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A coarse-grained picture of segregation layers in MgYZn alloys as a two-dimensional cluster systems bound in stacking faults has been justified by a combined use of Extended X-ray absorption fine structure (EXAFS), small-angle X-ray scattering, and scanning tunneling microscopy. EXAFS analysis showed an identical relaxed atomic configuration around Y and Zn atoms as a finger print of molecular-like L12 clusters, characteristic of Long Period Stacking Ordered (LPSO) structures. The fingerprint was confirmed for wide range of compositions of cast ternary alloys containing bulk LPSO structures. The clusters in dilute MgYZn alloys, whose segregation layers were sparsely dispersed in the a-Mg matrix, showed the same fingerprint. The results suggested that the Y-Zn clusters in the segregation layers of Mg-Y-Zn alloys are identical, regardless of the cluster density in the layers or the number of segregation layers.

Absolute measurements of small-angle X-ray scattering (SAXS) intensities at the K absorption edge of Mg have been performed using glassy carbon as an intensity standard. Glassy carbon samples polished down to give appropriate transmission have been prepared as a secondary standard to be used at 1.3 keV. Al–Mg binary alloys were used to assess the metastable phase boundary for the Al3Mg metastable precipitation from the absolute scattering intensity. The assessed phase boundary agreed with the previous reports. Glassy carbon was concluded to be an appropriate candidate for an intensity standard sample for transmission measurements of SAXS in the tender X-ray regions.

Precipitation process leading to the formation of long-period stacking ordered (LPSO) structures in dilute MgGdZn and MgYZn alloys during heating at a heating rate of 10 K/min have been examined by in situ synchrotron radiation small- and wide-angle scattering measurements. Samples were solution-treated and quenched prior to the measurements. During heating, two distinct temperature regions were observed for both alloys. The one at the lower temperature, clusters without in-plane order appeared, and then dissolved at higher temperatures. Clusters leading to LPSO structures appeared at a higher temperature above 600 K. Streaky peaks appeared above the temperature, suggesting that very thin layers of LPSO structure with relatively large domain size in the in-plane direction were formed. The average cluster–cluster distance in the segregation layer above 600 K was almost constant until dissolution of LPSO structure at 800 K. The average cluster–cluster distance is larger than the ideally ordered superstructures reported for stoichiometric LPSO alloys.

The effects of the size of the largest crack and size difference among cracks on critical current of superconducting tape with multiple cracks of different sizes in the superconducting layer were investigated by a model analysis and a Monte Carlo simulation, using the specimens consisting of a series circuit of local sections where each section has one crack of different size from each other. It was revealed that, with increasing distribution-width of crack size, the increase in the size of the largest crack acts to reduce the critical current and the increase in the crack size-difference among the sections acts to raise the critical current, and these conflicting two effects are summed up and determine the critical current value. To describe this feature quantitatively, we expressed the statistics of the size of the largest crack in specimens with the Gumbel’s extreme value distribution function. Also we monitored the effect of the difference in crack size among the sections on specimen’s critical current, using the number of the sections equivalent to the largest crack-section at the critical voltage for determination of specimen’s critical current. In this monitoring, small number of the sections equivalent to the largest crack-section corresponds to large difference in crack size among the sections. With the present approach, the effect of the increase in size of the largest crack, which acts to reduce critical current, and the effect of the increase in difference in crack size among the sections, which acts to raise critical current, with increase in distribution-width of crack size, could be estimated separately.

In-situ and simultaneous small- and wide-angle scattering measurements of liquid-quenched Mg₈₅Y₉Zn₆ alloy ribbons were performed to examine phase transition during isothermal annealing at the temperatures below the bifurcation temperature, where long-period stacking ordered (LPSO) structures are not formed yet in the previous work. Even below the temperature, sluggish structural transformation destroying hcp stacking sequence was observed, and development of in-plane and inter plane cluster structures, as imperfect LPSO structure, became noticeable at long time annealing. The characteristic time for structural transformation showed well-defined thermally activated process with Q = 173.6 +/- 14.4 kJ/mol.

Two dimensional anomalous small-angle scattering measurement at K absorption edge of Mg has been successfully demonstrated for concentrated Al-Mg binary alloys and MgO nanoparticles. Enhancing the contrast between Mg-rich precipitates and Al matrix was explained by the anomalous dispersion of Mg, and anisotropic SAXS pattern was in good agreement with the microstructure observed by transmission electron microscopy. Agreement of atomic scattering factor obtained from Al-Mg and MgO nanoparticles indicates that the origin of SAXS in the present Al-Mg alloys are Guinier-Preston zones, not the voids that grew from supersaturated vacancies.

In four probe sensing for measurement of voltage-current curve of superconducting layer-coated tapes, it has been reported that, when a large accidental defect is included in the region between the voltage probes, the critical current value estimated with the one micro-volt/cm criterion is low when the voltage probe spacing is small but it becomes higher when the spacing is larger. In the present work, a simulation study was carried out to reproduce the feature stated above and to describe the dependence of critical current value on the voltage probe spacing under the co-existence of a large crack and multiple small cracks. In simulation, the current shunting model at cracks and a Monte Carlo simulation method were applied to a model superconducting tape, which was composed of one local section with a large crack and multiple local sections with small cracks of different size from each other. The experimentally observed increase in critical current with increasing voltage probe spacing in the large defect included tape was reproduced well by the present simulation. Then, it was shown that the increase in critical current of the large crack-included region with increasing voltage probe spacing is caused by the increase in the ligament part-transported current and shunting current at the large crack due to the increase in critical voltage for determination of critical current. Furthermore, it was shown that the upper and lower bounds of the critical current of the region, in which a large crack and multiple small cracks exist, can be derived from the voltage-current curve of the section with a large crack, and the critical current of the region is given by the upper bound for a given size of the largest crack when the difference in size between the large crack and multiple small cracks is large.

Tomographic images constructed from small-angle X-ray scattering (SAXS) intensities utilizing microbeams have been examined for a model multilayered aluminum alloy sample heat-treated to form spatially modulated composition and microstructures. Spatial distributions of composition and precipitation microstructure have been examined by one-dimensional scanning SAXS measurements and two-dimensional tomographic images of attenuation parameters and integrated intensity of SAXS intensity. Reconstructed images using the integrated intensity reflected the distribution of precipitates in terms of their volume fraction over the sample inside the sample, and agreed with more detailed analysis made in the one-dimensional case.

An anomalous X-ray scattering experiment was performed on an amorphous Mg₈₅Zn₆Y₉ alloy. The experimental data were analyzed using a reverse Monte Carlo model to examine the existence of the seeds of Zn₆Y₈L1₂ impurity clusters. The results reveal the highly enhanced existence of Zn–Y bonds rather than a random distribution of the impurities in the host Mg atoms. With respect to the theoretical structure of the clusters in the crystal phase, shorter nearest-neighboring Zn–Y and shorter second-neighboring Zn–Zn interatomic distances are observed as the fragments of the L1₂ clusters.

A Monte Carlo simulation study was carried out to reveal the effects of crack size distribution and specimen length on the correlation between n-value and critical current in heterogeneously cracked superconducting tapes. First, it was shown that, with increasing distribution width of crack size, the distribution widths of critical current and n-values increase, and, the average critical current-value and average n-value of specimens decrease. Also, it was shown that the decrease in average n-value with increase in distribution width of crack size is more intense than the decrease in average critical current-value and this feature is more pronounced in longer specimens. Then it was revealed that plural n-values can exist for one critical current value since the n-value of specimen was dependent on the positional relation among the voltage-current curves of the sections, of which specimen is constituted. This phenomenon could be described by the difference in the resistance value in the current shunting circuit by application of a single equivalent crack-current shunting model in which the cracks within a specimen are replaced by a single equivalent crack. Based on this result, an approach, in which the resistance value in the current shunting circuit is used to describe the upper-lower bounds and the center of n-value in the correlation diagram between n-value and critical current, was presented. It was shown that the correlation diagrams at various distribution widths of crack size and specimen lengths, obtained by simulation and experiments, are described well by this approach.

Developments of microstructures during heating Mg85Y9Zn6 amorphous ribbons have been examined by in-situ synchrotron radiation small- and wide-angle scattering measurements. The samples show sharp crystallization peak in a DSC measurement at 450 K for a heating rate of 10 K/min. During and just after crystallization, clustering occurred first within supersaturated hcp crystallites, with concomitant hcp grain growth. Above 550 K, the spatial arrangements of the cluster became anisotropic, eventually lead to 18R LPSO structures accompanied by introduction of stacking faults.

We have determined experimentally that the n-value of tension-damaged bismuth strontium calcium copper oxide (BSCCO, Bi2223) filamentary superconducting tape decreases very sharply with decreasing critical current, compared with bending-damaged tape. In this work, the sharp decrease in the n-value associated with decreasing critical current under applied tensile stress/strain was studied with a current shunting model that assumes cracks in filamentary and coated superconductors. In a filamentary conductor containing collective filament cracks, defined as cracks composed of successively cracked filaments in a transverse cross-section, the decrease in the cross-sectional area of the superconducting current transportable-filaments reduces the critical current, and the shunting current at the crack reduces the n-value. In addition, the decrease in the electrical resistance in the current shunting circuit increases the critical current slightly and decreases the n-value sharply. The experimentally measured relationship between the n-value and the critical current for two BSCCO samples from different manufacturers was described by the upper and lower bounds calculated with the current shunting circuit resistance as a variable. The experimentally measured relationship between the n-value and the critical current for two different coated conductors were described in a similar manner.

The Mg-Y-Zn ternary alloy system contains a series of novel structures known as long-period stacking ordered (LPSO) structures. The formation process and its key concept from a viewpoint of phase transition are not yet clear. The current study reveals that the phase transformation process is not a traditional spinodal decomposition or structural transformation but, rather a novel hierarchical phase transformation. In this transformation, clustering occurs first, and the spatial rearrangement of the clusters induce a secondary phase transformation that eventually lead to two-dimensional ordering of the clusters. The formation process was examined using in situ synchrotron radiation small-angle X-ray scattering (SAXS). Rapid quenching from liquid alloy into thin ribbons yielded strongly supersaturated amorphous samples. The samples were heated at a constant rate of 10 K/min. and the scattering patterns were acquired. The SAXS analysis indicated that small clusters grew to sizes of 0.2 nm after they crystallized. The clusters distributed randomly in space grew and eventually transformed into a microstructure with two well-defined cluster-cluster distances, one for the segregation periodicity of LPSO and the other for the in-plane ordering in segregated layer. This transformation into the LPSO structure concomitantly introduces the periodical stacking fault required for the 18R structures.

Heterogeneity in annealed Zr-Cu-Al alloys with high ductility has been examined by high-energy small-angle scattering with strain variation method. Although the statistics is still poor for detailed analysis, it was found that the heterogeneity in the sample showed clear enhancement by applied tensile strain, and the characteristic size of the heterogeneity was of the same order of magnitude as the one observed by high resolution electron microscopy. With surface insensitivity of the present method, anomalous small-angle scattering results at Cu K absorption edge for the same sample was briefly discussed.

Grazing-incidence small-angle X-ray scattering (GISAXS) measurements with soft X-rays have been applied to Ge nanodots capped with a Si layer. Spatially anisotropic distribution of nanodots resulted in strongly asymmetric GISAXS patterns in the qy direction in the soft X-ray region, which have not been observed with conventional hard X-rays. However, such apparent differences were explained by performing a GISAXS intensity calculation on the Ewald sphere, i.e. taking the curvature of Ewald sphere into account.

The nanostructure of Mg(85)Y(9)Zn(6) ternary alloy ingot with long-period stacking ordered structure has been examined by synchrotron radiation small-angle X-ray scattering. The scattering patterns showed sharp reflections corresponding to large domains of 10H, 18R and 14H structures, with in-plane ordering. After annealing at 673 K, the peak intensity of 18R increased, and the diffraction peak corresponding to in-plane ordering sharpened. The domain size of in-plane ordering was much smaller than the domain thickness of 18R in the stacking direction.

The change in n-value and critical current with bending strain and the relation of n-value to critical current of bending-damaged Bi2223 composite tape were studied experimentally and analytically. The n-value of the bending-damaged Bi2223 filamentary composite tape decreased very slightly with increasing bending strain and with decreasing critical current, in comparison with that of tension-damaged tape. To describe the experimental result for bending-damaged tape, a damage evolution model was applied in which the steep tensile-strain variation in the thickness direction, the shape of the core into which the superconducting filaments are bundled and the damage strain parameters obtained from the analysis of the tensile stress–strain curve were incorporated. The measured change in n-value and critical current with bending strain and the relation of n-value to critical current under applied bending strain were described satisfactorily by the present approach.

Anomalous dispersion at the Si K absorption edge has been used to control the reflection from the interface between a film and an Si substrate, which otherwise complicates the nanostructure analysis of such a film, particularly for the soft-matter case, in grazing-incidence small-angle scattering. Such a reflectionless condition has been chosen for a triblock copolymer thin film, and two-dimensional grazing-incidence small-angle scattering patterns were obtained without the effect of the reflection. The present approach is useful for analysing nanostructures without introducing complicated corrections arising from the reflection.

Transport current and n-value of DyBCO-coated conductor pulled in tension were measured experimentally and their relation to crack-induced current shunting was analyzed with the partial crack-current shunting model. The following features were revealed. The shunting current increases with increasing transport current and with increasing crack size. At low voltage where shunting current is low, the transport current of cracked sample normalized with respect to the transport current in non-cracked state is described with the modified ratio of non-cracked area to overall cross-sectional area of superconducting layer. At high voltage where the shunting current is high, the normalized transport current becomes higher than the modified ratio of non-cracked area. The increase in shunting current with transport current (and voltage) leads to a decrease in n-value at high current (voltage). This phenomenon is enhanced by crack extension.

Two-dimensional grazing-incidence small-angle X-ray scattering (GISAXS) measurements of SEBS8 block copolymer films deposited on Si(001) substrates have been performed to demonstrate depth-sensitive GISAXS utilizing soft X-rays of 1.77 keV. Remarkable elongation of the Bragg spots in the qz direction, corresponding to microphase separation, was observed for an angle of incidence close to the critical angle. The elongation was explained in terms of the penetration depth, which limits the effective size in the direction perpendicular to the sample surface. Lattice distortion near the surface was confirmed.

The grazing incidence small-angle x-ray scattering (GISAXS) intensity from buried Ge nanodots is examined both by GISAXS/reflectivity measurements and by simulations with distorted wave Born approximation (DWBA). The validity and the condition of using the Born approximation (BA) are discussed using simulations based on the layer structures modeled from a reflectivity analysis. As expected in the previous kinematic analysis, use of the BA is reasonable in determining the size and the shape of very small or thin nanodots. Several effects of layer structures on the GISAXS analysis are discussed.

When many multi-filamentary Bi2223 composite specimens with different irreversible bending strain to each other are tested, number of damaged specimens among all increases with bending strain in the low bending strain region near the average irreversible strain. The present work attempted to predict the distribution of critical current among many specimens in such a low bending strain region with a proposed simulation method that uses the damage evolution model, Monte Carlo method and the experimental data measured at limited strains. With the proposed simulation method, statistical features in variation of distribution of critical current values among specimens near the average irreversible bending strain were elucidated.

An approach to predict the variation in critical current with applied tensile/bending strain of Bi2223/Ag/Ag alloy composite tapes from the tensile stress-strain curves was presented. Three different fabrication-route samples were used to examine the applicability of the present approach. The damage strain parameter, referring to the difference between the tensile fracture strain and residual strain of Bi2223 filaments along the sample length direction (current transport direction), was estimated from the variation in the slope of the tensile stress-strain curve. With the estimated damage strain parameter, the irreversible tensile strain for critical current was predicted, which agreed well with the experimental result in all samples. Also by substituting the estimated damage strain parameter into the core shape—incorporated model, the critical current-bending strain curve was predicted, which described satisfactorily the experimental result in all samples. The present approach could be a useful tool for prediction of critical current-dependence on applied tensile/bending strain.

Microstructure evolutions of nano-quasicrystals precipitated in ZrCuPt metallic glass ribbons during annealing has been examined by in-situ small-angle scattering and wide angle diffraction (SWAXS). The time-resolved measurements were made at a photon energy close to the Zr K absorption edge to obtain reasonable balance between transmission and resolution. During annealing the sample in vacuum, increase in SAXS intensity and diffraction peak at medium angle region was observed. The size obtained from SAXS and diffraction almost agreed, suggesting that the precipitation process in the glass ribbon is described by a growth process of single-crystalline nano-quasicrystals. Development of precipitated microstructure was further discussed by comparing SAXS profiles and diffraction profiles.

Tensile deformation and failure behavior at room temperature of the open cell nickel and copper foams with high porosity (96%) fabricated with the slurry foaming process at Mitsubishi Materials Corporation, Japan, was studied. In-situ observation of the deformation and failure behavior was conducted with a digital microscope. Stress-strain curves were measured, in which a non-contact extensometer was employed to detect the strain of the samples accurately. Electric resistance was measured to monitor the damage evolution. Finite element stress analysis was conducted to calculate the morphological change of cells with applied strain and the stress distribution in cells. It was revealed that the deformation and failure progressed through the following four stages; stage I characterized by the elastic deformation, stage II by plastic deformation, stage III by the co-occurrence of plastic deformation and cumulative failure of struts and stage IV by the chain reaction of strut failure nearly in a limited cross-section, respectively. Also it was found that the distribution of failure strain of struts in stage III, measured from the serrations in the stress-strain curve, could be described by the Weibull distribution, with which the transition from stage II to III was identified. Also, the result of the statistical analysis suggested that the average failure strain of the struts in the foam is much higher than the strain at ultimate stress of the foam.

The change of Young's modulus with increasing applied tensile strain in the open cell nickel and copper foams, fabricated by the slurry foaming process at Mitsubishi Materials Corporation, Japan, was investigated experimentally and analytically. Stress-strain curves were measured at room temperature, in which the loading-unloading-reloading process was performed on the sample at various applied strains. For measurement of the strain of the sample itself accurately, the non-contact extensometer was employed. The Young's modulus values at various applied tensile strains were estimated from the slope of the elastic region in the stress-strain curve in the unloading process. It was revealed that two competitive factors affect on the Young’ modulus value. One is the irreversible morphology-change of cells arising from the plastic deformation of the metal as a results of which, the cells are elongated and struts are straight forwarded in the tensile direction. This factor acts to raise the Young’s modulus with increasing applied strain. Another factor is the failure of struts, which tends to reduce the Young's modulus with increasing applied strain, especially beyond the strain where the struts are failed successively. Accordingly, due to the competition of the former and latter factors, the Young's modulus increases, reaching maximum and then decreases with increasing applied strain in both of the foams. The increase in Young's modulus with increasing applied strain due to the change of geometry of struts was confirmed by the experimental test of micro-samples composed of several struts and nodes and by the simulation based on the finite element analysis using a model micro-sample.

Critical current of bent-damaged Bi2223 composite tape differs from specimen to specimen. To describe the distributed critical current values of specimens, the three-parameter Weibull distribution function has been employed and has been demonstrated to describe the experimental results. In the present work, the reason for this was discussed by modeling analysis of the experimental results in a round robin test of VAMAS/TWA16. The distribution of the measured normalized critical current values was described well by using the damage evolution approach, in which the difference in damage evolution among the specimens was correlated to the distribution of critical current values. From this approach, the three-parameter Weibull distribution function for critical current values was derived, which gave almost the same parameter values for the minimum critical current, scale parameter and shape parameter as those obtained by the direct application of the Weibull distribution function to the experimental results. Based on this result, the reason why the normalized critical current values of bent-damaged composite tape is described by the three-parameter Weibull distribution function was accounted for in a quantitative manner by the difference in damage evolution among the specimens.

It has been reported that, when the (Bi, Pb)2Sr2Ca2Cu3Ox (hereafter noted as BSCCO)/Ag/Ag-alloy tape is laminated with stainless steel, the tensile strain tolerance of critical current is much improved. In this study, using the non-laminated and laminated BSCCO composite tapes fabricated at American Superconductor Corporation, the influences of lamination on the critical current and its distribution under bending strain were studied. The analysis of the measured variation of average critical current with bending strain based on the damage evolution model revealed that the laminated stainless steel acts to suppress the fracture of the BSCCO filaments. The experimentally observed high critical current retention of the laminated tape up to high bending strain was accounted for by the suppression of fracture of BSCCO filaments stated above and enhancement of the compressive residual strain in the filaments. The distributions of local critical current in non-laminated and laminated composite tape were described well by the three-parameter Weibull distribution function within the bending strain lower than 1.1%. The coefficient of variation of distribution of critical current of the laminated tape was similar to that of the non-laminated one under the same strain distribution in the core.

A prediction method of the critical current-bending strain relation of the Bi2223 composite tape, which was bent at room temperature and cooled down to 77 K for measurement of critical current, was presented. The present method consisted of (a) measurement of residual strain of Bi2223 filaments at room temperature in the sample length direction by the X-ray diffraction method, (b) estimation of tensile fracture strain of the filaments from the analysis of the load-strain curve at room temperature, (c) measurement of geometrical factors such as the thickness of the sample and shape of the core by observation of the cross-section with optical microscope, and (d) calculation of the critical current as a function of bending strain by using the measured parameters mentioned in (a)-(c). The predicted variation of critical current with bending strain by the present approach described well the experimental one.

Grazing incidence small-angle scattering (GISAXS) of capped Ge nanodots in the soft X-ray (SX) region using an anomalous dispersion effect at the Si K absorption edge has been analyzed and compared with results obtained using hard X-rays. The GISAXS profiles obtained at about 1.8 keV were found to give the same structure information for the nanodots as obtained from conventional GISAXS in the hard X-ray region. These could be explained by distorted wave Born approximation simulations. Enhancement of the contrast by anomalous dispersion was confirmed.

The final structure of molten syndiotactic polypropylene (sPP) sheared under different conditions was investigated by synchrotron small-angle x-ray scattering (SAXS) and wide-angle x-ray diffraction (WAXD) techniques to elucidate the shear effects on sPP crystalline structure. The results obtained from the WAXD show that there is no variation on crystalline form but a little difference on the orientation of the 200 reflection. The SAXS data indicate that the lamellar thickness and long period have not been affected by shear but the lamellar orientation is dependent on shear. The experimental data of sPP crystallization from sheared melt may indicate a mesophase structure that is crucial to the shear effects on the final polymer multiscale crystalline structures.

The distribution of the normalized critical transport current (critical current normalized with respect to the original value) of Bi2223/Ag/Ag alloy composite tape under bending strain of 0%–0.833% was studied experimentally and analytically. The experimental results were analyzed by a modeling approach based on the relation of the heterogeneous damage evolution to the distribution of the critical current. The main results are summarized as follows. (1) The measured distribution of the critical current values varying with bending strain was described well by the present approach. (2) When all specimens were damaged at high bending strains (0.338%–0.833% in the present work), the distribution of the critical current of the bent-damaged specimens was expressed by the three-parameter Weibull distribution function, the reason for which was revealed. (3) The distribution of the irreversible strain was estimated, with which the influence of the increase in the fraction of damaged specimens on the variation of critical current distribution in the low bending strain range (0%–0.35%) was elucidated.

The superconducting Bi2223/Ag/Ag alloy composite tape specimens with a length 6 cm, composed of a series circuit of six local elements with a length 1 cm, were bent by 0.37% and 1.0% for measurement of distributions of the overall (6 cm) and local (1 cm) critical transport current and n-value. When the damage amount was small (0.37% bending strain), the distributions of the measured local and overall critical currents were described by the three parameter Weibull distribution function, while when the damage amount was large (1.0% bending strain), those were described by the bimodal Weibull distribution function. The distributions of n-value in the diagram of n-value versus critical current for both local elements and overall specimens were expressed by the regression curve of n-value as a function of critical current and the normal distribution function for the deviation of the measured n-values from the regression curve. The experimentally measured critical current distribution and the diagram of the n-value versus critical current of the overall specimens were reproduced successfully in the computer by inputting the formulated distribution functions for the critical current and n-value of the local elements into the proposed simulation method, which used a Monte Carlo simulation method and a one-dimensional series circuit model for the generated voltage near the transition of superconducting to normal state.