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).     

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     

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.     

Loss of stress equivalence in solid-solution hardening

Available data on the temperature, T, and concentration, c, dependence of the critical resolved shear stress, , of numerous copper- and silver-based solid solutions have been examined with special reference to the stress equivalence of solid-solution hardening, i.e. a common single curve for all alloy concentrations and solute types in a correlation of =(78)–(298) with (78), as first demonstrated by Basinski et al. in 1972. For solid solutions based on a given solvent metal, the stress equivalence is lost if the value of exponent r in the relation (T) c^r varies with temperature. The critical concentration of the solute at which stress equivalence of solid-solution hardening is lost depends on the alloy system.     

Plasma Resonance of the Wigner Solid on the Free Surface of Normal and Superfluid 3He

The Wigner solid on liquid ³ He is used as a sensitive probe for the study of the surface dynamics. We have experimentally investigated the behavior of optical coupled plasmon-ripplon (CPR) resonances for temperatures down to 0.4 mK. We have used a linewidth of CPR resonance f for getting = (2f)^–l, the collision time in the scattering of surface electrons from the surface roughness. The collision time is in good agreement with single-electron-ripplon scattering theory down to 30 mK, while below 30 mK the collision time deviates from the theory, and at 1 mK experimental value of is one order of magnitude longer than the theoretically predicted one.     

Structure and decomposition behaviour of rapidly solidified AI-Cu-Li-Mg-Zr alloys

The microstructural characteristics of AI-Cu-Li-Mg-Zr alloys have been studied after rapid solidification by melt spinning and after subsequent annealing at temperatures in the range 160 to 500°C, by using a combination of optical microscopy, scanning and transmission electron microscopy, X-ray diffraction, differential scanning calorimetry and microhardness measurements. The as-melt-spun alloys consist of a cellular microstructure with fine scale precipitates and icosahedral particles distributed within the cells and at cell boundaries. The icosahedral structure is equivalent to the T₂ phase reported by Hardy and Silcock. Annealing the melt-spun alloys leads to a complex precipitation sequence: + I + + I + S + + I + + T₁ + T₂ (bcc) + two other phases. The icosahedral particles coarsen progressively during annealing, especially at higher annealing temperatures. Fine-scale precipitates grow during annealing at low temperature, dissolve at higher annealing temperatures below 500°C, and then reprecipitate during cooling after annealing at 500°C. During annealing at low temperature, plates of and S precipitate and then dissolve, providing solute atoms for icosahedral particle growth. Stable T₁, T₂ (bcc) and two other phases precipitate after decomposition of the icosahedral particles during annealing at 500°C.     

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.     

Motion of a thermal wave front in a nonlinear medium with absorption

We study the evolution of a thermal perturbation in a nonlinear medium whose thermal conductivity depends on the temperature and the temperature gradient according to a power law.Notation u temperature - k coefficient of thermal conductivity - t time - x spatial variable - x₊ a point on the thermal wave front - a ² generalized coefficient of thermal diffusivity - , , , and s parameters of the process - (x^s) Dirac delta-function - B[, ] a beta function - v(, x), (t) auxiliary functions - A, C, T_o, T_m, T*, R, r, p, and _m constants and parameters Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 4, pp. 728–731, October, 1980.     

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      

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.     

Rubber toughening of plastics

Creep measurements were made on a series of six ABS blends containing 0 to 20 vol% of 80m glass beads. At small strains, the beads raised the modulus of the ABS. However, debonding of the polymer from the glass resulted in a rapid drop in modulus with increasing strain and bead content, and at strains above 1.0% the order of stiffnesses was reversed. Debonding resulted in an increase in creep rate with, as measured by the time to reach 1% volume strain. Plots of In ^–1 against applied stress were linear, in accordance with the Eyring equation, and provided data for comparing stress concentration factors. The relationship between and fitted approximately to the Ishai Cohen effective area model. It is concluded that debonded glass beads accelerate multiple crazing by increasing average stresses in the ABS matrix, and in that respect resemble rubber particles. However, unlike rubber particles, debonded beads drastically reduce notched Charpy impact strength.     

Plasticity of lead single crystals in the superconducting and normal states at 4.2K

The flow stress increment _SN associated with a superconducting-normal phase transition has been studied as a function of deformation and strain rate for several lead single crystals at 4.2 K. In the linear work hardening range, the total applied stress _S determines the size of _SN. The dislocation inertial model recently proposed by Granato for the enhanced plasticity of the superconducting state is evaluated in detail with respect to the dependence of _SN on the distance between obstacles to dislocation movement. Reasonable agreement between theory and experimental results is obtained for the linear work hardening range, if it is assumed that the obstacles are forest dislocations. For the normal-state electronic drag coefficient a valueB _eN1.1×10^–4 dyn · sec/cm² is estimated.The experimental part of this work was performed at Materials Science Division, Argonne National Laboratory, Argonne, Illinois, under the auspices of the U.S. Atomic Energy Commission.     

Spin diffusion coefficient of the A and B phases of liquid3He

The spin diffusion coefficient tensors are calculated in the A and B phases of liquid ³ He in the _{L D} <1 regime by using the Kubo formula approach. The spin wave dispersions are also obtained in the presence of diffusive flow of the normal component. The results agree with Combescot's results qualitatively in the _{L D} <1 regime.     

The mechanisms of yield and plastic flow in HgTe and Cd x Hg1−x Te

Single crystals of HgTe and Cd _x Hg_1–x (0.18<x<0.30), oriented for single slip, have been deformed in four-point bending at strain rates 10^–4 sec^–1 and temperatures from –11 to +84° C for HgTe, and 20 to 195° C for Cd _x Hg_1–x Te. At the lowest temperatures, the stress-strain curve exhibits a sharp yield relaxation and subsequent zero work hardening regime, as commonly observed for other semiconductors. Experiments show that the yielding mechanism is that proposed by Johnston and Gilman for LiF. Possible explanations for the post-yield zero work hardening phenomenon are discussed. The influence of composition, temperature and strain rate on the stress-strain behaviour are reported. At 20° C, the upper and lower yield stresses ( _uy and _1y ) increase with increasingx in qualitative agreement with our earlier hardness results. For Cd_0.2Hg_0.8Te, _1y varies with temperature,T, at a strain rate of 10^–4 sec^–1, according to _1y exp (Q/kT) whereQ is 0.16 eV. For HgTe the comparable value is 0.11 eV. Atx=0.25 and constant temperature, _1y depends on strain rate as _1y ^1/n wheren is 4. The stress level for deformation of Cd_0.2Hg_0.8Te at 10^–4 sec^–1 and 20° C is 2–3 kg mm^–2, comparable with that for InSb at 300° C or Si at 1000° C. Strain rate cycling tests on Cd _x Hg_1–x Te give values of activation volumeV* around 10b³ at 20° C, independent of plastic strain (up to 2–3%), suggesting that deformation in these alloys is controlled by the Peierls mechanism, as observed in other II–VI compounds.     

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.     

Dielectric properties of (Ba,Sr)O-(Sm,La)2O3-TiO2 ceramics at microwave frequencies

The dielectric properties of (Ba, Sr)O-(Sm, La)₂O₃-TiO₂ material at microwave frequencies were investigated. By varying the amount of strontium from 0–25 mol% in the 0.15(Ba_1–x Sr _x )O-0.15Sm₂O₃-0.7TiO₂ composition, it was possible to adjust the frequency temperature coefficient, _f, from –13 p.p.m. °C^–1 to + 30 p.p.m. °C^–1. When 7 mol% Sr was substituted for barium, _f=0 p.p.m. °C^–1 was obtained. TiO₂ with rutile phase (_f400 p.p.m. °C^–1) acted as a dominant element in _f variation of the 0.15(Ba_1–x Sr _x )O-0.15(Sm_1–y La _y )₂O₃-0.7TiO₂ (0x0.25, 0y0.6) system. Additionally, increasing the quantity of lanthanum substitution for samarium had a greater positive effect on _f than strontium substitution for barium. When 60 mol% La was substituted for samarium with 7mol% Sr substitution barium, _f of the system reached 95 p.p.m. °C^–1. The effect on microwave dielectric characteristics of the 0.15(Ba_0.93Sr_0.07)O-0.15Sm₂O₃-0.7TiO₂ (BSST) ceramics by varying the calcination and/or sintering conditions or doping additives, were studied. The added SnO₂ acted as a firing agent to lower the sintering temperature, and the dielectricQ(Q _d) value was improved by properly adding CdO. With 1 wt% CdO addition, the highestQ _d value of the BSST resonator, after calcination at 1100 °C/2 h and sintering at 1370 °C/4 h, reached 4180 at 4 GHz with a small _f of –4 p.p.m. °C^–1 and an _r of 80.7 was obtained.     

Numerical calculation of a generalized thermal model of radio-electronic apparatus

A method is proposed for numerical calculation of the temperature field of a generalized model of electronic equipment with high component density.Notation x,y,z,x,y spatial coordinates, m - time, sec - L_x, L_v, L_z dimensions of heated zone, m - _x, _y, _z effective thermal-conductivity coefficients of heated zone, W/m·deg - ₂ thermal conductivity of chassis, W/m·deg - a _z thermal diffusivity of heated zone along z axis, m²/sec - c₁ effective specific heat of heated zone, J/kg·deg - ₁ effective density of heated zone, kg/m³ - c₃, ₃, c₂, ₂ thermophysical characteristics of cooling agent and chassis, J/kg·deg·kg/m³ - q_v(x, ), q(x, y) volume heat-source distribution, W/m³ - q_s (x) surface heat-source distribution, W/m² - p number of cooling agent channels - Fo Fourier number - Bi Biot number - Uⁱ coolant velocity in i-th channel, m/sec - T₁(x, ), T₂(x, ), T₃(x, ) temperature distribution of heated zone, chassis, and coolant, °K - T₃₀, T₁₀(x), T₂₀(x) initial temperatures, °K - T_3in coolant temperature at input to channel, °K - T_T(x) effective temperature distribution of heat loss elements, °K - T_C temperature of external medium, °K - dimensionless heated zone temperature - _v(x) local volume heat exchange coefficient, W/m³·deg - ₁₂(x), _1C(x), _1T(x) heat liberation coefficients - W/m²·sec; ₂₁(x, y), _2c(x, y), _2T(x, y) volume heat-exchange coefficients of chassis with heated zone, medium, and cooling elements, W/m³·deg Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 5, pp. 876–882, May, 1981.     

Low-Frequency Relaxation Rate in the Superconducting YBa2Cu3O6.7

The submillimeter-wave 3 cm ^–1 < < 40 cm ^–1 complex conductivity of the reduced YBa ₂ Cu ₃ O _6.7 film, (T _C =56.5 K) was investigated for temperatures 4 K < T < 300 K. The frequency dependence of the effective quasiparticle scattering rate 1/*() was extracted from the spectra. 1/* is shown to be frequency independent at low frequencies and high temperatures. On decreasing temperature the scattering rate increases with increasing frequencies. Finally, at 6 K it follows a power-law, 1/* ^1.75±0.3.     

Signal rise time of the magnetic bolometer

We present measurements of the temperature dependent signal rise time _S and discuss a model for calculating _S(T). The bolometer consists of a paramagnetic sample and an absorber. The lattice is heated up by absorbing - particles, and the relaxation of the magnetization is measured with a SQUID. With decreasing temperatures _S first increases as ₁1/T, but then decreases strongly. At 30 mK it is reduced by orders of magnitude compared with ₁. This result is in agreement with a theoretical model which takes into account the heat capacities of the lattice, the resonant phonons, the spins, and thermal resistances between these capacities. Under the condition of the bottleneck effect _S is found to be proportional to T³. At low temperatures the lowest values of _S of 2 ms may already be limited by the Kapitza resistance. These are the first measurements of the spin-lattice relaxation times with the energy being transferred from the lattice to the spins.     

Molar momentum and heat transfer

Universal relations governing the molar transfer of momentum and heat are derived on the basis of a hypothesis about the dependence of the boundaries of the molar transfer region on the flow structure and with the use of a special mathematical transformation.Notation u average longitudinal velocity, m/sec - T average temperature, °K - T_w wall temperature, °K - kinematic viscosity coefficient, m²/sec - density, kg/m³ - c_p specific heat, J/kg·K - tangential stress, N/m² - t_w tangential stress at wall, N/m² - q_w specific heat flux at wall, W/m² - u_*=_w/ dynamic velocity, m/sec - *=q_w/c_pu_* characteristic temperature, °K - thickness of boundary layer, m - ₀ thickness of laminar sublayer, m - l = /u transverse space scale of average mole at wall, m - y⁺ = y/l _22C6; dimensionless coordinate - u⁺=u/u* dimensionless velocity - ⁺=(T_w – T)/* dimensionless temperature - ⁺=/_w dimensionless tangential stress - R=In (y⁺/ _o ⁺ )/In (⁺/ _o ⁺ ) generalized dimensionless co-ordinate - U = (u⁺ - u _o ⁺ )/(u _o ⁺ - u _o ⁺ ) generalized dimensionless velocity - Pr Prandtl number Indices * flow parameters evaluated at y⁺=1 - parameters at y⁺=⁺ - 0 parameters at y⁺= _o ⁺ - w parameters at wall Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 41, No. 3, pp. 441–448, September, 1981.