The specific heat and critical magnetic field of superconducting PdH(D)

From the solution of the Eliashberg equations on the imaginary axis, the thermodynamic properties, specific heat, and critical magnetic field of PdH(D) have been calculated. The Eliashberg kernels ²()F() were constructed using a published value of ²(), and F() was obtained from inelastic neutron scattering data. The results for the specific heat are in good agreement with published experimental data. The critical magnetic field shows a nearly parabolic behavior as a function of temperature, in disagreement with the linear experimental behavior. The deviation function D(t) and the ratios C(T _c)/T _c and [T _c/H _c(0)]² indicate that the PdH(D) system is BCS-like. The functional derivative of T _c with respect to changes in the kernel is also calculated.On sabbatical leave from the Instituto de Investigaciones en Materiales, UNAM, Mexico.     

The optical properties and a.c. conductivity of magnesium phosphate glasses

Magnesium phosphate [X MgO-(100–X) P₂O₅] glasses in the composition range [X=20, 25, 30, 40, 45, 50 mol %] have been made. The optical properties and a.c. conductivities were measured and their amorphous nature confirmed by X-ray diffraction technique. The variation of relative density with x was anomalous. In the ultraviolet/visible regions it was found that the fundamental absorption edge is a function of glass compositions and lower absorption coefficients, () follow the so-called Urbach edge. At lower absorption levels (1<<10⁴cm^–1), the width of the tail of localized states in the band gap, E _g, did not vary significantly with glass composition and lay in the range (0.26–0.343) eV. In the high absorption region (()>10⁴ cm^–1), the behaviour of () suggests that there are two different transition energies for electrons in k-space, namely direct allowed transitions and non-direct transitions. In the infrared region at wavelengths =2.5–30 m, the transmission spectrum has four absorption bands. Using the Kramers-Kronig theory, the optical constants (refractive index n and extinction coefficient k) have been determined from the transmission spectrum. The a.c. conductivity, (), real and imaginary dielectric constants, ₁, ₂, and loss factor, tan , have been determined at room temperature in the frequency region, = 2×10⁴–10⁶ Hz. It has previously been established theoretically that () ^s and s was found to be in the range 0.64–0.73, depending on glass composition.     

Longitudinal dielectric function and collective surface oscillations in superconductors

The electrodynamic approach to the problem of collective oscillations in superconductors is considered. The kinetic equation for quasiparticles is used to find the longitudinal dielectric function ₁ (, k) of a pure superconductor at ( is the collision frequency). With the help of the evaluated ₁ (, k) the existence of collective oscillations localized near the boundary of the superconductor is investigated.     

Superconducting state in M3C60: Strong vs. weak coupling

The superconducting state in the doped fullerenes is due to strong coupling (e.g.,2.1 for Rb₃C₆₀) to low-frequency intramolecular modes _L 250 cm^–1 (^21/2). The analysis is based on an equation describingT _c for any strength of the coupling and on recent isotope effect and NMR data.     

Frequency and temperature dependencies of a.c. conductivity of polyvinyl alcohol (PVA)-CoCl2 composites

The a.c. conductivity for polyvinyl alcohol (PVA)-CoCl₂ composites prepared by a casting method has been measured at different frequencies (0.1–10 kHz) in the temperature range 300–450 K. At constant temperature, the frequency dependence of a.c. conductivity, (), was found to fit the established equation () = A ^s quite well. On the other hand, the temperature dependence of a.c. conductivity suggested an electronic hopping conduction mechanism in a thermally assisted electric field. Various theoretical mechanisms have been discussed to clarify the conduction processes in these samples. The correlated barrier hopping (CBH) mechanism, proposed by Elliott, was found to be the most appropriate one.     

Hot electrons in metals at low temperatures

Hot electrons in metals at helium temperatures under steady conditions can be produced by passing an electric current of moderate density ( 10⁶ A/cm²) through thin, narrow (~1 m wide) metallic films in good thermal contact with bulk single-crystal dielectric substrates. This paper is concerned with the theory of hot electrons in normal metals at low temperatures (when _D, where is the average electron energy and _D is the Debye temperature). The theory is formulated in terms of realistic electron and phonon dispersion laws, taking into account the experimental possibility of heat removal from the sample. In the case in which the temperature approximation of Kagnov, Lifshitz, and Tanatarov is not satisfied when elastic scattering of electrons is dominant in a steady state electric field, the kinetic equation is derived for the energy-dependent, hot electron distribution function, which determines the associated nonlinear responses. The solution of this equation is discussed for a simple model. It is shown that the experimental information on the electron-phonon interaction in a metal can be obtained in terms of the well-known spectral functions S() ² F() and g() _tr ² F(). This is illustrated by experiments determining the nonlinear field dependence of the resistance, by tunnel experiments, and by critical current hysteresis measurements (for superconducting metals). Theoretical estimates which support the observability of the effects under discussion are presented.     

Paramagnetic resonance in a “dirty” spin-glass

For a spin-glass with nonmagnetic defects (n _m ^1/3l 1, where n _m is the magnetic impurity concentration and l is the mean free path) an absorption function () is derived. Three ranges of temperature and external magnetic field are considered. In the vicinity of the transition the value of () d is estimated as a function of temperature and field.     

Dynamic scaling and ultrasonic attenuation in 4He near the superfluid transition point

Attenuation of first sound has been measured in ⁴He under saturated vapor pressure near the lambda temperature T at frequencies /2 ranging from 10.2 to 271 MHz. The frequency dependence of the critical part of the attenuation is determined and the dynamic scaling hypothesis is examined. Above the lambda point, it is found that the critical attenuation is described by a scaling function (, ) = ^1+y F(), where = ₀^–x and = T/T – 1, with the results x = 1.02±0.05 and y = 0.33±0.03. The characteristic frequency of the order-parameter fluctuation with the wave number k equal to the inverse correlation length is then proportional to ^x , which is in an excellent agreement with the prediction of dynamic scaling. Below the lambda point, a characteristic relaxation time or times shorter than previously expected at lower frequencies appears to exist in the present frequency range.Based on a Ph.D dissertation submitted by K. Tozaki to the University of Tokyo (1977).     

Critical field and specific heat of superconducting Tl-Pb-Bi alloys

The Eliashberg kernels ² ()F() obtained from tunneling experiments for a series of weak to strong coupling Tl-Pb-Bi alloys are used to calculate numerically on the imaginary axis the thermodynamic properties of these alloys in the superconducting state. The functional derivatives ofT _c andH _c with respect to changes in the kernel are also calculated.Research supported by the National Research Council of Canada.Partially supported by Conacyt, Mexico.     

Magnetic field dependence of zero-sound attenuation close to the pair-breaking edge in3He-B due toJ=1−,J z =±1 collective modes

Our previous theory yielded for the Zeeman splitting of the imaginaryJ=1 collective mode in³He-B the result =2+0.25J _z ( is the effective Larmor frequency). In this paper we take into account the downward shift of the pair-breaking edge from 2 to 2₂– (₂ and ₁ are the longitudinal and transverse gap parameters). This leads to a complex Landé factor: the frequencies of theJ _z =±1 components become =2+0.39J _z , and the linewidths of these resonances become finite: =0.18. The coupling amplitudes of theJ _z =±1 components to density are found to be proportional to gap distortion, (₁–₂/(/)². Our results for the ultrasonic attenuation due to theJ _z =±1,J=1 modes are capable of explaining the field dependence of the attenuation close to the pair-breaking edge as observed by Dobbs, Saunders, et al. The observed peak is caused by theJ _z =–1 component: its height increases due to gap distortion as the field is increased, and the peak shifts downward in temperature and its width increases with the field due to the complex Landé factor. TheJ _z =+1 component gives rise to a corresponding dip relative to the continuum attenuation.     

On the maximum reduced upper critical magnetic field in Eliashberg theory

Consideration of the functional derivative of the zero-temperature reduced upper critical magnetic fieldh _c2(0) with electron-phonon spectral density ² F() suggests that its value can be maximized, for a given areaA under ² F(), with the choice of a delta-function spectral density. We show thath _c2(0) is then independent ofA and that it increases steadily as the Einstein frequency _E of the delta function is lowered. We argue that there is a local maximum inh _c2(0) at _E=0. The value at maximum is very sensitive to impurity content and increases sharply from a clean-limit value of 1.5 atT _c /_E=1.33 to more than 3.45 in the dirty limit.     

On a simple wave approximation of a set of linear dispersive wave equations

Summary The validity of an approximation ₀ of one of the solutions of a set of two linear coupled dispersive wave equations has been discussed. ₀ is the solution of a linear Korteweg-de Vries equation and satisfies the same initial condition as . It is shown that for square integrable solutions having a spectral range not exceeding [–, ] the approximation is useful if ^{5 2}t«1 in the sense that –₀(t)« (t)(L ₂ -norm). is a measure for the dispersion. The approximation fails in that sense ast . Some remarks to a similar nonlinear problem are made.     

A.c. conductivity for amorphous TeO2-P2O5 glass system

The a.c. conductivity for the TeO₂-P₂O₅ glassy system was measured in the temperature range 300–573 K and in the frequency range 100 Hz to 10 kHz. The a.c. conductivity () increased with frequency according to the relation ()^s. The frequency exponent s was found to decrease with increasing temperature. The composition dependence of the conductivity was also investigated. The density of states was also calculated using the Elliott model. The a.c. conductivity increased over the studied temperature range. The obtained experimental data have been analysed with reference to various theoretical models. The analysis shows that the correlated barrier hopping (CBH) model is the most appropriate mechanism for conduction in the TeO₂-P₂O₅ glass system.     

NMR Studies on 3He-3He and 3He-4He tunneling motions in solid 3He-4He mixtures

Helium-3 nuclear spin relaxation times T ₁, T ₂, and T ₁have been measured for ³He-⁴He solid mixtures at the exchange plateau region (~0.5K). The ³He concentrations X ₃of the samples were 7.2, 2.9, 1.8, 1.4, 0.67, 0.65, and 0.22%, and their molar volumes varied between 19.9 and 20.9cm³/mole in hcp phase. The spectral density function J() for dipolar field fluctuations was determined in the low-frequency branch from T ₁measurements and in the high-frequency branch from conventional T ₁measurements. It was found that J() is given by J() = cJ()|_3–4 + (1–c)J()|_3–3, where J()|_3–4 is the spectral density function due to the ³He-⁴He tunneling motions, and J()|_3–3 is that due to the ³He-³He tunneling motions. Using the Torrey theory, the correlation frequency of the ³He-⁴He tunneling motions was evaluated from T ₁data, and was found to be in good agreement with Landesman 's theory.Supported in part by the Japan Society for the Promotion of Science through a grant to Y.H.     

Axi-symmetric natural frequencies and response of a spinning liquid column under strong surface tension

Summary The response of a solidly rotating anchored finite liquid column consisting of frictionless liquid is subjected to axial harmonic excitation. The response of the free liquid surface elevation and velocity distribution has been determined analytically in the elliptic (>2 ₀) and hyperbolic frequency range (>2 ₀). For the liquid surface displacement the response has been evaluated numerically as a function of the forcing frequency/2 ₀. In addition the first natural stuck-edge frequency has been determined and compared with the slipping case.List of symbols a radius of liquid bridge - h length of liquid bridge - I ₀,I ₁ modified Besselfunctions - J ₀,J ₁ Besselfunctions - p liquid pressure - r, ,z cylindrical polar coordinates - t time - u, v, w velocity distribution in rotating liquid - Weber number - z₀ axial excitation amplitude - elliptic case (>2 ₀) - hyperbolic case (>2 ₀) - liquid density - surface tension - liquid surface displacement - acceleration potential - ₀ rotational speed - axial forcing frequency - natural frequency of rotating system - _0n natural frequency of harmonic axial response     

Amplifier based on a field-effect triode with negative current feedback

Conclusions A field-effect triode amplifier with series negative current feedback allows a voltage gain of the order of 200–300 to be obtained for a load resistance R_s1 M. The coefficient K_u begins to decrease noticeably only for a feedback resistance above 500 .The current gain reaches (8–10)·10³. Increasing the resistances R_s and R_L to hundreds of ohms has practically no effect on K_i. For a further increase of R_s and R_L the coefficient K_i decreases.The power gain reaches its maximum value (of the order of 10⁴ or more) for R_s100 and R_L=10–100 k. An increase in R_s leads to a reduction of K_pmax and to a shift of the extremum of the function K_p=f(R_L) into the range of higher values of R_L.A large input resistance of the amplifier (tens of megohms and higher) is obtained when R_s increases to 10–100 M. The maximum input resistance is obtained for R_L and R_s and may exceed values of from hundreds of megohms to several gigaohms. The minimum input resistance is hundreds of kilohms for R_L and R_s0.The minimum input resistance (5–10 k or less) is ensured for R_g and R_L0. An increase of the output resistance to hundreds of megohms or higher occurs for R_g and R_s.Translated from Izmeritel'naya Tekhnika, No. 9, pp. 67–70, September, 1971.     

Response of a spinning liquid column to axial excitation

Summary The response of a solidly rotating finite liquid column consisting of frictionless liquid is subjected to axial harmonic excitation. The response of the free liquid surface elevation and velocity distribution has been determined in the elliptic (>2 ₀) and hyperbolic frequency range (>2 ₀).Notation a radius of liquid bridge - h length of liquid bridge - I ₀,I ₁ modified Besselfunctions - J ₀,J ₁ Besselfunctions - P liquid pressure - r, ,z cylindrical polar coordinates - t time - u, v, w velocity distribution in rotating liquid - axial excitation amplitude - elliptic case (>2 ₀) - hyperbolic case (>2 ₀) - liquid density - surface tension - liquid surface displacement - acceleration potential - ₀ rotational speed - axial forcing frequency - natural frequency of rotating system - _02n –1 natural frequency of harmonic axial response With 8 Figures     

Similarity solutions in axisymmetric mixed-convection boundary-layer flow

The similarity equations for mixed-convection axisymmetric boundary-layer flow are considered. The equations involve a buoyancy parameter and a curvature parameter . The equations are solved numerically and it is found that for large , and of O(1), an asymptotic solution is approached, the nature of which is discussed. When is also large, of O(^1/4), the problem, at leading order, becomes independent of the mainstream and the free-convection limit is obtained. This problem is also discussed, including the behaviour for large values of ₀, the free-convection curvature parameter. For < 0 we find that the solution can be continued past the point where the wall heat transfer becomes zero (where previous mixed-convection similarity solutions in plane geometry were terminated) with the solution ending as 0^–. The nature of this limit is also discussed. For < 0 it is also found that there are solutions only in _b = < 0 with two branches of solution bifurcating out of = _b , and values of _b are computed for a range of . The behaviour of the solution for large values of the curvature parameter , and of O(1), is discussed where it is shown that the solution proceeds in inverse powers of log .     

Investigation of the thermal and electrical transport properties of niobium and niobium films at temperatures between 9 and 50 K

The thermal conductivity and the electrical conductivity of niobium crystals and niobium films have been investigated in the normal state from 9 to 50 K. The deviations from the Matthiessen rule, w=/T+T², have been studied in detail for the thermal case. The investigation shows a slight dependence of the electron-phonon scattering coefficient upon the impurity content of the sample. With the specific electrical residual resistivity ₀ as the measure for the impurity content, the following correlation can be formulated: =1.2×10^-2[₀/-cm)]^0.04, being obtained in cm/W K. Above 20 K an additional scattering mechanism occurs. The temperature dependence of the additional resistance W between 20 and 50 K is proportional to T ^5.5 ··· T ⁴. Possible causes of this phenomenon are discussed. For the discussion, all the data available in the literature on the thermal conductivity of niobium in this temperature region are used.