A Rietveld-Type Analysis Code for Pulsed Neutron Bragg

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 060-8628, Japan

Bragg-edge transmission imaging using a pulsed neutron source is expected to be a new method to investigate the crystallographic andmetallographic structure of a material. This method has attracted the attention in the research field of material characterization for materialsdevelopment and industrial applications because it non-destructively provides the images on the texture and the microstructure inside a materialsuch as a thick steel bulk over the wide area of the material. For deducing such information from the Bragg-edge transmission spectrum, a dataanalysis code like a Rietveld analysis code for powder diffractometry is indispensable. So far, only the information on the crystallographicanisotropy has been deduced. However, this information is incomplete since both the preferred orientation and the crystallite size affect theBragg-edge transmission spectrum. Therefore, we have developed a Rietveld-type analysis code, RITS, that allows us to obtain the informationon preferred orientation and crystallite size at the same time. To examine the feasibility and the usefulness of the RITS code, we have analyzedthe Bragg-edge transmission spectra of rolled and welded �-iron plates, and we have successfully obtained the preferred orientation data and thecrystallite size data over the wide area of the bulk specimens. [doi:10.2320/matertrans.M2010328]

(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 (tex-ture) and microstructure (crystallite size) is very importantnot only for studying the effect of such characteristics on themetallurgical properties of existing materials but also fordeveloping high-performance structural or functional mate-rials. There exist various methods for analyzing texture andmicrostructure, for example, EBSD1) (electron backscatterdiffraction), X-ray diffraction,2) and X-ray phase-contrastmicroscopy and microtomography.3) However, these meth-ods give only the information near the surface of a material,and these methods cannot non-destructively obtain thecrystallographic and metallographic structural informationinside a bulk material with a realistic thickness. Therefore, sofar, neutron diffraction4) has been used to obtain suchinformation. However, it is frequently necessary to know thespatial-dependent changes of the structural information, forexample, in the bulk of an industrial product. In such cases,point-scan neutron diffraction measurements are performedto obtain the texture and microstructure information, andthese require a lot of the beam time.

On the other hand, neutron time-of-flight (TOF) spectro-scopic radiography using a pulsed neutron source cansimultaneously give the position-dependent Bragg-edgetransmission spectra of a material by using a neutron imagingdetector.5) The TOF transmission spectrum including Bragg-edge6–8) reflects the crystallographic and metallographicstructural information at each pixel position. In previousstudies, we have clarified the reason why the Bragg-edgetransmission spectrum changes depending on the texture andthe crystallite size; the spectra far from the edges have beendrastically changed by recrystallization during processessuch as quenching,9) annealing,10) welding,11) plastic defor-mation12) and phase transformation.13) As a result, we haveknown that the Bragg-edge transmission spectrum is sensi-

tive to the crystallographic and metallographic structuralchange, and a data analysis code to analyze the whole patternof the spectrum is indispensable for quantitatively extractingthe information on the texture and the microstructure fromthe Bragg-edge transmission spectrum. The most suitablemethod for such analysis is the Rietveld analysis technique14)

but is not the single peak profile analysis technique or thePawley analysis technique15) because these techniques cannotbe accessible to the spectrum far from the diffraction peaks.Therefore, we have developed a Rietveld-type spectral fittingcode for the Bragg-edge transmission imaging.16) Thus, wehave succeeded in non-destructively visualizing the crystal-lographic anisotropy inside a plastically deformed �-ironplate.16) However, the important information, for example,the crystal lattice planes strongly orientating in a certaindirection (the preferred orientation axis) and the crystallitesize, has not been evaluated yet. Therefore, a data analysiscode is needed to provide more detailed information on thetexture and the microstructure at the same time.

In this paper, we present the data analysis code, RITS(Rietveld Imaging of Transmission Spectra), developed forobtaining detailed information on texture and microstructure,and we have carried out a pulsed neutron transmissionimaging experiment of rolled and welded �-iron plates forexamining the feasibility and the usefulness of the pulsedneutron Bragg-edge transmission imaging with the RITScode.

2. RITS—a Data Analysis Code for the Bragg-EdgeTransmission Imaging to Quantitatively Evaluate theParameters of Texture and Microstructure

To analyze the Bragg-edge transmission spectrum, wemust take into account all scattering effects occurring ina material, which reflect the microscopic structural anddynamical information of the material. Therefore, we have

Materials Transactions, Vol. 52, No. 6 (2011) pp. 1294 to 1302#2011 The Japan Institute of Metals EXPRESS REGULAR ARTICLE

http://dx.doi.org/10.2320/matertrans.M2010328

formulated an analytical expression of the effective attenu-ation coefficient (the effective total cross section) obtained byusing a pulsed neutron source with the TOF method. Thisexpression includes the effects of the incident neutron pulseshape, the variation of the crystal lattice plane spacing, thecrystal orientation distribution due to the texture, and theextinction of diffracted neutrons inside one crystallite. In thedata analysis process, the RITS code simulates a neutrontransmission spectrum by using this formula, and then thecode fits the simulated result to an experimental result byadjusting the parameters included in the analytical formula.This procedure is performed over all pixels of the imagingdetector. We have used the non-linear least-squares fittingalgorithm, the Levenberg-Marquardt method,17) to deducethe quantitative values of the crystallographic structuralparameters. Here, we present the improved expression of theBragg-edge transmission spectrum implemented in the RITScode for quantitative imaging of texture and microstructure.

2.1 Pulsed neutron transmission spectrum with threenew factors

Figure 1 shows a schematic view of an experimental setupof the TOF radiography at a pulsed neutron source. Theneutron transmission Trð�Þ as a function of wavelength � isrepresented by the Beer-Lambert-Bouguer law, as follows:

Trð�Þ ¼ exp �Xp

�tot,pð�Þ�ptp

!: ð1Þ

Here, �tot,pð�Þ is the neutron total cross section, �p is thedensity, and tp is the thickness of the crystalline phase p.Each phase is usually composed of several nuclei. In the lowenergy region, the total cross section in the phase p consistsof elastic coherent scattering, elastic incoherent scattering,inelastic coherent scattering, inelastic incoherent scatteringand absorption parts, as follows:

�tot,pð�Þ ¼ �elacoh,pð�Þ þ �

elaincoh,pð�Þ þ �

inelacoh,pð�Þ

þ �inelaincoh,pð�Þ þ �abs,pð�Þ:

ð2Þ

The elastic coherent scattering cross section is the mostimportant for the texture and microstructure analysis becausethis component uniquely relates to the Bragg-edges andreflects the crystal structure. The other scattering compo-nents, relating to the dynamics of crystal structure (coherentcase) or each nucleus (incoherent case), and the absorption

component are calculated from the traditional total crosssection theory.18)

To describe an actual Bragg-edge transmission spectrumof a polycrystalline material, we have proposed a modifiedexpression of the Bragg-edge transmission cross section thatcombines the kinematical diffraction theory6,7,18) with threenew factors, Rhklð�; dhklÞ, Phklð�; dhklÞ and Ehklð�;FhklÞ, asfollows:

�elacoh,pð�Þ ¼

�2

2V0

Xhkl

jFhklj2dhklRhklð�; dhklÞ

� Phklð�; dhklÞEhklð�;FhklÞ;ð3Þ

where V0 is the unit cell volume, dhkl is the d-spacing,namely, the distance between the crystal lattice planes of{hkl}, and Fhkl is the crystal structure factor including theDebye-Waller factor. The first new factor, Rhklð�; dhklÞ, iscalled the resolution function or the edge profile function.This function describes the edge broadening due to theneutron pulse shape, the strain and the microstructure. TheDreele-Jorgensen-Windsor model7,19,20) that can evaluatethese effects has been adopted in the RITS code, especiallyfor the high resolution strain imaging.21)

The second new factor, Phklð�; dhklÞ, is the modifiedMarch-Dollase preferred orientation distribution function,20)

and the third new factor, Ehklð�;FhklÞ, is Sabine’s primaryextinction function for powder diffractometry.22) Hereafter,we explain these new factors representing the texturedependence and the microstructure dependence.

2.2 Modified March-Dollase preferred orientation dis-tribution function for texture analysis

The crystallographic anisotropy due to the preferredorientation in a polycrystalline material changes the wholeshape of the Bragg-edge transmission spectrum. To obtainthe information on the texture, we have implemented themodified March-Dollase preferred orientation distributionfunction20) in the RITS code. This function assumes anaxially symmetric orientation distribution around the beamdirection. The formulation is

Phklð�; dhklÞ ¼1

2�

Z2�0

R2B2hkl þ

1� B2hkl

R

� ��32

d�; ð4Þ

where

SpecimenPulsed neutron sourceTwo-dimensional imaging detector

Incident neutron beam I0(X,Y,TOF )

Transmitted neutron beam I(X,Y,TOF )

(X,Y,TOF )0I

I(X,Y,TOF )Tr (X,Y,TOF ) =

Intensity, I0

TOF(λ)

Transmission, Tr

TOF(λ)

Intensity, I

TOF(λ)

Bragg-edges

Fig. 1 Schematic view of a spatial-dependent Bragg-edge transmission spectra measurement at a pulsed neutron source.

A Rietveld Analysis Code for Pulsed Neutron Imaging and Quantitative Evaluation of Texture and Microstructure 1295

Bhkl ¼ cosAhkl sin �hkl þ sinAhkl cos �hkl sin�; ð5Þ

Ahkl ¼ arccoshH þ kK þ lLffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

h2 þ k2 þ l2p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

H2 þ K2 þ L2p

� �ð6Þ

and

�hkl ¼ arcsin�

2dhkl

� �: ð7Þ

’ represents the angle on a certain Debye-Scherrer ring of thescattering angle 2�. Ahkl is the angle between the Braggreflection plane {hkl} and the preferred crystal lattice plane{HKL} oriented in the beam direction. hHKLi is the preferredorientation axis parallel to the beam direction. The March-Dollase coefficient, R, provides the information about thedegree of crystallographic anisotropy. If there is noanisotropy (random orientation distribution), both R andPhklð�; dhklÞ are unity. When the texture is grown, R is awayfrom one. R ¼ 0 or 1 means a single crystal specimen.Figure 2(a) shows simulation examples of the total crosssection of �-iron depending on various values of hHKLi andR. In this simulation, the extinction function Ehklð�;FhklÞ isequal to one. The whole shape of the Bragg-edge trans-mission cross section, especially around the {110} Bragg-edge corresponding to the maximum d-spacing, is drasticallychanged by the anisotropy of the crystal orientation distri-bution.

2.3 Sabine’s primary extinction function for crystallitesize analysis

The primary extinction effect is caused by the re-diffraction phenomenon inside one perfect crystal block(the mosaic block or the crystallite) which is smaller than thegrain or coincides with the sub-grain in a ductile metal.22) Asa result, this effect reduces the diffracted intensity byreturning the diffracted neutrons in the direction of thetransmitted beam. Hence, this phenomenon increases thetransmitted neutron intensity and decreases the Bragg-edgetransmission cross section predicted by the kinematicaldiffraction theory. This effect of the re-diffraction has to beincluded in the RITS code since it also affects the result of theMarch-Dollase function and gives the crystallite size in-formation.

The factor of the primary extinction effect was presentedby the Darwin energy-transfer equations as a starting point.23)

Then, Sabine’s primary extinction function for powderdiffractometry was proposed,22,23) which we have adoptedin the RITS code. This formulation is expressed by combin-ing the backward-scattering (Bragg) component, EB, and theforward-scattering (Laue) component, EL, as follows:

Ehklð�;FhklÞ ¼ EB sin2 �hkl þ EL cos2 �hkl; ð8Þ

where

EB ¼1ffiffiffiffiffiffiffiffiffiffiffi

1þ xp ; ð9Þ

EL ¼ 1�x

2þ

x2

4�

5x3

48þ � � � for x � 1; ð10Þ

EL ¼ffiffiffiffiffiffi2

�x

r1�

1

8x�

3

128x2�

15

1024x3� � � �

� �for x > 1; ð11Þ

and

x ¼ S2 �Fhkl

V0

� �2

: ð12Þ

S is the crystallite size along the beam direction. Figure 2(b)shows simulation examples of the total cross section of �-irondepending on various values of S. In this simulation, thepreferred orientation distribution function Phklð�; dhklÞ isequal to one. The whole intensity of the Bragg-edgetransmission cross section is drastically reduced by theextinction of diffracted neutrons inside one crystallite.

3. Welded �-Iron Experiment for Deducing the Textureand Microstructure Information by Using the RITSCode

We have performed a verification experiment that showsthe feasibility and the usefulness of the Bragg-edge trans-mission imaging with the RITS code. For this purpose, wechose rolled �-iron plates and welded ones.

It has been predicted that a rolled sheet composed of body-centered-cubic (BCC) polycrystals has two types of fibertexture in the stable end of the rolling process.24) One is the �-

5

10

15

20

25

0.1

Neutron Wavelength, λ /nm

σto

t/10-2

8 m2

α-iron (293.6 K)

S = 10 μm

S = 5 μm

S = 1 μmWithout extinction effect

5

10

15

20

25

30

35

0.15


σto

t/10-2

8 m2

R = 1.0

{110

}

{200

}

{211

}

{220

}

{310

}

α-iron (293.6 K)<HKL> = <110> & R = 0.5

<HKL> = <111> & R = 0.45

<HKL> = <211> & R = 0.45

(a) Texture dependence (b) Extinction dependence

0.450.400.350.300.250.20 0.50.40.30.2

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.

1296 H. Sato, T. Kamiyama and Y. Kiyanagi

fiber, which has the preferred orientation axis h110i parallelto the rolling direction (RD). The other is the -fiber, whichhas the preferred orientation axis h111i parallel to the normaldirection (ND). The -fiber texture is equivalent to thetexture that h110i strongly orients in NDþ 35� (or RD�55�). This stable end rolling texture is known as {111} h01�11iin the notation of rolling texture. However, this stable endrolling texture is formed via {112} h1�110i or {001} h110iduring the rolling process.24) In particular, the preferredorientation axis h211i parallel to the ND (the -fiber) is veryclose to the -fiber in the pole figure because the -fibertexture is equivalent to the texture that h110i strongly orientsin NDþ 30� (or RD� 60�). The identification between the-fiber and the -fiber of a rolled BCC metal has not beenclear. For this reason, the major discussion point of thetexture imaging using the RITS code is whether the {111}h01�11i rolling texture can be clearly distinguished from theothers, especially {112} h1�110i.

Furthermore, the welding process drastically changes themicrostructure (the crystallite size). Therefore, we have alsointended to clarify the change of the crystallites size with theposition-dependent information.

3.1 Experimental setupWe carried out a TOF radiography experiment at the cold

neutron beam-line at the electron linear accelerator facility atHokkaido University in Japan (Hokkaido LINAC). In thisfacility, pulsed neutrons are generated by the photonuclearreaction caused by bremsstrahlung of 1 kW pulsed electrons.The electron energy is 33 MeV, the pulse width is 3 ms, thepulse repetition rate is 50 Hz, and the beam current is 33 mA.The neutron yield of the photonuclear reaction target is onlyabout 1012 s�1. In this experiment, we utilized a coupled-type18 K solid methane moderator. The pulsed neutron beam wastransported through an evacuated beam-tube of 3 m andboron-carbide collimators. The neutron flight path lengthfrom the source to the detector was 6.03 m. The neutron flux

at the detector position was about 103 cm�2s�1. The neutronwavelength resolution in this experiment was 2.7% at thewavelength of 0.4 nm. This resolution is not very good due tothe utilization of the coupled-type moderator and the shortflight path length. Therefore, we cannot observe tiny Bragg-edges of the pearlite in case of this experimental setup.

Figure 3 shows a schematic layout of the experimentalsetup and the data flow. We used a GEM (gas electronmultiplier) type two-dimensional neutron detector.25–27) Theprototype GEM detector used in this experiment consisted ofone aluminum cathode foil coated with a boron-10 layer of0.02 mm thickness for neutron-electron conversion, two GEMfoils coated with a boron-10 layer of 0.6 mm thickness forneutron-electron conversion, one GEM foil for electronamplification, and coincidence-type readout electrodes. Themixed gas of argon (70%) and carbon-dioxide (30%) wasused as a floating gas. The detection efficiency of the GEMdetector was 15% at the neutron wavelength of 0.4 nm. Thereadout board had the two-dimensional strips of 800 mmposition 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 forthe transmitted beam measurement and 3.3 h for the incidentbeam measurement so as to obtain the sufficient statistics forthe texture and microstructure imaging with good spatialresolution (small pixel size) under the condition of the weakneutron beam of Hokkaido LINAC and the low detectionefficiency of the GEM detector.

3.2 SpecimensThe specimens were rolled or TIG (tungsten inert gas) type

welded �-iron plates (JIS-SS400) classified as a BCCpolycrystalline material. Figure 4(a) shows a photograph ofthe specimens, and Fig. 4(b) shows a schematic view aroundthe welded zone. Table 1 shows a summary with respect tothe specimens: indicator, size, treatment and beam trans-mission direction. We measured four �-iron plates. Two

Neutron flight path length = 6.03 m

Neutron detection data (X,Y,TOF )

Boron-carbide collimator

Trigger (T0) signal from accelerator

Boron GEM

Normal GEM

Data accumulation computer

Data acquisition computer

Data analysis computer

RITS

Experimental setup Data processing setup

Boron & aluminum cathode foil

Readout board

Argon & carbon-dioxide gas

Pulsed neutrons

GEM-type neutron imaging detector

Specimens

Fig. 3 Experimental setup using the GEM detector at Hokkaido LINAC, and data flow for the spectral analyses using the RITS code.


rolled �-iron plates, (A) and (B) in Fig. 4(a) and Table 1,were placed at the top. Neutrons were transmitted through theND. One welded �-iron plate, (C) in Fig. 4(a) and Table 1,was placed at the bottom. The weld metal was the same as thebase metal, and it was welded from both sides of a weldgroove along the center line as shown in Fig. 4(b). The lastspecimen, (D) in Fig. 4(a) and Table 1, was a cut plane of thewelded �-iron plate, and it was placed at the middle. We notethat this specimen was cut out from the bottom specimen.Neutrons were transmitted through the RD only in thisspecimen. The welded two specimens (C) and (D) had theheat affected zone (HAZ) around the groove and the weldmetal of 6 mm width as shown in Fig. 4(b). The total width ofthe weld metal zone plus the HAZ was about 1 cm. Theneutron transmission thicknesses of all the specimens wereuniformly 6 mm. Thus, we simultaneously obtained fourkinds of neutron transmission spectrum: the ND transmission

data of rolled �-iron, the RD transmission data of rolled �-iron, the ND transmission data of welded �-iron, and the RDtransmission data of welded �-iron.

As a reference, Fig. 5 shows photographs of the grains inthe base metal and the weld metal, destructively observed byan optical microscope. We observed larger grains from 20 to50 mm in the base metal, and smaller grains from 8 to 20 mmin the weld metal. The grains in the weld metal were almost ahalf of the size of the grains in the base metal. This suggeststhat the crystallites also became smaller in the weld metalsince a grain observed by a microscope is generallyconstituted of many crystallites.22,28)

3.3 Rietveld-type fitting analyses of the Bragg-edgetransmission spectra

Figure 6 shows the four kinds of transmission spectrum:the ND transmission data of the base zone, the RD trans-mission data of the base zone, the ND transmission data ofthe weld zone, and the RD transmission data of the weldzone. The Bragg-edge transmission spectra have beendrastically changed in the wavelength region less than0.4 nm, as well as previous reports.11,12,29) This wavelengthregion is sufficiently sensitive for the texture and themicrostructure of �-iron.

Next, we analyzed the transmission spectra by using theRITS code. Here, we note two points about the data analyses.One is that only a ferrite (�-iron) model, without a pearlitemodel, has been used in the analyses. This is because we havenot been able to observe tiny Bragg-edges of the pearlite dueto the low d-spacing resolution in this experimental setup.The other is that the Rietveld-type analyses have beenperformed in the limited wavelength region from 0.30 nm to0.55 nm where the reliability of the analyses has beenassured. In the wavelength region less than the {200} Bragg-edge wavelength, some Bragg-edge sawteeth are stacked.Therefore, the uncertainty may increase, and the reliabilitymay decrease. Furthermore, we have not been able tomeasure the detailed neutron pulse shape data around theBragg-edges of {200}, {211} and so on since a neutronsource of Hokkaido LINAC is frequently reconstructed forvarious neutron experiments.

10 cm

10 cm

Welded zone

(A)

(a) Photograph of the specimens

Thickness : 6 mm

(b) Schematic viewaround the welded zone (View to RD)

Weld metal (Sandglass-like shape)

6 mm

6 mmND

RD

ND

RD

Base metalHAZ

10 mm

(B)

(D)

(C)

Fig. 4 (a) Photograph of the specimens. Pulsed neutrons were transmitted

through the ND, RD and ND 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 ND

(B) 4:4 cm� 5 cm� 6 mm Rolling ND

(C) 5 cm� 10 cm� 6 mm Welding ND

(D) 6 mm� 10 cm� 6 mm Welding RD

(a) Larger grains in the base metal (b) Smaller grains in the weld metal

ND

RD

ND

RD50 μm 50 μmFerrite 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.


Figure 7 shows figure enlargements of the best fittingcurves to the experimental transmission spectra shown inFig. 6, and also their refinement parameters with respect tothe texture and the microstructure: the preferred orientationaxis hHKLi, the March-Dollase coefficient R and thecrystallite size S. These indicate that the RITS code canreproduce the experimental Bragg-edge transmission spectra.It indicates that the implementation of the three new factors(the resolution function, the preferred orientation distributionfunction and the extinction function) has worked well foranalyzing the Bragg-edge transmission spectra.

Figure 8 shows pole density distributions of the {110}crystal lattice plane. These pole figures have been directlyextracted from the four fitting curves shown in Fig. 7. Thepole density is analytically defined by the value of the March-Dollase function Phklð�; dhklÞ, which corresponds to themultiples of the random orientation distribution (so-calledmrd). Then, the angle� in this figure is geometrically definedby 90� � �110 in case of the ND transmission of neutrons or�110 in case of the RD transmission of neutrons. We note thatthe Bragg angle �110 is already indicated at the top of eachgraph in Fig. 7, derived from the relation of eq. (7). In a

40

45

50

55

60

65

70

Neutron Flight Time, TOF /ms

Neu

tron

Tra

nsm

issi

on (

%)


Rolling direction (RD)

Normal direction (ND)

{200

}

{211

}

{110

}

40

45

50

55

60

65

70

1

Neutron Flight Time, TOF /ms

Neu

tron

Tra

nsm

issi

on (

%)


0.1 0.2

Rolling direction (RD)

Normal direction (ND)

{200

}

{211

}

{110

}

(a) In the base zone (b) In the weld zone

1098765432

0.60.50.40.3 0.1 0.2 0.60.50.40.3

1 1098765432

Fig. 6 Neutron transmission TOF spectra in (a) the base metal zone and (b) the welded zone of each direction.

40

45

50

55

60

65

70


Neu

tron

Tra

nsm

issi

on (

%)

ExperimentFitting

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45

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Neu

tron

Tra

nsm

issi

on (

%)

ExperimentFitting

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Neu

tron

Tra

nsm

issi

on (

%)

ExperimentFitting

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45

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55

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0.30


Neu

tron

Tra

nsm

issi

on (

%)

ExperimentFitting

<111> // ND, R = 0.54& S = 4.84 μm

<110> // RD, R = 0.63& S = 5.78 μm

<110> // RD, R = 0.77& S = 3.65 μm

<111> // ND, R = 0.74& S = 3.14 μm

(a) ND transmission in the base zone (b) RD transmission in the base zone

(c) ND transmission in the weld zone (d) RD transmission in the weld zone

Bragg Angle, θ 110 Bragg Angle, θ 110

Bragg Angle, θ 110

81° 81°

81° 81°

Bragg Angle, θ 110

60° 60°

60° 60°

48° 48°

48° 48°

0.550.500.450.400.35

0.30 0.550.500.450.400.35 0.30 0.550.500.450.400.35

0.30 0.550.500.450.400.35

Fig. 7 Neutron transmission spectra with the best fitting curves and parameters obtained by the RITS code.


neutron transmission experiment, we can observe theattenuation of neutrons due to the scattering. In a whiteneutron diffraction experiment, all neutrons can satisfy theBragg’s condition about all Bragg angles. Therefore, in awhite neutron transmission experiment like the pulsedneutron Bragg-edge transmission imaging, we can observethe attenuation of neutrons due to the diffraction about allBragg angles. We can observe it as a Bragg-sawtooth.According to eq. (7), the wavelength-dependent Bragg-sawtooth transmission data about the {hkl} crystal latticeplanes directly relate to the angle-dependent diffractedneutron intensities about the {hkl} crystal lattice planes.For example, the Bragg-sawtooth transmission spectrumfrom 0.300 nm to 0.405 nm of �-iron can cover the diffractedintensities about the Bragg angles from 47.8� to 90.0� of the{110} planes, as shown in Fig. 7. On the other hand, theMarch-Dollase function represents an orientation distributionas 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 distribu-tion from a Bragg-sawtooth without the rotation of aspecimen.

The trend of the pole densities is consistent with that oftypical rolled BCC metals. These pole densities indicate thatthe orientation distribution of the {110} crystal lattice planein the rolled zone has had the axes in the angle region fromNDþ 30� to NDþ 35�, and RD. This shows that either thepreferred orientation axis h211i (-fiber) or h111i (-fiber)may be parallel to the ND, and the preferred orientation axish110i (�-fiber) may be parallel to the RD. Furthermore, thepole densities indicate that the texture after the weldingprocess has become weaker than the rolling texture before thewelding process.

3.4 Results and discussion of the quantitative imaging ofthe textures and the microstructures

Figure 9(a) shows a two-dimensional spatial distributionof the March-Dollase coefficient, R. This image indicates the

degree of crystallographic anisotropy. The figure clarifiesthat the orientation anisotropies due to the rolling processhave become weaker in the weld metal zone except the HAZdue to the rapid cooling and recrystallization during thesolidification. This is because the zone of the weaker texturesof the middle specimen (D) forms the sandglass-like shape.This shape indicates only the weld metal zone as shown inFig. 4(b). Furthermore, the width of the zone of the weakertextures of the bottom specimen (C) corresponds to 6 mmwhich is the width of the weld groove.

Next, we present the most important two images in thisstudy: the preferred orientation axis and the crystallite size.Figure 9(b) shows an image of the preferred orientation axisparallel to the beam transmission direction. In the rolled zonefar from the welded zone of this image, it clearly indicatesthat the preferred orientation axis h111i is parallel to the ND(the -fiber), and the preferred orientation axis h110i isparallel to the RD (the �-fiber). On the other hand, thenumber of pixels indicating the preferred orientation axish211i (the -fiber) occupies only 7.3%, and the number ofpixels indicating the preferred orientation axis h100i occu-pies only 4.2%. In other words, the RITS code can clearlydistinguish the main preferred orientation axis from theothers, and the preferred orientation data accurately corre-spond to the typical stable end orientation data predicted bythe previous works.

The last image, Fig. 9(c), shows a spatial distributionof the bulk microstructure indicating the crystallites sizealong the beam transmission direction. We have clarifiedthat the crystallites size in the base metal zone is about4.8 mm (== ND) � 6.0 mm (== RD), and the crystallites sizein the welded zone is smaller, about 2.4 mm (== ND) �3.0 mm (== RD). This image indicates that the crystalliteshave become almost a half in the size after the weldingprocess, as estimated from the grain observations. Thisimage also indicates that the shape of the zone of thesmaller crystallites of the middle specimen (D) is ellipsoi-dal, and the width of the zone of the smaller crystallites ofthe bottom specimen (C) is about 1 cm. This corresponds tothe weld metal zone plus the HAZ as shown in Fig. 4(b),and it means that both regions have had the smallercrystallites of 2:4 mm� 3:0 mm although the effect of therolling texture has been left only at the HAZ as shown inFig. 9(a). Finally, the crystallites size depends on eachspecimen. This is indicated by the fact that the crystallites inthe specimen (A) are larger than those in the specimen (B).It indicates that the unevenness of industrial products can beeasily evaluated by using this method. Thus, it is clearlydemonstrated that the pulsed neutron Bragg-edge trans-mission imaging coupled with the RITS code can simulta-neously give quantitative information on the texture and themicrostructure inside a bulk material with the position-dependent information.

4. Conclusion

For quantitative visualization of information about thecrystallographic texture and the microstructure inside amaterial, we developed a Rietveld-like analysis code, RITS(Rietveld Imaging of Transmission Spectra), for the pulsed

80

90

100

110

120

0°°

Angle from ND (0°°) to RD (90°°) , Φ

{110

} P

ole

Den

sity

(%

)

From Fig. 7 (b)

From Fig. 7 (a)

From Fig. 7 (c)

From Fig. 7 (d)

ND

RD

Φ = 90° - θ110 (for ND specimens)

Φ = θ110 (for RD specimens)

90°°80°°70°°60°°50°°40°°30°°20°°10°°

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.


neutron Bragg-edge transmission imaging. To evaluate notonly the crystallographic anisotropy but also the preferredorientation axis and the crystallite size, we implemented themodified March-Dollase preferred orientation distributionmodel and Sabine’s primary extinction model. To confirmthe feasibility and the usefulness of the RITS code, wecarried out an experiment using a GEM-type neutronimaging detector at a pulsed cold neutron source installedat Hokkaido LINAC in Japan. By using the RITS code,we successfully obtained the quantitative images of thedegree of crystallographic anisotropy, the preferred orien-tation axis and the crystallite size inside rolled and welded�-iron plates. The results of the imaging were wellconsistent with the stable end orientation properties of therolling texture and the estimations given by an opticalmicroscope.

Our results indicate that the pulsed neutron Bragg-edgetransmission imaging coupled with the data analysis code,RITS, is a unique and powerful material analysis tool. This isbecause this method can quantitatively and non-destructivelyvisualize the spatial distributions of the wider area of thetextures and the microstructures inside a relatively thickermaterial than the traditional electron, X-ray and neutron

experiments. Furthermore, our findings have proved that theBragg-edge transmission imaging experiment can be per-formed even at weak pulsed neutron sources of the order of1012 s�1. This value is only 0.001% of a huge facility, forexample, the 1 MW pulsed spallation neutron source JSNSinstalled 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 forinvaluable support and discussions with respect to theGEM detector. We also thank Dr. T. Shibayama and Mr.H. Iwasa of Hokkaido University for experimental assis-tance and discussions. This work was partially supportedby Grant-in-Aid for Scientific Research (A) from JapanSociety for the Promotion of Science (No. 20246136).H. Sato was supported by Grant-in-Aid for JSPS Fellowsfrom Japan Society for the Promotion of Science(No. 20002121).

Degree of Crystallographic Texture (March-Dollase Coefficient, R)

0.50

0.84

0.67

- 5

+ 5

0

- 5 + 50

Position, x/cm

Pos

itio

n, y

/cm

- 5

+ 5

0

- 5 + 50

Preferred Orientation AxisParallel to the Beam Direction, < HKL>

<111>

<110>

<100>

<221>

<211>

<210>

Position, x/cm

Pos

itio

n, y

/cm

(b) Preferred orientation(a) Crystallographic anisotropy

Anisotropy

Isotropy

2.4

6.0

4.2

- 5

+ 5

0

- 5 + 50

Crystallite Size, S/μm

4.8

3.0

Position, x/cm

Pos

itio

n, y

/cm

(c) Crystallite size (d) Neutron transmission direction

ND ND

ND

RD

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.


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A Rietveld-Type Analysis Code for Pulsed Neutron Bragg