Spatial structure of the superconducting phase in heavy-fermion systems and anomalies in the excitation spectrum

A degenerate superconducting phase in a metal with strong spin-orbital coupling may have a domain structure at low temperatures. The domain walls (of width =v_F/₀) carry a finite density of states N(0)mk _f/² per unit volume, which in turn results in the presence of a linear term T in the electronic specific heatC _e (T). With the help of the Atiyah-Singer theorem, this can be proved for a wide class of domain structures.     

The influence of ageing on the stability of β-γ/γ′ derived microstructures in Ni-Al-Cr-(Co) alloys

Multiphase Ni-Al-(Fe)-(Cr)-(Co)-based intermetallics with (B2)- (A1)/(L1₂), - or - microstructures can exhibit significant room-temperature tensile ductility. In the case of Ni-Al-Cr-based alloys, microstructural development is complicated by the precipitation of -Cr, which can supplant the -phase during ageing of three-phase -/ microstructures. An investigation of the stability, during ageing, of cast Ni-Al-Cr-(Co) alloys with microstructures derived from -/ is reported. In the as-cast condition, the materials investigated consisted of a dendritic matrix containing L1₀ type martensite and interdendritic /. Extensive intra- and interdendritic -Cr precipitation was also observed. The stability during ageing of the interdendritic / microstructure is also considered and transformation of the L1₀ martensite is examined.     

Microstructure of laser melted/rapidly solidified γ/Cr3Si metal silicide “in situ” composites

In order to improve the ductility of Cr₃Si metal silicide alloys, rapidly solidified /Cr₃Si metal silicide in situ composites were fabricated by laser melting/rapid solidification technology using Cr-Si-Ni alloy powders. Microstructure of the /Cr₃Si in situ composites was characterized by OM, SEM, XRD and EDS. The effect of Ni content in the alloy powder on microstructure and hardness of the /Cr₃Si composites was investigated. The /Cr₃Si metal silicide in situ composites have high hardness and rapidly solidified fine microstructure consisting of primary Cr₃Si dendrites and the interdendritic /Cr₃Si eutectics. The volume fraction of the Cr₃Si primary dendrites in the laser melted/rapidly solidified /Cr₃Si metal silicide in situ composites decreases with the increasing nickel content. Because of the presence of the ductile nickel-base solid solution and the rapidly solidified fine microstructure, the /Cr₃Si metal silicide in situ composites are expected to have adequate combination of strength and toughness. The results demonstrate that laser melting/rapid solidification for /Cr₃Si metal silicide in situ composites is a promising toughening method for improving the ductility of Cr₃Si metal silicide alloys.     

Electron diffraction study of superlattices and orientation variants in Ca3SrAl6SO16

Samples having the nominal composition of Ca₃SrAl₆SO₁₆ were sintered at 1380 °C and analysed by electron diffraction. The frequent appearances of forbidden and satellite reflections in this compound imply the presence of a number of basal and nonbasal superlattices so that the microstructure of this cement clinker was characterized by various superstructures including one-, two- and even three-dimensional superstructures along the 0 0 1, 1 1 0, 1 1 2, 1 1 4 or 2 2 1, 0 1 3 and 1 2 3 directions with repeat periods of two or three times of that of basic one, respectively, and intergrowth of these. Various domain structures with 90°, 120° and 48.2°, etc., orientation relationships were also detected in these superstructures and the total number of these orientation variants related to the symmetry elements lost in the process of phase transformation, can be predicted according to the conclusions of Van Tendeloo and Amerlinckx, or they are equal to the number of those unique planes in the matrix.     

Temperature dependence of electrical resistivity of deformed and undeformed V-rich V3Si single crystals

The electrical resistivity (T) of V-rich V₃Si single crystals (T _c-11.4 K) was measured from 4.2 to 300 K along the directions of [1 0 0] and [1 1 1] before and after plastic deformation at 1573 K. Anisotropy of (T) was observed although V₃Si has the cubic A15 structure. Plastic deformation does not affect the normal-state (T) behaviour but changes the normal-superconducting transition width T_c. At low temperatures (T _c<T 40 K), (T) varies approximately as T ⁿ where n-2.5 and this behaviour does not contradict the (0)- phase-diagram plot proposed by Gurvitch, where is the electron-phonon coupling constant and (0) is the residual resistivity.     

Formation of Friction Layers and Wear Resistance of Steels under Conditions of Boundary Friction

We studied the influence of the lubricant compositions Grafitol with 10% graphite (1), Aerol containing 17% MoS₂ (2), Limol containing 60% MoS₂ (3), Limol + 10% chlorine-paraffin (4), and Limol + 10% copper powder (5) on the wear rate and formation of the fine structure of surface friction layers of structural steels. We established a correlation between the tribological characteristics of steels and lubricants. The abrasive wear of 40KhFA steel was minimum if it was lubricated with Limol + 10% copper powder. In this case, its wear was smaller by a factor of 10, 2, 1.25, and 7.25 as compared with lubricant compositions 1–4, respectively. In the course of minimum wear of 40KhFA steel, in the surface friction layers, we observed the minimum values of second-kind distortions (a/a) and of the true size of domains of X-ray coherent scattering (D) as well as the minimum difference between the crystal lattice constants (a) of steel before and after friction.     

Nonequilibrium kinetics of electrons and phonons in superconductors in intense UHF fields

The dependence of the superconducting gap of a thin superconducting film under irradiation by a UHF field is investigated for different values of the amplitude and frequency of the electromagnetic field and arbitrary temperatures. It is shown that the maximal stimulation of superconductivity does not exceed several percent. The distribution functions of nonequilibrium quasiparticles are found for different values of the parameters of the problem. A theoretical investigation of phonon emission from the film under UHF pumping is given. It is shown that in a small spectral interval of frequencies near the double gap value the film does not emit, but absorbs phonons from the substrate. This result is closely related to the stimulation of superconductivity by the UHF field and is due to the effective supercooling of the electron subsystem. The role of heating processes due to inelastic electron-electron collisions, which increase the total number of quasiparticles, is considered and their influence on the kinetics of nonequilibrium electrons and phonon emission is investigated.     

A high-resolution-electron-microscopy study of a γ/γ′-α directionally solidified eutectic alloy

The microstructure of a /- directionally solidified (DS) eutectic alloy with a nominal composition of Ni-30.26Mo-6.08Al-1.43V (wt%) was investigated by means of high-resolution electron microscopy (HREM) and analytical electron microscopy. The -fibres exhibited a typical morphology with a rectangular cross-section and they displayed the Bain orientation relationship (OR) with the / matrix; that is, [001][001] and (110)(010). Misfit dislocations and lattice strain fields existed at the / interface for different habit planes; that is, (110)(010) and (100)(110) were analysed. EDAX (Energy dispersive X-ray) analysis showed that the composition of the -phase was approximately Ni₄(Mo, Al, V); it contained 90° rotational domains of Ni₃(Mo, Al, V) with a DO₂₂ structure and Ni₂(Mo, Al, V) with a Pt₂Mo structure.     

Theory of thermohyperelasticity for near-incompressible elastomers

Summary Elastomers are often used in hot and confining environments in which thermomechanical properties are important. It appears that published constitutive models for elastomers are mostly limited to isothermal conditions. In this study, athermohyperelastic constitutive model for near-incompressible elastomers is formulated in terms of the Helmholtz free energy density . Shear and volume aspects of the deformation are decoupled. Thermomechanical coupling occurs mostly as thermal expansion. Criteria for thermodynamic stability are derived in compact form. As illustration, a particular expression for is presented which represents the thermomechanical counterpart of the conventional two-term incompressible Mooney-Rivlin model. It is used to analyze several adiabatic problems in a rubber rod.List of symbols A _i matrices appearing inD - c _e, _e, c _e specific heat at constant strain - C Cauchy strain tensor - C _R reduced Cauchy strain tensor - C ₁,C ₂ coefficients of Mooney-Rivlin model - c vectorial counterpart ofC: VEC (C) - c ₂ vectorial counterpart ofC ²: VEC (C ²) - D isothermal tangent stiffness matrix - e vectorial counterpart of : VEC () - deviatoric Lagrangian strain tensor - e _R reduced deviatoric Lagrangian strain tensor - e volume strain - e _T reduced volume strain - f thermal expansion function,=[1+(T–T ₀)/3]^–1 - F, F _T deformation gradient tensor - F _R reduced deformation gradient tensor - H Hessian matrix for the Gibbs free energy density - H related toH - I ₁,I ₂,I ₃ invariants ofC - I _1R,I _2R,I _3R invariants ofC _R - I, I ₉ identity matrix - i vectorial counterpart ofI: VEC (I) - J determinant ofF - J _R determinant ofF _R - J _T determinant ofF _T - J ₁,J ₂ invariants of /J _{R 2} ³ - J _1R,J _2R invariants of _R /R _J ^2/3 - k thermal conductivity coefficient - K ₁,K ₂,K ₃ invariants of /J ^2/3 - K _1R,K _2R,K _3R invariants ofe _R/J^2/3 - p hydrostatic pressure - s vectorial counterpart of stress : VEC () - s isotropic stress - T (absolute) temperature - T ₀ reference temperature - conventional (isothermal) strain energy density (per unit volume) - volumetric thermal expansion coefficient - thermal expansion vector - strain, Lagrangian strain - entropy density - isothermal bulk modulus - Lagrange multiplier - _i extension ratio - shear modulus - stability coefficient - mass density - stress, 2nd Piola-Kirchhoff stress - _i principal stress - Cauchy stress - _d deviatoric Cauchy stress - , _{M C T 0} Helmholtz free energy density - _i /I _i - _ij ²/I _i I _j - Gibbs free energy density - (.) variational operator - VEC (.) vectorization operator - operator for Kronecker product     

Shear viscosity of the B phase of superfluid3He

The shear viscosity (T) in the Balian-Werthamer (BW) state of superfluid ³ He is calculated variationally throughout the region 0t 1(t=T/T _c) from the transport equation for Bogoliubov quasiparticles. Coherence factors are treated exactly in the calculation of the collision integral. The numerical result for =_s= _s(T)/_n(T_c) agree very well with experiment in the range 0.8t1.0. Analytic expressions = 0.577 (1–1.0008t) and =1–(23/64) [=(T)/k _B T] are obtained in the low-temperature region and in the vicinity ofT _c, respectively. From the numerical analysis it is shown that the latter equation is valid only in the temperature range 0.9997t1.0.Supported by the Research Institute for Fundamental Physics, Kyoto University.     

On the dispersion of gases under the action of the medium

Some general regularities of dispersion of a gas emerging from a nozzle submerged in a liquid are considered. A condition for establishment of the so-called maximum dispersion state is formulated.Notation ₀ coefficient of surface tension at the liquidgas boundary - contact angle of wetting of the nozzle material surface by the liquid - p_at atmospheric pressure - p air pressure - density of the liquid - g gravitational acceleration - h height of the liquid column - ₁, and _g dynamic viscosity coefficients of the liquid and gas, respectively - R and r radii of the bubble and nozzle, respectively - Q and F dimensionless criteria - , , , , and undetermined coefficients - ratio of the circumference of a circle to its diameter     

Structure of martensite formed in Cu-Al-Fe single crystals duringin situ HVEM pseudoelastic tensile experiment

Single crystals of the CuAlFe alloy, containing 14.5 wt% Al and 2.2 wt% Fe were subjected toin situ tensile experiment using straining attachment in a 1 MV electron microscope. Loadelongation curves were obtained for three foil plane/tensile direction orientations: (001) [0 1 0], (0 0 1) [1 1 0] and (1 1 0) [¯1 1 2]. Each crystal was subjected to two cycles of pseudoelastic deformation up to maximum 2% strain, showing almost complete shape recovery. Structure observations and electron diffraction pattern indicated that during deformation of samples of (0 0 1) [1 1 0] and (1 1 0) [1 1 2] orientations, formation of ₁ martensite was observed and only at later stages narrow needles of ₁ nucleate in front of ₁. During pseudoelastic deformation in the (0 0 1) [1 0 0] direction, martensite forms as a mixture of narrow plates possessing either 2H or 18R structures. The following crystallographic relationship between the parent phase and both types of martensite was observed: [1 00] ₁ [101] ₁ and (0 0 1) ₁ (0 1 0)₁;(0 0 1) ₁ (0 1 0) ₁ and [1 1 0] ₁ [0 0 1] ₁. From the character of sidebands reflections presence of 1 0 1 1 0¯1 static displacement waves was inferred.     

Effects of dimensionality and crystal structure on bound states of point defects in quantum solids

The effects of dimensionality and crystal structure on the bound states of point defects in quantum crystals are investigated. It is shown that tightly bound states tunnel slowly in some lattices (e.g., bcc) while they tunnel quickly through other lattices (e.g., hcp). Explicit band calculations are made for ( ³ He) ₂ impurity molecules in solid host ⁴ He crystals. These illustrate the qualitative differences present in various molecular tunneling modes.     

Wetting of Rough Walls

Quenched geometric disorder of a wall delimiting a spectator phase can have dramatic effects on the nature of critical wetting transitions. We consider self-affine walls in 2D with roughness exponent _W. Transfer matrix results for directed interfacial models with short-range interactions suggest that wetting turns first-order as soon as _W exceeds ₀, the anisotropy index of interface fluctuations in the bulk. Discontinuous interface depinning is best identified by a peculiar two-peak structure in the statistical distributions of wall–interface contacts obtained by sampling over disorder. On the other hand, for _W<₀ wetting remains continuous, most plausibly in the same universality class as with flat walls. This occurs both with ordered (₀ = 1/2) and with bond-disordered (₀ = 2/3) bulk. A precise location of the thresholds at _W = ₀ can be argued on the basis of an analysis of different terms in the interfacial free energy. This analysis elucidates the peculiar role played by the intrinsic interfacial roughness and suggests extensions of the results to 3D and to long-range substrate forces.     

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 note on the solution of a differential equation arising in boundary-layer theory

Summary The differential equation f + ff + f² = 0 (where dashes denote differentiation with respect to the independent variable ) subject to the boundary conditions f(0)=0, f()=0 and either f(0)=1 or f(0)=–1 is considered. It is shown that by using pf as dependent variable and =C–f (where C=f()) as independent variable and then expanding in powers of , a very good approximation to the solution can be obtained using only a few terms in the expansion.     

Hot-press sintering studies of amorphous silicon nitride powders

The hot-press sintering behaviour of amorphous Si₃N₄ powders prepared from the ammonia pyrolysis of polycarbosilane or hydridopolysilazane polymers was studied. In the presence of yttria and alumina, the amorphous powders sintered to > 98% of theoretical density at 2023 K. Both the microstructure and average four-point MOR bend strengths, of test bars machined from the sintered compacts were comparable to those obtained from UBE SN-E-10 Si₃N₄ powder processed under the same conditions. However, in contrast to commercial crystalline powders, between approximately 1690 and 1700 K the amorphous Si₃N₄ powders underwent a rapid shrinkage corresponding to 50–60% of the total densification. In this narrow temperature regime, a radical change in morphology and phase composition of the amorphous powder occurred. Prior to 1690 K, the Si₃N₄ powders were totally amorphous as determined by X-ray diffraction analysis and consisted of angular shards with an average particle size of 2–3 m. Samples quickly cooled after heating to 1700 K, consisted of a 53/47 mixture of equiaxed and Si₃N₄ crystallites with an average particle size of 0.1–0.3 m. Thus, the rapid densification at R~ 1700 K is identified with the amorphous to ( + ) transition. Beyond 1700 K, these samples gradually densified to the maximum density as mentioned. The fully densified samples consisted of 100% -Si₃N₄ phase.     

Structure and Diamagnetic Properties of (Pb0.6SnyCu0.4 ? y)Sr2(Y1 ? xCax)Cu2Oz

The effect of Sn doping in (Pb_0.6Sn _y Cu_{0.4 – y} )Sr₂(Y_{1 – x} Ca _x )Cu₂O _z with 0 y 0.3 and 0 x 0.7 was investigated. It was established that a nearly pure 1212 phase can be obtained at 0 y 0.1 and 0 x 0.3. The obtained XRD patterns as well as the results of the EDX and ICP-AES analyses showed that Sn substitution is possible in the (Pb,Cu)-1212 phase. Superconductivity was observed at 0.4 x 0.7. The onset of the diamagnetic transitions varied from 10 to 30 K. The influence of the strong Pb deficiency on the superconducting properties of the samples was discussed.     

The constitution of the Ni-Al-Ru system

The constitution of the Ni-Al-Ru system has been investigated in the range 0 to 50 at% Al. Isothermal sections at 1523 and 1273 K have been determined using microstructural observations, electron probe microanalysis and X-ray diffraction. The phases present were: nickel-based solid solution (); (based on Ni₃Al); solid solutions based on NiAl and RuAl, respectively (designated ₁ and ₂), and ruthenium-based solid solution (Ru). The maximum solubility of Ru in was 5 at%. ₁, and ₂ show extensive range of solubilities, namely up to 20at% Ru in ₁ and up to 25 to 35 at% Ni in ₂. Three-phase equilibrium between , ₂ and (Ru) existed at 1523 and 1273 K. Also at 1523 K, three-phase equilibria existed between , and ₁ and ,₁ and ₂, while at 1273 K, the equilibria were between , ₁,₂ and , , ₂ indicating the occurrence of a reaction +₁, +₂ at a temperature between 1523 and 1273 K. Liquidus features have been deduced from data on as-solidified structures. Lattice parameter data and hardnesses are also reported.     

The generating groups of geometrically uniform spherical signal sets

An [M, n] spherical signal set is a collection ofM unit-norm vectors in the Euclideann-dimensional space ⁿ . Itsconfiguration matrix C is the matrix of the scalar products between pairs of vectors. isgeometrically uniform if, given any two vectors x _i , x _j there exists an isometry that transforms x _i to x _j while leaving invariant. Agenerating group of is a group of isometries of ⁿ that transform any given vector of into each of the vectors in while leaving invariant. In this paper we characterize the configuration matrix of a geometrically uniform spherical signal set and we show how its generating groups can be obtained.Parts of an earlier version of this paper were presented at the IEEE International Symposium on Information Theory, Ithaca, NY, 1977