated; it is found that the damping is a maximum at =_o for the soft-mode vibrational dynamics and at =0 for the relaxational dynamics.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 47–49, March, 1982.     

Electrical and optical properties of amorphous Te40As38Ge10Si12 thin films

Electrical, optical and structural, properties, of Te₄₀As₃₈Ge₁₀Si₁₀ thin films were studied. X-ray diffraction patterns indicate that these films are in an amorphous state. The dark electrical resistivity of Te₄₀As₃₈Ge₁₀Si₁₂ films was measured at room temperature and at elevated temperature. The thermal activation energy E was determined. The optical constants (refractive index n and absorption index k) of such films were determined in the spectral range of 0.5–2.0 m. The absorption coefficient () of this system was also determined using the known equation =4k/. The refractive index n has anomalous behaviour near the absorption edge. Analysis of the absorption spectrum reveals indirect optical transitions. The corresponding forbidden-band width was determined. Its value is approximately twice the thermal activation energy.     

Infrared absorption by free polarons

Expressions are obtained for the coefficient of absorption of a weak electromagnetic wave by free carriers in polar semiconductors with interaction of polarons with acoustic and optical phonons. The appearance in the absorption coefficient of Feynman variational parameters leads, in general, to a change in the frequency dependence. The results are applicable for the frequency range (), where () is the mean reciprocal relaxation time.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 76–80, July, 1980.     

An Equilibrium Lattice Model of Wetting on Rough Substrates

We consider a semi-infinite 3-dimensional Ising system with a rough wall to describe the effect of the roughness r of the substrate on wetting. We show that the difference of wall free energies (r)= _AW(r)– _BW(r) of the two phases behaves like (r)r(1), where r=1 characterizes a purely flat surface, confirming at low enough temperature and small roughness the validity of Wenzel's law, cos (r)r cos (1), which relates the contact angle of a sessile droplet to the roughness of the substrate