Growth Behavior of Pores and Hydrogen Desorption Behavior in Pure Aluminum and A6061 Aluminum Alloys

Abstract

An increase in the volume fraction of pores in aluminum alloys causes a decrease in the elongation and the strength of alloys. To improve the mechanical properties of aluminum alloys, it is important to understand the growth and shrinkage behavior of pores. In this study, we analyzed the relationship between hydrogen desorption behavior and the growth/shrinking behavior of pores in A6061 alloys and pure aluminum using thermal desorption analysis and synchrotron radiation X-ray tomography. In pure aluminum, the fine pores began to annihilate at temperatures above 500°C and the relatively large pores coarsened. In contrast, the pores shrank with increasing temperature in A6061 alloy. The influence of second-phase particles has been discussed as a possible explanation for the difference in the nature of pores at elevated temperatures in pure aluminum and A6061 alloys. As in the A6061 alloy, much of the hydrogen desorbed from the pores due to heating is released externally from the second-phase particles on the aluminum surface, resulting in pore shrinkage due to the internal pressure drop of pores.

 

This Paper was Originally Published in Japanese in J. JILM 73 (2023) 212–217.

Differences in hydrogen desorption and the related growth behavior of pores in 4N–Al and A6061 alloy, which attributed to the presence or absence of second-phase particles.

1. Introduction

In practical aluminum alloys, excluding pure aluminum, even in rolled materials, pores are present with number densities ranging from 10¹²∼10¹⁴ m⁻³.¹⁾ Pores are micrometer-sized voids dispersed within the aluminum, and it is believed that they are filled with hydrogen internally.^2–4) Pores are formed due to the precipitation of supersaturated hydrogen and volume shrinkage during solidification within the matrix. It has been reported that in Al–5.5Mg alloy, approximately 53% of the total hydrogen in the alloy is trapped hydrogen within the pores.²⁾ According to first-principles calculations, the hydrogen trapping energy on the surface of pores (aluminum surface) in aluminum alloys is estimated to be between 0.67 and 0.71 eV/atom.^5–7) This hydrogen trapping energy is higher than that of vacancies, which is between 0.21 and 0.36 eV/atom,⁸⁾ as well as that of high-angle grain boundaries, which is between 0.23 and 0.27 eV/atom.⁹⁾ Thus, the presence of hydrogen within the pores has been investigated through both experimental and computational approaches.

The influence of pores on the mechanical properties of aluminum has also been experimentally investigated, and it has been revealed that an increase in pore volume fraction leads to a decrease in the elongation and tensile strength of aluminum alloys.^10–12) Irinouchi et al. reported that the mechanical properties of aluminum alloy casting AC4CH significantly deteriorate when the pore volume fraction exceeds 0.2% through high-temperature solution treatment.¹⁰⁾ Toda et al. visualized the ductile fracture process of aluminum rolled materials using synchrotron X-ray tomography and concluded that many of the dimples formed on the fracture surface originate from pores that existed prior to the application of tensile load, rather than voids.¹²⁾

The size and distribution of pores undergo changes during high-temperature exposure, such as homogenization and solution treatment. This change is believed to involve two opposing behaviors: growth due to increased hydrogen pressure inside the pores and contraction resulting from the release of internal hydrogen. While these behaviors may appear contradictory, the creep growth of pores driven by internal pressure and the hydrogen desorption from pores at high temperatures can be interpreted as independent phenomena without contradiction.^2,13–15) This suggests that the growth and contraction behavior of pores at high temperatures depend on factors such as alloy composition and heating conditions. In this study, we investigated the relationship between the growth/shrinkage of pores and hydrogen desorption behavior at high temperatures. We conducted temperature-dependent desorption analysis (TDA) of hydrogen in A6061 alloy and pure aluminum. We stopped the TDA at specific temperatures and visualized the pore morphology of the retrieved samples using synchrotron X-ray tomography in 3D. Based on the experimental results obtained, we will discuss the hydrogen desorption and growth/shrinkage behavior of pores at high temperatures.

2. Experiments

2.1 Specimens

The test materials used in this study were A6061 alloy and pure aluminum (4N–Al), which are common samples provided by the “Hydrogen in Aluminum and Material Properties Research Committee” of the Japan Institute of Light Metals. The chemical compositions of these materials are presented in Table 1. For the A6061 alloy, the alloy was subjected to homogenization heat treatment after casting. Subsequently, it underwent hot and cold rolling processes, followed by solution treatment at 530°C for 1 hour and quenching in water. Aging treatment was then conducted at 160°C for 18 hours. The 4N–Al was used in the as-rolled condition without any further treatment. No degassing treatment was performed for both test materials. Six prismatic specimens with dimensions of 0.6 × 0.6 × 5 mm³ were prepared from each test material. Out of these, five specimens were subjected to TDA up to specific temperatures, and the remaining one specimen was used for synchrotron X-ray tomography without undergoing TDA.

Table 1 Chemical composition of specimen used.

2.2 TDA and synchrotron X-ray tomography

For TDA, a gas chromatograph-type analyzer (manufactured by NISSHA FIS, PDHA-1000) was used with a heating rate of 1.5°C/min and an Ar flow rate of 20 cc/min. TDA was stopped at temperatures of 400, 450, 500, 550, and 560°C for the specimens cut from A6061 alloy, and at temperatures of 400, 450, 500, 550, and 600°C for the specimens cut from 4N–Al. Immediately after stopping the TDA, the samples were removed from the apparatus and used for synchrotron X-ray tomography, as mentioned later. The reason for the difference in the TDA stop temperatures between 4N–Al and A6061 alloy is due to the difference in their respective melting points.

The synchrotron X-ray tomography was conducted at the BL20XU beamline of the high-brightness synchrotron facility SPring-8. We used a 2-crystal monochromator with a Si(111) surface to monochromatize X-rays to an energy of 20 keV. The detector consisted of a GAGG scintillator, a CMOS image sensor, and an optical lens combined together.¹⁶⁾ The pixel size of the X-ray transmission images in this setup was 0.5 µm, and considering the effects of image magnification by the lens and other optical factors, the spatial resolution was approximately 1 µm.¹⁷⁾ The distance between the sample and the detector was set to 20 mm, and 1800 X-ray transmission images were acquired while rotating the sample on a rotation stage by 180°. After the imaging process, the X-ray transmission images were reconstructed using the filtered backprojection method, and cross-sectional images of the sample were obtained.¹⁸⁾ Subsequently, the volumes, surface areas, and centroids of the pores and second-phase particles were analyzed in 3D using the Marching Cubes algorithm.¹⁹⁾ To remove noise and fringes in the cross-sectional images, features with a volume of 9 or more voxels were determined as particles or pores.

3. Results and Discussion

3.1 Pore growth and shrinkage behavior in 4N–Al

Figure 1 shows a partial 2D virtual cross-section of 4N–Al visualized using synchrotron X-ray tomography. The pores are visualized as dark contrasts due to the difference in X-ray absorption coefficient compared to the matrix phase. From Fig. 1(a) at room temperature (RT) to Fig. 1(f) at 600°C, it can be observed that the pores grow as the TDA stop temperature increases.

Fig. 1

Two-dimensional virtual cross-sections of 4N–Al captured by synchrotron X-ray tomography. The TDA termination temperature differs for each specimen and were (a) RT (without TDA), (b) 400°C, (c) 450°C, (d) 500°C, (e) 550°C, and (f) 600°C.

Figure 2(a) to (f) depict the 3D-rendered images of stacked virtual cross-sections from Fig. 1(a) to (f), showcasing the pores. At room temperature (RT), numerous small pores are observed, and their number density and size do not change significantly up to 450°C. However, beyond 500°C, the small pores decrease in number, and larger pores become prominent. This behavior is consistent with Ostwald ripening, which aligns with the growth behavior of pores observed during high-temperature exposure in Al–Mg alloys as reported in previous studies.²⁾

Fig. 2

Three-dimensional tomographic image of pores in 4N–Al. These 3D images are corresponding to the 3D stackings of 2D images in Fig. 1 and the TDA termination temperature differs for each specimen: (a) RT (without TDA), (b) 400°C, (c) 450°C, (d) 500°C, (e) 550°C, and (f) 600°C.

Figure 3(a), (b), and (c) display the average pore diameter, number density, and volume fraction, respectively, obtained from the 3D quantitative analysis of pores in 4N–Al. Figure 3(d) presents the hydrogen desorption curve obtained from TDA in 4N–Al. As shown in Fig. 3(a), the average pore diameter remains constant at approximately 2.5 µm from RT up to 450°C. However, with further heating, at 600°C, the average pore diameter increases to 3.8 µm. Consistent with the previous statement that pore growth follows Ostwald ripening, Fig. 3(b) demonstrates that the number density of pores decreased at high temperatures, with a value of 1.6 × 10¹² m⁻³ at RT and a decrease to 0.4 × 10¹² m⁻³ at 600°C. The coarsening of pores and the decrease in number density coincide, resulting in a similar volume fraction as shown in Fig. 3(c) from RT to 600°C. Furthermore, focusing on the hydrogen evolution curve in Fig. 3(d), no distinct peak was observed from RT to 500°C, but hydrogen release rapidly increased at temperatures above 500°C.

Fig. 3

Quantitative analysis of pores in 4N–Al: (a) mean diameter, (b) number density, and (c) volume fraction. (d) is the hydrogen desorption curves from TDA terminated at specific temperatures.

The results from Fig. 3(a)–(d) suggest a causal relationship between pore growth, decrease in number density, and hydrogen evolution due to heating. Regarding the interpretation of the hydrogen evolution curve in pure aluminum, various investigations have been conducted.^14,20,21) Young and Scully reported that the hydrogen released during the peak after 500°C originates from hydrogen desorbing from vacancies.²⁰⁾ On the other hand, Izumi and Itoh reported that the released hydrogen originates from hydrogen desorbing from pores and blisters.¹⁴⁾ The results shown in Fig. 3 support the interpretation that at temperatures above 500°C, the disappearance of fine pores leads to the transport of hydrogen from the pores to the matrix phase, which is then released to the external environment through diffusion. This interpretation aligns with the findings reported by Izumi and Itoh.

3.2 Growth and shrinkage behavior of pores and Mg₂Si in A6061 alloy

Figure 4 shows a part of the 2D virtual cross-sectional image of an A6061 alloy visualized by synchrotron X-ray tomography. In the A6061 alloy, not only pores but also the second-phase particles, Mg₂Si, are visualized in gray. In the A6061 alloy, the number density of pores increases from RT in Fig. 4(a) to 450°C in Fig. 4(c), but it turns to decrease after 500°C.

Fig. 4

Two-dimensional virtual cross-sections of A6061 alloys captured by synchrotron X-ray tomography. The TDA termination temperature differs for each specimen and were (a) RT (without TDA), (b) 400°C, (c) 450°C, (d) 500°C, (e) 550°C, and (f) 560°C. White arrows indicate Mg₂Si, which acts as a heterogeneous nucleation site for pores.

Figures 5(a) to 5(f) show the 3D rendered images of pores by stacking the 2D virtual cross-sections in Fig. 4(a) to 4(f), respectively. By focusing on the number density of pores, it can be seen that it increases from RT to 450°C and then decreases from 500°C to 560°C. Similarly to Fig. 5, Fig. 6 shows the 3D images of Mg₂Si observed in the A6061 alloy at each TDA stopping temperature. The changes in morphology and dispersion of Mg₂Si with high-temperature exposure shown in Fig. 6(a) to 6(f) were similar to those of pores in the A6061 alloy, increasing from RT to 450°C and decreasing at temperatures above that.

Fig. 5

Three-dimensional tomographic image of pores in A6061 alloys. These 3D images are corresponding to the 3D stackings of 2D images in Fig. 4 and the TDA termination temperature differs for each specimen: (a) RT (without TDA), (b) 400°C, (c) 450°C, (d) 500°C, (e) 550°C, and (f) 560°C.

Fig. 6

Three-dimensional tomographic image of Mg₂Si in A6061 alloys. These 3D images are corresponding to the 3D stackings of 2D images in Fig. 4 and the TDA termination temperature differs for each specimen: (a) RT (without TDA), (b) 400°C, (c) 450°C, (d) 500°C, (e) 550°C, and (f) 560°C.

Figures 7(a), (b), and (c) show the average diameter, number density, and volume fraction of pores and Mg₂Si in the A6061 alloy quantitatively analyzed in 3D. Figure 7(d) shows the hydrogen release curve of the A6061 alloy obtained by TDA. According to Fig. 7(a), the change in the average diameter of pores was limited compared to 4N–Al, with an increase of about 0.4 µm during the heating process from RT to 560°C. This increase in average diameter was not due to pore growth, but rather to the disappearance of small pores. Comparing the 3D images in Fig. 5(a) and Fig. 5(f), it can be seen that pore coarsening did not occur. The pore volume fraction and number density shown in Fig. 7(b) and (c) decreased in the later stages of TDA heating, indicating the disappearance of small pores. The limited pore growth and decrease in pore volume fraction were phenomena that did not occur in 4N–Al.

Fig. 7

Quantitative analysis of pores and Mg₂Si in A6061 alloys: (a) mean diameter, (b) number density, and (c) volume fraction. (d) is the hydrogen desorption curves from TDA terminated at specific temperatures.

Additionally, as shown in Fig. 7(b) and (c), Mg₂Si exhibits a broad peak in both volume fraction and number density at 400–500°C. Moreover, the hydrogen release curve shown in Fig. 7(d) also showed a maximum peak at 460°C. This suggests a correlation between the coarsening and disappearance of Mg₂Si and the release of hydrogen from the material. Recently, Yamaguchi et al. have calculated the hydrogen trapping energy of Mg₂Si non-coherent interfaces by first-principles calculations, revealing that it can reach up to 0.8 eV/atom.²²⁾ This indicates that the Mg₂Si non-coherent interfaces can be regarded as hydrogen trap sites. Based on this study, it can be inferred that the interface of Mg₂Si, which was analyzed in 3D, is non-coherent, as the analyzed particles are large, over 1 µm in size, and the interface shape is not flat. This inference is supported by previous studies.^23,24) Hydrogen release in TDA occurs not only through thermal-induced desorption but also through microstructural changes (disappearance or alteration of trap sites) caused by heating.²⁵⁾ Therefore, hydrogen trapped at the Mg₂Si misfit interface before TDA is believed to undergo detrapment during the interface migration associated with coarsening and contraction of Mg₂Si, and is subsequently released out of the specimen. It should be noted that this peak at 460°C did not appear in the case of 4N–Al.

In the continuous heating at 1.5°C/min by TDA, Mg₂Si in the A6061 alloy increased in both diameter and number density up to 450°C. I understand that the setup for the synchrotron X-ray tomography used in this study is called projection-based X-ray tomography, which has a spatial resolution limited to around 1 µm due to optical considerations.¹⁷⁾ The A6061 alloy used in the experiment was artificially aged, and it is believed that not only Mg₂Si second-phase particles visible at or above 1 µm, but also Mg₂Si precipitates below 1 µm, are dispersed.²⁶⁾ Therefore, the increase in Mg₂Si number density up to 450°C corresponds to the growth of Mg₂Si precipitates below 1 µm to a level that can be visualized. At temperatures above 500°C, Mg₂Si decomposes and dissolves as a solute atom into the matrix phase, resulting in a rapid decrease in Mg₂Si number density at 550°C and 560°C. Furthermore, as clearly shown in Fig. 4(c), Mg₂Si second-phase particles served as heterogeneous nucleation sites for pores. As a result, regions with a similar dispersion state of pores and Mg₂Si existed in the lower parts of Fig. 5(f) and Fig. 6(f) as a distinctive feature.

3.3 Growth and shrinkage behavior of pores and intrinsic hydrogen

The relationship between the growth and shrinkage behavior of pores and hydrogen desorption in 4N–Al and A6061 alloys was organized based on the size distribution of pores after each TDA. Figures 8(a) and (b) show the histograms of the pore diameter after TDA in 4N–Al and A6061 alloys, respectively. First, focusing on pores with diameters of 4 µm or less in 4N–Al shown in Fig. 8(a), there was no significant change between RT and 450°C, but a decreasing trend was observed at temperatures above 500°C. On the other hand, pores with diameters greater than 4 µm increased at 450°C and 500°C. The pore histogram of A6061 alloy shown in Fig. 8(b), unlike 4N–Al, showed an increase in pores with diameters of 3–4.5 µm at 450°C and a decreasing trend regardless of size at temperatures above 500°C.

Fig. 8

Histogram of pore diameter after TDA terminated at specific temperatures in (a) 4N–Al and (b) A6061 alloys.

We can discuss the differences in the growth and shrinkage behavior of pores in 4N–Al and A6061 alloys from the perspective of hydrogen desorption. Comparing the onset temperatures of the maximum peak in the hydrogen desorption curves during the heating stage of 4N–Al and A6061 alloys, as shown in Fig. 3(d) and Fig. 7(d), respectively, it is evident that 4N–Al shifted to higher temperatures by more than 50°C. This difference can be attributed to the difficulty of hydrogen desorption from second-phase particles in the sample. A schematic diagram showing the difference in hydrogen desorption behavior upon heating in 4N–Al and A6061 alloys is presented in Fig. 9. As shown in Fig. 9(a), a dense and passive film consisting of aluminum oxide containing crystal water is formed on the aluminum surface. In 4N–Al, a large amount of hydrogen released from the pores is inhibited by this passive film, making it difficult to release externally.²⁷⁾ By remaining in the matrix, the hydrogen released from the pores does not immediately reduce the hydrogen concentration in the matrix even when the temperature for hydrogen desorption from the pores is reached. This prevents a decrease in the hydrogen pressure inside the pores by blocking hydrogen transport from the pores to the matrix, and the decrease in hydrogen pressure drives the creep deformation of the pores, leading to coarsening at 450°C and 500°C. However, the passive film only suppresses hydrogen desorption and does not completely prevent it. Therefore, over time at high temperatures, hydrogen desorption continues and the hydrogen concentration inside the sample and the hydrogen pressure inside the pores decrease. It is believed that the number density of pores decreases significantly at temperatures above 550°C. In contrast, as shown in Fig. 9(b), Mg₂Si, the second phase particles, exist on the surface of A6061 alloy and there the passive film becomes discontinuous. It has been reported that the second phase particles on the alloy surface are the sites for hydrogen release, and hydrogen released from the pore diffuses into the matrix and is released from the surface second phase particles (Mg₂Si).^28–30) Therefore, it is considered that in A6061 alloy, hydrogen released from the pore is more easily released outside the material than in 4N–Al due to the presence of surface second phase particles. As a result, it is considered that the internal hydrogen pressure in the pore of A6061 alloy decreases more easily due to heating than in 4N–Al, and the growth mechanism driven by the internal hydrogen pressure at temperatures above 450°C does not work, leading to pore elimination or shrinkage. The amount of hydrogen in the pore, C_pore, can be estimated as

  

\begin{equation} C_{\text{pore}} = \sum \left(\frac{2\pi \gamma d_{i}^{2}}{3RT}\right) \end{equation} (1)

based on the energy balance between the surface energy of aluminum and the hydrogen pressure inside the pore.²⁾ Here, γ is the surface energy of aluminum, d_i is the diameter of each pore, R is the gas constant, and T is the temperature. Figure 10 shows the cumulative hydrogen release and total hydrogen content in the pores of 4N–Al and A6061 alloy at each temperature during TDA. The hydrogen release trend during the heating period related to pores is generally similar for both 4N–Al and A6061 alloy. However, the decrease in the total hydrogen content in the pores was more significant for A6061 alloy. The difference in the total hydrogen content in the pores between RT and the maximum TDA temperature is 0.007 mass ppm for 4N–Al and 0.226 mass ppm for A6061 alloy, indicating that the decrease in the hydrogen content in the pores due to heating is more significant for A6061 alloy and supporting the aforementioned analysis.

Fig. 9

Schematic illustration of differences in hydrogen desorption and the related growth behavior of pores in (a) 4N–Al and (b) A6061 alloys, which attributed to the presence or absence of second-phase particles.

Fig. 10

Total amount of hydrogen in pores and total cumulative content of hydrogen desorbed by TDA in (a) 4N–Al and (b) A6061 alloys.

In addition, not only hydrogen release but also the difference in high-temperature strength between 4N–Al and A6061 alloy is considered to be a factor that affects the growth behavior of pores under high-temperature exposure. Chinh and Koizumi have reported the high-temperature strength of 4N–Al and Al–Mg–Si alloy, respectively.^31,32) At 400°C, the maximum tensile strength is reported to be about 8 MPa for 4N–Al³¹⁾ and about 25 MPa for Al–Mg–Si alloy.³²⁾ Based on this, in the results of Fig. 8, it is considered that pores coarsened to 4 µm or more under high-temperature exposure for 4N–Al with low high-temperature strength, whereas in A6061 alloy with high high-temperature strength, plastic restraint around the pores was stronger than that in 4N–Al, making it difficult for the pores to grow.

4. Conclusion

In this study, the growth behavior of pores in 4N–Al and A6061 alloy was analyzed by TDA and synchrotron X-ray tomography. By analyzing the hydrogen release behavior and the growth and shrinkage behavior of pores under high-temperature exposure, the following insights were obtained:

In both 4N–Al and A6061 alloy, fine pores disappeared and coarse pores grew when the temperature exceeded 500°C. On the other hand, in A6061 alloy, the number density of pores decreased with the increase in the TDA stop temperature.

In 4N–Al without second phase particles, much of the hydrogen released from pores is inhibited by the passive film and cannot be released, causing the hydrogen concentration in the matrix to be relatively high and making it difficult for hydrogen in the pores to be released. As a result, the pressure inside the pores increased, leading to their growth. In A6061 alloy with second phase particles, much of the released hydrogen is emitted through the surface of the second phase particles, causing the pressure inside the pores to decrease, resulting in a tendency for the pores to shrink and disappear.

Acknowledgments

This study was supported by JST CREST “Nanomechanics” (JPMJCR1995) and JSPS KAKENHI (21K14037). The synchrotron radiation experiments were conducted under the research projects at SPring-8 (2020A1531, 2021A1002, 2021A1120, 2021B1123, 2021B1124, 2022A1113).

REFERENCES

• 1)   H.  Toda,  T.  Inamori,  K.  Horikawa,  K.  Uesugi,  A.  Takeuchi,  Y.  Suzuki and  M.  Kobayashi: Mater. Trans. 54 (2013) 2195–2201. doi:10.2320/matertrans.L-M2013832
• 2)   H.  Toda,  T.  Hidaka,  M.  Kobayashi,  K.  Uesugi,  A.  Takeuchi and  K.  Horikawa: Acta Mater. 57 (2009) 2277–2290. doi:10.1016/j.actamat.2009.01.026
• 3)   K.  Shimizu,  H.  Toda,  K.  Uesugi and  A.  Takeuchi: Metall. Mater. Trans. A 51 (2020) 1–19. doi:10.1007/s11661-019-05304-y
• 4)   T.  Shikagawa and  G.  Itoh: J. JILM 60 (2010) 433–437. doi:10.2464/jilm.60.433
• 5)   M.  Yamaguchi,  T.  Tsuru,  K.  Ebihara and  M.  Itakura: J. JILM 68 (2018) 588–595. doi:10.2464/jilm.68.588
• 6)   C.  Wolverton,  V.  Ozoliņš and  M.  Asta: Phys. Rev. B 69 (2004) 144109. doi:10.1103/PhysRevB.69.144109
• 7)   R.  Matsumoto,  M.  Sera and  N.  Miyazaki: Comput. Mater. Sci. 91 (2014) 211–222. doi:10.1016/j.commatsci.2014.04.051
• 8)   L.  Ismer,  M.S.  Park,  A.  Janotti and  C.G.  Van De Walle: Phys. Rev. B 80 (2009) 184110. doi:10.1103/PhysRevB.80.184110
• 9)   M.  Yamaguchi,  K.I.  Ebihara,  M.  Itakura,  T.  Tsuru,  K.  Matsuda and  H.  Toda: Comput. Mater. Sci. 156 (2019) 368–375. doi:10.1016/j.commatsci.2018.10.015
• 10)   Y.  Irinouchi,  H.  Toda,  T.  Sakai,  T.  Kobayashi and  L.  Wang: J. JILM 55 (2005) 159–163. doi:10.2464/jilm.55.159
• 11)   M.  Harada,  T.  Suzuki and  I.  Fukui: Imono 55 (1983) 742–750. doi:10.11279/imono.55.12_742
• 12)   H.  Toda,  H.  Oogo,  K.  Horikawa,  K.  Uesugi,  A.  Takeuchi,  Y.  Suzuki,  M.  Nakazawa,  Y.  Aoki and  M.  Kobayashi: Metall. Mater. Trans. A 45 (2014) 765–776. doi:10.1007/s11661-013-2013-3
• 13)   H.  Toda,  P.C.C.  Qu,  S.  Ito,  K.  Shimizu,  K.  Uesugi,  A.  Takeuchi,  Y.  Suzuki and  M.  Kobayashi: Int. J. Cast. Met. Res. 27 (2014) 369–377. doi:10.1179/1743133614Y.0000000123
• 14)   T.  Izumi and  G.  Itoh: Mater. Trans. 52 (2011) 130–134. doi:10.2320/matertrans.L-M2010825
• 15)   H.  Fujihara,  H.  Toda,  K.  Shimizu,  A.  Takeuchi and  K.  Uesugi: J. JILM 69 (2019) 186–193. doi:10.2464/jilm.69.186
• 16)   K.  Uesugi,  Y.  Suzuki,  N.  Yagi,  A.  Tsuchiyama and  T.  Nakano: Nucl. Instruments Methods Phys. Res. Sect. A 467–468 (2001) 853–856. doi:10.1016/S0168-9002(01)00491-0
• 17)   H.  Toda,  K.  Shimizu,  K.  Uesugi,  Y.  Suzuki and  M.  Kobayashi: Mater. Trans. 51 (2010) 2045–2048. doi:10.2320/matertrans.L-M2010819
• 18)  A.C. Kak and M. Slaney: Principles of Computerized Tomographic Imaging, (Society for Industrial and Applied Mathematics, 2001).
• 19)  W.E. Lorensen and H.E. Cline: Proc. 14th Annu. Conf. Comput. Graph. Interact. Tech. SIGGRAPH 1987. 21, (1987) pp. 163–169.
• 20)   G.A.  Young and  J.R.  Scully: Acta Mater. 46 (1998) 6337–6349. doi:10.1016/S1359-6454(98)00333-4
• 21)   K.I.  Ebihara,  M.  Yamaguchi,  T.  Tsuru and  M.  Itakura: J. JILM 68 (2018) 596–602. doi:10.2464/jilm.68.596
• 22)   M.  Yamaguchi,  K.  Ebihara,  T.  Tsuru and  M.  Itakura: Mater. Trans. 64 (2023) 2553–2559. doi:10.2320/matertrans.mt-m2023106
• 23)   D.G.  Eskin,  V.  Massardier and  P.  Merle: J. Mater. Sci. 34 (1999) 811–820. doi:10.1023/A:1004585216084
• 24)   H.  Suzuki and  M.  Kanno: J. JILM 31 (1981) 277–298. doi:10.2464/jilm.31.277
• 25)  M. Nagumo: Fundamentals of Hydrogen Embrittlement, (Uchida Rokakuho, 2008) pp. 48–67.
• 26)   D.  Maisonnette,  M.  Suery,  D.  Nelias,  P.  Chaudet and  T.  Epicier: Mater. Sci. Eng. A 528 (2011) 2718–2724. doi:10.1016/j.msea.2010.12.011
• 27)   M.  Imabayashi: J. JILM 23 (1973) 38–49. doi:10.2464/jilm.23.38
• 28)   S.  Osaki,  T.  Harano,  J.  Ikeda,  K.  Ichitani,  P.  Zhao and  Y.  Takeshima: J. JILM 58 (2008) 139–145. doi:10.2464/jilm.58.139
• 29)   G.  Itoh,  T.  Izumi and  T.  Tohyama: J. JILM 58 (2008) 15–21. doi:10.2464/jilm.58.15
• 30)   K.  Horikawa,  Y.  Takahashi and  H.  Kobayashi: J. JILM 66 (2016) 84–89. doi:10.2464/jilm.66.84
• 31)   N.Q.  Chinh,  J.  Illy,  Z.  Horita and  T.G.  Langdon: Mater. Sci. Eng. A 410–411 (2005) 234–238. doi:10.1016/j.msea.2005.08.086
• 32)   S.  Koizumi,  J.  Kobayashi and  G.  Itoh: Mater. Sci. Forum 838–839 (2016) 267–271. doi:10.4028/www.scientific.net/MSF.838-839.267