Investigating Hydrogen in Zirconium Alloys by Means of Neutron Imaging

Neutrons interact with the magnetic moment of the atomic shell of an atom, as is common for X-rays, but mainly they interact directly with the nucleus. Therefore, the atomic number and the related number of electrons does not play a role in the strength of an interaction. Instead, hydrogen that is nearly invisible for X-rays has a higher attenuation for neutrons than most of the metals, e.g., zirconium, and thus would be visible through dark contrast in neutron images. Consequently, neutron imaging is a precise, non-destructive method to quantify the amount of hydrogen in materials with low attenuation. Because nuclear fuel cladding tubes of light water reactors are made of zirconium (98%), the hydrogen amount and distribution in metallic claddings can be investigated. Even hydrogen concentrations smaller than 10 wt.ppm can be determined locally with a spatial resolution of less than 10 μm (with a high-resolution neutron microscope). All in all, neutron imaging is a very fast and precise method for several applications. This article explains the basics of neutron imaging and provides samples of investigation possibilities, e.g., for hydrogen in zirconium alloy cladding tubes or in situ investigations of hydrogen diffusion in metals.


Theory
Neutrons are electrically neutral, but have a magnetic moment.Thus, they interact with the magnetic moment of the electron shells of atoms, but mainly with the nucleus itself.The probability of an interaction between a nucleus and a neutron is described by the microscopic cross section σ.The interaction itself may be either an absorption of the neutron by the nuclei, an incoherent scattering process on the nuclei, or a coherent scattering process on the material's structure.All interactions together can be referred to as the total neutron cross section σ tot , which can be summed up with the absorption cross section σ a , the incoherent cross section σ i , and the coherent scattering cross section σ c : Examples of microscopic neutron cross sections relevant for the investigation of hydrogen in zirconium are presented in Table 1 for a neutron wavelength of 0.1798 nm.

Element
σ a (10 −24 m 2 ) σ c (10 −24 m 2 ) σ i (10 The coherent scattering is caused by the average value of the scattering lengths of the lattice points.It results in constructive scattering effects with characteristic scattering patterns like small angle scattering, Bragg scattering, and Fresnel or Frauenhofer scattering.In contrast to coherent scattering, incoherent scattering does not produce characteristic patterns.The scattering intensity is equal for all directions and produces a constant background.This scattering is caused by point-to-point variations in the scattering lengths.In the case of hydrogen, the point-to-point variation in the proton spin interacting with the neutron spin results in a large variation in the scattering lengths and, thus, in a large, incoherent cross section.Another reason for incoherent scattering can be high concentrations of different isotopes of an element with differing neutron scattering lengths.In mixed crystals where one element substitutes the other, or in materials with high vacancy concentrations, the scattering length varies from point to point as well.This type of incoherent scattering is also known as monotonic Laue scattering [18].
The total macroscopic cross section, on the other hand, refers to the sum of the individual products of the number density N of the isotope i and the corresponding total microscopic neutron cross section σ total i : The neutron's wavelength, its kinetic energy, and the material's structure are decisive factors for the probability of neutron absorption.Neglecting resonant absorption processes, the probability of such a process is higher if the wavelength is also higher.The neutron spectrum depends on the kind of source, for example, whether, e.g., thermal or cold neutrons are produced.The wavelength maximum of thermalized neutrons is in the range of 0.18 nm (25 meV), whereas the wavelength of cold neutrons thermalized in liquidhydrogen vessels is in the range from 0.3 to <1.2 nm (9 meV to <0.6 meV).
Contrarily to neutrons, the attenuation for X-rays depends on the atomic number of an element, because it increases with an increasing number of electrons in the shell.Thus, the attenuation coefficients for heavy metals are lower for neutrons than for X-rays, apart from cadmium and gadolinium.Elements with a high attenuation for neutrons that are appropriate for neutron imaging investigations are, e.g., hydrogen, lithium, and boron.These and further attenuation coefficients can be found in Figures 1 and 2: Materials 2024, 17, x FOR PEER REVIEW 3 of 15 The coherent scattering is caused by the average value of the scattering lengths of the lattice points.It results in constructive scattering effects with characteristic scattering patterns like small angle scattering, Bragg scattering, and Fresnel or Frauenhofer scattering.In contrast to coherent scattering, incoherent scattering does not produce characteristic patterns.The scattering intensity is equal for all directions and produces a constant background.This scattering is caused by point-to-point variations in the scattering lengths.In the case of hydrogen, the point-to-point variation in the proton spin interacting with the neutron spin results in a large variation in the scattering lengths and, thus, in a large, incoherent cross section.Another reason for incoherent scattering can be high concentrations of different isotopes of an element with differing neutron scattering lengths.In mixed crystals where one element substitutes the other, or in materials with high vacancy concentrations, the scattering length varies from point to point as well.This type of incoherent scattering is also known as monotonic Laue scattering [18].
The total macroscopic cross section, on the other hand, refers to the sum of the individual products of the number density N of the isotope i and the corresponding total microscopic neutron cross section  : The neutron's wavelength, its kinetic energy, and the material's structure are decisive factors for the probability of neutron absorption.Neglecting resonant absorption processes, the probability of such a process is higher if the wavelength is also higher.The neutron spectrum depends on the kind of source, for example, whether, e.g., thermal or cold neutrons are produced.The wavelength maximum of thermalized neutrons is in the range of 0.18 nm (25 meV), whereas the wavelength of cold neutrons thermalized in liquid-hydrogen vessels is in the range from 0.3 to <1.2 nm (9 meV to <0.6 meV).
Contrarily to neutrons, the attenuation for X-rays depends on the atomic number of an element, because it increases with an increasing number of electrons in the shell.Thus, the attenuation coefficients for heavy metals are lower for neutrons than for X-rays, apart from cadmium and gadolinium.Elements with a high attenuation for neutrons that are appropriate for neutron imaging investigations are, e.g., hydrogen, lithium, and boron.These and further attenuation coefficients can be found in Figures 1 and 2:   [19].

Figure 2. Periodic table with thermal neutron energy attenuation coefficients
In order to calculate the attenuation, the intensities of the neutron beam must be measured before (I0) and after it passes through a sample.With additional information about the neutron path length through the sample s and Σtotal, the attenuated intensity I is defined as: Additionally, a background noise IB must be considered for the determination of the correct Σtotal.It should include all relevant disturbances during the measurements, e.g., electronic noise and any activated components or gamma radiations by the neutron source.All in all, the Σtotal can be calculated as followed: IB is the background intensity caused, for instance, by electronic noise or γ rays from activated components.
Figure 3 illustrates the importance of beam geometry and a pinhole camera for neutron imaging applications.The aperture for a neutron beamline is much larger than for an X-ray tube.In order to make a compromise between a good spatial resolution and a good time resolution, and, thus, a sharp, good-quality neutron image in the end, it is important to choose appropriate L and D values for the measurements.With a larger L and smaller D and l1 values, the quality of the neutron image increases; thus, the aperture should be kept as far away and as small as possible.On the other hand, this leads to an intensity loss, which is why the sample should be placed right in front of or as close as possible to the detector.As can be seen in Figure 3, the neutrons follow the distance L from the aperture with the diameter D and then project a shadow of the sample on the detector.Thereby, their flight paths are not parallel.In order to calculate the attenuation, the intensities of the neutron beam must be measured before (I 0 ) and after it passes through a sample.With additional information about the neutron path length through the sample s and Σ total , the attenuated intensity I is defined as: Additionally, a background noise I B must be considered for the determination of the correct Σ total .It should include all relevant disturbances during the measurements, e.g., electronic noise and any activated components or gamma radiations by the neutron source.All in all, the Σ total can be calculated as followed: I B is the background intensity caused, for instance, by electronic noise or γ rays from activated components.
Figure 3 illustrates the importance of beam geometry and a pinhole camera for neutron imaging applications.The aperture for a neutron beamline is much larger than for an X-ray tube.In order to make a compromise between a good spatial resolution and a good time resolution, and, thus, a sharp, good-quality neutron image in the end, it is important to choose appropriate L and D values for the measurements.With a larger L and smaller D and l1 values, the quality of the neutron image increases; thus, the aperture should be kept as far away and as small as possible.On the other hand, this leads to an intensity loss, which is why the sample should be placed right in front of or as close as possible to the detector.As can be seen in Figure 3, the neutrons follow the distance L from the aperture with the diameter D and then project a shadow of the sample on the detector.Thereby, their flight paths are not parallel.In order to calculate the attenuation, the intensities of the neutron beam must be measured before (I0) and after it passes through a sample.With additional information about the neutron path length through the sample s and Σtotal, the attenuated intensity I is defined as: Additionally, a background noise IB must be considered for the determination of the correct Σtotal.It should include all relevant disturbances during the measurements, e.g., electronic noise and any activated components or gamma radiations by the neutron source.All in all, the Σtotal can be calculated as followed: IB is the background intensity caused, for instance, by electronic noise or γ rays from activated components.
Figure 3 illustrates the importance of beam geometry and a pinhole camera for neutron imaging applications.The aperture for a neutron beamline is much larger than for an X-ray tube.In order to make a compromise between a good spatial resolution and a good time resolution, and, thus, a sharp, good-quality neutron image in the end, it is important to choose appropriate L and D values for the measurements.With a larger L and smaller D and l1 values, the quality of the neutron image increases; thus, the aperture should be kept as far away and as small as possible.On the other hand, this leads to an intensity loss, which is why the sample should be placed right in front of or as close as possible to the detector.As can be seen in Figure 3, the neutrons follow the distance L from the aperture with the diameter D and then project a shadow of the sample on the detector.Thereby, their flight paths are not parallel.

Neutron Tomography
Instead of only investigating samples from a two-dimensional (2D) perspective, it is possible to reconstruct a three-dimensional (3D) tomography from several sample projections at different angles.For this purpose, the sample has to be rotated [21].According to the sampling theorem for tomography investigations, the following number of projections N projections is needed: where R sample is the radius of the circle including the whole sample and s pixel is the pixel size.For a precise reconstruction of tomography measurements with the usual pixel sizes, an amount of at least 400 images is crucial.Generally, the needed number of images can be calculated for each case using the maximum width (in pixels) of the sample projected on the detector.An example of a 3D reconstruction of hydrogen enrichments of fuel rod simulators from the QUENCH-LOCA-03 experiment is given in Figure 4. There, the hydrogen enrichments are visible through the dark contrast compared to the rod matrix.

Neutron Tomography
Instead of only investigating samples from a two-dimensional (2D) perspective, it is possible to reconstruct a three-dimensional (3D) tomography from several sample projections at different angles.For this purpose, the sample has to be rotated [21].According to the sampling theorem for tomography investigations, the following number of projections Nprojections is needed: where Rsample is the radius of the circle including the whole sample and spixel is the pixel size.
For a precise reconstruction of tomography measurements with the usual pixel sizes, an amount of at least 400 images is crucial.Generally, the needed number of images can be calculated for each case using the maximum width (in pixels) of the sample projected on the detector.An example of a 3D reconstruction of hydrogen enrichments of fuel rod simulators from the QUENCH-LOCA-03 experiment is given in Figure 4. There, the hydrogen enrichments are visible through the dark contrast compared to the rod matrix.

Facilities
There are several high-performance neutron imaging facilities in Europe (Table 2):

NEXT at ILL (High Flux Reactor) in Grenoble
The neutron and X-ray imaging facility NEXT at the ILL in Grenoble (France) [22] has been in operation since 2016.The facility uses cold neutrons and offers a spatial resolution of up to 5 μm.The maximal field of view is 170 mm × 170 mm at a spatial resolution of 83 μm.The high-flux ILL research reactor provides cold neutrons with a flux of 3•10 8 n/cm 2 /s at a collimation of L/D = 333.

Facilities
There are several high-performance neutron imaging facilities in Europe (Table 2):

NEXT at ILL (High Flux Reactor) in Grenoble
The neutron and X-ray imaging facility NEXT at the ILL in Grenoble (France) [22] has been in operation since 2016.The facility uses cold neutrons and offers a spatial resolution of up to 5 µm.The maximal field of view is 170 mm × 170 mm at a spatial resolution of 83 µm.The high-flux ILL research reactor provides cold neutrons with a flux of 3 × 10 8 n/cm 2 /s at a collimation of L/D = 333.

ANTARES at FRM-2 in Garching
The neutron imaging facility ANTARES at the FRM-2 reactor in Garching (Germany) [23] will be restarted in the second half of 2024.The neutron source provides a cold neutron flux of 6.4 × 10 7 n/cm 2 /s at a collimation of L/D = 500.Roughly estimated, it has about half of the flux of NEXT.

Neutron Imaging Instruments at SINQ, PSI in Villigen
At the Swiss spallation neutron source SINQ, several beamlines are used for neutron imaging.Dedicated to neutron imaging are the NEUTRA and ICON facilities.The NEUTRA facility [24] uses thermal neutrons with flux of about 6 × 10 6 n/cm 2 /s for L/D = 350 and a usual proton current on the SINQ target, producing neutrons of 1.2 mA.The ICON facility [25] has a cold spectrum neutron flux of 1.5 × 10 7 n/cm 2 /s for L/D = 343 and a SINQ proton current of 1.2 mA.The difference in the hydrogen dependencies on the total macroscopic neutron cross sections between the spectra of the two facilities is given in Figure 5.It is visible that the total macroscopic neutron cross section for hydrogenfree Zircaloy-4 is higher for thermal neutrons, but the effect of hydrogen is lower for the thermal spectrum than for the cold one.In addition to the NEUTRA and ICON beamlines, the beamlines BOA and POLDI are available, at least partially, for imaging experiments.The POLDI facility is a neutron diffractometer dedicated to strain measurements [26].Currently, it is partially used for neutron microscopy [27].The thermal neutron spectrum is comparable to that of the NEUTRA facility.The BOA beamline [28] was originally dedicated to the testing of neutron optical components.The neutron spectrum is even colder than that of ICON.The neutron flux of 2.7 × 10 7 n/cm 2 /s for L/D = 400 is given for BOA.

ANTARES at FRM-2 in Garching
The neutron imaging facility ANTARES at the FRM-2 reactor in Garching (Germany) [23] will be restarted in the second half of 2024.The neutron source provides a cold neutron flux of 6.4 × 10 7 n/cm 2 /s at a collimation of L/D = 500.Roughly estimated, it has about half of the flux of NEXT.

Neutron Imaging Instruments at SINQ, PSI in Villigen
At the Swiss spallation neutron source SINQ, several beamlines are used for neutron imaging.Dedicated to neutron imaging are the NEUTRA and ICON facilities.The NEU-TRA facility [24] uses thermal neutrons with flux of about 6 × 10 6 n/cm 2 /s for L/D = 350 and a usual proton current on the SINQ target, producing neutrons of 1.2 mA.The ICON facility [25] has a cold spectrum neutron flux of 1.5 × 10 7 n/cm 2 /s for L/D = 343 and a SINQ proton current of 1.2 mA.The difference in the hydrogen dependencies on the total macroscopic neutron cross sections between the spectra of the two facilities is given in Figure 5.It is visible that the total macroscopic neutron cross section for hydrogen-free Zircaloy-4 is higher for thermal neutrons, but the effect of hydrogen is lower for the thermal spectrum than for the cold one.In addition to the NEUTRA and ICON beamlines, the beamlines BOA and POLDI are available, at least partially, for imaging experiments.The POLDI facility is a neutron diffractometer dedicated to strain measurements [26].Currently, it is partially used for neutron microscopy [27].The thermal neutron spectrum is comparable to that of the NEUTRA facility.The BOA beamline [28] was originally dedicated to the testing of neutron optical components.The neutron spectrum is even colder than that of ICON.The neutron flux of 2.7 × 10 7 n/cm 2 /s for L/D = 400 is given for BOA.

IMAT at ISIS in the STFC Rutherford Appleton Laboratory at the Harwell Campus Didcot
The time-of-flight neutron imaging facility IMAT [29] offers a high wavelength resolution.The flux depends on the wavelength.The integral flux is 1.4 × 10 7 n/cm 2 /s for L/D=500, which is comparable to the flux provided at BOA.
In addition to these high-performance facilities, possibilities for neutron imaging exist in Swierg (Poland), Budapest (Hungary) and Dubna (Russia).Outside of Europe, highperformance neutron imaging facilities include RADEN at J-Parc Tokai (Japan) [30] and DINGO at ANSTO (Australia) [31].In the USA, further facilities are available and in operation: NIF at NIST [32], ERNI at LANSCE [33], and MARS [34] and VENUS [35] at ORNL.New high-performance neutron imaging facilities are currently under construction in China and Sweden.

IMAT at ISIS in the STFC Rutherford Appleton Laboratory at the Harwell Campus Didcot
The time-of-flight neutron imaging facility IMAT [29] offers a high wavelength resolution.The flux depends on the wavelength.The integral flux is 1.4 × 10 7 n/cm 2 /s for L/D = 500, which is comparable to the flux provided at BOA.
In addition to these high-performance facilities, possibilities for neutron imaging exist in Swierg (Poland), Budapest (Hungary) and Dubna (Russia).Outside of Europe, high-performance neutron imaging facilities include RADEN at J-Parc Tokai (Japan) [30] and DINGO at ANSTO (Australia) [31].In the USA, further facilities are available and in operation: NIF at NIST [32], ERNI at LANSCE [33], and MARS [34] and VENUS [35] at ORNL.New high-performance neutron imaging facilities are currently under construction in China and Sweden.

Hydrogen Diffusion Studies
As already mentioned, hydrogen uptake is a critical degradation/corrosion phenomenon for metals in various applications.In the framework of nuclear reactors, hydro-gen can be taken up by the metallic cladding that surrounds nuclear fuel pellets or pressure tubes in CANDU reactors.Because these tubes consist mainly of zirconium and are in direct contact to the surrounding cooling water during operation, the following corrosion reaction takes place: Because of the solute state of the hydrogen during operation, the integrity of the cladding tubes and, thus, the fuel rods remain intact.However, several phenomena come along with absorbed hydrogen and are relevant for safety.

Analysis of the Hydrogen Distribution in Cladding Tubes after Simulated Basis Loss of Coolant Accidents
The so-called secondary hydrogenation during the design basis loss of coolant accident (LOCA) scenarios (see Figure 6) degrade the toughness of the cladding tubes.This occurs after bursting of the tubes and an ingress of steam into the claddings.Then, highly hydrogen-rich zones can form, which increase the risk of brittle fractures due to thermal shock during the emergency cooling.Consequently, fuel pellets can be relocated, fission products can be released, and the coolability of the reactor core cannot be ensured any longer.Many studies focus on investigations of LOCA scenarios [36] with newly developed cladding materials and/or coatings [37].

Hydrogen Diffusion Studies
As already mentioned, hydrogen uptake is a critical degradation/corrosion phenomenon for metals in various applications.In the framework of nuclear reactors, hydrogen can be taken up by the metallic cladding that surrounds nuclear fuel pellets or pressure tubes in CANDU reactors.Because these tubes consist mainly of zirconium and are in direct contact to the surrounding cooling water during operation, the following corrosion reaction takes place: Because of the solute state of the hydrogen during operation, the integrity of the cladding tubes and, thus, the fuel rods remain intact.However, several phenomena come along with absorbed hydrogen and are relevant for safety.

Analysis of the Hydrogen Distribution in Cladding Tubes after Simulated Basis Loss of Coolant Accidents
The so-called secondary hydrogenation during the design basis loss of coolant accident (LOCA) scenarios (see Figure 6) degrade the toughness of the cladding tubes.This occurs after bursting of the tubes and an ingress of steam into the claddings.Then, highly hydrogen-rich zones can form, which increase the risk of brittle fractures due to thermal shock during the emergency cooling.Consequently, fuel pellets can be relocated, fission products can be released, and the coolability of the reactor core cannot be ensured any longer.Many studies focus on investigations of LOCA scenarios [36] with newly developed cladding materials and/or coatings [37].Eight large-scale tests simulating LOCA were performed at KIT.The tests were performed using a bundle of 21 fuel rod simulators, with cladding tubes made of zirconium alloys used in Germany (Zircaloy-4 (Framatome, Germany), ZIRLO™ (Westinghouse, Sweden), and M5 ® (Framatome, Germany)).The fuel rod simulator bundles had a prototypical geometry.The test protocol was developed according to the German nuclear rules for design-basis, large-break LOCA: heating in steam up to about 1000 °C at a rate of 5 to 6 K/s; cooling down for three minutes to about 600 °C, and water quenching to terminate the test.Neutron imaging was a very important part of the post-test examinations.Neutron radiography was performed with all cladding tubes, whereas tomography measurements were applied only at chosen ones, as they had had shown clear hydrogen enrichment in the neutron radiographies.The facilities ICON and BOA at PSI, the ANTARES beamline at TU Munich, and the CONRAD [38] facility at the Helmholtz Center Berlin (now out of operation) were used for the neutron imaging investigations.Pixel sizes of Figure 6.Scheme of a LOCA scenario dependent on temperature and time [38].
Eight large-scale tests simulating LOCA were performed at KIT.The tests were performed using a bundle of 21 fuel rod simulators, with cladding tubes made of zirconium alloys used in Germany (Zircaloy-4 (Framatome, Germany), ZIRLO™ (Westinghouse, Sweden), and M5 ® (Framatome, Germany)).The fuel rod simulator bundles had a prototypical geometry.The test protocol was developed according to the German nuclear rules for design-basis, large-break LOCA: heating in steam up to about 1000 • C at a rate of 5 to 6 K/s; cooling down for three minutes to about 600 • C, and water quenching to terminate the test.Neutron imaging was a very important part of the post-test examinations.Neutron radiography was performed with all cladding tubes, whereas tomography measurements were applied only at chosen ones, as they had had shown clear hydrogen enrichment in the neutron radiographies.The facilities ICON and BOA at PSI, the ANTARES beamline at TU Munich, and the CONRAD [39] facility at the Helmholtz Center Berlin (now out of operation) were used for the neutron imaging investigations.Pixel sizes of about 30 to 40 µm were applied.More details are given by Stuckert et al. [36].As an example, Figure 4 shows the results of the hydrogen distribution in nine claddings of the QUENCH-L3 test using ZIRLO™ tubes.The hydrogen-enriched positions are darker.Two types of hydrogen-enriched locations can be divided: firstly, hydrogen-enriched rings (c.f. Figure 4), which are non-perpendicularly oriented to the tube axis; and secondly, hydrogen-enriched strips parallel to the tube axis.The tomography results were analyzed statistically by

Hydrogen Diffusion in Zirconium Alloys
A possible reorientation of zirconium hydrides in the cladding tubes after the vacuumdrying process of spent nuclear fuel (SNF), where temperatures of up to 400 • C are reached, can affect the integrity of cladding tubes.Such a reorientation is mainly caused by - The fabrication history; -The material's texture; - The stress state in the cladding tube connected to the higher hoop stress generated by the fission products of the pellets.

Hydrogen Diffusion in Zirconium Alloys
A possible reorientation of zirconium hydrides in the cladding tubes after the vacuum-drying process of spent nuclear fuel (SNF), where temperatures of up to 400 °C are reached, can affect the integrity of cladding tubes.Such a reorientation is mainly caused by - The fabrication history; -The material's texture; - The stress state in the cladding tube connected to the higher hoop stress generated by the fission products of the pellets.The delayed hydride cracking (DHC) phenomena illustrated in Figure 8 can occur during operation or during the dry storage of SNF.The cladding tube fails after hours of constant mechanical load without any creeping.Hydrogen diffuses to a crack tip and precipitates there until a certain length of a hydride is reached.Then, breaking and further crack propagation are caused, and the whole process is repeated until the tube fails.The driving force of this process is the stress gradient created by the plastic deformed zone ahead of the crack tip in the bulk material.Neutron imaging serves as a non-destructive method by which to analyze the hydrogen behavior during the DHC process, and should be used for future studies to experimentally investigate the phenomenon in situ.Nevertheless, Soria et al. [15] have already been able to perform similar tests at 250 • C with two different zirconium alloys.Some of the results are shown in Figure 8, where the pathway of the crack propagation in one sample is shown during the in-situ experiment.The delayed hydride cracking (DHC) phenomena illustrated in Figure 8 can occur during operation or during the dry storage of SNF.The cladding tube fails after hours of constant mechanical load without any creeping.Hydrogen diffuses to a crack tip and precipitates there until a certain length of a hydride is reached.Then, breaking and further crack propagation are caused, and the whole process is repeated until the tube fails.The driving force of this process is the stress gradient created by the plastic deformed zone ahead of the crack tip in the bulk material.Neutron imaging serves as a non-destructive method by which to analyze the hydrogen behavior during the DHC process, and should be used for future studies to experimentally investigate the phenomenon in situ.Nevertheless, Soria et al. [15] have already been able to perform similar tests at 250 °C with two different zirconium alloys.Some of the results are shown in Figure 8, where the pathway of the crack propagation in one sample is shown during the in-situ experiment.Nevertheless, precise determinations of the hydrogen diffusion process, especially in cladding tubes, are only available to a limited extent.The reasons are the lack of experiments under real scenario conditions and the limited consideration of influencing parameters like the stress state, the texture, or the grain size.Nevertheless, hydrogen in cladding tubes/zirconium can be easily investigated using destructive methods such as metallography or carrier hot gas extraction (CHGE).But non-destructive investigations, and, thus, neutron imaging, offer more possibilities, even to observe samples in situ during different processes, e.g., crack initiation, crack development, ruptures, or diffusion (Figure 9) at high temperatures.Concerning diffusion experiments, the relevance of diffusion coefficients and, thus, the diffusion velocity dependent on its direction in the material's structure are of importance.The method of determining diffusion coefficients from neutron radiography data is described in Equation (7) Nevertheless, precise determinations of the hydrogen diffusion process, especially in cladding tubes, are only available to a limited extent.The reasons are the lack of experiments under real scenario conditions and the limited consideration of influencing parameters like the stress state, the texture, or the grain size.Nevertheless, hydrogen in cladding tubes/zirconium can be easily investigated using destructive methods such as metallography or carrier hot gas extraction (CHGE).But non-destructive investigations, and, thus, neutron imaging, offer more possibilities, even to observe samples in situ during different processes, e.g., crack initiation, crack development, ruptures, or diffusion (Figure 9) at high temperatures.Concerning diffusion experiments, the relevance of diffusion coefficients and, thus, the diffusion velocity dependent on its direction in the material's structure are of importance.The method of determining diffusion coefficients from neutron radiography data is described in Equation (7).If the diffusion coefficients are modeled [43] instead of experimentally determined, most, but not all, relevant parameters are taken into account; thus, the literature values obtained from pure zirconium with undefined textures and grain sizes are not comparable to the cladding tube materials.Hydrogen uptake starts when the very thin oxide layer which was formed at room temperature in air is dissoluted.The time needed for this dissolution is unknown because it depends on many parameters, like the humidity of the laboratory air, the time between polishing the sample and exposing it in the furnace, the quality of the vacuum, and the inert atmosphere in the furnace.As a consequence, the starting time of the diffusion process is difficult to specify.This is one intention of in situ neutron imaging and the experiment presented in Figure 9. Here, the beginning of the hydrogen uptake is clearly visible by changing the neutron transmission at the position of the hydrogen absorption.It is planned to determine the hydrogen diffusion coefficients for all relevant macroscopical axis directions, because they differ in their c-or a-axes.For the experiment, a Zry-4 cladding tube was peroxidized in air at 450 • C for several hours to produce an oxide layer a few micrometers thick that would prevent hydrogen uptake.A feasibility test was performed with a leak-tight sample capsule at the BOA facility at PSI, while using a capsule filled with the sample on ZrH 2 powder in a helium atmosphere.Hydrogen was taken up by the sample at the intended/grinded position.However, the large distance between the sample inside the furnace and the detector strongly reduced the spatial resolution, because a very good collimation of the beam of L/D > 1000 was not available with sufficient intensity at this beamline.Additionally, the furnace which was used needed 3 h to reach the predefined temperature.During the heating-up process, diffusion occurred.The diffusion coefficients were not determined precisely enough.Subsequent investigations are still ongoing.The results will be published elsewhere.
into account; thus, the literature values obtained from pure zirconium with undefined textures and grain sizes are not comparable to the cladding tube materials.Hydrogen uptake starts when the very thin oxide layer which was formed at room temperature in air is dissoluted.The time needed for this dissolution is unknown because it depends on many parameters, like the humidity of the laboratory air, the time between polishing the sample and exposing it in the furnace, the quality of the vacuum, and the inert atmosphere in the furnace.As a consequence, the starting time of the diffusion process is difficult to specify.This is one intention of in situ neutron imaging and the experiment presented in Figure 9. Here, the beginning of the hydrogen uptake is clearly visible by changing the neutron transmission at the position of the hydrogen absorption.It is planned to determine the hydrogen diffusion coefficients for all relevant macroscopical axis directions, because they differ in their c-or a-axes.For the experiment, a Zry-4 cladding tube was peroxidized in air at 450 °C for several hours to produce an oxide layer a few micrometers thick that would prevent hydrogen uptake.A feasibility test was performed with a leaktight sample capsule at the BOA facility at PSI, while using a capsule filled with the sample on ZrH2 powder in a helium atmosphere.Hydrogen was taken up by the sample at the intended/grinded position.However, the large distance between the sample inside the furnace and the detector strongly reduced the spatial resolution, because a very good collimation of the beam of L/D > 1000 was not available with sufficient intensity at this beamline.Additionally, the furnace which was used needed 3 h to reach the predefined temperature.During the heating-up process, diffusion occurred.The diffusion coefficients were not determined precisely enough.Subsequent investigations are still ongoing.The results will be published elsewhere.Different materials/metals have different diffusion coefficients depending on the crystallographic direction, e.g., hydrogen in zirconium depending on the diffusion direction in a hexagonal crystal lattice.Neutron radiography experiments, as performed by, e.g., Beyer et al. [43,44], shall help to determine precise values for this process.In the case of cladding tubes that consist mainly of zirconium, an additional difficulty is that the material immediately forms a zirconium oxide layer when it is in contact with air.Therefore, methods to investigate the hydrogen uptake process in situ after the dissolution of the oxide layer are suitable.In this context, measurements with the so-called in situ neutron radiography reaction (INNRO) furnace (Figure 10) at the ICON beamline at the PSI were performed.Different materials/metals have different diffusion coefficients depending on the crystallographic direction, e.g., hydrogen in zirconium depending on the diffusion direction in a hexagonal crystal lattice.Neutron radiography experiments, as performed by, e.g., Beyer et al. [44,45], shall help to determine precise values for this process.In the case of cladding tubes that consist mainly of zirconium, an additional difficulty is that the material immediately forms a zirconium oxide layer when it is in contact with air.Therefore, methods to investigate the hydrogen uptake process in situ after the dissolution of the oxide layer are suitable.In this context, measurements with the so-called in situ neutron radiography reaction (INNRO) furnace (Figure 10) at the ICON beamline at the PSI were performed.
Because of the large distance of about 300 mm between the sample inside the furnace and the detector, a collimation of L/D = 800 was applied, which decreased the neutron flux at the sample.In order to obtain a good contrast resolution for a precise determination of the local hydrogen concentration, each radiograph was illuminated for 120 s.The samples were solid cylinders 20 mm in length and 12 mm in diameter, and were made of Zircaloy-4.The samples were pre-oxidized at 1100 • C for 1 h to produce a 50 µm oxide layer on the surface, preventing hydrogen uptake.
The sample was heated at a rate of 10 K/min to the test temperature in flowing argon (flux: 50 L/h).After reaching the test temperature, hydrogen was injected with a flux of 4 L/h, in addition to the argon flux hydrogen.The isothermal tests were performed at 900, 1000, 1100, 1200, and 1300 • C. Figure 11 shows neutron radiographs taken at different diffusion times at 900 • C. The images were compared to the image of the initial state.Therefore, only changes in the neutron transmission became visible.The diffusion of the hydrogen (dark) could be observed visually during the measurements, without processing the data.From each neutron radiograph, the hydrogen distribution can be determined via the gray value distribution.Because of the large distance of about 300 mm between the sample inside the fur and the detector, a collimation of L/D = 800 was applied, which decreased the neutron at the sample.In order to obtain a good contrast resolution for a precise determinati the local hydrogen concentration, each radiograph was illuminated for 120 s.The sam were solid cylinders 20 mm in length and 12 mm in diameter, and were made of Zirc 4. The samples were pre-oxidized at 1100 °C for 1 h to produce a 50 μm oxide layer o surface, preventing hydrogen uptake.
The sample was heated at a rate of 10 K/min to the test temperature in flowing a (flux: 50 l/h).After reaching the test temperature, hydrogen was injected with a flux l/h, in addition to the argon flux hydrogen.The isothermal tests were performed at 1000, 1100, 1200, and 1300 °C. Figure 11 shows neutron radiographs taken at diffe diffusion times at 900 °C.The images were compared to the image of the initial s Therefore, only changes in the neutron transmission became visible.The diffusion o hydrogen (dark) could be observed visually during the measurements, without cessing the data.From each neutron radiograph, the hydrogen distribution can be d mined via the gray value distribution.The hydrogen concentration can be fitted using the analytical diffusion equatio assuming a one-sided infinite sample-c is the hydrogen concentration; c0 is the hydr concentration in equilibrium to the hydrogen partial pressure in the surrounding ga mosphere at the test temperature, according to Sieverts' law; x is the distance to the plane through which hydrogen was absorbed; D is the diffusion coefficient; and t the (, ) =  1 − erf  2√  Because of the large distance of about 300 mm between the sample inside the furnace and the detector, a collimation of L/D = 800 was applied, which decreased the neutron flux at the sample.In order to obtain a good contrast resolution for a precise determination of the local hydrogen concentration, each radiograph was illuminated for 120 s.The samples were solid cylinders 20 mm in length and 12 mm in diameter, and were made of Zircaloy-4.The samples were pre-oxidized at 1100 °C for 1 h to produce a 50 μm oxide layer on the surface, preventing hydrogen uptake.
The sample was heated at a rate of 10 K/min to the test temperature in flowing argon (flux: 50 l/h).After reaching the test temperature, hydrogen was injected with a flux of 4 l/h, in addition to the argon flux hydrogen.The isothermal tests were performed at 900, 1000, 1100, 1200, and 1300 °C. Figure 11 shows neutron radiographs taken at different diffusion times at 900 °C.The images were compared to the image of the initial state.Therefore, only changes in the neutron transmission became visible.The diffusion of the hydrogen (dark) could be observed visually during the measurements, without processing the data.From each neutron radiograph, the hydrogen distribution can be determined via the gray value distribution.The hydrogen concentration can be fitted using the analytical diffusion equation by assuming a one-sided infinite sample-c is the hydrogen concentration; c0 is the hydrogen concentration in equilibrium to the hydrogen partial pressure in the surrounding gas atmosphere at the test temperature, according to Sieverts' law; x is the distance to the base plane through which hydrogen was absorbed; D is the diffusion coefficient; and t the time: The hydrogen concentration can be fitted using the analytical diffusion equation by assuming a one-sided infinite sample-c is the hydrogen concentration; c 0 is the hydrogen concentration in equilibrium to the hydrogen partial pressure in the surrounding gas atmosphere at the test temperature, according to Sieverts' law; x is the distance to the base plane through which hydrogen was absorbed; D is the diffusion coefficient; and t the time: In order to determine the exact quantitative hydrogen content in the samples, it is advantageous to measure several calibration samples with different and known hydrogen contents under the same conditions.These calibration samples were produced by annealing the same material in hydrogen containing an inert gas until equilibrium between the hydrogen concentration in the sample and the hydrogen partial pressure in the gas atmosphere was reached.The hydrogen concentration in the sample was determined by a measurement of the weight gain of the sample.Sieverts' law describes the equilibrium correlation between the ratio of the number densities of hydrogen N H and zirconium N Zr and the hydrogen partial pressure in the gas atmosphere p H2 : with k S as the Sieverts' coefficient depending on the Arrhenius type.Figure 12 compares neutron radiographs of the calibration samples with different ratios of hydrogen and zirconium number densities.
hydrogen partial pressure in the gas atmosphere pH2: with kS as the Sieverts' coefficient depending on the Arrhenius type.Figure 12 compares neutron radiographs of the calibration samples with different ratios of hydrogen and zirconium number densities.With the intensity measurements of the calibration samples, a calibration curve of the correlation between the total macroscopic neutron cross section and the number density ratio, according to Equation ( 2), can be determined as shown in Figure 13.With its slope, it becomes possible to calculate the previously unknown hydrogen concentrations of the measured samples.It is essential to measure the calibration samples during each beam time, even if the same beamline is used.Only then can the effects of setup changes or neutron spectrum changes be excluded.These effects are well described by [30].It must be mentioned that the calibration curve determined for the tube-shaped samples from 3D analyses of neutron tomography data differs from the ones measured by means of neutron radiography (Figure 13).The differences increase with increasing hydrogen concentrations.The calibration curves are no longer linear, but flattened at the higher-concentration side of the diagram.The reason is that 3D reconstruction also uses positions with longer neutron path lengths.This can be associated with hardening of the neutron spectra and a stronger influence of multiple scattering.Therefore, if the CT value With the intensity measurements of the calibration samples, a calibration curve of the correlation between the total macroscopic neutron cross section and the number density ratio, according to Equation ( 2), can be determined as shown in Figure 13.With its slope, it becomes possible to calculate the previously unknown hydrogen concentrations of the measured samples.It is essential to measure the calibration samples during each beam time, even if the same beamline is used.Only then can the effects of setup changes or neutron spectrum changes be excluded.These effects are well described by [30].
hydrogen partial pressure in the gas atmosphere pH2: with kS as the Sieverts' coefficient depending on the Arrhenius type.Figure 12 compares neutron radiographs of the calibration samples with different ratios of hydrogen and zirconium number densities.With the intensity measurements of the calibration samples, a calibration curve of the correlation between the total macroscopic neutron cross section and the number density ratio, according to Equation ( 2), can be determined as shown in Figure 13.With its slope, it becomes possible to calculate the previously unknown hydrogen concentrations of the measured samples.It is essential to measure the calibration samples during each beam time, even if the same beamline is used.Only then can the effects of setup changes or neutron spectrum changes be excluded.These effects are well described by [30].It must be mentioned that the calibration curve determined for the tube-shaped samples from 3D analyses of neutron tomography data differs from the ones measured by means of neutron radiography (Figure 13).The differences increase with increasing hydrogen concentrations.The calibration curves are no longer linear, but flattened at the higher-concentration side of the diagram.The reason is that 3D reconstruction also uses positions with longer neutron path lengths.This can be associated with hardening of the neutron spectra and a stronger influence of multiple scattering.Therefore, if the CT value It must be mentioned that the calibration curve determined for the tube-shaped samples from 3D analyses of neutron tomography data differs from the ones measured by means of neutron radiography (Figure 13).The differences increase with increasing hydrogen concentrations.The calibration curves are no longer linear, but flattened at the higher-concentration side of the diagram.The reason is that 3D reconstruction also uses positions with longer neutron path lengths.This can be associated with hardening of the neutron spectra and a stronger influence of multiple scattering.Therefore, if the CT value is analyzed quantitatively, tomography measurements of the calibration samples are mandatory.

Conclusions
New methodical developments on the field of neutron imaging will provide promising possibilities for material investigations in the future.For instance, neutron microscopy offers spatial resolutions of less than 5 µm.Imaging experiments with short, pulsed beams allow the measurements of the lateral distribution of the Bragg edges to determine local stresses, textures, or the separation of special objects with given structures from complex micrographs.
However, a problem is the strong overbooking of the neutron imaging facilities, which will be difficult to solve.Therefore, the use of more beamlines for imaging experiments would be helpful.

Figure 3 .
Figure 3. Schematic illustration of the projection of a sample's shadow on the detector with the important L and D values that determine the quality of the neutron images [20].A high-quality measurement should at least contain an L/D = 300.

Figure 3 .
Figure 3. Schematic illustration of the projection of a sample's shadow on the detector with the important L and D values that determine the quality of the neutron images [20].A high-quality measurement should at least contain an L/D = 300.

Figure 3 .
Figure 3. Schematic illustration of the projection of a sample's shadow on the detector with the important L and D values that determine the quality of the neutron images [20].A high-quality measurement should at least contain an L/D = 300.

Figure 4 .
Figure 4. Three-dimensional reconstruction of the hydrogen distribution after a simulated design basis loss-of-coolant accident [17].

Figure 4 .
Figure 4. Three-dimensional reconstruction of the hydrogen distribution after a simulated design basis loss-of-coolant accident [17].

Figure 5 .
Figure 5.Comparison of the total cross sections of the thermal NEUTRA and the cold ICON spectra [4].

Figure 5 .
Figure 5.Comparison of the total cross sections of the thermal NEUTRA and the cold ICON spectra [4].

Figure 6 .
Figure 6.Scheme of a LOCA scenario dependent on temperature and time [36].

Figure 7 .
Figure 7. Illustration of circumferentially (a) and radially (b) oriented zirconium hydrides (black) in a cladding tube [40] with a light microscopic image of a Zry-4 cladding tube sample with mainly circumferentially orientated zirconium hydrides (c).

Figure 7 .
Figure 7. Illustration of circumferentially (a) and radially (b) oriented zirconium hydrides (black) in a cladding tube [39] with a light microscopic image of a Zry-4 cladding tube sample with mainly circumferentially orientated zirconium hydrides (c).

Figure 9 .
Figure 9. Neutron radiograph of an in situ hydrogen diffusion experiment with ZrH2 powder in a Zry-4 cladding tube at the BOA beamline at the PSI.

Figure 9 .
Figure 9. Neutron radiograph of an in situ hydrogen diffusion experiment with ZrH 2 powder in a Zry-4 cladding tube at the BOA beamline at the PSI.

Materials 2024 ,Figure 10 .
Figure 10.Scheme of the portable INRRO furnace of the Karlsruhe Institute of Technology [5]

Figure 11 .
Figure 11.In situ neutron radiography image sequences of the hydrogen diffusion in a Zry-4 ding tube at 900 °C, taken at the ICON beamline of the PSI [45].

Figure 10 .
Figure 10.Scheme of the portable INRRO furnace of the Karlsruhe Institute of Technology [5].

Figure 10 .
Figure 10.Scheme of the portable INRRO furnace of the Karlsruhe Institute of Technology [5].

Figure 11 .
Figure 11.In situ neutron radiography image sequences of the hydrogen diffusion in a Zry-4 cladding tube at 900 °C, taken at the ICON beamline of the PSI [45].

Figure 11 .
Figure 11.In situ neutron radiography image sequences of the hydrogen diffusion in a Zry-4 cladding tube at 900 • C, taken at the ICON beamline of the PSI [46].

Figure 12 .
Figure 12.A calibration sample set of Zircaloy-4 (Zry-4) cladding tube samples with heights of 20 mm, where the neutron attenuation increases with an increasing amount of hydrogen in the metal.The neutron radiographs were taken at the ICON beamline at the PSI.

Figure 13 .
Figure 13.Calibration curve plotted as the relation between the total macroscopic neutron cross section ∑ and the number density ratio between hydrogen and zirconium NH/NZr.The measurements were made at the ICON beamline at the PSI.

Figure 12 .
Figure 12.A calibration sample set of Zircaloy-4 (Zry-4) cladding tube samples with heights of 20 mm, where the neutron attenuation increases with an increasing amount of hydrogen in the metal.The neutron radiographs were taken at the ICON beamline at the PSI.

Figure 12 .
Figure 12.A calibration sample set of Zircaloy-4 (Zry-4) cladding tube samples with heights of 20 mm, where the neutron attenuation increases with an increasing amount of hydrogen in the metal.The neutron radiographs were taken at the ICON beamline at the PSI.

Figure 13 .
Figure 13.Calibration curve plotted as the relation between the total macroscopic neutron cross section ∑ and the number density ratio between hydrogen and zirconium NH/NZr.The measurements were made at the ICON beamline at the PSI.

Figure 13 .
Figure 13.Calibration curve plotted as the relation between the total macroscopic neutron cross section ∑ total and the number density ratio between hydrogen and zirconium N H /N Zr .The measurements were made at the ICON beamline at the PSI.

Table 2 .
Comparison of high-performance neutron imaging facilities in Europe.

Table 2 .
Comparison of high-performance neutron imaging facilities in Europe.