K, L, and M shell datasets for PIXE spectrum fitting and analysis

Nuclear Instruments and Methods in Physics Research B xxx (2015) xxx–xxx

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Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb

K, L, and M shell datasets for PIXE spectrum fitting and analysis David D. Cohen ⇑, Jagoda Crawford, Rainer Siegele Australian Nuclear Science and Technology Organisation, Locked Bag 2001, Kirrawee, DC NSW 2232, Australia

a r t i c l e

i n f o

Article history: Received 19 February 2015 Received in revised form 16 July 2015 Accepted 6 August 2015 Available online xxxx Keywords: PIXE Fluorescence yields Coster–Kronig transitions Emission rates Databases

a b s t r a c t Routine PIXE analysis programs, like GUPIX, GEOPIXE and PIXAN generally perform at least two key functions firstly, the fitting of K, L and M characteristic lines X-ray lines to a background, including unfolding of overlapping lines and secondly, the use of a fitted primary Ka, La or Ma line area to determine the elemental concentration in a given matrix. To achieve these two results to better than 3–5% the data sets for fluorescence yields, emission rates, Coster–Kronig transitions and ionisation cross sections should be determined to better than 3%. There are many different theoretical and experimental K, L and M datasets for these parameters. How they are applied and used in analysis programs can vary the results obtained for both fitting and concentration determinations. Here we discuss several commonly used datasets for fluorescence yields, emission rates, Coster–Kronig transitions and ionisation cross sections for K, L and M subshells and suggests an optimum set to obtain consistent results for PIXE analyses across a range of elements with atomic numbers from 5 6 Z 6 100. Ó 2015 Elsevier B.V. All rights reserved.

1. Introduction Particle induced X-ray emission (PIXE) has been around since the mid 1970’s. It is now a mature technique used in over fifty PIXE laboratories worldwide. Many of these laboratories are using or have developed their own analysis software to both fit characteristic K, L and M shell X-ray lines and to determine elemental concentrations within a given substrate or matrix for a broad range of elements from carbon to uranium. GUPIX [1], GEOPIXE [2,3] and PIXAN [4,5] are three of many such codes that have been in common use for several decades. To be successful these codes require a broad range of datasets spanning much of the periodic table. With modern high speed computers it is now possible to quickly and efficiently calculate ionisation cross sections for inner shell vacancy production by most heavy ions. These inner shell ionisation cross sections then require well determined fluorescence yields, Coster–Kronig transition rates and single line emission rate datasets which are used to calculate line intensities and element concentrations. Well established PIXE codes should be capable of predicting line intensities and elemental concentrations to 3–5% for the K shell, provided they have these datasets to the same order of uncertainty [6]. However, such low levels of uncertainty for the L and M shell are problematic. Here we discuss some of the commonly used datasets for fluorescence yields, emission rates, Coster–Kronig transitions and ⇑ Corresponding author. Tel.: +61 2 9717 3042. E-mail address: [email protected] (D.D. Cohen).

ionisation cross sections for K, L and M subshells covering a broad range of target atomic number (Z) and quantitatively show the differences between these datasets. We also suggest our preferred optimum set to obtain reliable, self-consistent results for PIXE analyses across a range of atomic numbers from 5 6 Z 6 100. We will not discuss here the effects of the choice of the X-ray mass attenuation coefficient datasets, on X-ray absorption, used in thick target analyses as this has been covered in a previous publication by Siegele et al. [7]. They recommended that the recent datasets of Chandler [8 and online] were preferred for PIXE analysis. We will also not consider here other input parameters, like X-ray energies, detector efficiencies and experimental geometries, which can also impact on the final analysis results. Most X-ray energies of interest to PIXE users (1–40 keV) are generally well determined compared to the uncertainties associated with the parameters considered here. The detector efficiencies and geometries are for the most situations specific to a given laboratory. Here we have chosen to focus on parameters that could be considered more generic and common to all users of analysis codes like GUPIX, GEOPIXE and PIXAN. 2. The PIXE datasets The current literature contains an enormous quantity of both theoretical and experimental data required to convert inner shell vacancies generated by MeV light ions such as protons and helium ions to X-ray yields. It is not our intention to do a full review of these data here but to select a few of the most commonly used datasets relevant to thin target PIXE analysis which cover the

http://dx.doi.org/10.1016/j.nimb.2015.08.012 0168-583X/Ó 2015 Elsevier B.V. All rights reserved.

Please cite this article in press as: D.D. Cohen et al., K, L, and M shell datasets for PIXE spectrum fitting and analysis, Nucl. Instr. Meth. B (2015), http://dx. doi.org/10.1016/j.nimb.2015.08.012

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broadest possible range of elements across the periodic table and X-ray energies from 1 keV to 40 keV and to quantitatively investigate the variability between these different datasets. Firstly, let us define a few common K, L and M shell equations to appropriately connect these individual data sets to the final PIXE X-ray yield results. For thin targets, the K, L and M shell X-ray yield in a peak p is a function of the X-ray production cross section rxK,L,Mp for that peak. 2.1. For the K shell

rXKp ¼ rIK xK

CK p CK

ð1Þ

where, rIK is the K shell ionisation cross section, xK is the K shell fluorescence yield and Ci is the emission rate for the peak i = Kp and the i = K, the total K shell respectively. 2.2. For the L shell, with three subshells, L1, L2 and L3 Similar equations for the L1, L2 and L3 subshells for an L shell peak Lp are,

CLp CL1

1

rXLp ¼ rI1 x1

2

rXLp ¼ rI1 f 12 þ rI2 x2

3

rXLp ¼ rI1 f 12 f 23 þ f 13 þ f 013 þ rI2 f 23 þ rI3 x3

ð2aÞ


CLp CL2

ð2bÞ





CLp CL3

ð2cÞ

where fij are the Coster Kronig transition probabilities for a vacancy moving from the ith subshell to the jth subshell within the L shell. The total L shell X-ray production cross section is related to the total ionisation cross section by the average L shell fluorescence  L , where, yield x

 L rILtot rXLtot ¼ x

ð2dÞ

where Ltot = sum of the three subshells L1, L2 and L3 2.3. For the M shell, with five subshells M1 to M5 Similar equations can be defined for the five M subshells as for the three L subshells, namely,

CMp CM 1

1

rXMp ¼ rI1 x1

2

rXMp ¼ rI1 f 12 þ rI2 x2

3

rXMp ¼ rI1 ðf 12 f 23 þ f 13 Þ þ rI2 f 23 þ rI3 x3

4

rXMp ¼ rI1 ðf 14 þ f 12 f 24 þ f 13 f 34 þ f 12 f 23 f 34 Þ þ rI2 ðf 24 þ f 23 f 34 Þ

ð3aÞ


CM p CM2

ð3bÞ


CM p CM3

ð3cÞ


CMp þrI3 f 34 þ rI4 x4

ð3dÞ

CM 4

5

r

X Mp

¼ ðr

I 1 ðf 15

þ f 12 f 25 þ f 13 f 35 þ f 14 f 45 þ f 12 f 23 f 35

þ f 12 f 24 f 45 þ f 12 f 23 f 34 f 45 Þ þ rI2 ðf 25 þ f 24 f 45 þ f 23 f 34 f 45 Þ þ rI3 ðf 35 þ f 34 f 45 Þ þ rI4 f 45 þ rI5 Þx5

CMp CM5

ð3eÞ

As with the L shell, the total M shell X-ray production cross section is related to the total M shell ionisation cross section by the  M , where, average M shell fluorescence yield x

 M rIMtot rXMtot ¼ x

ð3fÞ

and again Mtot is the sum of the five M subshells. So if we are to predict the K, L and M shell X-ray line intensities for thin targets we need to have datasets for ionisation cross sections rIKLM, for the fluorescence yields xKLM, for the line emission rates CKLM and for the Coster–Kronig transitions fij. Clearly as we go from K to L to M subshells the situation becomes much more complex and much more difficult to measure experimentally or predict theoretically. Table 1 shows the datasets we have selected for this study for the K, L and M shells and the range of ion energies and atomic number Z together with the references from which they were obtained. It is not exhaustive but does represent a broad cross section of datasets in common use by the PIXE community. We have used the theoretical ionisation cross sections of the ECPSSR and ECUSAR calculations of Brandt and Lapicki [9] as these have general acceptance at the 5% level or better for MeV light ions (protons, deuterons and helium ions) on most targets with 6 6 Z 6 100 for the K shell and a more restricted range for the L and M shells. Also we do not use the Scofield [30] relativistic Hartree Slater (RHS) compilations for K and L X-ray emission rates here but prefer the Scofield 1974 [16] relativistic Hartree Fock (HF) formulations for these emission rates as they are systematically larger and closer to the experimental measurements. 3. Results and discussion 3.1. Ionisation cross sections The theoretical ECPSSR and ECUSAR ionisation cross sections of Brandt and Lapicki [9,18] have been widely used for many years and are generally accepted ionisation cross sections by the PIXE community. These cross sections are based on a series of corrections to the plane wave born approximation (PWBA) for inner shell vacancy production by light ions on heavy targets and include corrections for, energy loss (E) and Coulomb deflection (C) of the bombarding ion, the perturbed stationary states (PSS) of the target atom as the ion passes by and the relativistic nature of the inner shell electrons (R) particularly for the heavier target atoms. Furthermore, being a theoretical calculation these cross sections can be obtained for most light ions (protons, deuterons and alphas) on any target element in the periodic table from carbon to uranium and beyond. Also experiments performed over many decades show that for these light ions with energies well above 1 MeV/amu the ECPSSR and ECUSAR cross sections predict the average experimental data to better than a few percent for the K shell [31], 5–15% for the L shell and 10–50% for the M subshells [32]. Cohen and Harrigan [10,33,34] have tabulated the ECPSSR ionisation cross section for protons, deuterons and alphas for atomic numbers 6 6 Z 6 100 for both K and L subshell ionisation as well as the L shell X-ray line intensities using the ECPSSR cross sections. 3.2. Inner shell fluorescence yields The X-ray production cross sections are linked to the ionisation cross sections by the fluorescence yields, as shown in Eqs. (1)–(3) above. They are essentially the probability that an inner shell vacancy is filled by an outer electron and the emission of an Xray usually in the keV energy range. We should state upfront that generally these fluorescence yields are for single hole vacancies only and do not include multiple vacancy which are clearly

Please cite this article in press as: D.D. Cohen et al., K, L, and M shell datasets for PIXE spectrum fitting and analysis, Nucl. Instr. Meth. B (2015), http://dx. doi.org/10.1016/j.nimb.2015.08.012

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D.D. Cohen et al. / Nuclear Instruments and Methods in Physics Research B xxx (2015) xxx–xxx Table 1 The K, L and M shell datasets used in this study. Shell

Quantity

Source

Type & range

Reference

Reference No.

K

Ionisation cross sections rIK

ECPSSR

p, D, He, Z = 6–100, Ei = 0.1–10 MeV

[9–11]

Fluorescence yield xK

Bambynek Krause WB Chen Scofield Salem

Expt Z = 5–92, and fitted Fits to expt data K, Z = 6–110 HS theory DHS theory Z = 18–96 RHF theory K, Z = 10–98 Fits to expt data K, Z = 12–100

Brandt and Lapicki (1979) Cohen and Harrigan (1985) Cohen (1988) Bambynek et al. (1972) Krause (1979) Walters and Bhalla (1971) Chen et al., (1980) Scofield (1974) Salem et al. (1974)

Ionisation cross sections rILi

ECPSSR

p, D, He, Z = 6–100, Ei = 0.1–10 MeV

Fluorescence yield, CK fij

ECUSAR Campbell

EJC Bambynek

p, He, Z = 74,79,82,90, Ei = 0.5–3 MeV Recommended & DHS data xi, fij, Z = 25–96, Fits to expt. data Li, Z = 10–110 RHF theory, Li, Z = 18–94 Fits to expt. data L, Z = 26–96 Polynomial fit to RDHS theory xi, fij,  L , Z = 25–96 x Polynomial fit to PIXAN data Z = 40–92 Polynomial fit to expt. data, Z = 23–96

ECPSSR PWBA CPWBA ECUSAR DHS DF DHS

p, D, He, Z = 6–100, Ei = 0.1–10 MeV p, D, He, Z = 6–100, Ei = 0.1–10 MeV p, D, He, Z = 6–100, Ei = 0.1–10 MeV p, He, Z = 74,79,82,90, Ei = 0.5–3 MeV DHS theory, Z = 67–92 DF theory, Z = 67–92 DHS theory, Z = 65–92

DF

DF theory, Z = 65–92

DHS DF Exp Bambynek

DHS theory, Z = 67–92 DF theory, Z = 67–92 Expt Z = 76–96 fij, f45, based on theory of McGuire, Z = 20–90 DHS theory, Z = 67–92

Emission rates CK L

Emission rates CLi L x

M

Ionisation cross sections rIMi

Fluorescence yields xMi, Emission rates CMi

M x

Coster–Kronig transitions fij

Krause Scofield Salem Puri

Chauhan and Puri

[12] [13] [14] [15] [16] [17]

Cohen and Harrigan (1985) Cohen (1988) Lapicki (2002) and private communication 2012 Campbell (2003, 2009)

[10,11] [18] [19,20]

Krause (1979) Scofield (1974) Salem 1974 Puri et al. (1993)

[13] [21] [17] [22]

Clayton et al. (1986, 1987) Bambynek et al. (1972)

[4,5] [12]

Crawford et al. 2011. Crawford et al. (2011) Crawford et al. (2011) Lapicki (2002) and private communication. Chauhan and Puri (2008) Chauhan and Puri (2008) Puri (2007) Bhalla (1970) Puri (2007) Chen et al. (1984) Chauhan and Puri (2008) Chauhan and Puri (2008) Durak et al. (2001) Bambynek et al. (1972) McGuire (1972) Chauhan and Puri (2008)

[23] [23] [23] [18] [24] [24] [25,26] [25,27] [24] [24] [28] [12,29] [24]

generated by the energetic MeV ions relevant to PIXE analyses. Furthermore, these fluorescence yields do not take into account chemical effects which are more important for the lighter atomic number elements where the outer valence electrons are more likely to influence inner shell vacancies. 3.2.1. The K shell The K shell fluorescence yield datasets are too numerous to review here. Kahoul et al. 2011 [35] have summarised several compilations for atomic numbers 6 6 Z 6 99 going back to data produced in 1966 together with their own compilations of data between 1994 and 2007. For empirical fits over a broad range of Z there is little difference between their recommended values and the experimental compilations of Krause 1979 [13] at the 5% level except for the heavier atomic number elements (Z > 60) which are generally not used in most PIXE analyses because of their much lower ionisation cross section probabilities. The K shell fluorescence yields for four different datasets, Bambynek et [12], Krause 1979 [13], Walters and Bhalla, [14] and Chen et al. [15] have been selected to show the expected range of typical variations and are displayed in Fig. 1 covering the atomic number range 6 6 Z 6 110. Fig. 2 shows the variations of these datasets normalised to the commonly used experimental compilations of Krause [13]. The four sets differ little except in the low Z region with the theoretical Dirac Hartree Slater (DHS) calculations of Chen et al. [15] and the Hartree Slater (HS) theory calculations of Walters and Bhalla [14] being more than 5% higher in the 15 6 Z 6 40 range than the

Fig. 1. K shell fluorescence yield for four different datasets; Bambynek [12], Krause [13], Walters and Bhalla [14], and Chen [15].

experimental compilations of Krause [13]. The fits of Bambynek et al. [12] to experimental data at the time are generally within 5% of the Krause data for Z P 15. 3.2.2. L Subshells Figs. 3a–3c show the experimental L subshell fluorescence yields (xLi ) of Krause [13] for 10 6 Z 6 110 and the yields from Campbell et al. [19,20] for 25 6 Z 6 96. Campbell has

Please cite this article in press as: D.D. Cohen et al., K, L, and M shell datasets for PIXE spectrum fitting and analysis, Nucl. Instr. Meth. B (2015), http://dx. doi.org/10.1016/j.nimb.2015.08.012

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D.D. Cohen et al. / Nuclear Instruments and Methods in Physics Research B xxx (2015) xxx–xxx

Fig. 3b. L2 subshell fluorescence yields.

Fig. 2. K shell fluorescence yield normalised to Krause [13].

recommended values for x1 for Z P 62, x2 and x3 for Z P 60 and for f12 for Z P 60, f13 for Z P 39 and for f23 for Z P 36. For Z below these values we have taken the Campbell 2003 DHS numbers as listed in his Tables 3 and 4 of this reference. Discontinuities in the L1 and L2 subshells result from possible Coster–Kronig transitions where the initial vacancy in the L1 or L2 subshell moves to the L2 or the L3 subshell before being filled by an X-ray transition. Fig. 4 plots the L1, L2 and L3 fluorescence yields normalised to the values of Campbell [19,20]. The L2 subshell data of Krause and Campbell are mostly within 10%, however differences of over 20% at the low and high Z ranges occur for the L1 and L3 subshells. The average L shell fluorescence yield can be used to calculate the La line intensity for a given element if the ratio of the La emission rate to the total L shell emission rate is known. So we provide  L in Fig. 5 for a range of different datasets. The trends data for x with atomic number Z are similar but differ significantly at the 5% level as shown in Fig. 6 where the same data is plotted normalised to the values of Campbell [19]. These differences can be larger than 20% for intermediate and high Z targets for the experimental fits of the earlier data of Bambynek et al. [12]. 3.2.3. M Subshells Extensive experimental M subshell fluorescence yields are scarce, less accurate than K and L shell data and rarely cover sufficient atomic number range to be useful in comprehensive PIXE analysis codes. So we consider the two slightly different Dirac Fock (DF) and Dirac Hartree Slater (DHS) theoretical datasets summarised recently in the compilations of Chauhan and Puri [24]. These cover the five M subshell Z range from 67 to 92 which is sufficient for most PIXE applications. The DF and DHS data from Chauhan and Puri are shown in Figs. 7a–e for the five M subshells. Differences are generally small (<10%) but significant and are

Fig. 3a. L1 subshell fluorescence yields; Campbell [19,20], Krause [13].

Fig. 3c. L3 subshell fluorescence yields.

Fig. 4. Krause [13] L subshell fluorescence yields normalised to Campbell [19,20].

Fig. 5. Average L shell fluorescence yields.

Please cite this article in press as: D.D. Cohen et al., K, L, and M shell datasets for PIXE spectrum fitting and analysis, Nucl. Instr. Meth. B (2015), http://dx. doi.org/10.1016/j.nimb.2015.08.012

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 2 ), Chauhan and Puri [24]. Fig. 7b. M subshell fluorescence yields (x

Fig. 6. Average L shell fluorescence yields normalised to the values of Campbell [19].

shown in Fig. 8 where the DHS values relative to the DF values for the five subshells have been plotted for the 67 6 Z 6 92. Again as with the L shell, the average M shell fluorescence yield can be used to determine the Ma line intensities (see Eq. (3f), so we  M plots in Fig. 9 for a range of different datasets including provide x some experimental data from Durak et al. [28]. Fig. 10 shows this  M data normalised to the recent DF data of experimental x Chauhan and Puri [24]. Variations within these datasets tend to be within 10% for Z P 65.

 3 ), Chauhan and Puri [24]. Fig. 7c. M subshell fluorescence yields (x

 4 ), Chauhan and Puri [24]. Fig. 7d. M subshell fluorescence yields (x

3.3. Coster–Kronig transitions For the L and M shells with multiple subshells, vacancies created in a lower subshell i by fast ion bombardment can move to a higher subshell j before being filled by an X-ray transition. This is called a Coster–Kronig (CK) transition and has a probability fij. Coster–Kronig transitions have cut offs and onsets varying with atomic number depending on the number of electrons in any given subshell. These cut offs produce discontinuities at key atomic numbers. This makes these parameters difficult to measure accurately particularly for the lower L and M subshells so they generally have quite large uncertainties associated with them. 3.3.1. L subshell CK transitions The L subshell has three possible CK transitions, f12, f13 and f23, plots of these for 25 6 Z 6 96 are shown in Fig. 11 for the datasets of Campbell et al. [19,20] and Krause [13]. The f13 CK transitions have a higher probability than other L subshell CK transitions and show sharp discontinuities at Z = 50 and 73 where the L1–L3M4 and the L1–L3M5 CK transitions are less probable. Fig. 12 is a plot of the same data normalised to the data of Campbell [19]. The experimental f12 transitions of Krause [13] are 100% higher than the more recent values of Campbell for low and high Z. This will affect X-ray line intensities originating from the L1 and L2 subshells like the Lc2 and Lb1 lines for example.

 1 ), Chauhan and Puri [24]. Fig. 7a. M subshell fluorescence yields (x

 5 ), Chauhan and Puri [24]. Fig. 7e. M subshell fluorescence yields (x

Fig. 8. DHS M subshell fluorescence yields normalised to DF, Chauhan and Puri [24].

3.3.2. M subshell CK transitions The M shell, having five subshells, has ten possible CK transitions, making the situation much more complicated and hence much less certain experimentally. There are very few comprehensive sets of experimentally measured fij’s for the M subshells. The early work of Bambynek et al. [12] and McGuire 1972 is still widely used today and the compilations of Chauhan and Puri [24] based on DHS theory are sufficiently extensive to be useful for modern PIXE codes. Figs. 13a–13j plots these two fij datasets and Figs. 14a and b show these ten Bambynek et al. fij’s normalised to the compilations of Chauhan and Puri.

Please cite this article in press as: D.D. Cohen et al., K, L, and M shell datasets for PIXE spectrum fitting and analysis, Nucl. Instr. Meth. B (2015), http://dx. doi.org/10.1016/j.nimb.2015.08.012

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D.D. Cohen et al. / Nuclear Instruments and Methods in Physics Research B xxx (2015) xxx–xxx

Fig. 9. Average M shell fluorescence yields for the DF and DHS compilations of Chauhan and Puri [24] and for experimental fits and data of Durak et al. [28].

Fig. 11. L subshell CK transition probabilities from Campbell et al. [19,20] and the experimental values of Krause [13].

There are typically differences of 30% and more between the Bambynek and Chauhan M subshell data. For the f12 and the f45 CK M subshell transitions this can be even larger. These significant differences in CK rates make for quite large uncertainties associated with the predictions of M shell line intensities particularly for the minor lines originating from these lower M subshells. Fortunately, for the PIXE community this is somewhat offset by the fact that M X-ray lines, although much more prolific than K and L lines, are generally much closer together in energy and hence not well resolved by modern semiconductor X-ray detectors. 3.4. X-ray line emission rates The relative X-ray line intensities within an inner atomic subshell K, Li, Mi are determined from the emission rate for the peak p Cp within the subshell divided by the total emission rate for that subshell CK,Li,Mi. The emission rates for the K and L subshells are relatively well determined both theoretically and experimentally whereas emission rates for the many peaks originating from the five M subshells are not so well known and the tendency is for PIXE codes to use the DHS or the DF theoretical calculations for M subshell emission rates as these at least span large atomic number ranges needed for such codes.

Fig. 12. The Krause L subshell CK transitions normalised to the values of Campbell [19].

3.4.1. K emission rates The K shell emission rates for most Ka and Kb peaks are fairly well determined both with the theoretical Relativistic Hartree

Fig. 13a. M subshell Coster Kronig rates (f12), Chauhan and Puri [24] and Bambynek [12].

Fig. 13b. M subshell Coster Kronig rates (f13), Chauhan and Puri [24] and Bambynek [12].

Fig. 10. The DHS and the experimental data of Fig. 9 normalised to the DF compilations of Chauhan and Puri [24].

Fock (RHF) compilations of Scofield [21] and the experimental tables of Salem et al. [17]. These two emission datasets contain data for the following eight key K lines, namely Ka1,2,3, Kb1,2,3,4,5.

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D.D. Cohen et al. / Nuclear Instruments and Methods in Physics Research B xxx (2015) xxx–xxx

Fig. 13c. M subshell Coster Kronig rates (f14), Chauhan and Puri [24] and Bambynek [12].

Fig. 13d. M subshell Coster Kronig rates (f15), Chauhan and Puri [24] and Bambynek [12].

Fig. 13e. M subshell Coster Kronig rates (f23), Chauhan and Puri [24] and Bambynek [12].

Fig. 13f. M subshell Coster Kronig rates (f24), Chauhan and Puri [24] and Bambynek [12].

Fig. 13g. M subshell Coster Kronig rates (f25), Chauhan and Puri [24] and Bambynek [12].

Fig. 15 shows these two emission rate datasets for the key Kb1 and Kb2 lines commonly used in PIXE analyses. The (Kb/Ka) emission rate ratios are less than 0.01 for elements lighter than Al (Z = 13). This together with the low K shell fluorescence yields (see Fig. 1, xK 6 0.05 for Z 6 13) for these elements, means that using low Z elements (Z 6 13) to determine PIXE elemental concentrations with 3–5% accuracy is problematic. Fig. 16 shows the Scofield [16] dataset normalised to the experimental values of Salem [17] for the key K lines Kb1 and Kb2 together with the (Ka12/Ktotal) emission ratios. The differences between these two data sets are in general less than 10% over most

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Fig. 13h. M subshell Coster Kronig rates (f34), Chauhan and Puri [24] and Bambynek [12].

Fig. 13i. M subshell Coster Kronig rates (f35), Chauhan and Puri [24] and Bambynek [12].

Fig. 13j. M subshell Coster Kronig rates (f45), Chauhan and Puri [24] and Bambynek [12].

of the useful atomic number range. The interesting point is also that the (Ka12/Ktotal) ratios differ by only a few percent and this is why PIXE codes tend to use this approach as summarised by Eq. (1) above to determine elemental concentrations using K line intensities. Note these data in Figs. 15 and 16 are normalised to the Ka = (Ka1 + Ka2) line as the two Ka lines are rarely resolved in most PIXE applications and the Ka yield is most commonly used to determine elemental concentrations. 3.4.2. Key L line emission rates The three L subshells have over twenty different commonly occurring lines associated with X-ray transitions and each one needs its own emission rate if it is to be fitted by an effective PIXE code (see Crawford and Cohen [23] for example). As with the K shell, to determine line intensities for a peak p we need to know the ratio of the emission rate for the line p and the total emission rate for the L subshell from which it originated. Many L subshell emission rate datasets contain data for between 15 and 20 different key L lines. Typically these include, Ll, La1,2, Lg, Lb1,2,3,4,5,6, Lc1,2,3,4,5,6. Figs. 17 and 18 show the emission ratios for the major L subshell lines La12, Lb1 and Lb3 originating from the L3, L2 and L1 subshells respectively for the datasets of Scofield [21] and Salem [17] and for the Scofield data normalised to the experimental compilations of Salem. Fig. 18 shows that for all three subshells the primary X-ray line emission ratios of Scofield and Salem are within 10% of each other. Indeed the larger L2 and L3 subshell ratios are even closer being within 6% over most of the range 25 6 Z 6 96. This means the 3–5% uncertainty for PIXE codes is

Please cite this article in press as: D.D. Cohen et al., K, L, and M shell datasets for PIXE spectrum fitting and analysis, Nucl. Instr. Meth. B (2015), http://dx. doi.org/10.1016/j.nimb.2015.08.012

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Fig. 15. The Kb/Ka emission rate ratios of Salem [17] and Scofield [16]. Fig. 14a. Bambynek [12] M subshell Coster Kronig rates normalised to Chauhan and Puri [24].

Fig. 16. The Kb/Ka emission rate ratios normalised to the experimental compilations of Salem [17].

Fig. 14b. Bambynek [12] M subshell Coster Kronig rates normalised to Chauhan and Puri [24].

obtainable for selected elements if the major La and Lb1,3 lines at least are used in their calculations. 3.4.3. Key M line emission rates The M shell has five subshells and over 40 different X-ray lines originating from these subshells. As shown above for initial vacancies in the lower M1 and M2 subshells CK transition rates are quite high and these vacancies are shifted to higher levels before they produce X-ray transitions. For most PIXE applications less than ten or so of these possible lines are applicable, these include, Ma, Mb, Md, Mc, Mn, M1, Mm1,2 lines. The experimental data for M subshell emission rates are very sparse and often does not span the required atomic number range needed for most PIXE analyses (65 6 Z 6 95). Hence the theoretical DF or DHS values compiled by Puri [25] and taken from the earlier work of Bhalla [26] and Chen et al. [27] are used here. These datasets cover the range 62 6 Z 6 92. Fig. 19 shows the DHS emission rates normalised to the DF values for five major X-ray transitions Ma/M5, Mb/M4, Mc1/M3, (M2-N4)/M2, (M1-N23)/M1 representing each of the five M subshells M5 to M1. The two theoretical datasets are within 7% of each other over the entire range 62 6 Z 6 92.

Fig. 17. Scofield (lines) and Salem (lines with dots) L subshell emission rates.

4. Preferred dataset option A FORTRAN computer code was written to produce input datasets for our local PIXAN code [5] to test the different datasets listed

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D.D. Cohen et al. / Nuclear Instruments and Methods in Physics Research B xxx (2015) xxx–xxx

9

(c) The 18 key L lines, Ll, La1, La2, Lg, Lb1, Lb2,15, Lb3, Lb4, Lb5, Lb6, Lc1, Lc2, Lc3, Lc440 , Lc5, Lc6, Lb9,10, La/Ltot over the atomic number range 25 6 Z 6 92. (d) The 23 key M lines, Mn, Ma, M5-N6, M5-O3, M4-N2, Md, Mb, M4-O3, M4-O2, M3-N1, M3-N2, M3-O1, M3-O45, M3-N5, Mc, Mm1, M1, Mm2, M2-O4, M2-N4, M1-N23, M1-O23, Ma/Mtot over the atomic number range 67 6 Z 6 92. Long term use by us of the preferred options of Table 2 over a wide range of different target matrices and comparisons with known standards has shown that this set can produce consistent, reliable and reproducible results for both spectrum fitting of K, L and M lines listed in a) to d) above as well as the use of Ka and La line intensities for elemental concentration calculations. We generally do not use the Ma line intensity to calculate elemental concentrations.

Fig. 18. Scofield L subshell emission rates normalised to Salem.

Fig. 19. The DHS emission rates normalised to the DF values for five key X-ray transitions Ma/M5, Mb/M4, Mc1/M3, (M2-N4)/M2, (M1-N23)/M1 representing each of the five M subshells M5 to M1.

in Table 1 for the K, L and M subshells. To date we have tested these datasets on dozens of PIXE spectra and used them to predict elemental concentrations across a broad range of target materials. It is difficult in the space provided to give a full and comprehensive account as to why we have selected our recommended option provided in Table 2 below. But for many of the materials and environmental applications used extensively by us at ANSTO we find this option to provide the most consistent, accurate and reliable fits across a broad range of different PIXE situations and elemental concentrations for a range of different matrices. At the 3% level there is little difference between the ECPSSR and the ECUSAR ionisation cross sections for PIXE using 1–5 MeV/amu protons, deuterons or helium ions [18,36]. So we have selected the ECPSSR cross sections as these are more widely available for the atomic number ranges needed here and the for the K, L and M subshells. In summary, our preferred dataset options given in Table 2 are generally applicable for PIXE analyses for: (a) The light ions protons, deuterons and helium in the energy range 1–5 MeV/amu. (b) The 10 key K lines, Ka1, Ka2, Ka3, Kb1, Kb2, Kb3, Kb4, Kb5, Kb/ Ka, Ka/Ktot over the atomic number range 13 6 Z 6 92.

5. Spectrum fitting As an example, the modified NBS obsidian reference standard NBS278 in a 20% carbon matrix has been fitted using our current preferred option datasets given in Table 2. The fits to the X-ray spectrum are shown in Fig. 20. All significant peaks are well fitted by the elements and their corresponding K, L and M lines listed in Table 3. A pinhole filter was used to keep the count rate into all peaks across the spectrum similar. The peak areas, uncertainties on these areas and the minimum detectable limits (MDLs) for 35 different X-ray lines are shown in Table 3 as well as the ratios of our older PIXAN dataset [4,5] fit to the current preferred option fit. The Table has been sorted in increasing X-ray energy so adjacent element overlaps can be readily identified. The older PIXAN datasets use ECPSSR ionisation cross sections [10,11], Krause [13] fluorescence yields and Salem [17] emission rates for the K L and M subshell lines. It also contains significantly fewer K, L and M lines which means that elemental overlaps in the energy spectrum will not be as well determined using this option. This is apparent in Table 3 where the peak areas for BrL, the RbL and the YL line areas do not appear in the PIXAN option at all. The MDLs were calculated from three standard deviations above the background shown as the dashed line in Fig. 20. K, L and M lines for all major elements in the range 1.2–20 keV were included in the fit. Table 3 shows the elemental lines that remained in each of the fits in increasing order of X-ray energy so overlapping peaks can be easily identified. For example, for an X-ray detector with around 150 eV resolution the BrLa and the AlKa and the RbLa and the SiKa lines all overlap as do the BaLabc and the TiKab and the AsKab and the PbLa lines. Under our preferred option fit these lines all have area estimates, even if they are in some instances below the calculated three standard deviation MDL limits. The linking of the relative K, L and M shell line intensities through their respective cross sections would provide more accurate unfolding of some of these elemental interferences and hence provide more accurate concentration estimates as well. 6. Summary There are many different datasets for ionisation cross sections, fluorescence yields, Coster–Kronig transitions and X-ray line emission rates for K, L and M subshells. These produce varying results for PIXE users when performing spectrum fitting and estimating elemental concentrations. Our experience has shown that different datasets can produce results, often varying by more than 10%. We have looked at several commonly used datasets and selected our preferred dataset which produces consistent reliable spectrum

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D.D. Cohen et al. / Nuclear Instruments and Methods in Physics Research B xxx (2015) xxx–xxx

Table 2 Recommended preferred option of datasets for K, L and M shell spectrum fitting and elemental concentration determination. Shell

Quantity

Source

Type & range

Reference

Reference No.

K

Ionisation cross sections rIK

ECPSSR

p, D, He, Z = 6–100, Ei = 0.1–10 MeV

[9–11]

Fluorescence yield xK Emission rates CK

Krause Salem

Fits to expt data K, Z = 6–110 Fits to expt data K, Z = 12–100

Brandt and Lapicki (1979) Cohen and Harrigan (1985) Cohen (1988) Krause (1979) Salem et al. (1974)

Ionisation cross sections rILi

ECPSSR

p, D, He, Z = 6–100, Ei = 0.1–10 MeV

Fluorescence yield, xL and Coster–Kronig CK fij Emission rates CLi L x

Campbell

Ionisation cross sections rIMi

L

M

Fluoresecnce yields xMi, Emission rates CMi

vMi

M x Coster–Kronig transitions fij

[13] [17]

Recommended & DHS data xi, fij, Z = 25–96,

Cohen & Harrigan (1985) Cohen (1988) Campbell (2003, 2009)

[19,20]

Salem Puri

Fits to expt data L, Z = 26–96  L , Z = 25–96 Polynomial fit to RDHS theory x

Salem 91974) Puri et al. (1993)

[17] [22]

ECPSSR

p, D, He, Z = 6–100, Ei = 0.1–10 MeV

[21,10]

DF DF

DF theory, Z = 67–92 DF theory, Z = 65–92

DF Chauhan and Puri

DF theory, Z = 67–92 DHS theory, Z = 67–92

Crawford (2011) Cohen & Harrigan (1985) Chauhan and Puri (2008) Puri S. (2007) Chen et al. (1984) Chauhan and Puri (2008) Chauhan and Puri (2008)

Fig. 20. Obsidian NBS278 standard fitted spectrum using the preferred datasets of Table 2.

fitting and elemental concentrations over the broadest range of elements for K, L and M subshell X-ray lines. For the K shell lines it is possible to both fit spectra and predict elemental concentrations with an accuracy of 3–5% or better, provided there are no adjacent element overlaps or L or M line interferences with the key lines being considered. For the La lines a similar uncertainties of 3–10% for fitting and elemental concentrations may be obtained for elements in the range 65 6 Z 6 92. If however Lb or Lc lines are to be used to determine concentrations then this uncertainty increases significantly to 10–30% or more depending on the ion energy, the target atomic number and the intensity of the line used relative to the major La line. For the lower atomic numbers, 25 6 Z 6 65, many of the Lb and Lc lines are not well resolved by modern semiconductor detectors and hence the uncertainty of prediction is again significantly worse. As expected the M shell lines being much more numerous and closer together in energy have worse uncertainty for PIXE

[10,11]

[24] [25,27] [24] [24]

spectrum fitting and concentration analysis. The larger uncertainties associated with the five M shell fluorescence yields, the ten ill-determined Coster–Kronig transitions fij and the lack of reliable experimental subshell emission rates means that uncertainties of between 15% and 50% are typical for spectrum fitting over the entire M shell range or for Ma lines for concentration predictions. These can become even larger if there are K, L or other M line interferences adjacent to the M lines of interest. These results have been summarised by us, together with the actual K, L and M abc ratios for selected proton and helium bombarding energies for a broad range of target atomic numbers in an external ANSTO report by Crawford et al. [23] which can be made available on request. Another important issue that became obvious during the spectrum fitting process was that the K, L and M lines for a given element needed to be linked and not to be independently varied during the spectrum fitting process. That is if an element had K, L and M lines all present in the same spectrum then the relative K, L and M intensities should be linked through their cross sections for all these lines. If this is not done then, for example, the BrKa line (11.922 keV) is well fitted in Fig. 20 but the BrLabc lines (at around 1.48 keV) overlap with the AlKab and will therefore affect the AlKa peak area estimates. Similarly the RbLabc lines affect the SiKab lines and the AsKab lines affect the PbLabc lines at similar energies. Interferences of this type can easily produce fitting errors of 50% and more in the minor peaks as demonstrated by some of the ratios provided in Table 3. In conclusion we feel that more experimental data needs to be obtained for; (a) L and M subshell fluorescence yields (xi) for proton and helium ion bombardment in the 1–5 MeV/amu range where multiple vacancies may occur especially for the lighter Z targets. Much of the current data is related to single hole vacancies which rarely occur with these ions. (b) Individual L and M subshell Coster–Kronig transitions rates fij across a broad range of atomic numbers (Z) as data around discontinuities is still very uncertain. (c) Further testing of the linkages between K, L and M shell line intensities for a range of bombarding ions and energies across a range of atomic numbers related to typical PIXE spectrum analyses (covering 1–40 keV X-ray energies).

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D.D. Cohen et al. / Nuclear Instruments and Methods in Physics Research B xxx (2015) xxx–xxx

Table 3 A comparison of the 35 peak areas, uncertainties and MDLs for a fit to the modified NBS obsidian glass reference standard NBS278 and a graphite mix for the PIXAN dataset option [4,5] and our preferred dataset option given in Table 2. The table is sorted in increasing X-ray energy. Elt

BrL Al RbL Si YL PbL ZrL NbL PbM Cl PdL ThM K Ca BaL Ti V NdL Cr Mn Fe Co Ni Cu Zn Ga As PbL Br ThL Rb Sr Y Zr Nb

E(keV)

1.480 1.486 1.694 1.740 1.922 2.013 2.042 2.166 2.345 2.622 2.838 2.996 3.313 3.691 4.465 4.510 4.951 5.229 5.414 5.898 6.403 6.929 7.477 8.048 8.637 9.250 10.542 10.550 11.922 12.967 13.393 14.163 14.956 15.772 16.612

Preferred option

PIXAN option

Area

Uncertainty

MDL

245 7,478 17,243 285,333 194 0 0 0 178 15,955 180 2,523 1,205,981 295,107 128 63,308 46 1,791 0 32,906 1,581,988 7,678 52,076 2,461 10,003 2,435 579 26 4,185 210 5,520 2,049 837 4,974 170

254 240 791 637 657 0 0 0 244 303 332 351 1,146 858 395 324 244 190 0 245 1,273 805 294 147 140 91 67 61 73 54 89 52 57 79 29

591 521 1,815 809 1,528 868 635 521 567 642 771 808 764 1,544 919 474 566 430 395 384 461 1,861 430 321 228 177 145 142 78 120 113 60 114 82 60

Ratio (PIXAN/preferred)

Area

Uncertainty

MDL

Area

Uncertainty

MDL

8,350

237

510

1.12

0.99

0.98

313,362

615

592

1.10

0.96

0.73

0 0 66 137 16,013 226 1,265 1,210,783 300,806 4,715 62,695 181 1,734 0 33,266 1,568,287 9,263 51,209 2,512 9,892 2,424 496 767 4,172 216 5,459 2,037 813 4,941 168

0 0 223 245 303 332 353 1,148 851 277 325 243 191 0 245 1,269 810 298 147 141 91 68 46 73 52 89 52 56 79 28

1,031 752 518 569 641 772 816 758 1,513 625 481 565 433 396 381 480 1,872 453 321 232 177 149 86 78 117 117 61 113 83 58

1.00 1.00

1.00 1.00

0.77 1.00 1.26 0.50 1.00 1.02 36.85 0.99 3.96 0.97 1.00 1.01 0.99 1.21 0.98 1.02 0.99 1.00 0.86 29.34 1.00 1.03 0.99 0.99 0.97 0.99 0.99

1.00 1.00 1.00 1.00 1.00 0.99 0.70 1.00 1.00 1.00 1.00 1.00 1.00 1.01 1.02 1.00 1.01 1.00 1.01 0.75 1.00 0.97 1.01 1.00 0.99 1.00 0.98

1.19 1.18 0.99 1.00 1.00 1.00 1.01 0.99 0.98 0.68 1.01 1.00 1.01 1.00 0.99 1.04 1.01 1.05 1.00 1.02 1.00 1.03 0.60 1.00 0.97 1.03 1.02 0.99 1.02 0.97

Acknowledgements We would like to thank G. Lapicki for providing selected L and M subshell proton and helium ion ECUSAR ionisation subshell cross sections for selected atomic numbers used in this work. References [1] J.L. Campbell, D. Higuchi, J.A. Maxwell, W.J. Teesdale, Quantitative PIXE microanalysis of thick specimens, Nucl. Inst. Meth. B77 (1993) 95–109. [2] C.G. Ryan, D.R. Cousens, S.H. Sie, W.L. Griffin, G.F. Suter, E. Clayton, Quantitative PIXE microanalysis of geological material using the CSIRO proton microprobe, Nucl. Inst. Meth. B47 (1990) 55–71. [3] C.G. Ryan, D.N. Jamieson, C.L. Churms, J.V. Pilcher, A new method for online true-elemental imaging using PIXE and the proton microprobe, Nucl. Inst. Meth. B104 (1995) 157–165. [4] E. Clayton, PIXAN: the Lucas Heights PIXE analysis computer package. AAEC/ M113, November 1986. [5] E. Clayton, D.D. Cohen, P. Duerden, A discussion of PIXAN, the AAEC PIXE analysis computer package, Nucl. Inst. Meth. B22 (1987) 64. [6] D.D. Cohen, R. Siegele, I. Orlic, E. Stelcer, Long term accuracy and precision of PIXE and PIGE measurements for thin and thick sample analyses, Nucl. Inst. Meth. B189 (2002). [7] R. Siegele, D.D. Cohen, Influence of different mass absorption coefficient datasets on PIXE yields, X-Ray Spectrom. 42 (2013) 541–545, http://dx.doi.org/ 10.1002/xrs.2517. 81-85. wileyonlinelibrary.com. [8] C.T. Chantler, Theoretical Form Factor, Attenuation, and Scattering Tabulation for Z = 1–92 from E = 1–10 eV to E = 0.4–1.0 MeV, J. Phys. Chem. Ref. Data, 24 (1994) 71-643. Plus, C. T. Chantler, K. Olsen, R. A. Dragoset, J. Chang, A. R. Kishore, S. A. Kotochigova, and D. S. Zucker, NIST X-Ray Form Factor, Atten., and Scattering Database, Detailed Tabulation of Atomic Form Factors, Photoelectric Absorption and Scattering Cross Section, and Mass Attenuation Coefficients for Z = 1–92 from E = 1–10 eV to E = 0.4–1.0 MeV. [Online] available: .

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