A Numerical Treatment of the rf SQUID: I. General Properties and Noise Energy

We investigate the characteristics and noise performance of rf Superconducting Quantum Interference Devices (SQUIDs) by solving the corresponding Langevin equations numerically and optimizing the model parameters with respect to noise energy. After introducing the basic concepts of the numerical simulations, we give a detailed discussion of the performance of the SQUID as a function of all relevant parameters. The best performance is obtained in the crossover region between the dispersive and dissipative regimes, characterized by an inductance parameter β′ _L ≡2π LI ₀/Φ ₀≈1; L is the loop inductance, I ₀ the critical current of the Josephson junction, and Φ ₀ the flux quantum. In this regime, the lowest (intrinsic) values of noise energy are a factor of about 2 above previous estimates based on analytical approaches. However, several other analytical predictions, such as the inverse proportionality of the noise energy on the tank circuit quality factor and the square of the coupling coefficient between the tank circuit and the SQUID loop, could not be well reproduced. The optimized intrinsic noise energy of the rf SQUID is superior to that of the dc SQUID at all temperatures. Although for technologically achievable parameters this advantage shrinks, particularly at low thermal fluctuation levels, we give examples for realistic parameters that lead to a noise energy comparable to that of the dc SQUID even in this regime.      

Effect of titanium on the structure and mechanical properties of Cu-Al-Ti alloys

The structure and mechanical properties of Cu10 wt% Al base alloys with 0–2.5 wt% Ti additions were investigated using transmission electron microscopy, optical microscopy and tensile tests. Addition of titanium has a decreasing effect on the grain size after quenching fromα + β region and causes significant strengthening of alloys. Alloy containing 1 wt%Ti quenched from 900° C shows mixture ofα, retainedβ (DO₃), disorderedβ′ (3R) and orderedβ′ ₁ (18R) martensites. Alloy with 2.5 wt% Ti addition after quenching containsα, retainedβ (DO₃), ordered T₁ phase of L2₁ superlattice and orderedβ′ ₁ martensite with either R18 or L1₀ structure indicating different stacking of ordered planes as the effect of titanium addition.     

Determination of the parent grain orientation and habit plane normals for β′1 martensite in a Cu–Al–Ni–Mn shape memory alloy

Martensite plates in β′₁ shape memory alloys commonly form self-accommodating groups of four plate variants with habit plane normals clustered about a {1 1 0} pole of the parent phase. In the present work, the crystallography of martensitic transformation in a Cu–Al–Ni–Mn shape memory alloy has been investigated with particular emphasis on accurate habit plane determination. The characteristically high martensite start (M _s) temperature of β′₁ alloys makes it impossible to analyse samples containing isolated plates within a β₁ grain at ambient temperature. However, the parent β₁ grain orientation has been determined in this work by means of a new method of junction plane trace analysis, which is based on the knowledge that the junction planes are precisely {1 1 0}_β1 planes. The mutual consistency of the experimental results indicates that this technique of junction plane traces analysis is a viable method for determining the parent β₁ grain orientation. Habit plane normals were determined by two surface trace measurements and referred to the parent crystal basis by using the β₁ grain orientation matrix. The habit plane normal was determined to be close to {1 5 5}_β1 with the scatter in a series of mean value determinations being less than ± 1.2°. This revised version was published online in November 2006 with corrections to the Cover Date.     

Revised heat capacity and thermodynamic functions of GdVO<Subscript>4</Subscript>

The heat capacity of GdVO₄ has been determined by adiabatic calorimetry in the range 5–345 K. The present experimental data and earlier results have been used to evaluate the thermodynamic functions of gadolinium orthovanadate (C _p ⁰(T), S ⁰(T), H ⁰(T) − H ⁰(0), and Φ⁰(T)) as functions of temperature (5–350 K). Its Gibbs energy of formation is determined to be Δ_f G ⁰(GdVO₄, 298.15 K) = −1684.5 ± 1.6 kJ/mol.     

High Dynamic Range SQUID Readout for Frequency-Domain Multiplexers

A 16-SQUID array has been designed and fabricated, which shows 0.12 μΦ ₀ Hz^−1/2 flux noise at 4.2 K. The readout amplifier based on a cryogenic silicon-germanium bipolar transistor employs short-delay negative flux feedback and reaches 7 MHz bandwith for a 1 Φ _0p-p signal. The −1 dB compression is reached approximately at 4.2 Φ _0p-p amplitude when the signal frequency is 1 MHz. In the feedback mode the flux noise is anomalously increased to 0.35 μΦ ₀ Hz^−1/2.      

dc SQUID: Noise and optimization

A computer model is described for the dc SQUID in which the two Josephson junctions are nonhysteretic, resistively shunted tunnel junctions. In the absence of noise, current-voltage(I–V) characteristics are obtained as functions of the applied flux, _a , SQUID inductanceL, junction critical currentI ₀ , and shunt resistanceR. The effects of asymmetry inL, I ₀ , andR are discussed.I–V characteristics, flux-voltage transfer functions, and low-frequency spectral densities of the voltage noise are obtained at experimentally interesting values of the parameters in the presence of Johnson noise in the resistive shunts. The transfer functions and voltage spectral densities are used to calculate the flux and energy resolution of the SQUID operated as an open-loop, small-signal amplifier. The resolution of the SQUID with ac flux modulation is discussed. The flux resolution calculated for the SQUID of Clarke, Goubau, and Ketchen is1.6 × 10 ^–5 ₀ Hz^–1/2 , approximately one-half the experimental value. Optimization of the SQUID resolution is discussed: It is shown that the optimum operating condition is =2LI ₀ / ₀ 1. Finally, some speculations are made on the ultimate performance of the tunnel junction dc SQUID. When the dominant noise source is Johnson noise in the resistive shunts, the energy resolution per Hz is4k _B T(LC) ^1/2 , whereC is the junction capacitance, and the constraintR=( ₀ /2CI ₀ ) ^1/2 has been imposed. This result implies that the energy resolution is proportional to (junction area) ^1/2 . In the limiteI ₀ R k _B T, the dominant noise source is shot noise in the junctions; for =1, the energy resolution per Hz is then approximatelyh/2.Work supported by the U.S. ERDA.     

Reaction sintering and the α-Si3N4/β′-sialon transformation for compositions in the system Si-Al-O-N

The reaction sintering of three powder compositions corresponding to points near theβ′-phase line in the region of z=0.75 has been studied using apparatus which allowed the continuous monitoring of the densification kinetics. The powder compositions were prepared from mixtures ofα-Si₃N₄, Al₂O₃ and AIN, and the weight changes in the compacts could be kept to less than ∼ 1% over a two hour period. The densification rate is sensitive to small changes in powder composition and decreases markedly as theβ∼'-sialon phase is approached from the oxygen-side. Theα-Si₃N₄ toβ′-sialon conversion rate, on the other hand, is almost independent of the powder composition. The sintering and transformation kinetic data, combined with surface area measurements and observations on the microstructure of the sintered compacts, indicate that the sintering behaviour is controlled by at least two processes, namely the vapour phase transport of material and a solution-diffusion-reprecipitation process involving a grain boundary liquid phase. Both processes result in the conversion ofα-Si₃N₄ toβ′-sialon and result in microstructural coarsening but only the second process leads to overall densification in the powder compact.     

dc SQUID: Current noise

The computer model used by Tesche and Clarke to calculate the voltage noise across the dc SQUID is extended to calculate the circulating current noise around the SQUID loop, and the correlation between the circulating current noise and the voltage noise across the SQUID. The parameters chosen are % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4baFfea0dXde9vqpa0lb9% cq0dXdb9IqFHe9FjuP0-iq0dXdbba9pe0lb9hs0dXda91qaq-xfr-x% fj-hmeGabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHYoGycqGH9a% qpcaaIYaacbaGaa8htaiaa-LeadaWgaaWcbaacbiGaa4hmaaqabaGc% caGGVaacciGae0NPdy0aaSbaaSqaaiab9bcaGiab9bdaWaqabaGccq% GH9aqpcaaIXaGaaiilaiaabccacqqFtoWrcqqF9aqpcqqFYaGmcqaH% apaCcaWGRbWaaSbaaSqaaiaadkeaaeqaaOGaa8hvaiaa-9cacaWFjb% WaaSbaaSqaaiaa+bcacaGFWaaabeaakiab9z6agnaaBaaaleaacqqF% GaaicqqFWaamaeqaaOGaeyypa0JaaeiiaiaabcdacaqGUaGaaeimai% aabwdaaaa!51F9!\[\beta = 2LI_0 /\Phi _{ 0} = 1,{\rm{ }}\Gamma = 2\pi k_B T/I_{ 0} \Phi _{ 0} = {\rm{ 0}}{\rm{.05}}\], and an applied flux of ₀/4 (L is the SQUID inductance, I ₀ is the critical current per junction, T is the temperature, and ₀ is the flux quantum). At frequencies well below the Josephson frequency and at the optimum current bias, the voltage power spectral density is approximately 16 kBTR, the current power spectral density is approximately 11k_B T/R and the voltage-current correlation spectral density is approximately 12k _B T, where R is the resistance per junction.This work was supported by the Division of Materials Sciences, Office of Basic Energy Sciences, U.S. Department of Energy.Guggenheim Fellow.     

Liquid–liquid phase equilibria,density difference,and interfacial tension in the Al–Bi–Si monotectic system

We have performed thermodynamic calculation of the phase equilibria in the ternary monotectic system Al–Bi–Si. The liquid–liquid miscibility gap in the Al–Bi–Si system extends over almost the entire concentration triangle. The thermal analysis data for (Al_0.345Bi_0.655)_100−x Si _x alloys (x = 2.5, 5, 7.5, and 10 wt%) excellently agree with the calculated phase diagram. The experimental density difference of the coexisting liquid phases shows a good agreement with the density difference calculated in the approximation of ideal solution using the densities of pure elements and the compositions of L′ and L′′ from the thermodynamic calculation. The liquid–liquid interfacial tension in the (Al_0.345Bi_0.655)_100−x Si _x liquid alloys increases with Si content. The experimental temperature dependence of the interfacial tension is well described by the power low in reduced temperature (T _C–T) at approach of the critical temperature with the exponent μ = 1.3, which is close to the value predicted by the renormalization group theory of critical behavior.     

Boundary Effects in Superfluid Films

We have studied the superfluid density and the specific heat of the x − y model on latticesL×L×H withL≫H (i.e. on lattices representing a film geometry) using the Cluster Monte Carlo method. In theH-direction we applied staggered boundary conditions so that the order parameter on the top and bottom layers is zero, whereas periodic boundary conditions were applied in theL-directions. We find that the system exhibits a Kosterlitz-Thouless phase transition at theH-dependent temperatureT _c ^2D below the critical temperature T_gl of the bulk system. However, right at the critical temperature the ratio of the areal superfluid density to the critical temperature isH-dependent in the range of film thicknesses considered here. We do not find satisfactory finite-size scaling of the superfluid density with respect toH for the sizes ofH studied. However, our numerical results can be collapsed onto a single curve by introducing an effective thicknessH _eff=H+D (whereD is a constant) into the corresponding scaling relations. We argue that the effective thickness depends on the type of boundary conditions. Scaling of the specific heat does not require an effective thickness (within error bars) and we find good agreement between the scaling functionf ₁ calculated from our Monte Carlo results,f ₁ calculated by renormalization group methods, and the experimentally determined functionf ₁.     

Thermal expansion coefficient of Y-α′-sialon

A sialon composite composed of Y-α′-sialon and β′-sialon has been fabricated by hot pressing mixtures of Si₃N₄, Y₂O₃ and AlN powders. Thermal expansion coefficients of the Y-α′-sialon and β′-sialon were determined by the high-temperature X-ray diffraction technique. The thermal expansion coefficient of Y-α′-sialon depended on the composition, being minimum at x=0.3 in the formula Y_x(Si_12-4.5x, Al_4.5x)(O_1.5x, N_16-1.5x). The coefficient of β′-sialon increased with increasing lattice constant, that is, the z value in the formula Si_6-zAl_zO_zN_8-z. The thermal expansion coefficient of sialon composites determined by a differential dilatometer increased with increasing amount of Y-α′-sialon. This revised version was published online in November 2006 with corrections to the Cover Date.     

Josephson Current Through Planar Pb–Cu–Pb Nanobridges

We report on the fabrication and characterization of coplanar Pb–Cu–Pb nanobridges. In such superconductor (S) – normal metal (N) – superconductor junctions the Josephson coupling is mediated via the proximity effect at the S–N interface. For a junction in the dirty limit (ℓ≪ ξ _N where ℓ is the mean free path and ξ _N is the coherence length in N) the Josephson current I _c is proportional to L/ξ _N ·exp(−L/ξ _N ). The relation defines an upper limit for the length L of the normal-metal bridge in order to observe Josephson coupling. A Josephson current of up to 750 μA at 1.5 K was observed in junctions with L/ξ _N = 0.82 which is only 1/8 of the theoretically expected value. The reduction might originate from oxide layers at the normal metal – superconductor interfaces.     

Effect of the chemical structure of aromatic polyimides on their thermal aging,relaxation behavior and mechanical properties

This article examines the effects of structural changes and thermal aging treatments on the relaxation processes and mechanical properties of three polyimides differing for their molecular structure i.e. PMDA-ODA, 6FDA-ODA, and 6FDA-6FpDA. These polyimides were obtained by thermal imidization of their polyamic acid precursors, which were synthesized from the respective dianhydrides [pyromellitic anhydride (PMDA), hexahydrofluoroisopropylidene diphthalic anhydride (6FDA)], and diamines [4,4′-diaminodiphenyl ether (ODA), 4,4′-(hexafluoroisopropylidene) dianiline (6FpDA)]. After the curing process, the polyimides were thermally aged at a fixed temperature for various times Dynamic mechanical measurements performed in a multi-frequency mode, were used to determine the glass-rubber and sub-glass transitions, as well as the activation energy of the β transition. It was found that the T _g decreased in the order PMDA-ODA > 6FDA-6FpDA > 6FDA-ODA as a result of an increased chain rigidity and molecular packing induced by charge transfer interactions during the thermal imidization process. The β sub-glass transition showed two relaxation processes identified as β′ and β′′. The β′ process was attributed to the local motion of the diamine constituents while the β′′ process was caused by the local motion of the dianhydride moiety. The cooperativity of these molecular motions was also assessed via the Starkweather method. The thermal aging enhanced the state of aggregation of polyimide chains and thus the T _g and the sub-glass transition properties. This effect was particularly marked for the PMDA-ODA polyimide. Also the mechanical properties were significantly affected by chemical structure and aging treatments. For non-aged samples the more influenced parameter was the elongation at break, which decreased in the order PMDA-ODA > 6FDA-ODA > 6FDA-6FpDA. The aging enhanced the elastic modulus and the tensile strength and reduced the elongation at break.     

Effect of rubber particle size on the impact tensile fracture behavior of MBS resin with a bimodal particle size distribution

We performed impact tensile fracture experiments on methylmethacrylate–butadiene–styrene (MBS) resin with small and large particles in a bimodal size distribution, and examined the effects of particle size on fracture behavior by fixing the total rubber content (28 wt%) and the small particle size (about 140 nm), and varying the size of large particles (about 490 nm or 670 nm). Dynamic load P′ and displacement δ′ of single-edge-cracked specimens were measured using a Piezo sensor and a high-speed extensometer, respectively. A P′−δ′ diagram was used to determine external work U _ex applied to the specimen, elastic energy E _e stored in the specimen, and fracture energy E _f for creating a new fracture surface A _s. Energy release rate was then estimated using G _f = E _f/A _s. Values of G _f were correlated with fracture loads and mean crack velocity v _m determined from load and time relationships. We then examined the effect of particle size on G _f and v _m, and results indicated that particle size plays an important role in changing the values of G _f and v _m.     

Josephson Bicrystal Junctions on Sapphire Substrates for THz Frequency Application

Thin film metal oxide superconducting bicrystal junctions on sapphire substrates with I _c R _N products up to 2.5 mV at 4.2 K for width 4 μm and normal-state junction resistance 10–60 Ω were fabricated and characterized at dc and THz frequency. Three types of samples—one with broadband log-periodic antenna, another with double-slot antenna for 300 GHz and third one with double-slot antenna for 400 GHz—have been investigated at THz frequency. New design of antenna coupling with Josephson junction was elaborated for minimization of THz frequency losses in superconducting film. For a particular case of f=320 GHz double-slot antenna, a ratio for bandwidth Q = f/Δf ≈ 10 was measured.     

Thermodynamic properties of Cu<Subscript>5</Subscript>SmSe<Subscript>4</Subscript>

The heat capacity of Cu₅SmSe₄ has been measured from 80 to 300 K. The results have been used to assess the main thermodynamic functions of Cu₅SmSe₄: entropy (S ⁰(T) − S ⁰(0)), enthalpy increment (H ⁰(T) − H ⁰(0)), and reduced Gibbs energy (Φ⁰(T)).     

Viscoelastic properties of composites of calcium alginate and hydroxyapatite

Calcium alginate was reinforced with hydroxyapatite (HA) particles, whose dimensions were a few micrometres, with mass fraction, m _f, values in the range 0–0.8. Cylindrical samples of these composite materials were subjected to cyclic compression in the frequency range f = 0.001–20 Hz; in these tests a sinusoidal load of amplitude 1 N was applied either side of a static compression of 2 N. Storage and loss moduli, E′ and E′′, respectively, were found to be independent of particle size; however, E′ increased with frequency consistent with the materials undergoing a glass transition. Above frequencies of about 0.05 Hz, for all materials. For each frequency, the dependence of the moduli on log₁₀ f could be represented by a third order polynomial; these equations can be used to calculate E′ and E′′ for a range of compositions. Approximate values of are predicted by a Reuss model.     

Dynamic moduli of CaCO3- and Mg(OH)2-filled polypropylene

Fillers suppressed the temperature dependence of storage modulus and caused the flattening of the temperature dependence of the loss modulus in the glass transition region of polypropylene (PP). The glass transition temperature (T _β) of PP did not change with filler content (v _f). This indicates that none of the fillers affect the mobility of PP in the bulk. A new loss maximum appeared at 50 °C forv _f>0.2. This maximum became more prominent when increasing either the filler content or filler specific surface area. Interparticle interactions, leading to the space network of weakly bonded particles, affected PP mobility indirectly. The enhanced interfacial adhesion led to a further decrease of PP mobility nearT _β and to the increase of the new loss maximum at 50 °C.     

Crystallization of Mg-containing phases in β′-Si-Al-O-N ceramics

The microstructures ofβ′-Si-Al-O-N ceramics of base composition Si₄Al₂O₂N₆ with large MgO additive (6 to 7 wt %) have been compared in the hot-pressed and sintered conditions. In both ceramics Mg shows only a small solubility inβ′ crystals and is mainly segregated in a “matrix” phase. In hot-pressed materials this is an Mg-Al-silicate glass whereas in sintered materials, inhomogeneities in composition and internal cavities are believed to catalyse its crystallization as the spinel phase (MgAl₂O₄ with partial Si substitution). A minor phase in sintered ceramics is the 15R “polytype” of the AlN structure.     

Magnetic and Superconducting Properties of Doped and Undoped Double Perovskite Sr<Subscript>2</Subscript>YRuO<Subscript>6</Subscript>

We report here SQUID (magnetization) measurements, along with supporting specific heat, Raman, SEM (scanning electron microscope), EDX (energy dispersive X-ray) and XRD (X-ray diffraction) measurements, on Cu-doped and undoped double perovskite Sr₂²⁺Y³⁺Ru⁵⁺O₆^2-\mathrm{Sr}_{2}^{2+}\mathrm{Y}^{3+}\mathrm{Ru}^{5+}\mathrm{O}_{6}^{2-} (abbreviated as SrY2116) system grown as single crystal using high-temperature solution growth technique. These measurements show the undoped system to be a nonmetallic (insulating) spin glass (SG) and the ∼5–30% Cu-doped (i.e. Cu-concentration/(Cu + Ru-concentration) ∼5–30%) system to be a spin glass superconductor (SGSC) with T _c (critical temperature) ∼28–31 K and superconducting volume fraction, f _sc∼2.2–9%. To mention, similar measurements done on undoped and Cu-doped BaY2116 and BaPr2116 systems show for them the same (SG, SGSC) behaviors. However they show a decrease in T _c and f _sc when diamagnetic Y³⁺ ions are replaced by Pr³⁺ spins, presumably due to enhanced internal pair breaking, and also decreased Cu–O–Cu overlap, owing to Pr³⁺ presence; these phenomena are known to exist in the Pr123 compound, PrBa₂Cu₃O_7−δ (δ∼0), due to ∼10% of Pr³⁺ ions having tendency to occupy Ba²⁺ sites. Measurements done on undoped and Cu-doped SrHo2116 show similar SG and SGSC properties. Further, the undoped and Cu-doped SrY2116 crystals grown by hydrothermal growth technique (i.e., grown using lower temperature and high pressure) show same behaviors. From these investigations it can be said that the undoped Ru-double perovskites (A₂BB′O₆, B′=Ru) are SG systems and that Cu-doped Ru-double perovskites (A₂BB′O _δ , δ∼6, B′=Ru_1−x Cu _x , 0<x≲0.3) are SG superconductors (SGSCs). Results are discussed.