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In-line x-ray phase-contrast tomography and diffraction-contrasttomography study of the ferrite-cementite microstructure in steelAlexander Kostenko, Hemant Sharma, E. Gözde Dere, Andrew King, Wolfgang Ludwig et al. Citation: AIP Conf. Proc. 1437, 63 (2012); doi: 10.1063/1.3703344 View online: http://dx.doi.org/10.1063/1.3703344 View Table of Contents: http://proceedings.aip.org/dbt/dbt.jsp?KEY=APCPCS&Volume=1437&Issue=1 Published by the American Institute of Physics. Related ArticlesNanoscale heterogeneity in alkyl-methylimidazolium bromide ionic liquids J. Chem. Phys. 134, 104509 (2011) Self-organized antireflecting nano-cone arrays on Si (100) induced by ion bombardment J. Appl. Phys. 109, 053513 (2011) Niobium substitution in Zr0.5Hf0.5NiSn based Heusler compounds for high power factors Appl. Phys. Lett. 98, 042106 (2011) Frequency-dependent electrical properties of ferroelectric BaTi2O5 single crystal J. Appl. Phys. 109, 024107 (2011) Improved hybrid functional for solids: The HSEsol functional J. Chem. Phys. 134, 024116 (2011) Additional information on AIP Conf. Proc.Journal Homepage: http://proceedings.aip.org/ Journal Information: http://proceedings.aip.org/about/about_the_proceedings Top downloads: http://proceedings.aip.org/dbt/most_downloaded.jsp?KEY=APCPCS Information for Authors: http://proceedings.aip.org/authors/information_for_authors

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In-line X-ray phase-contrast tomography anddiffraction-contrast tomography study of the

ferrite-cementite microstructure in steelAlexander Kostenko∗, Hemant Sharma†, E. Gözde Dere†, Andrew King∗∗,

Wolfgang Ludwig∗∗, Wim van Oel∗, S. Erik Offerman†, Sjoerd Stallinga∗ andLucas J. van Vliet∗

∗Dept. of Imaging Science & Technology, Delft University of Technology, Lorentzweg 1, Delft, The Netherlands†Dept. of Materials Science & Engineering, Delft University of Technology, Mekelweg 2, Delft, The Netherlands

∗∗European Synchrotron Radiation Facility, 6 rue Jules Horowitz, Grenoble, France

Abstract. This work presents the development of a non-destructive imaging technique for the investigation of the microstruc-ture of cementite grains embedded in a ferrite matrix of medium-carbon steel. The measurements were carried out at thematerial science beamline of the European Synchrotron Radiation Facility (ESRF) ID11. It was shown that in-line X-rayphase-contrast tomography (PCT) can be used for the detection of cementite grains of several microns in size. X-ray PCT ofthe cementite structure can be achieved by either a ’single distance’ or a ’multiple distance’ acquisition protocol. The latterpermits quantitative phase retrieval. A second imaging technique, X-ray diffraction-contrast tomography (DCT), was em-ployed to obtain information about the shapes and crystallographic orientations of the distinct ferrite grains surrounding thecementite structures. The initial results demonstrate the feasibility of determining the geometry of the cementite grains afterthe austenite-ferrite phase-transformation in a non-destructive manner. The results obtained with PCT and DCT are verifiedwith ex-situ optical microscopy studies of the same specimen.

(a) (b)

(c) (d)

Figure 1. Optical microscopy images of the cementite-ferritestructure. Images are acquired after 1, 10, 20 and 70 hours ofannealing at a temperature of 700ºC.

INTRODUCTION

Development of steel with high strength at elevated tem-peratures largely depends on advances in our understand-ing of phase transformations [1-3]. The accuracy of pre-dicting the kinetics of solid-state phase transformations

depends on microstructural parameters that are often dif-ficult or impossible to measure or calculate from ab-initio calculations, e.g. the activation energy for nucle-ation. This leads to a low predictive power of existingmodels and restricts their applicability to a limited rangeof experimental conditions. In earlier work [4] we haveshown by means of three-dimensional X-ray diffractionmicroscopy that the nucleation rate of ferrite in steel ismuch higher than predicted from state-of-the-art phasetransformation models at that time. Like ferrite formationin steel, cementite formation in steel is also well studied,but never by in-situ synchrotron radiation techniques thatreveal information of individual cementite grains in bulksteel specimens.

An in-situ study of the nucleation process and graingrowth inside the bulk is necessary for the developmentof more accurate quantitative models for the phase trans-formation kinetics. The study of incubation time beforenucleation, nucleation rate, grain growth rate, grain ori-entation and interface mobility as a function of time andtemperature will provide unique insights into the phasetransformation kinetics leading to a better control of themechanical and thermal properties of steel. The currentexperiment serves as a preparatory stage for a time-resolved in-situ study of the nucleation process and ce-

X-Ray Optics and MicroanalysisAIP Conf. Proc. 1437, 63-68 (2012); doi: 10.1063/1.3703344

© 2012 American Institute of Physics 978-0-7354-1027-5/$30.00

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Cementiteprecipitate

SampleDetector planeX-Ray

Phase-contrast from cementite(Fresnel di�raction)

Di�raction spot from ferrite

Di�raction spot from ferrite (at +180°)

(Bragg di�raction)

Extinction spot from ferrite

(Bragg di�raction)

Ferrite grain

2Θ2Θ

360°

Figure 2. Sketch of the phase-contrast and diffraction-contrast effects taking place when the steel sample is illumi-nated with a coherent X-ray beam.

mentite grain growth1.To investigate the microstructure of steel in a non-

invasive manner, imaging techniques based on severalnon-destructive contrast mechanisms are needed. The ce-mentite grains can be detected due to a slightly lowerdensity in comparison to the surrounding ferrite (approx-imately 3% difference). However, the size of the cemen-tite particles can vary from tens of micrometers downto the sub-micron scale (Figure 1) producing extremelylow attenuation contrast. Improving cementite detectionrequires the use of a phase-contrast imaging approachrather than attenuation-contrast imaging.

The structure of the ferrite grains cannot be recon-structed using phase-contrast imaging techniques sincethere is no variation of density or composition betweenthe grains. Instead, the Bragg diffraction of X-rays onthe ferrite lattice must be exploited. In order to performa time-resolved study, the imaging techniques must al-low for relatively short acquisition times (on the order of1 hour or less) for a complete 3D volume. That require-ment can be satisfied using X-ray diffraction-contrast to-mography [5].

MATERIALS AND METHODS

The composition of the sample used in the current ex-periment was established using X-ray fluorescense spec-trometry. The material contains 95.4wt% iron, 2.8wt%copper, 0.6wt% manganese, 0.6wt% carbon. The sam-ple was annealed in vacuum of 10−5 mbar at a con-stant temperature of 700°C for 70 hours. It was consec-utively cooled down to the room temperature at a rate of2°C/min. Such a treatment leads to the formation of largecementite grains as depicted in Figure 1. A miniature rod

1 This work was partially supported by the Care4U project with finan-cial support of Point One, an innovation program of the Ministry ofEconomic Affairs in The Netherlands.

with a diameter of approximately 400µm was manufac-tured from the annealed material.

Experimental techniques

The combination of two complementary techniques:X-ray PCT and X-ray DCT, can be used to study the mi-crostructure of cementite grains in a ferrite matrix. A sin-gle imaging beamline with sufficient spatial coherenceand a suitable X-ray detector can be utilized for both PCTand DCT without significant changes to the beamline ge-ometry or the components (Figure 2).

The in-line phase-contrast image of cementite grainembedded in ferrite can be recorded using a high-resolution detector behind the object (Figure 2). Multipleacquisitions taken at several object-to-detector distancesare usually required for each object projection. A suitablephase-contrast sinogram can be recorded using either a180° or a 360° scan protocol.

In the diffraction-contrast regime, Bragg diffractionspots produced by individual ferrite grains are recordedas shown in Figure 2. When the beamline is switchedfrom PCT to DCT mode only the detector has to berealigned to allow for the desired angular resolution and asufficiently large field of view. A suitable scan series hasto be recorded using a 360° scan protocol, which permitsa reconstruction based on Friedel pair matching [5].

Our experiment is carried out at the material sciencebeamline ID11 of the European Synchrotron RadiationFacility (ESRF). The beamline is based on the undula-tor X-ray source with a source size of 57×10µm (HxV)FWHM. The beamline is equipped with a Laue-Laue Si(111) monochromator operated at 40KeV beam energywith a bandwidth 4E/E = 10−4. A specimen is placedin the first experimental hutch where the source-to-objectdistance is approximately 48m. This corresponds to ahorizontal spatial coherence length Lcoh ∼ 9µm. We usedthe Frelon 2K CCD detector optically coupled to a 30µmscintillator resulting in 20x magnification. The best ef-fective detector resolution was estimated from the ac-quired images to be approximately 1.4µm for a samplingpitch of 0.75µm.

Acquisition of a single phase-contrast projection im-age involves the recording of three intensity images ofthe specimen at 3mm, 68mm and 208mm object-to-detector distance. The image at the shortest distanceshows mainly attenuation-contrast, the two others aretaken in order to reconstruct the phase image [6]. Im-ages are acquired in 1024x1024 format with a pixel sizeof 0.75µm (Figure 3b).

The diffraction-contrast images are recorded at 9.5mmobject-to-detector distance using full CCD (2048x2048format) with optical magnification corresponding to a

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3mm� 68mm� 208mm�

PCT data (single projec�on at object�detector distance: 3, 68, 208mm):�

(a) (b)

Figure 3. (a) A single projection of the DCT dataset. (b)Three single projections of the sinograms recorded at differentobject-to-detector distances for PCT.

3.75µm sampling pitch (Figure 3a). The DCT acquisi-tion was done separately for five subsections of the com-plete volume of the specimen in order to reduce the com-plexity of the reconstruction.

Data preprocessing

Data acquired for phase retrieval was preprocessedusing the following steps:

1. Dark-field and flat-field correction2. Extinction spots reduction3. Intra-sinogram registration of the projections4. Inter-sinogram registrationThis procedure approximates the flat-field as a simple

transmission effect (no phase effects from the propaga-tion of the flat-field through the specimen are accountedfor). Therefore the corrected image is calculated as:

I =Irec− Idark

I f lat − Idark,

where Irec is the recorded intensity image, Idark the dark-field image of the detector, and I f lat the flat-field image,i.e. the intensity field irradiating the specimen. A dark-field image is recorded once during the tomographic ac-quisition (Figure 4a), whereas the flat-field may changesignificantly over a short time and must be updated foreach individual projection. During the acquisition a ref-erence flat-field image is recorded after every 100 projec-tions. A dedicated flat-field image for each projection canbe calculated using linear interpolation (Figure 4b). Af-ter the first flat-field correction, a second correction mustbe performed in order to account for the fast changesof the flat-field that are not captured by the referencedata. Since the object remains in the central part of therecorded projection images, we can calculate a flat-fieldimage using the left and right sides in each row of theprojection images. The central part of the flat-field image(attenuated by the object) is then calculated by interpola-tion (Figure 4c).

Extinction spot reduction. Extinction spots (regionswith lower intensity) are produced by Bragg diffraction

Dark-field: counts

110

115

120

125

130

135

140Flat-field: counts

6000

7000

8000

9000

10000

11000

12000

13000

14000

(a) (b)Flat-field: intensity

0.9

0.91

0.92

0.93

0.94

0.95

0.96

0.97

0.98

0.99

1

(c) (d)

Figure 4. (a) Dark-field of the Frelon 2K detector; (b) Flat-field from the beginnig of the tomographic scan series at 208mm; (c) Object intensity image; (d) Flat-field derived fromobject intensity image

of X-rays on large ferrite grains that surround the cemen-tite structure. This may lead to very weak artefacts afterPCT reconstruction. The extinction spot of a particularferrite grain may appear only in the direction that cor-responds to a certain Bragg angle with a small angularacceptance (~1 deg). They can be significantly reducedby simply applying a median filter to the phase-contrastsinogram of the object in the angular direction with akernel larger than 1 deg.

Intra-sinogram registration of the projections. Eachprojection of a phase-contrast sinogram has to be re-aligned in order to minimize the effects of irregularmovements of the rotation table or the optical system.Such realignment can be done iteratively using the fol-lowing steps:

1. Reconstruction by Filtered Back-Projection of asegment of the recorded data AFBP.

2. Calculation of the reconstructed sinogram SFP byforward-projection of the reconstructed volume AFBP.

3. Alignment of each single recorded image with thecorresponding image from the sinogram SFP.

4. Correction of the recorded data for the small shiftbetween the recorded and re-projected data.

5. Repeat steps 1 through 4 until convergence isreached...

Inter-sinogram registration. The fourth and the laststep of the data preprocessing corrects for the globalmotion of the object in the field of view of the cameraand relatively to the rotation axis when the sinogram isrecorded at different object-to-detector distances. The re-

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-1.5 -1 -0.5 0 0.5 1 1.5

x 106

-150

-100

-50

0

50

100

150

Frequency

3mm68mm208mm

Figure 5. Dual phase-attenuation contrast transfer functions(CTF) for the steel sample. CTF for the object-to-detectordistances of 3mm, 68mm and 208mm are shown in blue, redand black color corresopondingly.

sult of such motion can be that the object appears at adifferent location in each reconstructed volume. Correc-tion involves a comparison between all three sinogramsrecorded for phase retrieval. First, the vertical shift of theobject (shift along the rotation axis) is registered after av-eraging the sinogram in the horizontal and angular direc-tions. Second, a reconstruction by Filtered Back Projec-tion is calculated for each of the three sinograms (aver-aged in vertical direction). Now the vector (Xs,Ys) of theobject shift relative to the rotation axis can be calculatedin the horizontal plane. Finally, the object can be cen-tred in the horizontal plane by shifting each projection inthe sinogram by the shift vector Xs · cos(γ)−Ys · sin(γ),where γ is a projection angle. The angular orientation ofthe object is assumed to be accurately alligned betweenthe sinograms. However, it can be also corrected by peri-odic shifting of the sinograms with respect to eachotherin the angular direction.

In-line phase retrieval

The phase retrieval method is based on the so-calledMixed TIE-CTF formalism [7]:

F̂(IR) = cos(πλRu2

M) · F̂(I0)+2sin(

πλRu2

M) · F̂(I0 ·φ),

(1)where F̂(IR) is the Fourier transform of image IR, an in-tensity image recorded at the distance R, I0 an attenuationimage of the object, φ a phase image, λ the radiationwavelength, R/M the object-to-detector distance dividedby magnification and u a spatial frequency.

Expression (1) is a linearised version of the Fres-nel integral assuming slowly varying phase and attenu-ation. The approximation holds only when |φ(x)−φ(x+λRuM )| � 1 and is in fact violated in our experiment close

to the boundaries of the object or anywhere near thesteel-to-air interfaces (including pores inside the speci-men). However, the approximation holds for the ferrite-

cementite interface and therefore the approach will leadto a correct image reconstruction of the cementite struc-ture ’far’ away from the specimen boundaries.

It is well-known that the problem of phase retrieval isill-posed at low spatial frequencies and for all frequen-cies where the second term of (1) becomes zero. A solu-tion to that problem is to combine both phase and attenu-ation terms into one as it is done in the phase-attenuationduality approach proposed by Wu [8]:

F̂(Ir) = (cos(πλRu2

M)+2α · sin(

πλRu2

M)) · F̂(I0), (2)

where α is essentially a constant ratio between the phaseand attenuation coefficients of the object. A small thirdterm used in [8] is ommited. The original approach wasderived for homogeneous objects or objects composedfrom light elements imaged using X-rays with energybelow 60KeV [8]. The same approach can be used incases where the object is composed of two materialshaving different chemical compositions [9].

Formula (2) allows us to calculate the attenuation im-age of the object (which is in that case proportional tothe phase image) directly from a single phase-contrastimage. The image can be calculated at low spatial fre-quencies. However, the sum of the attenuation and thephase term expressed via cosine and sine functions canhave zero crossings at high frequencies and the prob-lem of the phase retrieval remains ill-posed around thisset of frequencies. We can overcome this by using infor-mation from the sinograms acquired at different object-to-detector distances as it is conventionally done in theMixed TIE-CTF approach [10]:

F̂(I0)=∑R

ARF̂(IR)

∑R

A2R + ε

,AR = cos(πλRu2

M)+2α ·sin(

πλRu2

M),

(3)where ε is a small regularization constant, which can beset to zero when ∑

RA2

R does not have any zero crossings.

Now the image can be reconstructed correctly for the en-tire frequency range in exchange for additional acquisi-tion time. It has to be noted again that the image will beerroneously reconstructed around air-steel interfaces dueto both violation of the assumptions in (1) and due thewrong value of the factor α (2).

RESULTS OF PCT RECONSTRUCTION

The phase-contrast tomographic reconstruction of thecementite microstructure can be performed using thefollowing distinct approaches:

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(a) (b)

(c) (d)

Figure 6. Results of the different phase retrieval techniquesthat were used prior to the reconstruction by FBP. (a) Nophase retrieval. (b) Mixed TIE-CTF. (c) Single distance dualphase-attenuation retrieval. (d) Multiple distance dual phase-attenuation retrieval

1. Direct Filtered Back Projection (FBP) of therecorded phase-contrast data

2. FBP after phase retrieval obtained from multipledistance acquisition

3. FBP after attenuation retrieval (2) from a single dis-tance acquisition using phase-attenuation duality princi-ple

4. FBP after attenuation retrieval (4) from multipledistance acquisition using an extended phase-attenuationduality principle.

The first approach does not require a solution of thephase retrieval problem as such and thus is computation-ally simple. It provides a radiometric image of the ob-ject based on a single sinogram recorded in the phase-contrast regime (Figure 6a). As it is shown in Figure 6a,the cementite microstructure is apparent and can be anal-ysed using this method. The main disadvantage of thismethod is the qualitative nature of the reconstructed im-age. In order to obtain a quantitative reconstruction thatcorresponds to the object’s density or refraction indexone needs to use one of the phase retrieval algorithms.

The phase retrieval algorithm can be based on themixed TIE-CTF formalism as described by (1). The FBPreconstruction after the phase retrieval (1) is shown inFigure 6b. Unfortunately, this method does not allowreconstruction of the low frequency components of thephase image. Hence, the information about the averagevalues of phase is lost and the reconstructed image re-mains largely qualitative.

(a) (b)

Figure 7. Results of the dual phase-attenaution retrieval ap-plied to one slice only (a) (CTF is inverted in one dimention inthe 2D sinogram) or to the whole volume (b) (CTF is invertedin two dimentions in the 3D sinogram).

Since the sample is known to consist of only two ho-mogeneous materials (cementite and ferrite) with knownrefraction indexes, we can calculate the ratio between theattenuation and phase effects around cementite-ferrite in-terfaces using (3) and apply the phase-attenuation du-ality formula (2). This method allows reconstructionof the attenuation image of the object using a singlephase-contrast sinogram (Figure 6c). However, as it wasdescribed in the Section V, the problem of phase re-trieval remains ill-posed around the spatial frequenciesfor which the phase effect is zero or undetectable. Forthe sinogram recorded at 208 mm distance from the ob-ject this frequency corresponds to a periodic distortionsignal with a period of approximately 3µm. A wave-likeartefact that originates from that effect can be observedin Figure 6c.

In order to reconstruct the attenuation image of the ob-ject over the full range of spatial frequencies a modifica-tion to the phase-attenuation duality approach describedin Section V can be conducted. As it follows from (4),the attenuation image of the object can be calculated us-ing multiple sinograms recorded at different object-to-detector distances. Figure 6d shows the result of attenua-tion retrieval based on three sinograms recorded at 3mm,68mm and 208 mm behind the object. It can be observedthat the periodic artefacts that are present in the single-distance approach vanish when a multiple-distance ap-proach is used.

The resolution of the various PCT reconstruction re-sults was estimated from the amount of blur around thecementite-ferrite boundaries (Figure 8). The standard de-viation of the Gaussian blur is approximately equal to1 pixel (0.75 microns). The blur most likely occurs dueto resolution limitations of the beamline and uncorrectedmisalignments in the sinograms. The standard deviationof the noise in the reconstructed volume is approximately15% of the intensity contrast between cementite andsteel.

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Figure 8. The results of the PCT reconstructions (red chan-nel) overlayed with the optical images (green channel) of thecorresponding section of the specimen.

RESULTS OF THE DCTRECONSTRUCTION

The data recorded in diffraction-contrast mode was pro-cessed using the grain tracking algorithm proposed byLudwig [5]. The algorithm is based on the assumptionthat the investigated material is composed of crystallinegrains that will diffract radiation according to the Bragglaw depending on their crystalline orientation. Each grainis assumed to be an ideal single crystal that produces adiffraction spot that corresponds to the geometrical pro-jection of the grain in that direction. This method permitsvolumetric reconstruction of the granular structure of thespecimen based on the full field images of the diffractionpatterns acquired in 360º view range. Unfortunately, themethod is unable to reconstruct information about the lo-cal orientation gradients inside single grains. As a resultof deformations inside individual grains such gradientsare present in the specimen under study causing the re-construction approach to become inaccurate.

The result of DCT reconstruction based on the graintracking approach [5] is shown in Figure 9. Differentgrains reconstructed from DCT data are colour-codedand overlaid with the images obtained from opticalmicroscopy. Comparison with the optical data clearlydemonstrates that the current DCT approach fails insidethe regions that most likely have a significant local gra-dient of crystalline orientation. These erroneous regionsseem to occur around the grain boundaries and in thoseparts of the volume where many large cementite grainsare found.

From Figure 9 it can be estimated that the recon-structed grain volumes cover approximately 80% of theactual ferrite grain volume. The grain boundaries are de-termined within 15-20 microns accuracy. A convention-ally used morphological dilation algorithm can be ap-plied to the reconstructed DCT data to ’fill-in’ the gaps,does not improve the image quality significantly as theregions where the reconstruction fails are to large.

Figure 9. The results of the DCT grain tracking (color labels)overlayed with the optical images (gray) of the correspondingsection of the specimen.

CONCLUSIONS

The values of the signal-to-noise ratio and resolution es-timated for the PCT reconstructions allow us to concludethat the demonstrated imaging approach will be suitablefor the detection of the cementite structures down to amicrometer size. We expect that in the further experi-ments it will be possible to acquire data on the kineticsof the nucleation and individual cementite grain growthin steel exposed to the thermal treatment.

However, the grain tracking approach used to recon-struct the DCT data was not found to be accurate enoughfor the investigation of the cementite-ferrite microstruc-ture formation. The regions of ’undetected’ crystallineorientations of ferrite are too large to determine the mu-tual orientation of the cementite grains against ferritegrains. Thus, the problem of sufficiently quick and accu-rate detection method for the ferrite granular structure inthe presence of cementite remains unsolved. Most likely,the accuracy required for the purpose of our research canbe achieved by using 3DXRD approach [11].

REFERENCES

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