unstructuredio/SCORE-Bench · Datasets at Hugging Face

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(a) Incident X-ray Sample WAXS SAXS USAXS
2θ q
q = 4π/λ sin(θ)
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(b)
Incident X-ray Bonse-Hart Crystals Sample Bonse-Hart Crystals Detector
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Figure 2
Schematics of two primary types of USAXS Instruments. (a) Pinhole configuration: in this setup, the scattering pattern is typically recorded on a 2D area detector. USAXS data are generally collected using the maximum feasible sample-to-detector distance, contingent on the specific sample-to-detector distance and the X-ray wavelength. (b) Bonse–Hart Type USAXS instrument: the q resolution depends on the crystal optics, the order of reflection and the X-ray wavelength.
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detectors with pixel sizes smaller than 100 μm (e.g. Eiger¹ from Dectris), which is beneficial for USAXS because small pixels, with their small solid angles, improve the q resolution required for USAXS. X-rays are focused on the detector plane, as opposed to focusing on the sample plane, to reduce the footprint of the incident X-ray beam on the detector and allow the detector to access the smallest possible q. These instruments typically have a long flight tube that allows for a sample-to-detector distance exceeding 8 m. The beamstop and other optical elements that can introduce parasitic scattering also need to be carefully configured for the data to qualify as USAXS. Even with a flight tube length between 8 and 10 m, an X-ray energy below 8 keV will be required to meet the USAXS definition. This low X-ray energy requirement, as detailed in the subsection below, makes such instruments difficult to utilize with hard materials. For pinhole instruments to access the USAXS range at sufficiently high energy (20 keV and higher), a longer flight tube, potentially 20 m or more, would be required.


Facility based SAXS instruments are often designed and configured to meet the primary needs of their respective user communities. Although solid-state phase transformations in alloys were among the first applications of SAXS (Guinier, 1938), the flourishing of SAXS as a technique in today’s materials science would not be possible without generations of soft-material scientists who see the value of SAXS in characterizing nanoscopic and mesoscopic structures of a broad range of materials, such as polymers and colloids (Pedersen,


¹ Certain commercial products or company names are identified here to describe our study adequately. Such identification is not intended to imply recommendation or endorsement by the National Institute of Standards and Technology, nor is it intended to imply that the products or names identified are necessarily the best available for these purposes.


1997, Ballauff, 2001) that have feature sizes on the orders of nanometres and above. These materials often do not possess long-range order, making methods such as X-ray diffraction less effective. Because of this, many of the existing SAXS instruments are best suited for characterizing soft materials or materials where sample transmission is typically not a concern. When used at higher energies, their q range would be reduced, making larger scattering features in hard materials inaccessible.


The characteristics of the pinhole camera are widely known. For brevity, we will not enumerate these characteristics here. Instead, we will compare the critical aspects of two types of USAXS designs in a later section.


The second design is based on Bonse–Hart type optics. A schematic of a Bonse–Hart USAXS device is shown in Fig. 2(b). Bonse–Hart devices, designed for either X-rays or
neutrons, use a specialized setup of analyzer crystals, known as ‘channel-cut’ crystals, to measure the intensity of the beam scattered from a sample. These ‘channel-cut’ crystals allow for multiple Bragg diffractions from single crystals, thereby selecting an extremely angularly narrow beam based on its angular (or reciprocal) space position.


Such a setup typically involves two pairs of crystals: the first pair, called collimating crystals, is positioned before the sample to precisely collimate the incoming beam. The second pair, known as analyzer crystals, is located after the sample to ‘analyze’ or measure the scattered intensity. Both crystal sets utilize Bragg diffraction where, according to dynamic diffraction theory, the width of the crystal diffraction curve (rocking curve) becomes exceptionally narrow (Δq/q is ≃ 10⁻⁴ or smaller). Employing multiple diffractions within the channel-cut crystals further enhances this effect, reducing the intensity of the rocking curve tail exponentially (Bonse &


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678
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Zhang and Ilavsky • Bridging length scales in hard materials with USAXS IUCrJ (2024). 11, 675–694
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topical reviews
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For example, USAXS results have elucidated the formation mechanism of the detrimental δ phase precipitates in AM Inconel 625, an Ni-based superalloy (Zhang, Levine et al., 2018). This phase, typically forming after thousands of hours at temperatures higher than 800°C, appears in substantial volumes within 1 h at 800°C. Using USAXS data, time–temperature–transformation (TTT) curves for the δ phase were constructed (Lindwall et al., 2019), and a general methodology for investigating the response of AM materials to heat treatments was established. The USAXS data are also integral components of the Additive Manufacturing Benchmark Series (AM-Bench) of 2018 (Zhang et al., 2019) and 2022 (Zhang et al., 2024), aimed at using high-pedigree experimental data to guide the development of computer models to ensure the continued development of AM technologies.


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4.2. Ceramics
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Traditionally used as structural materials, ceramics have become an essential class of material in modern science, technology and industry development because of their unique properties and applications (Allen, 2005, 2023). Ceramics exhibit exceptional high-temperature stability, high hardness and wear resistance, wide-ranging electrical properties from insulators to semiconductors to superconductors, and high
chemical stability, making them the materials of choice for numerous applications such as energy storage and conversion, aerospace components, and electronic devices.


One of the significant applications of USAXS in the study of ceramic materials involves analyzing the microstructures of thermal barrier coatings (Renteria et al., 2007; Kulkarni et al., 2004; Ilavsky, 2010). These coatings, which can be created using various technologies such as electron beam physical vapor deposition (EB-PVD) and different types of thermal spraying, result in distinct microstructures. Applied to engine components, these coatings act as a thermal insulation layer, protecting the critical components from the extreme temperatures generated during engine operation. This allows engines to operate at higher combustion temperatures, enhancing efficiency and performance. A key feature for these coatings to function effectively as thermal barriers is a high level of porosity, as this characteristic significantly reduces thermal conductivity. The pore structure is complex. For example (Fig. 6), in a study of Y₂O₃-stabilized ZrO₂ coating prepared by EB-PVD (Kulkarni et al., 2006), USAXS data revealed that the coating exhibits a hierarchical microstructure consisting of pores of at least three different sizes, consistent with observations made using SEM. The q-dependent anisotropic scattering behavior illustrates the volume-averaged hierarchy of pore sizes within the coating: inter-


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EBPVD YSZ at 0.00026A⁻¹
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1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
60 30 0 330 300 270 240 210 180 150 120
Deposition direction
WD = 4 mm 10μm
Mag = 00 KX
Intra Columnar Fine porosity
--------------------------------------------------- Unstructured Caption Begin
EBPVD YSZ at 0.0006 A⁻¹
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0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40
90 30 0 330 300 270 240 210 180 150
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EBPVD YSZ at 0.000747A⁻¹
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0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
60 30 0 330 300 270 240 210 180 150 120
--------------------------------------------------- Unstructured Caption Begin
EBPVD YSZ at 0.00302A⁻¹
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0.20 0.18 0.16 0.14 0.12 0.10 0.08 0.06 0.04 0.02 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20
30 0 330 300 270 240 210 180 150
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Figure 6
2D USAXS measurements revealing the size (q) dependent microstructural anisotropy in a Y₂O₃-stabilized ZrO₂ coating produced by electron beam-physical vapor deposition. This figure was adapted from Kulkarni et al. (2006).
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686
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Zhang and Ilavsky • Bridging length scales in hard materials with USAXS IUCrJ (2024). 11, 675–694
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(a) Incident X-ray Sample WAXS SAXS USAXS

2θ q

q = 4π/λ sin(θ)

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(b)

Incident X-ray Bonse-Hart Crystals Sample Bonse-Hart Crystals Detector

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Figure 2

Schematics of two primary types of USAXS Instruments. (a) Pinhole configuration: in this setup, the scattering pattern is typically recorded on a 2D area detector. USAXS data are generally collected using the maximum feasible sample-to-detector distance, contingent on the specific sample-to-detector distance and the X-ray wavelength. (b) Bonse–Hart Type USAXS instrument: the q resolution depends on the crystal optics, the order of reflection and the X-ray wavelength.

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detectors with pixel sizes smaller than 100 μm (e.g. Eiger¹ from Dectris), which is beneficial for USAXS because small pixels, with their small solid angles, improve the q resolution required for USAXS. X-rays are focused on the detector plane, as opposed to focusing on the sample plane, to reduce the footprint of the incident X-ray beam on the detector and allow the detector to access the smallest possible q. These instruments typically have a long flight tube that allows for a sample-to-detector distance exceeding 8 m. The beamstop and other optical elements that can introduce parasitic scattering also need to be carefully configured for the data to qualify as USAXS. Even with a flight tube length between 8 and 10 m, an X-ray energy below 8 keV will be required to meet the USAXS definition. This low X-ray energy requirement, as detailed in the subsection below, makes such instruments difficult to utilize with hard materials. For pinhole instruments to access the USAXS range at sufficiently high energy (20 keV and higher), a longer flight tube, potentially 20 m or more, would be required.

Facility based SAXS instruments are often designed and configured to meet the primary needs of their respective user communities. Although solid-state phase transformations in alloys were among the first applications of SAXS (Guinier, 1938), the flourishing of SAXS as a technique in today’s materials science would not be possible without generations of soft-material scientists who see the value of SAXS in characterizing nanoscopic and mesoscopic structures of a broad range of materials, such as polymers and colloids (Pedersen,

¹ Certain commercial products or company names are identified here to describe our study adequately. Such identification is not intended to imply recommendation or endorsement by the National Institute of Standards and Technology, nor is it intended to imply that the products or names identified are necessarily the best available for these purposes.

1997, Ballauff, 2001) that have feature sizes on the orders of nanometres and above. These materials often do not possess long-range order, making methods such as X-ray diffraction less effective. Because of this, many of the existing SAXS instruments are best suited for characterizing soft materials or materials where sample transmission is typically not a concern. When used at higher energies, their q range would be reduced, making larger scattering features in hard materials inaccessible.

The characteristics of the pinhole camera are widely known. For brevity, we will not enumerate these characteristics here. Instead, we will compare the critical aspects of two types of USAXS designs in a later section.

The second design is based on Bonse–Hart type optics. A schematic of a Bonse–Hart USAXS device is shown in Fig. 2(b). Bonse–Hart devices, designed for either X-rays or

neutrons, use a specialized setup of analyzer crystals, known as ‘channel-cut’ crystals, to measure the intensity of the beam scattered from a sample. These ‘channel-cut’ crystals allow for multiple Bragg diffractions from single crystals, thereby selecting an extremely angularly narrow beam based on its angular (or reciprocal) space position.

Such a setup typically involves two pairs of crystals: the first pair, called collimating crystals, is positioned before the sample to precisely collimate the incoming beam. The second pair, known as analyzer crystals, is located after the sample to ‘analyze’ or measure the scattered intensity. Both crystal sets utilize Bragg diffraction where, according to dynamic diffraction theory, the width of the crystal diffraction curve (rocking curve) becomes exceptionally narrow (Δq/q is ≃ 10⁻⁴ or smaller). Employing multiple diffractions within the channel-cut crystals further enhances this effect, reducing the intensity of the rocking curve tail exponentially (Bonse &

--------------------------------------------------- Unstructured Page Footer Begin

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678

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Zhang and Ilavsky • Bridging length scales in hard materials with USAXS IUCrJ (2024). 11, 675–694

--------------------------------------------------- Unstructured Page Footer End

--------------------------------------------------- Unstructured Plain Text Format 1.0.4

--------------------------------------------------- Unstructured Page Header Begin

topical reviews

--------------------------------------------------- Unstructured Page Header End

For example, USAXS results have elucidated the formation mechanism of the detrimental δ phase precipitates in AM Inconel 625, an Ni-based superalloy (Zhang, Levine et al., 2018). This phase, typically forming after thousands of hours at temperatures higher than 800°C, appears in substantial volumes within 1 h at 800°C. Using USAXS data, time–temperature–transformation (TTT) curves for the δ phase were constructed (Lindwall et al., 2019), and a general methodology for investigating the response of AM materials to heat treatments was established. The USAXS data are also integral components of the Additive Manufacturing Benchmark Series (AM-Bench) of 2018 (Zhang et al., 2019) and 2022 (Zhang et al., 2024), aimed at using high-pedigree experimental data to guide the development of computer models to ensure the continued development of AM technologies.

--------------------------------------------------- Unstructured Title Begin

4.2. Ceramics

--------------------------------------------------- Unstructured Title End

Traditionally used as structural materials, ceramics have become an essential class of material in modern science, technology and industry development because of their unique properties and applications (Allen, 2005, 2023). Ceramics exhibit exceptional high-temperature stability, high hardness and wear resistance, wide-ranging electrical properties from insulators to semiconductors to superconductors, and high

chemical stability, making them the materials of choice for numerous applications such as energy storage and conversion, aerospace components, and electronic devices.

One of the significant applications of USAXS in the study of ceramic materials involves analyzing the microstructures of thermal barrier coatings (Renteria et al., 2007; Kulkarni et al., 2004; Ilavsky, 2010). These coatings, which can be created using various technologies such as electron beam physical vapor deposition (EB-PVD) and different types of thermal spraying, result in distinct microstructures. Applied to engine components, these coatings act as a thermal insulation layer, protecting the critical components from the extreme temperatures generated during engine operation. This allows engines to operate at higher combustion temperatures, enhancing efficiency and performance. A key feature for these coatings to function effectively as thermal barriers is a high level of porosity, as this characteristic significantly reduces thermal conductivity. The pore structure is complex. For example (Fig. 6), in a study of Y₂O₃-stabilized ZrO₂ coating prepared by EB-PVD (Kulkarni et al., 2006), USAXS data revealed that the coating exhibits a hierarchical microstructure consisting of pores of at least three different sizes, consistent with observations made using SEM. The q-dependent anisotropic scattering behavior illustrates the volume-averaged hierarchy of pore sizes within the coating: inter-

--------------------------------------------------- Unstructured Image Begin

--------------------------------------------------- Unstructured Caption Begin

EBPVD YSZ at 0.00026A⁻¹

--------------------------------------------------- Unstructured Caption End

1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

60 30 0 330 300 270 240 210 180 150 120

Deposition direction

WD = 4 mm 10μm

Mag = 00 KX

Intra Columnar Fine porosity

--------------------------------------------------- Unstructured Caption Begin

EBPVD YSZ at 0.0006 A⁻¹

--------------------------------------------------- Unstructured Caption End

0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

90 30 0 330 300 270 240 210 180 150

--------------------------------------------------- Unstructured Caption Begin

EBPVD YSZ at 0.000747A⁻¹

--------------------------------------------------- Unstructured Caption End

0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

60 30 0 330 300 270 240 210 180 150 120

--------------------------------------------------- Unstructured Caption Begin

EBPVD YSZ at 0.00302A⁻¹

--------------------------------------------------- Unstructured Caption End

0.20 0.18 0.16 0.14 0.12 0.10 0.08 0.06 0.04 0.02 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20

30 0 330 300 270 240 210 180 150

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Figure 6

2D USAXS measurements revealing the size (q) dependent microstructural anisotropy in a Y₂O₃-stabilized ZrO₂ coating produced by electron beam-physical vapor deposition. This figure was adapted from Kulkarni et al. (2006).

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--------------------------------------------------- Unstructured Page Footer Begin

--------------------------------------------------- Unstructured Page Number Block Begin

686

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Zhang and Ilavsky • Bridging length scales in hard materials with USAXS IUCrJ (2024). 11, 675–694

--------------------------------------------------- Unstructured Page Footer End

--------------------------------------------------- Unstructured Plain Text Format 1.0.4