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.     

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     

Effect of phase transitions in copper-germanium thin film alloys on their electrical resistivity

An investigation was carried out to study the phase transitions in Cu-Ge thin films (80–200 nm in thickness) containing 0, 5, 15, 20, 25, 30, 35, 40, 45 and 50 at% Ge, and the corresponding effects on electrical resistivity. For these films, the phase transitions were found to follow the sequence: -phase (disordered face centred cubic, fcc, solid solution); 5 at% Ge -phase (disordered hexagonal close packed, hcp); 15 at% Ge -phase + ₁-phase (ordered orthorhombic, Cu₃Ge); 20 at% Ge ₁-phase; 25 at% Ge (₁-phase + progressively increasing proportions of a disordered Ge-rich solid solution); 30–50 at% Ge. Germanium was found to have no marked effect on grain size of all films studied excluding grain boundaries as electron scattering centres. Transition of the -phase into the -phase was found to occur in a highly coherent manner, which could be related to the reduced stacking fault energy of Cu by the addition of Ge. Most evidence pointed out that the initial increase in resistivity within the -phase range was related to hcp scattering centres, which could be associated with a localized high concentration of Ge. At 15 at% Ge, the resistivity reached a maximum value of about 50 cm associated with the complete transformation of -phase into the -phase. With continued increase in Ge concentration, the resistivity was found to gradually decrease reaching a minimum value of about 10 at 25 at% Ge, which was correlated with complete transition of the -phase into the ordered ₁-phase (Cu₃Ge). It was shown that the superlattice of Cu₃Ge could directly be derived from the disordered -phase by minor atom rearrangement on the [0 0 0 1]_hcp plane. Even though, minor proportions of a Ge-rich solid solution containing a small concentration of Cu were formed at Ge concentrations above 25 at%, the minimum resistivity of 10 cm was maintained as the Ge concentration was increased to 35 at%. Subsequently, the resistivity was increased reaching about 46 cm at 50 at% Ge.     

Thermodynamic properties of superconducting niobium

The thermodynamic properties of superconducting Nb are calculated numerically from the solution of the Eliashberg equations on the imaginary axis for several possible electron-phonon spectral densities ²()F(). Comparison with experiment is made in order to see which spectrum gives the best agreement, and functional derivatives with respect to ²()F() are used to estimate how this agreement might be improved by small changes in ²()F(). Possible gap anisotropy effects are also considered with the help of a simple model anisotropy for the interaction.Research supported by Natural Science and Engineering Research Council of Canada.     

Response of a spinning liquid column to pitch excitation

Summary The response of a solidly rotating liquid bridge consisting of inviscid liquid is determined for pitch excitation about its undisturbed center of mass. Free liquid surface displacement and velocity distribution has been determined in the elliptic (>2₀) and hyperbolic (<2₀) excitation frequency range.List of symbols a radius of liquid column - h length of column - I ₁ modified Besselfunction of first kind and first order - J ₁ Besselfunction of first kind and first order - r, ,z cylindrical coordinates - t time - u, v, w velocity distribution in radial-, circumferential-and axial direction resp. - mass density of liquid - free surface displacement - velocity potential - ₀ rotational excitation angle - ₀ velocity of spin - forcing frequency - _1n natural frequency - surface tension - acceleration potential - for elliptic range >2₀ - for hyperbolic range >2₀     

Electron-phonon coupling as a mechanism for high-temperature superconductivity

We have solved the Eliashberg gap equations which are valid for arbitrary phonon frequency, (_ph), electron-phonon coupling constant, (), and screened Coulomb interaction, ( ^*). We have used values of (_ph),, and ( ^*) appropriate to the cuprate superconductors, and calculated the density of states, the pair potential., and the value of the gap at T=0 K. Using the linearized Eliashberg equations in the matrix representation, we have calculatedT _c and 2/k T _c . We have found that we can account for the highT _c 's in the cuprates with reasonable values for, ^*, and _ph.     

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.     

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.     

Electronic Transport Properties of Speer Carbon Resistors—Experimental Results and Semi-empirical Fits

Speer carbon composition resistors, in particular the 470 and 220 1/2 W grade 1002 resistors, have been used as secondary thermometers at temperatures below 4 K for many years. Their zero field resistances have been measured between 300 K and 4 K using a dip probe. Above 10 K, the resistance behavior can be explained using a simple temperature power law, R(T) R₀/T^0.16. The resistance measurements have been extended to 0.02 K using dilution refrigerators. Between 4 K and 0.3 K, the resistances exhibited activated laws having hopping exponents y 0.5. Below 0.3 K, the 470 resistors exhibit a crossover to a weaker activated law. Crossover resistance expressions suggest that the resistances follow a Mott variable-range hopping (VRH) law below 0.05 K. The low temperature magnetoresistance (MR) data showed changes of less than ±12 % of the zero field resistance values in fields up to 10 T. Fits using the wave function shrinkage and the forward interference models gave only fair agreement with the MR data.     

The θ projection method and small creep strain interpolations in a commercial Titanium alloy

The paper describes the early and final uniaxial creep behaviour of a Titanium alloy used for manufacturing intermediate power compressor disks and blades. Tests were conducted at the operating temperature (773 K) for such components and for rupture lives up to 3600 hours. Creep curves were fitted using either the conventional 4 model or the recently developed 6 equation. Parameters allowing the interpolation of times to small strains were produced and their accuracy checked against experimental values using distributions found to be most supported by the data. At strains above 0.75% both methods yielded zero mean interpolation errors. At strains above 0.27% and below 0.75% the 4 equation produced systematic errors in interpolation but the 6 function gave errors which were not statistically different from zero. For strains below 0.27% both techniques produced systematic interpolation errors but the 6 interpolations were always significantly better than their 4 counterparts. Both the 6 and 4 techniques produced systematic errors when predicting the failure time using interpolated rupture strains. Unlike the 4 function, the 6 equation produced unbiased predictions of the minimum creep rate and so produced failure time interpolations from the Monkman–Grant relation that were indistinguishable from zero.     

Varistor characteristics in PTCR-type (Ba,Sr)TiO3 ceramics prepared by single-step firing in air

This paper deals with donor, acceptor-codoped (Ba_0.4Sr_.6)TiO₃ ceramics with distinct varistor characteristics at room temperature, which were prepared by single-step firing in air. The materials, with the Curie point at around –90 °C, exhibited a large PTCR (positive temperature coefficient of resistivity) effect of more than seven orders of magnitude in the temperature range –90 °C (the resistivity 10³ · cm) to room temperature ( > 10¹⁰ · cm). An apparent dielectric constant of >20000 and tan < 0.05 (at 100 kHz) were observed for the present materials at room temperature, and moreover, the materials exhibited nonlinear current-voltage characteristics with the nonlinear coefficient, , in the range 7–12 and the varistor field, E_v, in the range 0.3–1.0 kV/cm. The value of in the present materials increased systematically with increasing in their PTCR temperature range. It has been found that there exists a close correlation between and the grain-boundary potential barrier height, e, obtained from the -T characteristic of the materials. An almost linear relationship was also found to exist between and log E_v for the present materials.     

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.     

Order parameters and energies of analytic and singular vortex lines in rotating3He-A

We present the expressions of the generalized Ginzburg-Landau (GL) theory for the free energy and the supercurrent in terms of thed vector, the magnetic fieldH, and operators containing the spatial gradient and the rotation. These expressions are then specialized to the Anderson-Brinkman-Morel (ABM) state. We consider eight single-vortex lines of cylindrical symmetry and radiusR=[2m/]^–1/2: the Mermin-Ho vortex, a second analytic vortex, and six singular vortices, i.e., the orbital and radial disgyrations, the orbital and radial phase vortices, and two axial phase vortices. These eight vortex states are determined by solving the Euler-Lagrange equations whose solutions minimize the GL free energy functional. For increasing field, the core radius of the texture of the Mermin-Ho vortex tends to a limiting value, while the core radius of the texture goes to zero. The gap of the singular vortices behaves liker forr 0, where ranges between and . The energy of the radial disgyration becomes lower than that of the Mermin-Ho vortex for fieldsH6.5H*=6.5×25 G (atT=0.99T _c and forR=10L*=60 µm, or=2.9 rad/sec). ForR 2 _T ( _T is the GL coherence length) or _c2 (upper critical rotation speed), the energies of the singular vortices become lower than the energies of the analytic vortices. This is in agreement with the exact result of Schopohl for a vortex lattice at _c 2. Finally, we calculate the correction of order (1 -T/T _c ) to the GL gap for the axial phase vortex.     

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.     

A note on the similarity solutions for free convection on a vertical plate

Summary The similarity solutions for free convection on a vertical plate when the (non-dimensional) plate temperature is x and when the (non-dimensional) surface heat flux is –x are considered. Solutions valid for 1 and 1 are obtained. Further, for the first problem it is shown that there is a value ₀, dependent on the Prandtl number, such that solutions of the similarity equations are possible only for >₀, and for the second problem that solutions are possible only for >–1 (for all Prandtl numbers). In both cases the solutions becomes singular as ₀ and as –1, and the natures of these singularities are discussed.     

Transport results from untwinned YBCO: Washboard frequency of the vortex lattice,and the quasiparticle mean free path

The washboard frequency of the moving vortex lattice in untwinned YBa₂ Cu₃ O_6.93 may be observed through mode-locking to an externally applied ac current of frequency _ext. The interference between and _ext results in jumps in the dc current-voltage characteristics when and _ext are harmonically related¹. The interference effect disappears in the vortex liquid state. The Hall conductivity _xy below T_c in YBCO contains contributions² from a positive quasiparticle (qp) term (H) and a negative vortex term (1/H). The qp term is surprisingly large well below T_c and implies a large gap anisotropy and a long qp mean free path (mfp). The thermal Hall effect³ _xy is closely related to the qp _xy; _xy is produced by asymmetric scattering of qp by pinned vortices. The qp mfp at H = 0, extracted from _xy and extended to low T by _xy, increases remarkably from 90 Å at T_c to more than 0.5m at 22 K.     

An indenter moving on an anisotropic elastic half-space

Summary The problem is considered of a semi-infinite homogeneous anisotropic elastic solid deformed in plane strain by an indenter moving steadily over its surface. General expressions are derived for the components of stress throughout the medium for arbitrary anisotropy of the elastic modulus tensor. It is shown that the distribution of normal traction under the indenter and the normal displacement of the free surface outside the region of contact depend on the elastic modulus components and the velocity of the indenter through a single constant, denoted by . A simple, practical method of calculating is presented.The solutions are examined in detail for the case of orthotropic materials and analytical expressions are given for and for the complete stress distribution throughout the medium in this case. Representative numerical results are presented graphically to illustrate the angular variations of the scaled radial shear and tangential stress components near the edge of the punch.

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Ein bewegter Stempel auf einem anisotropen elastischen Halbraum

Zusammenfassung Das Problem eines homogenen, anisotropen, elastischen Halbraumes, auf dessen Oberfläche sich ein Stempel stetig bewegt, wird betrachtet. Allgemeine Ausdrücke werden für die Spannungskomponenten im Körper für beliebige Anisotropie des Elastizitätsmodultensors abgeleitet. Es wird gezeigt, daß die Normaldruckverteilung unter dem Stempel und die Normalverschiebung der freien Oberfläche außerhalb des Kontaktbereiches von den Elastizitätsmodulkomponenten und der Stempelgeschwindigkeit durch eine einzige Konstante, bezeichnet mit , abhängen. Eine einfache praktische Methode zur Bestimmung von wird angegeben.Die Lösungen werden für den Fall eines orthotropen Materials bestimmt, und die analytischen Ausdrücke für und für die Spannungsverteilung im Körper für diesen Fall angegeben. Numerische Ergebnisse werden graphisch angegeben zur Darstellung der Radialschub-und Tangentialspannungskomponenten in der Nähe der Stempelspitze.

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With 2 Figures     

Viscous response of an anchored spinning liquid column to various axial excitations

Summary For a solidly rotating viscous cylindrical liquid column of finite length the response to axial synchronous, counter- and one-sided excitation is determined for anchored contact lines at the disc-rim. For a rotating column additional responses of inertial waves (hyperbolic range) appear for < 2 ₀, while in the elliptic range < 2 ₀ the sloshing response occurs. The various responses for the free surface displacement have been numerically evaluated. Only in the one-sided exitation case all resonance peaks appear, while for synchronous excitation only the odd resonances and for counter-excitation only the even resonance peaks occur.Notation a radius of column - h length of liquid bridge - I _n modified Bessel function - p liquid pressure - r, ,z cylindrical polar coordinates - t time - u, v, w velocity distribution - Weber number - z ₀ excitation amplitude - liquid density - surface tension - surface tension parameter - Ohnesorge number - liquid surface displacement - kinematic viscosity - ₀ rotational speed - dimensionless rotational speed - forcing frequency - dimensionless forcing frequency - dimensionless forcing frequency for non-viscous liquid - a= root of bi-cubic Eq.(33) - root of bi-cubic Eq.(33)     

Microstructure and mechanical properties of rapidly quenched L20 and L20+L12 alloys in Ni-Al-Fe and Ni-Al-Co systems

Ductile L2₀-type wires and+L1₂-type duplex wires with high strengths and large elongation in the Ni-Al-Fe and Ni-Al-Co ternary systems have been manufactured directly from the liquid state by an in-rotating-water spinning method. The wire diameter was in the range 80 to 180m and the average grain size was 2 to 4m for the wires and 0.2 to 1.0m for the+ wires. _y, _f and _p of the wires were found to be about 360 to 760 MPa, 560 to 960 MPa, and 0.2 to 5.5%, respectively, for the Ni-Al-Fe system, those of the+ wires were about 395 to 660 MPa, 670 to 1285 MPa, and 3.5 to 17%, respectively, for the Ni-Al-Fe system, and about 260 to 365 MPa, 600 to 870 MPa, and 4.0 to 7.0%, respectively, for the Ni-Al-Co system. Cold-drawing caused a significant increase in _y and _f and the values attained were about 1850 and 2500 MPa, respectively, for Ni-20Al-30Fe and Ni-25Al-30Co wires drawn to about 90% reduction in area. The high strengths, large elongation and good cold-workability of the melt-quenched and+ compound wires have been inferred to be due to the structural change into a low-degree ordered state containing a high density of phase boundaries, suppression of grain-boundary segregation and refinement of grain size.     

MOCVD of highly conductive CdO thin films

Thin films of cadmium oxide have been deposited onto alumino–silicate glass substrates by atmospheric pressure metal organic chemical vapor deposition using DMCd and n-butanol, a novel oxygen source. Studies were conducted to evaluate how different conditions such as temperature and precursor concentration influenced the film growth. Film characterization showed that at an optimum temperature range of 270–290 °C, CdO exhibits low spreading resistance of 17.1 per square, for a 400 nm film, compared with 10 per square for 1.1 m indium tin oxide film, and high transmittance, between 600 and 900 nm, up to 90% with a band gap of 2.4 eV. Within this optimum temperature range, the grain size and surface roughness are shown to be a minimum.