- Email: [email protected]
A tunable monochromatic X-ray source for metrological studies in the 1–20 keV energy range: application to the measurement of attenuation coefficients
ARTICLE IN PRESS
Applied Radiation and Isotopes 60 (2004) 159–165
A tunable monochromatic X-ray source for metrological studies in the 1–20 keV energy range: application to the measurement of attenuation coefficients Marie-Christine Le! py*, Laurent Ferreux, Johann Plagnard BNM/Laboratoire National Henri Becquerel, CEA Saclay, Gif-Sur-Yvette Cedex F-91191, France
Abstract A tunable monochromatic X-ray source operating in the 1–20 keV energy range is described. An X-ray tube provides initial photons. A dispersive crystal performs the energy selection, according to Bragg’s law. An X-ray detector is connected to the monochromator fixed exit. This setup can be used for metrological studies. A first application consists in measuring attenuation coefficients in the 4–10 keV energy range. Results for aluminum and copper are given, with average relative uncertainties (1s) of 1% and 3% respectively. r 2003 Elsevier Ltd. All rights reserved. Keywords: X-ray source; Monochromator; Detector calibration; Attenuation coefficient; Aluminum; Copper
1. Introduction In the field of X-ray spectrometry, efficiency calibration of semi-conductor detectors is traditionally performed using standard radionuclides. However, in the low-energy range (Eo5 keV) difficulties in performing accurate calibration dramatically increase, due to: * * *
uncertainty on the emission intensities; self-absorption in the source; limited discrete photon emissions, in terms of both energy and intensity.
The weaker the energy, the more difficult the task. To avoid these constraints linked to the use of radionuclides, relative efficiency calibration of X-ray spectrometers have been successfully conducted using monochromatized synchrotron radiation and a proportional counter as a reference (L!epy et al., 1997, 2000). However, the synchrotron facility (LURE, Orsay, France) previously used will close in late 2003. To continue to perform such studies and to develop new
ones, it has been decided to install a tunable monochromatic X-ray source at the Laboratoire National Henri Becquerel (BNM-LNHB). The SOLEX (Source Of Low-Energy X-rays) source has been studied by the Laboratoire de Chimie Physique Mati"ere et Rayonnement (Universit!e Pierre et Marie Curie, Paris, France). This facility has been designed to provide monochromatic radiation in the 1–20 keV energy range with a stable flux of some hundreds of photons per second at the output. Due to the wide range of detectors to be characterized (semi-conductor detectors, cryogenic detectors, photodiodes, etc.), it was decided to preserve a constant output direction to keep the detector under study in the same position. The source characteristics and performance levels are described, as well as the first experimental development using SOLEX, relating to the determination of attenuation coefficients; the first measurements were conducted with aluminum and copper in the 4–10 keV energy range.
2. Experimental set-up *Corresponding author. Tel.: +33-1-69-08-2448; fax: +33-169-08-2619. E-mail address: [email protected] (M.C. L!epy).
The tunable monochromatic X-ray source comprises three main components, an X-ray tube, a dispersive
0969-8043/$ - see front matter r 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.apradiso.2003.11.010
ARTICLE IN PRESS 160
M.C. L!epy et al. / Applied Radiation and Isotopes 60 (2004) 159–165
crystal and a monochromator, housed in a vacuum chamber. The whole experiment is controlled by a microcomputer using LabVIEWt software. This setup has been previously described (Bonnelle et al., 2003), only the main features are therefore mentioned here. 2.1. The X-ray tube The initial X-ray beam is produced by a windowless X-ray tube. The electron source is a tungsten filament; a high-voltage power supply applies 0–50 kV between the anode and the cathode. The current can be adjusted between 0 and 100 mA, with a relative stability of 102. Both the copper tube body and the anode are cooled by water circulation. The absence of a window avoids absorption of radiation with energy as low as a few hundreds eV. The radiation emitted includes a continuous spectrum due to Bremsstrahlung, whose maximum energy depends on the applied voltage, and characteristic X-ray lines of the anode material. Different anodes can be used (Cu, Au, Hastelloy Cs, etc.) to supply initial beams of various energy distributions, thus providing Xray lines, used as references for both energy and resolution calibrations. 2.2. The dispersive crystal The wavelengths of the emission spectrum provided by the X-ray tube are dispersed by a cylindrically bent crystal of radius R: The wavelength dispersion follows Bragg’s law: a set of reticular planes hkl selects radiation of wavelength l in a direction given by Bragg’s angle y; according to the relation:
Fig. 1. Top view of the SOLEX apparatus.
2.4. The vacuum chamber The X-ray tube, the curved crystal spectrometer and the detector are all placed in a large circular vacuum chamber (diameter: 1 m, height: 0.40 m), whose stainless steel walls (thickness: 1 cm) serve also as a shield against scattered radiation. To ensure the safe functioning of the windowless tube in the chamber, a very low pressure (105–104 Pa) is required. This is achieved by using two primary pumps relayed by three turbomolecular pumps once the internal pressure is low enough (50 Pa). The turbomolecular pumps are water-cooled and the pressure is permanently checked. An internal view of the vacuum chamber is displayed in Fig. 1.
nl ¼ 2dhkl ð1 TÞsin y; where dhkl is the spacing of the planes reflecting the incident rays, n is the order of reflection and T is a correction term taking into account the effect of the refractive index at the n order. Different crystals are used (beryl, InSb, LiF, quartz, etc.) to cover the 1–20 keV energy range. 2.3. The spectrometer The central part of this setup is the mechanical device that ensures that Bragg’s condition is always satisfied. However, unlike with the geometries traditionally used in wavelength-dispersive spectroscopy, both the tube and the crystal can be moved to fulfill Bragg’s condition and send the outgoing beam in the direction of the fixed X-ray detector. The X-ray source and its entrance slit, the axis normal to the bent crystal and the exit slit are all connected by radial arms. Bragg’s angle is set by adjusting the distances between the entrance slit and the crystal on one arm, and the crystal and the exit slit on the other arm.
3. Source performance 3.1. Count rate Various detectors can be connected to the fixed exit of the vacuum chamber. For the first tests, we used conventional semiconductor detectors (Si(Li) and HPGe) and also a silicon drift detector. These detectors can be used either in counting mode or in energydispersive mode. In both cases, the counting rate is dependent on the energy range, the tube high-voltage and current, the luminosity of the spectrometer, i.e. the crystal reflectivity and the passband width, and the detector efficiency. In the absence of a characteristic line, a few tens to a few hundreds counts per second are easily obtained at each position over the entire energy range. Thus, studies such as detector response function characterization can be performed from the Bremsstrahlung, i.e. at any given wavelength. When a characteristic X-ray line is selected, the counting rate attains several tens of thousands counts per second.
ARTICLE IN PRESS M.C. L!epy et al. / Applied Radiation and Isotopes 60 (2004) 159–165
3.2. Energy calibration For energy and resolution calibrations, the detector is used in the counting mode and both the tube and the crystal are moved to perform an energy scanning, what gives the emitted spectral distribution. The calibration is performed by using the characteristic X-ray lines of the anode: for example copper L lines are used around 900 eV and K lines in the 8–9 keV energy range. The energy of the lines (in eV) versus the spectrometer position (in motor increment units) gives the calibration factors that can be used to drive the X-ray source directly in electronvolts. 3.3. Resolution calibration The energy resolution of the source characterizes the monochromaticity of the radiation. It is determined from the broadening of a peak with respect to its true width. An example of the resolution calibration is displayed in Fig. 2, where the CuKa1 ; a2 emissions of copper, at 8048 and 8028 eV, are displayed. The experimental full widths at half maximum are respectively 4.5 and 4.9 eV. The spectrum has been fitted using Voigt functions including the Lorentzian shape corresponding to the natural widths of the Ka1 and Ka2 lines (2.1 and 2.5 eV), and the Gaussian experimental broadening. Here, the widths of the Gauss components are, respectively, 1.5 and 1.6 eV; this corresponds to a relative instrumental resolution ðDE=EÞ ¼ 2 103 : 3.4. Spectral purity
Counts per step
The spectral purity of the beam reaching a semiconductor detector has been determined by using it in the energy-dispersive mode. This measurement allows measuring the intensity of the background relative to that of the main peak, the intensity of eventual harmonics and the presence of spurious peaks. A spectrum correspond-
8000 7000 6000 5000 4000 3000
161
ing to 5 keV selected photon energy was recorded with a high-purity germanium detector. Without any protection, the main peak was superimposed upon a relatively high background due to non-dispersed scattered radiation reaching directly the detector. This radiation and parasitic fluorescence peaks were significantly reduced in a second step when the detector was equipped with a copper collimator and the crystal holder was covered with polyimide. In the resulting spectrum, the background-to-peak ratio is 7.8 103. This can be compared to the spectrum obtained at the same energy with the double crystal monochromator of the LURE synchrotron facility (Le! py et al., 2000), equipped with a very small collimator and the same detector, where the background-to-peak ratio was 6.6 103. 3.5. Metrological studies The performances checking shows that SOLEX is suitable for performing accurate measurements in the field of metrology. Indeed, this setup intrinsically includes three running modes allowing different kind of studies: *
*
First, it can work as a high resolution spectrometer, simply by using the dispersive crystal and the exit detector. Second, the monochromatic radiation can be used to characterize the response function of detectors and optical components, or to determine transmission characteristics of different materials. Both options are now available: * the detector can be installed on a moving support allowing displacement along both the X and the Y axes, in a plane perpendicular to the exit beam direction. This equipment is designed to examine the homogeneity of the detector response function, and determine the effective detector area. * a sample holder can be interposed between the monochromatic radiation and the semiconductor detector (see below). * Last, equipped in the near future with a reference detector, the whole system will allow absolute efficiency calibration of X-ray detectors.
4. Measurement of attenuation coefficients
2000 1000 800 600 400 200 100
8020
8030
8040 Energy (keV)
8050
8060
Fig. 2. Ka doublet from the copper anode fitted by Voigt functions (solid lines). The experimental full widths at half maximum are, respectively, and 4.5 and 4.9 eV.
The first application using the SOLEX source is a setup for measuring attenuation coefficients in the energy range below 10 keV, developed by Ferreux (2003). It basically includes a sample-holder which can be normally interposed through the monochromatic photon path. According to Beer–Lambert’s law, for an incident energy E; the linear attenuation coefficient, m; is derived from the measurement of the photon
ARTICLE IN PRESS M.C. L!epy et al. / Applied Radiation and Isotopes 60 (2004) 159–165
162
fluxes, without (I0 ) and with the sample (I) of known thickness, x: I ¼ I0 emx : 4.1. Principle Although the measurement principle is very simple, particular care must be taken to derive accurate attenuation coefficients with low uncertainties. Indeed, according to Chantler et al. (2001), compilation of experimental data shows large variations of up to 30%, due to several experimental difficulties such as * * * * *
energy calibration, X-ray beam purity and divergence, detector linearity, scattering, sample thickness and purity determination.
The present measurement setup avoids some of the drawbacks of the conventional experimental techniques: *
*
*
The SOLEX source delivers a monochromatic beam whose energy and intensity are tunable. It is accurately energy-calibrated using characteristic X-ray lines from the anode material. Thus, the relative energy uncertainty is a few thousandths. The beam purity is checked by the use of an energydispersive detector equipped with a circular collimator reducing the entrance window to 2 mm diameter to protect the detector from any scattered radiation and ensure a constant solid angle between the source exit slit and the detector entrance window. Moreover, only the full-energy peak is selected in the spectra, this avoids contribution of parasitic peaks or harmonics that would be included in a counting system. Indeed relative intensity of harmonic components can reach several hundredths, according to the dispersive crystal and the selected energy (Tran et al., 2003). The linearity of the detector and associated electronics versus the counting rate has been studied and showed that input rates up to 3 104 s1 can be processed without count losses. Materials selected for the measurements (aluminum and copper) have been chosen for the availability of high purity samples. Both are provided with mass purity higher than 99.99%.
4.2. Silicon drift detector The photons fluxes are recorded using a silicon drift detector (SDD). The peculiarity of these detectors is the extremely low anode capacitance, which is moreover completely independent of the active area (Lechner et al., 2001). The SSD design includes, on one side of the
structure, a concentric ring-shaped p+ strip system for the generation of a drift field and the collecting anode in its center. The opposite surface is covered by a nonstructured p+ junction acting as homogeneous radiation entrance window. This feature allows higher energy resolution because the signal is less sensitive to the noise contribution of the subsequent amplifying electronics. Thus, it can be used without cooling or with a moderate cooling (10 C, 20 C) such as obtained using a thermoelectric cooler (Peltier effect device). The detector and its cooling element are included in a compact module, easy to use and to store. The detector is connected to the supply unit that also provides amplifying and processing of the signal. The Peltier element integrated in the detector module is also powered via this module. The detector has an active area of diameter 2.5 mm and is equipped with a 8 mm beryllium window and a zirconium collimator. The detector resolution (FWHM) is 170 eV at 5.9 keV. Spectra recorded with this setup are processed using the COLEGRAM software (Ruellan et al., 1996) to fit a mathematical function to the experimental data. The fitting process is a reduced w2 or least-squares minimization using the Marquardt–Levenberg algorithm. Due to the simple spectrum shape, here, the fitting function is a Gaussian superimposed on a linear background with a step; the escape peak is fitted using a Gaussian. 4.3. Uncertainties The relative uncertainty on the attenuation coefficients depends on the relative uncertainty on the thickness sample and on the measured photon fluxes via lnðI=I0 Þ: " 2 # uðmÞ 2 u ðxÞ I0 2 uðIÞ2 uðI0 Þ2 : ¼ þ ln þ 2 m x2 I I2 I0 For a given attenuation coefficient measurement, as the energy is constant, photons fluxes are directly linked to the full-energy peak area recorded by the energydispersive detector. Counting times ranged from 50 to 1000 s; they are adjusted to get about 105 counts in each peak to maintain the relative counting uncertainties to a few thousandths. The stability of the source emission was checked: over 5 h, the photon flux decreased by a factor of 2%, the largest variation being observed during the first hour due to temperature stabilization of the X-ray tube. This variation is about 0.2% for 1000 s counting time and is taken into account in the final uncertainty budget. As early studied by Nordfors (1960) and recently extended by Chantler et al. (2001), the major factor lnðI=I0 Þ must be between 0.4 and 6 to keep the final uncertainty low. To fulfill this requirement in the 4–10 keV energy range, it is necessary to use different
ARTICLE IN PRESS M.C. L!epy et al. / Applied Radiation and Isotopes 60 (2004) 159–165
absorbing materials with different nominal thickness: 50, 100 and 500 mm for aluminum and 20 and 50 mm for copper. Finally, the dominant uncertainty factor comes from the thickness. The thicker aluminum samples were measured by the BNM/Laboratoire National d’Essais by an optical interferometry method as (510.471.5) and (10371) mm. The uncertainty is limited by the sample area inhomogeneity. The thickness of the third sample was derived from the absorption measurement at 5 keV using the attenuation coefficient determined with the 100 mm sample. The resulting thickness is (50.970.8) mm. For the copper samples, the uncertainties are higher because the thickness determination was performed by weighing and area measurement; the results are (47.571.2) mm for the thicker sample and (18.670.9) mm for the thinner one. It should be noted that the thin sample thickness was also measured from absorption measurements at 5.6 and 5.8 keV using the attenuation coefficient determined with the first sample. These measured thickness are (18.3970.44) and (18.2670.43) mm, respectively. 4.4. Results Table 1 shows the linear attenuation coefficients of aluminum and copper in the 4–10 keV energy range which have been measured in 200 eV steps. However, for copper, the measurement at 9000 eV was not performed: this energy is too close to the copper K binding energy (8989 eV) and near edge X-ray absorption fine structures (NEXAFS) occur which strongly disturb the general shape of the attenuation coefficient curve versus energy. The associated uncertainties are given within the brackets. The relative uncertainties are between 0.6% and 1.7% for aluminum, depending on the energy range, according to the sample thickness measurement. For copper, due to the less accurate determination of sample thickness, the relative uncertainties are between 2.5% and 4.8% depending on the energy range. The higher uncertainties associated with copper could be significantly improved if more accurate thickness measurements were made.
5. Comparison with previously published data The results of the present experiment are compared to those given by other experimental studies and tabulated data in Tables 2a and b. As these values are quoted as mass attenuation coefficients (cm2 g1), to establish direct comparison, the present linear attenuation coefficients are multiplied by the material density, i.e., 2.69 and 8.94 g cm3 for aluminum and copper, respectively. Moreover, to discuss about the same energies, the present data versus the energy have been adjusted using
163
Table 1 Linear attenuation coefficients (cm1) of aluminum and copper for photon energies ranging from 4 to 9.9 keV. The uncertainties are given within the brackets, in terms of the less significant digits Energy (eV)
Aluminum
Copper
4000 4200 4400 4600 4800 5000 5200 5400 5600 5800 6000 6200 6400 6600 6800 7000 7200 7400 7600 7800 8000 8200 8400 8600 8800 9000 9100 9300 9500 9700 9900
979 (15) 851 (13) 746 (12) 664 (11) 589 (9) 524 (8) 464 (5) 413 (5) 381.7 (4.3) 339.0 (3.8) 309.1 (3.5) 285.0 (3.2) 256.7 (2.9) 235.6 (2.6) 215.9 (2.4) 200.6 (2.3) 181.9 (2.0) 162.7 (1.8) 155.1 (1.7) 140.9 (1.6) 132.3 (1.5) 121.1 (1.5) 116.2 (0.7) 108.5 (0.7) 100.7 (0.6) 95.0 (0.6) 89.5 (0.6) 83.5 (0.5) 78.0 (0.5) 73.9 (0.5) 70.0 (0.5)
3220 2810 2450 2180 1940 1750 1570 1390 1280 1155 1056 972 878 816 759 694 635 579 551 509 477 427 414 384 359 — 2290 2250 2216 2155 2004
(160) (140) (120) (110) (95) (85) (75) (70) (60) (31) (27) (25) (22) (21) (19) (18) (16) (15) (14) (13) (12) (11) (11) (10) (9) (110) (110) (110) (95) (88)
a linear log–log function and interpolation is made to derive values for intermediate energies. As measured values are rare, no final conclusions can be drawn. For aluminum, a systematic bias is observed between the present values and tabulated data by Chantler (1995), and Henke et al. (1993), which are about 6% and 3% higher, respectively. Better agreement exists with the table published by Creagh and Hubbell (1992), within about 1%. Rare measurement results are available; agreement is within 1–2% with results from Millar and Greening (1974). For copper, the same tendency is observed when comparing the present results to tabulated data. However, here more experimental data are published : in the energy range below the copper K binding energy, the agreement is within about 2% with data from Unonius and Suorti (1988). Above 8989 eV, experimental data from Chantler et al. (2001) are available: around this
ARTICLE IN PRESS M.C. L!epy et al. / Applied Radiation and Isotopes 60 (2004) 159–165
164 Table 2 Energy (eV)
This study
Chantler (1995)
Creagh and Hubbell (1992)
Henke et al. (1993)
Kerur et al. (1994)
Millar and Greening (1974)
(a) Mass attenuation coefficients (cm2 g1) for aluminum derived from this study compared with previously published data 4055 357 334.05 — — — — 4335 294 276.75 — — — — 4509 262 — 259 250 — 255.4 4952 199 189.98 — 191 — — 5412 154 — 155 148 — 153.6 5895 120 — 121 116 121.53 6400 94.5 — 95.9 — — 93.92 6915 75.4 74.02 — — — — 7472 60.1 — 61.3 58 — 61.30 8041 48.6 — 49.6 46.8 50.47 50.04 8448 42.1 41.19 — — — — 8905 36.1 — 36.8 — — — 9031 34.6 33.81 — — — — 9654 28.5 27.58 — — — — 9876 26.7 — — — — 27.23 9886 26.6 — — 25.6 — — 10320 23.5 22.49 — — — — (b) Mass attenuation coefficients (cm2 g1) for copper derived from this study compared with previously published data Energy This study Chantler Creagh and Henke et al. Unonius Kerur et al. (eV) (1995) Hubbell (1993) and Suorti (1994) (1992) (1988) 4055 348 318.38 — — — — 4335 289 264.55 — — — — 4509 259 — 251 248 264.1 — 4952 200 182.75 — 192 205.4 — 5412 156 — 153 151 158 — 5895 123 — 121 119 124.9 120.75 6400 97.5 — 98.6 — — — 6915 78.53 72.42 — — — — 7472 63.3 — 63.3 61.5 64.0 — 8041 51.5 — 51.8 — 51.1 52.08 8448 51.4 — — 50 — — 8905 38.8 — 39.2 — 39.1 — 9031 265 233.59 — — — — 9032.6 265 — — — — — 9572 242 — 240 — 261 — 9835.6 232 — — — — — 9876 231 — — — 229.1 — 9886 231 — — 223 — —
value, large variations are due to the NEXAFS phenomenon, but a bit farther from the edge (E > 9500 eV) the agreement in within 1%.
6. Conclusions The SOLEX source now available at the BNMLNHB provides tunable monochromatic photons in the low-energy range. Its performance (monochromaticity, resolution and counting rate) have shown that this setup
Chantler et al. (2001) — — — — — — — — — — — — — 315.38 — 231 — —
is suitable for developing metrological studies. The first application concerns the measurement of attenuation coefficients: besides the simplicity of the principle, this measurement requires careful attention to derive accurate values with low associated uncertainties. Experimental determinations of linear attenuation coefficients have been performed for aluminum and copper continuously in the 4–10 keV energy range in 200 eV steps. The results are given with relative uncertainties ranging from 0.6% to 5% depending on the energy and the material. Comparison of the present results with
ARTICLE IN PRESS M.C. L!epy et al. / Applied Radiation and Isotopes 60 (2004) 159–165
previously published data shows reasonable agreement, although experimental values are rare. This lack of data points out the need for further measurements of these coefficients, which are widely used in many applications.
Acknowledgements The authors wish to thank Pr C. Bonnelle, Dr P. Jonnard and colleagues from the Laboratoire de Chimie Physique Mati"ere et Rayonnement (Universit!e Pierre et Marie Curie, Paris, France) for creating SOLEX. The implementation of SOLEX has been possible thanks to the financial support from the Bureau National de M!etrologie. Thanks are also due to Dr. G.P. Vailleau (BNM, Laboratoire National d’Essais) for the thickness measurements of aluminum samples.
References Bonnelle, C., Jonnard, P., Andr!e, J.-M., Avila, A., Laporte, D., Ringuenet, H., L!epy, M.-C., Plagnard, J., Ferreux, L., Protas, J.-C., 2003. Solex: A tunable monochromatic X-ray source in the 1–20 keV energy range. Nucl. Instrum. Methods Phys. Res. A 516, 594–601. Chantler, C.T., 1995. Theoretical form factor, attenuation and scattering tabulations for Z=1–92 from E=1–10 eV to E=0.4–1.0 MeV. J. Phys. Chem. Ref. Data 24, 71–643. Chantler, C.T., Tran, C.Q., Barnea, Z., Paterson, D., Cookson, D.J., Balaic, D.X., 2001. Measurement of the X-ray mass attenuation coefficient of copper using 8.85–20 keV synchrotron radiation. Phys. Rev. A 64, 062506-1-062506-15. Creagh, D.C., Hubbell, J.H., 1992. X-ray absorption (or attenuation) coefficients. In: Wilson, A.J.C. (Ed.), International Tables for Crystallography, Vol. C. Kluwers Academic Publishers, Dordrecht (Hingham, MA), pp. 29–45. Ferreux, L., 2003. Dispositif experimental pour la mesure des coefficients d’att!enuation pour des photons d’!energie inf!erieure a" 10 keV. M!emoire Conservatoire National des Arts et M!etiers, Paris.
165
Henke, B.L., Gullikson, E.M., Davis, J.C., 1993. X-ray interactions: photoabsorption, scattering, transmission and reflexion at E=50–30,000 eV, Z=1–92. Atom. Nucl. Data Tables, 54, 181–342. Kerur, B.R., Thontadarya, S.R., Hanumaiah, B., 1994. Anomalous X-ray attenuation coefficients around the absorption edge using MnKa and CuKa X-rays interactions. Appl. Radiat. Isotopes, 45, 159–163. Lechner, P., Fiorini, C., Hartmann, R., Kemmer, J., Krause, . N., Leutenegger, P., Longoni, A., Soltau, H., Stotter, D., . Stotter, R., Struder, . L., Weber, U., 2001. Silicon drift detectors for high count rate X-ray spectroscopy at room temperature. Nucl. Instrum. Methods Phys. Res. A 458, 281–287. L!epy, M.-C., Plagnard, J., Stemmler, P., Ban, G., Beck, L., Dhez, P., 1997. Si(Li) detector efficiency and peak shape calibration in the low-energy range using synchrotron radiation. X-ray Spectrom. 26, 195–202. L!epy, M.-C., Campbell, J.L., Laborie, J.-M., Plagnard, J., Stemmler, P., Teesdale, W.J., 2000. Experimental study of the response of semiconductor detectors to low-energy photons. Nucl. Instrum. Methods Phys. Res. A 439, 229–246. Millar, R.H., Greening, J.R., 1974. Experimental X-ray mass attenuation coefficients for materials of low atomic number in the energy range 4–25 keV. J. Phys. B: Atom. Mol. Phys. 7, 2332–2343. Nordfors, B., 1960. The statistical error in X-ray absorption measurements. Arkiv fysik 18 (3), 37–47. Ruellan, H., L!epy, M.C., Etcheverry, M., Plagnard, J., Morel, J., 1996. A new spectra processing code applied to the analysis of 235U and 238U in the 60–200 keV energy range. Nucl. Instrum. Methods Phys. Res. A 369, 651–656. Tran, C.Q., Barnea, Z., de Jonge, M.D., Dhal, B.B., Paterson, D., Cookson, D.J., Chantler, C.T., 2003. Quantitative determination of major systematics in synchrotron X-ray experiments: seeing through harmonic components. X-ray Spectrom. 32, 69–74. Unonius, L., Suorti, P., 1988. Mass attenuation coefficients of the elements Ti, V, Fe, Co, Ni, Cu and Zn for the K emission lines between 4.51 and 10.98 keV. J. App. Crystallogr. 22, 46–52.
Applied Radiation and Isotopes 60 (2004) 159–165
A tunable monochromatic X-ray source for metrological studies in the 1–20 keV energy range: application to the measurement of attenuation coefficients Marie-Christine Le! py*, Laurent Ferreux, Johann Plagnard BNM/Laboratoire National Henri Becquerel, CEA Saclay, Gif-Sur-Yvette Cedex F-91191, France
Abstract A tunable monochromatic X-ray source operating in the 1–20 keV energy range is described. An X-ray tube provides initial photons. A dispersive crystal performs the energy selection, according to Bragg’s law. An X-ray detector is connected to the monochromator fixed exit. This setup can be used for metrological studies. A first application consists in measuring attenuation coefficients in the 4–10 keV energy range. Results for aluminum and copper are given, with average relative uncertainties (1s) of 1% and 3% respectively. r 2003 Elsevier Ltd. All rights reserved. Keywords: X-ray source; Monochromator; Detector calibration; Attenuation coefficient; Aluminum; Copper
1. Introduction In the field of X-ray spectrometry, efficiency calibration of semi-conductor detectors is traditionally performed using standard radionuclides. However, in the low-energy range (Eo5 keV) difficulties in performing accurate calibration dramatically increase, due to: * * *
uncertainty on the emission intensities; self-absorption in the source; limited discrete photon emissions, in terms of both energy and intensity.
The weaker the energy, the more difficult the task. To avoid these constraints linked to the use of radionuclides, relative efficiency calibration of X-ray spectrometers have been successfully conducted using monochromatized synchrotron radiation and a proportional counter as a reference (L!epy et al., 1997, 2000). However, the synchrotron facility (LURE, Orsay, France) previously used will close in late 2003. To continue to perform such studies and to develop new
ones, it has been decided to install a tunable monochromatic X-ray source at the Laboratoire National Henri Becquerel (BNM-LNHB). The SOLEX (Source Of Low-Energy X-rays) source has been studied by the Laboratoire de Chimie Physique Mati"ere et Rayonnement (Universit!e Pierre et Marie Curie, Paris, France). This facility has been designed to provide monochromatic radiation in the 1–20 keV energy range with a stable flux of some hundreds of photons per second at the output. Due to the wide range of detectors to be characterized (semi-conductor detectors, cryogenic detectors, photodiodes, etc.), it was decided to preserve a constant output direction to keep the detector under study in the same position. The source characteristics and performance levels are described, as well as the first experimental development using SOLEX, relating to the determination of attenuation coefficients; the first measurements were conducted with aluminum and copper in the 4–10 keV energy range.
2. Experimental set-up *Corresponding author. Tel.: +33-1-69-08-2448; fax: +33-169-08-2619. E-mail address: [email protected] (M.C. L!epy).
The tunable monochromatic X-ray source comprises three main components, an X-ray tube, a dispersive
0969-8043/$ - see front matter r 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.apradiso.2003.11.010
ARTICLE IN PRESS 160
M.C. L!epy et al. / Applied Radiation and Isotopes 60 (2004) 159–165
crystal and a monochromator, housed in a vacuum chamber. The whole experiment is controlled by a microcomputer using LabVIEWt software. This setup has been previously described (Bonnelle et al., 2003), only the main features are therefore mentioned here. 2.1. The X-ray tube The initial X-ray beam is produced by a windowless X-ray tube. The electron source is a tungsten filament; a high-voltage power supply applies 0–50 kV between the anode and the cathode. The current can be adjusted between 0 and 100 mA, with a relative stability of 102. Both the copper tube body and the anode are cooled by water circulation. The absence of a window avoids absorption of radiation with energy as low as a few hundreds eV. The radiation emitted includes a continuous spectrum due to Bremsstrahlung, whose maximum energy depends on the applied voltage, and characteristic X-ray lines of the anode material. Different anodes can be used (Cu, Au, Hastelloy Cs, etc.) to supply initial beams of various energy distributions, thus providing Xray lines, used as references for both energy and resolution calibrations. 2.2. The dispersive crystal The wavelengths of the emission spectrum provided by the X-ray tube are dispersed by a cylindrically bent crystal of radius R: The wavelength dispersion follows Bragg’s law: a set of reticular planes hkl selects radiation of wavelength l in a direction given by Bragg’s angle y; according to the relation:
Fig. 1. Top view of the SOLEX apparatus.
2.4. The vacuum chamber The X-ray tube, the curved crystal spectrometer and the detector are all placed in a large circular vacuum chamber (diameter: 1 m, height: 0.40 m), whose stainless steel walls (thickness: 1 cm) serve also as a shield against scattered radiation. To ensure the safe functioning of the windowless tube in the chamber, a very low pressure (105–104 Pa) is required. This is achieved by using two primary pumps relayed by three turbomolecular pumps once the internal pressure is low enough (50 Pa). The turbomolecular pumps are water-cooled and the pressure is permanently checked. An internal view of the vacuum chamber is displayed in Fig. 1.
nl ¼ 2dhkl ð1 TÞsin y; where dhkl is the spacing of the planes reflecting the incident rays, n is the order of reflection and T is a correction term taking into account the effect of the refractive index at the n order. Different crystals are used (beryl, InSb, LiF, quartz, etc.) to cover the 1–20 keV energy range. 2.3. The spectrometer The central part of this setup is the mechanical device that ensures that Bragg’s condition is always satisfied. However, unlike with the geometries traditionally used in wavelength-dispersive spectroscopy, both the tube and the crystal can be moved to fulfill Bragg’s condition and send the outgoing beam in the direction of the fixed X-ray detector. The X-ray source and its entrance slit, the axis normal to the bent crystal and the exit slit are all connected by radial arms. Bragg’s angle is set by adjusting the distances between the entrance slit and the crystal on one arm, and the crystal and the exit slit on the other arm.
3. Source performance 3.1. Count rate Various detectors can be connected to the fixed exit of the vacuum chamber. For the first tests, we used conventional semiconductor detectors (Si(Li) and HPGe) and also a silicon drift detector. These detectors can be used either in counting mode or in energydispersive mode. In both cases, the counting rate is dependent on the energy range, the tube high-voltage and current, the luminosity of the spectrometer, i.e. the crystal reflectivity and the passband width, and the detector efficiency. In the absence of a characteristic line, a few tens to a few hundreds counts per second are easily obtained at each position over the entire energy range. Thus, studies such as detector response function characterization can be performed from the Bremsstrahlung, i.e. at any given wavelength. When a characteristic X-ray line is selected, the counting rate attains several tens of thousands counts per second.
ARTICLE IN PRESS M.C. L!epy et al. / Applied Radiation and Isotopes 60 (2004) 159–165
3.2. Energy calibration For energy and resolution calibrations, the detector is used in the counting mode and both the tube and the crystal are moved to perform an energy scanning, what gives the emitted spectral distribution. The calibration is performed by using the characteristic X-ray lines of the anode: for example copper L lines are used around 900 eV and K lines in the 8–9 keV energy range. The energy of the lines (in eV) versus the spectrometer position (in motor increment units) gives the calibration factors that can be used to drive the X-ray source directly in electronvolts. 3.3. Resolution calibration The energy resolution of the source characterizes the monochromaticity of the radiation. It is determined from the broadening of a peak with respect to its true width. An example of the resolution calibration is displayed in Fig. 2, where the CuKa1 ; a2 emissions of copper, at 8048 and 8028 eV, are displayed. The experimental full widths at half maximum are respectively 4.5 and 4.9 eV. The spectrum has been fitted using Voigt functions including the Lorentzian shape corresponding to the natural widths of the Ka1 and Ka2 lines (2.1 and 2.5 eV), and the Gaussian experimental broadening. Here, the widths of the Gauss components are, respectively, 1.5 and 1.6 eV; this corresponds to a relative instrumental resolution ðDE=EÞ ¼ 2 103 : 3.4. Spectral purity
Counts per step
The spectral purity of the beam reaching a semiconductor detector has been determined by using it in the energy-dispersive mode. This measurement allows measuring the intensity of the background relative to that of the main peak, the intensity of eventual harmonics and the presence of spurious peaks. A spectrum correspond-
8000 7000 6000 5000 4000 3000
161
ing to 5 keV selected photon energy was recorded with a high-purity germanium detector. Without any protection, the main peak was superimposed upon a relatively high background due to non-dispersed scattered radiation reaching directly the detector. This radiation and parasitic fluorescence peaks were significantly reduced in a second step when the detector was equipped with a copper collimator and the crystal holder was covered with polyimide. In the resulting spectrum, the background-to-peak ratio is 7.8 103. This can be compared to the spectrum obtained at the same energy with the double crystal monochromator of the LURE synchrotron facility (Le! py et al., 2000), equipped with a very small collimator and the same detector, where the background-to-peak ratio was 6.6 103. 3.5. Metrological studies The performances checking shows that SOLEX is suitable for performing accurate measurements in the field of metrology. Indeed, this setup intrinsically includes three running modes allowing different kind of studies: *
*
First, it can work as a high resolution spectrometer, simply by using the dispersive crystal and the exit detector. Second, the monochromatic radiation can be used to characterize the response function of detectors and optical components, or to determine transmission characteristics of different materials. Both options are now available: * the detector can be installed on a moving support allowing displacement along both the X and the Y axes, in a plane perpendicular to the exit beam direction. This equipment is designed to examine the homogeneity of the detector response function, and determine the effective detector area. * a sample holder can be interposed between the monochromatic radiation and the semiconductor detector (see below). * Last, equipped in the near future with a reference detector, the whole system will allow absolute efficiency calibration of X-ray detectors.
4. Measurement of attenuation coefficients
2000 1000 800 600 400 200 100
8020
8030
8040 Energy (keV)
8050
8060
Fig. 2. Ka doublet from the copper anode fitted by Voigt functions (solid lines). The experimental full widths at half maximum are, respectively, and 4.5 and 4.9 eV.
The first application using the SOLEX source is a setup for measuring attenuation coefficients in the energy range below 10 keV, developed by Ferreux (2003). It basically includes a sample-holder which can be normally interposed through the monochromatic photon path. According to Beer–Lambert’s law, for an incident energy E; the linear attenuation coefficient, m; is derived from the measurement of the photon
ARTICLE IN PRESS M.C. L!epy et al. / Applied Radiation and Isotopes 60 (2004) 159–165
162
fluxes, without (I0 ) and with the sample (I) of known thickness, x: I ¼ I0 emx : 4.1. Principle Although the measurement principle is very simple, particular care must be taken to derive accurate attenuation coefficients with low uncertainties. Indeed, according to Chantler et al. (2001), compilation of experimental data shows large variations of up to 30%, due to several experimental difficulties such as * * * * *
energy calibration, X-ray beam purity and divergence, detector linearity, scattering, sample thickness and purity determination.
The present measurement setup avoids some of the drawbacks of the conventional experimental techniques: *
*
*
The SOLEX source delivers a monochromatic beam whose energy and intensity are tunable. It is accurately energy-calibrated using characteristic X-ray lines from the anode material. Thus, the relative energy uncertainty is a few thousandths. The beam purity is checked by the use of an energydispersive detector equipped with a circular collimator reducing the entrance window to 2 mm diameter to protect the detector from any scattered radiation and ensure a constant solid angle between the source exit slit and the detector entrance window. Moreover, only the full-energy peak is selected in the spectra, this avoids contribution of parasitic peaks or harmonics that would be included in a counting system. Indeed relative intensity of harmonic components can reach several hundredths, according to the dispersive crystal and the selected energy (Tran et al., 2003). The linearity of the detector and associated electronics versus the counting rate has been studied and showed that input rates up to 3 104 s1 can be processed without count losses. Materials selected for the measurements (aluminum and copper) have been chosen for the availability of high purity samples. Both are provided with mass purity higher than 99.99%.
4.2. Silicon drift detector The photons fluxes are recorded using a silicon drift detector (SDD). The peculiarity of these detectors is the extremely low anode capacitance, which is moreover completely independent of the active area (Lechner et al., 2001). The SSD design includes, on one side of the
structure, a concentric ring-shaped p+ strip system for the generation of a drift field and the collecting anode in its center. The opposite surface is covered by a nonstructured p+ junction acting as homogeneous radiation entrance window. This feature allows higher energy resolution because the signal is less sensitive to the noise contribution of the subsequent amplifying electronics. Thus, it can be used without cooling or with a moderate cooling (10 C, 20 C) such as obtained using a thermoelectric cooler (Peltier effect device). The detector and its cooling element are included in a compact module, easy to use and to store. The detector is connected to the supply unit that also provides amplifying and processing of the signal. The Peltier element integrated in the detector module is also powered via this module. The detector has an active area of diameter 2.5 mm and is equipped with a 8 mm beryllium window and a zirconium collimator. The detector resolution (FWHM) is 170 eV at 5.9 keV. Spectra recorded with this setup are processed using the COLEGRAM software (Ruellan et al., 1996) to fit a mathematical function to the experimental data. The fitting process is a reduced w2 or least-squares minimization using the Marquardt–Levenberg algorithm. Due to the simple spectrum shape, here, the fitting function is a Gaussian superimposed on a linear background with a step; the escape peak is fitted using a Gaussian. 4.3. Uncertainties The relative uncertainty on the attenuation coefficients depends on the relative uncertainty on the thickness sample and on the measured photon fluxes via lnðI=I0 Þ: " 2 # uðmÞ 2 u ðxÞ I0 2 uðIÞ2 uðI0 Þ2 : ¼ þ ln þ 2 m x2 I I2 I0 For a given attenuation coefficient measurement, as the energy is constant, photons fluxes are directly linked to the full-energy peak area recorded by the energydispersive detector. Counting times ranged from 50 to 1000 s; they are adjusted to get about 105 counts in each peak to maintain the relative counting uncertainties to a few thousandths. The stability of the source emission was checked: over 5 h, the photon flux decreased by a factor of 2%, the largest variation being observed during the first hour due to temperature stabilization of the X-ray tube. This variation is about 0.2% for 1000 s counting time and is taken into account in the final uncertainty budget. As early studied by Nordfors (1960) and recently extended by Chantler et al. (2001), the major factor lnðI=I0 Þ must be between 0.4 and 6 to keep the final uncertainty low. To fulfill this requirement in the 4–10 keV energy range, it is necessary to use different
ARTICLE IN PRESS M.C. L!epy et al. / Applied Radiation and Isotopes 60 (2004) 159–165
absorbing materials with different nominal thickness: 50, 100 and 500 mm for aluminum and 20 and 50 mm for copper. Finally, the dominant uncertainty factor comes from the thickness. The thicker aluminum samples were measured by the BNM/Laboratoire National d’Essais by an optical interferometry method as (510.471.5) and (10371) mm. The uncertainty is limited by the sample area inhomogeneity. The thickness of the third sample was derived from the absorption measurement at 5 keV using the attenuation coefficient determined with the 100 mm sample. The resulting thickness is (50.970.8) mm. For the copper samples, the uncertainties are higher because the thickness determination was performed by weighing and area measurement; the results are (47.571.2) mm for the thicker sample and (18.670.9) mm for the thinner one. It should be noted that the thin sample thickness was also measured from absorption measurements at 5.6 and 5.8 keV using the attenuation coefficient determined with the first sample. These measured thickness are (18.3970.44) and (18.2670.43) mm, respectively. 4.4. Results Table 1 shows the linear attenuation coefficients of aluminum and copper in the 4–10 keV energy range which have been measured in 200 eV steps. However, for copper, the measurement at 9000 eV was not performed: this energy is too close to the copper K binding energy (8989 eV) and near edge X-ray absorption fine structures (NEXAFS) occur which strongly disturb the general shape of the attenuation coefficient curve versus energy. The associated uncertainties are given within the brackets. The relative uncertainties are between 0.6% and 1.7% for aluminum, depending on the energy range, according to the sample thickness measurement. For copper, due to the less accurate determination of sample thickness, the relative uncertainties are between 2.5% and 4.8% depending on the energy range. The higher uncertainties associated with copper could be significantly improved if more accurate thickness measurements were made.
5. Comparison with previously published data The results of the present experiment are compared to those given by other experimental studies and tabulated data in Tables 2a and b. As these values are quoted as mass attenuation coefficients (cm2 g1), to establish direct comparison, the present linear attenuation coefficients are multiplied by the material density, i.e., 2.69 and 8.94 g cm3 for aluminum and copper, respectively. Moreover, to discuss about the same energies, the present data versus the energy have been adjusted using
163
Table 1 Linear attenuation coefficients (cm1) of aluminum and copper for photon energies ranging from 4 to 9.9 keV. The uncertainties are given within the brackets, in terms of the less significant digits Energy (eV)
Aluminum
Copper
4000 4200 4400 4600 4800 5000 5200 5400 5600 5800 6000 6200 6400 6600 6800 7000 7200 7400 7600 7800 8000 8200 8400 8600 8800 9000 9100 9300 9500 9700 9900
979 (15) 851 (13) 746 (12) 664 (11) 589 (9) 524 (8) 464 (5) 413 (5) 381.7 (4.3) 339.0 (3.8) 309.1 (3.5) 285.0 (3.2) 256.7 (2.9) 235.6 (2.6) 215.9 (2.4) 200.6 (2.3) 181.9 (2.0) 162.7 (1.8) 155.1 (1.7) 140.9 (1.6) 132.3 (1.5) 121.1 (1.5) 116.2 (0.7) 108.5 (0.7) 100.7 (0.6) 95.0 (0.6) 89.5 (0.6) 83.5 (0.5) 78.0 (0.5) 73.9 (0.5) 70.0 (0.5)
3220 2810 2450 2180 1940 1750 1570 1390 1280 1155 1056 972 878 816 759 694 635 579 551 509 477 427 414 384 359 — 2290 2250 2216 2155 2004
(160) (140) (120) (110) (95) (85) (75) (70) (60) (31) (27) (25) (22) (21) (19) (18) (16) (15) (14) (13) (12) (11) (11) (10) (9) (110) (110) (110) (95) (88)
a linear log–log function and interpolation is made to derive values for intermediate energies. As measured values are rare, no final conclusions can be drawn. For aluminum, a systematic bias is observed between the present values and tabulated data by Chantler (1995), and Henke et al. (1993), which are about 6% and 3% higher, respectively. Better agreement exists with the table published by Creagh and Hubbell (1992), within about 1%. Rare measurement results are available; agreement is within 1–2% with results from Millar and Greening (1974). For copper, the same tendency is observed when comparing the present results to tabulated data. However, here more experimental data are published : in the energy range below the copper K binding energy, the agreement is within about 2% with data from Unonius and Suorti (1988). Above 8989 eV, experimental data from Chantler et al. (2001) are available: around this
ARTICLE IN PRESS M.C. L!epy et al. / Applied Radiation and Isotopes 60 (2004) 159–165
164 Table 2 Energy (eV)
This study
Chantler (1995)
Creagh and Hubbell (1992)
Henke et al. (1993)
Kerur et al. (1994)
Millar and Greening (1974)
(a) Mass attenuation coefficients (cm2 g1) for aluminum derived from this study compared with previously published data 4055 357 334.05 — — — — 4335 294 276.75 — — — — 4509 262 — 259 250 — 255.4 4952 199 189.98 — 191 — — 5412 154 — 155 148 — 153.6 5895 120 — 121 116 121.53 6400 94.5 — 95.9 — — 93.92 6915 75.4 74.02 — — — — 7472 60.1 — 61.3 58 — 61.30 8041 48.6 — 49.6 46.8 50.47 50.04 8448 42.1 41.19 — — — — 8905 36.1 — 36.8 — — — 9031 34.6 33.81 — — — — 9654 28.5 27.58 — — — — 9876 26.7 — — — — 27.23 9886 26.6 — — 25.6 — — 10320 23.5 22.49 — — — — (b) Mass attenuation coefficients (cm2 g1) for copper derived from this study compared with previously published data Energy This study Chantler Creagh and Henke et al. Unonius Kerur et al. (eV) (1995) Hubbell (1993) and Suorti (1994) (1992) (1988) 4055 348 318.38 — — — — 4335 289 264.55 — — — — 4509 259 — 251 248 264.1 — 4952 200 182.75 — 192 205.4 — 5412 156 — 153 151 158 — 5895 123 — 121 119 124.9 120.75 6400 97.5 — 98.6 — — — 6915 78.53 72.42 — — — — 7472 63.3 — 63.3 61.5 64.0 — 8041 51.5 — 51.8 — 51.1 52.08 8448 51.4 — — 50 — — 8905 38.8 — 39.2 — 39.1 — 9031 265 233.59 — — — — 9032.6 265 — — — — — 9572 242 — 240 — 261 — 9835.6 232 — — — — — 9876 231 — — — 229.1 — 9886 231 — — 223 — —
value, large variations are due to the NEXAFS phenomenon, but a bit farther from the edge (E > 9500 eV) the agreement in within 1%.
6. Conclusions The SOLEX source now available at the BNMLNHB provides tunable monochromatic photons in the low-energy range. Its performance (monochromaticity, resolution and counting rate) have shown that this setup
Chantler et al. (2001) — — — — — — — — — — — — — 315.38 — 231 — —
is suitable for developing metrological studies. The first application concerns the measurement of attenuation coefficients: besides the simplicity of the principle, this measurement requires careful attention to derive accurate values with low associated uncertainties. Experimental determinations of linear attenuation coefficients have been performed for aluminum and copper continuously in the 4–10 keV energy range in 200 eV steps. The results are given with relative uncertainties ranging from 0.6% to 5% depending on the energy and the material. Comparison of the present results with
ARTICLE IN PRESS M.C. L!epy et al. / Applied Radiation and Isotopes 60 (2004) 159–165
previously published data shows reasonable agreement, although experimental values are rare. This lack of data points out the need for further measurements of these coefficients, which are widely used in many applications.
Acknowledgements The authors wish to thank Pr C. Bonnelle, Dr P. Jonnard and colleagues from the Laboratoire de Chimie Physique Mati"ere et Rayonnement (Universit!e Pierre et Marie Curie, Paris, France) for creating SOLEX. The implementation of SOLEX has been possible thanks to the financial support from the Bureau National de M!etrologie. Thanks are also due to Dr. G.P. Vailleau (BNM, Laboratoire National d’Essais) for the thickness measurements of aluminum samples.
References Bonnelle, C., Jonnard, P., Andr!e, J.-M., Avila, A., Laporte, D., Ringuenet, H., L!epy, M.-C., Plagnard, J., Ferreux, L., Protas, J.-C., 2003. Solex: A tunable monochromatic X-ray source in the 1–20 keV energy range. Nucl. Instrum. Methods Phys. Res. A 516, 594–601. Chantler, C.T., 1995. Theoretical form factor, attenuation and scattering tabulations for Z=1–92 from E=1–10 eV to E=0.4–1.0 MeV. J. Phys. Chem. Ref. Data 24, 71–643. Chantler, C.T., Tran, C.Q., Barnea, Z., Paterson, D., Cookson, D.J., Balaic, D.X., 2001. Measurement of the X-ray mass attenuation coefficient of copper using 8.85–20 keV synchrotron radiation. Phys. Rev. A 64, 062506-1-062506-15. Creagh, D.C., Hubbell, J.H., 1992. X-ray absorption (or attenuation) coefficients. In: Wilson, A.J.C. (Ed.), International Tables for Crystallography, Vol. C. Kluwers Academic Publishers, Dordrecht (Hingham, MA), pp. 29–45. Ferreux, L., 2003. Dispositif experimental pour la mesure des coefficients d’att!enuation pour des photons d’!energie inf!erieure a" 10 keV. M!emoire Conservatoire National des Arts et M!etiers, Paris.
165
Henke, B.L., Gullikson, E.M., Davis, J.C., 1993. X-ray interactions: photoabsorption, scattering, transmission and reflexion at E=50–30,000 eV, Z=1–92. Atom. Nucl. Data Tables, 54, 181–342. Kerur, B.R., Thontadarya, S.R., Hanumaiah, B., 1994. Anomalous X-ray attenuation coefficients around the absorption edge using MnKa and CuKa X-rays interactions. Appl. Radiat. Isotopes, 45, 159–163. Lechner, P., Fiorini, C., Hartmann, R., Kemmer, J., Krause, . N., Leutenegger, P., Longoni, A., Soltau, H., Stotter, D., . Stotter, R., Struder, . L., Weber, U., 2001. Silicon drift detectors for high count rate X-ray spectroscopy at room temperature. Nucl. Instrum. Methods Phys. Res. A 458, 281–287. L!epy, M.-C., Plagnard, J., Stemmler, P., Ban, G., Beck, L., Dhez, P., 1997. Si(Li) detector efficiency and peak shape calibration in the low-energy range using synchrotron radiation. X-ray Spectrom. 26, 195–202. L!epy, M.-C., Campbell, J.L., Laborie, J.-M., Plagnard, J., Stemmler, P., Teesdale, W.J., 2000. Experimental study of the response of semiconductor detectors to low-energy photons. Nucl. Instrum. Methods Phys. Res. A 439, 229–246. Millar, R.H., Greening, J.R., 1974. Experimental X-ray mass attenuation coefficients for materials of low atomic number in the energy range 4–25 keV. J. Phys. B: Atom. Mol. Phys. 7, 2332–2343. Nordfors, B., 1960. The statistical error in X-ray absorption measurements. Arkiv fysik 18 (3), 37–47. Ruellan, H., L!epy, M.C., Etcheverry, M., Plagnard, J., Morel, J., 1996. A new spectra processing code applied to the analysis of 235U and 238U in the 60–200 keV energy range. Nucl. Instrum. Methods Phys. Res. A 369, 651–656. Tran, C.Q., Barnea, Z., de Jonge, M.D., Dhal, B.B., Paterson, D., Cookson, D.J., Chantler, C.T., 2003. Quantitative determination of major systematics in synchrotron X-ray experiments: seeing through harmonic components. X-ray Spectrom. 32, 69–74. Unonius, L., Suorti, P., 1988. Mass attenuation coefficients of the elements Ti, V, Fe, Co, Ni, Cu and Zn for the K emission lines between 4.51 and 10.98 keV. J. App. Crystallogr. 22, 46–52.