Kα relative X-ray emission rate for Ti, V, Fe, Co, Ni, Cu and Zn measured with a tunable monochromatic X-ray source

Nuclear Instruments and Methods in Physics Research B 268 (2010) 2477–2486

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Mass attenuation coefficients in the range 3:8 6 E 6 11 keV, K fluorescence yield and K b =K a relative X-ray emission rate for Ti, V, Fe, Co, Ni, Cu and Zn measured with a tunable monochromatic X-ray source Y. Ménesguen *, M.-C. Lépy CEA, LIST, LNHB, Gif-sur-Yvette, F-91191, France

a r t i c l e

i n f o

Article history: Received 29 July 2009 Received in revised form 3 May 2010 Available online 12 May 2010 Keywords: Mass absorption coefficient K-absorption jump-ratio K-fluorescence yield K b =K a relative X-ray emission rate

a b s t r a c t This work presents new measurements of mass attenuation coefficients in the range 3:8 6 E 6 11 keV, K-absorption jump-ratios, K a and K b fluorescence yields for Ti, V, Fe, Co, Ni, Cu and Zn. We use the experimental facility SOLEX, a tunable monochromatic X-ray source combined with an energy-dispersive high-purity germanium detector. The results are compared with theoretical values as well as with other experimental data and show a relatively good agreement. However, the derived K-jump-ratios appear larger than those widely used in the XCOM database. The K a and K b fluorescence yields and the corresponding relative emission rates K b =K a are also derived, which was made possible by the use of energy-dispersive detectors with good spectral resolution. Ó 2010 Elsevier B.V. All rights reserved.

1. Introduction Numerous analytical methods are based on X-ray fluorescence spectrometry, not only for the analysis of metals or chemical compounds in heavy industries, but also in some recent applications that can be used in non-destructive testing, biology, archaeometry, etc. The new capabilities of X-ray detectors permit trace-element analysis, which may be one of the most widely used applications of X-ray fluorescence analysis. In order to obtain quantified results, most users of this technique compare the spectra from the analysed sample with a standard reference material, the main difficulty being the preparation and preservation of the standard samples. To avoid the drawback of preserving reference samples, it is possible to use the fundamental parameters such as mass attenuation coefficients, absorption jump-ratios or atomic fluorescence yields to quantify the elemental concentrations. The direct quantification of the elemental composition of a sample via a detailed spectrum analysis would be independent of any standard materials, but requires a reliable database. The mass attenuation coefficient is one of the parameters that describe the interactions between photons and matter. It characterizes the attenuation of a photon beam in matter, and depends on the material and the photon energy. Many tables of attenuation coefficients have been already published, and some compilations include experimental data as well as theoretical calculations. Saloman et al. compiled available experimental data and the * Corresponding author. Tel.: +33 169085088. E-mail address: [email protected] (Y. Ménesguen). 0168-583X/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2010.05.044

results of calculations obtained with a relativistic Hartree–Slater model [1] for energies between 100 eV and 100 keV, Henke et al. proposed a semi-empirical set of data in the 50 eV to 30 keV energy range [2]. More recently, a paper from Hubbell [3] presented a state-of-the-art review on photon cross sections, which includes photoeffect cross-sections, the coherent and incoherent scattering, as well as pair and triplet production. Chantler has performed extensive theoretical calculations concerning the mass attenuation and the scattering cross-sections [4], as well as a more detailed study in the 0.1–10 keV region but restricted to elements with atomic numbers Z in the ranges 30–36 and 60–89 [5]. The fluorescence yield represents the probability of a vacancy in an atomic shell to be filled through radiative emission during the de-excitation process. Since there are no subshells, the K-fluorescence yield xK is simply the ratio of the average number of emitted KX-rays photons fK over the average number of vacancies v K created in the K-shell. Several methods for creating vacancies in the K-shell are reported, including capture of an electron of the K-shell [6,7], internal conversion [8], charged-particle impact and photoionization. Another method consists in directly using the energydispersive detector response when the studied element is part of the ionization medium. When an absorbed photon has an energy above the K-binding energy of the material of the detector, a fluorescence photon can escape from the detector, and this results in a deficit in the total absorbed energy detected. This generates an ‘‘escape peak” in the spectrum. The intensity ratio of the escape peak to the main peak is simply related to the K-fluorescence yield and mass attenuation coefficients. This method was used for gas proportional counters [9] and for semiconductors such as Si [10,11]

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and Ge [10,12]. The disadvantage of such an experimental procedure is that it requires a precise theoretical knowledge of the detector response to process the experimental spectra and obtain a reliable value for xK . Most of the available experimental data concerning fluorescence yields were determined more than 30 years ago [13,14], and the lighter the Z, the larger the associated uncertainty. Krause [15] estimated the uncertainties of adopted fluorescence yields xK for Z ¼ 20—30 to range between 3% and 5%. For light elements, a low xK value means that the de-excitation process will preferentially occur via an Auger effect, since the number of X-ray photons is very low. As a consequence, the associated relative uncertainties will be high. In some previous studies, the vacancies in the K-shell were created through photoionisation using radionuclides as a primary photon source, by using 55 Fe [16], 241 Am [17–20], 57 Co, 51 Cr and 141 Ce [21,22] or 57 Co [23]. However, while the radioactive decay of nuclides can provide a monoenergetic gamma emission, the available photon energies are very high compared with the K-binding energies, so the absorption in the sample is weak. Moreover, obtaining a good accuracy with such measurements requires well-defined solid angles between the radioactive source and the target, as well as between the target and the detector when the X-ray fluorescence is detected in reflection [16,17]. This means that only a small solid angle is used, which implies it is necessary to have a strong radioactive source with a very well-known activity. Today, available experimental facilities, such as monochromatic radiation (tunable X-ray source or synchrotron) and improved semiconductor detectors should offer new perspectives for accurate experimental measurements. In the present study, we propose a new experimental approach using the tunable X-ray source of the Laboratoire National Henri Becquerel. The first part of this study focuses on the total photon mass attenuation coefficients, which are measured on thin metal foils within the range 3.8–11 keV. The second part deals with the K-fluorescence yields arising after photoionization using a simplified dedicated experimental setup. 2. Experimental setup The experimental setup comprises optimized measurement conditions as described in [24]. The source is composed of an Xray tube with a monochromator crystal to produce an energyselectable excitation beam. An energy-dispersive semiconductor detector and a dedicated signal processing and amplifying system are used to record the spectra. The samples are thin enough to be studied in transmission, and two setups are discussed according to whether we are dealing with mass attenuation coefficients or fluorescence yields.

where dhkl is the spacing of the planes reflecting the incident rays, n the order of the reflection, k the wavelength of the photon, T is a correction term due to the refractive index and h is the output angle of emission, which can vary between 14° and 56°. An exit slit is used to shield the scattered beam and accurately define the incident photon flux used in the experiment. With the exit slit remaining stationary, the crystal and the X-ray tube move on stages describing a Rowland circle in order to select the incidence Bragg angle h. Different crystals with different dhkl parameters are used to select different energy ranges. Once the crystal is chosen, it is necessary to calibrate the simultaneous motions/positions of the crystal and the X-ray tube. In the 3.8–11 keV energy range, a LiFð200Þ crystal is used and calibration of the motions versus energies is performed through the characteristic Cu Ka and Kb emission lines of the X-ray tube corresponding to the anode material. A scan of the Bragg angles is performed around the energies of the Cu Ka and Kb emission lines, the detector being used in the counting mode. The result is shown on Fig. 1. Then, a calibration is established between the motor positions at the maximum peaks of the corresponding energies of the copper Ka and Kb lines according to Deslattes et al. [27]. The accuracy of the resulting energy selection is better than 1 eV around the Cu Ka and Kb lines, and elsewhere is better than 10 eV. The emitted spectral resolution, DE, is estimated to be around 20 eV. We could achieve a better resolution with this experimental setup by reducing the slit widths to define a smaller source point and a smaller focussing area, but the near-focussing Johann geometry of the setup would dramatically reduce the output flux. 2.2. Detector and experimental setup To ensure accurate selection of the energy of interest and avoid counting photons that do not belong to the transmitted photon flux (arising from external fluorescence, for example), the spectra are acquired using an energy-dispersive detector. The setup consists of a high-purity germanium (HPGe) detector of 10 mm2 surface area and 4 mm thickness, coupled to an acquisition system based on digital signal processing. This type of detector works at cryogenic temperature (77 K), and is characterized by a high energy resolution, typically 115 eV of full width at half-maximum (FWHM) at 5.9 keV. Since mass attenuation coefficients require only relative measurements, an extensive knowledge of the detector efficiency is not necessary for this purpose. On the contrary, an accurate efficiency calibration of the detector is needed to measure the fluorescence yields in the dedicated setup configuration. The detector has several layers between the beryllium entrance

2.1. X-ray excitation source The Source Of Low-Energy X-rays (SOLEX) [25,26] produces a monochromatic X-ray beam in the 1–20 keV energy range, and consists of a windowless X-ray tube inside a vacuum chamber operating at a very low pressure (104 —105 Pa). The X-ray tube is composed of a 15 mm-long tungsten wire and a 30-mm diameter electrode, with a the take-off angle of 5°, which corresponds to the tilt of the tube in order to work with horizontal emission. Different anode materials are available; here, we selected copper with a gold layer. The tube can deliver an adjustable emission current between 0 and 100 mA stabilized at better than ±1 mA. An adjustable slit set at the output of the X-ray tube defines the source point. A cylindrical bent crystal is used as a monochromator which disperses the whole range of the radiation according to the Bragg’s law:

nk ¼ 2dhkl ð1  TÞ sinðhÞ

ð1Þ

Fig. 1. Energy scan obtained by varying the Bragg angle.

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window and the germanium crystal: a boron layer is deposited on the beryllium window, the electrical contact on the germanium is made of nickel, and an aluminium layer prevents infra-red photons from reaching the germanium crystal. All these layers contribute to reducing the overall efficiency of the detector, which was previously characterized [28]. The samples are thin enough to be studied in transmission, and a specific experimental setup is adapted to the measurement of either mass attenuation coefficients or fluorescence yields. Indeed, mass attenuation coefficients are measured by comparison of two recorded spectra, the first one with the sample and the other without it, while the incoming flux remains identical. Thus, the samples are mounted on step-motor stages which place one of the samples (or none) in the path of the X-ray beam at every measurement energy step [26]. The step-motors have very good reproducibility, which ensures the X-ray excitation beam will irradiate the same spot from one energy to another. The irradiated spot is around 1 mm2 , which allows the averaging of surface roughness effects. The experimental setup for the fluorescence yield measurements is shown on Fig. 2. The monochromatic photon beam ionizes atoms in the sample metal sheet, and a collimator selects the solid angle of the fluorescence spectrum recorded by the HPGe detector. The sample is held tightly by means of a strained thin Mylar foil in front of the central pinhole, in order to ensure positioning without any vacuum between the sample and the collimator. A lead collimator is installed in front of the detector to accurately define the solid angle with the source. This small collimator ensures that the photon flux is included in the central part of the crystal and does not reach the edges, where any change in the response function of the detector could disturb the spectrum. The collimator is a 2.053(2) mm-thick lead sheet with a central hole of 610ð11Þ lm diameter, thus the solid angle seen by the detector is 6:710  102 sr. The diameter of the central hole is measured by comparison of the 31.4, 31.7 and 35.6 keV peaks from a 133 Ba source between a well-calibrated hole and the small lead pinhole.

Table 1 Metal foil parameters. Element

A (mm2)

M (mg)

Ti V Fe Co Ni Cu Zn

11.7895 (6) 32.5161 (9) 48.607 (1) 56.503 (3) 50.892 (3) 42.3590 (3) 4.2931 (6)

252.494 619.236 635.543 656.128 605.652 254.469 78.540

(2) (1) (1) (1) (1) (2) (4)

Table 2 Fitting equation parameters of mass attenuation coefficients in cm2/g, where E is the energy in eV. Z

Element

E < EK

E > EK

A

B

A

B

22 23 26 27 28 29 30

Ti V Fe Co Ni Cu Zn

3.101 4.715 3.347 3.142 3.082 6.688 5.150

2.863 2.891 2.801 2.784 2.762 2.844 2.802

9.855 6.557 21.18 21.19 9.372 34.22 495.6

2.738 2.678 2.771 2.764 2.661 2.797 3.075

Table 3 K-jump-ratios of mass attenuation coefficients in cm2/g. Z

Element

Fitted values

XCOM [31]

D in %

22 23 26 27 28 29 30

Ti V Fe Co Ni Cu Zn

664 563 392 332 298 261 240

604.2 514.2 354.8 308.9 284.7 239.7 218.9

+9.9 +9.5 +10.6 +7.4 +4.7 +8.9 +9.9

2.3. Sample characteristics The different targets are metal foils provided by Goodfellow [29] and are considered as ‘‘pure” element materials, since their purity is higher than 99.99%. These samples are placed inside the vacuum chamber in the path of the X-rays photons, between the detector window and the output slit of the X-ray monochromator. The samples are weighed and their area is measured; the results are reported along with their associated measurement uncertainties in Table 1. We assume that the density properties of these

Table 4 Fluorescence yields for K-ionization and relative X-ray intensities. Z

Element

xK a

xK b

22 23 26 27 29 30

Ti V Fe Co Cu Zn

0.206 0.219 0.323 0.332 0.384 0.427

(23) (9) (16) (29) (16) (19)

0.0233 0.0269 0.0452 0.0427 0.0535 0.0682

xK (55) (32) (24) (38) (30) (33)

0.230 0.246 0.369 0.375 0.437 0.495

(28) (12) (18) (33) (19) (22)

metal foils are the same as the bulk material, since the samples are not produced by sputtering or other growing techniques in which the density could be significantly different from the bulk. 3. Mass attenuation coefficients 3.1. Transmission spectra Mass attenuation coefficients are the energy-dependent parameters of a decreasing exponential law describing the attenuation of an X-ray beam in matter at normal incidence, as given in Eq. (2).

It ðEÞ ¼ I0 ðEÞe

Fig. 2. Experimental setup.

lðEÞ q qL

lðEÞ M q A

¼ I0 ðEÞe

ð2Þ

The equation gives the transmitted X-ray intensity It ðEÞ at energy E as a function of the incident intensity I0 ðEÞ, with L representing the sample thickness, lðEÞ=q the mass attenuation coefficient,

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q the density of the element, M the sample mass and A the sample surface area. The mass attenuation coefficient can then be obtained as follows: 

lðEÞ 1 It ðEÞ ln ¼ M=A I0 ðEÞ q



The peaks have Gaussian shapes and are processed using COLEGRAM software [30], by means of a fitting algorithm that is a leastsquares minimization method based on the Levenberg–Marquardt algorithm.

ð3Þ

The recorded spectra of incoming photons exhibit one or more peaks, which are illustrated in Figs. 3 and 4. The main peak corresponds to the energy defined by the monochromator and the secondary peaks are the Ka and Kb lines of the elements in Fig. 4, while the low-energy peaks around 1000 eV result from the detector electronics. The L lines of the samples are not visible because of the poor efficiency of the HPGe detector below 1 keV. All the selected energies stay below the GeK-binding energy, which avoids escape peak problems. As we can measure the mass attenuation coefficients, we are only interested here by the main peak at the energy selected by the monochromator. The counting time is set to have a minimum of 104 counts at the peak, but is more generally around 105 when counting does not last too long (several minutes) with an acquisition dead-time remaining below 2%. The secondary peaks around 1 keV result from electronic noise and remain below 1 count/sec/channel, which has a negligible effect on the dead-time.

3.2. Results and discussion We present our experimental measurements in Tables 5–11, and use a graphic representation on Figs. 7–13 to compare the data with some literature values. We represent our measurements as black circles. The associated uncertainties take into account the relative uncertainty on the sample thickness, and the measured photon fluxes and are given by:

 2 uðlÞ

l

2

 2

2

6u ðMÞ u ðAÞ ¼4 þ 2 þ M2 A

3 2 þ u IðI2 0 Þ 7 0  2 5 It ln I0

u2 ðIt Þ I2t

We compare our experimental measurements with other experimental data points, as well as the data provided by XCOM [31] (dashed lines) and also with the theoretical calculations of Chantler [4]. We also fit our data by a linear regression on a log-log scale, which are shown as black solid lines. To avoid any influence of the near-edge structures due to the electronic environment, the linear regression is performed by skipping the first point above the K-edge for Zn, the two first points above the K-edge for V, Co and Cu and the three first points above the K-edge for Ni. The fitting equations have the form l=qðEÞ ¼ A  1012  EB , using the parameters A and B as given in Table 2. For iron, our experimental data show a relatively good agreement with previous measurements, and a relatively good agree-

Table 5 Ti mass attenuation coefficients measurements E (eV)

Fig. 3. Spectra of the monochromatic beam at 8048 eV with the 20 lm thick Cu target (red) and without (black). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 4. Spectra of the monochromatic beam at 9600 eV with the 20 lm thick Cu target (red) and without (black). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

3800 4000 4100 4350 4510 4700 4932 5100 5300 5500 5700 5900 6100 6300 6500 6700 6930 7200 7478 7700 7900 8100 8300 8500 8700 8900 9100 9400 9572 9800 10,000 10,200 10,400 10,600 10,800 11,000

l (cm2/g) 167.7 155.9 146.0 122.2 108.2 96.6 74.4 699.9 634.8 559.7 515.7 466.9 423.4 389.6 344.7 335.4 299.6 274.9 243.8 228.4 212.4 198.4 183.1 174.1 165.2 154.5 143.8 134.4 125.3 115.1 111.7 102.6 100.5 91.0 89.3 80.8

lðcm2 =gÞ.

NIST-XCOM [31] (29) (28) (29) (30) (19) (15) (25) (24) (26) (25) (30) (27) (28) (27) (30) (17) (13) (17) (16) (16) (15) (11) (14) (14) (15) (14) (13) (12) (11) (11) (10) (11) (11) (11) (11) (11)

174 152 142 121 109 97.5 85.4 668 621 565 508 456 411 375 343 317 290 264 240 223 209 196 184 173 165 153 144 131 125 117 111 105 99.3 94.2 89.4 85.0

% diff. 3.6 2.5 2.8 1.0 0.7 0.9 12.8 4.8 2.2 0.9 1.5 2.4 3.0 3.9 0.5 5.8 3.3 4.1 1.6 2.4 1.6 1.2 0.5 0.6 0.1 1.0 0.1 2.6 0.3 1.6 0.6 2.3 1.2 3.4 0.1 4.9

Y. Ménesguen, M.-C. Lépy / Nuclear Instruments and Methods in Physics Research B 268 (2010) 2477–2486 Table 6 V mass attenuation coefficients measurements l (cm2/g). E (eV)

l (cm2/g)

NIST-XCOM [31]

4000 4200 4400 4600 4800 4952 5100 5250 5427 5600 5800 6000 6200 6404 6550 6700 6930 7058 7200 7478 7649 7700 7900 8048 8265 8300 8500 8700 8900 9200 9400 9600 9800 10,000 10,200 10,400 10,600 10,800 11,000

178.5 (16) 161.3 (27) 135.8 (27) 127.2 (27) 104.5 (25) 98.7 (27) 86.0 (27) 89.5 (26) 69.5 (23) 668.8 (25) 554.3 (25) 495.7 (23) 457.7 (20) 419.3 (21) 394.2 (21) 372.9 (20) 337.4 (20) 327.1 (20) 304.2 (20) 274.5 (20) 259.7 (19) 254.7 (16) 235.4 (20) 231.3 (19) 211.3 (18) 211.6 (19) 196.7 (20) 185.6 (19) 171.4 (19) 157.0 (18) 151.0 (19) 136.4 (17) 131.8 (19) 128.0 (17) 124.1 (19) 113.8 (18) 106.3 (19) 102.3 (17) 101.4 (18)

171 150 132 117 104 95.4 88.0 81.2 74.2 554 509 469 432 398 376 355 325 309 294 265 250 246 229 218 203 201 188 177 167 152 144 136 129 122 115 109 104 98.8 94.0

Table 7 Fe mass attenuation coefficients measurements % diff. 4.4 7.6 2.9 8.7 0.5 3.4 2.3 10.2 6.3 20.7 8.9 5.7 5.9 5.4 4.8 5.0 3.8 5.8 3.5 3.6 3.9 3.5 2.8 6.1 4.1 5.3 4.6 4.9 2.6 3.3 4.8 0.3 2.2 4.9 7.9 4.4 2.2 3.5 7.9

ment with theoretical calculations. Below the K-edge, the values calculated by Chantler [4] are below all other values, whether experimental or XCOM adopted values. These theoretical values compare well with the XCOM adopted values above the K-edge, but do not reproduce the fine structure. The same remarks concerning the Chantler calculations apply to the other elements. We also note that our results and other experimental values for V, Fe, Ni, Cu and Zn are larger than the XCOM adopted values, especially above the K-edge where discrepancies can be significant, i.e. more than 5% (see tables). Neither XCOM adopted values nor our experimental results reproduce the fine structure above the K-edge. In detail, our experimental measurements are in excellent agreement with XCOM data for Ti, and the relative discrepancies are less than 5%, with an average of around 2% or 3% on average. For V, the discrepancies are higher and we observe a relative bias of around +4% compared with XCOM data above the K-edge. In the case of Fe, our results are in good agreement, but remain slightly higher by about +2%, except in the 1000 eV range above the K-edge, where our values diverge from XCOM data and reproduce more closely the Del Grande data [32], except for the fine near-edge structures which are not accessible with the resolution of our experimental setup. In the case of Co, the agreement with XCOM data is good, but our results are still a little higher by about 3%, while the relative difference is larger than 5% above the K-edge. For Ni, our values below the K-edge are around +4% above XCOM data, and the discrepancies are even higher just above the K-edge. For Cu, our experimental points are more than +5% higher than the

2481

lðcm2 =gÞ.

E (eV)

l (cm2/g)

NIST-XCOM [31]

% diff.

4000 4200 4400 4600 4800 4952 5100 5250 5427 5600 5800 6000 6200 6404 6550 6700 6930 7058 7200 7478 7649 7700 7900 8048 8265 8300 8500 8700 8900 9200 9400 9600 9800 10,000 10,200 10,400 10,600 10,800 11,000

271.0 (13) 239.6 (18) 205.7 (15) 184.3 (18) 161.5 (18) 154.3 (18) 135.8 (18) 128.9 (18) 111.7 (17) 102.6 (17) 92.0 (17) 87.9 (12) 81.2 (12) 74.8 (13) 69.6 (13) 64.6 (13) 56.8 (12) 58.2 (13) 433.7 (14) 400.0 (14) 368.3 (13) 361.1 (14) 329.8 (14) 313.9 (14) 292.4 (14) 291.7 (13) 271.1 (14) 256.6 (14) 238.8 (13) 218.6 (13) 205.5 (12) 195.4 (13) 185.5 (10) 174.8 (12) 169.5 (12) 160.2 (13) 150.7 (13) 142.1 (12) 134.4 (12)

257 225 198 175 156 144 132 122 112 102 93.1 84.8 77.5 70.9 66.7 62.6 57.1 54.3 396 361 342 336 315 301 281 278 262 247 232 213 201 190 180 171 162 154 146 139 132

5.4 6.5 3.9 5.3 3.5 7.2 2.9 5.7 0.3 0.6 1.2 3.7 4.8 5.5 4.4 3.2 0.6 7.3 9.5 10.8 7.7 7.5 4.7 4.3 4.0 4.9 3.5 3.9 2.9 2.6 2.2 2.8 3.1 2.2 4.6 4.0 3.2 2.2 1.8

XCOM data below 5 keV, and then the relative difference gradually decreases to fit XCOM values below the K-edge. Above the K-edge, the difference with XCOM data is important, but our results are in very good agreement with Chantler et al. as regards the near-edge attenuation measurements [33]. Finally, for Zn, our data are +8% higher than XCOM values just above the K-edge. To sum up, the largest differences compared to the widely used XCOM database appear for high values of mass attenuation coefficient, especially above the K-edge, where longer acquisition times are necessary and a good signal-to-noise (S/N) ratio is required to avoid counting events that do not belong to the main transmission peak.

3.3. K-absorption jump-ratios As the fitting curves are based on several consistent experimental points above and below the K-binding energy, we used our calculated fitting equations to evaluate the K-jump-ratios of the studied elements. The results are given in Table 3. These jumpratios are evaluated for each element at their theoretical binding energies provided by the recent and comprehensive study of Deslattes et al. [27]. Our calculated K-jump-ratios strongly differ from the values provided by XCOM [31], and we present the relative deviations with respect to XCOM data in the fifth column of Table 3. We find values that are significantly higher by about 10%, except for Ni where the agreement is better but the deviation is still positive. These discrepancies are linked with the large

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Table 8 Co mass attenuation coefficients measurements l(cm2/g). E (eV)

l (cm2/g)

NIST-XCOM [31]

4000 4200 4400 4600 4800 4952 5100 5250 5427 5600 5800 6000 6200 6404 6550 6700 6930 7058 7200 7478 7649 7700 7900 8048 8265 8300 8500 8700 8900 9200 9400 9600 9800 10,000 10,200 10,400 10,600 10,800 11,000

295.0 (11) 257.3 (16) 227.6 (15) 201.6 (16) 179.9 (15) 162.2 (16) 152.2 (15) 140.7 (14) 123.0 (15) 114.7 (15) 98.7 (15) 96.3 (13) 87.6 (11) 82.5 (12) 75.6 (11) 70.4 (11) 64.6 (11) 61.6 (11) 56.5 (11) 51.9 (10) 48.0 (11) 49.4 (11) 391.1 (12) 350.2 (12) 315.2 (12) 313.6 (12) 288.5 (12) 269.9 (12) 255.5 (12) 236.0 (12) 219.4 (12) 208.8 (12) 198.5 (11) 187.0 (10) 175.3 (11) 166.1 (11) 157.1 (11) 149.3 (11) 143.2 (10)

283 248 218 194 172 158 146 135 123 113 103 93.7 85.6 78.3 73.6 69.2 63.1 60.0 56.8 51.2 48.1 47.3 335 320 300 297 279 264 249 229 216 205 194 184 175 166 158 150 143

Table 9 Ni mass attenuation coefficients measurements l (cm2/g). % diff. 4.2 3.7 4.4 3.9 4.6 2.7 4.3 4.2 0 1.5 4.2 2.8 2.3 5.3 2.7 1.8 2.3 2.6 0.5 1.4 0.2 4.4 16.8 9.4 5.1 5.6 3.4 2.2 2.6 3.0 1.6 1.9 2.3 1.6 0.2 0 0.5 0.5 0.1

differences in mass attenuation coefficients just above the K-edge as already discussed. 4. Fluorescence yields After determining the mass attenuation coefficients characterizing the samples, we measured the fluorescence yields using the experimental setup presented in Fig. 2. The setup allows simultaneous recording of the exciting beam and the fluorescence X-rays, since the good spectral resolution of our small HPGe detector is sufficient to discriminate the Ka and the Kb lines as well as the exciting beam. Thus, the fluorescence yield xK can be decomposed into the Ka and Kb intensities, which we denote as xK a and xK b , respectively, where xK ¼ xK a þ xK b . The fluorescence yield is derived from the formula given in [34]. As the setup works in transmission mode, the detector is exposed to the transmitted excitation beam as well as to the fluorescence lines of the sample. The following formula is used to derive the Ka and Kb X-ray fluorescence yields, xK a and xK b , respectively:

IK i

gK i

¼

Z

1

M I0  A g0 0 4p    M ð1  xÞ l0 =q  lK i =q dx  exp A

X

 xK i  sK ðE0 Þ=q 

ð4Þ

where IK i represents the intensity of the K i X-ray fluorescence, I0 being the intensity of the excitation beam, derived from spectrum analysis. These intensities are determined from the spectra using

E (eV)

l (cm2/g)

NIST-XCOM [31]

% diff.

4000 4200 4400 4600 4800 4952 5100 5250 5427 5600 5800 6000 6200 6404 6550 6700 6930 7058 7200 7478 7649 7700 7900 8048 8265 8300 8500 8700 8900 9200 9400 9600 9800 10,000 10,200 10,400 10,600 10,800 11,000

349.5 (15) 299.7 (19) 263.6 (17) 237.6 (17) 207.7 (15) 189.7 (17) 178.1 (17) 163.3 (16) 147.1 (16) 136.5 (16) 120.9 (16) 112.9 (14) 104.5 (13) 95.4 (13) 91.3 (13) 84.5 (12) 78.9 (12) 74.1 (12) 66.3 (12) 57.8 (12) 57.5 (11) 55.4 (11) 53.7 (13) 50.5 (12) 45.1 (11) 48.7 (12) 370.8 (12) 320.2 (13) 296.6 (13) 265.3 (13) 249.8 (13) 236.1 (13) 226.0 (13) 212.2 (11) 200.7 (12) 191.4 (13) 182.1 (12) 172.1 (12) 165.4 (11)

328 287 253 225 200 184 170 157 143 132 120 109 99.6 91.1 85.6 80.5 73.3 69.8 66.1 59.5 56.0 55.0 51.3 48.7 45.3 44.8 314 296 280 258 244 232 220 209 199 189 180 171 163

6.6 4.4 4.2 5.6 3.8 3.1 4.7 4.0 2.8 3.4 0.8 3.6 4.9 4.7 6.6 4.9 7.6 6.2 0.3 2.8 2.8 0.8 4.7 3.7 0.5 8.7 18.1 8.2 5.9 2.8 2.4 1.8 2.7 1.5 0.9 1.3 1.2 0.6 1.5

the COLEGRAM software [30]. lK i =q and l0 =q are the mass attenuation coefficients in the sample at the K i X-ray energy and the excitation energy, respectively, obtained from the fitting equations in Table 2, expressed in cm2/g. gK i and g0 are the full energy peak efficiencies of the detector for the K i X-ray fluorescence and the excitation energies, respectively, as determined in [28]. X ¼ 6:710 102 sr is the solid angle defined by the lead collimator and xK i is the fluorescence yield of the K i X-ray. sK ðE0 Þ=q is the photoelectric mass absorption coefficient (cm2/g) calculated as:

sK ðE0 Þ=q  l0 =q  lK ðE0 Þ=q  scs ðE0 Þ=q  sics ðE0 Þ=q

ð5Þ

where l K ðE0 Þ=q is the mass absorption coefficient for only the L-shells and above at the excitation energy E0 , which is given by an extrapolation of the mass attenuation coefficient values on the lower energy branch. scs ðE0 Þ=q is the mass coherent scattering coefficient and is taken from the XCOM tables [31]. sics ðE0 Þ=q is the mass incoherent scattering coefficient, which can be considered negligible in this energy range. Eq. (4) gives:

  lK i = q  l0 = q 4p  IK i  g0    xK i ¼  X  I0  gK i  sK ðE0 Þ=q 1  exp  M l =q  l =q Ki 0 A ð6Þ The fluorescence yields were measured for all the previous samples except Ni, because the electrode of the HPGe detector is made of the same material, as shown on Fig. 2. Thus, it is impossible to

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Y. Ménesguen, M.-C. Lépy / Nuclear Instruments and Methods in Physics Research B 268 (2010) 2477–2486 Table 10 Cu mass attenuation coefficients measurements l (cm2/g).

Table 11 Zn mass attenuation coefficients measurements l (cm2/g).

E (eV)

l (cm2/g)

NIST-XCOM [31]

% diff.

E (eV)

l (cm2/g)

NIST-XCOM [31]

4000 4400 4600 4800 4952 5100 5250 5427 5600 5800 6000 6200 6404 6550 6700 6930 7058 7200 7478 7649 7700 7900 8048 8265 8300 8500 8700 8900 9200 9400 9600 9800 10,000 10,200 10,400 10,600 10,800 11,000

376.3 (9) 295.2 (22) 259.8 (18) 229.5 (15) 213.3 (16) 190.8 (10) 172.4 (8) 159.3 (8) 145.2 (8) 129.8 (8) 118.3 (8) 108.8 (6) 100.2 (6) 95.1 (6) 88.1 (6) 80.1 (6) 78.2 (6) 72.3 (6) 63.5 (6) 58.8 (6) 59.9 (6) 54.2 (6) 51.5 (5) 48.1 (6) 48.2 (6) 44.4 (6) 42.0 (6) 38.5 (6) 300.4 (9) 270.2 (7) 248.4 (6) 236.6 (6) 221.9 (6) 210.2 (6) 199.1 (6) 189.2 (6) 178.0 (6) 171.2 (6)

347 268 238 212 195 180 166 152 139 127 116 106 96.6 90.8 85.4 77.8 74.0 70.1 63.2 59.4 58.3 54.4 51.7 48.1 47.5 44.5 41.7 39.2 263 250 238 227 216 206 196 187 178 170

8.4 10.2 9.2 8.3 9.4 6.0 3.9 4.8 4.5 2.2 1.9 2.6 3.7 4.7 3.2 2.9 5.7 3.2 0.5 0.9 2.7 0.4 0.4 0.1 1.4 0.2 0.8 1.7 14.2 8.1 4.4 4.2 2.7 2.1 1.6 1.2 0 0.7

6700 6930 7058 7200 7478 7700 7900 8100 8300 8450 8500 8639 8700 8800 8900 9100 9200 9400 9500 9572 9700 9800 9900 10,000 10,100 10,200 10,300 10,400 10,500 10,600 10,800 11,000

97.4 (12) 89.4 (12) 83.2 (12) 81.5 (12) 70.9 (12) 66.2 (23) 62.4 (23) 58.4 (24) 53.4 (11) 51.6 (22) 50.0 (11) 46.7 (11) 48.2 (12) 46.4 (24) 43.8 (10) 40.8 (10) 40.8 (12) 35.8 (11) 35.9 (12) 37.3 (12) 275.3 (25) 262.5 (14) 256.9 (12) 247.5 (13) 242.4 (25) 232.4 (10) 228.0 (24) 219.1 (12) 207.5 (24) 205.7 (13) 197.8 (13) 186.3 (11)

95.3 86.9 82.7 78.3 70.6 65.2 60.8 56.8 53.1 50.5 49.7 47.6 46.7 45.2 43.8 41.3 40.0 37.8 36.7 35.9 251 245 239 233 227 222 217 212 207 202 193 184

% diff. 2.2 2.8 0.7 4.1 0.4 1.6 2.6 2.9 0.6 2.2 0.5 2.0 3.2 2.8 0.1 1.3 1.9 5.2 2.3 4.0 9.7 7.1 7.5 6.2 6.8 4.7 5.0 3.4 0.2 1.8 2.5 1.2

measure within any reliable uncertainty the fluorescence yields of Ni, since the contribution to the K-fluorescence lines of the 50 nm-thick electrode are of the same order of magnitude as the collimated 10-lm-thick sample. 4.1. Results and discussion For each element, several spectra were recorded at different excitation energies within the range of the measured mass attenuation values to ensure that the mass attenuation fits remained valid. The results obtained are reported in Table 4 and presented in Fig. 5. The Ka, b fluorescence yields are measured at five different energies for Ti, V and Fe, three different energies for Zn and seven different energies were used for Co and eight for Cu. The uncertainty associated with each xK is the combined standard deviation of all experimental fluorescence yield measurements and the uncertainty associated with the solid angle X, the uncertainties associated with the other terms in Eq. (6) being negligible. The results of the fluorescence yield measurements are compared with the values adopted by Bambynek [35], as well as with theoretical calculations and recent experimental results. These values are presented on Fig. 5. The theoretical results also presented here are from Kostroun [36] and Chen [37], and are indicated as green and purple points, respectively. Values from previous compilations are due to Bambynek [35,38], and are indicated as red solid lines with their associated uncertainties in black lines. Other experimental values from the literature are shown on the same graph. The present measurements are in good agreement with adopted values, and satisfactorily reproduce the general increasing

Fig. 5. K-fluorescence yield, xK , as a function of atomic number. Red solid line [35], red points [39], green points [40], orange points [19], cyan points [41], dark yellow points [42], blue points [43], green points [36], purple points [37]. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

tendency. Fluorescence yields for Ti, Co and Zn have a relative deviation of less than 2% compared to the Bambynek adopted values, the discrepancy being around 3% for Fe, and below 5% for V and Cu. 4.2. Ka and Kb relative emission ratios Numerous experimental and theoretical studies also deal with the ratio of the Kb/Ka fluorescence lines, which can also be calculated from the ratio of the associated fluorescence yields xK b =xK a . Results from the present experiments are shown in Fig. 6, where they are compared with theoretical calculations and

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Fig. 6. K b =K a relative X-ray emission ratios. Black points: this study, dash dotted black line [47], dotted black line [48], orange crosses [49], green crosses [44], red crosses [41], blue crosses [46], purple crosses [45], red line [38] and black lines: associated uncertainties. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 9. Mass attenuation coefficients l for Fe in cm2/g. Other points come from XCOM [31,2] (He93), [51] (Ca67), [53] (Da69) and [32] (De71), [4] (Ch95).

Fig. 10. Mass attenuation coefficients l for Co in cm2/g. Other points come from [2] (He93), [51] (Ca67), [52] (Ho68) in [1,55] (Hop59), [4] (Ch95). Fig. 7. Mass attenuation coefficients l for Ti in cm2/g. Other points come from [2] (He93), [50] (Hu66), [51] (Ca67), [52] (Ho68) in [1,53] (Da69), [4] (Ch95).

Fig. 11. Mass attenuation coefficients l for Ni in cm2/g. Other points come from [2] (He93), [50] (Hu66), [51] (Ca67), [52] (Ho68) in [1,53] (Da69), [4] (Ch95). Fig. 8. Mass attenuation coefficients l for V in cm2/g. Other points come from [2] (He93), [51] (Ca67), [52] (Ho68) in [1,53] (Da69) and [54] (Pa74), [4] (Ch95).

other experimental points. First of all, the widely accepted theoretical calculations due to Scofield [44], which are derived from a rel-

ativistic Hartree–Fock approach, lead to a better reproduction of the experimental points presented here [45,46] and the data compiled by Schönfeld [38]. While our results are compatible with the adopted values within their uncertainties, it should be pointed out

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measurements should be undertaken in this region to improve the coverage and accuracy of mass attenuation databases. We also provide a new evaluation of K-fluorescence yields by carrying out a direct measurement of the K a and K b fluorescence yields, xK a and xK b , which, to our knowledge, has so far not been reported, and which leads to an independent measurement of the relative emissions ratios. These new measurements confirm the previously adopted fluorescence yield values and contribute to a new appraisal of the uncertainties associated with these data. Our experimental setup makes it possible to measure fluorescence yields with a low degree of uncertainty, and other materials should be studied where large uncertainties persist, for example, in determining the K-fluorescence yield of lighter elements, L-fluorescence yields and Coster–Kronig coefficients. References Fig. 12. Mass attenuation coefficients l for Cu in cm2/g. Other points come from [2] (He93), [4] (Ch95), [56] (Cr92), [57] (Un88), [33] (Ch01), [50] (Hu66), [52] (Ho68) in [1,53] (Da69).

Fig. 13. Mass attenuation coefficients l for Zn in cm2/g. Other points come from [2] (He93), [51] (Ca67), [4] (Ch95).

that several authors report a great dispersion of experimental values. Recent experimental points provided by Han et al. [41] are always below the adopted values and are closer to previous theoretical calculations. Unfortunately, our experimental results cannot demonstrate whether there is a plateau in the K b =K a ratio between Z ¼ 20 and Z ¼ 30, or whether this ratio is situated between 0.11 and 0.12 or between 0.13 and 0.14.

5. Conclusion In this study, we measure the mass attenuation coefficients around the K-transition edges for the elements Ti, V, Fe, Co, Ni, Cu and Zn, and establish an uncertainty estimate for each experimental point. We use these data to calculate fitting equations below and above the K-absorption edges, which are then used to determine the K-absorption jumps. All these data are compared with previously tabulated data [31]. The most significant discrepancies are found just above the K-edge, where our experimental values are higher by several percent. This leads to a relative deviation of about +10% in the determination of the K-absorption jump for all the studied elements. Our experimental setup is not able to measure fine structures above the K-edge, so further experimental

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