Effect of a magnetic field on the specific heat jump of a superconducting alloy containing paramagnetic impurities with local states within the gap

The effect of a uniform magnetic field on the specific heat jump \({\Delta C}\) of a superconductor containing paramagnetic impurities has been investigated. The impurities are described by the Shiba-Rusinov model. Taking the normalized position of the bound state within the BCS gap ε₀=0.8 and 0.0 and the parameter α(=〈S _z ² 〉/S²)=1.0 and 1/3 as typical values, we find the detailed dependence of \({\Delta C}\) on the impurity concentration \(\bar c\) and the transition temperature T_c. In some cases \({\Delta C}\) diverges at certain values of \(\bar c\) or T_c, signaling a change of the normal-superconductor phase transition from second order to first order.     

Cross-slip on the first order pyramidal plane (10\bar 11) of a-type dislocations [1\bar 210] in the plastic deformation of α-titanium single crystals

The nature of the cross-slip plane was determined by electron microscopy observations of α-titanium single crystal specimens, oriented for single prismatic slip (10 \(\bar 1\) 0) [1 \(\bar 2\) 10]. The occurrence of cross slip on the first order pyramidal plane (10 \(\bar 1\) 1) was proved for a-type dislocations [1 \(\bar 2\) 10]. Furthermore, two types of dislocation configuration due to the double cross-slip were observed: edge dislocation dipoles and loops elongated along the Burger's vector.     

Generalized fracture mechanics of ductile steels

The generalized fracture mechanics approach is applied to two ductile steels, namely mild steel and 18/8 stainless steel in plane stress. The theory defines a fracture parameter \(\mathcal{T}\) , which is a truly plastic analogue of theJ contour integral and, for an edge crack specimen, is given by $$\mathcal{T} = k_1 ( \in _0 )cW_{0_c } $$ wherek ₁ is an explicit function,c is the crack length andε ₀, W_0c are respectively the strain and input energy density at fracture, remote from the crack. The functionk ₁(ε _o) is derived experimentally and the constancy of \(\mathcal{T}\) with respect to crack length and applied load is demonstrated. The variation of \(\mathcal{T}\) with crack extension during slow growth is investigated, as is the rate dependence of \(\mathcal{T}\) in mild steel.     

Measurements of the Kapitza resistance and Onsager cross-coefficient for the4He crystal-superfluid interface

The effect of a heat current across the atomically rough crystal-superfluid interface in⁴He has been studied below 1 K. The chemical potential difference Δμ and temperature difference ΔT were measured simultaneously, the ΔT by means of a “superfluid melting-curve thermometer.” The results give the mean phonon transmission coefficient across the interface \(\bar \tau \) and a dimensionless quantity β that determines the Onsager coefficient linking Δμ with the heat current. The transmission probability \(\bar \tau \) is proportional toT ² below 0.2 K, in agreement with other experiments and with various theories, and it depends slightly on the crystal orientation, increasing near thec axis. The coefficient β, which is roughly independent of temperature and orientation, agrees with a recent theory of Bowley and Edwards.     

Decomposition of the Heusler alloy Cu2MnAl at 360°C

During thermomagnetic studies, the as-quenched Heusler alloy Cu_2.00 Mn_1.00 Al_1.01 exhibits two Curie temperatures \(\theta _{C_I } \) and \(\theta _{C_{II} } \) . After 98 h at 360° C, above the Curie point, X-ray diffraction patterns indicate two ferromagnetic phases: Cu₂MnAl (I) witha _I=5.8707 Å and \(\theta _{C_I } \) = 151 ± 10° C; Cu₂MnAl (II) witha _II=5.9656 Å and \(\theta _{C_{II} } \) = 332 ± 4° C, whereas the 850° C as-quenched alloy exhibitsa=5.9612 Å andθ _c=341±5° C. The results are discussed in terms of the early stages of the decomposition of the Heusler phase. A mechanism, involving mainly the atomic migration of manganese, is suggested in order to reach the equilibrium phases of the ternary Cu-Mn-Al diagram. The kinetics of the decomposition should be ruled by the nucleation and the growth of the Cu₃Mn₂Al intermetallic compound.     

Computer simulation of vortex pinning in type II superconductors. II. Random point pins

Pinning of vortices in a type II superconductor by randomly positioned identical point pins is simulated using the two-dimensional method described in a previous paper (Part I). The system is characterized by the vortex and pin numbers (N _v ,N _p ), the vortex and pin interaction ranges (R _v ,R _p ), and the amplitude of the pin potentialA _p . The computation is performed for many cases: dilute or dense, sharp or soft, attractive or repulsive, weak or strong pins, and ideal or amorphous vortex lattice. The total pinning forceF as a function of the mean vortex displacementX increases first linearly (over a distance usually much smaller than the vortex spacing and thanR _p ) and then saturates, fluctuating about its average \(\bar F\) . We interpret \(\bar F\) as the maximum pinning forcej _c B of a large specimen. For weak pins the prediction of Larkin and Ovchinnikov for two-dimensional collective pinning is confirmed: \(\bar F\) =const· \(\bar W\) /R _p c ₆₆, where \(\bar W\) is the mean square pinning force andc ₆₆ is the shear modulus of the vortex lattice. If the initial vortex lattice is chosen highly defective (“amorphous”) the constant is 1.3–3 times larger than for the ideal triangular lattice. This finding may explain the often observed “history effect”. The function \(\bar F\) (A _p ) exhibits a jump, which for dilute, sharp, attractive pins occurs close to the “threshold value” predicted for isolated pins by Labusch. This jump reflects the onset of plastic deformation of the vortex lattice, and in some cases of vortex trapping, but isnot a genuine threshold. For strong pins \(\bar F\) ～(N _p \(\bar W\) )^1/2 approaches the direct summation limit. For both weak and strong pinningj _c B is related to the mean squareactual (not maximum) force of each pin. This mean square in general is not proportional toA _p ² but, due to relaxation of the vortex lattice, may be smaller or larger than its rigid-lattice limit. Therefore, simple power lawsj _c ～n _p A _p ² orj _c ～n _p A _p in general donot hold except for very weak or unphysically strong pinning.     

Dielectric function for the Anderson model

In recent years the study of alloys and compounds containing rare-earth and actinide elements is receiving increasing attention. The Anderson model is most popularly used for studying the theory of these systems. As it displays a large number of anomalous characters in magnetic and electrical properties, it was felt worthwhile to study the dielectric properties of this model. Using the linear response theory of Kubo, the energy and wave vector-dependent dielectric function \(\varepsilon \left( {\bar q,E} \right)\) is related to the retarded Green’s function of Fourier components of electron density fluctuations \(\left\langle {\left\langle {\rho _{\bar q} ;\rho _{ - \bar q} } \right\rangle } \right\rangle \) . Thus a many-body calculation of \(\varepsilon \left( {\bar q,E} \right)\) requires the calculation of \(\left\langle {\left\langle {\rho _{\bar q} ;\rho _{ - \bar q} } \right\rangle } \right\rangle \) . The Greens function is calculated using the equation-of-motion method with RPA decoupling. Further, since certain ensemble averages are required as inputs to the calculation, the relevant single-particle Green’s functions are also evaluated.     

Superconducting transition temperature of aluminum,indium, and lead fine particles

Aluminum, indium, and lead fine particles with free surfaces were made by evaporation in helium gas to study the size dependence of the superconducting transition temperatureT _c in very small particles. The transition temperature was determined from the change of diamagnetic susceptibility with temperature. The present experiment shows thatT _c rises with decrease of the average diameter \(\bar d\) for aluminum and indium, while it remains nearly constant for lead. The enhancement factorsT _c /T _c ^b (T _c ^b isT _c for the bulk material) in the case of \(\bar d = 100 {\AA}\) are determined as 1.45, 1.15, and 1.0 for aluminum, indium, and lead, respectively. The effect of the soft phonon mode arising from the increasing fraction of surface satisfactorily explains the experiment with respect to both the size dependence and the difference among elements by a rather simple model.     

Electrical conductivity of polycrystalline tin dioxide and its solid solution with ZnO

Electrical conductivity (σ) of “pure” and ZnO doped SnO₂ has been measured at different temperatures and oxygen partial pressures ( \(p_{{\text{O}}_{\text{2}} } \) )- From the variation of electrical conductivity of these materials three partial pressure ranges have been identifieD. In the high partial pressure rangeσ increases with decreasing \(p_{{\text{O}}_{\text{2}} } \) followed by a \(p_{{\text{O}}_{\text{2}} } \) independent region at lower \(p_{{\text{O}}_{\text{2}} } \) ´s and finally increases once again with a further decrease of \(p_{{\text{O}}_{\text{2}} } \) . These variations have been explained on the basis of an anti-Frenkel type defect structure and an interstitial solid solution of ZnO in SnO₂. The activation energy for the conduction process has been estimated and the values are found to differ in two different temperature ranges. In the low temperature range the conductivity is attributed mainly to the chemisorption of oxygen on the surface of the specimen.     

Generation of thermal strains in GRP

The temperature dependence of the linear expansion coefficients in the longitudinal (α _l) and transverse directions \((\alpha _{t_1 } and \alpha _{t_2 } )\) of unidirectional glass fibre laminates and their matrix resins (α _m) has been studied. The results for the dry, fully post-cured polyester, epoxy resins and laminates have been found to be consistent with the predictions of the Schapery equations. An anomalous moisture phenomenon, in the form of a peak in theα _m (T)/T andα _t (T)/Tcurves for the polyester resin and laminates has been observed. A difference between \(\alpha _{t_1 }\) and \(\alpha _{t_2 }\) has been observed for partially cured polyester laminates, which is also perturbated in the presence of water. Both these moisture effects, which are not found in the epoxy specimens, are considered to result from a two-phase polyester matrix and the latter to continued curing below the softening point of the resin. These results have a considerable consequence on the magnitude of the thermal strains which develop in polyester composites.     

Transient and steady state creep behaviour of polycrystalline MgO

Stress change experiments during compressive creep tests at high stresses on polycrystalline MgO at 1596 K have shown that the creep rate at any instant during transient and steady state creep is predicted by the ratio,r/h, wherer is the rate of recovery (=??σ/t6t) andh is the coefficient of strain hardening (=?σ/?ε). Over most of transient and steady state creep, whenh is constant and the decrease in creep rate, \(\dot \in\) , is a direct result of a decrease inr, the variation of the creep strain,ε, with time,t, is accurately described as $$ \in = \in _0 + \in _T (1 - e^{ - mt} ) + \dot \in _s t$$ whereε ₀ is the instantaneous strain on loading,ε _T the transient creep strain,m relates to the rate of exhaustion of transient creep and \(\dot \in _s\) is the steady creep rate. Deviations from this equation occur during the initial 10 to 15% of the transient creep life, whenh increases rapidly. The variations in \(\dot \in\) ,r andh during transient and steady state creep are explained in terms of a model for creep in which the rate-determining process is the diffusion controlled growth of the three-dimensional dislocation network within subgrains to form dislocation sources allowing slip to occur.     

Study of an operating characteristic function of the sampling inspection plan of concrete lots

This paper makes an overall analysis of the Sampling Inspection Plan of Concrete Lots based on the estimation \(f_k = \bar f_n - \lambda S_n \) of the mechanical svrength of this building material. With the help of the non-central t variable, two valuesλ _S andλ _E of the acceptance factor λ are determined for each value of n in the set {5, 6,..., 29, 30)}. These λ values have the important propriety of making it possible that inspection plans be formulated for the concrete which does not comply either with the economy or the safety prescribed by the Joint Committee RILEM/CEB on the statistical control of the quality of concrete. Finally, an extremely simple process which permits to obtain the OCC corresponding to \(\hat f_k \) estimator without using the tables of the non-central variable t is presented.     

Containerless Measurements of Density and Viscosity for a Cu_{48}Zr_{52} Liquid

The densities of solid and liquid Cu \(_{48}\) Zr \(_{52}\) and the viscosity of the liquid were measured in a containerless electrostatic levitation system using optical techniques. The measured density of the liquid at the liquidus temperature (1223 K) is (7.02 \(\pm \) 0.01) g \(\cdot \) cm \(^{-3}\) and the density of the solid extrapolated to that temperature is (7.15 \(\pm \) 0.01) g \(\cdot \) cm \(^{-3}\) . The thermal expansion coefficients measured at 1223 K are (6.4 \(\pm \) 0.1) \(\,\times \,10^{-5}\) K \(^{-1}\) in the liquid phase and (3.5 \(\pm \) 0.3) \(\,\times \,10^{-5}\) K \(^{-1}\) in the solid phase. The viscosity of the liquid, measured with the oscillating drop technique, is of the form \(A\exp \left[ \left( {{E}_{0}}+{{E}_{1}}\left( 1/T-1/{{T}_{0}} \right) \right) \times \left( 1/T-1/{{T}_{0}} \right) \right] \) , where \({{T}_{0}}=1223\) K, \(A= (0.0254 \pm 0.0004)\) Pa \(\cdot \) s, \({{E}_{0}}\) =  (8.43 \(\pm \) 0.26) \(\,\times \,10^3\) K and \({{E}_{1}}\) =  (1.7 \(\pm \) 0.2) \(\,\times 10^7\) K \(^{2}\) .     

Evaluation of microstructural instability during the differential strain rate test of a superplastic alloy

Stress (σ)-strain rate ( \(\dot \varepsilon \) ) data of banded and elongated grain microstructures of the Pb-Sn eutectic alloy were analysed over 298 to 443 K to evaluate microstructural instability during differential strain rate tests in the superplastic region. With reference to a stable equiaxed microstructure exhibiting uniqueσ- \(\dot \varepsilon \) relation, banded structure is more susceptible to strain hardening while the elongated grain microstructure exhibits either strain softening or strain hardening depending on the test temperature. This flow behaviour is considered in terms of a change in grain size, represented by the cube root of the grain volume. Activation energy for grain growth calculated from the differential strain rate test data indicates that the activation energy depends on strain rate and type of microstructure.     

Quartz Tuning Forks as Cryogenic Vacuum Gauges

We report measurements of the mechanical \(Q\) of a 32.7 kHz quartz tuning fork as a function of pressure for helium and argon at T  \(=\)  300 K and for helium in the temperature range 7.0–0.7 K. In the low pressure ballistic regime, the damping due to the surrounding gas is inversely proportional to \(P\) , while for higher pressures, a hydrodynamic treatment accounts for most of the variation of \(Q\) with \(P\) . We have combined the ballistic and hydrodynamic models together with calculations of the thermal transpiration correction to correlate the tuning fork \(Q\) at low temperature with the pressure measured with a room temperature pressure gauge. The fork was found to be useful as an in situ pressure gauge for pressures above \(\sim \) 0.1 mTorr. A dissipation peak and frequency drop associated with the superfluid transition in the adsorbed helium film is also observed for \(T<1.4\)  K.     

Comparing Transition-Edge Sensor Response Times in a Modified Contact Scheme with Different Support Beams

We present measurements of the thermal conductance, G, and effective time constants, \(\tau \) , of three transition-edge sensors (TESs) populated in arrays operated from 80–87 mK with T \(_\mathrm{C}\)   \(\sim \)  120 mK. Our TES arrays include several variations of thermal architecture enabling determination of the architecture that demonstrates the minimum noise equivalent power, the lowest \(\tau \) , and the trade-offs among designs. The three TESs we report here have identical Mo/Cu bilayer thermistors and wiring structures, while the thermal architectures are: (1) a TES with straight support beams of 1 mm length, (2) a TES with meander support beams of total length 2 mm and with two phonon-filter blocks per beam, and (3) a TES with meander support beams of total length 2 mm and with six phonon-filter blocks per beam. Our wiring scheme aims to lower the thermistor normal state resistance R \(_{N}\) and increase the sharpness of the transition \(\alpha =\)  dlogR/dlogT at the transition temperature T \(_\mathrm{C}\) . We find an upper limit of \(\alpha \) given by ( \(25\pm 10\) ), and G values of 200 fW/K for (1), 15 fW/K for (2), and 10 fW/K for (3). The value of \(\alpha \) can be improved by slightly increasing the length of our thermistors.     

Superconductivity of YBa2−x Nd x Cu3O y Solid Solution

The solubility of Nd at the Ba sites and the superconductivity of YBa_2?x Nd _x Cu₃O _y were investigated by X-ray powder diffraction and measurements of the electrical resistance and ac susceptibility. The single Re123 phase was obtained for x≤0.30. The onset transition temperature $T_{\text{c}}^{{\text{on}}}$ is insensitive to the Nd content x in the region of x≤0.40. All are higher than 95 K. The zero resistance transition temperatures $T_{\text{c}}^{{\text{zero}}}$ , however, exhibits two-step variation with the increase of x. For x≤0.25, $T_{\text{c}}^{{\text{zero}}}$ are all above 92 K. The highest $T_{\text{c}}^{{\text{zero}}}$ of 94 K was obtained for x=0.25. For x≥0.3 $T_{\text{c}}^{{\text{zero}}}$ drops sharply to about 84 K. Finally $T_{\text{c}}^{{\text{zero}}}$ falls to 30 K and $T_{\text{c}}^{{\text{zero}}}$ is below 10 K for x=0.5. The two-step variation of T _c might be an indication of the existence of two trap levels for holes.     

Superconductivity at 25 K under Hydrostatic Pressure for FeTe 0 . 5 Se 0 . 5 Superconductor

We report the impact of hydrostatic pressure on the superconductivity and normal-state resistivity of FeTe_0.5Se_0.5 superconductor. At the ambient pressure, the FeTe_0.5Se_0.5 compound shows the superconducting transition temperature \(T_{\mathrm {c}}^{\text {onset}} \) at above 13 K and \(T_{\mathrm {c}}^{\rho =0} \) at 11.5 K. We measure pressure-dependent resistivity from 250 to 5 K, which shows that the normal-state resistivity increases initially for the applied pressures of up to 0.55 GPa, and then the same is decreased monotonically with increasing pressure of up to 1.97 GPa. On the other hand, the superconducting transition temperatures ( \(T_{\mathrm {c}}^{\text {onset}} \) and \(T_{\mathrm {c}}^{\rho =0} )\) increase monotonically with increasing pressure. Namely the \(T_{\mathrm {c}}^{\text {onset}} \) increases from 13 to 25 K and \(T_{\mathrm {c}}^{\rho =0} \) from 11.5 to 20 K for the pressure range of 0–1.97 GPa. Our results suggest that superconductivity in this class of Fe-based compounds is very sensitive to pressure as the estimated pressure coefficient d T _c(onset)/dP is ～5.8 K/GPa. It may be suggested that the FeTe_0.5Se_0.5 superconductor is a strong electron-correlated system. The enhancement of T _c with applying pressure is mainly attributed to an increase of charge carriers at the Fermi surface.     

Measurement of the (p, \rho,T) Properties for Pure Hydrocarbons at Temperatures up to 600 K and Pressures up to 200 MPa

The data available for the thermodynamic properties of propane, \(n\) -butane, and isobutane at temperatures above 440 K are outdated and show significant discrepancies with each other. The ambiguity associated with these data could be limiting to the development of any understanding related to the effects of mixing of these substances with other materials such as \(\text{ CO}_{2}\) , ammonia, and non-flammable or lower-flammable HFC refrigerants. In this study, the (p, \(\rho \) , T) properties of propane, \(n\) -butane, and isobutane were measured at temperatures ranging from (360 to 600) K and pressures ranging from (50 to 200) MPa. Precise measurements were carried out using a metal-bellows variable volumometer with a thermostatted air bath. The expanded uncertainties \((k = 2)\) in the temperature, pressure, and density measurements were estimated to be \(<\) 5 mK, 0.02 MPa, and 0.88 kg  \(\cdot \)  m \(^{-3}\) ( \(T\le 423\)  K, \(p<100\)  MPa), 0.76 kg  \(\cdot \)   \(\text{ m}^{-3}\) ( \(T\le 423\)  K, \(p\ge 100\)  MPa), 0.76 kg  \(\cdot \)   \(\text{ m}^{-3}\) ( \(T>423\)  K, \(p < 100\)  MPa), and 2.94 kg  \(\cdot \)   \(\text{ m}^{-3}\) ( \(T>423\)  K, \(p \ge 100\)  MPa), respectively. The data obtained throughout this study were systematically compared with the calculated values derived from the available equations of state. These models agree well with the measured data at higher temperatures up to 600 K, demonstrating their suitability for an effective and precise examination of the mixing effects of potential alternative mixtures.