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.     

Critical behavior of liquid4He at negative pressures

We examine the equation of state of liquid⁴He at negative pressures close to the spinodal density _s where the hydrodynamic speed of sound vanishes. The non-analytic behavior of the equation of state and the speed of sound in the vicinity of the spinodal density are calculated in two and in three dimensions; we find for the speed of sound the non-analytic behavior mc _s ² ( — _s)^2/5 in three dimensions and mc _s ² [(-_s)/¦ln(-_s)¦]^1/2 in two dimensions.We then examine the low density regime numerically, using a semi-analytic microscopic theory. It is found that non-analytic exponents are visible only in a negligible density regime around the spinodal point. Estimates for the spinodal densities, and the range of critical fluctuations are provided.     

Van der Pauw measurement of metal fibre orientation in a plastic-metal composite

Stainless steel fibres in ABS plastic form a composite with an anisotropic resistivity. Samples are rectangular shapes with uniform thickness. By assuming two principal resistivities and by using van der Pauw's technique, we find ² = _{x y} . For rectangular samples, field theory determines _y / _x and hence fibre direction. Results for three sample geometries agree with the theoretical predictions of the fibre patterns and with X-ray data. Samples formed by a centre-sprue feed are the best for fabricating large, uniform samples, while samples with a large length-to-width ratio have the most uniform metal density and fibre orientation. Resistivity was also measured by the more-common two-probe technique. Results correlate well to van der Pauw data, with 95% confidence.     

Electrical properties of In/Yb/n-Hg1 − x Cd x Te contacts

The specific contact resistance, _c, and the modified sheet R _sk, of In/Hg_{1 – x} Cd _x Te contacts incorporating a Yb diffusion barrier were measured as a function of the layer thickness and composition (x = 0.32–0.65). Significant increases in _c, were evident only for x 0.56 and at Yb thicknesses between 2.5 and 6.0 nm, depending on the x-value. Analytical examination of the interfaces by Rutherford backscattering spectrometry (RBS) also showed a progressive reduction in the extent of inward diffusion of In with increasing thickness of the Yb interlayer.     

Plastic zones in Fe-3Si steel double-cantilever-beam specimens

Plastic zones generated in double-cantilever-beam specimens of an Fe-3Si steel are revealed by etching. Zones corresponding to relative stress intensity levels in the range 0.4 (in.)<K/_Y< 0.8(in.), beam height to length ratios H/W = 0.125 and 0.35, and conditions approaching plane strain are examined. The fürthest extent of the zones, p 0.13 (K/_Y)², is about half that previously observed in plates loaded in tension to comparable K-levels. The results are consistent with previous, measurements by Clark and lend support to Wilson's calculations. At high stress levels, when the zone size to beam height ratio /H 0.09, the zone begins to tilt backwards and undergoes a transition from a crack- to a beam-zone. Implications of this transition with respect to the minimum beam height requirement are examined.

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Zusammenfassung In Doppelkamileverproben aus Fe-3 Si-Stahl gebildete plastische Zonen werden durch Ätzen sichtbar gemacht. Zonen welche einem relativen Spannungsintensitätsniveau im Bereich von 0,4,(in.)<K/_Y< 0,8,(in.) entsprechen, Höhen zu Längen-Verhältnisse H/W = 0,125 und 0,35 sowie Bedingungen, welche sich der planen Verformung annähern, werden untersucht.Die größte Ausbreitung dieser Zonen, 0,13 (K/_Y)² erreicht nur die Hälfte derer die früher in Blechen beobachtet worden waren, welche bei gleichen K-Werten Zugspannungen ausgesetzt wurden. Diese Ergebnisse sind in guter Übereinstimmung mit den schon von Clark durchgeführten Messungen und bekräftigen die Berechnungen von Wilson.Bei hohem Spannungsniveau, wo das Verhältnis /H 0,09 ist, beginnt die Zone sich nach rückwärts zu beugen und sich vom Rissbereich ins Innere des Trägers zu verschieben. Die sich hieraus ergebende Folgerung für die erforderliche minimale Trägerhöhe wird untersucht.

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Résumé Les zones de déformation plastique qui se développent dans des éprouvettes en forme de double poutre cantilever d'acier Fe-3Si ont été mises en évidence par attaque chimique. On envisage les zones correspondant aux conditions suivantes: niveaux relatifs de l'intensité de contraintes compris dans la fourchette: 0,4(in)<K/y<0,8(in) et rapports hauteur/longueur de poutre H/W = 0,125 et 0,350. On examine les conditions voisines de l'état plan de déformation. L'épanouissement le plus large des zones, exprimé par 0,13 (K/_Y)², est la moitié de celui que l'on a observé précédemment dans le cas de tôles sollicitées en traction à des niveaux K comparables.Ces résultats sont compatibles avec les mesures qu'a obtenues Clark, et confirment les calculs de Wilson. Sous contraintes élevées, lorsque le rapport de la dimension de la zone plastifiée à la hauteur de la poutre /H 0,09, cette zone commence à se cambrer vers l'arrière et passe de la fissure au corps même de la poutre.On examine les implications que comporte cette transition sur les hauteurs minimum de poutres à observer.

     

Determination of rolling anisotropy by extensometry

A theory is presented for the determination of three coefficients characterizing anisotropic materials. These new coefficients of anisotropy advantageously replace Lankford's classic empirical coefficient,r, in the definition of the anisotropy of a rolled sheet. It is shown how these coefficients ₀, ₄₅ and ₉₀ may be deduced from the theory, provided certain assumptions are made concerning the rolled material. The validity of the theory was tested through experiments on rolled ultra high-purity iron sheet, ₀, ₄₅ and ₉₀ being determined by means of a special purpose-built extensometer.     

The microhardness of injection moulded polystyrene and polyethylene

Injection moulded plaques of polystyrene and of two types of high density polyethylene have been produced under different moulding conditions. The mean density of each plaque together with its surface microhardnessV _H have been measured. Polystyrene shows only a slight increase in with increasing mould temperatureT _m together with a reduced spread in andV _H values. In polyethylene, however, andV _H both increase linearly withT _m, giving a usefulV _H against relation, which is attributed to increased percentage crystallinity.     

Electronic transport in tungsten and iron-doped tungsten below 1 K

The electrical resistivity and the thermoelectric ratio G have been measured for zone-refined single crystals of both tungsten and iron-doped tungsten from 5 K down to 40 mK. The samples had residual resistance ratios RRR ranging from 1750 to 90,000. The observed behavior is conveniently divided into two classes, normal and anomalous. Completely normal behavior was displayed by only three W samples with high RRRs. The Fe-doped W and the remaining W samples contained one or more anomalies. Normal behavior is that which would be expected for W containing impurities with no internal degrees of freedom. In normal behavior decreased monotonically with decreasing temperature and was consistent with the equation = _o + AT ² below about 1.5 K. This form for is taken as evidence that electron-electron scattering dominates electron-phonon scattering in for W at such low temperatures. For the range of sample purities studied, A increased slightly with increasing ₀, but did not vary systematically with either the sample diameter d or with the ratio (273 K)/d(T). In normal behavior, G was positive and constant below about 0.5 K, increased in magnitude as T rose to 4 or 5 K, and then began to decrease, becoming negative above about 7 K. An explanation is provided for this behavior. Those samples that fell into the anomalous class displayed at least one of three anomalies: (1) a minimum in the electrical resistivity, with an approximately logarithmic variation with T at temperatures below the minimum; (2) a positive contribution to G which increased in magnitude with decreasing temperature approximately as T ^–1/2from about 4 K down to at least 0.5 K; and (3) a negative contribution to G which set in at about 0.5 K, varied approximately as log T, and dominated G at the lowest temperatures. These anomalies are presumably due to one or more impurities dissolved in the W, possibily including Fe. However, chemical and spectroscopic analyses of pieces from several samples, including the Fe-doped W, failed to establish a clear link between any specific impurities and the observed anomalies. At the moment we neither know the source nor understand the nature of these anomalies.Supported in part by NSF Grants DMR-77-04680 and DMR-78-07892.Part of this work was done while the author was at the Physics Department, University of Lancaster, Lancaster, England, during a sabbatical.Part of this work was done while the author was at the Physics Department, Catholic University, Nijmegen, The Netherlands, during a sabbatical.     

NMR Studies on 3He-3He and 3He-4He tunneling motions in solid 3He-4He mixtures

Helium-3 nuclear spin relaxation times T ₁, T ₂, and T ₁have been measured for ³He-⁴He solid mixtures at the exchange plateau region (~0.5K). The ³He concentrations X ₃of the samples were 7.2, 2.9, 1.8, 1.4, 0.67, 0.65, and 0.22%, and their molar volumes varied between 19.9 and 20.9cm³/mole in hcp phase. The spectral density function J() for dipolar field fluctuations was determined in the low-frequency branch from T ₁measurements and in the high-frequency branch from conventional T ₁measurements. It was found that J() is given by J() = cJ()|_3–4 + (1–c)J()|_3–3, where J()|_3–4 is the spectral density function due to the ³He-⁴He tunneling motions, and J()|_3–3 is that due to the ³He-³He tunneling motions. Using the Torrey theory, the correlation frequency of the ³He-⁴He tunneling motions was evaluated from T ₁data, and was found to be in good agreement with Landesman 's theory.Supported in part by the Japan Society for the Promotion of Science through a grant to Y.H.     

The effect of a magnetic field on fourth sound in 3He

The influence of a magnetic field on the propagation of fourth sound in superfluid ³He is studied. The field and temperature dependences of the average superfluid density \- _s / and fourth sound Q are measured. The field dependence of \- _s / is very different in a porous medium than predicted by Ginzburg-Landau theory applied to bulk liquid. In particular, a magnetic suppression of \- _s / is observed in the temperature and pressure ranges corresponding to the A phase in bulk liquid. There is strong evidence of a magnetic suppression of T _c itself. The measured \- _s / has a slight history dependence in a magnetic field, but none in zero field. The fourth-sound Q values are compared to the theoretical work of Smith, Jensen, and Wolfle. Quantitative confirmation of their work is problematic.     

Anomalous electrical resistive behaviour of Al-O-Pb sputtered alloys

Application of the sputtering technique to (Al-O) _x Pb_100-x alloys containing an immiscible lead element has been found to result in the formation of a duplex material consisting of f cc lead particles dispersed in an amorphous Al _x O _y oxide matrix. The particle size and interparticle distance of the lead phase were about 10 to 50 nm and 10 to 40 nm, respectively. The Al-O-Pb alloys have been found to exhibit an extremely high electrical resistivity (), e.g., 4.06 x 10⁶ cm for (Al-O)_87.5 Pb_12.5 at 273 K, as well as a large positive temperature-dependent resistivity reaching 92% Of 273. The peculiar resistivity behaviour was interpreted by assuming the mechanism that only the lead phase embedded in Al_xO_y matrix contributes to electrical conductivity and the mobility of lead electrons is greatly reduced in the intervening oxide region among lead phases. It has thus been demonstrated that the composite material exhibiting peculiar characteristics, which cannot be achieved in metallic composite materials, is obtained by simultaneously sputtering oxide and an insoluble metallic element.     

C-Axis resistivities of single- and double-layered Bi-system cuprates: A comparative study

The measurements of anisotropic resistivities of single- and double-layered Bi-system cuprates at different doping levels are presented. The two types of materials exhibit qualitatively common features in both doping and temperature dependences of their c-axis resistivities. The c-axis conduction is incoherent in nature because the _c data are deeply on the insulating side of the Mott limit, even though positive slopes (d_c/dT>0) are observed below room temperature for overdoped samples. Some differences are revealed by quantifying the trend of _c(T) data, which may reflect differences in the charge excitation spectra.     

Ohm resistivity of electroless copper layers as a function of their thicknesses

The electric Ohm resistivity of electroless Cu depositions on dielectric substrates as a function of their thicknesses is studied. Substantial deviations (up to 10–20 times) from the standard resistivity ( = 1.7 cm^–1) below 0.5 (m thicknesses are observed. The experimental data show for the entire region of thicknesses (d 0.07–5 m) a power function between the relative resistivity changes (/) and the inverse thickness of depositions (d )–(/ (1/d )^0.8. This empirical relation is discussed as an effect of the porous structure of the metallic layers deposited on the substrate. A scanning electron micrography was applied in order to visualize the morphology of the depositions. The micrographs clearly show the evolution of the deposition profile: starting from separate islands at the very beginning of the process, and gradually covering the entire area with continuous but porous metal layers.     

Thermal effects in high density polyethylene and low density polyethylene at high hydrostatic pressures

The temperature changes as a result of rapid hydrostatic pressure applications are reported for high density polyethylene (HDPE) and low density polyethylene (LDPE) in the reference temperature range from 298 to 423 K and in the pressure range from 13.8 to 200 MN m^–2. The adiabatic temperature changes were found to be a function of pressure and temperature. A curve fitting analysis showed that the empirical curve (/P) =ab(P)^b–1 described the experimental thermoelastic coefficients obtained from the experiments. The data were analyzed by determining the predicted thermoelastic coefficients derived from the Thomson equation (/P) = T ₀/C _p. The experimental and predicted Grüneisen parameter _T were also determined.     

The critical tensile stress criterion for cleavage

An elastic-plastic analysis was used to accurately measure the microscopic cleavage strength _inff ^sup* of notched bars of high nitrogen steel in bending. It was found that _inff ^sup* increases as the root radius of the notch decreases. For > 0.010, the variation of _inff ^sup* with , and the difference between _ingff ^sup* and the cleavage fracture strength of a plane tensile specimen, _f, may result from a statistical effect, due to differences in the volume of highly stressed material in the plastic zone. For < .010, the primary reason for the apparent increase in _inff ^sup* with decreasing , is the steep stress gradient at the notch tip, which forces the critical plastic zone size to extend further to insure that unstable microcraek propagation can occur. Both the statistical and stress gradient effects have been quantitatively evaluated and found to be in good agreement with the experimental data.

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Zusammenfassung Man benutzte eine elastisch-plastische Analyse, um die miktoskopische Spaltungssärke _inff ^sup* von eingekerbten Stahlbarren mit hohem Stickstoffgehalt im Krümmen sorgfältig zu messen. Man stellte fest, dass _inff ^sup* sich vergrösserte während der Wurzelradius der Kerbe sick verringerte. Da > 0.010 ist, ist die Variation von _inff ^sup* mit der Spaitungsfrakturstärke einer planaren Spannungsprobe, _f durch einen statistischen Effekt und durch Unterschiede in dem Volumen von stark angespanntem Material in der plastischen Zone verursacht. Da > 0.010 ist, ist der ursprüngliche Grund für die augenscheinliche Zunahme in _f mit verringertem , der tiefe Anspannungsgradiente an der Kerbenspitze, durch welche sich die kritische, plastische Zonengrösse weiter ausdehnen muss, um die labile Mikrorissausbreitung zu sichern. Die statistischen und Anspannungsgradienteffekte wurden quantitative ausgewertet und man fand gute Übereinstimmung mit den experimentellen werten.

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Résumé Une analyse élastoplastique a été utilisée pour la mesure précise de la résistance microscopique du clivage _inff ^sup* de barreaux entaillées d'acier à haute teneur en azote et soumis à flexion.On a trouvé que _inff ^sup* s'accroit lorsque diminue le rayon d'arrondi à la racine de fentaille. Lorsque est supérieur à 0,25 mm, la variation de _inff ^sup* en fonction de est due à un effet statistique du aux différences de volume de matière soumis, dans la zone de déformation plastique, à des contraintes; élevées. Il en est également de même l'écart entre _inff ^sup* et la contrainte de rupture par clivage dune éprouvette de traction sans entaille.Lorsque est inférieur à 0,25 mm, la raison principale de l'accroissement de _inff ^sup* avec des valeurs de décroissantes réside dans l'existence d'un gradient aigu des contraintes à la pointe de la fissure. Un tel gradient force à s'accrcître lesdimensions de la zone critique de deformation plastique, pour que puisse se produire une propagation instable dune microfissure.On a pu évaluer quantitativement ces effets statistiques d'une part et de gradients de contraintes d'autre part, et l'on s'est trouvé en accord satisfaisant avec les données expérimenetales.

     

Theory of electrical resistivity of metal-matrix composites at cryogenic and higher temperatures

This paper presents a theory describing the electrical resistivity (conductivity) in the axial direction of unidirectional fibre-reinforced metal-matrix composite (MMC) materials at cryogenic and higher temperatures. The theory is derived from the solution of Boltzmann's equation. A triple-integral expression is obtained to describe the change in the electrical conductivity in the matrix metal due to electron scattering from the fibre surfaces. It is shown that at cryogenic temperatures, the electrical resistivity can rise by a factor of 2200 over a decrease in temperature of about 6 K below about 10 K. This effect is due entirely to electron scattering from fibre surfaces. The model developed shows that the composite resistivity agrees well with known experimental data at temperatures above 80 K. At very low temperatures, _c (T) _c (T _R) (1–CT ^–4)^–1, whereT is the absolute temperature. Shortcomings and implications of the theory are discussed.     

Standard Gibbs' energies of formation of BaCuO2, Y2Cu2O5 and Y2BaCuO5

The Gibbs' energies of formation of BaCuO₂, Y₂Cu₂O₅ and Y₂BaCuO₅ from component oxides have been measured using solid state galvanic cells incorporating CaF₂ as the solid electrolyte under pure oxygen at a pressure of 1.01×10⁵ Pa BaO + CuO BaCuO₂ G _f,ox ^o (± 0.3) (kJ mol^–1)=–63.4–0.0525T(K) Y₂O₃ + 2CuO Y₂Cu₂O₂ G _f,ox ^o (± 0.3) (kJ mol^–1)=18.47–0.0219T(K) Y₂O₃ + BaO + CuO Y₂BaCuO₅ G _f,ox ^o (± 0.7) (kJ mol^–1)=–72.5–0.0793T(K) Because the superconducting compound YBa₂Cu₃O_7– coexists with any two of the phases CuO, BaCuO₂ and Y₂BaCuO₅, the data on BaCuO₂ and Y₂BaCuO₅ obtained in this study provide the basis for the evaluation of the Gibbs' energy of formation of the 1-2-3 compound at high temperatures.     

Effects of aluminium on the electrical and mechanical properties of PTCR BaTiO3 ceramics as a function of the sintering temperature

The effect of AI additions on the electrical behaviour of positive temperature coefficient of resistance (PTCR) BaTiO₃ ceramic sintered in air at temperatures ranging between 1220 and 1400° C have been investigated. Two batches of material, both showing a PTCR effect, were prepared identically except that additions of AI₂O₃ (0.55 mol %) were made to one of them. It has been confirmed that the presence of aluminium results in an increase in the temperature at which the maximum resistivity, _max, occurs as well as reducing the sintering temperature, in the presence of silicon, to 1240° C. Additionally, direct comparisons between the two materials have demonstrated that such additions result in an increase of 100% in the minimum resistivity, _min, at sintering temperatures beyond 1280° C. A similar increase in _max for sintering temperatures below 1360° C and a five-fold reduction in the ratio of _max/_min in samples sintered above 1320° C have also been attributed to the presence of aluminium. It was further found that aluminium increases the average grain size by 30% and promotes the formation of a liquid phase.     

Thermal conductivity of methane

This paper reports thermal conductivity data for methane measured in the temperature range 120–400 K and pressure range 25–700 bar with a maximum uncertainty of ± 1%. A simple correlation of these data accurate to within about 3% is obtained and used to prepare a table of recommended values.Nomenclature a _k ,b _ij ,b _k Parameters of the regression model, k= 0 to n; i =0 to m; j =0 to n - P Pressure (MPa or bar) - Q _kl Heat flux per unit length (mW · m^–1) - t time (s) - T Temperature (K) - T _cr Critical temperature (K) - T _r reduced temperature (= T/T _cr) - T _w Temperature rise of wire between times t ₁ and t ₂ (deg K) - T ^* Reduced temperature difference (TT _cr)/T _cr - Thermal conductivity (mW · m^–1 · K^–1) - ₁ Thermal conductivity at 1 bar (mW · m^–1 · K^–1) - _bg Background thermal conductivity (mW · m^–1 · K^–1) - _cr Anomalous thermal conductivity (mW · m^–1 · K^–1) - _e Excess thermal conductivity (mW · m^–1 · K^–1) - Density (g · cm^–3) - _cr Critical density (g · cm^–3) - _r Reduced density (= / _cr) - ^* Reduced density difference (– _cr )/ _cr      

A five-mode truncation of the Navier-Stokes equations on a three-dimensional torus

After defining a general N-mode truncation of the three-dimensional Navier-Stokes equations for an incompressible fluid with periodic boundary conditions, a particular 5-mode truncation is considered, with an external force independent of time and acting on one mode only. The truncated system, which originally consists of twenty first order nonlinear differential equations depending on four external parameters, thanks to its peculiar features, can be reduced to only five equations with two parameters, and R ₂. The study of this reduced model is performed in deep detail in the case = 1, and only roughly for varying. In the former case a behavior is found which is quite similar to the ones of the Lorenz model and of a 5-mode truncation of the two-dimensional Navier-Stokes equations previously studied.Work supported in part by Ministero della Pubblica Istruzione