Measurements of absolute M-subshell X-ray production cross sections of Th by electron impact

Chemical Physics 440 (2014) 18–24

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Measurements of absolute M-subshell X-ray production cross sections of Th by electron impact A. Moy a,b,⇑, C. Merlet a, O. Dugne b a b

GM, CNRS, Université de Montpellier II, Place E. Bataillon, F-34095 Montpellier, France CEA, DEN, DTEC, SGCS, LMAC, F-30207 Bagnols-sur-Cèze, France

a r t i c l e

i n f o

Article history: Received 24 April 2014 In final form 2 June 2014 Available online 12 June 2014 Keywords: M subshells X-ray production cross section Ionization cross section Thorium EPMA Standardless

a b s t r a c t Measurements of absolute M-subshell X-ray production cross sections for element Th were made by electron impact for energies ranging from the ionization threshold up to 38 keV. Experimental data were obtained by measuring the X-ray intensity emitted from ultrathin Th films deposited onto self-supporting C backing films. The measurements were conducted with an electron microprobe using high-resolution wavelength dispersive spectrometers. Recorded intensities were converted into absolute X-ray production cross sections by means of atomic data and estimation of the number of primary electrons, target thickness, and detector efficiency. Our experimental X-ray production cross sections, the first to be reported for the M subshells of Th, are compared with X-ray production cross sections calculated with the mean of ionization cross sections obtained from the distorted-wave Born approximation. The Ma X-ray production cross section calculated is in excellent agreement with the measurements, allowing future use for standardless quantification in electron probe microanalysis. Ó 2014 Elsevier B.V. All rights reserved.

1. Introduction In many fields of materials science, electron probe microanalysis (EPMA) is widely used to qualitatively and quantitatively characterize the elemental composition of samples. However, quantitative analysis is not always possible to achieve due to the lack of standard samples, especially for heavy elements like actinides. Standardless quantification methods are then employed with the help of calculated standards. To be reliable, the predictions of calculated standards require knowledge of accurate atomic data and especially accurate X-ray production cross sections. In the case of actinides, experimental acquisitions cannot be performed systematically due to overly high radiotoxicity or too short a lifetime. The values of the cross sections are therefore predicted by theoretical models, but their reliability for the heavy elements is not well established, especially near the ionization threshold, and needs to be confirmed experimentally. Despite the fact that the measurement of X-ray production cross sections has been the subject of intense studies over several decades, available experimental data is still very scarce [1]. Most of the experimental data pertains to the K shell, while there is almost ⇑ Corresponding author at: CEA, DEN, DTEC, SGCS, LMAC, F-30207 Bagnols-surCèze, France. Tel.: +33 466339257. E-mail address: [email protected] (A. Moy). http://dx.doi.org/10.1016/j.chemphys.2014.06.001 0301-0104/Ó 2014 Elsevier B.V. All rights reserved.

no data for the L and M shells. The main reason which may explain this lack of experimental data for the L and M shells is that the X-ray production cross sections are more complicated to determine than the K shell because they involve multiple subshell cross sections, Coster Kronig (CK) transitions and super-Coster–Kronig (sCK) transitions which are not well known. When available, experimental data has large uncertainties and results obtained from different authors sometimes differ by more than the quoted uncertainties. The reliability of experimental and calculated X-ray production cross sections by electron impact, which are also required in practical applications such as in astrophysics, plasma physics, radiation physics, and Auger electron spectroscopy, is thus extremely difficult to determine. To assess the reliability of calculated X-ray production cross sections of heavy elements, previous measurements were conducted on the elements Pb and U [2,3]. Continuing this theme, the element Th was chosen here because of its practical interest in the study of U–Th–Pb samples e.g., monazite rocks used in geochronology [4] or lunar rocks. To the authors’ knowledge, no experimental data exists for the element Th in the M subshells. Accurate new measurements were therefore needed. In this work, we report experimental measurements of the Ma, Mb, Mc, M2N4, and M1N3 X-ray production cross sections by electron impact, with energies ranging from the ionization threshold up to 38 keV. A correspondence between the Siegbahn notation

A. Moy et al. / Chemical Physics 440 (2014) 18–24

and the IUPAC notation [5] of the measured X-ray lines is summarized in Fig. 1. The measurement of these five X-ray lines enables the determination of the ionization cross sections for the five M subshells. The recorded Ma, Mb, Mc, M2N4 and M1N3 X-ray lines were chosen because they correspond to the most intense X-ray lines produced by the relaxation of the M5, M4, M3, M2 and M1 subshells, respectively. X-ray production cross sections were measured on thin Th films deposited onto self-supported C backing films and recorded using an electron microprobe equipped with wavelength dispersive spectrometers (WDSs) which ensure a high spectral resolution. Measured X-ray intensities were converted into X-ray production cross section with help of a complex methodology using experimental parameters such as the number of incident electrons, target thickness, and detector efficiency. Experimental X-ray production cross sections were compared with theoretical X-ray production cross sections calculated by Bote et al. [6] within the distorted-wave Born approximation (DWBA). This model predicts values of ionization cross sections which then need to be converted into X-ray production cross sections for comparison. This conversion requires atomic data such as X-ray emission rates, fluorescence yields, CK and sCK yields, and vacancy-transfer probabilities. 2. Materials and methods The experimental procedure used in this work corresponds to that described in the references [2,7]. X-ray production cross sections were deduced from measurements of X-rays emitted from ultrathin self-supported targets. For ultrathin samples and for incident electrons with sufficiently high energy, the latter are assumed to penetrate the sample following a straight trajectory without losing energy. For an ultrathin self-supported sample of thickness t, X-ray production cross-section rX of a given X-ray line is expressed by:

rX ðEÞ ¼

4p N0 ne eðEph ÞDX t

NX ðEÞ

19

voltage generator from the ionization threshold up to 38 keV. Each microprobe used in this work was equipped with five WDSs. The absolute X-ray production cross sections were recorded with three different WDSs for each microprobe. The M X-ray lines were measured by a pentaerythritol (PET) monochromator crystal in a Johann configuration or a large pentaerythritol (LPET) monochromator crystal in a Johansson configuration. The inter-reticular distance of these crystals is 4.375 Å. The electron beam was set perpendicular to the sample and the X-rays were collected at a take-off angle of 40° from the sample. A flow proportional counter using a P10 (90% Ar-10% CH4) gas associated with a pulse-height analyzer (PHA) were used to record the diffracted X-rays. 2.2. Samples The samples used in this study consisted of an ultrathin film of Th deposited by vacuum evaporation onto a self-supported C backing film. The C substrate was chosen because it gives a low backscattering yield and good mechanical properties. In order to further reduce the backscattering effects, which appear mainly at low electron energy, the carbon thickness was reduced by using an oxygen plasma cleaner. During the evaporation, five sets of targets were made with different thicknesses of Th in a range from 0.8 to 4.4 nm, by assuming a mass density of 11.7 g/cm3. In order to determine the target thickness, the Ma X-ray intensity emitted from the self-supported samples was recorded depending on the electron energy and compared with the Ma X-ray intensity emitted from a bulk sample of Th. The ratio of these two quantities, called the k-ratio, was analyzed with the EPMA code XFILM as a function of the incident electron energy, as described in [8,9]. Using an analytical model, the code was able to calculate the Th film thickness. The thickness of the thinner set of samples was found to be 0.966 lg/cm2 and for the thicker set of samples it was found to be 5.198 lg/cm2. The uncertainty associated with the sample thickness determination was estimated to be better than 5% [9].

ð1Þ

where NX(E) is the intensity of recorded characteristic X-rays, N0 is the number of atoms per unit volume, ne and E denotes the total number and the energy of incident electrons impacting the sample, respectively, e(Eph) is the spectrometer efficiency at the photon energy Eph of the recorded X-ray line, and DX is the solid angle of collection.

2.3. M X-ray measurements The use of WDSs enabled a good discrimination between the M X-ray lines, as shown in Fig. 2. This spectrum was acquired on a 5.198 lg/cm2 thick Th sample at 15 keV and 5000 nA, with an LPET crystal. The spectrum was corrected from the variation of the spectrometer gain depending on the photon energy by means of an

2.1. Instrumentation The measurements were carried out by two CAMECA SX100 electron microprobes, one located at the CEA Marcoule and the other at the University of Montpellier II. Two instruments were used in order to strengthen the measurement results and to reduce uncertainties. The monoenergetic electron beam was generated by an electron gun and accelerated to the desired energy by a high

Fig. 1. Correspondence between M X-ray line designations (Siegbahn) and subshell electronic transitions (IUPAC convention).

Fig. 2. Th M X-ray line spectrum acquired on a 5.198 lg/cm2 thick Th sample with a 15 keV electron beam.

20

A. Moy et al. / Chemical Physics 440 (2014) 18–24

analytical calculation. Because the measurements were performed on ultrathin self-supported samples, M-subshell absorption edges are not visible on the spectrum. Characteristic X-ray energies used to label the lines were taken from [10] except for the M1N2 X-ray line. Ref. [10] references this line at 3957 eV, just before the M3O4,5 lines located at 3959 eV. But a detailed spectrum does not show any evidence of the presence of the M1N2 line at this energy and furthermore, Ref. [11] locates the M3O4 and M3O5 X-ray lines at 3950.5 eV and 3957.8 eV, respectively. However, an unreferenced line is clearly visible at 4013 eV and this energy corresponds to the energy difference between the M1 subshell (5182 eV) and the N2 subshell (1168 eV) [10]. The M1N2 line was then found to be located at 4013 eV on the spectrum. This result is consistent with data found in the Evaluated Atomic Data Library (EADL) [12] which locates the M1N2 line at a higher energy than the M3O4,5 lines. The measured energy of the most intense X-ray lines is in agreement with previous studies [13]. The Ma (M5N6,7 transitions), Mb (M4N6 transition), Mc (M3N4,5 transitions), M2N4, and M1N3 X-ray lines are well resolved, but extraction of their intensity is not a straightforward task. A detailed Ma X-ray line spectrum acquired at 15 kV on a 5.198 lg/cm2 thick Th sample with an LPET crystal is shown in Fig. 3. The Ma line is composed of the Ma1 (M5N7 transition) and the Ma2 (M5N6 transition) diagram lines. The X-ray lines observed in the high-energy side of the Ma line correspond to satellite lines. These satellite lines arise from the relaxation of double- or triple-vacancy states with the main hole in the M5 subshell and one or two ‘spectator’ vacancies in the N and/or O subshells. The latter vacancies result from shake off, Auger and/or CK transitions. The energy shift of the maximum of the N satellite structure from the maximum of the diagram line was found to be 8 eV for the Ma line and 7 eV for the Mb line. These results are in agreement with the calculation of Polasik et al. [14]. For each line of interest, a detailed spectrum was acquired around the characteristic X-ray energy with a 15 keV electron beam. Because both diagram and satellite lines can be represented by pseudo-Voigt functions, which consist of a weighted sum of Gaussian and Lorentzian functions [15], the spectra were fitted with a combination of these functions. For each incident electron energy, the area of a given X-ray line was determined by the product of the net counting rate measured at the peak maximum and the normalized peak area. The M X-ray intensity at the maximum of each line of interest was recorded for incident electron energies varying from the ionization threshold up to 38 keV. The X-ray intensity was recorded

with an energy step of 0.5 keV for energies from the ionization threshold up to 10 keV, of 1 keV for energies from 10 up to 30 keV, and of 2 keV for energies from 30 up to 38 keV. The Ma, Mb and Mc X-ray lines were measured on the Th 0.966 lg/cm2 sample, while the M2N4 and M1N3 X-ray lines were measured on the Th 5.198 lg/cm2 sample because of their low intensity. With the latter sample, at low energy, electron energy loss and electron straggling cannot be considered negligible. To take these phenomena into account, the intensities recorded at low energy were corrected by a factor corresponding to the ratio between the Ma X-ray intensity recorded on the thickest sample and the Ma X-ray intensity recorded on the thinnest sample at the same energy. This correction, which was applied for energies up to 19 keV, lowers the measured intensities by 4% on average. The use of self-supported samples ensured a high signalto-noise ratio, which was found to be better than 75 for the Ma line measured at 10 keV with an LPET crystal on a Th 5.198 lg/cm2 sample. This ensured a high accuracy in the measurement of the X-ray intensity and in the determination of the X-ray line area. 2.4. WDS efficiency The total spectrometer efficiency, which is the product of the intrinsic spectrometer efficiency by the solid angle of collection, can be expressed by [7]:

eðki ÞDX ¼ R Eðki Þ

Ni Dk

Eðki þDkÞ

NðEÞdE

ð2Þ

where the product eðki ÞDX denotes the total spectrometer efficiency, ki is the wavelength channel of interest, Dk is the channel width, Ni is the experimental number of X-rays detected between (ki , ki þ Dk) per incident electron, and N(E)dE is the theoretical number of bremsstrahlung photons emitted from the reference sample per incident electron with energies between E and E + dE. The bremsstrahlung measurements were performed on a C reference sample at the energies of the measured M X-ray lines with electron incident energies of 6 and 10 keV and with a beam current of 600 nA. In order to reduce the contribution of multiple diffraction effects and specular reflection, pulse height analyzers (PHAs) were set in differential mode with a narrow voltage window. The theoretical bremsstrahlung spectrum N(E) was calculated by means of the Monte Carlo code PENELOPE [16]. A previous study [17] demonstrated the reliability of this code in simulating absolute bremsstrahlung spectra for several elements. For carbon, the accuracy of the simulated values is better than 5%. 2.5. Theoretical calculation of X-ray production cross sections

Fig. 3. High-resolution Ma X-ray spectrum emitted from a 5.198 lg/cm2 Th sample. The dots represent the experimental spectrum, while the solid lines represent the fitted profiles.

M subshell electron-impact ionization cross sections of Th were calculated using the analytical formula of Bote et al. [18]. These authors gave useful parameterizations of ionization cross sections obtained from extensive cross-section calculations. The calculations were obtained by using a composite scheme that combines the distorted-wave Born approximation (DWBA) with the plane wave Born approximation (PWBA) to produce cross sections with the reliability of the DWBA for electrons with energies from ionization threshold up to 1 GeV for the K, L and M shells of elements from hydrogen (Z = 1) to einsteinium (Z = 99) [6]. In order to compare our experimental measurements with the calculated M-subshell ionization cross sections, the latter were converted to Ma, Mb, Mc, M2N4, and M1N3 X-ray production cross sections. This conversion depends on the shell considered and the measured X-ray line. Note that in the experimental energy range used here, 3–38 keV, vacancies cannot be produced in the K shell of Th.

21

A. Moy et al. / Chemical Physics 440 (2014) 18–24 Table 1 M-subshell fluorescence yields xMi for Th adopted in this study [12].

Table 5 Measured rMa, rMb, rMc, rM2N4 and rM1N3 X-ray production cross sections for Th (in barn).

xM 5

xM 4

xM 3

xM2

xM 1

0.050

0.052

0.012

0.009

0.006

Table 2 M-subshell Coster–Kronig yields Sij and f45 for Th adopted in this study [12]. S12

S13

S14

S15

S23

S24

S25

S34

S35

f45

0.096

0.59

0.096

0.128

0.092

0.598

0.096

0.060

0.626

0.062

Table 3 Ratios of the X-ray emission rates CMiNj for the Mi–Nj radiative transitions to the total emission rates CMiTotal for all possible transitions to the Mi subshell for Th adopted in this study [12].

CM5 N6;7 =CM5 Total CM4 N6 =CM4 Total CM3 N4;5 =CM3 Total CM2 N4 =CM2 Total CM1 N3 =CM1 Total 0.961

0.940

0.638

0.547

0.232

The Ma, Mb, Mc, M2N4, and M1N3 X-ray production cross sections can be expressed, respectively, as:

rM a ¼

CM5 N6;7  L2 M 5 þ r L3 g  L3 M 5 x ðr g þ r L2 g CM5 Total M5 L1 L1 M5  L1 M1 þ rL2 g  L2 M1 þ rL3 g  L3 M 1 Þ þ ðrM1 þ rL1 g  ðS15 þ S12 S25 þ S13 S35 þ S12 S23 S35 þ f45 ðS14 þ S12 S24 þ S13 S34 þ S12 S23 S34 ÞÞ  L1 M2 þ rL2 g  L2 M2 þ rL3 g  L3 M 2 Þ þ ðrM2 þ rL1 g  ðS25 þ S23 S35 þ f45 ðS24 þ S23 S34 ÞÞ  L1 M3 þ rL2 g  L2 M3 þ rL3 g  L3 M3 ÞðS35 þ S34 f45 Þ þ ðrM3 þ rL1 g  L1 M4 þ rL2 g  L2 M4 þ rL3 g  L3 M4 Þf45 þ rM5 Þ þ ðrM4 þ rL1 g

rM b ¼

ð3Þ

CM 4 N 6  L2 M4 þ rL3 g  L3 M 4 x ðr g þ rL2 g CM4 Total M4 L1 L1 M4

E (keV)

rMa

rMb

rM c

rM2N4

rM1N3

3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 32 34 36 38

0.8 151 384 553 672 733 789 834 870 870 882 883 890 892 870 859 843 830 807 784 768 758 740 735 718 703 690 679 666 654 647 629 623 606 593 578 559 567 565

40.5 179 277 352 412 451 485 507 512 520 529 529 537 528 523 511 504 489 481 472 462 454 450 441 433 426 417 409 403 399 387 384 382 386 365 362 356 356

1.5 3.1 20.1 34.1 45.2 52.2 59.1 64.6 66.7 70.3 72.2 74.2 73.9 74.8 75.3 75.2 73.9 72.7 71.3 70.4 70.6 69.1 68.8 67.5 66.4 63.9 64.9 63.3 62.1 61.5 59.4 58.7 57.0 54.9 56.9 52.4 53.7 51.9

0.1 1.0 2.9 4.1 5.3 6.2 6.8 7.5 7.8 8.4 8.5 8.4 8.9 9.1 9.0 9.0 8.7 8.8 8.8 8.9 8.7 8.5 8.6 8.2 8.2 8.1 8.0 7.6 7.5 7.4 7.2 7.2 6.8 6.7 6.3 6.5

0.17 0.14 0.49 0.79 1.29 1.64 1.74 1.61 1.82 2.12 2.08 2.07 2.21 2.14 2.27 2.30 2.18 2.16 2.18 2.21 2.10 2.04 2.08 1.85 1.89 1.88 1.84 1.61 1.54 1.57 1.58 1.60 1.41 1.48 1.27 1.32

 L1 M 1 þ r L2 g  L2 M 1 þ r L3 g  L3 M 1 Þ þ ðrM1 þ rL1 g  ðS14 þ S12 S24 þ S13 S34 þ S12 S23 S34 Þ  L1 M 2 þ r L2 g  L2 M 2 þ r L3 g  L3 M2 ÞðS24 þ S23 S34 Þ þ ðrM2 þ rL1 g  L1 M 3 þ r L2 g  L2 M 3 þ r L3 g  L3 M3 ÞS34 þ rM4 Þ þ ðrM3 þ rL1 g

rM c ¼

the Mi subshell, rMi and rLi are the ionization cross sections for the Mi and Li subshells, respectively, and nLi Mj is the radiative plus non-radiative yield for transitions of vacancies from the Li subshell to the Mj subshell. Finally, Sij and f45 are the yields for CK transitions in the Mj subshell produced in the first decay step of an Mi vacancy. Notice that super-CK transitions are not allowed for elements with Z P 65 [19]. M-subshell relaxation parameters are available from the theoretical calculations of McGuire [20] and Chen et al. [21,22]. M-subshell fluorescence yields and CK transition yields have been compiled by Sögˇüt et al. [23], Chauhan and Puri [24] and Kaur and Mital [25] from the available calculations. Vacancy transfer probabilities have been compiled by Chauhan et al. [26]. The atomic relaxation parameters can also be extracted from the EADL [12]. To the authors’ knowledge, the experimental values of these atomic parameters for element Th are not available in the literature. For the sake of internal consistency, all the atomic parameters required to convert the M-subshell ionization cross sections into the M X-ray production cross sections were extracted from the EADL and are listed in Tables 1–4.

ð4Þ

CM3 N4;5  L2 M3 þ rL3 g  L3 M 3 x ðr g þ rL2 g CM3 Total M3 L1 L1 M3  L1 M 1 þ r L2 g  L2 M 1 þ r L3 g  L3 M1 ÞðS13 þ S12 S23 Þ þ ðrM1 þ rL1 g    L3 M2 ÞS23 þ rM3 Þ þ ðrM2 þ rL1 gL1 M2 þ rL2 gL2 M2 þ rL3 g

rM 2 N 4 ¼

rM 1 N 3 ¼

ð5Þ

CM2 N4  L2 M 2 þ r L3 g  L3 M 2 x ðr g þ r L2 g CM2 Total M2 L1 L1 M2  L1 M1 þ rL2 g  L2 M1 þ rL3 g  L3 M1 ÞS12 þ rM2 Þ þ ðrM1 þ rL1 g

ð6Þ

CM1 N3  L2 M 1 þ r L3 g  L3 M 1 þ r M 1 Þ x ðr g þ r L2 g CM1 Total M1 L1 L1 M1

ð7Þ

where CMi Nj is the X-ray emission rate for electronic transitions between the subshells of interest Mi and Nj, and CMi Total is the X-ray emission rate for all the possible transitions from the Mi subshell to an outer shell. xMi is the fluorescence yield for

Table 4 Radiative plus non-radiative probabilities for the transitions of vacancies from the L subshells to the Mi subshells for Th adopted in this study [12].

gL1 M5

gL2 M5

gL3 M5

gL1 M4

gL2 M4

gL3 M4

gL1 M3

gL2 M3

gL3 M3

gL1 M2

gL2 M2

gL3 M2

gL1 M1

gL2 M1

gL3 M1

0.775

0.295

0.660

0.427

0.578

0.214

0.295

0.119

0.273

0.115

0.195

0.053

0.121

0.047

0.054

22

A. Moy et al. / Chemical Physics 440 (2014) 18–24

Fig. 4. Ma, Mb, Mc, M2N4, M1N3 X-ray production cross sections versus incident electron energy for the element Th. The dots represent the experimental values found and the solid lines represent the X-ray production cross sections calculated using the DWBA. The uncertainty bars plotted represent the global uncertainties of the measurements, to one standard deviation. Grey shaded areas are the uncertainties of the calculated cross sections.

Table 6 Uncertainties in the experimental M-line X-ray production cross sections. Source

Random uncertainties Electron current Target thickness Detector efficiency Fitting procedure Quadrature sum

Uncertainty (%) Ma

Mb

Mc

M2N4

M1N3

2.3 1 5 5.8 2 8.5

2.8 1 5 6.3 2 9

5.4 1 5 5.3 1 9.5

6.8 1 5 5.2 1 10

23.5 1 5 5.2 1 25

3. Results and discussion In the following, experimental X-ray production cross sections are compared to predicted converted theoretical ionization cross sections. Table 5 presents the experimental results and Fig. 4 displays the experimentally determined M X-ray production cross sections in comparison with the Bote et al. calculations converted with the

atomic parameters extracted from the EADL. In Fig. 4, the error bars represent the global uncertainties of the measurements (to one standard deviation). Measured X-ray production cross sections are affected by both random and systematic uncertainties. Random uncertainties are introduced during the X-ray measurements and mainly come from counting statistics, but also from stray radiation, sample non uniformity and instrumental drift. These uncertainties were evaluated from repeated measurements with sufficiently long counting times. For each energy measured, the random uncertainties are different and therefore they affect the cross section curve shapes. During the conversion of the measured X-ray yields into X-ray production cross sections (Eq. (1)), systematic uncertainties arise from the values adopted for the number of incident electrons, target thickness, spectrometer efficiency (which includes that of Monte Carlo simulation results) and the fitting procedure. Systematic uncertainties are the same for each measured energy and therefore they do not affect the cross section curves but only their absolute value. For each measured X-ray production cross section, the sources of random and systematic uncertainties are given in Table 6. The total uncertainties are obtained as the sum in quadrature of each

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A. Moy et al. / Chemical Physics 440 (2014) 18–24

Fig. 5. Relative contribution to the Ma and M1N3 X-ray emission cross sections produced by the different L and M subshells, as indicated by the legends.

component. They are estimated to be 8.5% for the M. line, 9% for the M. line, 9.5% for the M. line, 10% for the M2N4 line and 25% for the M1N3 line. In Fig. 4, the grey shaded areas represent the global uncertainties of the calculated cross sections, which are due to the uncertainties of the values adopted for the relaxation parameters. M-shell emission rates and fluorescent yields extracted from the EADL are believed to be accurate to 20% and 15%, respectively. The CK yield for the M1 subshell is believed to be accurate to 30% and the CK yields for the other M subshells are believed to be accurate to 15%.The width of the uncertainty bands is estimated to be about 40%. Globally, experimental results are in agreement with the theoretical predictions within the uncertainties. The experimental Ma X-ray production cross section agrees particularly well with the calculated cross section in both shape and magnitude. Except for the Ma line, the converted predictions of the DWBA calculations of Bote et al. tend to underestimate our measurements. However, the curve shapes of the DWBA cross sections for all the X-ray lines reproduce the curve shapes of the measurements well, especially near the ionization threshold. The calculated Mc X-ray production cross section is 45% lower than the measured cross section. To assess the reliability of the experimental results for the Mc cross section, an absolute measurement of the M3N1 X-ray production cross section at 10 keV was carried out. As for the Mc X-ray line, the M3N1 X-ray line arises from a radiative transition with primary vacancy located in the M3 subshell. The experimental M3N1 X-ray production cross section at 10 keV was found to be 16.5 ± 1.7 barn, while the corresponding calculated cross section, computed with an emission rate extracted from the EADL and equal to 0.158, was estimated to be 10.1 barn. The disagreement between the experimental and the calculated results is of the same order of magnitude for the Mc and the M3N1 X-ray production cross section. This strengthens the experimental results of the Mc line. The discrepancy is probably due to the atomic parameter values adopted for the conversion of the calculated ionization cross section into an X-ray production cross section. As the relative contribution of the M1 and M2 subshell ionization cross sections account for only 11% in the production of the Mc line, the discrepancy noted is probably mainly due to the value adopted for the fluorescence yield. Fig. 5 shows the relative contribution to the Ma and M1N3 X-ray production cross sections from the different L and M subshells, calculated using the formula of Bote et al. as a function of the electron incident energy. The main contribution of the Ma line comes from the M5 and M3 subshells. The contribution of the other subshells is one or several times lower. For the M1N3 line, the main contribution is due to the M1 subshell, while the contribution of the L-subshells is two orders of magnitude lower. Therefore, in Eqs. (3)–(7), we can safely disregard the contribution of the L-subshells and solve this set of

equations for the ionization cross sections rMi , beginning by rMi and solving the other equations by substitution. Note that, for incident electron energies lower than the ionization threshold of the L3 subshell, say 16.3 keV, the expressions of the ionization cross sections are exact. Results, calculated with atomic relaxation parameters extracted from the EADL, are listed in Table 7. Due to the uncertainties on the atomic parameters adopted, global uncertainties for the experimental M-subshell ionization cross sections are found to be 35%, 30%, 30%, 30%, and 45% for the M1, M2, M3, M4, and M5 subshells, respectively.

Table 7 Experimental M-subshell ionization cross sections of Th (in barn). E (keV)

rM5

rM4

rM3

rM2

rM1

3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 32 34 36 38

16 2981 7509 9501 10,730 10,932 11,432 11,681 11,907 11,723 11,652 11,496 11,428 11,479 10,968 10,679 10,362 10,199 9847 9516 9255 9053 8802 8743 8506 8288 8273 7966 7830 7696 7631 7456 7393 7175 7079 6640 6620 6709 6822

817 3635 5500 6812 7694 8269 8735 8992 9012 9058 9171 9077 9224 9048 8889 8618 8473 8187 8075 7891 7672 7517 7476 7312 7140 7090 6894 6759 6672 6641 6423 6387 6374 6479 6101 6084 6016 5995

191 404 2547 4375 5650 6414 7081 7632 7842 8358 8507 8635 8615 8740 8728 8745 8522 8353 8228 8122 8132 7931 7940 7795 7625 7413 7523 7318 7183 7210 6968 6867 6646 6352 6707 6097 6364 6098

189 548 773 987 1145 1264 1412 1464 1552 1578 1564 1647 1695 1676 1665 1608 1639 1642 1651 1612 1585 1603 1534 1535 1507 1489 1443 1419 1394 1360 1348 1294 1256 1194 1238

98 349 564 925 1175 1248 1159 1309 1522 1496 1486 1591 1540 1630 1655 1564 1551 1567 1585 1508 1466 1497 1328 1359 1349 1323 1155 1109 1125 1132 1153 1012 1062 910 949

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4. Conclusion In conclusion, accurate measurements were carried out for the Ma, Mb, Mc, M2N4 and M1N3 X-ray production cross sections for Th in the energy range of 3–38 keV, using self-supported thin film targets, two different electron microprobe instruments and several high-resolution WDSs. The experimental cross sections were compared with the DWBA prediction calculated by Bote et al. and converted using atomic parameters extracted from the EADL. The Ma X-ray production cross-section calculated was found to be in excellent agreement with the measurements, within the uncertainties of the measurements and the relaxation parameters adopted. This result confirms our previous studies performed on the heavy elements Au, Pb, Bi and U [2,3,27] and reinforces the reliability of the M5 subshell DWBA calculations for a practical use in standardless quantification methods. For the Mb X-ray production cross section calculated, the same trends were found as for the previous measurements performed on Pb and U: the curve shape of the cross sections calculated is in good agreement with the measurements, but in absolute value the calculations tend to underestimate the measurements. This deviation is probably due to the value adopted for the fluorescence yield. From all the measurements performed on Pb, U and Th, the X-ray production cross sections obtained with the DWBA calculations of the M1, M2, and M3 subshells are globally in agreement with the measurements though uncertainties are quite large and results seem to fluctuate. For a more definite assessment of the reliability of the DWBA values for the M1, M2, M3, and M4 subshells, the knowledge of the atomic relaxation parameters needs to be improved. Conflict of interest There are no known conflicts of interest associated with this publication. References [1] X. Llovet, C.J. Powell, F. Salvat, A. Jablonski, Cross sections for inner-shell ionization by electron impact, J. Phys. Chem. Ref. Data 43 (2014) 013102.

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