ISSN 1027�4510, Journal of Surface Investigation. X�ray, Synchrotron and Neutron Techniques, 2014, Vol. 8, No. 2, pp. 374–379. © Pleiades Publishing, Ltd., 2014.Original Russian Text © A.N. Artemiev, A.D. Belyaev, N.A. Artemiev, A.A. Demkiv, A.G. Maevsky, O.Yu. Gorobtsov, B.F. Kirillov, G.A. Knyazev, S.I. Tyutyunnikov, V.N. Shalyapin,2014, published in Poverkhnost’. Rentgenovskie, Sinkhrotronnye i Neitronnye Issledovaniya, 2014, No. 4, pp. 76–82.

1

374

INTRODUCTION

The Debye–Scherrer method has been well knownfor a long time. With the use of X�rays it received thename of the Hull–Debye–Sñherrer method [1]. It isknown that the luminosity of the method is quite lowand, therefore, it is reasonable to use the method in syn�chrotron radiation (SR) sources. The most importantfeature here is the possibility of accurately adjusting theradiation energy in a wide range. This allows one to comeclose to backscattering (close to the angle 2θ = 180°), asclose as is permissible by the geometry of the experiment,which multiply increases the method’s sensitivity. Thespecific features of the method using SR are estimated inthe first part of this work [2].

Publication [3] can be considered the closest to ourstudy, where a technique was implemented at a syn�chrotron�radiation source and a diffractometer wasdesigned for Debye–Scherrer diffraction in the back�scattering geometry with an imaging plate. However,the range of diffraction angles in this diffractometerwas limited to 160°. It is important to emphasize thatthe advantages of the method, described in our publi�cations, start to manifest themselves sufficientlyclearly only at angles higher than 175°.

Let us note that a technique for backscatteringfrom single�crystal sampls has been developed and isused to provide ultrahigh resolution with respect toenergy [4]. The relative change in the lattice constantis accurately determined using single�crystal samplesin the backscattering geometry.

EQUIPMENT

A method of Debye–Sñherrer diffraction in thebackscattering geometry has been developed at the

SIBIR’�2 large storage ring of the Kurchatov Synchro�tron Radiation Source [6]. EXAFS�D spectrometerequipment is used in part in the setup described [7].

Figure 1 schematically shows the experimentalsetup. A “white"�light synchrotron beam from a bend�ing magnet propagates through slits along the 6.2 SRchannel and is incident on a plane crystal, i.e., amonochromator with a horizontal dispersion plane.The monochromatized synchrotron beam is incidenton the sample under study. A detector which recordsdiffraction patterns and a sample supporti aremounted onto the swing support of the EXAFS�Dspectrometer.

Figure 2 shows a picture of the setup for recording theX�ray diffraction (XRD) patterns by the method ofDebye–Sñherrer diffraction in the backscattering geom�etry. The distance from the point of emission to themonochromator crystal is 22 m. A Si (111) single crystalplaced inside a vacuum�helium hood was used as themonochromator. The monochromatized synchrotronbeam propagates a little higher than the screen, whichrecords the backscattering pattern, and is incident on thesample under study, which is fixed to a separate support.Beam transmission over the recording screen ensures itsminimal ambient illumination. There is no trace of thedirect beam on the screen in this geometry. The corre�sponding center of the diffraction pattern is determinedby a fitting method using a program developed anddescribed below.

At first glance, it is expedient to use a two�dimen�sional detector on the basis of a two�dimensional elec�tronic matrix and luminophor as the detector. Such adetector is extremely convenient and allows on�linedigital diffraction patterns to be obtained. Unfortu�nately, the design features of such detectors do not allow

Debye–Scherrer Diffraction in the Backscattering Geometry at the Kurchatov Synchrotron Radiation Source:

Part 2. Equipment, Pilot Experiments, and Data ProcessingA. N. Artemieva, A. D. Belyaeva, N. A. Artemievb, A. A. Demkiva, A. G. Maevskya, O. Yu. Gorobtsova,

B. F. Kirillova, G. A. Knyazeva, S. I. Tyutyunnikovc, and V. N. Shalyapinc

aNational Research Center Kurchatov Institute, Moscow, RussiabAdvanced Light Source, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, CA 94720, USA

cJoint Institute of Nuclear Research, Dubna, RussiaReceived March 4, 2013

Abstract—Equipment is constructed, a technique is developed, and experimental results on Debye–Scherrerdiffraction in the backscattering geometry are obtained. A special program for diffraction ring processing isdeveloped. The prospects for use of this technique for materials science purposes are discussed.

DOI: 10.1134/S1027451014010054

JOURNAL OF SURFACE INVESTIGATION. X�RAY, SYNCHROTRON AND NEUTRON TECHNIQUES Vol. 8 No. 2 2014

DEBYE–SCHERRER DIFFRACTION IN THE BACKSCATTERING GEOMETRY 375

their sensitive region to be moved close to the primaryphoton beam, which is incident on the sample. This, inturn, does not allow scattering angles rather close to2θ = 180° to be used. Therefore, we use commercialImaging Plates (IPs) [8] as the recording screen. IPs areplastic plates 200 × 250 mm in size covered with a layerof luminophor, the main feature of which is its ability to“remember” X�ray photons that are incident on it andretain the corresponding latent X�ray image for severalhours. Let us note that the decay of a latent X�ray imagehas a multiexponential character with a decay time con�stant of about 0.7, 18, and 520 h. This can be importantfor the case when it is necessary to compare quantita�tively the intensities of diffraction rings recorded in dif�ferent experiments. In the case under study, when thesizes of diffraction rings are compared, this circum�stance is not important.

After the end of exposure, the plate is placed insidea scanner that reads the latent X�ray image. After scan�ning, the remnants of the X�ray images are erased byvisible light, and the plate is then ready to record thenext X�ray image. The number of possible cycles ofX�ray image overwriting on the plate is, in practice,restricted by plastic loss during plate transference.Thus, an IP is almost an exact analog of an X�ray filmfrom the functional point of view. Let us note impor�tant differences. The process of image recording,scanning, and erasing from an IP is totally dry; there�fore, small variations in the X�ray size during swellingwhen treating in solution and drying are absent; theyare important for the problem considered. Thesechanges in the X�ray film have a 3D character and candetermine the boundaries of method application in thecase of a “wet” photoprocess. Another differencebetween an IP and a common X�ray film is its low spa�tial resolution, i.e., the size of an IP pixel scanned is25–100 μm for different types of scanners. Neverthe�less, the statistical character of the measurement andthe corresponding mathematical processing allows

sufficiently high accuracy in determining the diffrac�tion�ring center and radius.

IPs are intended for medical purposes; their stan�dard cassettes do not satisfy our requirements. In par�ticular, it is impossible to fix these plates relative to thesample under study over and over again with therequired repeatability. To achieve high repeatability forthe sample–screen distance, the following equipmenthas been designed. An IP is pressed by atmosphericpressure to the flat surface of the support�suction cup;for this purpose, there is an evacuated cavity inside thesupport. About 500 holes 1 mm in diameter are drilledinto the working surface of the support, which are cov�ered by the IP.

1

2

34

56

7

Fig. 1. Layout of the setup for recording XRD patterns by the Hull–Debye–Sñherrer method in backscattering geometry:“white” synchrotron beam (1), slits (2), crystal�monochromator (3), monochromatized synchrotron beam (4), sample understudy (5), diffracted radiation cone (6), and recording screen (7).

47

35

6

1

2

Fig. 2. Setup for recording XRD patterns by the Hull–Debye–Sñherrer method in backscattering geometry:channel for SR output (1), vacuum�helium hood of themonochromator (2), recording screen (3), support for thesample under study (4), support�suction cup of the recordingscreen (5), hose for evacuating the suction cup of the record�ing screen (6), and air�scattered radiation screen (7).

376

JOURNAL OF SURFACE INVESTIGATION. X�RAY, SYNCHROTRON AND NEUTRON TECHNIQUES Vol. 8 No. 2 2014

ARTEMIEV et al.

Using the screen 5, the IP is screened from the air�scattered X�ray photons of a direct beam. This is veryimportant when recording low�intensity backscatter�ing diffraction patterns. The sample mounting unit isdesigned so that the sample holder fixed to this unitallows the front surface of each sample under study to

be positioned in a certain basal plane again and againwith a repeatability of no worse than 10 μm. Weshowed in [2] that this repeatability allows repeatabil�ity of the diffraction�ring size of no worse than 1 μm,which is quite acceptable for the method considered.

The scattering intensity in the backscatteringgeometry is low. Therefore, even weak isotropic fluo�rescence of a sample can significantly contribute to thebackground image. To decrease this background, wemount corresponding filters directly in front of the IP.

PILOT EXPERIMENTS IN THE SR BACKSCATTERING GEOMETRY USING CHROME�NICKEL STEEL SAMPLES

During the experiments the typical parameters ofthe SR source were as follows: the electron energy inthe storage was 2.5 GeV, and the electron current was50–100 mA. The monochromator was adjusted to anenergy of ε = 9.696 keV. The exposure below is givenin mA min, where mA is the current of accumulatedelectrons.

Figure 3a exemplifies the diffraction pattern of achrome�nickel steel sample recorded in the backscat�tering geometry. The size of the diffraction ring corre�sponds to the Fe(332) reflection accurate to severalpercent. The exposure is 2350 mA min. The size of thesynchrotron beam on the sample is 1.5 × 1.5 mm; thesample–screen distance is 300 mm. To absorb the Fefluorescence emission, an aluminum foil filter 100 μmin depth is placed between the sample and the screen.The size of an IP pixel is 100 μm. The light verticalstripe on the left shows the IP part not covered by thealuminum filter. The rectangle in the center of the pat�tern shows the boundaries within which averaging hasbeen carried out to obtain a profile of the diffractionring cross section (Fig. 3b).

PROCESSING OF DIFFRACTION IMAGES

The typical software for processing Debye–Sñher�rer diffraction rings, e.g., FIT2d [9], operates in sev�eral ways. In the first variant, the center of the diffrac�tion pattern should be experimentally recorded in it,which is a direct beam print. An operator detects thecenter of the direct beam image manually. Evidently,manual detection of the diffraction�pattern centercannot be more accurate than 10–20% of the width ofthe diffraction ring profile.

The second variant assumes the manual indicationof several points on the XRD pattern ring. Then a pro�gram detects the XRD pattern center and the ringradius using the above points. It is essential that thecoordinates of the XRD pattern center found directlydepend on the points indicated by the operator. Thus,detection of the XRD pattern center and, hence, thering radius is evidently subjective, and the detectionaccuracy is low. One can state that the accuracy is nobetter than several percent of the width of the diffrac�

2500

2000

1500

1000

500

0

160012008004000

600

550

500

450

400

4003002001000

2000

Rows

Columns

I, rel. units

Pixels

(a)

(b)

Fig. 3. (a) Diffraction pattern of chrome�nickel steel mea�sured in backscattering geometry with an energy of9.659 keV: 332 reflection; the exposure is 2350 mA min; thesize of the synchrotron beam on the sample is 1.5 × 1.5 mm;the IP–sample distance is 300 mm; the fluorescence�emission filter width is 100 µm; the IP pixel size is 100 µm.The light vertical stripe on the left shows the part of the IPnot covered by the aluminum filter. The elongated rectan�gle at the center of the pattern shows the boundaries withinwhich averaging is carried out to get the diffraction�ringprofile. (b) Profile of the experimental diffraction ringconstructed with the use of the FIT2d program.

JOURNAL OF SURFACE INVESTIGATION. X�RAY, SYNCHROTRON AND NEUTRON TECHNIQUES Vol. 8 No. 2 2014

DEBYE–SCHERRER DIFFRACTION IN THE BACKSCATTERING GEOMETRY 377

tion ring profile. The reasons for this are easily under�standable. The FIT2d program was developed forphase analysis via the processing of Debye–Sñherrerdiffraction rings obtained in the forward geometry.The accuracy of determining the diffraction�ringradius in the FIT2d program is quite sufficient forsolving this problem. However, the accuracy is insuffi�cient for the problem of measuring small differences ininterplane distances in the samples compared which isconsidered in this work.

We have developed a special program that allows asignificant increase in the measurement accuracy ofdiffraction ring radii. The idea consists in the statisti�cal processing of all pixels that form the diffractionring. Let us consider the radial cross section of the dif�fraction ring as the first step. This cross section is adome�like curve with a clearly pronounced peakspaced a little way from the diffraction�pattern center.The distance from the peak to the center is the sought�for diffraction�ring radius. At first glance, it seems thatthe narrower the peak, the more accurate one candetect its center of gravity and, correspondingly, thedistance to the diffraction�ring center. However, oneshould take into account the following. The number ofpixels that participate in formation of the image of thering under consideration increases with the width ofthe diffraction�ring profile. If the characteristic dif�fraction�ring radius is 20 mm and the pixel size is50 μm, the total number of pixels processed is 106. Inour case, the numerical value of a normally exposedpixel, obtained using a scanner, is 104 counts. Thus,the total number of events recorded is about 1010.Thus, all the parameters considered have statisticalspreads. However, such a large number of events pro�vides for high statistical accuracy.

In our program, an operator manually determinesthe approximate coordinates of several (at least three)points on a visible diffraction ring. Then the programautomatically, but again approximately, determinesthe coordinates of the diffraction�ring center using acircle model. These values are evidently subjective andused only as initial values for subsequent fitting. It isassumed that the diffraction�ring profile is Gaussian.Autofitting is carried out by the circle model, with theuse of values of all pixels in the ring with a width equalto the doubled total width at half maximum of the dif�fraction�ring profile. The following parameters are fit�ted: the coordinates of the diffraction�pattern center(two parameters), the ring radius (one parameter), theheight and width of the diffraction peak (two parame�ters), and the height and slope of the background(two parameters). In total, seven parameters are fitted.The fitting results are almost independent of thechoice of the initial parameters. The processing timeof a diffraction pattern is about 2 min when using acomputer with a clock frequency of 2GHz.

To test the program, the calculation was carried outmany times using one array of initial experimentaldata but different initial values of the parameters fitted.

The spread of the fitted diffraction�ring radius did notexceed several tenths of a pixel, which approximatelycorresponds to several tens of microns. This value ofstatistic uncertainty should be compared withexpected shifts of the diffraction�ring profile with arelative change in the interplane distance Δd/d = 10–5

calculated in [2]. This shift is higher than 100 microns.

550

500

450

400

4003002001000

I, rel. units

Pixels

2500

2000

1500

1000

500

0160012008004000 2000

Rows

Columns

350

300

250

200

150

0

(a)

(b)

Fig. 4. Processing program developed by the authors:(a) the white field is the region of fitting the diffraction�ring model to experimental data from Fig. 3a; the elon�gated rectangle at the center shows boundaries withinwhich averaging was carried out to get the profile of the fit�ted model diffraction ring. (b) Profile of the radial intensitydistribution of the model diffraction pattern fitted to theexperimental one from Fig. 3a; the profile is constructedusing the FIT2d program.

378

JOURNAL OF SURFACE INVESTIGATION. X�RAY, SYNCHROTRON AND NEUTRON TECHNIQUES Vol. 8 No. 2 2014

ARTEMIEV et al.

Thus, the experimental technique and processing pro�gram developed are adequate for the problem stated.

The work of the FIT2d program was similarlytested using the same initial array. The statistical errorwas estimated in repeated program runs to be higherthan 10 pixels.

Figure 4a shows the region of fitting of the abovedescribed diffraction�ring model to the experimentaldata from Fig. 3a. The rectangle in the middle of thepattern shows the boundaries within which the averag�ing was carried out to get the profile of the fitted modeldiffraction ring. Figure 4b shows the profile of radialdistribution of the intensity of the model diffractionpattern fitted to the experimental one shown inFig. 3a. The profile was constructed using the FIT2dprogram. Figure 5 shows the interface of the programdeveloped for processing Debye–Scherrer rings in thebackscattering geometry.

DISCUSSION OF RESULTS

In the above model for diffraction�pattern process�ing, we assumed as the first approximation that the dif�fraction pattern has the form of regular circle and theintensity is uniformly distributed over the azimuthalangle. One can assume that changes in the sample lat�tice constant can be measured within this model dur�ing sample loading (e.g., expansion) under the action

of a synchrotron beam. These experiments can alsoprovide for data on Young’s modulus of the material.

Real diffraction patterns are more complex thanthe above model. The following factors can be men�tioned. The recording screen deviates from the normalto the primary beam, which turns the diffraction ringfrom a circle to an ellipse. Polarization of the synchro�tron radiation causes inhomogeneous azimuthal dis�tribution of the ring intensity. The sample structurecauses the same. When comparing two samples, thefirst two factors can be similar and relatively easy takeninto account. As for the texture of different samples,the situation can be more difficult.

It seems at first glance that the huge number ofevents recorded for an IP (1010) contains a large“stock” of statistical accuracy. We see the followingways for further significant improvement of the pro�cessing. First, it is necessary to switch to the recordingand processing of a complete closed diffraction ring,not only because of information doubling, but alsobecause the fitting of half a ring requires the formula�tion of boundary conditions for the processed array,which contains additional, not quite impartial aspects.There is another important point, i.e., a need to (soft�ware) erase bad image areas.

We also foresee some difficulties in furtherincreases in the accuracy and repeatability of theresults. It is probable that changes caused by the tem�

Fig. 5. Interface of the program for Debye–Sñherrer ring processing in the backscattering geometry.

JOURNAL OF SURFACE INVESTIGATION. X�RAY, SYNCHROTRON AND NEUTRON TECHNIQUES Vol. 8 No. 2 2014

DEBYE–SCHERRER DIFFRACTION IN THE BACKSCATTERING GEOMETRY 379

perature difference during exposure and recording andinevitable instability in scanner operation determinethe practical limits of the method accuracy. The influ�ence of different factors limiting the method accuracyis studied and will be considered in subsequent studies.

The authors hope that the method developed canbe used in investigations of materials exposed to differ�ent factors, such as temperature, radiation, alloying,residual stresses, and so on.

ACKNOWLEDGMENTS

The authors are grateful to V.N. Yal’tsev for his helpin this work and useful discussions.

The work was financially supported by the Ministryof Science and Education of the Russian Federationwithin the Federal Targeted Program “Investigationsand Projects in Priority Development Fields of theRussian Science and Technology Sector for 2007–2013 (state contract no. 16.552.11.7055) using equip�ment of the Kurchatov Center for Synchrotron Radi�ation and Nanotechnology.

REFERENCES

1. www.google.ru/search?q=Hull%2FDebye+Scherrer+&ie=utf�8&oe=utf�8&aq=t&rls=org.mozilla:ru:official&client=firefox�a

2. A. N. Artemiev, A. D. Belyaev, N. A. Artemiev,A. A. Demkiv, A. G. Maevskii, O. Yu. Gorobtsov,B. F. Kirillov, S. I. Tyutyunnikov, and V. N. Shalyapin,Poverkhnost’ (2013, in press).

3. R. F. Garrett, D. J. Cookson, G. J. Foran, T. M. Sabine,B. J. Kennedy, and S. W. Wilkins, Rev. Sci. Instrum. 66,1351 (1995).

4. S. Kikuta, Y. Imai, T. Iizuka, Y. Yoda, X.�W. Zhang, andK. Hirano, J. Synchrotr. Rad. 5, 670 (1998).

5. K. Munakata and A. Okazaki, Acta Crystallogr. A 60 33(2004).

6. A. N. Artemiev, A. A. Snigirev, V. N. Korchuganov,A. G. Valentinov, V. V. Kvardakov, N. A. Artemiev,A. V. Zabelin, V. A. Rezvov, A. G. Maevskii,O. V. Naida, and A. A. Dyatlov, J. Surf. Invest. X�ray,Synchrotr. Neutron Tech. 1, 528 (2007).

7. S. I. Tyutyunnikov, V. N. Shalyapin, V. L. Aksenov,A. N. Artemiev, A. V. Zabelin, B. F. Kirillov,M. V. Koval’chuk, A. G. Maevskii, A. D. Belyaev,A. V. Porokhova, and V. A. Rezvov, Phys. Part. Nucl.Lett. 6, 483 (2009).

8. Y. Amemiya, J. Synchrotr. Rad. 2, 13 (1995).

9. www.esrf.eu/computing/scientific/FIT2D/fit2d_abstract.html

Translated by O. Ponomareva

1

1

SPELL: 1. ok