Special Issue

Superconductivity

Analysis of Superconductors and Metals
Using Small-Angle X-ray and Neutron Scattering
Hirokazu Sasaki*1, Satoshi Yamazaki *1, Yojiro Oba*2, Masato Onuma*3

Small-Angle X-ray (SAXS) and Small-Angle Neutron scattering (SANS) wereused to analyze metallic nanoparticles, artificial pins in high-temperature superconducting wires, and precipitates of copper alloys. Small-angle scattering provides an average
information on the size, the shape and the spacing of these finely dispersed nanoscale structures. In order to ensure the validity of the SAXS or SANS profile analysis, it is necessary to
make complementary use of real-space observation techniques such as TEM and 3-D atom
probe. This paper illustrates several cases of their use.

ABSTRACT1.

INTRODUCTION

This paper details Small-Angle X-ray and Small-Angle
Neutron Scattering analysis for the development of hightemperature superconducting wires and metallic materials. There are various factors that determines the criticalcurrent density in magnetic fields, which is a typical product characteristic of superconducting wires, such as theorientation of superconducting crystals, the formation of
normal-conductive phases, and the artificial pins that trap
magnetic flux quanta. Among these factors, the fabrication of artificial pins that are formed in the form of rods ofa few nm in diameter as designed is important for the
production and development of superconducting wires
with a high critical current density in magnetic fields.
On the other hand, in order to put many metal materials, including copper alloys, into practical use, it is necessary to improve their material properties such as strength,
electrical conductivity, thermal conductivity and workability. There are various factors that govern these characteristics. In particular, strength can be improved by finely
dispersing precipitates as small as several nanometers toseveral tens of nanometers.
As described above, in order to utilize superconducting
wires and metal materials, it is important to appropriately
finely disperse nano-order structures of several nanometers to several tens of nanometers. Then, it is necessary
to analyze whether these structures are formed appropriately not only at the product development stage but also
at the manufacturing stage. A typical analysis method isTransmission Electron Microscopy (TEM), which has a
Sustainable Technology Laboratory, R&D Division
Toyohashi University of Technology*3
Hokkaido University*1*2

spatial resolution of 1 Å or less. Using TEM, you canactually observe and understand the size and shape.
However, with TEM, the number of structures that a person can analyze one by one is actually only a few hundred at most, so statistically significant differences may
not be found between multiple samples. In this case,
Small-Angle X-ray Scattering (SAXS), which can quantitatively evaluate the size and shape of finely dispersed
structures, is effective. In addition, a variety of information
can be obtained by complementary use of Small-Angle
Neutron Scattering (SANS) 1)-7). None of these methods isthe most effective, but by combining and considering
multiple analytical data, it is possible to grasp theessence of nano-order structures. This paper presents
analysis examples that use real space analysis methods
such as TEM and three-dimensional atom probes in acomplementary manner with SAXS and SANS.

2.

SMALL-ANGLE X-RAY AND
SMALL-ANGLE NEUTRON SCATTERING

2.1 Small-Angle X-ray Scattering
The experimental setup of SAXS is simple. As shown in
Figure 1(a), the sample is irradiated with X-rays, and the
X-rays scattered at low angles are detected by a twodimensional detector. Figure 1(b) shows a scattering
image from copper containing precipitates, and the scattering can be clearly detected. Next, the scattering image
is circularly integrated to create a SAXS profile. When
comparing this SAXS profile between a copper alloy containing precipitates and pure copper without precipitates,
as shown in Figure 1(c), a shoulder can be clearly seen in
the sample containing precipitates. In this figure, the vertical axis of the SAXS profile is the scattering intensity I(q)and the horizontal axis is the absolute value of the scatFurukawa Electric Review, No. 55 2024

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Analysis of Superconductors and Metals Using Small-Angle X-ray and Neutron Scattering

Scattered X-ray
X-ray

5

10

（b）

（c）

10 4

10 5

10 3
10 2

q-4

10 1

Copper with
precipitated phase

2

10 1

8
6
4

Pure copper

10 0

8
6

10 -1

2

3

4 5 6 7 89

q / nm-1

10 0

2

Schematic diagram of small-angle X-ray scatteringand obtained data.

(1)The shape factor F depends on the shape of the particle. Spheres, core-shell structures, ellipsoids, cylinders,and disks have been formulated by previous studies 8). For
the simplest spherical particles, the shape factor F can be
expressed by Equation (2). Where r is the radius of thesphere.
(2)Thus, it is possible to obtain the theoretical scattering
intensity from these equations. For example, for a spherical particle whose volume-weighted frequency distribution N(r )∙V(r) follows a lognormal distribution as shown in
Figure 2(a), the scattering curve calculated using theanalysis software Irena 7) with Equation (1) is shown in
Figure 2(b). One of the characteristics of this profile isthat the slope of the curve after the shoulder decreases inproportion to q –4. It is known that the slope depends on
the shape of the particle. For cylinders, it decreases inproportion to q –1, and for disks, it decreases in proportion

20

Background 1

10 4
10 3

Background 2

10 2
10 1
10 0

3 4 56

Figure 2

8
6
4

15

r / nm10 -1 2 3 4 56 10 0 2 3 4 5

q / nm-1

2

Intensity / arb. unit

5

0

（c）

2

10

0

10 0

10 2

Figure 1

15

Intensity / arb. unit

Sample（b）（a）

Intensity / arb. unit

2D detector（a）to q –2 8). This means that the shape of the particle can be
estimated based on what power of q the slope is basedon.

Frequency

tering vector q. The SAXS profile is shown as a doublelogarithmic graph. By analyzing this intensity profile,information on particle shape, size, number density, andcomposition can be obtained. In general, profile I(q) canbe expressed by equation (1) 2) -7). Where, Δ ρ is the scattering length density difference for X-rays, N(r) is thenumber density distribution, V(r) is the volume of the particle, and F(q,r) is the shape factor. The scattering lengthdensity difference Δρ is the difference between the scattering length density of finely dispersed particles and thatof the matrix phase.

3 4 5610 1

2 3 4 56

10 0 2 3 4 5

q / nm-1

Calculated SAXS profiles.

When determining the particle size distribution from themeasured SAXS profile, curve fitting is performed fromthe measured data. In this case, fitting is performed under
several assumptions. For example, particles are assumed
to be spherical, and the volume-weighted frequency distribution is assumed to be a lognormal distribution thatcan be expressed by the equation (3). Then the distribution which is the most suitable for measured SAXS profile
is obtained where a, σ, and r 0 are constants.
(3)

Therefore, the distribution obtained by fitting fromSAXS is not the true distribution of particle sizes, but aninterpreted distribution based on the assumptions used in
the fitting.
In SAXS measurements of metallic materials, it is rare
to obtain only a clear scattering curve as shown in
Figure 2 (b), and various backgrounds are superimposedin actual measurements. Figure 2 (c) shows a typical
SAXS profile that is often seen in practice. In this figure,the dashed line represents the profile due to scatteringfrom particles, and the solid line represents the profile
including the backgrounds. There are mainly two types ofbackgrounds. Background 1 is derived from coarse structures, which is noticeable on the low-q side. Incoherent
scattering-derived background 2 that appears in the highq region above q = 2 nm –1 also often appears. For thesebackgrounds, SAXS measurements of samples containing only the matrix phase without fine structures shouldbe performed to determine the background trends, andthe effects of these backgrounds should be taken into
account in the fitting process. It should be noted, howevFurukawa Electric Review, No. 55 2024

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Analysis of Superconductors and Metals Using Small-Angle X-ray and Neutron Scattering

Scattering length for neutron / fm

tor KUR, Hokkaido University, and RIKEN have small neutron sources that can be used for SANS.
15

200

Scattering length for neutron
Scattering length for X-ray

150

10

100
5
50
0

-5

Figure 3

0

10

20

30

40

Atomic number

50

-50
60

Scattaring length for X-ray / fm

Scattering length of X-ray and neutron beam.

2.3 Complementary Use of TEM and SAXSWhile there are many options for analyzing finely dispersed nanoscale structures, TEM, which is a widelyused and real-space analysis method, is generally used
first. On the other hand, the results obtained by SAXS are
average information, but if the average information is thedominant factor in material properties, SAXS is also effective as an analysis method for nano-scale structures.
A brief comparison of the differences in measurement
volume between SAXS and TEM is as follows. As shownin Figure 4(a), in the case of SAXS, if the X-ray beam
diameter is 100 μm and the sample thickness is 20 μm,
the measurement volume is 157,000 μm3. On the other
hand, in TEM, as shown in Figure 4(b), if one side of theobservation field is 0.1 μm and the TEM sample thickness
is 0.02 μm, the measurement volume is 0.0002 μm3.
Thus, the measurement volume of SAXS is about 9 digits
larger than that of TEM, indicating that average information can be obtained. Therefore, using SAXS may make iteasier to obtain correlations with material properties. On
the other hand, since only the profile shown in Figure 1(c)can be obtained from SAXS, analysis is often difficultfrom SAXS data alone. Generally, when analyzing a SAXS
profile, it is necessary to understand information such as
shape through real-space observations such as TEM, so
it is important to use SAXS and TEM in a complementarymanner for analysis.
（b）TEM（a）SAXS
SampleX-ray

0.1 µmer, that incoherent scattering is slightly different between
the case with only the matrix and the case with microstructures.
Another important factor to keep in mind when measuring metals and superconductors is the X-ray transmittance. In the case of a SAXS system with a Cu sourcethat uses X-rays with an energy of 8 keV, which is widelyused in the field of soft matters, metallic materials suchas steel, which have a low X-ray transmittance, require
grinding to a thickness of 10 μm or less to make the sample thinner and making the sample preparation extremely
difficult. On the other hand, if the SAXS system uses a
Mo source that produces X-rays with an energy of 17 keV,the X-rays can penetrate sufficiently if the sample is 20 to
30 μm thick, making the sample preparation at a realistic
level of difficulty. Another option is to perform SAXS measurements using a high-energy X-rays at synchrotron
radiation facilities such as SPring-8.
2.2 Small-Angle Neutron Scattering
While basic principle is the same as that of SAXS, the difference is that a neutron beam is used in this case.
Among the several features of SANS, it is noteworthy thatneutrons have a strong ability to penetrate materials andcan measure thick samples. In the case of metals, it ispossible to measure in thicknesses from several millimeters to several centimeters. In many cases, SANS does
not require trimming of the specimens, but rather stacking as many specimens as possible to increase the scattering intensity. In addition, the fact that no pretreatment
is required is an advantage when the material is soft anddifficult to grind. In which case, SANS is more suitable
than SAXS.
The difference between SAXS and SANS is not only inthe penetration power and the presence or absence ofpretreatment, but also in the measurement volume. SAXS
measurements require the metal sample to be made thinon the order of μm, meaning that only a small portion of
the material is being measured. SANS can measure samples even several millimeters thick, so the measurement
volume is 100,000 to 1,000,000 times larger than SAXS.
The size of the measured volume is important for practical material evaluation methods, and if it is large enough,the correlation between material properties and finely dispersed structures may be better understood.
Another major motivation for using SANS is that, asshown in Figure 3, the scattering length of neutrons is notproportional to the atomic number like the scattering
length of X-rays. That is, the scattering length density difference Δρ in equation (1) is different from that of X-rays.
By utilizing this difference in the scattering length densityof neutrons and X-rays, that is, the contrast difference, it
is also possible to obtain information such as the composition and density of the precipitates.
Because SANS uses neutrons, facilities that can measure it are limited. Representative facilities in Japan are
J-PARC and JRR3, each of which has multiple SANS
beamlines. In addition, Kyoto University’s research reac-

100 µm
20 µm
Figure 4

Measurement volumes of SAXS and TEM.

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Analysis of Superconductors and Metals Using Small-Angle X-ray and Neutron Scattering

FOV 1

FOV 2

FOV 3

（b）10
（a）
15

Particles 1
Particles 2
Particles 3

10
5
0

0

5

10

r / nm15

20

Intensity / arb. unit（a）

As described above, when analyzing a finely dispersed
structure, depending on the target material, TEM alone
may be sufficient in some cases, while SAXS alone may
be sufficient if the geometry of the structure is known. In
other cases, it may be desirable to use both TEM and
SAXS for the analysis.

Frequency

Depending on the material, it is often possible to discuss using TEM alone. For example, assume that the sizeand shape of finely dispersed structures are relatively
uniform, and there is no large difference in particle size nomatter which field of view is observed with TEM, as
shown in Figure 5 (a). In this case, by measuring the size
from the TEM image and estimating the particle size distribution, a sufficient correlation with the material properties can be obtained.

4

Particles 1
Particles 2
Particles 3

10 3

10 2

10 1

10 0

6 7 89

10 1

FOV 2

FOV 3

Figure 63.
Schematic of particles observed by TEM.

On the contrary, it is difficult to obtain an accurate particle size distribution from the TEM image alone when thesize of the structure varies depending on the field of view,
as shown in Figure 5 (b). Let us consider a case in whichsmall-sized particles are observed in field of view 1, particles of medium size are observed in field of view 2, andrelatively large particles are observed in field of view 3.
When the particle size distribution is obtained from theparticle images observed in these three fields of view andthe average particle size is calculated, it is not always
correct. Even if one hundred fields of view wereobserved, such a number would not be enough. The
results of the average particle size will differ if there happen to be many fields of view in which particles with large
diameters are present, or if there are many fields of viewin which particles with small diameters are present. Whenthe particle size varies greatly depending on the field ofview, SAXS which has measurement volume several
orders of magnitude larger, is effective.
Even if the difference in particle size distribution issmall, SAXS is still effective when the difference has alarge effect on material properties. TEM can realisticallymeasure only a few hundred particles, and differences
between samples may not be detected unless the number of particles is measured several orders of magnitudelarger. For example, when considering three volumeweighted frequency distributions as shown in Figure 6 (a)for spherical particles, SAXS simulations show different
shoulder positions as shown in Figure 6(b), and the differences between them can be detected. In order to capture
this difference with TEM, it is necessary to measure as
many particles as possible, but this is often difficult inpractice.

10 0

2

MEASUREMENT RESULTS

3.1 Metal Nanoparticles
Nanoscale metal particles were fabricated under multiple
manufacturing conditions and SAXS measurements were
performed to analyze particle size. The measurements
were performed at BL8S3, one of the beamlines of Aichi
Synchrotron, a synchrotron radiation facility. The energyof the X-rays used in the experiment was 8.2 keV. The
camera length, which is the distance between the detector and the sample, was selected to be 1 m and 6 m, andthe results of each measurement were connected to produce a single SAXS profile. SAXS profiles of two samples
prepared under different manufacturing conditions areshown in Figure 7(a). As indicated by the arrows, shoulders from the metal particles were observed in both samples. Note that because this sample contains large structures, a coarse structure-derived background with a slopeof q –4 also appears in the low-q region below q = 0.1 nm–1.
The background appearing in the high-q region aboveq = 2 nm – 1 is due to incoherent scattering and atmospheric effects. From these SAXS profiles, it can be seenthat the shoulder of the particles produced under condition A is located on the left side of the graph, i.e., on the
low-q side, compared to the shoulder of the particles pro（a）

10 9

Intensity / arb. unit

Figure 5

3 4 5 6 7 89

q / nm -1

SAXS profiles from various distributions of radii.

Manufacturing condition A
Manufacturing condition B

10 8
10 7
10 6
10 5
10 4
10 3
10 2
101

（b）
frequency（b） FOV 12

3 4 56

Figure 7

10 -1

2 3 4 56

q / nm-1

10 0

10
8
6
4
2
0
0

Manufacturing condition A
Manufacturing condition B

510

r / nm15

20

2 3 45SAXS profiles of metal nanoparticles and their radius
distribution.

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Analysis of Superconductors and Metals Using Small-Angle X-ray and Neutron Scattering

duced under condition B. Since q as the absolute valueof the scattering vector corresponds to the inverse of thereal space distance, the appearance of a shoulder at asmaller q implies that the scattering is from a larger structure. These two SAXS profiles indicate that the metallic
particles produced under condition A are larger thanthose produced under condition B. Thus, the average
information of the particles can be read from the SAXS
profiles alone, and can be used for optimization of production conditions and quality control.
Next, assuming that the metal particles are sphericaland the volume-weighted frequency distribution follows alognormal distribution, curve fitting was performed fromthese SAXS profiles. The results are shown in Figure 7(b).
Although there is no significant difference in the peak
position of the distribution between the two samples, thedistribution for condition A has a tail in the region of larger
diameter, indicating that there are many particles that arelarger than those in condition B. This means that the particles in condition A have a larger variation in particle size.
In this case, r 0 in the log-normal distribution is 4.5 nm forthe metal particles fabricated under condition A and
3.9 nm for the metal particles fabricated under condition
B, so larger particles are formed under condition A. Thus,
the particle size can be analyzed from the SAXS profileand the results can be fed back to the manufacturingconditions to optimize the particle size.
3.2 Superconducting Wires 9)
To develop high current density materials, it is necessary
to appropriately control magnetic flux quanta. That is theproper pinning of the magnetic flux quanta in the normal
conducting parts (pins). Challenges in the development ofsuperconducting wires arise when the causal relationshipbetween physical properties and superconducting thinfilm structures such as pinning centers is not fully understood. Controlling pinning center is difficult because thefactors that generate it are complex, such as twins andoxygen deficiency. Therefore, rods with several nm indiameter are artificially fabricated perpendicular to thesuperconducting film10) -13). The diameters and density of
the artificial pins are the main factors determining the critical current density of superconducting wires. If the artificial pins can be introduced as designed, the superconducting phase can be maintained even in high magnetic
fields, and wires with high critical current density in magnetic fields can be realized.
Against this background, it is important for high-quality
superconducting wires to conduct material analysis todetermine whether the artificial pins are fabricated as
designed. TEM observation is commonly used to analyze
artificial pins. However, the observation area is small, a
few μm range, and may not be sufficient for quantitativeevaluation of the size distribution of artificial pins over theentire wire. In response to these requests, we analyzed
nanorod artificial pins using SAXS. The sample used wasa GdYBCO superconducting wire with Zr added to form
BaZrO 3 artificial pins. The composition of the supercon-

ducting layer is approximately (Gd,Y)1Ba 2Cu3 O 7, and thethickness of the superconducting layer is 2 μm. A crystal
orientation-controlled intermediate layer was laminatedon Hastelloy with a thickness of approximately 50 μm,
and a superconducting layer containing artificial pins was
deposited on the top of this. Figure 8 (a) shows a TEM
image of the artificial pins observed from a direction perpendicular to the surface of the superconducting thin film.
It can be seen that artificial pins with a diameter of several nanometers are formed. Figure 8 (b) shows a HAADF(High Angle Annular Dark Field) - STEM (Scanning
Transmission Electron Microscopy) image of a magnified
image of a part of the GdYBCO. It can be seen that theartificial pins and GdYBCO are partially bonded and stably formed. Figure 8 (c) shows a TEM image of the artificial pins observed from the cross-sectional direction of
the superconducting thin film. Rod-shaped artificial pinsare formed in the growth direction of the thin film.
（b）

（a）

2 nm

50 nm

Artiﬁcial pinning center

BaZrO3

GdYBaCuO（c）

GdYBCO
2 µm
Buﬀer
Layer
Hastelloy
50 µm
Figure 8

50 nm
TEM images of artificial pins in superconducting wire.

Although there is a previous study of SAXS analysis ofartificial pins in superconducting thin films using Au artificial pins14), it was expected to be difficult for BaZrO 3 artificial pins because the contrast between the electron density of the base phase (Gd, Y) 1Ba 2Cu 3O 7 and BaZrO 3 artificial pins is small. Furthermore, superconducting wires
have nanoscale structures other than the artificial pins,
which may also provide scattering. In addition, the scattering from the substrate Hastelloy provides a background that affects the scattering of the artificial pins.
Therefore, artificial pin evaluation was performed using
Anomalous Small-Angle X-ray Scattering (ASAXS) using
the Zr absorption edge. ASAXS can selectively capture
scattering from BaZrO 3 artificial pins containing Zr
because the atomic scattering factor changes as the incident energy approaches the Zr absorption edge.
The experiment was conducted at beamline BL19B2 ofSPring-8. SAXS measurements were performed by
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Analysis of Superconductors and Metals Using Small-Angle X-ray and Neutron Scattering

10 -2

10 -3

10 -4
10 -1

10-1
9
8
7
6
5
4

Intensity / arb. unit

Figure 9

35
1.0
30
L

dN

25
10

0.5
30

20

2x10-1q / nm-1

2

8

7

6

5

0

10

20

30

Zr content / %Figure 10 Average structural information analyzed from ASAXS
measurement.

-3 eV
-8 eV
-13 eV-113 eV334

5 6 7 89q / nm-1

10 0

2

10-2

10-3

10 -1

1.5

Zr content / %（b） 10-1

10-4

（b）

40

Average diameter / nm

10 -1

（a）
Interparticle distance L / nm

-3 eV
-8 eV
-13 eV-113 eV

Intensity / arb. unit

Intensity / arb. unit（a） 10 0

may be due to interparticle interference effects, suggesting that the artificial pins are densely packed in the superconducting layer. Curve fittings for these peaks were performed by approximating a Gaussian function and a linear function as the background to estimate the peak
position q peak17). From the result of the sample containing
25% Zr, the average distance between artificial pins L =2π / q peak was estimated to be 27 nm. The distance
between artificial pins, which is closely related to the critical current density, can be quantified using ASAXS measurements. Figure 10 (a) shows the results of analysis ofsamples with Zr addition amounts of 15%, 20% and25%. Figure 10 (a) also shows the density of artificial pins
calculated from the distance between pins. It was analyzed that as the Zr concentration increases, the distance
between the pins decreases and the density of the artificial pins increases. In addition, for the 7.5 % Zr containing sample, the interference peak did not appear andcould not be calculated because the density of the artificial pins was low and the interference effect was weak.
Areal number density dN（1011 cm-2）

arranging the samples so that X-rays were transmitted in
the direction of growth of the superconducting thin films
to investigate the in-plane nanostructures. ASAXS measurements were performed at incident energies of –3 eV,–8 eV, –13 eV, and –113 eV away from the Zr absorption
edge. As a preliminary experiment, we conducted XANES
measurements of ZrO 2 powder and performed energy
calibration assuming that the Zr-K absorption edge was
17.998 keV 15). The camera length was 3040 mm, and themeasurements were performed in the region where the qvalue was approximately 0.06 to 3.5 nm –1. The scattering
intensity was calibrated at each energy using glassy carbon as a standard sample 16).
Figure 9 (a) shows the Anomalous Small-Angle X-ray
Scattering results of a (Gd,Y) 1Ba 2Cu3O7 thin film with 25%
Zr added. A shoulder was observed near q = 0.2-1.0 nm –1,
confirming the formation of nanostructures of several tensof nanometers in the superconducting layer. Compared tothe profile of –113 eV, which is sufficiently far from theabsorption edge, the –3 eV, –8 eV, and –13 eV profiles
have increased peak intensities around q = 0.3 nm–1. Thissuggests that these peaks are scattering derived from
artificial pins of BaZrO 3 containing Zr.

25 mol%2015
7.5

q / nm-1

10 0

ASAXS profiles of artificial pins insuperconductor.

Figure 9 (b) shows the results of subtracting the –113 eV
profiles from the –3 eV profiles. The measured samples
contained 7.5%, 15%, 20%, and 25% Zr. The scatteringprofiles of BaZrO 3 have a peak-like feature aroundq = 0.25 nm –1, as indicated by the arrow in the figure. ThisTo calculate the diameter of the artificial pins, curve fitting was performed assuming an oriented rod model. As
the TEM image in Figure 8 (c) shows that the rod is slightly
tilted with respect to the growth direction of the thin film,
the rod tilt was also taken into account in the SAXS fitting. In addition, since a peak appeared, the influence ofinterparticle interference was also taken into account. The
fitting results are shown in Figure 9 (b). The average diameters of the artificial pins obtained from these results areshown in Figure 10 (b). In this type of samples, the diameters tend to increase as the Zr concentration increases,
but it reaches saturation at 20%. As described above, wewere able to analyze average information on artificial pin
spacing, density, and size using ASAXS. By performing
such analyzes appropriately, it becomes possible todevelop and manufacture high-quality superconducting
wires.
3.3 Copper Alloys 18)
Copper products require strength, electrical conductivity,
thermal conductivity, and workability. One of the copper
alloys that meet these required properties is Cu-Ni-Si
alloy, and it is known that heat treatment improves
strength by finely dispersing Ni-Si compounds in the copFurukawa Electric Review, No. 55 2024

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Analysis of Superconductors and Metals Using Small-Angle X-ray and Neutron Scatteringinterdiffused at the interface between the precipitatedphase and the copper matrix. By closely observing the
diffused area, two characteristics can be found. One is
the region indicated by arrow 1, where the Si composition
is constant and the Ni composition decreases toward thecopper matrix side. This region is considered to beδ(Ni 1-y,Cu y) 2Si 29). The other region is indicated by arrow 2,
where Ni and Si are diffused into the copper matrix at aconcentration of 10% or less. Figure 13 shows a model
diagram of the precipitates estimated from these TEM
and 3-D atom probes. As shown above, it is important toanalyze small-angle scattering after understanding thestructure and size of the precipitates to some extent
through real-space analysis in order to draw a reliableconclusion.
（a）

（b）
100

Composition / atomic %per matrix. This Cu-Ni-Si alloy is called Corson alloy, andit has both high strength and high electrical conductivity.
Today, various Cu-Ni-Si alloys have been developed byadding various additives to improve their properties, andthese alloys are widely used in electronic devices such as
smartphones, making them indispensable metallic materials in our daily lives.
The sample analyzed was a Cu-Ni-Si alloy containing
2.5 mass% Ni and 0.6 mass% Si. The Cu-Ni-Si alloy wasmelted and cast, and then heat-treated, rolled, annealed,and solution heat-treated. After that, aging treatment was
performed. We analyzed the alloys after samples had
been solution heat-treated and heat-treated at aging temperatures of 425, 450, 500 and 550°C. The aging timewas 2 h.
Figure 11 (a) shows a bright-field TEM image of the
Ni-Si precipitate in a Cu-Ni-Si alloy that was heat-treatedat 550°C for aging precipitation. The TEM image shows
numerous precipitates of about 10 nm in size. The copper
matrix surrounding the precipitates shows contrast due todistortion. A magnified HAADF-STEM image of one of the
precipitates is shown in Figure 11 (b). Analysis of thisimage with a two-dimensional fast Fourier pattern (details
omitted here) revealed that the precipitate was δNi 2Si 19), 20).
Many previous studies of Ni-Si precipitates by TEM haveshown that the precipitates are δNi 2Si 21) - 26) .

1

80

Cu
Ni
Si

60
40
2

20

2

0

10 nm

0

5

10

15

Distance / nm

20

Figure 12 Three-dimensional atom probe result of precipitate.

（a）

（b）
Shell 2：diﬀusion layer in Cu parent phase

Ni2Si

100 nm

5 nm

Figure 11 TEM images of precipitate from Cu-Ni-Si alloy.

In order to analyze the structure of the precipitatedphase in detail, we used a 3-D atom probe to analyze it.
In the 3-D atom probe method, the material is evaporated, the evaporated atoms are detected by a 2-D detector,
and the data are reconstructed to visualize the 3-D structure on the nanometer order 27). The apparatus used was
LEAP5000XS. The measured temperature was 30 K. A
pulsed ultraviolet laser with a wavelength of 355 nm wasused as the light source to assist evaporation 28). Figure 12
shows the analysis results of the sample heat-treated at
550°C. Figure 12 (a) shows an iso-concentration surfaceof 7 atomic% Si. The precipitates were not spherical but
ellipsoidal, close to a disk. Figure 12 (b) shows the concentration profile of the precipitate created in the direction indicated by the arrow in Figure 12 (a). The Ni/Si ratioof 2:1 in the center suggests that the precipitates are
Ni 2Si. It can also be confirmed that Ni, Si, and Cu are

Shell 1： (Ni,Cu)2Si
Figure 13 Core-shell model diagram ofprecipitate.

Rigaku NANO-Viewer was used for SAXS measurements. The Mo-Kα source was used, the incident X-ray
energy was 17.47 keV, and the camera length was 0.5 m.
Furthermore, Ultra Small Angle X-ray Scattering (USAXS)
measurements were performed at SPring-8’s Hyogo
Prefecture Beamline BL08B2. The incident X-ray energy
was 18 keV, and the camera length was 16 m. The sample was trimmed to a thickness of approximately 20 μm.
For the laboratory SAXS profile, the absolute value of thestrength was calculated using glassy carbon 16). The
USAXS profiles were connected to the intensity of thatSAXS profile to create a single SAXS profile. SANS measurements were performed using SANS-J installed at
JRR3 30) . The sample for SANS measurements wasapproximately 2.1 mm thick. The measurement results of
SAXS and SANS are shown in Figure 14 (a), (b). The figure
shows small-angle scattering profiles for solution annealFurukawa Electric Review, No. 55 2024

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Analysis of Superconductors and Metals Using Small-Angle X-ray and Neutron Scattering

ing only and for samples heat-treated at aging temperatures of 425, 450, 500, and 550°C. Compared to the
Corson alloy that was only solution treated, the 425°C
aging precipitation heat-treated product shows a shoulder indicating the formation of nanoparticles in the regionof q = 0.4 to 2 nm –1. It can be observed that the shoulder
showing scattering moves to the low-q side as the aging
heat treatment temperature increases. These results suggest that the Ni-Si precipitates are gradually coarsening.
（a）SAXS（b）SANS

10 6

as
425
450
500
550

10 4
10 3
10 2
10 1
10 0

10 1
10 0
10 -1
10 -2

10 -1
10 -2

as
425
450
500
550

10 2

Intensity / cm-1

Intensity / cm-1

10 5

2

4 68

10 -1

2

4 68

10 0

4 56

4 68

2

10 -1

q / nm-1

2 3 4 56

10 0

2 3 4

q / nm-1

As a result of fitting with the SAXS profile, the average
major axis radius of the ellipsoid was 8.9 nm. On theother hand, the average major axis radius of the ellipsoid
fitted with the SANS profile was 6.6 nm. The reason forthe difference in results between SAXS and SANS is thedifference in scattering contrast of the diffuse layer ofδ(Ni 1-y,Cuy)2 Si, in which Cu diffuses into the precipitatedphase. Figure 16 shows the results of calculating thescattering contrast of the δ(Ni 1-y,Cu y) 2 Si diffusion layer
based on the X-ray and neutron scattering lengths shownin Figure 3. From these results, the scattering contrast ofthe δ(Ni 1-y,Cuy)2 Si diffusion layer in the copper matrix islarge for X-rays but small for neutrons. Therefore, it isconsidered that the precipitated phase was measured
large in SAXS and small in SANS. By using SAXS andSAXS in a complementary manner in this way, it is possible to quantitatively analyze the average size of precipitates, taking into account the diffusion layer. In practice,product development is conducted based on the correlation between such analysis results and material properties such as strength and electrical conductivity.

Figure 14 SAXS and SANS profiles of Cu-Ni-Si alloy.

SANS
SANS ﬁtting
SAXS
SAXS ﬁtting

10 6
10 5

Intensity / cm-1

10 4
10 3
10 2
10 1
10 0
10 -1
10 -2
2

4 68

10 -1

2

4 68

q / nm

10 0

2

4 68

-1

Figure 15 SAXS and SANS profiles of 550°C aging
samples.

(diﬀerence in SLD) 2
for X-ray (1022 cm-4)

1.0
1.5
0.8
(Ni1-y,Cu y) 2 Si
X-ray
neutron

0.6

1.0

0.4
0.5
0.2
0.0

0

10

20

30

(diﬀerence in SLD) 2
for neutron (1020 cm-4)

Based on the TEM and 3-D atom probe results of the
precipitated phase, the SANS results were analyzed.
Figure 15 shows the SANS and SAXS results for the
550°C-aged sample. Since the precipitates of the 550°C
aged sample were assumed to be ellipsoids close todisks, the SAXS and SANS profiles were fitted assumingthat they were ellipsoids. The axis ratio of the ellipsoid
was assumed to be 0.3. In this fitting, the backgroundderived from incoherent scattering that appears in thehigh-q region of approximately q = 2 nm –1 or more is set
to a constant value, and the coarse structure-derived
background that becomes prominent in the low-q side
was taken as q –4.

2.0

1.2

0.0
40

y in (Ni1-y ,Cu y)2Si / %Figure 16 X-ray and neutron contrast of δ(Ni1-y,Cu y)2 Si diffusion
layer in copper.

4.

CONCLUSION

In this paper, we have shown that SAXS and SANS areuseful for the analysis of finely dispersed nanoscale
structures such as metallic nanoparticles, artificial pins inhigh-temperature superconducting wires and precipitatesin copper alloys. Complementary use of real-spaceobservation techniques, such as TEM and 3-D atom
probe, enables analysis of reasonable small-angle scattering profiles. There are many materials analysis techniques other than those illustrated in this paper, and it isimportant to discuss them based on the results of appropriately combining multiple methods. We plan to continue
using this technology in the development of various new
products and in ensuring the reliability of various existingproducts.

The fitting results are shown by solid and dashed lines
in Figure 15. The shoulder near q = 0.3 nm –1, indicated by
the arrow in the figure, corresponds to the precipitates.
Furukawa Electric Review, No. 55 2024

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Analysis of Superconductors and Metals Using Small-Angle X-ray and Neutron Scattering

ACKNOWLEDGMENTS

The laboratory-based SAXS measurements of copper
alloys were performed under the collaboration of theInstitute for Integrated Radiation and Nuclear Science,
Kyoto University. SPring-8 ASAXS measurements ofsuperconductivity were performed at BL19B2 (Proposal
No. 2016B1790). SAXS measurements of copper alloys at
SPring-8 were performed at the Hyogo Prefecture
Beamline BL08B2 (Proposal No. 2019A3337), and SANS
measurements were performed at the SANS-J of the
JAEA JRR3 (Proposal No. 2021A-A43). The HAADFSTEM observation was supported by the University ofTokyo Advanced Characterization Nanotechnology
Platform in the Nanotechnology Platform Project sponsored by the Ministry of Education, Culture, Sports,
Science and Technology of Japan. 3-D atom probe measurement of copper alloys was performed with the cooperation of Dr. Jun Uzuhashi, Dr. Kyoko Suzuki, and Dr.
Tadakatsu Okubo of the National Institute for Materials
Science.
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