Thermodynamic properties of antiferromagnetic superconductors containing nonmagnetic,magnetic, and spin-orbit impurities

Effects of all types of impurities (nonmagnetic, magnetic, and spin-orbit) on an antiferromagnetic superconductor (AFSC) have been investigated by studying the transition temperatureT _c and the specific heat jump. We have assumed a one-dimensional electron band. The impurity scattering is treated within the self-consistent Born approximation. We find that: (a) the molecular fieldH _Q and the magnetic impurities depress superconductivity of AFSC and their pair-breaking effect is additive; (b) the effect of spin-orbit impurities is the same as that of nonmagnetic impurities—these enhance superconductivity by screening the molecular field; and (c) in the extreme dirty limit, the AFSC is described in terms of an effective pair-breaking parameter given by 1/_eff=1/₂+H _Q ² where 1/=1/₁+2/3_so(1/₁, 1/₂, and 1/_so, respectively, are the scattering rates from nonmagnetic, magnetic and spin-orbit impurities).     

Alpha irradiated YNi2B2C studied from positron lifetime measurements

For YNi₂B₂C, a typical borocarbide superconductor, we have carried out positron annihilation lifetime measurements, before and after a 40 MeV -irradiation to a fluence of 2X10¹⁶ particles/cm². A 3-lifetime fit, giving improved variance, showed a third lifetime longer than 1 ns and of low (1 to 2%) intensity. This lifetime is due to positronium formation and o-Ps to p-Ps conversion in the porous samples. The irradiation increases the bulk lifetime. B, calculated from ₁ and ₂, from 181 ps to 213 ps.     

Use of adjoint functions in investigations of heat conduction and transfer processes

An examination is made of the use of adjoint functions in heat conduction and convection theory. Formulas of perturbation theory are obtained for steady and unsteady cases, an interpretation of the physical meaning of adjoint temperature is given, and some applications of the theory are discussed.Notation (r,) thermal conductivity - t(r,) temperature - t *(r,) adjoint temperature - q_V(r,) density of heat release sources - p(r,) a parameter of adjoint equation - r generalized coordinate - time - (r_s, ) heat transfer coefficient - I linear functional of temperature - (r,;r₀,₀) and *(r,; r₀,₀) Green's function for t(r, ) and t *(r, ) - C(r,) volume specific heat - W(r, ) vector distribution of flow velocities - V, S volume and surface areas of body - R radius of HRE - r, radial and angular coordinates - F_in, F_out inlet and outlet flow areas of channel     

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.     

Inhomogeneous shear flows of linear polymers

Solutions of a system of equations of nonlinear viscoelastic fluid motion describing inhomogeneous shear flows of linear polymers are indicated.Notation _ij stress tensor - p pressure - F_i mass force vector - _ij Kronecker delta - coefficient of shear viscosity - relaxation time - _ij inner parameter - _ij=vi/x_j velocity gradient tensor - ₀ initial value of the shear viscosity coefficient - ₀ initial value of the relaxation time - D dimensionless first invariant of the additional stress tensor - A, B, C constants of integration - f(D) universal function characterizing the material - r, , z cylindrical coordinates - u=v_z axial component of the velocity vector - v=v circumferential component of the velocity vector - ₁, ₂ first and second differences of the normal stress - Q volume mass flow rate - R radius of a circular tube - R₁, R₂ radii of the inner and outer cylinders, respectively - M moment per unit length Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 41, No. 3, pp. 449–456, September, 1981.     

The critical curve in an antiferromagnetic superconductor with nonmagnetic impurities

The critical curve of a transition of the second kind in an antiferromagnetic superconductor (AFS) with nonmagnetic impurities has been studied. The AFS is described by using the mean-field model given by Nass, Levin, and Grest and assuming a one-dimensional electron band. We find that the points on the critical curve satisfy the thermodynamic stability condition for 0₁/₀5.04 and 0.49H_Q/₀1.64.Here ₁ is the inverse lifetime of a conduction electron for nonmagnetic impurity scattering,H _Q is the antiferromagnetic molecular field, ₀ is the zero-temperature order parameter of a superconductor in the absence ofH _Q and impurities. Further, ₁ and H_Q denote the values of these quantities for points on the critical curve. For ₁/₀>5.04 and H_Q/₀>1.64, the phase transition from the superconducting to the normal state is always of the second kind. Some thermal properties of the system near the critical curve have also been investigated and we find that these depends dramatically on the impurity concentration.     

Microscopic elastic limit of disperse-hardened condensed Cu-Mo materials

The concentration dependence of the microscopic elastic limit _s of vacuum Cu-Mo condensates before and after thermomechanical treatment is investigated. The value of _s was determined by the method of freely damping torsional oscillations. It is demonstrated that the relationship between the _s of the condensates and the molybdenum concentration is expressed by a curve with a maximum in the 2.7–3% Mo interval. It is established as a result of structural investigations that a reduction in _s in Cu-Mo condensates with high molybdenum concentrations is governed by the development of relaxation processes (transition from slip to microtwinning).Translated from Problemy Prochnosti, No. 6, pp. 18–23, June, 1993.     

Thermal conductivity of hydrocarbons in the naphthene group under high pressures

The thermal conductivity of hydrocarbons in the naphthene group has been experimentally determined. An equation is now proposed for calculating the thermal conductivity over the given temperature and pressure ranges.Notation thermal conductivity - ₂₀ and ₃₀ values of the thermal conductivity at 20 and 30°C, respectively - t₀,P₀ thermal conductivity at t₀, p₀ - _t p thermal conductivity at temperature t and under pressure P - change in thermal conductivity - P pressure - P_melt melting pressure - P₀ atmospheric pressure - t₀ 20°C temperature - T, t temperature - T_cr critical temperature - temperature coefficient of thermal conductivity - ₂₀ temperature coefficient of density - density - ₂₀ density at 20°C - _cr critical density - M molar mass - =T/T_cr referred temperature - v specific volume - v₀ specific volume at 20°C - v change in specific volume - _{3 0} a coefficient - B (t) a function of the temperature - S a quadratic functional - W_i, weight of the i-th experimental point - _i error of the i-th experimental value of thermal conductivity - B _{y, =0.6} value of B (t) at T = 0.6T_cr - B = B (t)/B_{, =0.6} referred value of coefficient B (t) Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 41, No. 3, pp. 491–499, September, 1981.     

Phase transformations in Mn-Al permanent magnet alloys

Phase transformation studies have been made of the Mn-Al alloys with compositions near the equiatomic range with or without small amounts of carbon, copper and nickel, using differential thermal analysis, X-ray diffraction and optical and electron microscopy. The high temperature hexagonal phase obtained by quenching, transforms to the ferromagnetic phase between 500 and 550° C and on further heating transforms back to the hexagonal phase between 750 and 950° C. Also, on controlled cooling of the phase from about 900° C, the ferromagnetic phase is formed between 800 and 670° C. TEM studies have shown the presence of the B19 ordered phase, ferromagnetic phase and Mn₅Al₈ precipitates even in quenched alloys.     

Critical dynamics of a sheared micellar solution

We have investigated the dynamic behavior of a nonionic micellar solution of tetra-ethylene glycoln-decylether (C₁₀ E₄) in water near its critical point in the presence of shear. The non-Newtonian behavior of the viscosity can be represented by * = [ 1 +a(S₄)=]², where* is the viscosity in the absence of shear,S is the shear rate. ₄ is the lifetime of the critical Iluctuations,a is a system-dependent constant, and = 0.02 In addition, we have found that, before attaining a steady state, the sheared mixture undergoing phase separation shows significant shear-dependent rheological effects due to the presence of concentration domains.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24. 1994, Boulder, Colorado, U.S.A.     

The transverse acoustic impedance of dilute solutions of3He in superfluid4He

The transverse acoustic impedanceZ=R–iX of dilute solutions of³He in superfluid⁴He has been measured at a frequency (/2) of 20.5 MHz at temperaturesT from 30 mK to the transition at T. The³He concentrations studied werec=0.014, 0.031, 0.053, 0.060, and 0.092 below 1 K, thoughc decreased slightly near the point. The impedance was found from the temperature dependence of the quality factor and the resonant frequency of anAT-cut quartz crystal resonator immersed in the liquid. Below 1 K,Z is due to the Fermi gas of³He quasiparticles, and in the collisionless limit, 1 ( is a relaxation time),R remains constant whileX goes to zero. Measurements ofR(c, T) andX(c, T) were analyzed to determine the momentum accommodation coefficient (c, T) and (c, T). The relaxation times were in good agreement with previous work, while (c, T) was independent ofc, but increased from 0.29±0.03 below 0.1 K to 1.0±0.1 above 0.8 K. Various mechanisms are suggested to explain this. Between 1.0 and 1.5 K the³He quasiparticles and the thermally excited rotons are in the hydrodynamic region, 1. Values of the total viscosity (c, T) were obtained and analyzed to give the³He gas viscosity and the³He-³He and roton-³He scattering rates, both of which were energy-dependent. The superfluid healing length a was also measured. Near the point we founda=(0.1±0.03)^–2/3 nm, where =1–T/T, proportional to the phase coherence length . Our data are consistent with the hypothesis that _s/T is a universal constant for superfluid dilute solutions, where _s is the superfluid density. Between 1.0 and 1.8 K we found thata(c, T) was comparable to measurements in³He-⁴He films.     

A finite volume technique to simulate the flow of a viscoelastic fluid

Hydrodynamically developing flow of Oldroyd B fluid in the planar die entrance region has been investigated numerically using SIMPLER algorithm in a non-uniform staggered grid system. It has been shown that for constant values of the Reynolds number, the entrance length increases as the Weissenberg number increases. For small Reynolds number flows the center line velocity distribution exhibit overshoot near the inlet, which seems to be related to the occurrence of numerical breakdown at small values of the limiting Weissenberg number than those for large Reynolds number flows. The distributions of the first normal stress difference display clearly the development of the flow characteristics from extensional flow to shear flow.List of symbols D rate of strain tensor - L slit halfheight - P pressure, indeterminate part of the Cauchy stress tensor - R the Reynolds number - t time - U average velocity in the slit - u velocity vector - u,v velocity components - W the Weissenberg number based on the difference between stress relaxation time and retardation time - W ₁ the Weissenberg number based on stress relaxation time - x,y rectangular Cartesian coordinates - ratio of retardation time to stress relaxation time - zero-shear-rate viscosity, ₁ + ₂ - ₁ non-Newtonian contribution to - ₂ Newtonian contribution to - ₁ stress relaxation time - ₂ retardation time - density - (, , ) xx, yy and xy components of ₁, respectively - determinate part of the Cauchy stress tensor - ₁ non-Newtonian contribution to - ₂ Newtonian contribution to      

New manifestations of the Josephson effect in helium

Using a method due to Bloch, it is shown that in thermodynamic equilibrium an annular container of mean radiusR, massM, containingN atoms of helium II of massm each will, when subjected to a torque , evince oscillations in its angular acceleration about the classical value. The frequency, , of these oscillations is given by /m=/(M+Nm). The difficulty of achieving equilibrium is pointed out.Supported in part by US Air Force Office of Scientific Research through Grant No. AFOSR 565-66.     

Fluctuation conductivity in a superconducting proximity sandwich

The fluctuation conductivity above the transition temperatureT _c is calculated in a superconducting proximity sandwich containing magnetic impurities. The calculations are carried out in the framework of the Kaiser-Zuckermann theory based on the McMillan tunneling model, under the condition _S,N T _c1, where _S,N are the lifetimes of electrons associated with the tunneling process. The role of the proximity effect is to suppress the fluctuation conductivity by renormalizing the coefficients of the Aslamazov-Larkin and Maki-Thompson terms, and the third term. On the other hand, magnetic impurities affect mostly the Maki-Thompson contribution via the pair-breaking parameter, which is derived as a quantity depending on _S,N, the spin-flip lifetime, and temperature.Financial support provided by the Post-Doctoral Fellowship Commission in Science and Engineering Research Laboratory, Waseda University.     

Nonlinear axisymmetric response of orthotropic thin truncated conical and spherical caps

Summary An approximate analytical solution of the large deflection axisymmetric response of polar orthotropic thin truncated conical and spherical shallow caps is presented. Donnell type equations are employed. The deflection is approximated by a one term mode shape satisfying the boundary conditions. The Galerkin's method is used to get the governing equation for the deflection at the hole. Nonlinear free vibration response and the response under uniformly distributed static and step function loads are obtained. The effect of various parameters is investigated.Notations A, A ^* Inward and outward amplitudes - a, b, h Base radius, inner radius and thickness of the cap - D M h ³/[12(–v ² )] - E ,E Young's moduli - H ^*,H Apex height, dimensionless apex heght:H ^*/h - N _, Stress resultants - p ^1/2 - q Uniformly distributed load - Q,Q₀ Dimensionless load: , dimensionless step load - Q, Q ₀ Dimensionless load: , step load - t, Time, dimensionless time: t - T _A Ratio of nonlinear periodT for inward amplitudeA and the linear periodT _L - w ^* Normal displacement at middle surface - w Dimensionless displacement:w ^*/h - ₁ Linear parameter of static response - Orthotropic Parameter:E /E - Mass density - ₂,₃ Quadratic and cubic nonlinearity parameters - b/a - v ,v Poisson's ratios - Dimensionless radius:r/a - ^*, Stress function, dimensionless stress function: - ₀ ^* ,₀ Linnear frequency, dimensionless frequency: With 7 Figures     

Transport in the low-temperature limit of a Landau Fermi liquid

The Boltzmann equation for Landau quasiparticles is solved for T 0 by a specialization of a method discussed by Sykes and Brooker. The quasiparticle distribution function is expanded in Legendre polynomials, assuming a boundary condition which imposes axial symmetry, and even-order terms are assumed to relax together with relaxation time _e , odd-order terms with relaxation time _o . By letting wavelength , with finite, one obtains a first-sound solution, and by lettingT 0, and then , one obtains a zero-sound solution. When these solutions are used to calculate the pressure, it is found that the first-sound solution is consistent with hydrodynamics, exhibiting viscosity = _s , while the zero-sound velocityc ₁=[^–1(B₁+4/3_s)]^1/2, so that phenomenologically zero-sound propagates like a longitudinal elastic wave in a glass. A higher zero-sound mode is also predicted, but is heavily damped. The heat flux is calculated and found to obey Vernotte's equation, which contains an intertial term, added to Fourier's law, that becomes significant asT 0.     

Experimental study of electric field influence on low-temperature,long-time relaxation in crystalline ferroelectrics

Calorimetric measurements with polycrystalline Pb_0.915La_0.085. (Zr_0.65Ti_0.35)O₃ were performed at liquid helium temperatures in an electric fieldE (0E4.3 kV/cm). Heat released after cooling fromT ₁ (1.3 K<T ₁35 K) toT ₀=1.3 K is very similar to that in amorphous metals and dielectrics. Experimental results disagree with the standard tunneling model. The observed heat release may be explained assuming the existence of a maximum energy _f in the distribution function. The maximum relaxation time _max was found as a function ofT ₁. A similar heat release is observed after switching on or off the electric field, independent ofT for 1.1 KT3 K, proportional toE ² with _maxE. No heat release was observed in the KH₂PO₄ single crystal.On leave of absence from the Technical University, Dresden, German Democratic Republic.On leave of absence from the Institute of Physics, Czechoslovak Academy of Sciences, Prague, Czechoslovakia.On leave of absence from the Central Institute for Solid State Physics and Material Research, Dresden, German Democratic Republic.     

Pulse determination of thermal diffusivity and thermal conductivity for hemispherical specimens: nickel

A method is described for determining the thermal diffusivity, specific heat, and thermal conductivity in a hemispherical volume on the basis of duration of the reference signal.Notation r radius - R radius - r dimensionless coordinate - dimensionless temperature - time - _i duration of heat pulse - _1/2 time for temperature signal at r to attain half the maximum value - q_o amount of heat - a thermal diffusivity - thermal conductivity - density - c_p heat capacity Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 5, pp. 864–869, May, 1981.     

Strength of the pyroceram So115M under lengthy static loading

The article presents the results of long-time strength tests of the casting pyroceram SO115M at room temperature by the method of three-point bending. We obtained the power dependence of the time to failure _f on the applied load : _f ^–11.7.Translated from Problemy Prochnosti, No. 1, pp. 102–104, January, 1996.     

Effects of alloying in the dilute limit on the quantum states of electrons in magnesium

The electron quantum interference phenomenon was used to determine the effects of substitutional alloying upon the quantum-state lifetime and band gapsE _g at the Fermi energy in single crystals of pure Mg. Vapor-grown alloys containing either Zn or Cd in concentrationsC0.3–15 ppm were studied. The magnetic field dependence of the interference oscillation amplitudes for these samples indicates reductions in and significant increases inE _g relative to pure Mg (impurity concentration 10^–8). Within experimental accuracy the observed quantum-state lifetime satisfies the relation ^–1=C, with 2.7×10¹⁰ sec^–1 per ppm of Cd and 2×10¹¹ sec^–1 per ppm of Zn. The band gap corresponding to Bragg reflection from the (0001) plane of the hcp structure (which in pure Mg arises solely from spin-orbit coupling) was found to increase by more than a factor of two upon the addition of only 10 ppm Cd to Mg. These results are discussed within the framework of the pseudopotential theory of alloying. It is shown that there are discrepancies of more than three orders of magnitude between the experimental and theoretical values forE _g and of about one order of magnitude for in these dilute-limit alloys.Work supported by the National Science Foundation.Submitted to the Department of Physics, the University of Chicago in partial fulfillment of the requirements for the degree of Doctor of Philosophy.Fannie and John Hertz Foundation Fellow.