RECONSTRUCTION OF ORIGINAL INTENSITY FROM COVERED SAMPLES

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1 RECONSTRUCTION OF ORIGINAL INTENSITY FROM COVERED SAMPLES 163 R.I. Barabash, T.R. Watkins, R.A. Meisner, T.D. Burchell, T.M. Rosseel Oak Ridge National Laboratory, Oak Ridge TN 37831, USA ABSTRACT The characterization of the surface of activated samples with x-rays often necessitates a thin film covering for containment to eliminate any potential for contamination of equipment. While candidate covering films appear visually transparent, they are not necessarily x-ray transparent. Each film material has unique beam attenuation. Further amorphous peaks can be superimposed onto those from the sample. To reconstruct the scattering of only the underlying activated sample alone, the effect of x-ray attenuation and signal due to the film need to be removed from that of the sample. This requires the calculation of unique attenuation parameters for the covering film. The development of a reconstruction procedure for a contained/covered samples is described for -2 scans and applied to pole figures. Key words: diffraction, pole figures, absorption, attenuation, reconstruction

2 This document was presented at the Denver X-ray Conference (DXC) on Applications of X-ray Analysis. Sponsored by the International Centre for Diffraction Data (ICDD). This document is provided by ICDD in cooperation with the authors and presenters of the DXC for the express purpose of educating the scientific community. All copyrights for the document are retained by ICDD. Usage is restricted for the purposes of education and scientific research. DXC Website ICDD Website -

3 INTRODUCTION 164 Diffraction measurements of activated samples often require a sealed container for the sample or an encapsulating covering around the sample to avoid particulate contamination of the instruments and people. The problem with such diffraction measurements is that the intensity of the sample is inhomogeneously attenuated by the covering film due to the changing angle of x- ray incidence and that the film often contributes to the diffraction pattern. To reconstruct the intensity of the contained activated sample alone, the contribution from the film should be calculated, and the sample diffraction intensity should be recovered from the total or observed intensity. A reconstruction procedure developed for covered samples is described below. EXPERIMENTAL A. MEASUREMENT METHODS AND DATA PROCESSING Measurements were performed in Bragg-Brentano symmetric geometry. Continuous - 2 scans were collected from 5 to 90 2 at a rate of 0.5 /min. Pole figures were also collected with continuous azimuthal/phi,, rotation of 100 /min, recorded at 5 intervals and at 5 chi tilts from 0 to 70 (Fig. 1). All scans were taken on a 4-axis ( ) Scintag PTS goniometer (Krause and Haase, 1986) using CoK radiation ( = Å) at 40 kv, 36 ma and a Scintag liquid N 2 -cooled Ge detector. The incident beam was collimated using 1.7 Soller slits and a 1.5mm diameter pinhole collimator, and the diffracted beam was collimated with a 0.25 radial divergence limiting (RDL) Soller slits. Specimen alignment was accomplished using a dial gauge probe accurate to ±5 µm.

4 165 Figure 1. Sketch of the goniometer geometry and definitions of chi and phi angles. B. ENCAPSULATING FILMS Four different encapsulating films were examined: mylar (1), tape plus kapton (2), polyethylenelinear low density (LLDPE; re-sealable zipper storage bag) (3) or kapton (4). A comparison of diffraction patterns obtained from the plain polycrystalline silicon standard disk uncovered and covered by each one of the above materials is shown in Fig. 2. A visible difference is apparent in both background and attenuation of the silicon peaks from each film. For three of the films, additional peaks appear. Consequently, kapton was chosen for further evaluation due to the smaller change in background, minimal attenuation of the silicon peaks and no additional diffraction peaks.

5 166 Figure 2. XRD patterns of a standard silicon disk covered with mylar (5), Tape plus kapton (4), LLDPE (re-sealable zipper storage bag) (3), kapton film (2) along with the bare or uncovered polycrystalline silicon standard disk (1). C. SAMPLES Graphite samples for the advanced gas-cooled reactor moderator were measured with and without a kapton film. The kapton film thickness was ~ 30µm. RESULTS AND DISCUSSION A. MAIN EQUATIONS To recover the intensity, I, diffracted from the covered sample, the contribution of the kapton film is calculated. A sketch of the beam path of the diffracted radiation (Fig. 3) illustrates that the

6 To 167 be clear, since the angle of incidence changes with both -2 scans and pole figures, the intensity of the sample is inhomogeneously attenuated by the covering film. Attenuation of the film can be calculated using the attenuation law (Cowley, 1995; Warren, 1969):, (1) where is the intensity of the incident beam, µ is the mass absorption coefficient of the kapton film, and l (or L as in Fig. 3) is the total length of the beam path within the kapton film. This equation can be re-written as follows:, (2) where is incident angle, an X is a film thickness (Fig. 3). For measuring single crystals or for texture measurements, the dependence of on and was taken into account as follows:, (3) where = 0 when the surface normal is in the diffraction plane of the goniometer. The dependence of on and is further illustrated in Table I. B. CALCULATION OF THE ABSORPTION COEFFICIENT OF THE FILM Absorption coefficient can be exactly evaluated using the following equation (Brennan and Cowan, 1992; Chantler, 1995; Elam et al., 2002; Henke et al., 1993; Hubbell, 1982): =, (4)

7 168 Figure 3. Schematic of the X-ray paths diffracted from the graphite sample covered with kapton film. Table I. Dependence of alpha, the angle of incidence, on omega and chi. omega ( ) chi ( ) alpha ( ) omega ( ) chi ( ) alpha ( )

8 where,, and are is the mass density of the material as a whole, the mass fraction, and 169 mass absorption coefficient of the i th element, respectively. The chemical formula of kapton is C 22 H 10 N 2 O 5. The following parameters were chosen for the elemental composition of the film (see Chantler, 1995; Henke et al., 1993; McMaster et al., 1969): O =2.106; C =0.881; N =1.386; H =0.397; =80/M; =264/M; =28/M; =10/M; and M=382 g/mol, the molecular weight of the compound. For example, with these parameters the absorption coefficient for kapton is equal to m -1 at 14 kev for the synchrotron radiation. Absorption further depends on the radiation energy or wavelength and on the incident angle of the beam relative to the sample surface, (Eq. 2 and Fig. 3). Mass absorption coefficient is equal to , and m -1 for Cu, Co and Cr k radiations, respectively. The comparison of the intensity attenuation of kapton, namely the ratio between the diffracted intensity from the covered sample, I, to the intensity of the sample without cover,,, is shown in Fig. 4 for three different wavelengths of incident radiation from Cu, Co, Cr targets in a broad range of incident angles. C. APPLICATION OF RECONSTRUCTION - s (Fig. 5) and pole figures. The - blue and green from the covered and uncovered graphite samples correspondingly (Fig. 5). The reconstructed original intensity for covered sample is shown in red color. Complete diffraction pattern is shown in the Fig.5a. Dashed rectangles mark the part of the pattern around reflection (002) (Fig.5b) and around (100),

9 170 Figure 4. Comparison of attenuation of kapton for different wavelengths as a function of incidence angle.

10 Figure 5. (a) Experimentally measured ߠ ʹߠ scan for covered (blue) and uncovered (green) graphite samples; (b) Enlarged (002) reflection region; (c) Enlarged region of the scan with (100), (101) and (004) reflections. 1- Experimentally measured ߠ ʹߠ scan with cover (blue); 2for uncovered (green) graphite sample; 3- reconstructed from covered sample (red). 171

11 (101) and (004) reflections (Fig. 5b). The attenuation is larger for small incidence angles, =, as 172 it increases with the length of the X-ray beam path in the film. At the same time, the maxima positions remain the same. To reconstruct a pole figure, the absorption of the intensity due to the film was first calculated. The ratio for the pole figure is shown in Fig. 6, which demonstrates that the attenuation over the pole figure differs for large and small angles of incidence. Hence, the pole figure will be distorted by the kapton film. An example of the reconstruction of the experimental pole figure is shown in Fig. 7. Here, the sample was measured with and without kapton film and compared to the reconstructed intensity. The numbers near the isointensity contours (shown by thin black lines) mark relative values of the intensity. It is visible that kapton film reduces the intensity by almost twice for certain contours. After reconstruction the intensity values are recovered (Compare Figs. 7 b and c). SUMMARY A reconstruction formula was developed to determine the intensities of both -2 scans and pole figures by accounting for a semi-transparent x-ray covering. Specifically, absorption of diffracted radiation from a kapton film covering a graphite sample was removed. The covering was needed to prevent contamination from an activated sample. The reconstruction depends upon the thickness of the film, wavelength and incidence angle. While the reconstruction does not change the maximum position, it does change the background and the relative intensities with the shallow angles of incidence needing the most correction.

12 173 Figure 6. A pole figure showing the calculated attenuation of the (002) graphite reflec intensity by a 30 m thick kapton film as a function of the angle of incidence. Figure 7. Comparison of the (002) graphite pole figures: intensity diffracted from the graphite sample without kapton film (a), covered with kapton film (b), and (b) reconstructed using experimental intensity from the covered sample and the approach in section III (removing the influence of kapton attenuation) (c).

13 174 ACKNOWLEDGEMENT This research was performed at the Oak Ridge National Laboratory (ORNL) and sponsored by EDF-Energy Nuclear Generation, Ltd under the Work-for-Others Program, project number NFE , with the U.S. Department of Energy under contract with UT-Battelle, LLC. REFERENCES Brennan, S. and Cowan, P. L. (1992). of programs for calculating x-ray absorption, reflection, and diffraction performance for a variety of materials at arbitrary wavelengths, Rev. Sci. Instrum. 63, Chantler, C. T. (1995). Theoretical form factor, attenuation, and scattering tabulation for Z=1-92 from E=1-1- ev to E= MeV, J. Phys. Chem. Ref. Data 24, Cowley J. M. (1995). Diffraction Physics (Elsevier, Amsterdam), 3 rd ed. Elam, W. T., Ravel, B., and Sieber, J. R. (2002). -ray Radiat. Phys. Chem. 63, Henke, B. L., Gullikson, E. M., and Davis, J. C. (1993). X-ray interactions photoabsorption, scattering, transmission and reflection at E=50-30,000 ev, Z=1-92, Atomic Data and Nuclear Data Tables 54, Hubbell, J. H. (1982). Photon Mass Attenuation and Energy-Absorption Coefficients from 1 kev to 20 MeV, Int. J. Appl. Radiat. Isot. 33,

14 Krause, H. and Haase, A. (1986). X-ray diffraction system PTS for powder, texture and stress 175 analysis, in Experimental Techniques of Texture Analysis, edited by H. J. Bunge (DGM ) pp McMaster, W. H., Kerr Del Grande, N., Mallett, J. H., and Hubbell, J. H. (1969). Compilation of X-ray Cross Sections Section IV (Report UCRL Sec. IV). Lawrence Radiation Laboratory, University of California, Livermore. Warren, B. E. (1969). X-ray Diffraction (Addison-Wesley, Reading, MA).

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