Subgap peak and Tomash-McMillan-Anderson oscillations in the density of states of SNS Bridges

The quasiparticle spectra and the densities of states of superconducting-normal-superconducting junctions are computed from the WKBJ transformed Bogoliubov-de Gennes Equations (BdGE), which are solved by Picard iteration and numerical integration. It is shown that the influence of the proximity effect on the bound states can be modeled by a rectangular pair potential well of effective normal layer thickness 2a*= _–L ^L [1–(z)/]dz, where (z) is the pair potential of the junction, is its asymptotic constant value, and 2L is the total length of the sample. The density of states exhibits a subgap peak at energies less than besides the BCS peak atE=; forE> there are geometrical resonances which are due to electron-hole interferences in finiteS layers of thicknessL-a*.     

An apparatus for measuring the thermal conductivity and diffusivity of solid materials

An apparatus is described for measuring the thermal conductivity and diffusivity on small specimens of solid materials; also the results are shown which have been obtained for refractive high-alumina concrete by such measurements.Notation thermal conductivity at the mean temperature of specimens, W/m· °C - Q power of the central heater, W - F cross section area of a specimen, m² - t_1,2 temperature drop across the specimens, °C - ₁, ₂ difference in heights between the thermocouple beads, center-to-center, in the first and in the second specimen respectively, m - t temperature, °C - time coordinate, min - d₁= (d_1u+d_1l )/2 mean distance between specimen contact plane and nearest thermocouple beads, for the upper and lower specimen, m - d₂= (d_2u+d_2l )/2 mean distance between specimen contact plane and farthest thermocouple beads, for the upper and lower specimen, m - dt(d₁,)/d rate of temperature rise at section d₁ of the specimen at time, °C/h - t=t₁+t₂ sum of temperature drops in the specimens at time, °C - m heating rate, h^–1 - a thermal diffusivity of specimens, referred to their mean temperature, m²/h - =m/a, m^–1 b=¦(t_u–t_l)/t_u¦ heating nonuniformity factor Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 22, No. 6, pp. 1049–1054, June, 1972.     

On mode I and mode II energy release rates of an interface crack

The opening (mode I) and sliding (mode II) components of the energy that is released during an incremental extension of an interface crack between two different elastic materials are evaluated by the Irwin's crack closure method. Each component of the energies (G _I and G _II ) is expressed in terms of the functions of the length of the incremental crack extension (a) and the real and imaginary part of the complex stress intensity factor defined by Malyshev and Salganik. It is found that values of G _I /a and G _II /a oscillate violently when a approaches zero and that, hence, in contrast with the case for homogeneous materials, each energy release rate should be defined as G _I /a and G _II /a for an actual crack growth step size.     

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.     

The unzipping model of fatigue crack growth and its application to a two-phase steel

The unzipping analysis, based on the alternate shear deformation process of two intersecting shear planes at a crack tip, is extended to study fatigue crack growth in a two-phase martensitic-ferritic steel. The unzipping crack increment a _uz is directly related to K and J in the case of small scale yielding. It is preferrable to use a _uz is directly related to K and J in the case of small scale yielding. It is preferable to use a _uz as a physical parameter to correlate with the growth rates of micro-cracks and fatigue cracks in a multi-phase material. In the case of micro-cracks, K is often not applicable because of extensive plastic deformation; and in the case of multi-phase material, neither K nor J is applicable because of material inhomogeneity. The effective K, K _eff, is defined in terms of a _uz. The relations between the endurance limit of a two-phase steel and crack nucleus size, ferrite layer thickness, the constraint by the strong martensite on crack tip deformation in the ferrite domain, and K _th's of the martensite and ferrite are analyzed.

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Résumé Une analyse de rupture progressive et continue des liaisons, basée sur un processus de déformation de cisaillement alterné de deux plants de cisaillement s'intersectant à l'extrémité d'une fissure, a été étendue à l'analyse de la propagation des fissures de fatigue dans un acier martensito-ferritique à deux phases. L'accroissement de la fissure a est directement en relation avec K et J dans le cas de déformation plastique de faible étendue. II est préférable d'utiliser a comme paramètre physique en corrélation avec les vitesses de croissance de microfissures et des fissures de fatigue dans un matériau à phases multiples. Dans le cas de microfissures, K n'est souvent pas applicable en raison de la déformation plastique importante. Dans le cas de matériau multiphase ni K ni J ne sont applicables en raison de l'inhomogénéité du matériau. La valeur effective K _eff est définie en terme de a. Les relations entre la limite d'endurance d'un acier à deux phases et la taille du nodule de fissuration, l'épaisseur de la couche de ferrite, la contrainte qu'exerce une zone martensitique dure sur le domaine ferritique, sur la déformation à l'extrémité de la fissure en domaine ferritique, et les valeurs de K de la martensite et de la ferrite sont analysées.

     

Asymptotic expansions for constant-composition dew-bubble curves near the critical locus

Explicit functional representations are developed for constant-composition dew and bubble curves near critical according to the modified Leung-Griffiths theory. The pressure and temperature incrementsP=P–P _c andT= T–T _c, where c denotes critical, are linearly transformed to new variablesP andT. In the transformed space, the coexistence curves are no longer double-valued and can be expressed as a nonanalytic expansion, where the coefficients are functions of the critical properties and their derivatives. A similar asymptotic expansion is developed forT in terms of the density increment=– _c. In the approximation that the critical exponents=0 and=1/3, the critical point in temperature-density space is shown to be a point of maximum concave upward curvature, rather than an inflection point as previously conjectured.Paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.Formerly National Bureau of Standards     

Localized single-particle excitations and the density of states for superconducting composites

The problem of localized single-particle excitations and the density of states (DOS) for an inhomogeneous system consisting of a spherical superconductor (with radius a and order parameter ₁) embedded in another superconductor (order parameter ₂) of infinite size is considered. With the assumption of constant values of ₁ and ₂, the Bogoliubov equations are solved for general values of l (the orbital angular momentum quantum number). For a fixed value of ₁/₂ and different values of ₂/E _F, the dependence of the excitation energy (l=0)/₂ on the particle sizek _F a is shown (k _F is the Fermi wave vector andE _F is the Fermi energy). Fork _F a=300, 450, and 800 and a fixed value of ₂/E _F, the variations in the DOS by changing ₁/₂ are also shown.     

Third sound in a restricted geometry

Bergman's general treatment of third sound waves has been extended to a (restricted) parallel plate geometry. In a parallel plate geometry two independent third sound modes can propagate: a symmetric and an antisymmetric one. Calculations show that at temperatures below 1 K the antisymmetric mode carries the most important part of the temperature amplitude. Because of the relatively strong substrate influence the temperature amplitude of the symmetric mode is suppressed. The T/h versus T measurements by Laheurteet al. ¹ and of the T/h versus measurements by Elliset al. ² are explained.     

ESR line broadening in Cr3+/MgO at liquid helium temperatures

Line broadening has been observed at 9 GHz in the ESR absorption spectrum of Cr³⁺ in MgO in the liquid helium temperature range, for a range of Cr³⁺ concentrations from 800 7400 ppm. The broadened linewidths at 4.2 K are about two times larger than those at 77 K and depend on polar angle. The lineshapes are Gaussian, in contrast to the Lorentzian lineshape between 293 and 77 K. The broadening is interpreted by the combined effects of strain, due to the charge misfit of Cr³⁺ and the host cation, and temperature which causes both exchange striction and departure from the cubic symmetry to a lower symmetry. Analysis of the linewidth data gives D=(5.25±0.40)×10^–4 cm^–1 and confirms that the total linewidth, H _t, is given by H _t=H ₀+(2D/g) cos _H where H ₀ is the linewidth independent of concentration, temperature and polar angle, _H.     

Supercooling of In2Bi and InBi Melts

The effect of melt overheating T ⁺ on the critical supercooling T ^– of liquid In₂Bi and InBi is studied by cyclic thermal analysis. It is shown that, the T ^– for In₂Bi is 2.0 K, independent of the melt preheating temperature. In contrast, the T ^– for InBi varies jumpwise with T ⁺: T ^– 1.0–1.6 K at T ⁺ < 5 K, and T ^– 16 K at T ⁺ = 5–300 K, independent of the cooling rate (varied from 0.002 to 8.0 K/s). The solidification behaviors of In₂Bi and InBi are shown to correlate with the structures of their liquid and solid phases.     

Equation of state of3He near its liquid-vapor critical point

We report high-resolution measurements of the pressure coefficient (P/T) for³He in both the one-phase and two-phase regions close to the critical point. These include data on 40 isochores over the intervals–0.1t+0.1 and–0.2+0.2, wheret=(T–T _c )/T _c and =(– _c )/ _c . We have determined the discontinuity (P/T) of (P/T) between the one-phase and the two-phase regions along the coexistence curve as a function of . The asymptotic behavior of (1/) (P/T) versus near the critical point gives a power law with an exponent (+–1)^–1=1.39±0.02 for0.010.2 or–1×10 ^–2t–10 ^–6 , from which we deduce =1.14±0.01, using =0.361 determined from the shape of the coexistence curve. An analysis of the discontinuity (P/T) with a correction-to-scaling term gives =1.17±0.02. The quoted errors are fromstatistics alone. Furthermore, we combine our data with heat capacity results by Brown and Meyer to calculate (/T) _c as a function oft. In the two-phase region the slope (²/T ²)_c is different from that in the one-phase region. These findings are discussed in the light of the predictions from simple scaling and more refined theories and model calculations. For the isochores 0 we form a scaling plot to test whether the data follow simple scaling, which assumes antisymmetry of – ( _c ,t) as a function of on both sides of the critical isochore. We find that indeed this plot shows that the assumption of simple scaling holds reasonably well for our data over the ranget0.1. A fit of our data to the linear model approximation is obtained for0.10 andt0.02, giving a value of =1.16±0.02. Beyond this range, deviations between the fit and the data are greater than the experimental scatter. Finally we discuss the (P/T) data analysis for ⁴ He by Kierstead. A power law plot of (1/) P/T) versus belowT _c leads to =1.13±0.10. An analysis with a correction-to-scaling term gives =1.06±0.02. In contrast to ³ He, the slopes (²/T ²)_c above and belowT _c are only marginally different.Work supported by a grant from the National Science Foundation.     

Changes in surface characteristics of dental resin composites after polishing

The objectives of this study were (1) to determine in vitro changes in surface roughness and color of dental resin composites after application of three finishing and polishing systems; (2) to evaluate the difference in color stability after immersion in a dye solution after polishing; and (3) to evaluate the effects of surface condition, especially roughness, on measured color depending on the color measuring geometries of specular component excluded (SCE) and specular component included (SCI). Color and surface roughness (R_a) of resin composites of four brands of A2 shade and one brand of Yellow Enamel shade were measured after polymerization, after polishing with Enhance (Dentsply), Sof-Lex (3M ESPE), or Super-Snap (Shofu) composite finishing and polishing systems. Color was also measured after immersion in 2% methylene blue solution. Color was measured according to the CIELAB color scale. Color changes (E*_ab) after polishing/staining and by the measuring geometry were calculated by the equation; E*_ab = [(L*)² + (a*)² + (b*)²]^1/2. Ra value was measured with a surface roughness tester. E*_ab and L* values after polishing and after staining varied among polishing systems when measured with SCE geometry. Composites polished with Super-Snap and Sof-Lex systems showed higher E*_ab and L* values than those polished with Enhance polishing system with SCE geometry. E*_ab and L* values between specimens with different surface conditions measured with SCE geometry were significantly higher than those with SCI (p < 0.01). Changes in R_a value after polishing was insignificant in most cases.     

Thermodynamic properties of liquid3He-4He mixtures near the tricritical point. II. Data analysis by the scaling-field method

The scaling theory for tricritical phenomena by Riedel is applied to the analysis of thermodynamic properties of liquid³He-⁴He mixtures near the tricritical point. Within this theory experimental data for the phase diagram, the³He molar concentrationX, and the concentration susceptibility (X/) _T are discussed in terms of two scaling fields that are functions of the temperatureT and the difference = ₃ – ₄ of the chemical potentials of the two helium isotopes. The quantitiesX and (X/) _T in terms of thefields T and as independent variables are obtained for the intervals –0.1<T – T _t<0.53 K and –9< – _t <0.8 J/mole, from vapor pressure and calorimetric data described in a previous paper by Goellner, Behringer, and Meyer. The transformed data are analyzed to yield the tricritical exponents, amplitudes, scaling fields, and scaling functions. The values of the tricritical exponents are found to agree with those predicted by the renormalization-group theory of Riedel and Wegner. (Logarithmic corrections are beyond the precision of the present experiment.) Relations between amplitudes are derived and tested experimentally. The (linear) scaling fields are determined by using their relationship to geometrical features of the phase diagram. The data forX and (X/) _T are found to scale in terms of these generalized scaling variables. The sizes of the tricritical scaling regions in the normal and superfluid phases are estimated; the range of apparent tricritical scaling is found to be appreciably larger in the normal-fluid phase than in the superfluid phase. The tricritical scaling function for the concentration susceptibility is compared with the analogous scaling function for the compressibility of pure³He near thecritical gas—liquid phase transition. Finally, when the critical line near the tricritical point is approached along a path of constant < _t , the experimental data are found to exhibit the onset of the crossover from tricritical to critical behavior in qualitative agreement with crossover scaling.Work supported in part by the National Science Foundation through Grant No. GH-36882 and Grant No. GH-32007, and by a grant of the Army Research Office (Durham).     

Application of a new iterative method for elastic-plastic stress analysis

A new iterative method for elastic-plastic stress analysis based on a new approximation of the constitutive equations is proposed and compared with standard methods on the accuracy and the computational time in a test problem. The proposed method appears to be better than the conventional methods on the accuracy and comparable with others on the computational time. Also the present method is applied to a crack problem and the results are compared with experimental ones. The agreement of both results are satisfactory.List of symbols u = (u ₁, u ₂) displacements u ^(H) = u ⁽ⁿ⁺¹⁾ - u ⁽ⁿ⁾ u _k ⁽ⁿ⁾ = u _(k ^{(n + 1)} - u ⁽ⁿ⁾ (n, k = 0, 1, 2, ...) - = ₁₁, ₂₂, ₁₂) stresses - = (₁₁, ₂₂, ₁₂) strains - = (₁₁, ₂₂, ₁₂) center of yield surface - D elastic coeffficient matrix, C = D ^–1 - von Mises yield function. The initial yielding is given by f() = _Y - f {f/} - ^* transposed f - H hardening parameter (assumed to be a positive constant for kinematic hardening problems) - time derivative of - [K] total elastic stiffness matrix - T traction vector - = [B] relation between nodal displacements and strains     

Interaction between a dislocation and an impurity in KCl: Mg2+ single crystals

The interaction between a dislocation and the impurity in KCl: Mg²⁺ (0.035 mol% in the melt) was investigated at 77–178 K with respect to the two models: one is the Fleischer's model and the other the Fleischer's model taking account of the Friedel relation. The latter is termed the F-F. The dependence of strain-rate sensitivity due to the impurities on temperature for the specimen was appropriate to the Fleischer's model than the F-F. Furthermore, the activation enthalpy, H, for the Fleischer's model appeared to be nearly proportional to the temperature in comparison with the F-F. The Friedel relation between effective stress and average length of the dislocation segments is exact for most weak obstacles to dislocation motion. However, above-mentioned results mean that the Friedel relation is not suitable for the interaction between a dislocation and the impurity in the specimen. Then, the value of H(T _c) at the Fleischer's model was found to be 0.61 eV. H(T _c) corresponds to the activation enthalpy for overcoming of the strain field around the impurity by a dislocation at 0 K. In addition, the Gibbs free energy, G ₀, concerning the dislocation motion was determined to be between 0.42 and 0.48 eV on the basis of the following equation ln / = G ₀/(kT_p0)1 – (T/T _c)^{1/2 –1}(T/T _c)^1/2 + ln ₀/where k is the Boltzmann's constant, T the temperature, T _c the critical temperature at which the effective stress due to the impurities is zero, _p0 the effective shear stress without thermal activation, and ₀ the frequency factor.     

Ordered state of one-dimensional antiferromagnetic superconductors in the presence of a homogeneous magnetic field

Assuming a one-dimensional electron band and examining the free energy difference F (=F _S–F _N) for an antiferromagnetic superconductor in the presence of a homogeneous magnetic field H₀, it is shown that (i) for temperatureT=0, the spatially varying order parameter _Q (having the same period as the antiferromagnetic fieldH _Q) and the BCS order parameter coexist when |–H _QH ₀<+H _Q (here, the pairing coupling constant for _Q is assumed small), and (ii) forT near the second-order phase transition temperature the coexistence of _Q and is always realized whenH ₀0.Work supported in part by a grant from the Natural Sciences and Engineering Research Council of Canada.On leave of absence from Physics Department, Tohoku University, Sendai, Japan.     

Influence of various divalent impurities on dislocation density in KCl:Mg2+, Ca2+, Sr2+ or Ba2+ single crystals

Single crystals of nominally pure KCl and KCl doped with Mg²⁺, Ca²⁺, Sr²⁺ or Ba²⁺ were deformed by compression at 77–254 K; during the tests strain-rate cycling was conducted in association with ultrasonic oscillation. The data were analyzed in terms of strain-rate sensitivity ((/ln)) versus stress decrement (). The curve for KCl doped with the divalent impurities has two bending points and two plateau regions. It is proposed that the variation of strain-rate sensitivity at the second plateau place on the curve with shear strain ((/ln)/) is due to a change in forest dislocation density with shear strain. The forest dislocation density for the specimens seemed to increase by the divalent additions in the compression test on account of the jogs on the screw dislocations. It depended on the concentration of impurities and also on the size of impurity in the specimens at a given temperature. Unfortunately, it was not possible to determine whether a change in the size of impurity influences mobile dislocation density, , from the values of / for KCl doped with Ca²⁺, Sr²⁺ or Ba²⁺.     

A correlation of ΔK th-value with the exponent,m, in the equation of fatigue crack growth for various steels

Literature (mainly in Japan) relating to fatigue-crack-growth-data at R=0 in an air environment for a wide range of steels is reviewed with particular attention to the threshold stress intensity, K _th. The collected data are analyzed in terms of the exponent, m(the slope of the linear portion of the log(da/dN)-logD relationship) by taking account of microstructure, material strength, fracture toughness and specimen thickness. The mean rate of fatigue crack growth for ductile steels in the range from the intermediate growth rate to threshold level and the relevant threshold values at R=0, K _th0, can be represented asda/dN = 1.700 × 10^-4(K103.6)^m - 10^-6andK _th0 = 103.6(5.88 × 10^-3)^1/m,where (da/dN) and K are measured by the units of mm/cycle and kgf/mm^3/2, respectively. Contrary to this, in the case of extremely brittle steels with K _IC-value below 200 kgf/mm^3/2 (the fracture occurs by the intergranular separation), the relationships are given byda/dN = 2.893 × 10^-5(K/49.94)^m - 2.5 × 10^-7andK _th0 = 49.94(8.64 × 10^-3)^1/m.

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Résumé La littérature, principalement japonaise, relative aux données sur la propagation des fissures de fatigue pour R=0 dans un environnement d'air et pour une large catégorie d'aciers fait l'objet d'une revue avec une attention particulière pour l'intensité de contrainte de seuil, K _th. Les données collectées sont analysées en terme de l'éxposant m (qui représente la pente de la portion linéaire de la relation log(da/dN)-log K, en tenant compte de la microstructure, de la résistance du matériau, de la ténacité à la rupture et de l'épaisseur de l'éprouvette. La vitesse moyenne de propagation d'une fissure de fatigue dans le cas des aciers ductiles dans la fourchette entre la vitesse intermédiaire de fissuration et le niveau critique, et les valeurs correspondantes de seuil à R=0, K _th0 peuvent être représentées par la relation:da/dN = 1.700 × 10^-4(K103.6)^m - 10^-6etK _th0 = 103.6(5.88 × 10^-3)^1/m,où (da/dN) et K sont mesurés en unités de mm/cycle et en kgf/mm^3/2 respectivement. En contraste, dans le cas d'aciers extrèmement fragiles avec des valeurs K _IC en dessous de 200 kgf/mm^3/2 (la rupture se produit par une séparation intergranulaire), ces relations sont données par:da/dN = 2.893 × 10^-5(K/49.94)^m - 2.5 × 10^-7etK _th0 = 49.94(8.64 × 10^-3)^1/m.

     

Theory of the Surface Tension Maximum of Liquid 3He

Recently Matsumoto et al. performed very precise measurements of the surface tension of liquid ³He, (T), at low temperatures and found that (T) exhibits a small maximum at about 100 mK. Existing theories are unable to explain this anomaly. On the basis of a local approximation for the entropy in which the Fermi liquid effect is included, we can evaluate the variation of (T), (T)=(T)–(0), as a function of T and of the number density (or the interaction strength). It is found that (T) consists of two terms; a T² term and T⁴ ln T term. We predict that, for the density of real liquid ³He, exhibits a tiny minimum and a small but relatively larger maximum. This prediction explains qualitatively and quantitatively all salient features of the observed (T).     

Low endurance fatigue in metals and polymers

The fatigue behaviour of commercially pure aluminium and of nylon under sequentially varying strain amplitudes is compared with a damage law of the type suggested by Miner. Aluminium obeys such a law for both cyclic and uniaxial prestrains but the behaviour of nylon is significantly affected by microcracking, which produces a marked effect of loading sequence.Appendix N Number of strain cycles at a given time - N _f Value of N at failure - True tensile stress - True stress range for a strain cycled specimen - _h Value of at half the life of the specimen - True tensile strain - Total true strain range - _p True plastic strain range (= the breadth of the hysteresis loop at = 0) - _d True diametral strain range - E Young's modulus - Linear strain hardening rate when tested at a particular value of _p - D Damage due to cycling - D _p Damage due to prestrain - _p Prestrain. C, K, K₁, , are constants