Flux motion in anisotropic type-II superconductors nearH c 2 with arbitrary vortex orientation

Flux motion in anisotropic type-II superconductors near H_{c 2} is studied in the framework of the time-dependent Ginzburg-Landau (TDGL) theory for the case that the average flux densityB is oriented in an arbitrary direction relative to the principal axes of the sample. The linearized TDGL equation for a uniformly translating order parameter is solved and expressions for all elements of the flux-flow resistivity tensor _ij (including the off-diagonal Hall elements) are obtained. The diagonal elements _ii show the angular scaling property that _ii(B) = _ii(B/H_{c 2}(, ø)), whereas the Hall elements _ij (i j) have additional angular dependences that are not contained in H_c2. For the case that the normal state Hall elements _ij ⁽ⁿ⁾ B _k with i j k, the ratios _ij/ _ij ⁽ⁿ⁾ are functions of B/H_c2 (, ) only.     

Method for heat transfer calculation using isothermal coordinates

Equations for steady-state heat transfer are considered in curvilinear coordinates. The equations are shown to be simplest when one of the families of coordinates are isotherms. Conditions are obtained for which these coordinate systems and some exact solutions of the heat conduction equations must satisfy.Notation a ₁, a₂, ..., a_n coefficients determining the temperature dependence of thermal conductivity (see formula (8)) - f() function of the -coordinate (see formula (4)) - H ₁,H ₂,H ₃ coefficients of the first differential form (Lamé coefficients) (see formula (2)) - n number of a term of the series in formula (8) - q heat flux - Q power of volume heat release - x, y, z Cartesian coordinates - , , general curvilinear orthogonal coordinates - ₁, ₂ coordinates of the boundary surfaces on which the temperatures are prescribed - x ₀₁ thermal conductivity att=0 - () function of the -coordinate (see formula (4)) - () -function determining temperature distribution in the case of constant heat flux along the coordinate lines Scientific-Research and Design-Technological Institute of Machine Manufacture, Scientific-Production Subbranch Novator, Kramatorsk, Ukraine. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 68, No. 4, pp. 651–659, July–August, 1995.     

Interpretation of Hall effect measurements in nonuniform magnetic fields

The interpretation of Hall effect data obtained with a long thin-film transducer of width a is discussed; the size of Hall probe contact pad and the characteristic dimension of the magnetic field nonuniformity are and l _n respectively. A diagram of local sensitivity of the transducer to the magnetic field has been plotted for l _i and a. Several particular examples of Hall emf measurement in a nonuniform magnetic field are considered.Translated from Izmeritel'naya Tekhnika No. 4, pp. 41–43, April, 1994.The author is grateful to V. B. Sandomirskii for proposing the problem and to A. A. Sukhanov and P. S. Sul'zhenko for a discussion of this work.     

Anisotropic Electrical Transport in MgB2 Single Crystals

We report on study of transport properties of MgB₂ single crystals. The normal state resistivity has been found to be anisotropic with resistivity ratio _c / _ab =3.5. In agreement with the results of band structure calculations the normal state Hall effect measurements with H//ab-planes and H//c-axis show two type carrier behavior. Below T _c, the in-plane as well as the out-of-plane Hall resistivity, _xy and _zx , display no sign change anomaly. Furthermore, both _xy and _zx have been found to scale with corresponding longitudinal resistivity with the same exponent =1.5.     

Spin hydrodynamic equations with external disturbances and suitable Green's functions for superfluid3He-B. New onsager relations

The spin hydrodynamic equations for superfluid³He-B have been obtained for the case of external, time-dependent fields. On the basis of a microscopic approach, expressions are found for additional terms in equations containing these fields. Considering the linear response of the system to the switching on of external fields, formulas are found for suitable Green's functions (magnetization-magnetization, rotation-rotation, magnetization-rotation, rotation-magnetization). The rotation-rotation Green's function has the 1/q ² singularity characteristic of superfluid systems. Connections between Green's functions lead to relations among kinetic coefficients v, ₁, and ₂. It is also shown that there is a conserved quantityQ ^(B) = div v _s ^(B) that describes sources or magnetic type charges (monopoles) of the superfluid velocity v _s ^(B) . Comparison with the phenomenological approach suggests thatQ ^(B) is proportional to a pseudoscalar giving the projection of the spin density onto the vector describing the axis of rotation.     

Observation of Hall Scaling in MgB2 Thin Films

We have measured the Hall resistivity, _xy , and the longitudinal resistivity, _xx , in superconducting MgB₂ thin films in a mixed-state while changing the magnetic field and the current density. A Hall scaling behavior without the anomalous Hall effect was observed with a exponent of 2.0±0.1 in _xy =A _xx . This exponent is observed to be constant, i.e., independent of magnetic field, temperature, and current density.     

Nonlinear Response of a Continuous Wave NMR Spectrometer for Samples with a Large Magnetization

We present a new insight in the response of a CW NMR spectrometer for highly magnetized samples above 100 MHz. The spectrometer is a bridge made of a magic T. The output of the bridge is proportional to the reflection coefficient, , of a resonant circuit, which is built with a coil containing the sample. The sensitivity of the reflection coefficient to the complex susceptibility of the sample, () = () – j(), depends on the quality factor, Q, of the circuit and filling factor, . When the condition Q 1 is not fulfilled, we show indeed that the use of a simple crystal detector, which is only sensitive to || gives rise to a strong nonlinear response of the spectrometer. Measurements of the complex value of by means of phase sensitive detection allow to recover a linear behavior. We discuss and illustrate those issues with a few circuits we designed for our measurements on liquid ³ He with spin polarizations up to 15 %. A method is described to build in a reproducible and predictable way resonant circuits matched to 50 in the frequency range 100 – 400 MHz with a quality factor as high as 1000 at 4 K.     

Angular variation of coercivity of interacting fine acicular skeleton particles

For fine, acicular skeleton particles of -Fe prepared from -FeOOH, the effect of interparticle interaction on the angular variation ofH _c was numerically investigated using a direct expansion scheme of the chain-of-spheres fanning model to an interacting chain system forming an orthorhombic type of regular space lattice. The model theory reveals that only magnetostatic lateral interchain interaction can affect the angular variation ofH _c. The results have been used to explain the experimentally observed effects of particle morphology and packing fraction on the angular variation ofH _c in systems made from fine acicular particles prepared for audio/video magnetic recording media. It is suggested that a local aggregate of the so-called multiple type, is unavoidably generated in the system.     

The Interplay of Electronic and Nuclear Magnetism in PtFe x at Milli-, Micro-, and Nanokelvin Temperatures

We have measured ac susceptibility, nuclear magnetic resonance, and nuclear heat capacity of two PtFe _x samples with concentrations of magnetic impurities x = 11 ppm and 41 ppm at magnetic fields (0 ± 0.05) mTB248 mT. The susceptibility data have been measured at temperatures of 0.3 KT100 mK, no hint for nuclear magnetic ordering could be detected to a temperature of 0.3 K. The nuclear heat capacity data taken at 1.4 KT10 mK show enhanced values which scale with x at low polarization. This effect is described by a model assuming an internal magnetic field caused by the impurities. No indication for nuclear magnetic ordering could be detected to 1.4 K. The nuclear magnetic resonance experiments have been performed on these samples at 0.8 KT0.5 mK and 2.5 mTB22.8 mT as well as on three other samples with x = 5, 10, 31 ppm in a different setup at 40 KT0.5 mK and at 5.4 mTB200 mT. Spin-lattice and effective spin-spin relaxation times ₁and ₂ ^* of ¹⁹⁵ Pt strongly depend on x and on the external magnetic field. No temperature dependence of ₁and ₂ ^* could be detected and the NMR data, too, give no hint for nuclear magnetic ordering to 0.8 K.     

Nucleate boiling

The study deals with the effect of the surface conditions on the nucleate boiling curve. A relation is proposed which describes the complete nucleate boiling curve.Notation q thermal flux - q* thermal flux at which the liquid boils after one-phase convection - q_c thermal flux during one-phase convection - q_cr1, q_cr2 first and the second critical thermal flux - T saturation temperature - T superheat of the heating surface relative to the saturation temperature - T* superheat prior to boiling of the liquid after one-phase convection - T_cr1 superheat during the first boiling crisis - T_cr3min minimum superheat at which the third boiling crisis can occur - P pressure - P_cr critical pressure - heat transfer coefficient during nucleate boiling - R_cr radius of a critical vapor forming nucleus - coefficient of surface tension - r latent heat of evaporation - thermal conductivity of the liquid - kinematic viscosity of the liquid - , densities of the liquid and the vapor - g gravitational constant - k Boltzmann constant - N Avogadro number - h Planck's constant Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 3, pp. 394–401, March, 1981.     

Microstructure refinement with forced convection in aluminium and superalloys

The cooling and average local solidification times were determined for slow solidifiation of Al-4.4 wt% Cu alloy under natural convection and under electromagnetically forced axisymmetric rotation during liquid cooling and solidification in graphite moulds. Cooling rates were measured within situ thermocouples. The conditions needed to stabilize the radial temperature gradient with rotation were established. The microstructure size decreased with increasing rotation, as did the local solidification times. The average grain and dendrite size without imposed rotation is coarser near the mould wall compared with the centre of the casting. This trend is reversed with imposed rotation. Rotation also led to a smaller spread of grain and dendrite size at any chosen height of the casting. These results are discussed in relation to existing theories, and several reasons for an improved heat transfer coefficient with rotation are presented. Forced convective solidification was then carried out for various shapes of integral investment cast Nimonic-90 alloy solidifying under modified conditions that prevented columnar grain formation. Similar results to those recorded for the aluminium case were obtained and are presented here. The major conclusion is that observations indicating a reduction of microstructure spacing during forced convection should also consider improved heat extraction at the mould-metal interface.List of symbols Gr Grashof number =gTZ ^{3 3}/ ³ - g _r acceleration in radial direction - g acceleration in direction - g _z acceleration inZ direction (gravity) - h heat transfer coefficient - k _l thermal conductivity of liquid - Nu _z Nusselt number =hZ/k _l - Pr Prandtl number =/ - Ra Rayleigh numberGr Pr - R radius of mould - Re _r Reynolds number =V ₀ R/ - T temperature - T temperature difference in radial direction - Ta Taylor number = ²4H ⁴ W ²/ ² - V velocity - W r.p.m. - thermal diffusivity - coefficient of volume expansion - viscosity - density Mr G. S. Reddy is also a post graduate student registered at the Banaras Hindu University, Varanasi, India.     

Intensity of critical opalescence of helium-4

We present measurements of the critical opalescence of helium-4. The results are analyzed by the Einstein and Ornstein-Zernike theory and the power laws. We obtain ==1.17±0.02, ==0.62±0.1,/=4.5±0.3,P _c =1706.008 mm Hg, andT _c =5,189.863 mK (T ₅₈ ). The critical behavior of helium-4 is almost the same as that of classical fluids and the influence of the quantum nature of helium-4 is not as evident as has been claimed.     

Some observations on the deformation characteristics of bulk polycrystalline zirconium hydrides

The deformation behaviour of bulk polycrystalline zirconium hydrides in the composition range ZrH_1.27 to ZrH_1.66 has been investigated by compressive loading at temperatures between room temperature and 500° C. Single-phase -zirconium hydride is brittle below 100° C. Analyses of slip traces on specimens deformed at temperatures between 100 and 250° C have shown that the glide planes are {111} types. The deformation characteristics of and ( + ) alloys at temperatures between 100 and 500° C are consistent with the hydrogen vacancies in the -phase providing significant lattice friction to the movement of dislocations in the zirconium lattice of the hydride structure. The room temperature fracture stress of ( + ) alloys increases with the volume fraction of the -phase and this can be related to the resistance offered by platelets to the propagation of cleavage cracks in the matrix. In a ( + + ) alloy the resistance to crack propagation at room temperature is further increased by the soft -zirconium phase.     

A gradient method of defining smooth solutions to inverse boundary-value problems in thermal conduction

An iterative algorithm is described for solving boundary-value inverse problems in thermal conduction by steepest descent, which utilizes information on the smoothness of the solution.Notation A, B linear operators - u element of solution space U - f exact reference data - f reference data uncertainty - value of reference data uncertainty - A^–1 inverse operator - u^(k)() k-th derivative of function u - _m length of observation interval - _i(t) polynomials of degree i–1 - A^*, B^*, L^* operators conjugate to the operators A, B, L - Jg discrepancy functional gradient - _n descent step along the discrepancy antigradient for the n-th iteration - K( –) kernel of integral equation - q() heat flux - T() measured temperature inside body Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 2, pp. 259–263, August, 1980.     

Magnetic penetration depth measurements with the microstrip resonator technique

The microstrip resonator technique is a convenient way to sensitively measure the temperature dependence of the magnetic penetration depth (T) in superconducting thin films. Because the method relies on measuring the resonant frequency of a high-Q transmission line resonator at microwave frequencies, one can very precisely measure small changes in (T). This technique is applied to studying the low-temperature dependence of (T), since that is in principle a measure of the low-lying pair-breaking excitations of the superconductor. We find that the penetration depth in niobium films is consistent with the predictions of weak coupled BCS theory. The low-temperature dependence of (T) inc-axis YBa₂Cu₃O_7– films can be interpreted as either a weak exponential or as a power law. In addition, the measured value of (0) is found to be strongly dependent on the form of the temperature dependence for (T) used in fitting the data. Best fits over the entire temperature range are obtained with a BCS temperature dependence having values for 2(0)/k _BT_c strictly less than 3.5, consistent with our measurements of the temperature dependence of (T) at low temperatures in YBa₂Cu₃O_7– .     

Spectral shape dependence in the very strong coupling regime of Eliashberg theory

The effect of ² F() shape dependence on several physical properties of superconductors is studied at various values of the strong coupling indexT _c/ _ln . Our results indicate that the degree of shape dependence of each property is sensitive to the value ofT _c/ _ln . Generally, for the region we examine, 0.25T _c/ _ln 1.3, the dependence on shape is found to be higher than in the conventional strong coupling regimeT _c/ _ln 0.2. However, with the exception of the mass enhancement parameter , the amount of shape dependence does not increase steadily withT _c/ _ln and there appears to be regions of maximum shape sensitivity.     

Instability of the Critical State in NdBa2Cu3O7−δ Single Crystals

Instabilities of the critical state are observed in various NdBa ₂ Cu ₃ O _7– single crystals by means of direct magneto-optic (MO) imaging while warming up flux states containing vortices of opposite polarity. Using the same samples as in the MO investigations, we observe for the first time characteristic steps in the integral magnetization measured by means of a SQUID system, which allows a constant temperature sweep. The integral measurement technique enables the study of the instability phenomenon (turbulence) in a much wider range of temperatures and fields than the MO investigations, and also in the orientations H _a c and H _a c. As a result, we find turbulence not only in a narrow window of temperatures (65 T 80 K), but also in a window of applied negative fields ranging between 30 and 80 mT.     

Spatial Evolution of High Frequency Phonons in Superfluid 4He from a Pulse-Heated Metal Film

An almost monochromatic spectrum of high frequency (/k _B 10 K) phonons in superfluid ⁴ He is created by a short ( 0.1s) pulse of Joule-heating in a metal film submerged in the liquid at saturated vapour pressure (svp). These phonons have lifetimes that tend to infinity as T 0, and are the ones effective in quantum evaporation experiments. Most of these high frequency (hf) phonons are not injected into the liquid ⁴ He across the metal—liquid interface, but are created in the liquid by energy-increasing interactions which begin with the injected phonons of much lower energy (/k _B 1 K). These hf phonons are created up to 5 millimetres in front of the heater, hence the time of flight from a heater to a detector only gives an approximate value (lower bound) of their energies. Here we present measurements at svp of phonon energy fluxes in liquid ⁴ He at various distances from a pulse-heated metal film. Analysis of these signals gives an improved determination of the hf phonon spectrum (peaked at 10.20 ± 0.05 K with HWHM 0.2 K on the high energy side).     

Transient heat conduction in hollow spheres with a moving inner boundary

The finite integral transform method is used to obtain the solution of unsteady heat conduction problems for a hollow sphere with a moving internal boundary and various boundary conditions at the outer surface. For the solution of the problems of interest integral transform formulas are presented with kernels (16), (20), and (24) and the corresponding inversion formulas (18), (22), (26), (29) and characteristic equations (17), (21), (25), (28), (31), (33).Nomenclature a, thermal diffusivity and conductivity - t temperature of phase transformation - density - heat transfer coefficient - Q total quantity of heat passing through inner boundary - F latent heat of phase transformation - Fo(1,)=a/R ₁ ² , Fo(i,)=/r _i ² , Fo(i, _i)=a _i/r _i ² Fourier numbers - Bi₂=R₂/ Biot number