CHAPTER-1 PHYSICAL PARAMETERS FOR PROCESSES FOLLOWING INNER-SHELL PHOTOIONIZATION

Transcription

1 CHAPTER-1 PHYSICAL PARAMETERS FOR PROCESSES FOLLOWING INNER-SHELL PHOTOIONIZATION 1.1 INTRODUCTION PHOTOIONIZATION OF ATOMIC INNER-SHELLS DE-EXCITATION OF INNER-SHELL VACANCIES Radiative Transitions Non-Radiative Transitions CURRENT STATUS OF PHYSICAL PARAMETERS Photoionization Cross Sections X-ray, Auger and Coster-Kronig Transition Rates Fluorescence and Coster-Kronig Yields Vacancy Transfer Probabilities X-ray Production Cross Sections (XRP) PRESENT WORK 14 REFERENCES 17

2 1.1 INTRODUCTION The emission of characteristic X-rays following inner-shell ionization by photons and charged particles has been studied for a long time. From the early days of Bohr s theory of atom, photon spectroscopy of the characteristic X-rays has been cultivated because the inner-shell processes involved are easily interpreted in terms of the radiative one-electron transitions. Theoretical models are available, which facilitate the extrapolation or interpolation of relevant physical parameters explaining the inner-shell processes. In the field of atomic physics, the most important application of these models is in determining ionization cross sections in particle collision processes. Another interesting feature is the fluorescence of highly ionized atomic states following de-excitation of inner-shell holes by vacancy cascades. The knowledge about these highly ionized states is very important in astrophysics, plasma physics and laser technology. The development of high resolution solid state detectors made it possible to distinguish between elements in the periodic table by measuring their characteristic fluorescent K X-rays. This has led to the application of inner-shell ionization in obtaining the compositional information in terms of the atomic species present in various kinds of samples. 1.2 PHOTOIONIZATION OF ATOMIC INNER-SHELLS Depending upon energy of incident photon, its interaction with matter can be classified into three main processes, namely, photoelectric absorption, Compton scattering and pair production. In low energy region (<100KeV), the photoelectric absorption predominates. In this process, the interacting photon is completely absorbed by the atom and a mono energetic electron is ejected from the atomic shell/sub-shell. This emitted photoelectron has kinetic energy equal to the difference 2

3 between incident photon energy and binding energy of the emitted electron. The process of creation of atomic inner-shell/sub-shell vacancies is called photoionization. The ejected photoelectron leaves a vacancy in the shell/sub-shell of specimen s atom which is frequently filled by outer-shell/sub-shell electron. The distribution of electrons in the ionized atom is then out of equilibrium and within an extremely short time (~10-12 s) returns to the normal state, by transitions of electrons from outer to inner-shells/sub-shells. These vacancies decay through radiative, non-radiative transitions. 1.3 DE-EXCITATION OF INNER-SHELL VACANCIES The inner-shell vacancies produced following photoionization can rapidly filled-up by an outer-shell/sub-shell electron whereby either a photon (characteristic X-ray) or an Auger electron is emitted out. These transitions are referred to as radiative and non-radiative transitions, respectively. In either of these two alternative decay modes, the primary vacancy is transferred to a higher shell/sub-shell and additional higher shell/sub-shell vacancies may be created. This vacancy cascade process continues until all vacancies reach the outermost occupied shell/sub-shell. However, for most of practical purposes, the atom is assumed to return to the ground state following decay of a primary vacancy by either of the two competing decay modes Radiative Transitions In a radiative transition, the inner-shell vacancy is filled by an electron from outer-shell thereby shifting the inner-shell vacancy to the outer-shell and the difference in the energy of the two shells is emitted as characteristic X-ray (Fig. 1.1). 3

4 K - series n l j K 1 0 1/2 L 1 L 2 L 3 M1 M 2 M3 M4 M 5 a 2 a 1 b 3b1 b 2 5 b 5 b 2 2 b 1 2b 4 b 4 b3 b9 g3 g4 1 b4 b10 g11 g2 g4 h b1 g5 b17 L - series g1 g8 n g6 l t s a2 a1 b6 u b15 b2 u b7 b5 b5 g2 g1 M - series a1 x1 a2 x2 b 2 0 1/ / / /2 1/ / / /2 N 1 N 2 N 3 N4 N 5 N 6 N / / / / / / /2 O 1 O 2 O 3 O 4 O / / / / /2 Figure 1.1: Energy level diagram showing various K-, L-, M-shell transition. All the transitions from one shell to another shell do not result in characteristic X-ray emission, since there are certain selection rules which must be satisfied. These selection rules are n 1 l = 1 j = 0, ±1 4

5 where n is the change in principal quantum number, l is the change in orbital momentum quantum number and j (j = l ± s) is the change in total angular momentum quantum number. Different fluorescent X-rays arising from the allowed transitions are placed in to different groups (K, L, M.) depending on the energy level which contains the initial vacancy. The allowed transitions involved in some of the K, L, M X-ray groups are shown above in Fig Non-Radiative Transitions In case of de-excitation through the non-radiative transitions, the inner-shell vacancy is filled by an outer-shell electron and the available energy of transition is used to eject another outer-shell electron. The ejected electron is called Auger electron and the process is termed as Auger process. This term is used to describe both, the inner-shell vacancy decay by electron emission and those transitions in which a vacancy in an atomic shell leads to two vacancies in one or two different principal shells. In such decays, different processes have acquired specific names mentioned below depending on the final state of the atom. (a) In an Auger transition both the final state vacancies are produced in a shell other than the one containing initial vacancy. (b) In Coster-Kronig transition one of the two vacancies produced in a different sub-shell of the same principal shell containing initial vacancy. (c) In the Super Coster-Kronig transition both the final state vacancies are produced in same shell containing the initial vacancy. Different non-radiative transitions, namely, Auger transitions, Coster-Kronig (CK) transitions and Super Coster-Kronig (SCK) transitions are also depicted in Fig

6 Figure 1.2: Shows different non-radiative transitions (a) Auger transtions (b) Coster- Kronig (CK) transitions and (c) Super Coster-Kronig (SCK) transitions. 1.4 CURRENT STATUS OF PHYSICAL PARAMETERS The atomic inner-shell vacancy decay processes comprising of radiative and non-radiative transitions are characterized by the physical parameters, namely, photoionization cross sections; X-ray, Auger and Coster-Kronig (CK) transition rates; fluorescence and CK yields; and vacancy transfer probabilities. Accurate data on different physical parameters are required to calculate X-ray production (XRP) cross sections and relative X-ray line intensities, which in turn are required in a variety of applications, namely, the radiation shielding, radiation transport and mass attenuation calculations, dosimetric computations, quantitative elemental analysis using X-ray emission techniques (EDXRF and PIXE), industrial irradiation processes and surface chemical analysis. The current status of different physical parameters is presented below. 6

7 1.4.1 Photoionization Cross Sections The probability of causing the ionization in an atom by an incident photon is expressed in terms of photoionization cross section ( ij ), which depends on the nature of target material and energy of the incident photon. The theoretical treatment of photoionization is well developed [1] and the most comprehensive theoretical tabulation is based on the relativistic Hartree-Fock-Slater (HFS) model calculations, in which electron is assumed to be moving in the same Hartree-Slater potential both and after the absorption of photon. The K-, L- and M-shell, L i (i=1-3) and M i (i=1-5) sub-shell and total atom photoionization cross sections in the energy range kev for all elements with Z=1-101 have been included in this tabulation [2]. Later on, more refined calculations based on the self-consistent Dirac-Hartree-Fock-Slater model (DHFS) were carried out by Creagh et al. [3] and Chantler [4]. The reliability of the tabulated cross sections can be checked by comparing the measured mass attenuation coefficients with those evaluated from these tabulated values by summing the cross sections for all sub-shells and adding the minor contribution of elastic and inelastic photon scattering cross sections. A large body of experimental data on the mass attenuation coefficients available up to 1996 has been compiled by Saloman et al. [5] and Hubbell [6]. The measured mass attenuation coefficients were found to be in good agreement [5-8] with those evaluated using the tabulated photoionization cross sections [2] for all elements X-ray, Auger and Coster-Kronig Transition Rates The radiative transitions are explained by two different model calculations employing independent particle approximation [1]. The first approach is based on the Dirac-Hartree-Slater (DHS) model calculations in which the average potential is 7

8 assumed to be same for both the initial and final states of an atom undergoing transition. The second approach is the Dirac-Fock (DF) model calculations which assume different potentials for initial and final states, thereby including the exchange and overlapping effects. Two sets of X-ray emission rates for the K-[9,10] and L-[9,11,12] and M- [13,14] shells are available in the literature. The K- and L-shell X-ray emission rates based on the DHS model calculations [9] were available for all the elements with 5 Z 104. The DF model based K-shell X-ray emission rates were available for some elements with 10 Z 98 [10] and the L-shell rates were tabulated for dipole transitions only for some elements with 18 Z 94 [11]. In case of the M-shell, the first set of X- ray emission rates based on the DHS model was tabulated for only six elements with 48 Z 93 [13] and the second one based on the DF model was tabulated for only ten elements with 48 Z 92 [14]. For the K-shell and L-shell X-ray emission rates, the two potential model based DF model calculations [10-12] including overlap and exchange effects were found to be in better agreement with measured relative K X-ray [15] and L X-ray [16,17] intensities as compared to those based on the DHS model [9]. Recently, Puri [18] have reported complete set of the L i (i=1-3) and M i (i=1-5) subshell X-ray emission rates/relative intensities. The intensities for different L i (i=1-3) sub-shell X-ray lines have been computed relative to the most intensive line in each series, for elements with 30 Z 92, from published X-ray emission rates [11,12] based on the DF model. In case of the M i (i=1-5) sub-shell X-ray lines, complete sets of emission rates based on both the DHS and the DF models have been generated for elements with 65 Z 92 by logarithmic interpolation from the data available [13,14] for a limited number of elements. The intensities for different M X-ray lines were computed relative to the most intense line in each series using these two sets of 8

9 emission rates. The L i (i=1-3) and M i (i=1-5) sub-shell X-ray relative intensities computed from the DF model based emission rates were least-squares-fitted to polynomials in atomic number (Z) for use in different software packages for quantitative elemental analysis using X-ray emission techniques and other applications. To explain the non-radiative transitions theoretically, the production and deexcitation of inner-shell vacancies is assumed as a two-step process, i.e. decay is separated from excitation. This assumption is valid only when the incident photon energy is well above the ionization threshold energy. The Auger transition energies are of the order of initial-state energy and theoretical calculations of transition rates are less sensitive to the transition energies. However, the CK transition energies are, generally, considerably small as compared to initial state energy and the calculated transition rates depend strongly on the detailed shape of the wave function and the angular momentum coupling. The non-radiative transition probabilities [19] for the atomic K- and L-shell calculated using the DHS model is available in the literature. These calculations give reasonably good predictions of the Auger decay rates but are expected to overestimate the CK transition rates in case of heavy elements Fluorescence and Coster-Kronig Yields Fluorescence yield (ω i ) represents the probability that a characteristic X-ray will be emitted once an i th shell/sub-shell vacancy is created. It is defined as the ratio of number of X-rays emitted to the total number of vacancies created in that shell/subshell. The Coster-Kronig yields (f ij ) is defined as the probability that a vacancy in i th sub-shell of the given shell is filled by an electron transition from the j th (>i th ) subshell of the same shell. 9

10 The fluorescence and Coster-Kronig yields can be computed [20] from the radiative and non-radiative transition rates. The theoretical values of the K-shell fluorescence yields (ω K ) based on the DHS model have been calculated for 25 elements with 18 Z 96 by Chen et al. [21] The semi-empirical values of ω K have been compiled by Krause [22] for different elements with 5 Z 110 using the measured data available till Later, in 1984, Bambynek [23] presented a revaluation incorporating new measurements. Subsequently, Hubbell et al. [24] have obtained the ω K values by fitting the available experimental data, for the period , for elements with 11 Z 99. These tabulated values are in general agreement with the DHS values [21] except for differences up to 10% for elements below Z=20. Three set of the L i (i=1-3) sub-shell fluorescence (ω i ) and Coster-Kronig (f ij ) yields are available. Krause [22] tabulated a set of semi-empirical fitted values of ω i and f ij yields based on the experimental data available till 1979 for all elements with 12 Z 110. Chen et al. [25] reported these yields for 25 elements with 25 Z 96 calculated using the DHS model based radiative [9] and non-radiative [19] transition rates. The L 1 sub-shell yields (f 12, f 13 and ω 1 ) display abrupt discontinuities at atomic numbers, where the energy thresholds are located for certain intense CK transitions. This makes the interpolation of these parameters difficult from the available DHS model data [25]. To circumvent this difficulty, Puri et al. [26] calculated the ω i and f ij yields for all the elements with 25 Z 96 using radiative transition rates based on the DHS model [9] and the non-radiative rates interpolated from the DHS model based data given by Chen et al. [19] for limited elements considering the onset and cut-off of different CK transitions in accordance with the CK transition energy calculations [27]. Recently, Campbell [28] provided a third set of recommended values of the i and f ij yields based on experimental data available till 2003 for the elements with 10

11 62 Z 96 and subsequently reported [29] the revised set of recommended values only for the L 1 sub-shell fluorescence and Coster-Kronig yields, bearing uncertainties ~15-30%, for all elements with 64 Z 92, except for Z=75 and 76. In case of the L 2 and L 3 sub-shell fluorescence yields, the recommended values [28] are same as the DHS values [26] and the recommended values [28] of Coster-Kronig yield, f 23, differ from the DHS values [30] up to ~30%. In case of the L 1 sub-shell yields (f 12, f 13 and ω 1 ), the agreement between the DHS values [26] and the recommended values [28, 29] is not so good (5-10%) with exceptionally significant differences (~50%) for elements in vicinity of atomic numbers where cut-off/onset of certain intense Coster-Kronig transitions occur. Recently, a complete set of the interpolated M i (i=1-5) sub-shell fluorescence and Coster-Kronig yields for all the elements with 67 Z 92 were reported by Chauhan et al. [31] considering the cut-off/onset of different Coster- Kronig transitions. Experimental techniques for measuring the fluorescence and Coster-Kronig yields have been described in a comprehensive review article, covering the work until 1970 [20]. Subsequent progress in measurements of different L i (i=1-3) sub-shell yields [ω i, f 12, f 13 and f 23 ] has been reviewed in few other articles [22, 24, 28, 30]. Most of the reported data pertained to measurements of the L i (i=1-3) sub-shell yields for heavy elements [28-30] and only a few reports are available on such measurements for rare-earth elements [32] Vacancy Transfer Probabilities The atomic inner-shells vacancies can arise either from direct ionization by photons/charged particles or from the decay of an inner-shell vacancy. The probabilities for transfer of a K-shell vacancy to the L i (i=1-3) sub-shell (η KLi ) and 11

12 the M-shell (η KM ) and from the L i (i=1-3) sub-shell to the M-shell (η LiM ) through the radiative and non-radiative transitions were evaluated by Rao et al. [33 ] for a limited number of elements with 26 Z 93, using the X-ray emission rates tabulated by Scofield [9] and non-radiative transition rates calculated in jj-coupling with nonrelativistic hydrogenic wave functions. Puri et al. [34] have tabulated these probabilities for all the elements with 18 Z 96 using the DHS model based radiative [9] and non-radiative [19] transition rates. The calculated vacancy transfer probabilities were least squares fitted to the polynomials to obtain analytical relations that represent these probabilities as a function of atomic number (Z) for use in different applications. Further, the probabilities, (η JMi ) [i=1-5; J=K/L j (j=1-3)] and (η JMi ) [i=1-5; J=K/L j (j=1-3)] representing the number of M i (i=1-5) sub-shell vacancies produced following decay of the primary K-shell/L j (j=1-3) sub-shell vacancies through single step and multi-step processes, respectively, have also been reported by Chauhan et al. [35]. The probability, η LM, representing the total number of M-shell vacancies produced following decay of primary L i (i=1-3) sub-shell vacancies through all possible transitions including multi-step processes, were deduced by Puri et al. [36] for the elements in atomic region 70 Z 92 by measuring the M X-ray yields from the targets excited by 5.96 kev and 22.6 kev incident photon energy i.e. below and above the L-edge of the target element. The measured probabilities were found to be agree well with the DHS values [34] and theoretically predicted onset of the L 1 -L 3 M 5 Coster-Kronig transition [27] at Z=75 was confirmed from these measurements. Similarly, the measured probabilities for transfer of vacancies from the K to the L- shell, for the element with 37 Z 42, were found to be in good agreement with the DHS values [37]. 12

13 1.4.5 X-ray Production Cross Sections (XRP) The K/L/M shell XRP cross sections can be calculated using the theoretical physical parameters, namely, photoionization cross sections; X-ray emission rates; fluorescence and CK yields; and vacancy transfer probabilities. The first compilation of the K and L XRP cross sections was given by Krause et al. [38] in This work included the Kα 1,2 and Kβ 1,3 XRP cross sections for elements with 5 Z 101 at incident photon energies E K <E inc 200keV (E K represent the K-shell ionization threshold energy) and the Lα 1,Ll, Lβ 1, Lβ 2,15, Lβ 3, Lγ 1, Lγ 4 XRP cross sections for elements 12 Z 101 at incident photon energies, E Li <E inc <E K [E Li (i=1-3) represent the L i sub-shell ionization threshold energy calculated using the relativistic HFS model based photoionization cross sections tabulated by Scofield [2]; the K- and L-shell fluorescence and CK yields tabulated by Krause [22] and the DHS model based X-ray emission rates [9]. Later on, Puri et al. [39] reported the Kα and Kβ XRP cross sections for elements with 13 Z 92 in photon energy range, E K <E inc 200keV (E K represent the K-shell ionization threshold energy), and the Lα, Ll, Lβ, and Lγ XRP cross sections for elements 35 Z 92 in photon energy range, E L1 <E inc 200keV, calculated using the relativistic HFS model based photoionization cross sections tabulated by Scofield [2] DHS model based X-ray emission rates [9], the K-shell fluorescence yields recommended by Hubbell et al. [24] and the DHS model based L i (i=1-3) sub-shell fluorescence CK yields [26] and vacancy transfer probabilities [34]. From the tabulated [39] X-ray production (XRP) cross sections, the gross intensity ratios, I (j l,β, γ) can be deduced, however, for most of the /I Lj Lα applications including elemental analysis, the knowledge of relative intensities for different resolved X-ray components/lines originating from the individual L i (i=1-3) 13

14 sub-shells are required. Moreover, the intensity ratios for some of the L k X-ray components are expected to exhibit abrupt discontinuities in the atomic regions where the cut-off or onset of certain intense Coster-Kronig transitions occur. Similar discontinuities in the values of intensity ratios for given element are expected at incident photon energies in vicinity of the K-shell ionization threshold energy. A thorough literature search revealed the non-availability of any tabulation of intensity ratios for the resolved L X-ray components/lines produced following photoionization. Further, the investigations of chemical effects on the L X-ray intensity ratios are scarce [40, 41]. Recently, the X-ray production (XRP) cross sections for the M k (k= x, a b, g m 1 and m 2 ) groups of X-rays have been reported by Chauhan et al. [35] for all the elements with 67 Z 92 at incident photon energies ranging E M1 <E inc 150keV, calculated using the photoionization cross sections tabulated by Scofield [2]; and recently reported M-shell X-ray emission rates [18] and fluorescence and Coster- Kronig yield [31]. At incident photon energies above the K-shell/L 3 sub-shell ionization thresholds, the contribution to the M XRP cross sections as a result of the additional M i (i=1-5) sub-shell vacancies created following decay of the primary K- shell/l i (i=1-3) sub-shell vacancies have also been included in these tabulated values. 1.6 PRESENT WORK The present study has been done keeping in view the current status of different physical parameters involved in the inner-shell photoionization. A new energy dispersive X-ray fluorescence (EDXRF) spectrometer involving sealed disc sources of 109 Cd (20mCi) / 241 Am (300mCi) procured from RITVERC, Russia and a Peltier cooled Si-PIN detector (AMPTEK: XR-100CR, 6mm m, FWHM 152eV at

15 kev, Be window 0.5 mil thick) attached to a PC based digital pulse processor (PX4, AMPTEK) has been established and used for all the measurements. The current chapter included the brief description of processes following atomic inner-shell photoionization. These processes are described by different physical parameters, namely, the photoionization cross sections, X-ray, Auger and Coster-Kronig transition rates, Fluorescence and Coster-Kronig yields and vacancy transfer probabilities. The current status of these physical parameters has been presented in this chapter. The experimental setup used for present work and the methods of data analysis are described in Chapter II. The L 1 and L 2 sub-shell fluorescence yields for elements with 64 Z 70 deduced from the measured L k (k=l, a, β 1,4, β 3,6, β 2,15,9,10,7, g 1,5 and g 2,3,4 ) XRP cross sections using theoretical photoionization cross sections have been presented in Chapter III. For these measurements, spectroscopically pure self-supporting pressed pellets of Gd 2 O 3, Tb 4 O 7, Dy 2 O 3, Ho 2 O 3, Er 2 O 3 and Yb 2 O 3 of thicknesses ~100 mg/cm 2 were used as targets. In Chapter IV, the theoretical L X-ray intensity ratios, I (k l,η,α,β,β,β,β,β,β,β,γ,γ,γ,γ ) 2 1 2, ,7 6 9,10 1,5 6,8 2,3 4 evaluated for elements Lk /I Lα1 with 36 Z 92 at incident photon energies ranging E L1 <E inc <200keV are presented. The important features pertaining to dependence of the tabulated intensity ratios on the incident photon energy and atomic number (Z) have been discussed. At incident photon energies above the K-shell ionization threshold, the contribution to the production of different L X-rays due to the additional L i (i=1-3) sub-shell vacancies created following decay of the primary K-shell vacancies have also been included in the present calculations. 15

16 The Chapter V describes measurements of the L X-ray intensity ratios for 80Hg, 66 Dy and some of their compounds performed in order to check the predicted dependence of these ratios on the incident photon energy and also investigate the influence of chemical effects on these ratios for a d-block and f-block elements, respectively. The last chapter describes the quantitative elemental analysis of Castrol Activ 4-stoke multi grade motorbike engine oil (SAE 20W-40), taken from a petrol driven motor bike after travelling specific kilometers performed using energy dispersive X- ray fluorescence (EDXRF) technique employing fundamental parameter approach in an attempt to assess the wear and tear of the engine. 16

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