Division of Quantum Science and Engineering, Graduate School of Engineering, Hokkaido University, Sapporo , Japan

Transcription

1 Materials Transactions, Vol. 52, No. 6 (2011) pp to 1302 #2011 The Japan Institute of Metals EXPRESS REGULAR ARTICLE A Rietveld-Type Analysis Code for Pulsed Neutron Bragg-Edge Transmission Imaging and Quantitative Evaluation of Texture and Microstructure of a Welded -Iron Plate Hirotaka Sato, Takashi Kamiyama and Yoshiaki Kiyanagi Division of Quantum Science and Engineering, Graduate School of Engineering, Hokkaido University, Sapporo , Japan Bragg-edge transmission imaging using a pulsed neutron source is expected to be a new method to investigate the crystallographic and metallographic structure of a material. This method has attracted the attention in the research field of material characterization for materials development and industrial applications because it non-destructively provides the images on the texture and the microstructure inside a material such as a thick steel bulk over the wide area of the material. For deducing such information from the Bragg-edge transmission spectrum, a data analysis code like a Rietveld analysis code for powder diffractometry is indispensable. So far, only the information on the crystallographic anisotropy has been deduced. However, this information is incomplete since both the preferred orientation and the crystallite size affect the Bragg-edge transmission spectrum. Therefore, we have developed a Rietveld-type analysis code, RITS, that allows us to obtain the information on preferred orientation and crystallite size at the same time. To examine the feasibility and the usefulness of the RITS code, we have analyzed the Bragg-edge transmission spectra of rolled and welded -iron plates, and we have successfully obtained the preferred orientation data and the crystallite size data over the wide area of the bulk specimens. [doi: /matertrans.m ] (Received September 21, 2010; Accepted March 4, 2011; Published May 18, 2011) Keywords: pulsed neutron imaging, Bragg-edge transmission, Rietveld-type analysis, texture, crystallite size 1. Introduction The characterization of crystallographic anisotropy (texture) and microstructure (crystallite size) is very important not only for studying the effect of such characteristics on the metallurgical properties of existing materials but also for developing high-performance structural or functional materials. There exist various methods for analyzing texture and microstructure, for example, EBSD 1) (electron backscatter diffraction), X-ray diffraction, 2) and X-ray phase-contrast microscopy and microtomography. 3) However, these methods give only the information near the surface of a material, and these methods cannot non-destructively obtain the crystallographic and metallographic structural information inside a bulk material with a realistic thickness. Therefore, so far, neutron diffraction 4) has been used to obtain such information. However, it is frequently necessary to know the spatial-dependent changes of the structural information, for example, in the bulk of an industrial product. In such cases, point-scan neutron diffraction measurements are performed to obtain the texture and microstructure information, and these require a lot of the beam time. On the other hand, neutron time-of-flight (TOF) spectroscopic radiography using a pulsed neutron source can simultaneously give the position-dependent Bragg-edge transmission spectra of a material by using a neutron imaging detector. 5) The TOF transmission spectrum including Braggedge 6 8) reflects the crystallographic and metallographic structural information at each pixel position. In previous studies, we have clarified the reason why the Bragg-edge transmission spectrum changes depending on the texture and the crystallite size; the spectra far from the edges have been drastically changed by recrystallization during processes such as quenching, 9) annealing, 10) welding, 11) plastic deformation 12) and phase transformation. 13) As a result, we have known that the Bragg-edge transmission spectrum is sensitive to the crystallographic and metallographic structural change, and a data analysis code to analyze the whole pattern of the spectrum is indispensable for quantitatively extracting the information on the texture and the microstructure from the Bragg-edge transmission spectrum. The most suitable method for such analysis is the Rietveld analysis technique 14) but is not the single peak profile analysis technique or the Pawley analysis technique 15) because these techniques cannot be accessible to the spectrum far from the diffraction peaks. Therefore, we have developed a Rietveld-type spectral fitting code for the Bragg-edge transmission imaging. 16) Thus, we have succeeded in non-destructively visualizing the crystallographic anisotropy inside a plastically deformed -iron plate. 16) However, the important information, for example, the crystal lattice planes strongly orientating in a certain direction (the preferred orientation axis) and the crystallite size, has not been evaluated yet. Therefore, a data analysis code is needed to provide more detailed information on the texture and the microstructure at the same time. In this paper, we present the data analysis code, RITS (Rietveld Imaging of Transmission Spectra), developed for obtaining detailed information on texture and microstructure, and we have carried out a pulsed neutron transmission imaging experiment of rolled and welded -iron plates for examining the feasibility and the usefulness of the pulsed neutron Bragg-edge transmission imaging with the RITS code. 2. RITS a Data Analysis Code for the Bragg-Edge Transmission Imaging to Quantitatively Evaluate the Parameters of Texture and Microstructure To analyze the Bragg-edge transmission spectrum, we must take into account all scattering effects occurring in a material, which reflect the microscopic structural and dynamical information of the material. Therefore, we have

2 A Rietveld Analysis Code for Pulsed Neutron Imaging and Quantitative Evaluation of Texture and Microstructure 1295 Pulsed neutron source Specimen Two-dimensional imaging detector Intensity, I 0 Incident neutron beam I 0 (X,Y,TOF ) Intensity, I Transmitted neutron beam I(X,Y,TOF ) Tr (X,Y,TOF) = Transmission, Tr Bragg-edges I(X,Y,TOF ) I 0 (X,Y,TOF) TOF(λ) TOF(λ) TOF(λ) Fig. 1 Schematic view of a spatial-dependent Bragg-edge transmission spectra measurement at a pulsed neutron source. formulated an analytical expression of the effective attenuation coefficient (the effective total cross section) obtained by using a pulsed neutron source with the TOF method. This expression includes the effects of the incident neutron pulse shape, the variation of the crystal lattice plane spacing, the crystal orientation distribution due to the texture, and the extinction of diffracted neutrons inside one crystallite. In the data analysis process, the RITS code simulates a neutron transmission spectrum by using this formula, and then the code fits the simulated result to an experimental result by adjusting the parameters included in the analytical formula. This procedure is performed over all pixels of the imaging detector. We have used the non-linear least-squares fitting algorithm, the Levenberg-Marquardt method, 17) to deduce the quantitative values of the crystallographic structural parameters. Here, we present the improved expression of the Bragg-edge transmission spectrum implemented in the RITS code for quantitative imaging of texture and microstructure. 2.1 Pulsed neutron transmission spectrum with three new factors Figure 1 shows a schematic view of an experimental setup of the TOF radiography at a pulsed neutron source. The neutron transmission TrðÞ as a function of wavelength is represented by the Beer-Lambert-Bouguer law, as follows: TrðÞ ¼exp X tot,p ðþ p t p!: ð1þ p Here, tot,p ðþ is the neutron total cross section, p is the density, and t p is the thickness of the crystalline phase p. Each phase is usually composed of several nuclei. In the low energy region, the total cross section in the phase p consists of elastic coherent scattering, elastic incoherent scattering, inelastic coherent scattering, inelastic incoherent scattering and absorption parts, as follows: tot,p ðþ ¼coh,p ela ðþþela incoh,p ðþþinela coh,p ðþ þ incoh,p inela ðþþ ð2þ abs,pðþ: The elastic coherent scattering cross section is the most important for the texture and microstructure analysis because this component uniquely relates to the Bragg-edges and reflects the crystal structure. The other scattering components, relating to the dynamics of crystal structure (coherent case) or each nucleus (incoherent case), and the absorption component are calculated from the traditional total cross section theory. 18) To describe an actual Bragg-edge transmission spectrum of a polycrystalline material, we have proposed a modified expression of the Bragg-edge transmission cross section that combines the kinematical diffraction theory 6,7,18) with three new factors, R hkl ð;d hkl Þ, P hkl ð;d hkl Þ and E hkl ð;f hkl Þ,as follows: coh,p ela 2 X ðþ ¼ jf hkl j 2 d hkl R hkl ð;d hkl Þ 2V 0 hkl ð3þ P hkl ð;d hkl ÞE hkl ð;f hkl Þ; where V 0 is the unit cell volume, d hkl is the d-spacing, namely, the distance between the crystal lattice planes of {hkl}, and F hkl is the crystal structure factor including the Debye-Waller factor. The first new factor, R hkl ð;d hkl Þ,is called the resolution function or the edge profile function. This function describes the edge broadening due to the neutron pulse shape, the strain and the microstructure. The Dreele-Jorgensen-Windsor model 7,19,20) that can evaluate these effects has been adopted in the RITS code, especially for the high resolution strain imaging. 21) The second new factor, P hkl ð;d hkl Þ, is the modified March-Dollase preferred orientation distribution function, 20) and the third new factor, E hkl ð;f hkl Þ, is Sabine s primary extinction function for powder diffractometry. 22) Hereafter, we explain these new factors representing the texture dependence and the microstructure dependence. 2.2 Modified March-Dollase preferred orientation distribution function for texture analysis The crystallographic anisotropy due to the preferred orientation in a polycrystalline material changes the whole shape of the Bragg-edge transmission spectrum. To obtain the information on the texture, we have implemented the modified March-Dollase preferred orientation distribution function 20) in the RITS code. This function assumes an axially symmetric orientation distribution around the beam direction. The formulation is where P hkl ð;d hkl Þ¼ 1 2 Z 2 0 R 2 B 2 hkl þ 1 3 B2 2 hkl d; ð4þ R

3 1296 H. Sato, T. Kamiyama and Y. Kiyanagi σ tot /10-28 m 2 (a) Texture dependence α-iron (293.6 K) {310} {220} {211} {200} <HKL> = <110> & R = 0.5 <HKL> = <211> & R = 0. <HKL> = <111> & R = 0. R = 1.0 {110} σ tot /10-28 m 2 (b) Extinction dependence α-iron (293.6 K) Without extinction effect S = 1 μm S = 5 μm S = 10 μm Fig. 2 (a) Whole shape change of the effective total cross section of -iron, depending on the preferred orientation axis hhkli and the crystallographic anisotropy parameter R of the modified March-Dollase model. (b) Whole intensity change of the effective total cross section of -iron, depending on the crystallite size S of Sabine s powder extinction model. In each simulation, the other model has not been worked at all. and B hkl ¼ cos A hkl sin hkl þ sin A hkl cos hkl sin ; hh þ kk þ ll A hkl ¼ arccos pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffipffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi h 2 þ k 2 þ l 2 H 2 þ K 2 þ L 2 hkl ¼ arcsin 2d hkl ð5þ ð6þ : ð7þ represents the angle on a certain Debye-Scherrer ring of the scattering angle 2. A hkl is the angle between the Bragg reflection plane {hkl} and the preferred crystal lattice plane {HKL} oriented in the beam direction. hhkli is the preferred orientation axis parallel to the beam direction. The March- Dollase coefficient, R, provides the information about the degree of crystallographic anisotropy. If there is no anisotropy (random orientation distribution), both R and P hkl ð;d hkl Þ are unity. When the texture is grown, R is away from one. R ¼ 0 or 1 means a single crystal specimen. Figure 2(a) shows simulation examples of the total cross section of -iron depending on various values of hhkli and R. In this simulation, the extinction function E hkl ð;f hkl Þ is equal to one. The whole shape of the Bragg-edge transmission cross section, especially around the {110} Braggedge corresponding to the maximum d-spacing, is drastically changed by the anisotropy of the crystal orientation distribution. 2.3 Sabine s primary extinction function for crystallite size analysis The primary extinction effect is caused by the rediffraction phenomenon inside one perfect crystal block (the mosaic block or the crystallite) which is smaller than the grain or coincides with the sub-grain in a ductile metal. 22) As a result, this effect reduces the diffracted intensity by returning the diffracted neutrons in the direction of the transmitted beam. Hence, this phenomenon increases the transmitted neutron intensity and decreases the Bragg-edge transmission cross section predicted by the kinematical diffraction theory. This effect of the re-diffraction has to be included in the RITS code since it also affects the result of the March-Dollase function and gives the crystallite size information. The factor of the primary extinction effect was presented by the Darwin energy-transfer equations as a starting point. 23) Then, Sabine s primary extinction function for powder diffractometry was proposed, 22,23) which we have adopted in the RITS code. This formulation is expressed by combining the backward-scattering (Bragg) component, E B, and the forward-scattering (Laue) component, E L, as follows: E hkl ð;f hkl Þ¼E B sin 2 hkl þ E L cos 2 hkl ; ð8þ where 1 E B ¼ p ffiffiffiffiffiffiffiffiffiffiffi ; ð9þ 1 þ x E L ¼ 1 x 2 þ x2 5x3 þ for x 1; ð10þ 4 48 rffiffiffiffiffiffi 2 E L ¼ 1 1 x 8x x2 1024x 3 for x > 1; ð11þ and x ¼ S 2 F 2 hkl : ð12þ V 0 S is the crystallite size along the beam direction. Figure 2(b) shows simulation examples of the total cross section of -iron depending on various values of S. In this simulation, the preferred orientation distribution function P hkl ð;d hkl Þ is equal to one. The whole intensity of the Bragg-edge transmission cross section is drastically reduced by the extinction of diffracted neutrons inside one crystallite. 3. Welded -Iron Experiment for Deducing the Texture and Microstructure Information by Using the RITS Code We have performed a verification experiment that shows the feasibility and the usefulness of the Bragg-edge transmission imaging with the RITS code. For this purpose, we chose rolled -iron plates and welded ones. It has been predicted that a rolled sheet composed of bodycentered-cubic (BCC) polycrystals has two types of fiber texture in the stable end of the rolling process. 24) One is the -

4 A Rietveld Analysis Code for Pulsed Neutron Imaging and Quantitative Evaluation of Texture and Microstructure 1297 Experimental setup Data processing setup Trigger (T 0 ) signal from accelerator Neutron detection data (X,Y,TOF ) Data acquisition computer Boron & aluminum cathode foil Boron GEM Normal GEM Data accumulation computer Pulsed neutrons Boron-carbide collimator Specimens Neutron flight path length = 6.03 m Readout board Argon & carbondioxide gas GEM-type neutron imaging detector Data analysis computer RITS Fig. 3 Experimental setup using the GEM detector at Hokkaido LINAC, and data flow for the spectral analyses using the RITS code. fiber, which has the preferred orientation axis h110i parallel to the rolling direction (). The other is the -fiber, which has the preferred orientation axis h111i parallel to the normal direction (). The -fiber texture is equivalent to the texture that h110i strongly orients in þ 35 (or ). This stable end rolling texture is known as {111} h011i in the notation of rolling texture. However, this stable end rolling texture is formed via {112} h110i or {001} h110i during the rolling process. 24) In particular, the preferred orientation axis h211i parallel to the (the -fiber) is very close to the -fiber in the pole figure because the -fiber texture is equivalent to the texture that h110i strongly orients in þ 30 (or ). The identification between the -fiber and the -fiber of a rolled BCC metal has not been clear. For this reason, the major discussion point of the texture imaging using the RITS code is whether the {111} h011i rolling texture can be clearly distinguished from the others, especially {112} h110i. Furthermore, the welding process drastically changes the microstructure (the crystallite size). Therefore, we have also intended to clarify the change of the crystallites size with the position-dependent information. 3.1 Experimental setup We carried out a TOF radiography experiment at the cold neutron beam-line at the electron linear accelerator facility at Hokkaido University in Japan (Hokkaido LINAC). In this facility, pulsed neutrons are generated by the photonuclear reaction caused by bremsstrahlung of 1 kw pulsed electrons. The electron energy is 33 MeV, the pulse width is 3 ms, the pulse repetition rate is Hz, and the beam current is 33 ma. The neutron yield of the photonuclear reaction target is only about s 1. In this experiment, we utilized a coupled-type 18 K solid methane moderator. The pulsed neutron beam was transported through an evacuated beam-tube of 3 m and boron-carbide collimators. The neutron flight path length from the source to the detector was 6.03 m. The neutron flux at the detector position was about 10 3 cm 2 s 1. The neutron wavelength resolution in this experiment was 2.7% at the wavelength of 0.4 nm. This resolution is not very good due to the utilization of the coupled-type moderator and the short flight path length. Therefore, we cannot observe tiny Braggedges of the pearlite in case of this experimental setup. Figure 3 shows a schematic layout of the experimental setup and the data flow. We used a GEM (gas electron multiplier) type two-dimensional neutron detector ) The prototype GEM detector used in this experiment consisted of one aluminum cathode foil coated with a boron-10 layer of 0.02 mm thickness for neutron-electron conversion, two GEM foils coated with a boron-10 layer of 0.6 mm thickness for neutron-electron conversion, one GEM foil for electron amplification, and coincidence-type readout electrodes. The mixed gas of argon (%) and carbon-dioxide (30%) was used as a floating gas. The detection efficiency of the GEM detector was 15% at the neutron wavelength of 0.4 nm. The readout board had the two-dimensional strips of 800 mm position resolution. The detection area was 10 cm 10 cm. The TOF resolution was 10 ns. The neutron exposure time in this experiment was 5.0 h for the transmitted beam measurement and 3.3 h for the incident beam measurement so as to obtain the sufficient statistics for the texture and microstructure imaging with good spatial resolution (small pixel size) under the condition of the weak neutron beam of Hokkaido LINAC and the low detection efficiency of the GEM detector. 3.2 Specimens The specimens were rolled or TIG (tungsten inert gas) type welded -iron plates (JIS-SS0) classified as a BCC polycrystalline material. Figure 4(a) shows a photograph of the specimens, and Fig. 4(b) shows a schematic view around the welded zone. Table 1 shows a summary with respect to the specimens: indicator, size, treatment and beam transmission direction. We measured four -iron plates. Two

5 1298 H. Sato, T. Kamiyama and Y. Kiyanagi rolled -iron plates, (A) and (B) in Fig. 4(a) and Table 1, were placed at the top. Neutrons were transmitted through the. One welded -iron plate, (C) in Fig. 4(a) and Table 1, was placed at the bottom. The weld metal was the same as the base metal, and it was welded from both sides of a weld groove along the center line as shown in Fig. 4(b). The last specimen, (D) in Fig. 4(a) and Table 1, was a cut plane of the welded -iron plate, and it was placed at the middle. We note that this specimen was cut out from the bottom specimen. Neutrons were transmitted through the only in this specimen. The welded two specimens (C) and (D) had the heat affected zone (HAZ) around the groove and the weld metal of 6 mm width as shown in Fig. 4(b). The total width of the weld metal zone plus the HAZ was about 1 cm. The neutron transmission thicknesses of all the specimens were uniformly 6 mm. Thus, we simultaneously obtained four kinds of neutron transmission spectrum: the transmission (a) Photograph of the specimens (A) (B) (D) (C) 10 cm Welded zone 10 cm Thickness : 6 mm (b) Schematic view around the welded zone (View to ) Base metal Weld metal (Sandglass-like shape) 6 mm 10 mm HAZ 6 mm Fig. 4 (a) Photograph of the specimens. Pulsed neutrons were transmitted through the, and for the top, middle and bottom specimens, respectively. (b) Schematic view around the weld groove. Table 1 Indicator, size, process and beam transmission direction of each specimen. Specimen Size Process Direction (A) 4:4 cm 5 cm 6 mm Rolling (B) 4:4 cm 5 cm 6 mm Rolling (C) 5 cm 10 cm 6 mm Welding (D) 6 mm 10 cm 6 mm Welding data of rolled -iron, the transmission data of rolled - iron, the transmission data of welded -iron, and the transmission data of welded -iron. As a reference, Fig. 5 shows photographs of the grains in the base metal and the weld metal, destructively observed by an optical microscope. We observed larger grains from 20 to mm in the base metal, and smaller grains from 8 to 20 mm in the weld metal. The grains in the weld metal were almost a half of the size of the grains in the base metal. This suggests that the crystallites also became smaller in the weld metal since a grain observed by a microscope is generally constituted of many crystallites. 22,28) 3.3 Rietveld-type fitting analyses of the Bragg-edge transmission spectra Figure 6 shows the four kinds of transmission spectrum: the transmission data of the base zone, the transmission data of the base zone, the transmission data of the weld zone, and the transmission data of the weld zone. The Bragg-edge transmission spectra have been drastically changed in the wavelength region less than 0.4 nm, as well as previous reports. 11,12,29) This wavelength region is sufficiently sensitive for the texture and the microstructure of -iron. Next, we analyzed the transmission spectra by using the RITS code. Here, we note two points about the data analyses. One is that only a ferrite (-iron) model, without a pearlite model, has been used in the analyses. This is because we have not been able to observe tiny Bragg-edges of the pearlite due to the low d-spacing resolution in this experimental setup. The other is that the Rietveld-type analyses have been performed in the limited wavelength region from 0.30 nm to 0. nm where the reliability of the analyses has been assured. In the wavelength region less than the {200} Braggedge wavelength, some Bragg-edge sawteeth are stacked. Therefore, the uncertainty may increase, and the reliability may decrease. Furthermore, we have not been able to measure the detailed neutron pulse shape data around the Bragg-edges of {200}, {211} and so on since a neutron source of Hokkaido LINAC is frequently reconstructed for various neutron experiments. (a) Larger grains in the base metal (b) Smaller grains in the weld metal μm μm Ferrite Pearlite Ferrite Pearlite Fig. 5 Photographs of the grains in (a) the base metal and (b) the weld metal, taken by an optical microscope. The white grains are ferrites, and the black grains are pearlite (cementite). The volume fraction of the pearlite is 18% in the base metal and is 24% in the weld metal.

6 (a) In the base zone A Rietveld Analysis Code for Pulsed Neutron Imaging and Quantitative Evaluation of Texture and Microstructure 1299 Neutron Wavelength, λ/nm Rolling direction Rolling direction () () Normal direction Normal direction () () Neutron Flight Time, TOF /ms Neutron Flight Time, TOF /ms {211} {200} {110} (b) In the weld zone {211} {200} {110} Fig. 6 Neutron transmission TOF spectra in (a) the base metal zone and (b) the welded zone of each direction. (a) transmission in the base zone (b) transmission in the base zone Bragg Angle, θ 110 Bragg Angle, θ Experiment Fitting <111> //, R = 0.54 & S = 4.84 μm 0. Experiment Fitting <110> //, R = 0.63 & S = 5.78 μm (c) transmission in the weld zone (d) transmission in the weld zone Bragg Angle, θ 110 Experiment Fitting Bragg Angle, θ 110 Experiment Fitting <111> //, R = 0.74 <110> //, R = 0.77 & S = 3.14 μm & S = 3. μm Fig. 7 Neutron transmission spectra with the best fitting curves and parameters obtained by the RITS code. Figure 7 shows figure enlargements of the best fitting curves to the experimental transmission spectra shown in Fig. 6, and also their refinement parameters with respect to the texture and the microstructure: the preferred orientation axis hhkli, the March-Dollase coefficient R and the crystallite size S. These indicate that the RITS code can reproduce the experimental Bragg-edge transmission spectra. It indicates that the implementation of the three new factors (the resolution function, the preferred orientation distribution function and the extinction function) has worked well for analyzing the Bragg-edge transmission spectra. Figure 8 shows pole density distributions of the {110} crystal lattice plane. These pole figures have been directly extracted from the four fitting curves shown in Fig. 7. The pole density is analytically defined by the value of the March- Dollase function P hkl ð;d hkl Þ, which corresponds to the multiples of the random orientation distribution (so-called mrd). Then, the angle in this figure is geometrically defined by in case of the transmission of neutrons or 110 in case of the transmission of neutrons. We note that the Bragg angle 110 is already indicated at the top of each graph in Fig. 7, derived from the relation of eq. (7). In a

7 1300 H. Sato, T. Kamiyama and Y. Kiyanagi {110} Pole Density (%) From Fig. 7 (a) 10 From Fig. 7 (c) From Fig. 7 (d) From Fig. 7 (b) Angle from (0 ) to (90 ), Φ Φ = 90 - θ 110 (for specimens) Φ = θ 110 (for specimens) neutron transmission experiment, we can observe the attenuation of neutrons due to the scattering. In a white neutron diffraction experiment, all neutrons can satisfy the Bragg s condition about all Bragg angles. Therefore, in a white neutron transmission experiment like the pulsed neutron Bragg-edge transmission imaging, we can observe the attenuation of neutrons due to the diffraction about all Bragg angles. We can observe it as a Bragg-sawtooth. According to eq. (7), the wavelength-dependent Braggsawtooth transmission data about the {hkl} crystal lattice planes directly relate to the angle-dependent diffracted neutron intensities about the {hkl} crystal lattice planes. For example, the Bragg-sawtooth transmission spectrum from nm to 0.5 nm of -iron can cover the diffracted intensities about the Bragg angles from 47.8 to 90.0 of the {110} planes, as shown in Fig. 7. On the other hand, the March-Dollase function represents an orientation distribution as a function of the Bragg angle, averaged over each Debye- Scherrer ring. Therefore, by fitting the March-Dollase model, we can analytically estimate the widely orientation distribution from a Bragg-sawtooth without the rotation of a specimen. The trend of the pole densities is consistent with that of typical rolled BCC metals. These pole densities indicate that the orientation distribution of the {110} crystal lattice plane in the rolled zone has had the axes in the angle region from þ 30 to þ 35, and. This shows that either the preferred orientation axis h211i (-fiber) or h111i (-fiber) may be parallel to the, and the preferred orientation axis h110i (-fiber) may be parallel to the. Furthermore, the pole densities indicate that the texture after the welding process has become weaker than the rolling texture before the welding process. 3.4 Results and discussion of the quantitative imaging of the textures and the microstructures Figure 9(a) shows a two-dimensional spatial distribution of the March-Dollase coefficient, R. This image indicates the Fig. 8 Pole densities of the {110} crystal lattice plane, extracted from the best fitting curves shown in Fig. 7 by using the March-Dollase model. degree of crystallographic anisotropy. The figure clarifies that the orientation anisotropies due to the rolling process have become weaker in the weld metal zone except the HAZ due to the rapid cooling and recrystallization during the solidification. This is because the zone of the weaker textures of the middle specimen (D) forms the sandglass-like shape. This shape indicates only the weld metal zone as shown in Fig. 4(b). Furthermore, the width of the zone of the weaker textures of the bottom specimen (C) corresponds to 6 mm which is the width of the weld groove. Next, we present the most important two images in this study: the preferred orientation axis and the crystallite size. Figure 9(b) shows an image of the preferred orientation axis parallel to the beam transmission direction. In the rolled zone far from the welded zone of this image, it clearly indicates that the preferred orientation axis h111i is parallel to the (the -fiber), and the preferred orientation axis h110i is parallel to the (the -fiber). On the other hand, the number of pixels indicating the preferred orientation axis h211i (the -fiber) occupies only 7.3%, and the number of pixels indicating the preferred orientation axis h100i occupies only 4.2%. In other words, the RITS code can clearly distinguish the main preferred orientation axis from the others, and the preferred orientation data accurately correspond to the typical stable end orientation data predicted by the previous works. The last image, Fig. 9(c), shows a spatial distribution of the bulk microstructure indicating the crystallites size along the beam transmission direction. We have clarified that the crystallites size in the base metal zone is about 4.8 mm (== ) 6.0 mm (== ), and the crystallites size in the welded zone is smaller, about 2.4 mm (== ) 3.0 mm (== ). This image indicates that the crystallites have become almost a half in the size after the welding process, as estimated from the grain observations. This image also indicates that the shape of the zone of the smaller crystallites of the middle specimen (D) is ellipsoidal, and the width of the zone of the smaller crystallites of the bottom specimen (C) is about 1 cm. This corresponds to the weld metal zone plus the HAZ as shown in Fig. 4(b), and it means that both regions have had the smaller crystallites of 2:4 mm 3:0 mm although the effect of the rolling texture has been left only at the HAZ as shown in Fig. 9(a). Finally, the crystallites size depends on each specimen. This is indicated by the fact that the crystallites in the specimen (A) are larger than those in the specimen (B). It indicates that the unevenness of industrial products can be easily evaluated by using this method. Thus, it is clearly demonstrated that the pulsed neutron Bragg-edge transmission imaging coupled with the RITS code can simultaneously give quantitative information on the texture and the microstructure inside a bulk material with the positiondependent information. 4. Conclusion For quantitative visualization of information about the crystallographic texture and the microstructure inside a material, we developed a Rietveld-like analysis code, RITS (Rietveld Imaging of Transmission Spectra), for the pulsed

8 Position, y/cm A Rietveld Analysis Code for Pulsed Neutron Imaging and Quantitative Evaluation of Texture and Microstructure 1301 (a) Crystallographic anisotropy Degree of Crystallographic Texture (March-Dollase Coefficient, R) Position, x/cm 0.84 Isotropy Anisotropy (b) Preferred orientation Position, y/cm Preferred Orientation Axis Parallel to the Beam Direction, < HKL> Position, x/cm <111> <110> <100> <221> <211> <210> (c) Crystallite size (d) Neutron transmission direction Crystallite Size, S/μm Position, y/cm Position, x/cm Fig. 9 Quantitative images of the information on the texture and the microstructure inside the -iron plates. (a) Degree of the crystallographic anisotropy. (b) Preferred orientation axis that is parallel to the beam transmission direction. (c) Size of the crystallite where the primary extinction phenomenon occurs. (d) Neutron transmission direction in each specimen. neutron Bragg-edge transmission imaging. To evaluate not only the crystallographic anisotropy but also the preferred orientation axis and the crystallite size, we implemented the modified March-Dollase preferred orientation distribution model and Sabine s primary extinction model. To confirm the feasibility and the usefulness of the RITS code, we carried out an experiment using a GEM-type neutron imaging detector at a pulsed cold neutron source installed at Hokkaido LINAC in Japan. By using the RITS code, we successfully obtained the quantitative images of the degree of crystallographic anisotropy, the preferred orientation axis and the crystallite size inside rolled and welded -iron plates. The results of the imaging were well consistent with the stable end orientation properties of the rolling texture and the estimations given by an optical microscope. Our results indicate that the pulsed neutron Bragg-edge transmission imaging coupled with the data analysis code, RITS, is a unique and powerful material analysis tool. This is because this method can quantitatively and non-destructively visualize the spatial distributions of the wider area of the textures and the microstructures inside a relatively thicker material than the traditional electron, X-ray and neutron experiments. Furthermore, our findings have proved that the Bragg-edge transmission imaging experiment can be performed even at weak pulsed neutron sources of the order of s 1. This value is only 0.001% of a huge facility, for example, the 1 MW pulsed spallation neutron source JSNS installed at Materials and Life Science Experimental Facility (MLF) at Japan Proton Accelerator Research Complex (J-PARC) in Japan. Acknowledgements The authors are very thankful to Dr. S. Uno and Dr. H. Ohshita of High Energy Accelerator Research Organization (KEK), and Mr. K. Morita of Hokkaido University for invaluable support and discussions with respect to the GEM detector. We also thank Dr. T. Shibayama and Mr. H. Iwasa of Hokkaido University for experimental assistance and discussions. This work was partially supported by Grant-in-Aid for Scientific Research (A) from Japan Society for the Promotion of Science (No ). H. Sato was supported by Grant-in-Aid for JSPS Fellows from Japan Society for the Promotion of Science (No ).

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