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Determination of ratios of emission probabilities of Auger electrons and K–L-shell radiative vacancy transfer probabilities for 17 elements from Mn to Mo at 59.5 keV
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Journal of Quantitative Spectroscopy & Radiative Transfer 97 (2006) 41–50 www.elsevier.com/locate/jqsrt
Determination of ratios of emission probabilities of Auger electrons and K–L-shell radiative vacancy transfer probabilities for 17 elements from Mn to Mo at 59.5 keV Elif O¨z Atatu¨rk University, Department of Physics, Faculty of Arts and Science, 25240 Erzurum, Turkey Received 17 November 2004; accepted 23 December 2004
Abstract The measurements of the K X-ray intensity ratio IðKb Þ=IðKa Þ for the 17 elements Mn, Fe, Co, Ni, Cu, Zn, Ga, Ge, As, Se, Br, Rb, Sr, Y, Zr, Nb and Mo have been done following ionization by 59.5 keV g-rays from a 241Am point source. Ratios of emission probabilities of Auger electrons and the vacancy transfer coefficients have been extracted in terms of the intensity ratios. It is found that the present results agree well with earlier fitted values and the semi-empirical values. r 2005 Elsevier Ltd. All rights reserved. Keywords: Intensity ratio’s
1. Introduction The creation of a vacancy in an atomic shell initiates a series of rearrangement process which may become quite complicated. A single vacancy created, for example, in the K-shell is filled in a time of the order of 1017 21014 s by an electron coming from some higher shell (e.g., the L2 subshell), thus shifting the vacancy to the higher shell. The difference in the binding energy between the two shells (e.g., the K-L2 energy difference) either is released as a K X-ray photon or is transferred to another bound electron which is ejected. This results in an atom with two Tel.: +90 4462 240089/1220.
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vacancies. Continuation of this process gives rise to the emission L, M, N, etc. X-rays and Auger electrons, resulting in an atom with multiple vacancies in its outermost shells; i.e., a highly charged ion. The radiative transitions can be adequately explained in terms of multipole theory which predicts that by far the most important mode is the electric dipole. The nonradiative or Auger transitions occur because of Coulomb interaction existing among different electrons in the atom [1]. It is shown that ratios for the emission probabilities of Auger electrons ejected from different shells can be expressed by the ratio of emission probabilities of Kb and Ka radiation if it is assumed that complementary Auger electrons with same energy also have equal emission probabilities and the ratios of emission probabilities of X-rays and Auger electrons that take place after K-shell vacancy filling (called inverse processes) are equal [2]. The X-ray intensity ratio IðKb Þ=IðKa Þ has been extensively studied in recent years. It is the ratio of the radiative transition probabilities when a K vacancy is filled from the M, N, O, etc. shells to that for filling from the L-shell, and is thus a gross ratio involving several transitions. Prior to 1974, a systematic discrepancy emerged across the entire Periodic Table between IðKb Þ=IðKa Þ ratios measured by Si(Li) and Ge(Li) spectrometers and the predictions of Scofield’s relativistic Hartree–Slater (RHS) calculations. This appeared to be resolved by Scofield’s relativistic Hartree–Fock (RHF) calculations which took proper account of overlap and exchange effects. However, a compilation of measured values by Berenyi et al. suggests that at Zo40 the trend of experimental data actually falls between the RHS and RHF predictions [3]. Ka ; Kb and radiative Auger photon intensities for electron-capture sources in K X-ray spectra from atoms in the atomic number range 20–40 were measured by Campbell et al. [3]. Maxwell and Campbell [4] measured some relative transition probabilities by Ge spectroscopy for the atoms having Z ¼ 70; 78, 82, and 92. K-shell fluorescence yield, mean L-shell fluorescence yield, ratios of X-ray emission probabilities and ratios of emission probabilities of Auger electrons were collected from the literature and evaluated by Scho¨nfeld et al. [2]. In earlier investigations, the variation of the chemical effect of Kb =Ka X-ray intensity ratios was studied in Refs. [5–7]. Ertugˇrul et al. [8] investigated the Ka and Kb X-rays polarization degree and polarization effect on the Kb =Ka intensity ratio. Measurement of Ka and Kb X-ray fluorescence cross-sections and the Kb =Ka intensity ratios for elements in the range 22pZp29 by 10 keV photons was reported by Baydas- et al. [9]. K and L X-ray production cross-sections and intensity ratios of rare-earth elements for proton impact in the energy range 20–25 MeV were reported by Hajivaliei et al. [10]. Allawadhi et al. [11] investigated the effects of Coster–Kronig transitions and incident photon energy on the L subshell X-ray intensity ratios of 4f transition elements. L X-ray fluorescence cross-sections, fluorescence yields and intensity ratios for Au and Pb at excitation energies 21.56, 31.64 and 34.17 keV were investigated by Rao et al. [12]. In this work, ratios of X-ray emission IðKb Þ=IðKa Þ probabilities were experimentally determined for some elements in the atomic number range 25–42 using photoionization method with energy-dispersive X-ray deduction system. An attempt has been made to find the ratios of emission probabilities Auger electrons (KLX/KLL and KXY/KLL) and the vacancy transfer coefficients in terms of ðKb Þ=ðKa Þ emission probabilities for the same atomic range.
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Fig. 1. Experimental setup.
2. Experimental The experimental setup used in the present study is shown in Fig. 1. The targets were excited at 59.5 keV g-rays from a 241Am point source. Fluorescent X-rays spectra from various targets were recorded by a colimated Si(Li) X-ray spectrometer (FWHM ¼ 160 eV at 5.96 keV, active area ¼ 12:5 mm2 ; sensitivity depth ¼ 3:5 cm: Be window thickness ¼ 12:5 mm) coupled to a nuclear data MCA system (ND66B) consisting of a 4096 channel analyser, an ADC and a spectroscopy amplifier. Circular samples (31 mm diameter) of thickness ranging from 17 to 93 mg cm2 have been used for the measurements. The net peak areas of the K X-rays of each target were determined after background subtraction, talling and escape-peak corrections [13].
3. Measurement of Kb =Ka intensity ratio The experimental Kb to Ka X-ray intensity ratios are evaluated using the following relation: IðKb Þ NðKb Þ bðKa Þ ðKa Þ ¼ , IðKa Þ NðKa Þ bðKb Þ ðKb Þ
(1)
where NðKb Þ and NðKa Þ are the net counts observed under the peaks corresponding to Kb and Ka X-rays, respectively, bðKa Þ and bðKb Þ are the target self-absorption correction factors, ðKa Þ and ðKb Þ are photopeak efficiency values of the detector which are determined by using the radiations
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of isotope source b¼
241
Am. The b values were calculated using the relation
1 expðX rDÞ X rD
where X is the total absorption coefficient, which is given by m m X ¼ inc þ emt , cos y1 cos y2
(2)
(3)
where minc and memt are the mass absorption coefficients ðcm2 gÞ [14] at the incident and emitted energies, respectively. The angles of incident and emitted photons to the normal of sample surface, y1 and y2 ; were fixed at 45 : rD is the mass thickness of the target ðg cm2 Þ: The vacancy transfer probability ZKLi is defined as the mean number of primer Li subshell vacancies produced by one vacancy in the K-shell through radiative ZKLi ðRÞ and nonradiative ZKLi ðAÞ transition (15): ZKLi ¼ ZKLi ðRÞ þ ZKLi ðAÞ.
(4)
The quantity ZKLi ðRÞ is proportional to probability that a K-Li radiative transition takes place ZKLi ðRÞ ¼ oK ½IðKLi Þ=I K ðRÞ
(5)
where IðKLi Þ is the K-Li X-ray intensity and I K ðRÞ is the total intensity of K X-rays. The IðKL1 Þ intensity is negligible because K-L1 transitions are forbidden according to the selection rule D‘ ¼ 0; 1; ‘ þ ‘0 X1 (‘ is orbital angular momentum quantum number) for radiative transitions. For K-L2 and K-L3 transitions, vacancy transfer probabilities were evaluated from K X-ray intensity ratios using the relations [15] IðKa2 Þ IðKa2 Þ IðKb Þ 1 , (6) ZKL2 ðRÞ ¼ oK 1þ 1þ IðKa1 Þ IðKa1 Þ IðKa Þ ZKL3 ðRÞ ¼ oK
IðKa2 Þ IðKb Þ 1 1þ , 1þ IðKa1 Þ IðKa Þ
(7)
where oK is the K-shell fluorescence yield, IðKa2 Þ=IðKa1 Þ and IðKb Þ=IðKa Þ are K X-ray intensity ratios. Theoretical ZKL2 ðRÞ and ZKL3 ðRÞ radiative vacancy transfer probabilities were calculated using the relations [15] ZKL2 ðRÞ ¼ GR ðKL2 Þ=GK ,
(8)
ZKL3 ðRÞ ¼ GR ðKL3 Þ=GK .
(9)
4. Procedure We considered that a K-shell vacancy may be filled by a L electron or M electron by radiative transition (Ka ¼ K-L2 ; L3 ; Kb ¼ K-M) or by Auger transition (K-LL, or K-LX); X denotes M-N,
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etc. shell electrons. K-LX is the probability that a K-shell vacancy is filled by an L-shell vacancy is filled by a L-shell electron with the excess energy carried off by an X-shell electron. The aim here is to measure the ratios of X-ray emission probabilities ðKb =Ka Þ and then to calculate the ratios of emission probabilities of Auger electrons and vacancy transfer coefficients ðZKL Þ from these X-ray emission ratios. Kb =Ka X-ray emission probabilities have been determined using experimental procedure for some elements in the atomic number range 25–42. In many experiments, Kb =Ka emission probabilities were measured under different excitation conditions. In this work, measured Kb =Ka X-ray emission probabilities for some elements in the atomic number range 25–42 is given in Table 1. A terminology with three letters is widely used for the characterization of Auger electrons. The first letter describes the shell that has the initial vacancy, the second defines the shell from which an electron fills this vacancy, and the third specifies the shell from which the Auger electron is ejected. For example, a KLM Auger electron is an electron ejected from the M-shell when a Kshell vacancy is filled by an electron. The above notation implies that the Auger process is a twostage process, while the existence of KL1 X Auger electrons indicates a one-stage process since L1 ! K transitions are forbidden according to selection rule D‘ ¼ 1 (‘ ¼ orbital angular momentum quantum number) for radiative transitions. Nevertheless, the Auger process is considered to be a process that occurs in two closely connected steps and not in two independent steps. Thus, complementary Auger electrons (for example KLM and KML, both conventionally denoted as KLM Auger electrons) have both the same energy and the same emission probability p : After the ejection of a KLM or KML Auger electron, the vacancy in the K-shell is filled and the atom is left with one vacancy in the L-shell and one vacancy in the M-shell, independent of the Table 1 Ratios of X-ray emission probabilities ðx ¼ IðKb Þ=IðKa ÞÞ Z
x ¼ IðKb Þ=IðKa Þ Present data
x ¼ IðKb Þ=IðKa Þ [2]
x ¼ IðKb Þ=IðKa Þ [25]
25 26 27 28 29 30 31 32 33 34 35 37 38 39 40 41 42
0:132 0:011 0:134 0:012 0:137 0:011 0:138 0:011 0:139 0:013 0:141 0:010 0:143 0:011 0:152 0:012 0:157 0:011 0:162 0:011 0:169 0:010 0:175 0:011 0:183 0:010 0:188 0:010 0:193 0:014 0:196 0:012 0:202 0:010
0:1359ð14Þ 0:1368ð14Þ 0:1372ð14Þ 0:1378ð14Þ 0:1391ð14Þ 0:1417ð12Þ 0:1457ð12Þ 0:1509ð12Þ 0:1566ð13Þ 0:1626ð13Þ 0:1683ð14Þ 0:1788ð15Þ 0:1835ð15Þ 0:1878ð16Þ 0:1918ð16Þ 0:1953ð16Þ 0:1986ð16Þ
0:131 0:013 0:133 0:010 0:133 0:012 0:135 0:013 0:134 0:013 0:136 0:010 — — 0:152 0:011 0:157 0:012 0:168 0:010 0:171 0:01 0:181 0:016 — 0:191 0:016 — 0:193 0:016
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type (KLM or KML). If p denotes the emission probability which corresponds exactly to the notation, then pðKLMÞ ¼ p ðKLMÞ þ p ðKMLÞ ¼ 2p ðKLMÞ ¼ 2p ðKMLÞ.
ð10Þ
Equal probability ratios for the inverse process are assumed: pðL ! KÞ : pðM ! KÞ : pðN ! KÞ : . . . pðLÞ : pðMÞ : pðNÞ : . . . .
ð11Þ
It is assumed in the formation of Eq. (11) that the ratios of the probabilities pðL ! KÞ etc., for filling a vacancy in the K-shell by an L, M, N, etc. electron are the same as the ratios of the probabilities pðLÞ etc. for the ejection of an electron from the L, M, N, etc. shell if the energy for the latter process is available from the filling of a K-shell vacancy. The left-hand side of Eq. (11) contains the ratios of the emission probabilities of the X-ray quanta, while the right-hand side defines the ratios of the emission probabilities of the Auger electrons for the same element with pðLÞ ¼ pðKLLÞ þ p ðKMLÞ þ p ðKNLÞ þ . . . , pðMÞ ¼ p ðKLMÞ þ pðKMMÞ þ p ðKNMÞ þ . . . , pðNÞ ¼ p ðKLNÞ þ p ðKMNÞ þ pðKNNÞ þ . . . .
ð12Þ
Nothing can be said about the probabilities of the subshell processes because such splitting is determined by quantum mechanical selection rules, wave function overlapping and other related effects. Introducing the Siegbahn notation for X-rays [16] and summing up the right-hand terms of Eqs. (12) gives pðL ! KÞ ¼ pðKa Þ, pðM ! KÞ þ pðN ! KÞ þ . . . ¼ pðKb Þ, pðLÞ ¼ pðKLLÞ þ p ðKXLÞ; X ¼ M þ N þ . . . , pðMÞ þ pðNÞ þ . . . ¼ p ðKLXÞ þ pðKXYÞ; Y ¼ M þ N þ . . . to yield pðKb Þ pðKLLÞ þ p ðKXLÞ ¼ . pðKa Þ p ðKLXÞ þ pðKXYÞ
ð13Þ (14)
The definition of x can be written as x¼
pðKb Þ pðKa Þ
(15)
using Eqs. (10)–(15) results in 1 1 þ u=2 ¼ . x u=2 þ v
(16)
The definition of u as given by Eq. (3) can be written as u¼
pðKXYÞ p ðKXLÞ . p ðKXLÞ pðKLLÞ
(17)
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According to the rule of equal relative emission probabilities for inverse processes, each of two factors in Eq. (17) is equal to x to give u ¼ x2 ,
(18)
substituting this value in Eq. (16) u ¼ 2x.
(19)
Semi-empirical values of u ¼ pðKLXÞ=pðKLLÞ and u ¼ pðKLXÞ=pðKLLÞ have been calculated in terms of measured values of x using Eqs. (18) and (19) for elements in the range 25pZp42: In this work, the number of independent constants required to characterize the atomic processes in the K shell has been decreased by expressing both u and u in terms of x: A further quantity requiring definition ZKL (vacancy transfer coefficient) is the mean number of vacancies produced in the L-shell by one vacancy in the K-shell. If all radiative and nonradiative processes and the production of two vacancies in the L-shell by the ejection of the KLL Auger electrons are taken into account, the quantity ZKL is given by [17,18] ZKL ¼
1 2u þ u oK þ ð1 oK Þ, 1þx 1þuþu
(20)
using Eqs. (18) and (19) gives the simple expression ZKL ¼
2 oK . 1þx
(21)
Semi-empirical values of ZKL have been calculated using Eq. (21) for elements in the range 25pZp42: In Eq. (21), the values of oK is taken from Bambynek et al. [19].
5. Results and discussion Berenyi et al. [20] observed that values of IðKb Þ=IðKa Þ measured by Si(Li) and Ge(Li) spectroscopy using electron-capture (EC) radionuclides tend to be lower than those obtained by proton, or electron bombardment. Early investigations [21–23], centering on Cr, Mn, and Fe demonstrated significant variations of IðKb Þ=IðKa Þ with chemical environment but the range of results was less in photoionization ð 6%Þ than electron capture ð 18%Þ: These early studies disagreed with the existence of a correlation between IðKb Þ=IðKa Þ and the emitting atoms valance state. Chemical variations are twice as large in EC as in photoionization (PI) (photon) and proton (PIXE) ionization. Brunnerr et al. [24] found variations of up to 5% with chemical environment with essentially the same behavior in PI and PIXE. A comparison between PI and EC is not well defined since the atoms involved cannot exist in identical chemical environments. Ertugˇrul et al. measured the Kb =Ka intensity ratios for elements in the range 22pZp69 at 59.5 keV. Ratios of X-ray emission probabilities ðxÞ; ratios of emission probabilities of Auger electrons (u and u) and vacancy transfer coefficient ðZKL Þ have been derived, presented and tabulated. The number of independent constants required to characterize the atomic processes in the K-shell has been decreased by expressing u and u in terms of x:
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The ratio of the emission probabilities of Kb and Ka radiation ðx ¼ IðKb Þ=IðKa ÞÞ are measured under PI excitation conditions for the atomic number range 25–42, except for Z ¼ 36: The errors due to uncertainties in the various parameters used to deduce the measured values, namely, peak area evaluation (p2% for Ka and 3–4% for Kb peaks), absorption correction factor (2%) and counting statistics (3%). The uncertainty in the area of K X-ray peak was evaluated by the weighted average method. Table 1 includes the ratios of X-ray emission probabilities ðxÞ: Present measured values of x are compared with experimental data of Ertugˇrul et al. [25] and fitted values by Scho¨nfeld et al. [2]. As seen Table 1, the present values of x are in agreement with (2%) with fitted values by Scho¨nfeld et al. [2] and the present data of x are greater than (2–5%) the values of Ertugˇrul et al. [25]. In our experiment, we calculated ratios of emission probabilities of Auger electrons (u and u) for the same atomic range. The values of u and u derived semi-empirically from Eqs. (18) and (19) are comparatively presented in Table 2. For comparison, we also calculated ratios of emission probabilities of Auger electrons (u and u) and vacancy transfer coefficient ðZKL Þ using the x values of Ertugˇrul et al. [25]. The values of u and u are in agreement with (p2% for u and 2–6% for u) the fitted values by Scho¨nfeld et al. [2]. The data for u are greater than (2–9%) the values of Ertugˇrul et al. [25]. The values of Ertugˇrul et al. [25] for u differs less than (3–5%) with our present data. The relative standard uncertainties of the semi-empirical values of u were assumed to be equal to the relative standard uncertainties of the values of x although this may be too optimistic. However, there seems to be no basis for the estimation of any additional uncertainty from the theoretical investigations. We calculated the uncertainty of the semi-empirical values of u using the relative error adopted for Eq. (18). These errors are presented in Table 2. Fewer experimental values are available for u; and their relative uncertainties are larger than those of u: Table 2 Ratios of emission probabilities of Auger electrons (u and u) Z
u ¼ 2x Present data
u [2]
u [25]
u ¼ x2 Present data
u [2]
u [25]
25 26 27 28 29 30 31 32 33 34 35 37 38 39 40 41 42
0:264 0:02 0:268 0:02 0:274 0:02 0:276 0:02 0:278 0:03 0:282 0:02 0:286 0:02 0:304 0:02 0:314 0:02 0:324 0:02 0:338 0:02 0:350 0:02 0:366 0:02 0:376 0:02 0:386 0:03 0:392 0:02 0:404 0:02
0.272(3) 0.274(3) 0.274(3) 0.276(3) 0.278(3) 0.283(3) 0.291(3) 0.302(3) 0.313(3) 0.325(3) 0.337(3) 0.358(3) 0.367(3) 0.376(3) 0.384(3) 0.391(4) 0.397(4)
0.262 0.266 0.266 0.270 0.268 0.272 — — 0.304 0.314 0.336 0.342 0.362 — 0.382 — 0.386
0:0174 3E-03 0:0180 3E-03 0:0188 3E-03 0:0190 3E-03 0:0193 4E-03 0:0199 3E-03 0:0204 3E-03 0:0231 4E-03 0:0246 3E-03 0:0262 4E-03 0:0286 3E-03 0:0306 4E-03 0:0335 4E-03 0:0353 4E-03 0:0372 6E-03 0:0384 5E-03 0:0408 4E-03
0.0185(4) 0.0187(4) 0.0188(4) 0.0190(4) 0.0193(4) 0.0201(4) 0.0212(5) 0.0228(4) 0.0245(5) 0.0264(5) 0.0283(5) 0.0320(6) 0.0337(6) 0.0353(6) 0.0368(6) 0.0381(7) 0.0394(7)
0.0171 0.0177 0.0177 0.0182 0.0180 0.0185 — — 0.0231 0.0246 0.0282 0.0292 0.0328 — 0.0364 — 0.0372
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Table 3 Vacancy transfer coefficient ðZKL Þ Z
ZKL Present data
ZKL [2]
ZKL [25]
oK [19]
25 26 27 28 29 30 31 32 33 34 35 37 38 39 40 41 42
1:483 0:12 1:451 0:13 1:418 0:11 1:388 0:11 1:357 0:12 1:327 0:09 1:298 0:10 1:262 0:10 1:231 0:09 1:203 0:08 1:174 0:07 1:128 0:07 1:102 0:07 1:081 0:06 1:061 0:07 1:044 0:06 1:028 0:05
1.478(4) 1.447(4) 1.418(4) 1.388(4) 1.357(4) 1.326(4) 1.294(4) 1.263(4) 1.232(4) 1.202(4) 1.174(4) 1.125(4) 1.102(4) 1.081(4) 1.062(4) 1.045(4) 1.029(4)
1.484 1.452 1.423 1.391 1.364 1.333 — — 1.237 1.211 1.175 1.132 1.104 — 1.0629 — 1.0333
0.321(5) 0.355(4) 0.388(4) 0.421(4) 0.454(4) 0.486(4) 0.517(4) 0.546(4) 0.575(4) 0.602(4) 0.628(4) 0.674(4) 0.696(4) 0.716(4) 0.734(4) 0.751(4) 0.767(4)
Semi-empirical values of ZKL have been calculated using Eq. (21) for elements in the range 25pZp42 and are presented in Table 3. In Eq. (21), the values of oK is taken from the Bambynek fit [19]. Because of good agreement between fitted and theoretical values, the Bambynek fit [19] has been adopted as before to generate the best defined set of values for oK : The assigned standard uncertainties correspond to the recommendations of Bambynek who gave the uncertainties in certain regions of Z [2]. The values of the Bambynek fit are listed in Table 3. For comparison, we also calculated the semi-empirical values of ZKL using the x values of Ertugˇrul et al. [25]. But, in Eq. (21), the values of oK is taken from Hubbell et al. [26]. When the values of ZKL are compared with Scho¨nfeld et al. [2] and Ertugˇrul et al. [25], it is seen that the uncertainties are below 1%. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10]
Fink RW, Jopson RC, Mark H, Swift CD. Rev Mod Phys 1989;38:3. Scho¨nfeld E, JanBen H. Nucl Instrum Methods: Phys Res A 1996;369:527. Campbell JL, Perujo A, Teesdale WJ, Millman BM. Phys Rev A 1986;33:4. Maxwell JA, Campbell JL. Phys Rev A 1984;29:3. So¨gˇu¨t O¨, Bu¨yu¨kkasap E, Erdogan H. Radiat Phys Chem 2002;64:343. Raj S, Padhi HC, Polasik M. Nucl Instrum Methods B 2000;160:443. Raj S, Padhi HC, Polasik M. Nucl Instrum Methods B 1999;155:143. Ertugˇrul M, S- ims-ek O¨, Dogan O, O¨z E, So¨gu¨t O¨, Turgut U¨. Nucl Instrum Methods B 2001;179:465. Baydas- E, Bu¨yu¨kkasap E, Sahin Y. JQSRT 2002;75:473. Hajivalie M, Puri S, Garg ML, Mehta D, Kumar A, Chamoli SK, Avasthi DK, Mandal A, Nandi TK, Singh KP, Singh N, Govil IM. Nucl Instrum Methods B 2000;160:203.
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E. O¨z / Journal of Quantitative Spectroscopy & Radiative Transfer 97 (2006) 41–50 Allawadhi KL, Arora SK, Singh N, Phutela SL. Radiat Phys Chem 1998;51:347. Rao DV, Cesareo R, Gigante GE. Radiat Phys Chem 1995;46:17. Sahin Y, Durak R, Kurucu Y, Erzeneogˇlu S. J Radioanal Chem 1994;177:403. Hubbell JH, Seltzer SM. National Institute of Standards and Technology. Physics National Report No. NISTIR 5632, 1995. Rao PV, Chen MH, Crasemann B. Phys Rev A 1972;5:997. Jenkins R, Manne R, Robin R, Senemaud C. X-ray Spectrosc 1991;30:149. Robinson BL, Fink RW. Rev Mod Phys 1960;32:117. Bambynek W, Crasemann B, Fink RW, Freund H-U, Mark H, Swift CD, Price RE, Venugopala Rao P. Rev Mod Phys 1972;44:716. Bambynek W. In: Meisel A, editor. X-84. X-ray and inner shell process in atoms, molecules and solids. Leipzig: DDR; 1984. Berenyi D, Hock G, Ricz S, Schlenk B, Valek A. J Phys B 1978;11:709. Lazzarini ALF, Lazzarini E, Bettoni MM. Radiochim Acta 1978;25:81. Tanaki Y, Omari T, Shikawa T. Radiochem Radioanal Lett 1979;37:39. Paci-Mazzilli B, Urch DS. In: Inner-shell and X-ray physics of atoms and solids. New York: Plenum; 1981. p. 741. Brunnerr G, Nagel M, Hartmann E, Arndt E. J Phys B 1982;15:4517. Ertugˇrul M, So¨gˇu¨t O¨, S- ims-ek O¨, Bu¨yu¨kkasap E. J Phys B: At Mol Opt Phys 2001;34:909. Hubbell JH, Trehan PN, Singh N, Chand B, Mehta D, Garg ML, Garg RR, Singh S, Puri S. J Phys Chem 1994;23:339 [Ref Data].
Journal of Quantitative Spectroscopy & Radiative Transfer 97 (2006) 41–50 www.elsevier.com/locate/jqsrt
Determination of ratios of emission probabilities of Auger electrons and K–L-shell radiative vacancy transfer probabilities for 17 elements from Mn to Mo at 59.5 keV Elif O¨z Atatu¨rk University, Department of Physics, Faculty of Arts and Science, 25240 Erzurum, Turkey Received 17 November 2004; accepted 23 December 2004
Abstract The measurements of the K X-ray intensity ratio IðKb Þ=IðKa Þ for the 17 elements Mn, Fe, Co, Ni, Cu, Zn, Ga, Ge, As, Se, Br, Rb, Sr, Y, Zr, Nb and Mo have been done following ionization by 59.5 keV g-rays from a 241Am point source. Ratios of emission probabilities of Auger electrons and the vacancy transfer coefficients have been extracted in terms of the intensity ratios. It is found that the present results agree well with earlier fitted values and the semi-empirical values. r 2005 Elsevier Ltd. All rights reserved. Keywords: Intensity ratio’s
1. Introduction The creation of a vacancy in an atomic shell initiates a series of rearrangement process which may become quite complicated. A single vacancy created, for example, in the K-shell is filled in a time of the order of 1017 21014 s by an electron coming from some higher shell (e.g., the L2 subshell), thus shifting the vacancy to the higher shell. The difference in the binding energy between the two shells (e.g., the K-L2 energy difference) either is released as a K X-ray photon or is transferred to another bound electron which is ejected. This results in an atom with two Tel.: +90 4462 240089/1220.
E-mail address: [email protected]. 0022-4073/$ - see front matter r 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.jqsrt.2004.12.016
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vacancies. Continuation of this process gives rise to the emission L, M, N, etc. X-rays and Auger electrons, resulting in an atom with multiple vacancies in its outermost shells; i.e., a highly charged ion. The radiative transitions can be adequately explained in terms of multipole theory which predicts that by far the most important mode is the electric dipole. The nonradiative or Auger transitions occur because of Coulomb interaction existing among different electrons in the atom [1]. It is shown that ratios for the emission probabilities of Auger electrons ejected from different shells can be expressed by the ratio of emission probabilities of Kb and Ka radiation if it is assumed that complementary Auger electrons with same energy also have equal emission probabilities and the ratios of emission probabilities of X-rays and Auger electrons that take place after K-shell vacancy filling (called inverse processes) are equal [2]. The X-ray intensity ratio IðKb Þ=IðKa Þ has been extensively studied in recent years. It is the ratio of the radiative transition probabilities when a K vacancy is filled from the M, N, O, etc. shells to that for filling from the L-shell, and is thus a gross ratio involving several transitions. Prior to 1974, a systematic discrepancy emerged across the entire Periodic Table between IðKb Þ=IðKa Þ ratios measured by Si(Li) and Ge(Li) spectrometers and the predictions of Scofield’s relativistic Hartree–Slater (RHS) calculations. This appeared to be resolved by Scofield’s relativistic Hartree–Fock (RHF) calculations which took proper account of overlap and exchange effects. However, a compilation of measured values by Berenyi et al. suggests that at Zo40 the trend of experimental data actually falls between the RHS and RHF predictions [3]. Ka ; Kb and radiative Auger photon intensities for electron-capture sources in K X-ray spectra from atoms in the atomic number range 20–40 were measured by Campbell et al. [3]. Maxwell and Campbell [4] measured some relative transition probabilities by Ge spectroscopy for the atoms having Z ¼ 70; 78, 82, and 92. K-shell fluorescence yield, mean L-shell fluorescence yield, ratios of X-ray emission probabilities and ratios of emission probabilities of Auger electrons were collected from the literature and evaluated by Scho¨nfeld et al. [2]. In earlier investigations, the variation of the chemical effect of Kb =Ka X-ray intensity ratios was studied in Refs. [5–7]. Ertugˇrul et al. [8] investigated the Ka and Kb X-rays polarization degree and polarization effect on the Kb =Ka intensity ratio. Measurement of Ka and Kb X-ray fluorescence cross-sections and the Kb =Ka intensity ratios for elements in the range 22pZp29 by 10 keV photons was reported by Baydas- et al. [9]. K and L X-ray production cross-sections and intensity ratios of rare-earth elements for proton impact in the energy range 20–25 MeV were reported by Hajivaliei et al. [10]. Allawadhi et al. [11] investigated the effects of Coster–Kronig transitions and incident photon energy on the L subshell X-ray intensity ratios of 4f transition elements. L X-ray fluorescence cross-sections, fluorescence yields and intensity ratios for Au and Pb at excitation energies 21.56, 31.64 and 34.17 keV were investigated by Rao et al. [12]. In this work, ratios of X-ray emission IðKb Þ=IðKa Þ probabilities were experimentally determined for some elements in the atomic number range 25–42 using photoionization method with energy-dispersive X-ray deduction system. An attempt has been made to find the ratios of emission probabilities Auger electrons (KLX/KLL and KXY/KLL) and the vacancy transfer coefficients in terms of ðKb Þ=ðKa Þ emission probabilities for the same atomic range.
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Fig. 1. Experimental setup.
2. Experimental The experimental setup used in the present study is shown in Fig. 1. The targets were excited at 59.5 keV g-rays from a 241Am point source. Fluorescent X-rays spectra from various targets were recorded by a colimated Si(Li) X-ray spectrometer (FWHM ¼ 160 eV at 5.96 keV, active area ¼ 12:5 mm2 ; sensitivity depth ¼ 3:5 cm: Be window thickness ¼ 12:5 mm) coupled to a nuclear data MCA system (ND66B) consisting of a 4096 channel analyser, an ADC and a spectroscopy amplifier. Circular samples (31 mm diameter) of thickness ranging from 17 to 93 mg cm2 have been used for the measurements. The net peak areas of the K X-rays of each target were determined after background subtraction, talling and escape-peak corrections [13].
3. Measurement of Kb =Ka intensity ratio The experimental Kb to Ka X-ray intensity ratios are evaluated using the following relation: IðKb Þ NðKb Þ bðKa Þ ðKa Þ ¼ , IðKa Þ NðKa Þ bðKb Þ ðKb Þ
(1)
where NðKb Þ and NðKa Þ are the net counts observed under the peaks corresponding to Kb and Ka X-rays, respectively, bðKa Þ and bðKb Þ are the target self-absorption correction factors, ðKa Þ and ðKb Þ are photopeak efficiency values of the detector which are determined by using the radiations
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of isotope source b¼
241
Am. The b values were calculated using the relation
1 expðX rDÞ X rD
where X is the total absorption coefficient, which is given by m m X ¼ inc þ emt , cos y1 cos y2
(2)
(3)
where minc and memt are the mass absorption coefficients ðcm2 gÞ [14] at the incident and emitted energies, respectively. The angles of incident and emitted photons to the normal of sample surface, y1 and y2 ; were fixed at 45 : rD is the mass thickness of the target ðg cm2 Þ: The vacancy transfer probability ZKLi is defined as the mean number of primer Li subshell vacancies produced by one vacancy in the K-shell through radiative ZKLi ðRÞ and nonradiative ZKLi ðAÞ transition (15): ZKLi ¼ ZKLi ðRÞ þ ZKLi ðAÞ.
(4)
The quantity ZKLi ðRÞ is proportional to probability that a K-Li radiative transition takes place ZKLi ðRÞ ¼ oK ½IðKLi Þ=I K ðRÞ
(5)
where IðKLi Þ is the K-Li X-ray intensity and I K ðRÞ is the total intensity of K X-rays. The IðKL1 Þ intensity is negligible because K-L1 transitions are forbidden according to the selection rule D‘ ¼ 0; 1; ‘ þ ‘0 X1 (‘ is orbital angular momentum quantum number) for radiative transitions. For K-L2 and K-L3 transitions, vacancy transfer probabilities were evaluated from K X-ray intensity ratios using the relations [15] IðKa2 Þ IðKa2 Þ IðKb Þ 1 , (6) ZKL2 ðRÞ ¼ oK 1þ 1þ IðKa1 Þ IðKa1 Þ IðKa Þ ZKL3 ðRÞ ¼ oK
IðKa2 Þ IðKb Þ 1 1þ , 1þ IðKa1 Þ IðKa Þ
(7)
where oK is the K-shell fluorescence yield, IðKa2 Þ=IðKa1 Þ and IðKb Þ=IðKa Þ are K X-ray intensity ratios. Theoretical ZKL2 ðRÞ and ZKL3 ðRÞ radiative vacancy transfer probabilities were calculated using the relations [15] ZKL2 ðRÞ ¼ GR ðKL2 Þ=GK ,
(8)
ZKL3 ðRÞ ¼ GR ðKL3 Þ=GK .
(9)
4. Procedure We considered that a K-shell vacancy may be filled by a L electron or M electron by radiative transition (Ka ¼ K-L2 ; L3 ; Kb ¼ K-M) or by Auger transition (K-LL, or K-LX); X denotes M-N,
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etc. shell electrons. K-LX is the probability that a K-shell vacancy is filled by an L-shell vacancy is filled by a L-shell electron with the excess energy carried off by an X-shell electron. The aim here is to measure the ratios of X-ray emission probabilities ðKb =Ka Þ and then to calculate the ratios of emission probabilities of Auger electrons and vacancy transfer coefficients ðZKL Þ from these X-ray emission ratios. Kb =Ka X-ray emission probabilities have been determined using experimental procedure for some elements in the atomic number range 25–42. In many experiments, Kb =Ka emission probabilities were measured under different excitation conditions. In this work, measured Kb =Ka X-ray emission probabilities for some elements in the atomic number range 25–42 is given in Table 1. A terminology with three letters is widely used for the characterization of Auger electrons. The first letter describes the shell that has the initial vacancy, the second defines the shell from which an electron fills this vacancy, and the third specifies the shell from which the Auger electron is ejected. For example, a KLM Auger electron is an electron ejected from the M-shell when a Kshell vacancy is filled by an electron. The above notation implies that the Auger process is a twostage process, while the existence of KL1 X Auger electrons indicates a one-stage process since L1 ! K transitions are forbidden according to selection rule D‘ ¼ 1 (‘ ¼ orbital angular momentum quantum number) for radiative transitions. Nevertheless, the Auger process is considered to be a process that occurs in two closely connected steps and not in two independent steps. Thus, complementary Auger electrons (for example KLM and KML, both conventionally denoted as KLM Auger electrons) have both the same energy and the same emission probability p : After the ejection of a KLM or KML Auger electron, the vacancy in the K-shell is filled and the atom is left with one vacancy in the L-shell and one vacancy in the M-shell, independent of the Table 1 Ratios of X-ray emission probabilities ðx ¼ IðKb Þ=IðKa ÞÞ Z
x ¼ IðKb Þ=IðKa Þ Present data
x ¼ IðKb Þ=IðKa Þ [2]
x ¼ IðKb Þ=IðKa Þ [25]
25 26 27 28 29 30 31 32 33 34 35 37 38 39 40 41 42
0:132 0:011 0:134 0:012 0:137 0:011 0:138 0:011 0:139 0:013 0:141 0:010 0:143 0:011 0:152 0:012 0:157 0:011 0:162 0:011 0:169 0:010 0:175 0:011 0:183 0:010 0:188 0:010 0:193 0:014 0:196 0:012 0:202 0:010
0:1359ð14Þ 0:1368ð14Þ 0:1372ð14Þ 0:1378ð14Þ 0:1391ð14Þ 0:1417ð12Þ 0:1457ð12Þ 0:1509ð12Þ 0:1566ð13Þ 0:1626ð13Þ 0:1683ð14Þ 0:1788ð15Þ 0:1835ð15Þ 0:1878ð16Þ 0:1918ð16Þ 0:1953ð16Þ 0:1986ð16Þ
0:131 0:013 0:133 0:010 0:133 0:012 0:135 0:013 0:134 0:013 0:136 0:010 — — 0:152 0:011 0:157 0:012 0:168 0:010 0:171 0:01 0:181 0:016 — 0:191 0:016 — 0:193 0:016
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type (KLM or KML). If p denotes the emission probability which corresponds exactly to the notation, then pðKLMÞ ¼ p ðKLMÞ þ p ðKMLÞ ¼ 2p ðKLMÞ ¼ 2p ðKMLÞ.
ð10Þ
Equal probability ratios for the inverse process are assumed: pðL ! KÞ : pðM ! KÞ : pðN ! KÞ : . . . pðLÞ : pðMÞ : pðNÞ : . . . .
ð11Þ
It is assumed in the formation of Eq. (11) that the ratios of the probabilities pðL ! KÞ etc., for filling a vacancy in the K-shell by an L, M, N, etc. electron are the same as the ratios of the probabilities pðLÞ etc. for the ejection of an electron from the L, M, N, etc. shell if the energy for the latter process is available from the filling of a K-shell vacancy. The left-hand side of Eq. (11) contains the ratios of the emission probabilities of the X-ray quanta, while the right-hand side defines the ratios of the emission probabilities of the Auger electrons for the same element with pðLÞ ¼ pðKLLÞ þ p ðKMLÞ þ p ðKNLÞ þ . . . , pðMÞ ¼ p ðKLMÞ þ pðKMMÞ þ p ðKNMÞ þ . . . , pðNÞ ¼ p ðKLNÞ þ p ðKMNÞ þ pðKNNÞ þ . . . .
ð12Þ
Nothing can be said about the probabilities of the subshell processes because such splitting is determined by quantum mechanical selection rules, wave function overlapping and other related effects. Introducing the Siegbahn notation for X-rays [16] and summing up the right-hand terms of Eqs. (12) gives pðL ! KÞ ¼ pðKa Þ, pðM ! KÞ þ pðN ! KÞ þ . . . ¼ pðKb Þ, pðLÞ ¼ pðKLLÞ þ p ðKXLÞ; X ¼ M þ N þ . . . , pðMÞ þ pðNÞ þ . . . ¼ p ðKLXÞ þ pðKXYÞ; Y ¼ M þ N þ . . . to yield pðKb Þ pðKLLÞ þ p ðKXLÞ ¼ . pðKa Þ p ðKLXÞ þ pðKXYÞ
ð13Þ (14)
The definition of x can be written as x¼
pðKb Þ pðKa Þ
(15)
using Eqs. (10)–(15) results in 1 1 þ u=2 ¼ . x u=2 þ v
(16)
The definition of u as given by Eq. (3) can be written as u¼
pðKXYÞ p ðKXLÞ . p ðKXLÞ pðKLLÞ
(17)
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According to the rule of equal relative emission probabilities for inverse processes, each of two factors in Eq. (17) is equal to x to give u ¼ x2 ,
(18)
substituting this value in Eq. (16) u ¼ 2x.
(19)
Semi-empirical values of u ¼ pðKLXÞ=pðKLLÞ and u ¼ pðKLXÞ=pðKLLÞ have been calculated in terms of measured values of x using Eqs. (18) and (19) for elements in the range 25pZp42: In this work, the number of independent constants required to characterize the atomic processes in the K shell has been decreased by expressing both u and u in terms of x: A further quantity requiring definition ZKL (vacancy transfer coefficient) is the mean number of vacancies produced in the L-shell by one vacancy in the K-shell. If all radiative and nonradiative processes and the production of two vacancies in the L-shell by the ejection of the KLL Auger electrons are taken into account, the quantity ZKL is given by [17,18] ZKL ¼
1 2u þ u oK þ ð1 oK Þ, 1þx 1þuþu
(20)
using Eqs. (18) and (19) gives the simple expression ZKL ¼
2 oK . 1þx
(21)
Semi-empirical values of ZKL have been calculated using Eq. (21) for elements in the range 25pZp42: In Eq. (21), the values of oK is taken from Bambynek et al. [19].
5. Results and discussion Berenyi et al. [20] observed that values of IðKb Þ=IðKa Þ measured by Si(Li) and Ge(Li) spectroscopy using electron-capture (EC) radionuclides tend to be lower than those obtained by proton, or electron bombardment. Early investigations [21–23], centering on Cr, Mn, and Fe demonstrated significant variations of IðKb Þ=IðKa Þ with chemical environment but the range of results was less in photoionization ð 6%Þ than electron capture ð 18%Þ: These early studies disagreed with the existence of a correlation between IðKb Þ=IðKa Þ and the emitting atoms valance state. Chemical variations are twice as large in EC as in photoionization (PI) (photon) and proton (PIXE) ionization. Brunnerr et al. [24] found variations of up to 5% with chemical environment with essentially the same behavior in PI and PIXE. A comparison between PI and EC is not well defined since the atoms involved cannot exist in identical chemical environments. Ertugˇrul et al. measured the Kb =Ka intensity ratios for elements in the range 22pZp69 at 59.5 keV. Ratios of X-ray emission probabilities ðxÞ; ratios of emission probabilities of Auger electrons (u and u) and vacancy transfer coefficient ðZKL Þ have been derived, presented and tabulated. The number of independent constants required to characterize the atomic processes in the K-shell has been decreased by expressing u and u in terms of x:
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The ratio of the emission probabilities of Kb and Ka radiation ðx ¼ IðKb Þ=IðKa ÞÞ are measured under PI excitation conditions for the atomic number range 25–42, except for Z ¼ 36: The errors due to uncertainties in the various parameters used to deduce the measured values, namely, peak area evaluation (p2% for Ka and 3–4% for Kb peaks), absorption correction factor (2%) and counting statistics (3%). The uncertainty in the area of K X-ray peak was evaluated by the weighted average method. Table 1 includes the ratios of X-ray emission probabilities ðxÞ: Present measured values of x are compared with experimental data of Ertugˇrul et al. [25] and fitted values by Scho¨nfeld et al. [2]. As seen Table 1, the present values of x are in agreement with (2%) with fitted values by Scho¨nfeld et al. [2] and the present data of x are greater than (2–5%) the values of Ertugˇrul et al. [25]. In our experiment, we calculated ratios of emission probabilities of Auger electrons (u and u) for the same atomic range. The values of u and u derived semi-empirically from Eqs. (18) and (19) are comparatively presented in Table 2. For comparison, we also calculated ratios of emission probabilities of Auger electrons (u and u) and vacancy transfer coefficient ðZKL Þ using the x values of Ertugˇrul et al. [25]. The values of u and u are in agreement with (p2% for u and 2–6% for u) the fitted values by Scho¨nfeld et al. [2]. The data for u are greater than (2–9%) the values of Ertugˇrul et al. [25]. The values of Ertugˇrul et al. [25] for u differs less than (3–5%) with our present data. The relative standard uncertainties of the semi-empirical values of u were assumed to be equal to the relative standard uncertainties of the values of x although this may be too optimistic. However, there seems to be no basis for the estimation of any additional uncertainty from the theoretical investigations. We calculated the uncertainty of the semi-empirical values of u using the relative error adopted for Eq. (18). These errors are presented in Table 2. Fewer experimental values are available for u; and their relative uncertainties are larger than those of u: Table 2 Ratios of emission probabilities of Auger electrons (u and u) Z
u ¼ 2x Present data
u [2]
u [25]
u ¼ x2 Present data
u [2]
u [25]
25 26 27 28 29 30 31 32 33 34 35 37 38 39 40 41 42
0:264 0:02 0:268 0:02 0:274 0:02 0:276 0:02 0:278 0:03 0:282 0:02 0:286 0:02 0:304 0:02 0:314 0:02 0:324 0:02 0:338 0:02 0:350 0:02 0:366 0:02 0:376 0:02 0:386 0:03 0:392 0:02 0:404 0:02
0.272(3) 0.274(3) 0.274(3) 0.276(3) 0.278(3) 0.283(3) 0.291(3) 0.302(3) 0.313(3) 0.325(3) 0.337(3) 0.358(3) 0.367(3) 0.376(3) 0.384(3) 0.391(4) 0.397(4)
0.262 0.266 0.266 0.270 0.268 0.272 — — 0.304 0.314 0.336 0.342 0.362 — 0.382 — 0.386
0:0174 3E-03 0:0180 3E-03 0:0188 3E-03 0:0190 3E-03 0:0193 4E-03 0:0199 3E-03 0:0204 3E-03 0:0231 4E-03 0:0246 3E-03 0:0262 4E-03 0:0286 3E-03 0:0306 4E-03 0:0335 4E-03 0:0353 4E-03 0:0372 6E-03 0:0384 5E-03 0:0408 4E-03
0.0185(4) 0.0187(4) 0.0188(4) 0.0190(4) 0.0193(4) 0.0201(4) 0.0212(5) 0.0228(4) 0.0245(5) 0.0264(5) 0.0283(5) 0.0320(6) 0.0337(6) 0.0353(6) 0.0368(6) 0.0381(7) 0.0394(7)
0.0171 0.0177 0.0177 0.0182 0.0180 0.0185 — — 0.0231 0.0246 0.0282 0.0292 0.0328 — 0.0364 — 0.0372
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Table 3 Vacancy transfer coefficient ðZKL Þ Z
ZKL Present data
ZKL [2]
ZKL [25]
oK [19]
25 26 27 28 29 30 31 32 33 34 35 37 38 39 40 41 42
1:483 0:12 1:451 0:13 1:418 0:11 1:388 0:11 1:357 0:12 1:327 0:09 1:298 0:10 1:262 0:10 1:231 0:09 1:203 0:08 1:174 0:07 1:128 0:07 1:102 0:07 1:081 0:06 1:061 0:07 1:044 0:06 1:028 0:05
1.478(4) 1.447(4) 1.418(4) 1.388(4) 1.357(4) 1.326(4) 1.294(4) 1.263(4) 1.232(4) 1.202(4) 1.174(4) 1.125(4) 1.102(4) 1.081(4) 1.062(4) 1.045(4) 1.029(4)
1.484 1.452 1.423 1.391 1.364 1.333 — — 1.237 1.211 1.175 1.132 1.104 — 1.0629 — 1.0333
0.321(5) 0.355(4) 0.388(4) 0.421(4) 0.454(4) 0.486(4) 0.517(4) 0.546(4) 0.575(4) 0.602(4) 0.628(4) 0.674(4) 0.696(4) 0.716(4) 0.734(4) 0.751(4) 0.767(4)
Semi-empirical values of ZKL have been calculated using Eq. (21) for elements in the range 25pZp42 and are presented in Table 3. In Eq. (21), the values of oK is taken from the Bambynek fit [19]. Because of good agreement between fitted and theoretical values, the Bambynek fit [19] has been adopted as before to generate the best defined set of values for oK : The assigned standard uncertainties correspond to the recommendations of Bambynek who gave the uncertainties in certain regions of Z [2]. The values of the Bambynek fit are listed in Table 3. For comparison, we also calculated the semi-empirical values of ZKL using the x values of Ertugˇrul et al. [25]. But, in Eq. (21), the values of oK is taken from Hubbell et al. [26]. When the values of ZKL are compared with Scho¨nfeld et al. [2] and Ertugˇrul et al. [25], it is seen that the uncertainties are below 1%. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10]
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