The study on the critical temperature, composition, and microstresses in a Nb3Sn layer

Monofilamentary Nb₃Sn wires of large diameter with niobium tube, which were obtained by the method of solid-phase diffusion, are well suited for the study of the distribution of the critical temperature T_c in Nb₃Sn layers. Three regions with different gradients of Sn and Nb concentration and different Cu content can be distinguished in Nb₃Sn layer. In the central part of the layer, the Sn content comprises 24.5 at.% and the gradient of Sn concentration is negligibly small. Measurements on specimens of 1.2 mm in diameter with a slit cut along the cylinder generatrix showed that the critical temperature of the Nb₃Sn region adjacent to Cu(Sn) bronze is lower than the critical temperature of the central part of the layer. Fluctuations of T_c in the central part of the layer exceed the change of T_c related to the gradient of the Sn concentration, which is very small. These fluctuations spread both the R(T) curve and the high-temperature part of the temperature transition registered by the inductive method.     

Growth of Nb3Sn in multifilamentary bronze composites

Growth of Nb₃Sn layers in multifilamentary composites has been investigated and their superconducting critical temperatures are measured using both resistive and inductive techniques. The growth parameters are discussed in the light of the analytical models of Reddi et al. Results show that for the composites studied, the rate controlling step for Nb₃Sn growth is diffusion of tin through grain boundaries of Nb₃Sn with the time exponent n determined by both the initial grain size and grain growth. T _c measurements show that for composites with a higher filament number, the width of superconducting transition is broader with no significant change in the onset T _c.     

Invariant temperature and field strain functions for Nb3Sn composite superconductors

The observed strain dependence of Nb₃Sn over an extended range of applied strain requires revision of the functions used previously to represent that strain dependence. The concept and various definitions of the strain function for the upper critical field and the critical temperature are reviewed. An invariant strain function for the critical temperature is derived from the strain energy potential of the general invariant strain analysis. The invariant strain function is applied to a study of uniaxial longitudinal applied strain on wire and tape conductors. Uniaxial forms of the general strain function are derived, and parameter values of the strain function are determined from a fit of the uniaxial forms to published uniaxial strain data for the critical temperature. The concept of precompression is examined in the context of the strain function. The invariant strain function, as an analytic function, is compared with numerical calculations of the general invariant strain analysis for longitudinal and transverse applied strain. The correspondence between the strain dependence of the critical temperature and the upper critical field is discussed, and a form of the invariant strain function for the upper critical field is presented.     

Growth and structural studies of multifilamentary Nb3Sn formed by solid state diffusion

Growth of Nb₃Sn layer formed in a multifilamentary composite of bronze matrix by solid state diffusion has been investigated and its T_c values are measured after different time periods of diffusion anneal. The grain boundary structures are also systematically studied with scanning electron microscopy. Results obtained beyond reasonable doubt conclude that the rate controlling process for growth of Nb₃Sn is via diffusion through grain boundaries of Nb₃Sn layer, and grain growth significantly affects the layer growth. Both T_c and the transition width ΔT_c change in a regular way as annealing progresses, and the variation of these parameters is related to changes in the grain structure and internal strains of the sample.     

Microstructure,composition and critical current density of superconducting Nb3Sn wires

The production of superconducting Nb₃Sn multifilamentary wires with optimized critical currents requires a detailed knowledge of various processes, involving both the mechanical deformation and the reaction kinetics. The physical properties of the Nb₃Sn phase are briefly reviewed, the precise knowledge of their variation as a function of the Sn content being essential for the optimization of the critical current density, J_c. The variation of the transition temperature T_c, the upper critical field, B_c2(0), and the normal state electric resistivity ρ_o, as a function of the Sn content, β, in the binary system Nb_1?βSn_β is carefully analyzed. The effect of Ta, Ti and Ta + Ti additives to Nb₃Sn on the physical properties is discussed in detail. Low temperature specific heat measurements are introduced for determining the T_c distribution inside Nb₃Sn filaments while avoiding shielding effects.The microstructure of the superconducting phase in Bronze Route and Internal Sn Diffusion processed wires is studied, taking into account the unique microstructure of Bronze Route filaments, comprising an equiaxed and a columnar grain region, their areas being comparable. The Sn content increases gradually, from 18 to 22 at.% in columnar and from 22 to 25 at.% in equiaxed grains. Taking into account the equiaxed grains only in Bronze Route wires, it is found that the pinning force density F_GB is essentially the same as in the superconducting part of Internal Sn and PIT wires. The lower values of the overall F_GB in Bronze Route wires is due to the presence of columnar grains, with lower T_c and B_c2. The presence of columnar grains also explains the deviation from linearity of the Kramer rule in Bronze Route wires.The mechanism leading to the variation of J_c vs. ε, where ε is the uniaxial applied strain, is correlated to the elastic tetragonal distortion of the A15 phase in the filaments, caused by the matrix precompression or by Lorentz forces. The behavior of J_c (ε) is found to show systematic differences between Bronze Route and Internal Sn processed wires. Possible reasons for the stronger variation of J_c (ε) up to 21 T in Internal Sn wires are discussed.     

Heat treatment of Nb3Sn conductors

Magnet coils made out of Nb₃Sn superconductors usually are manufactured by the wind- and react-technique. Due to the brittleness of the A15 material the superconductive layer is formed only after the winding of the magnet. This is done by a heat treatment in which Sn diffuses via a matrix into Nb filaments and the superconducting layer is formed. Depending on the exact temperature and time of the heat treatment, the physical properties of the superconductor such as critical current density J_c, upper critical field B_c2, critical temperature T_c and n-value can be varied over a wide range. This is because the diffusion process determines the grain size distribution, the thickness of the superconductive layer as well as the Sn distribution within the layer.This article will provide a review of the investigations concerning different aspects of heat treatment over recent years.     

A Study of the Paramagnetic to Ferromagnetic Transition in the Optimally Doped CMR Compound La0.65Ca0.35MnO3 and Its Dependence on Oxygen Mass

We present a study of the paramagnetic to ferromagnetic transition in the CMR compound La_0.65Ca_0.35MnO₃ and its dependence on magnetic field and oxygen mass. The transition is characterized by two temperatures, the thermodynamic transition temperature at T _c, obtained from specific heat and thermal expansion data, and the resistive transition obtained from the resistivity maximum. The resistive transition occurs well within the paramagnetic range. The magnetic susceptibility in the paramagnetic range is isotope dependent up to 400 K. The magnitude of the Curie-Weiss constant indicates the presence of small clusters of about 4–5 unit cells. The resistive transition occurs when the percolation limit for these clusters is reached.     

A Study of the Paramagnetic to Ferromagnetic Transition in the Optimally Doped CMR Compound La0.65Ca0.35MnO3 and Its Dependence on Oxygen Mass

We present a study of the paramagnetic to ferromagnetic transition in the CMR compound La_0.65Ca_0.35MnO₃ and its dependence on magnetic field and oxygen mass. The transition is characterized by two temperatures, the thermodynamic transition temperature at T _c, obtained from specific heat and thermal expansion data, and the resistive transition obtained from the resistivity maximum. The resistive transition occurs well within the paramagnetic range. The magnetic susceptibility in the paramagnetic range is isotope dependent up to 400 K. The magnitude of the Curie-Weiss constant indicates the presence of small clusters of about 4–5 unit cells. The resistive transition occurs when the percolation limit for these clusters is reached.     

Strain characteristics of Nb3Sn multifilamentary wires with CuNb reinforcing stabilizer

Bronze processed multifilamentary Nb₃Sn superconducting wires, with a CuNb reinforcing stabilizer instead of the conventional Cu stabilizer, were fabricated. The mechanical properties and the strain dependence of the critical current I_c were evaluated at 4.2 K and a magnetic field of 15 T. A remarkable increase in the yield stress (70%) and the plastic flow stress as compared to the values for the wire with Cu stabilizer was observed. The strain for the peak I_c was also increased by 0.2%. I_c on unloading was reversible within the strain range of 1.5%. The strain sensitivity of I_c in the CuNb/Nb₃Sn wire was almost the same as that of the Cu/Nb₃Sn wire. A decrease in the wire diameter from 0.8 to 0.5 mm resulted in a slight increase in the yield stress of the CuNb/Nb₃Sn wire, but no change in the strain dependence of I_c. An increase in the heat treatment temperature from 700 to 750°C resulted in a decrease in the flow stress of 15%, but no change in the strain dependence of I_c. A marked change in the morphology of the Nb filament in the CuNb reinforcing stabilizer was evidenced during heat treatment.     

Changes ofT c,J c,B c2 and the lattice parameter of the Nb3Sn phase formed at the initial stage of growth in a multifilamentary superconductive wire

Investigations were made of the superconducting transition temperature,T _c, the upper critical flux density,B _c2, and the critical current density,J _c, of Nb₃Sn layers in filamentary wire in a bronze matrix. The lattice parameter,a ₀, andT _c of Nb₃Sn layers in 259-filament wire were determined after removal of the bronze matrix. The microstructure and layer thickness were studied using scanning electron microscopy. The diffusion formation of Nb₃Sn phase at 1023 K was studied until the complete reaction of the niobium filaments. It was found that the Nb₃Sn layer begins to form in the manufacturing process during the intermediate annealing at 793 K, and that there is a considerable degradation of critical parameters due to the non-stoichiometry of the Nb₃Sn phase in layers thinner than 1m.     

Critical current distributions in superconducting composites

The transition from the flux pinning state to the full flux flow state occurs over a range of current in composite superconductors. The critical current, therefore, does not have a single, unique value, there being a distribution of critical currents throughout the composite. This Paper describes a technique for deriving the critical current distribution from the resistive critical current transition. The analysis has been applied to Nb---Ti and Nb₃Sn composites of different types. The technique has been used to analyse good quality conductors, where the l_c is largely determined by the intrinsic fluxoid-microstructure interactions, At the other extreme, composites with irregular filaments in which the transport critical current is significantly less than the intrinsic critical current, have also been examined. The analysis shows that good conductors have narrow resistive transitions with average l_c values within 5–10% of a high sensitivity measurement of l_c. This difference broadens to ≈ 35% for a badly sausaged composite. A relationship between the n value of the resistive transition and the relative width of the l_c distribution is presented. A simple but accurate method of deriving the average l_c from the resistive transition is also presented.     

The Influence of Dispersedly Distributed Cracks on Critical Current of the Nb<Subscript>3</Subscript>Sn Strand

The Nb₃Sn strand is the presently most widely used high field superconductor. However, one important fact is that the transport properties of an Nb₃Sn strand will degrade obviously when it is subjected to high mechanical loads. Based on the dispersed distribution of cracks in the bronze strand due to a high axial tensile strain, we propose an analytical strand model to describe the influence of cracks on the critical current of the Nb₃Sn strand. The dependence of the critical current I _c of the strand on crack density is investigated theoretically. It is shown that the calculation results by this model agree with the experimental data. The influence of filament-to-matrix resistance r _c on transport degradation is also discussed since r _c is a key parameter for the total voltage calculation and its realistic value is of great importance for accurate results. We also compared the influence of dispersed and collective cracks on transport properties with specific conditions.     

Elastic stiffness model for the critical temperature Tc of Nb3Sn including strain dependence

A calculation is established for the critical temperature T_c of the superconductor Nb₃Sn that includes the dependence on applied mechanical strain. The calculation employs the formalism of strong coupling phonon superconductivity, as usually given in frequency space. The directional nature of strain is included by expressing the equations of strong coupling in wave vector space. The relation between wave number and frequency is provided by the dispersion relations incorporating the effective elastic constants for the symmetry directions of the cubic crystal. An analytical formalism is established in which the elastic constants are derived in a unified way from an assumed strain energy potential function. The form of the strain energy potential is governed by the cubic symmetry. The scalar invariants of the strain tensor under the cubic symmetry group are determined as a set of basis functions for the strain energy potential. In the harmonic approximation, the relation between the strain energy function and the elastic constants determines the harmonic amplitudes of the strain potential from the measured dispersion relations. The electron-phonon coupling characteristic is approximated in a simple analytic form determined by inspection of the experimentally determined tunneling and phonon density of states. The critical temperature is calculated, through the equations of strong coupling, as a sum over the crystal symmetry directions. The anharmonic terms of the strain energy potential are introduced as the source of the strain dependence of the critical temperature. The allowed form of the anharmonic terms is again governed by cubic symmetry. The amplitudes of the anharmonic terms are determined from the strain dependence characteristics of single crystals and composite superconductors. The calculations are found to represent the observed strain dependence well with a strain energy function that contains three scalar invariants of the strain tensor, including the spherical (hydrostatic) strain invariant, and the principle parts of the second and third invariants of the deviatoric strain tensor. The formalism is applied to the analysis of composite conductors. The characteristics of the strain dependence of wire and tape geometries under longitudinal and transverse loads are related to the symmetry of the conductor and direction of applied load. Implications of conductor symmetry and constraint on the measurement of the strain dependent properties are identified.     

Magnetic field orientation dependence of critical current in industrial Nb3Sn strands

In usual superconducting devices such as magnets for NMR, the magnetic field is perpendicular to the superconducting strand axis. But in some special devices, such as magnets for the toroidal field system of fusion machines, the strands can experience any field orientation. For NbTi strands, the pinning force is dependent on the field orientation because of the drawing process (Takacs, S., Polak, M. and Krempasky, L., Critical currents of NbTi tapes with differently oriented anisotropic defects, Cryogenics, 1983, 23, 153–159). In the case of Nb₃Sn strands, the draw and react process suggests that the pinning force is isotropic. In fact, preliminary experiments have shown the contrary, which is why the magnetic field orientation dependence of the critical current for two types of industrial Nb₃Sn strands has been measured. These measurements have been performed for seven field orientations at field strengths up to 20 T. A clear anisotropic effect has been observed, which cannot be explained by Kramer's pinning law. The results are in very good agreement with an empirical law proposed in a recent study by Takayasu et al. (Takayasu, M., Montgomery, D.B. and Minervini, J.V., Effect of magnetic field direction on the critical current of twisted multifilamentary superconducting wires, Inst. of Phys. Conf. Ser., 1997, 158, 917–920). The parameters to be used in this law could be specific to the manufacturing process.     

Optical properties of (1−<Emphasis Type="Italic">x</Emphasis>)PbZn<Subscript>1/3</Subscript>Nb<Subscript>2/3</Subscript>O<Subscript>3</Subscript>−<Emphasis Type="Italic">x</Emphasis>PbTiO<Subscript>3</Subscript> single crystals

The temperature dependence of the optical transmission and small-angle light scattering with and without applied constant electric field was studied in relaxor single crystals of 0.91PbZn_1/3Nb_2/3O₃-0.09PbTiO₃ (PZN-PT 91/9) and 0.93PbZn_1/3Nb_2/3O₃-0.07PbTiO₃ (PZN-PT 93/7) solid solutions in the region of two phase transitions: (i) from cubic paraelectric to tetragonal ferroelectric phase at T=T _c and (ii) from tetragonal ferroelectric to rhombohedral ferroelectric phase at T=T _rt. In the absence of external electric field, only the phase transition at T _c proceeds in both PZN-PT 91/9 and PZN-PT 93/7 crystals according to a percolation mechanism and is accompanied by the appearance of a sharp maximum in the small-angle light scattering intensity curve. In PZN-PT 93/7 crystals, the application of a relatively weak electric field induces an additional percolation type phase transition at T _rt.     

Structure and properties of Nb<Subscript>3</Subscript>Sn coatings produced by unsteady-current electrocodeposition of Nb and Sn

We have studied the effect of electric-current mode on the structure and characteristics of niobium stannide coatings produced by electrochemical coreduction of niobium and tin ions at the cathode in molten salts. The results demonstrate that single-phase Nb₃Sn coatings with a superconducting transition temperature T _c = 17.3–17.9 K can be obtained using unsteady-current deposition. The coatings produced in galvanostatic mode and by ac deposition at a frequency of 50 Hz have a columnar grain structure. Current-reversal deposition with pulse ratios above 7–9 results in a layered microstructure with layers parallel to the substrate surface, instead of the columnar microstructure, and ensures a considerably higher critical current.     

Dielastic interaction of the flux line lattice with internal stresses of crystal imperfections. I. The change of elastic constants in an inhomogeneous,type II superconductor

Analytical expressions for the change of the elastic constants due to the superconducting phase transition are derived within the framework of the micromagnetic theory of superconductivity. In particular, the variation of the shear modulus in the environment of a single vortex is discussed, which is important for the second-order interaction (E effect) between flux lines and crystal dislocations. Furthermore, the change of elastic moduli in the mixed state, as caused by the periodic flux line lattice, is investigated, and its field dependence is studied. Numerical values for the material parameters that describe the strain dependence of the critical fieldH _c and the critical temperatureT _c are presented for Nb and Nb ₃ Sn.     

Effects of the IVa element addition on the composite-processed superconducting Nb3Sn

The effect of the IVa element addition to the niobium core and that of gallium addition to the matrix on the composition, growth rate and superconducting properties of the composite-processed Nb₃Sn have been studied. The IVa elements added to the niobium core enhance the growth rate of Nb₃Sn, and prevent the grain coarsening of Nb₃Sn. A much larger amount of titanium is incorporated into Nb₃Sn than zirconium or hafnium. T_c shows a slight maximum against the IVa element concentration in the niobium core. J_c at high magnetic fields is more significantly increased by titanium addition than zirconium or hafnium additions. The gallium substitution for tin in the matrix is effective for increasing T_c and J_c in high fields, except for the specimen with Nb-Ti alloy core. The simultaneous addition of hafnium and gallium is most effective for the enhancement of J_c in high fields.     

Stress/strain characteristics of Cu-alloy sheath MgB2 superconducting wires

The mechanical properties of Cu and Cu-alloy (Cu-Zr, Cu-Be and Cu-Cr) sheath in situ PIT-processed MgB₂ superconducting wires were studied at room temperature (RT) and 4.2 K. The effects of stress/strain on the critical current (I_c) of the wires have also been studied at 4.2 K and in magnetic fields up to 5 T. Alloying the Cu sheath significantly increased the yield stress of the wires. The 0.5% flow stresses of the Cu-alloy sheath wires were 147-237 MPa, whereas that of Cu was 55 MPa. At RT, the serration in the stress-strain curves corresponding to the multiple cracking was observed around a strain of 0.4% and the curve almost saturated beyond that point. The strain dependence of I_c prior to the critical strain (ε_irr) was different depending on the magnetic field; being almost constant at 2 T and increased with strain at 5 T. The I_c decreased beyond ε_irr, which was much larger for Cu-alloy sheath wires as compared with Cu sheath wire. The magnitude of ε_irr is due to the difference in the thermal compressive strain in the MgB₂ core, which was relaxed by yielding in the sheath materials. The transverse compression tests revealed that the I_c of the Cu-alloy sheath wire did not degrade up to about 95 MPa, which is also higher than that of Cu sheath wire.