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A new term “Jzeff” derived from measured total attenuation coefficients of photons near the absorption edges of some compounds
Nuclear Instruments and Methods in Physics Research A 621 (2010) 358–363
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Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
A new term ‘‘Jzeff’’ derived from measured total attenuation coefficients of photons near the absorption edges of some compounds Recep Polat a, Orhan _Ic- elli b,n a b
Department of Physics Education, Education of Faculty, Erzincan University, 24030 Erzincan, Turkey Department of Physics, Faculty of Art and Sciences, Yıldız Technical University, Davutpas- a, 34220 Istanbul, Turkey
a r t i c l e in f o
a b s t r a c t
Article history: Received 23 March 2010 Received in revised form 7 April 2010 Accepted 16 April 2010 Available online 27 April 2010
In order to determine the effect of XAFS (X-ray absorption fine structure) on Jzeff, we have measured m/r values of compounds, which are determined by the mixture rule or the independent atomic model. Also, we want to obtain both XAFS effect and non-applicability or applicability of mixture rule. The most crucial finding in this study is that measurement of the effective atomic number is not appropriate near the absorption edge and the effective atomic number is affected by near the absorption edge. The results obtained have been compared with theoretical values. Also, the objective of this study is to show that there is a term ‘‘Jzeff’’ between effective atomic numbers and absorption jump factor. & 2010 Elsevier B.V. All rights reserved.
Keywords: Mass attenuation coefficients Molecular Atomic cross-sections Effective atomic number Jump ratio Jump factor
1. Introduction The scattering and absorption of X-ray and gamma radiation are related to the density and atomic numbers of an element. In composite materials it is related to the density and effective atomic number. A single number therefore cannot represent the atomic number uniquely across the entire energy range, as the partial interaction cross-sections have different element number dependence. This number in composite materials is called the effective atomic number and it varies depending on energy [1]. Effective atomic number is a highly beneficial parameter for many fields of scientific applications. This parameter is introduced to describe the properties of these composite materials in terms of equivalent elements. The atomic number, Z, is a ubiquitous parameter in atomic and nuclear physics where it occurs in almost any formula. For a complex medium, the effective atomic number, Zeff, is in some cases a convenient parameter for representing X-ray and gamma ray interactions, e.g. in designs of radiation shielding or in calculations of absorbed dose in radiotherapy. For each of the different processes, by which X-rays and gamma rays can interact with matter, the various atomic numbers in the material have to be weighted differently. Accordingly, Zeff is no true constant for a given material, but a parameter varying with photon energy depending on the interaction processes involved.
n
Corresponding author. Tel.: + 90 4 46 224 0089; fax: +90 446 2231901. E-mail addresses: [email protected], [email protected] (O. _Ic- elli).
0168-9002/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2010.04.061
Various researchers have determined the effective atomic number for some materials [1–16]. Also, effective atomic numbers of some compounds have been determined by means of a practical method by _Ic- elli [17]. But, as seen in the literature, a relation or study between absorption jump ratio and measured effective atomic number is absent around the K absorption edge of absorbers, especially. The aim of the present paper is to fill this gap in the literature and ‘‘JZeff’’ term to acquire to the literature. The study of the absorption of gamma radiations in materials has been an important subject in the field of radiation physics and is potentially useful in the development of semi-empirical formulations of high accuracy. Benefiting from the mass attenuation coefficient, a number of related parameters can be derived, such as the mass energy-absorption coefficients, the total interaction cross-section, the molar extinction coefficient, molecular, atomic, electronic cross-sections, the effective atomic number, and the effective electron density. In addition to these, we have measured absorption jump factors by using mass attenuation coefficient near the absorption edge, which have been represented as simple abrupt discontinuities in absorption coefficients at a photon energy just sufficient to expel electrons from a specific inner level in the atom. The fine structure consists of deviations from this simple step function and includes deviations both in the abrupt rise and in the region on the highenergy side of the rise. In general, fine structure is confined to within 200 eV of the edge [18]. XAFS, i.e. the oscillatory structure in the X-ray absorption coefficient, contains much quantitative information concerning the local structure near the absorbing atom [19].
R. Polat, O. _Ic- elli / Nuclear Instruments and Methods in Physics Research A 621 (2010) 358–363
We attempt here to demonstrate the effect of XAFS on jump ratio measured by using m/r values, which is determined with the mixture rule near the absorption edge of selected elements used as secondary source. The objective of this study is to provide the literature with the term ‘‘JZeff’’ and theoretical and experimental measurement and calculations. The second aim of this study is to provide data for present compounds near the absorption edge and to demonstrate the effect of XAFS (X-ray absorption fine structure). Also, chemical effects on ‘‘JZeff’’ are not very well known. However, it is pointed out and also well known that X-ray spectra depend on the chemical surrounding of the atom. The second aim of this study is to support the systematic investigation of the lately published study [20]. Summarily, the present study aims that there is a considerable linear combination between the effective atomic numbers and the absorption jump factor. This is the first time we have measured the JZeff values of selected compounds at o100 keV energies, so there are no data available in the literature for comparison with these results. It is important that determination of JZeff is a new study in the same experimental station and method [20]. La2O3 is used in X-ray image intensifying screens, phosphors, dielectric ceramics, conductive ceramics, and barium titanate capacit. Ba(OH)2 is used in analytical chemistry for the titration of weak acids, particularly organic acids. CsHCO3 is used as a base in organic reactions. Various forms of cesium, especially cesium nitrate, cesium carbonate and cesium bicarbonate, are used as glass components to achieve various objectives. The refractive index of optical glass – in the bulk or on the surface only – can be modified by the addition of cesium salts. Through surface ion exchange with cesium salt melts or solutions, the glass surface can be made resistant to corrosion or breakage. Behrens [21] has studied the electronic structure of silver oxides investigated by AgL XANES Spectroscopy. Due to the above-mentioned reasons, it is important to determine the JZeff and Zeff of the selected absorbers.
2. Basic formulas
359
The total atomic and electronic cross-sections are related to the effective (Zeff) through the following relation: Zeff ¼
st,a : st,el
2.1. Absorption jump factors Effective atomic number of any compound also varies with the wavelength or energy of the absorbed X-rays. If Zeff is plotted against wavelength for any chosen absorber it will show a general increase towards the longer, or ‘softer’ wavelength, as might be expected. However, the variation is not continuous, instead it is marked by a series of abrupt discontinuities called absorption edges. The ratio between the upper and lower edge is called the jump ratio. The difference between the upper and lower edge values directly gives the photo effect cross-section of that particular shell without the necessity of assuming any other partial cross-section. It is important since it is a measure of the photo effect due to the particular shell relative to other competing interaction processes. If the scattering component is thus neglected, the absorption curve may be seen to be made up of the additive effects of photoelectric absorption due to each of the absorption edges. We have seen that three phenomena – photoelectric absorption, scatter, and pair production – constitute total absorption. In the wavelenght region of X-ray spectrochemistry, pair production does not occur, and photoelectric absorption predominates overscatter. Consequently, m/r is largely determined by ttotal. At wavelengths shorter than the K edge,
ttotal ¼ tK þ ðtLI þ tLII þ tLIII Þ þ ðtMI þ tMII :::Þ þ::::
ð1Þ
Here ttotal being the photoelectric mass-absorption coefficients is itself the sum of a series of coefficients representing photon absorption due to electron expulsion from each of the atomic levels. As the K edge is passed towards lower energies or longer wavelength, the tK component disappears. The ratio rK of absorptions immediately on either side of the edge,
tK þ tL þ tM þ ::: tL þ tM þ :::
Equations and calculations related with the total mass attenuation coefficients, the total atomic cross-section, the total electronic cross-section, the effective atomic number and electron densities of mixtures are given by Polat and _Ic-elli [20]. Values of the mass attenuation coefficients of Polat et al. [22] have been used in order to determine JZeff. A quick reminder of the basic formulas: The total mass attenuation coefficients, mt (cm2/g), of elements and compounds are calculated from the following equation obtained from: m 1 I0 ln : ¼ r rx I
is called the absorption jump or absorption jump ratio, in this case for the K absorption edge [23]. In subsequent developments, absorption jump values, r, will be used to calculate absorption jump factors, J, i.e. the probability Jli that an incident photon will eject electrons from a K, L, M,... energy level. For example, the probability that a K level electron of elements i will be ejected rather than one from an L or M level is given by
Values of mass attenuation coefficients can be used to determine the total molecular cross-section, st,m, by the following relation: X 1 m st,m ¼ ðni Ai Þ: N r comp i
As seen in Figs. 1–4, in the graph of total effective atomic number versus energy, absorption jump factors give the ratio between the upper and lower edge.
The total atomic cross-section, st,a, can be easily determined from above as 1 i ni :
st,a ¼ st,m P
The total electronic cross-section, st,e, for the individual element is expressed by the following formula: 1 X fi Ai m st,e ¼ : N i Zi r i
rK ¼
JK ¼
ðrK 1Þ rK
JZeff ¼
ðZeff Þ þ ðZeff Þ ðZeff Þ þ
ð2Þ
ð3Þ
ð4Þ
Here, (Zeff) + and (Zeff) represent upper edge and lower edge, respectively. It is seen that all graphs have been fitted to first degree linear regression for both (Zeff) + and (Zeff) . The graphs show that the equation fit the first degree linear regression for both (Zeff) + and (Zeff) . The equation is y ¼ ax þ b:
ð5Þ
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360
Ba(OH)2
80
100
La2O3
70
Effective Atomic Number (Zeff)
Effective Atomic Number (Zeff)
80
60
40
60
50
40
30
20 20
Theoretical
37.0
37.2
37.4 37.6 37.8 Photon Energy (keV)
38.0
Theoretical
10
Experimental
38.2
Fig. 1. Effective atomic numbers of Ba(OH)2 versus photon energy, around K absorption edges.
Here, a and b are constant coefficients; x represents K absorption edge of absorber and y represents the effective atomic number. The parameters mentioned above have been experimentally measured and compared with theoretically calculated values.
3. Experimental procedure The mass attenuation coefficients for some selected compounds, Ag2O3, CsHCO3, Ba[(OH)2], and La2O3, were measured in the X-ray energy range from 25 up to 39 keV using a Si(Li) detector with a thin (25 mm) Be window and variable-energy X-ray source. The X-ray source was Am-241 whose g-rays were stopped in four secondary sources (Sn, Pr, Nd, and Sm), thus producing Ka and Kb X-ray emission. The energies of Ka and Kb X-rays published from secondary sources (Sn, Pr, Nd, and Sm) must be within the range of values Kabs of absorber (Ag2O, CsHCO3, Ba[(OH)2], and La2O3). They are used in different energy ranges and separated Ka1 and Ka2 , Kb1, and Kb2 peaks calculating the absoption coefficients. The calculations made by considering the conditions of intensities of the photons dropped to each channel before and after the absorption and, respectively, for every channel of energy and by taking the whole peaks. The schematic arrangement of the experimental setup used in the present compound is given in [22]. The total attenuation coefficients and K X-rays absorption jump factors were determined by using transmission geometry. In the present experiment a Si(Li) detector was used with an ND66B multichannel analyzer for detection of X-rays. FWHM value is 160 eV in 5.96 keV. This shows that FWHM depends on energy rather than being constant for all. This detector was coupled
Experimental
38.4
38.6
38.8 39.0 39.2 Photon Energy (keV)
39.4
39.6
Fig. 2. Effective atomic numbers of La2O3 versus photon energy, around K absorption edges.
to a computerized 1024-multichannel analyzer through a spectroscopy automatic fine-tuning research amplifier. The statistical errors in the intensities of X-ray in unit of time arising from radioisotope and characteristical X-rays arising from secondary source had been minimized by taking the counting time long enough. These statistical errors are always less than 1%. To obtain statistical accuracy, each sample was measured by collecting the spectra from selected elements for a period of 72 103 s. High purity (99.9%) samples of Ag2O3, CsHCO3, Ba[(OH)2], and La2O3 were measured using a radioactive annular source of Am-241 of strength 3.7 109 Bq (100 mCi) and g-photon energy 59.5 keV. The mass thicknesses of these mixtures have been determined as 8.49 10 2 g/cm2. Mass thickness values measurements with gravimetric method in g/cm2 units are always the same. In this experiment, the net counts without absorber (I0) and with absorber (I) were obtained at the same time and experimental conditions. Also, we have considered the change in the detector efficiency as there was no change in the absorbed peaks and unabsobed peaks. The studied compounds with the bond structure, oxidation state, and crystalline form are given in Table 1.
4. Result and discussion The experimental and theoretical Zeff are listed in Table 2. The experimental and theoretical effective atomic numbers of Ba(OH)2, La2O3, Ag2O3, and CsHCO3 around K absorption edges versus photon energy incident over the absorber are shown graphically in Figs. 1–4. It is clearly seen from the figures that effective atomic number depends on the photon energy. As shown
R. Polat, O. _Ic- elli / Nuclear Instruments and Methods in Physics Research A 621 (2010) 358–363
350
140 CsHCO3
Ag2O3
300
120
250
100
Effective Atomic Number (Zeff)
Effective Atomic Number (Zeff)
361
200
150
80
60
40
100
Theoretical
20
Theoretical
50
Experimental
Experimental
35.4
25.0
25.2
25.4 25.6 25.8 Photon Energy (keV)
26.0
Fig. 3. Effective atomic numbers of Ag2O3 versus photon energy, around K absorption edges.
in Figs. 1–4, effective atomic number of compounds, in order, increased up to absorption edge energy but sharply increased after near the absorption edge. These discontinuities can be attributed to the absorption edge of present compounds Ba(OH)2 (BaKabs 37.41 keV), La2O3 (LaKabs 38.93 keV), Ag2O3 (AgKabs 25.51 keV), and CsHCO3 (CsKabs 35.96 keV). As shown in Table 2, the effective atomic numbers of each compound increased with increase in energy near the absorption edges of each element, generally. This can be attributed to the individual elements that predominantly absorb the incident photons in these regions. The trend of Zeff versus energy in Figs. 1–4 indicates that Zeff increases near the absorption edge. The scattering and absorption of X-rays or gamma radiations are related to the density and atomic number of an element, while it is related to density and effective atomic number in composite materials. The effective atomic number values of the samples varied with the density of electron in materials such that they increased with the increasing X-rays or gamma rays energies for the same material, generally. The experimental and theoretical JZeff are listed in Table 3. It is shown that a linear harmony with WinXCom has not been obtained for compounds. In this case, it is concluded that these deviations may not be directly explained by the molecular weight of compound. To the best of our knowledge, the results reported are the first of their kind and have not been reported earlier. So, we have not compared with the literature experimental values. Also, the study is first used to determine XAFS effect on the measurement of absorption jump factors. The experiment involves measurement of the effective atomic numbers and accuracy of mixture rule near the absorption edge.
35.6
35.8 36.0 36.2 36.4 Photon Energy (keV)
36.6
36.8
Fig. 4. Effective atomic numbers of CsHCO3 versus photon energy, around K absorption edges.
Table 1 The studied compounds with the bond structure, oxidation state and crystalline form. Sample
Bond structure
Oxidation state
Crystalline form
Ag2O3 CsHCO3 Ba(OH)2 La2O3
Ionic Ionic Ionic Ionic
+3 +1 +2 +3
Planar square Orthorhombic Octahedral Hexagonal
The values of measured effective atomic numbers of compounds are in agreement out side of near to the absorption edge, generally. However, this agreement breaks down in the near to the absorption edge. These discontinuities can be attributed to absorption edge of the present compounds. In other words, present discontinuities may be attributed to XAFS. The experimental effective atomic numbers of Ba(OH)2, La2O3, Ag2O3, and CsHCO3 of around K absorption edges versus photon energy incident on absorber are also graphically shown in Figs. 1–4. These effects may be seen as simple abrupt discontinuities in Figs. 1–4. In Figs. 1–4, the Zeff value for a compound may vary substantially for incident photon energies that lie within about 1.2 keV above the absorption edge. The Zeff value in the XAFS region is very sensitive to the incident photon energies. We may consider the observed deviation to be due to the effect of the XAFS and the effects of the Zeff value and hence conclude that the mixture rule is not applicable at these energies for these compounds. This state, also, may be attributed to chemical effects, and molecular and thermal environment of present compounds, because it is well known that chemical effects are appreciable only in the vicinity of absorption edges. In the present method,
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Table 2 . Experimental and theoretical effective atomic numbers (Zeff) of absorbers. Energy (keV)
Ag2O3
Energy (keV)
Theoretical Experimental 25.0 25.0 25.1 25.1 25.2 25.2 25.3 25.3 25.3 25.4 25.4 25.5 25.5 25.6 25.6 25.7 25.7 25.8 25.8 25.9 25.9
51.4 51.6 51.7 51.8 51.8 52.0 52.2 52.3 52.4 52.6 307.1 301.2 291.2 283.4 274.8 266.8 258.6 252.1 245.1 238.5 231.7
61.6 61.9 62.6 63.0 63.4 63.6 64.1 64.4 70.2 76.0 82.3 97.7 127.1 151.5 185.6 215.1 219.6 226.5 205.6 209.2 212.8
CsHCO3
Energy (keV)
Theoretical Experimental 35.4 35.5 35.5 35.6 35.6 35.7 35.7 35.8 35.8 35.9 35.9 36.0 36.0 36.1 36.1 36.2 36.2 36.2 36.3 36.3 36.4 36.4 36.5 36.5 36.6 36.6
26.4 26.2 26.1 25.9 25.7 25.5 25.3 25.1 25.0 24.8 24.6 131.4 130.6 129.3 128.8 127.6 126.7 125.9 125.1 124.2 123.4 122.6 121.8 121.0 120.1 119.3
33.9 33.1 32.0 30.5 29.4 28.9 28.0 28.2 29.1 30.8 33.3 45.0 61.4 71.6 85.3 95.8 102.2 108.8 116.4 114.6 118.0 118.2 122.7 125.1 124.3 127.0
Table 3 Experimental and theoretical (JZeff) of absorbers. Compounds
Experimental
Theoretical (XCOM)
Ba(OH)2 La2O3 Ag2O3 CsHCO3
0.62 0.72 0.72 0.75
0.81 0.80 0.82 0.81
secondary source (Sn, Pr, Nd, and Sm) producing Ka and Kb X-ray emission with an interaction of gamma rays of Am-241 reaching the secondary source is a convenient selection to obtain energies near the absorption edges of absorbers (Ag2O3, CsHCO3, Ba(OH)2 and La2O3) with ideal transmission geometry. Choosing a secondary source is very important to ideal transmission geometry for incident photon on absorber. The most important section of this method could be regulated values of energy near each other between Ka and Kb X-ray emission of secondary source and Kabs values of absorber with the help of X-ray criticalabsorption and emission energies chart. It is important the regulated values of energy near each other between Ka and Kb X-ray emission of secondary source and Kabs values of absorber. The present method is simple, direct and fast in determining Zeff and JZeff. It is shown that agreement has not been achieved with WinXcom based XCOM for compounds [24,25]. In this case, we concluded that these deviations may not be directly explained by the number of atoms increasing or decreasing in a compound. Still, Ba(OH)2 and CsHCO3 have a large of Z’s from 1 (H) to 57 (La) due to which the variation in its effective atomic number with energy is very clear and smaller in comparison with other compounds. In this case, it is concluded that these deviations may not be directly explained with the molecular weight of compound. Differences between the present experimental and theoretical values may be attributed to chemical composition variations of
Ba(OH)2
Energy (keV)
Theoretical Experimental 36.9 37.0 37.0 37.1 37.1 37.2 37.2 37.3 37.3 37.3 37.4 37.4 37.5 37.5 37.6 37.6 37.7 37.7 37.8 37.8 37.9 37.9 38.0 38.0 38.1 38.1
19.0 18.9 18.7 18.6 18.5 18.4 18.2 18.1 18.0 17.9 94.6 94.0 93.4 92.8 92.2 91.5 90.9 90.4 89.8 89.1 88.5 87.9 87.4 86.8 86.5 85.9
23.5 23.6 23.8 24.3 24.5 24.7 24.7 24.5 24.5 24.5 24.7 23.3 25.4 26.1 27.3 28.7 31.4 37.1 42.4 52.0 61.3 67.1 69.1 68.9 69.4 69.6
La2O3 Theoretical Experimental
38.4 38.4 38.5 38.5 38.6 38.6 38.7 38.7 38.8 38.8 38.9 38.9 39.0 39.0 39.1 39.1 39.2 39.2 39.3 39.3 39.4
15.3 15.2 15.1 15.0 14.9 14.8 14.7 14.6 14.5 14.4 75.6 75.1 74.6 74.3 73.9 73.4 72.9 72.4 72.0 71.5 71.0
15.3 15.9 20.9 25.0 32.1 38.5 43.9 51.9 59.1 63.9 69.2 72.5 75.3 77.0 76.8 73.2 75.8 73.4 76.3 70.3 75.7
the samples and nature of the mixture rule, which negligibly affects each other at atoms in compounds. Besides, determinate thickness values for compounds are different from each other. The differences in thickness values are expected to have an affect on experimental results. This affect may be attributed to the affect of chemical environment on pellets. Measured parameters based on total mass attenuation coefficients are calculated using WinXCOM program. This program is based on the mixture rule, which gives the attenuation coefficients of any substance as the sum of appropriately weighted contributions from the individual atoms. In this respect, the mixture rule may be responsible for experimental and theoretical differences. A few measurements have been made on the non-validity of the mixture rule [15,16,20,22,26–31]. The JZeff value in the XAFS region is very sensitive to the incident photon energies. We may conclude for these compounds that the mixture rule is not applicable near the absorption edge. This result may be attributed to chemical, molecular, and thermal environments of present compounds. We think that the principal explanation is the fact that the chemical effects are appreciable for only near the absorption edges. As can be seen from Table 1, it can be stated that the crystalline form and oxidation number of compound also affect the involvement of outer orbital in the emission of K X-rays when vacancy is created in a shell. It is known that different bonding energies and interatomic distances depend on different interactions between the central atom and ligands in the chemical compounds. These effects play a role in the K X-ray transitions. The outer energy levels are sensitive to the chemical environment and they are strongly influenced by ligands in terms of the crystal field theory. In the bond formation, valence state of an atom has important effects on the related parameters of the spectrum such as relative and transmitted intensities. Oxidation number is the most important chemical feature that contributes to wavelenght shift of an X-ray spectral line [32]. So it can be concluded that there is an indirect or direct chemical effect on JZeff.
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It is estimated that the maximum errors in the measured values are less than 3.3%. These errors are attributed to statistical errors in I and I0 ( r1%), sample thickness ( r1%), sample weighing ( r1%), geometric factor ( r1%), source intensity ( r1%), and systematic errors (r 2%). Further investigations of gamma ray absorption in materials are in progress, besides effective atomic numbers and related parameters for photon interaction. To reach a more definitive conclusion about the absorption jump factor and to confirm the accuracy of the present method, we plan to extend these measurements to various compounds and even alloys at different energies.
5. Concluding remarks In this study, the experimental and theoretical JZeff values of compounds are determined for near the absorption edge of selected compounds. The measured values are compared with the theoretical ones obtained using WinXcom being a Windows version of XCOM on the basis of the mixture rule. We want to determine whether the well-known equations available in the literature will be sufficient to measure the JZeff factor near the absorption edge and XAFS is valid. One of the most important part of this method is that the selected energy range of Ka and Kb X-rays published from secondary sources must be within the range of values Kabs of absorber (Ag2O, CsHCO3, Ba[(OH)2], and La2O3). The present study indicates that there is a considerable relation between JZeff and energy variation near the absorption edge. It is clearly seen from Figs. 1–4 that Zeff depends on the photon energy for o100 keV, especially, near the absorption edge. This study shows the existence of a term JZeff. The present results constitute the first measurement, so we could not compare the findings reported in the literature. The most crucial finding of this study is the determination of validity of Eq. (4) measuring a term as JZeff. Also, it is clearly seen that effects of XAFS cannot be neglected for uncertainties in the determination of Zeff and JZeff. As a result, Zeff and JZeff terms can be measured simply, directly, reliably and quickly with the help of ideal trasmission geometry and selection of an appropriate energy range.
363
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Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
A new term ‘‘Jzeff’’ derived from measured total attenuation coefficients of photons near the absorption edges of some compounds Recep Polat a, Orhan _Ic- elli b,n a b
Department of Physics Education, Education of Faculty, Erzincan University, 24030 Erzincan, Turkey Department of Physics, Faculty of Art and Sciences, Yıldız Technical University, Davutpas- a, 34220 Istanbul, Turkey
a r t i c l e in f o
a b s t r a c t
Article history: Received 23 March 2010 Received in revised form 7 April 2010 Accepted 16 April 2010 Available online 27 April 2010
In order to determine the effect of XAFS (X-ray absorption fine structure) on Jzeff, we have measured m/r values of compounds, which are determined by the mixture rule or the independent atomic model. Also, we want to obtain both XAFS effect and non-applicability or applicability of mixture rule. The most crucial finding in this study is that measurement of the effective atomic number is not appropriate near the absorption edge and the effective atomic number is affected by near the absorption edge. The results obtained have been compared with theoretical values. Also, the objective of this study is to show that there is a term ‘‘Jzeff’’ between effective atomic numbers and absorption jump factor. & 2010 Elsevier B.V. All rights reserved.
Keywords: Mass attenuation coefficients Molecular Atomic cross-sections Effective atomic number Jump ratio Jump factor
1. Introduction The scattering and absorption of X-ray and gamma radiation are related to the density and atomic numbers of an element. In composite materials it is related to the density and effective atomic number. A single number therefore cannot represent the atomic number uniquely across the entire energy range, as the partial interaction cross-sections have different element number dependence. This number in composite materials is called the effective atomic number and it varies depending on energy [1]. Effective atomic number is a highly beneficial parameter for many fields of scientific applications. This parameter is introduced to describe the properties of these composite materials in terms of equivalent elements. The atomic number, Z, is a ubiquitous parameter in atomic and nuclear physics where it occurs in almost any formula. For a complex medium, the effective atomic number, Zeff, is in some cases a convenient parameter for representing X-ray and gamma ray interactions, e.g. in designs of radiation shielding or in calculations of absorbed dose in radiotherapy. For each of the different processes, by which X-rays and gamma rays can interact with matter, the various atomic numbers in the material have to be weighted differently. Accordingly, Zeff is no true constant for a given material, but a parameter varying with photon energy depending on the interaction processes involved.
n
Corresponding author. Tel.: + 90 4 46 224 0089; fax: +90 446 2231901. E-mail addresses: [email protected], [email protected] (O. _Ic- elli).
0168-9002/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2010.04.061
Various researchers have determined the effective atomic number for some materials [1–16]. Also, effective atomic numbers of some compounds have been determined by means of a practical method by _Ic- elli [17]. But, as seen in the literature, a relation or study between absorption jump ratio and measured effective atomic number is absent around the K absorption edge of absorbers, especially. The aim of the present paper is to fill this gap in the literature and ‘‘JZeff’’ term to acquire to the literature. The study of the absorption of gamma radiations in materials has been an important subject in the field of radiation physics and is potentially useful in the development of semi-empirical formulations of high accuracy. Benefiting from the mass attenuation coefficient, a number of related parameters can be derived, such as the mass energy-absorption coefficients, the total interaction cross-section, the molar extinction coefficient, molecular, atomic, electronic cross-sections, the effective atomic number, and the effective electron density. In addition to these, we have measured absorption jump factors by using mass attenuation coefficient near the absorption edge, which have been represented as simple abrupt discontinuities in absorption coefficients at a photon energy just sufficient to expel electrons from a specific inner level in the atom. The fine structure consists of deviations from this simple step function and includes deviations both in the abrupt rise and in the region on the highenergy side of the rise. In general, fine structure is confined to within 200 eV of the edge [18]. XAFS, i.e. the oscillatory structure in the X-ray absorption coefficient, contains much quantitative information concerning the local structure near the absorbing atom [19].
R. Polat, O. _Ic- elli / Nuclear Instruments and Methods in Physics Research A 621 (2010) 358–363
We attempt here to demonstrate the effect of XAFS on jump ratio measured by using m/r values, which is determined with the mixture rule near the absorption edge of selected elements used as secondary source. The objective of this study is to provide the literature with the term ‘‘JZeff’’ and theoretical and experimental measurement and calculations. The second aim of this study is to provide data for present compounds near the absorption edge and to demonstrate the effect of XAFS (X-ray absorption fine structure). Also, chemical effects on ‘‘JZeff’’ are not very well known. However, it is pointed out and also well known that X-ray spectra depend on the chemical surrounding of the atom. The second aim of this study is to support the systematic investigation of the lately published study [20]. Summarily, the present study aims that there is a considerable linear combination between the effective atomic numbers and the absorption jump factor. This is the first time we have measured the JZeff values of selected compounds at o100 keV energies, so there are no data available in the literature for comparison with these results. It is important that determination of JZeff is a new study in the same experimental station and method [20]. La2O3 is used in X-ray image intensifying screens, phosphors, dielectric ceramics, conductive ceramics, and barium titanate capacit. Ba(OH)2 is used in analytical chemistry for the titration of weak acids, particularly organic acids. CsHCO3 is used as a base in organic reactions. Various forms of cesium, especially cesium nitrate, cesium carbonate and cesium bicarbonate, are used as glass components to achieve various objectives. The refractive index of optical glass – in the bulk or on the surface only – can be modified by the addition of cesium salts. Through surface ion exchange with cesium salt melts or solutions, the glass surface can be made resistant to corrosion or breakage. Behrens [21] has studied the electronic structure of silver oxides investigated by AgL XANES Spectroscopy. Due to the above-mentioned reasons, it is important to determine the JZeff and Zeff of the selected absorbers.
2. Basic formulas
359
The total atomic and electronic cross-sections are related to the effective (Zeff) through the following relation: Zeff ¼
st,a : st,el
2.1. Absorption jump factors Effective atomic number of any compound also varies with the wavelength or energy of the absorbed X-rays. If Zeff is plotted against wavelength for any chosen absorber it will show a general increase towards the longer, or ‘softer’ wavelength, as might be expected. However, the variation is not continuous, instead it is marked by a series of abrupt discontinuities called absorption edges. The ratio between the upper and lower edge is called the jump ratio. The difference between the upper and lower edge values directly gives the photo effect cross-section of that particular shell without the necessity of assuming any other partial cross-section. It is important since it is a measure of the photo effect due to the particular shell relative to other competing interaction processes. If the scattering component is thus neglected, the absorption curve may be seen to be made up of the additive effects of photoelectric absorption due to each of the absorption edges. We have seen that three phenomena – photoelectric absorption, scatter, and pair production – constitute total absorption. In the wavelenght region of X-ray spectrochemistry, pair production does not occur, and photoelectric absorption predominates overscatter. Consequently, m/r is largely determined by ttotal. At wavelengths shorter than the K edge,
ttotal ¼ tK þ ðtLI þ tLII þ tLIII Þ þ ðtMI þ tMII :::Þ þ::::
ð1Þ
Here ttotal being the photoelectric mass-absorption coefficients is itself the sum of a series of coefficients representing photon absorption due to electron expulsion from each of the atomic levels. As the K edge is passed towards lower energies or longer wavelength, the tK component disappears. The ratio rK of absorptions immediately on either side of the edge,
tK þ tL þ tM þ ::: tL þ tM þ :::
Equations and calculations related with the total mass attenuation coefficients, the total atomic cross-section, the total electronic cross-section, the effective atomic number and electron densities of mixtures are given by Polat and _Ic-elli [20]. Values of the mass attenuation coefficients of Polat et al. [22] have been used in order to determine JZeff. A quick reminder of the basic formulas: The total mass attenuation coefficients, mt (cm2/g), of elements and compounds are calculated from the following equation obtained from: m 1 I0 ln : ¼ r rx I
is called the absorption jump or absorption jump ratio, in this case for the K absorption edge [23]. In subsequent developments, absorption jump values, r, will be used to calculate absorption jump factors, J, i.e. the probability Jli that an incident photon will eject electrons from a K, L, M,... energy level. For example, the probability that a K level electron of elements i will be ejected rather than one from an L or M level is given by
Values of mass attenuation coefficients can be used to determine the total molecular cross-section, st,m, by the following relation: X 1 m st,m ¼ ðni Ai Þ: N r comp i
As seen in Figs. 1–4, in the graph of total effective atomic number versus energy, absorption jump factors give the ratio between the upper and lower edge.
The total atomic cross-section, st,a, can be easily determined from above as 1 i ni :
st,a ¼ st,m P
The total electronic cross-section, st,e, for the individual element is expressed by the following formula: 1 X fi Ai m st,e ¼ : N i Zi r i
rK ¼
JK ¼
ðrK 1Þ rK
JZeff ¼
ðZeff Þ þ ðZeff Þ ðZeff Þ þ
ð2Þ
ð3Þ
ð4Þ
Here, (Zeff) + and (Zeff) represent upper edge and lower edge, respectively. It is seen that all graphs have been fitted to first degree linear regression for both (Zeff) + and (Zeff) . The graphs show that the equation fit the first degree linear regression for both (Zeff) + and (Zeff) . The equation is y ¼ ax þ b:
ð5Þ
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360
Ba(OH)2
80
100
La2O3
70
Effective Atomic Number (Zeff)
Effective Atomic Number (Zeff)
80
60
40
60
50
40
30
20 20
Theoretical
37.0
37.2
37.4 37.6 37.8 Photon Energy (keV)
38.0
Theoretical
10
Experimental
38.2
Fig. 1. Effective atomic numbers of Ba(OH)2 versus photon energy, around K absorption edges.
Here, a and b are constant coefficients; x represents K absorption edge of absorber and y represents the effective atomic number. The parameters mentioned above have been experimentally measured and compared with theoretically calculated values.
3. Experimental procedure The mass attenuation coefficients for some selected compounds, Ag2O3, CsHCO3, Ba[(OH)2], and La2O3, were measured in the X-ray energy range from 25 up to 39 keV using a Si(Li) detector with a thin (25 mm) Be window and variable-energy X-ray source. The X-ray source was Am-241 whose g-rays were stopped in four secondary sources (Sn, Pr, Nd, and Sm), thus producing Ka and Kb X-ray emission. The energies of Ka and Kb X-rays published from secondary sources (Sn, Pr, Nd, and Sm) must be within the range of values Kabs of absorber (Ag2O, CsHCO3, Ba[(OH)2], and La2O3). They are used in different energy ranges and separated Ka1 and Ka2 , Kb1, and Kb2 peaks calculating the absoption coefficients. The calculations made by considering the conditions of intensities of the photons dropped to each channel before and after the absorption and, respectively, for every channel of energy and by taking the whole peaks. The schematic arrangement of the experimental setup used in the present compound is given in [22]. The total attenuation coefficients and K X-rays absorption jump factors were determined by using transmission geometry. In the present experiment a Si(Li) detector was used with an ND66B multichannel analyzer for detection of X-rays. FWHM value is 160 eV in 5.96 keV. This shows that FWHM depends on energy rather than being constant for all. This detector was coupled
Experimental
38.4
38.6
38.8 39.0 39.2 Photon Energy (keV)
39.4
39.6
Fig. 2. Effective atomic numbers of La2O3 versus photon energy, around K absorption edges.
to a computerized 1024-multichannel analyzer through a spectroscopy automatic fine-tuning research amplifier. The statistical errors in the intensities of X-ray in unit of time arising from radioisotope and characteristical X-rays arising from secondary source had been minimized by taking the counting time long enough. These statistical errors are always less than 1%. To obtain statistical accuracy, each sample was measured by collecting the spectra from selected elements for a period of 72 103 s. High purity (99.9%) samples of Ag2O3, CsHCO3, Ba[(OH)2], and La2O3 were measured using a radioactive annular source of Am-241 of strength 3.7 109 Bq (100 mCi) and g-photon energy 59.5 keV. The mass thicknesses of these mixtures have been determined as 8.49 10 2 g/cm2. Mass thickness values measurements with gravimetric method in g/cm2 units are always the same. In this experiment, the net counts without absorber (I0) and with absorber (I) were obtained at the same time and experimental conditions. Also, we have considered the change in the detector efficiency as there was no change in the absorbed peaks and unabsobed peaks. The studied compounds with the bond structure, oxidation state, and crystalline form are given in Table 1.
4. Result and discussion The experimental and theoretical Zeff are listed in Table 2. The experimental and theoretical effective atomic numbers of Ba(OH)2, La2O3, Ag2O3, and CsHCO3 around K absorption edges versus photon energy incident over the absorber are shown graphically in Figs. 1–4. It is clearly seen from the figures that effective atomic number depends on the photon energy. As shown
R. Polat, O. _Ic- elli / Nuclear Instruments and Methods in Physics Research A 621 (2010) 358–363
350
140 CsHCO3
Ag2O3
300
120
250
100
Effective Atomic Number (Zeff)
Effective Atomic Number (Zeff)
361
200
150
80
60
40
100
Theoretical
20
Theoretical
50
Experimental
Experimental
35.4
25.0
25.2
25.4 25.6 25.8 Photon Energy (keV)
26.0
Fig. 3. Effective atomic numbers of Ag2O3 versus photon energy, around K absorption edges.
in Figs. 1–4, effective atomic number of compounds, in order, increased up to absorption edge energy but sharply increased after near the absorption edge. These discontinuities can be attributed to the absorption edge of present compounds Ba(OH)2 (BaKabs 37.41 keV), La2O3 (LaKabs 38.93 keV), Ag2O3 (AgKabs 25.51 keV), and CsHCO3 (CsKabs 35.96 keV). As shown in Table 2, the effective atomic numbers of each compound increased with increase in energy near the absorption edges of each element, generally. This can be attributed to the individual elements that predominantly absorb the incident photons in these regions. The trend of Zeff versus energy in Figs. 1–4 indicates that Zeff increases near the absorption edge. The scattering and absorption of X-rays or gamma radiations are related to the density and atomic number of an element, while it is related to density and effective atomic number in composite materials. The effective atomic number values of the samples varied with the density of electron in materials such that they increased with the increasing X-rays or gamma rays energies for the same material, generally. The experimental and theoretical JZeff are listed in Table 3. It is shown that a linear harmony with WinXCom has not been obtained for compounds. In this case, it is concluded that these deviations may not be directly explained by the molecular weight of compound. To the best of our knowledge, the results reported are the first of their kind and have not been reported earlier. So, we have not compared with the literature experimental values. Also, the study is first used to determine XAFS effect on the measurement of absorption jump factors. The experiment involves measurement of the effective atomic numbers and accuracy of mixture rule near the absorption edge.
35.6
35.8 36.0 36.2 36.4 Photon Energy (keV)
36.6
36.8
Fig. 4. Effective atomic numbers of CsHCO3 versus photon energy, around K absorption edges.
Table 1 The studied compounds with the bond structure, oxidation state and crystalline form. Sample
Bond structure
Oxidation state
Crystalline form
Ag2O3 CsHCO3 Ba(OH)2 La2O3
Ionic Ionic Ionic Ionic
+3 +1 +2 +3
Planar square Orthorhombic Octahedral Hexagonal
The values of measured effective atomic numbers of compounds are in agreement out side of near to the absorption edge, generally. However, this agreement breaks down in the near to the absorption edge. These discontinuities can be attributed to absorption edge of the present compounds. In other words, present discontinuities may be attributed to XAFS. The experimental effective atomic numbers of Ba(OH)2, La2O3, Ag2O3, and CsHCO3 of around K absorption edges versus photon energy incident on absorber are also graphically shown in Figs. 1–4. These effects may be seen as simple abrupt discontinuities in Figs. 1–4. In Figs. 1–4, the Zeff value for a compound may vary substantially for incident photon energies that lie within about 1.2 keV above the absorption edge. The Zeff value in the XAFS region is very sensitive to the incident photon energies. We may consider the observed deviation to be due to the effect of the XAFS and the effects of the Zeff value and hence conclude that the mixture rule is not applicable at these energies for these compounds. This state, also, may be attributed to chemical effects, and molecular and thermal environment of present compounds, because it is well known that chemical effects are appreciable only in the vicinity of absorption edges. In the present method,
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Table 2 . Experimental and theoretical effective atomic numbers (Zeff) of absorbers. Energy (keV)
Ag2O3
Energy (keV)
Theoretical Experimental 25.0 25.0 25.1 25.1 25.2 25.2 25.3 25.3 25.3 25.4 25.4 25.5 25.5 25.6 25.6 25.7 25.7 25.8 25.8 25.9 25.9
51.4 51.6 51.7 51.8 51.8 52.0 52.2 52.3 52.4 52.6 307.1 301.2 291.2 283.4 274.8 266.8 258.6 252.1 245.1 238.5 231.7
61.6 61.9 62.6 63.0 63.4 63.6 64.1 64.4 70.2 76.0 82.3 97.7 127.1 151.5 185.6 215.1 219.6 226.5 205.6 209.2 212.8
CsHCO3
Energy (keV)
Theoretical Experimental 35.4 35.5 35.5 35.6 35.6 35.7 35.7 35.8 35.8 35.9 35.9 36.0 36.0 36.1 36.1 36.2 36.2 36.2 36.3 36.3 36.4 36.4 36.5 36.5 36.6 36.6
26.4 26.2 26.1 25.9 25.7 25.5 25.3 25.1 25.0 24.8 24.6 131.4 130.6 129.3 128.8 127.6 126.7 125.9 125.1 124.2 123.4 122.6 121.8 121.0 120.1 119.3
33.9 33.1 32.0 30.5 29.4 28.9 28.0 28.2 29.1 30.8 33.3 45.0 61.4 71.6 85.3 95.8 102.2 108.8 116.4 114.6 118.0 118.2 122.7 125.1 124.3 127.0
Table 3 Experimental and theoretical (JZeff) of absorbers. Compounds
Experimental
Theoretical (XCOM)
Ba(OH)2 La2O3 Ag2O3 CsHCO3
0.62 0.72 0.72 0.75
0.81 0.80 0.82 0.81
secondary source (Sn, Pr, Nd, and Sm) producing Ka and Kb X-ray emission with an interaction of gamma rays of Am-241 reaching the secondary source is a convenient selection to obtain energies near the absorption edges of absorbers (Ag2O3, CsHCO3, Ba(OH)2 and La2O3) with ideal transmission geometry. Choosing a secondary source is very important to ideal transmission geometry for incident photon on absorber. The most important section of this method could be regulated values of energy near each other between Ka and Kb X-ray emission of secondary source and Kabs values of absorber with the help of X-ray criticalabsorption and emission energies chart. It is important the regulated values of energy near each other between Ka and Kb X-ray emission of secondary source and Kabs values of absorber. The present method is simple, direct and fast in determining Zeff and JZeff. It is shown that agreement has not been achieved with WinXcom based XCOM for compounds [24,25]. In this case, we concluded that these deviations may not be directly explained by the number of atoms increasing or decreasing in a compound. Still, Ba(OH)2 and CsHCO3 have a large of Z’s from 1 (H) to 57 (La) due to which the variation in its effective atomic number with energy is very clear and smaller in comparison with other compounds. In this case, it is concluded that these deviations may not be directly explained with the molecular weight of compound. Differences between the present experimental and theoretical values may be attributed to chemical composition variations of
Ba(OH)2
Energy (keV)
Theoretical Experimental 36.9 37.0 37.0 37.1 37.1 37.2 37.2 37.3 37.3 37.3 37.4 37.4 37.5 37.5 37.6 37.6 37.7 37.7 37.8 37.8 37.9 37.9 38.0 38.0 38.1 38.1
19.0 18.9 18.7 18.6 18.5 18.4 18.2 18.1 18.0 17.9 94.6 94.0 93.4 92.8 92.2 91.5 90.9 90.4 89.8 89.1 88.5 87.9 87.4 86.8 86.5 85.9
23.5 23.6 23.8 24.3 24.5 24.7 24.7 24.5 24.5 24.5 24.7 23.3 25.4 26.1 27.3 28.7 31.4 37.1 42.4 52.0 61.3 67.1 69.1 68.9 69.4 69.6
La2O3 Theoretical Experimental
38.4 38.4 38.5 38.5 38.6 38.6 38.7 38.7 38.8 38.8 38.9 38.9 39.0 39.0 39.1 39.1 39.2 39.2 39.3 39.3 39.4
15.3 15.2 15.1 15.0 14.9 14.8 14.7 14.6 14.5 14.4 75.6 75.1 74.6 74.3 73.9 73.4 72.9 72.4 72.0 71.5 71.0
15.3 15.9 20.9 25.0 32.1 38.5 43.9 51.9 59.1 63.9 69.2 72.5 75.3 77.0 76.8 73.2 75.8 73.4 76.3 70.3 75.7
the samples and nature of the mixture rule, which negligibly affects each other at atoms in compounds. Besides, determinate thickness values for compounds are different from each other. The differences in thickness values are expected to have an affect on experimental results. This affect may be attributed to the affect of chemical environment on pellets. Measured parameters based on total mass attenuation coefficients are calculated using WinXCOM program. This program is based on the mixture rule, which gives the attenuation coefficients of any substance as the sum of appropriately weighted contributions from the individual atoms. In this respect, the mixture rule may be responsible for experimental and theoretical differences. A few measurements have been made on the non-validity of the mixture rule [15,16,20,22,26–31]. The JZeff value in the XAFS region is very sensitive to the incident photon energies. We may conclude for these compounds that the mixture rule is not applicable near the absorption edge. This result may be attributed to chemical, molecular, and thermal environments of present compounds. We think that the principal explanation is the fact that the chemical effects are appreciable for only near the absorption edges. As can be seen from Table 1, it can be stated that the crystalline form and oxidation number of compound also affect the involvement of outer orbital in the emission of K X-rays when vacancy is created in a shell. It is known that different bonding energies and interatomic distances depend on different interactions between the central atom and ligands in the chemical compounds. These effects play a role in the K X-ray transitions. The outer energy levels are sensitive to the chemical environment and they are strongly influenced by ligands in terms of the crystal field theory. In the bond formation, valence state of an atom has important effects on the related parameters of the spectrum such as relative and transmitted intensities. Oxidation number is the most important chemical feature that contributes to wavelenght shift of an X-ray spectral line [32]. So it can be concluded that there is an indirect or direct chemical effect on JZeff.
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It is estimated that the maximum errors in the measured values are less than 3.3%. These errors are attributed to statistical errors in I and I0 ( r1%), sample thickness ( r1%), sample weighing ( r1%), geometric factor ( r1%), source intensity ( r1%), and systematic errors (r 2%). Further investigations of gamma ray absorption in materials are in progress, besides effective atomic numbers and related parameters for photon interaction. To reach a more definitive conclusion about the absorption jump factor and to confirm the accuracy of the present method, we plan to extend these measurements to various compounds and even alloys at different energies.
5. Concluding remarks In this study, the experimental and theoretical JZeff values of compounds are determined for near the absorption edge of selected compounds. The measured values are compared with the theoretical ones obtained using WinXcom being a Windows version of XCOM on the basis of the mixture rule. We want to determine whether the well-known equations available in the literature will be sufficient to measure the JZeff factor near the absorption edge and XAFS is valid. One of the most important part of this method is that the selected energy range of Ka and Kb X-rays published from secondary sources must be within the range of values Kabs of absorber (Ag2O, CsHCO3, Ba[(OH)2], and La2O3). The present study indicates that there is a considerable relation between JZeff and energy variation near the absorption edge. It is clearly seen from Figs. 1–4 that Zeff depends on the photon energy for o100 keV, especially, near the absorption edge. This study shows the existence of a term JZeff. The present results constitute the first measurement, so we could not compare the findings reported in the literature. The most crucial finding of this study is the determination of validity of Eq. (4) measuring a term as JZeff. Also, it is clearly seen that effects of XAFS cannot be neglected for uncertainties in the determination of Zeff and JZeff. As a result, Zeff and JZeff terms can be measured simply, directly, reliably and quickly with the help of ideal trasmission geometry and selection of an appropriate energy range.
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