- Email: [email protected]
Determination of mass attenuation coefficients, effective atomic numbers, effective electron numbers and kermas for Earth and Martian soils
Nuclear Instruments and Methods in Physics Research B 288 (2012) 42–47
Contents lists available at SciVerse ScienceDirect
Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Determination of mass attenuation coefficients, effective atomic numbers, effective electron numbers and kermas for Earth and Martian soils A. Un a,⇑, Y. Sahin b a b
_ Ag˘rı Ibrahim Çeçen University, Faculty of Arts and Sciences, Department of Physics, 04100 Ag˘rı, Turkey Atatürk University, Faculty of Sciences, Department of Physics, 25240 Erzurum, Turkey
a r t i c l e
i n f o
Article history: Received 2 May 2012 Received in revised form 21 July 2012 Available online 7 August 2012 Keywords: Mass attenuation coefficient Effective atomic and electron number Kerma Earth soil and Martian soil
a b s t r a c t Total mass attenuation coefficients, effective atomic numbers, effective electron numbers and kerma values for Earth and Martian soils are calculated in the energy range from 1 keV to 100 GeV. The values of mass attenuation and absorption coefficients used in calculations are taken from the WinXCOM program and correct data base. Contributions of different scatterings on the total mass attenuation coefficients of the soils are presented. In addition, the obtained results for Martian soils are compared with the results for Earth soils. The similarities of Earth and Martian soils are also investigated. Crown Copyright Ó 2012 Published by Elsevier B.V. All rights reserved.
1. Introduction Soil is an important natural and cheap material for radiation shielding. Although many types of it, soils have chemical composition characterized by the presence of SiO2, Al2O3, Fe2O3, CaO, MgO, B2O3 and others in variable concentrations [1,2]. Due to the widespread use of soil, determination of soil properties and physical parameters is important. The gamma-rays are often used for the soil researches [3,4]. The most relevant parameter determining the photon interaction in the soil and the other materials is the mass attenuation coefficient. The mass attenuation coefficient lm is a measure of probability of interactions of incident photons with the thickness (g/cm2) of target material [5]. The mass attenuation coefficients of different soils are determined by some works [1– 3,6]. There are a great number of experimental and theoretical investigations of lm values [7–11]. For composite materials such as soil, it is related to effective atomic number, Zeff. Since partial interaction cross-section depends on the composite material of elements, a single atomic number being a characteristic of element will not describe the atomic number of composite material in the all energy range. This new number for composite materials is called to be Zeff that varies with energy and theoretical expressions to evaluate Zeff values for the individual partial photon interaction processes have been suggested by Hine [12]. Some works to determine the Zeff values of composite materials various alloys [13,14], GaAs and InP crystals [15], some
⇑ Corresponding author. Tel.: +90 472 215 11 88; fax: +90 472 215 11 82. E-mail address: [email protected] (A. Un).
solutions and amino acids [16–18] and boron ores [19] have been reported in the literature. The other important physical parameter is kerma on radiation interaction with matter. Kerma (Kinetic energy released per unit mass) is defined as the initial kinetic energy of all secondary charged particles released per unit mass at a point of interest by uncharged radiation [20]. Kerma, effective atomic number and effective electron density Neff for some boron ores and some fatty acids have been reported by Un and Sahin [19] and Manohara et al. [21], respectively. The knowledge of the interaction of radiation with matter in a wide energy range is important. Therefore, in this work, the calculation of the total mass attenuation coefficient, Zeff, Neff and KERMA is aimed for energies in the range from 1 keV to 100 GeV. In the present work, the total mass attenuation coefficient, Zeff, Neff and KERMA of 5 different Martian and 14 different Earth soils have been reported. The calculated values of Martian and Earth soils have been compared. The chemical compositions of Earth soils are taken from the works of Baytas and Akbal [3] (labeled S1-Ankara, S3-Konya, S4-Fatsa, S5-Bergama, S6-Batman), Demir et al. [2] (labeled S2-Erzurum), Wielopolski et al. [22] (labeled S7, S9-the median value of world soils), Miller and Turk [23] (labeled S8) and Medhat [24] (labeled S10–14). In the soils, bulk density, moisture content, porosity and field capacity are very important parameters. For the soils S1–S6 bulk density, moisture content, porosity and field capacity have been determined in previous works [2,3,6]. The bulk density and porosity of the soils S7, a carbon rich loam soil S8 and S9 have been determined [22]. Moisture, bulk density, porosity and field capacity of the soil samples from five different agricultural zones in Egypt with different
0168-583X/$ - see front matter Crown Copyright Ó 2012 Published by Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.nimb.2012.07.031
43
A. Un, Y. Sahin / Nuclear Instruments and Methods in Physics Research B 288 (2012) 42–47 Table 2 Elemental composition of Earth soils S8–S14.
Table 1 Elemental composition of Earth soils S1–S7.
a b c d e f g
Element
S1a
S2b
S3c
S4d
S5e
S6f
S7g
Element
S8a
S9b
S10c
S11d
S12e
S13f
S14g
H Li B C N O F Na Mg Al Si P S Cl K Ca Sc Ti V Cr Mn Fe Co Ni Cu Rb Y Zr Ba Nd Sm Hf Pb Bi Th
– – – – – 41.920 6.560 0.850 0.630 3.720 15.990 10.250 0.270 – 1.400 8.720 – – – – – 8.550 – – – – – – – – – – – – –
– – 0.714 5.960 – 54.716 – 1.559 1.736 7.310 20.250 0.109 0.026 0.009 1.438 2.579 – 0.881 – 0.014 0.098 2.351 – 0.010 0.005 0.007 – 0.018 0.031 – – – – – –
– – – – – 33.118 8.854 0.307 1.872 4.000 17.118 14.446 0.124 – 1.344 16.096 – – – – – 0.941 – – – – – – – – – – – – –
– – – – – 44.400 2.980 1.980 0.570 10.080 24.650 4.860 0.070 – 3.710 2.680 – – – – – 2.310 – – – – – – – – – – – – –
– – – – – 44.410 2.880 1.660 1.134 8.520 26.610 4.700 0.110 – 2.170 3.580 – – – – – 1.660 – – – – – – – – – – – – –
– – – – – 44.850 3.660 1.100 2.240 6.960 27.140 5.980 0.090 – 1.800 3.900 – – – – – 2.010 – – – – – – – – – – – – –
0.2100 0.0013 0.0013 0.1950 0.0032 53.0032 0.0046 0.2450 0.0881 1.0960 43.7600 0.0128 – 0.0108 0.2250 0.1180 0.0005 0.1228 0.0035 0.0029 0.0151 0.7240 0.0007 0.0009 0.0012 0.0058 0.0035 0.0545 0.0540 0.0063 0.0012 0.0029 0.0050 0.0051 0.0037
H Li B C N O F Na Mg Al Si P Cl K Ca Sc Ti V Cr Mn Fe Co Ni Cu Rb Y Zr Ba Hf Pb Th
2.81 – – 14.43 0.001 49.64 – 0.82 – 8.93 21.32 – – 0.56 0.54 – – – – – 0.96 – – – – – – – – – –
– 0.0030 0.0010 2.0000 0.1000 48.8700 0.0200 0.6300 0.5000 7.1000 33.3000 0.0650 0.0100 1.4000 1.3700 0.0007 0.5000 0.0100 0.1000 0.0850 3.8000 0.0008 0.0040 0.0020 0.0100 0.0050 0.0300 0.0500 0.0006 0.0010 0.0005
– – – – – 49.803 – 1.558 1.272 5.988 31.336 – – 3.875 2.370 – 0.600 – – – 2.839 – – – – – – – – – –
– – – – – 50.039 – 2.389 1.134 2.571 37.033 – – 3.651 1.185 – 0.582 – – – 1.253 – – – – – – – – – –
– – – – – 49.784 – 1.729 1.596 9.939 24.457 – – 2.855 3.113 – 0.540 – – – 5.023 – – – – – – – – – –
– – – – – 51.952 – 1.743 0.858 8.920 28.104 – – 2.763 2.663 – 0.546 – – – 4.795 – – – – – – – – – –
– – – – – 48.897 – 2.515 1.656 10.408 21.094 – – 2.705 2.435 – 0.600 – – – 6.363 – – – – – – – – – –
Composition Composition Composition Composition Composition Composition Composition
of of of of of of of
a b c d e
Ankara soil taken from Baytas and Akbal [3]. Erzurum soil taken from Demir et al. [2]. Konya soil taken from Baytas and Akbal [3]. Fatsa soil taken from Baytas and Akbal [3]. Bergama soil taken from Baytas and Akbal [3]. Batman soil taken from Baytas and Akbal [3]. Earth soil taken from Wielopolski et al. [22].
f g
a b
2. Theory
c d
The mass attenuation coefficients of the different materials can be determined by the transmission. This process can be described by the following equation
I ¼ I0 e
of of of of of of of
Earth soil taken from Miller and Turk [23]. Earth soil taken from Wielopolski et al. [22]. Egypt soil taken from Medhat [24]. Egypt soil taken from Medhat [24]. Egypt soil taken from Medhat [24]. Egypt soil taken from Medhat [24]. Egypt soil taken from Medhat [24].
Table 3 Elemental composition of Martian soils MS1–MS5.
fractions of sand, coarse silt, fine silt, coarse clay and fine clay have been also determined by Medhat [24]. The chemical compositions of Earth soils considered were carried out using wavelength dispersive X-ray fluorescence (WDXRF) spectrometer, set of chemical reactions and conventional methods [2,3,24]. The chemical compositions of five Martian soils are taken from the work of Economou [25] (labeled MS1-Meridiani, MS2-Gusev, MS3-MPF, MS4-Viking and MS5-Guadalupe). The elemental contents of Martian soils were determined by the Alpha Scattering Instrument (ASI). A beam of alpha particles from 242Cm of homogenous energy of 6.1 MeV was used and the scattered alpha particles were detected by solid-state Si detector.
lmt
Composition Composition Composition Composition Composition Composition Composition
ð1Þ
where I0 denotes the number of photons incoming in unit time with energy E, incoming intensity; I the number of outgoing in unit time photons with energy E, outgoing intensity after attenuation; lm = l/ q (cm2/g) is the mass attenuation coefficient and t (g/cm2) is sample mass thickness (the mass per unit area). The total lm values for
e
Element
MS1a
MS2b
MS3c
MS4d
MS5e
O Na Mg Al Si P S Cl K Ca Ti Cr Mn Fe
51.084 1.558 5.136 5.327 20.702 0.389 1.884 0.510 0.174 4.855 0.300 0.335 0.271 6.993
50.411 2.656 5.904 5.829 20.898 0.445 2.467 0.620 0.141 4.040 0.120 0.192 0.217 5.558
51.778 2.003 4.020 5.237 20.174 0.262 2.080 0.800 0.580 3.927 0.480 0.205 0.232 8.120
51.060 – 3.840 4.232 21.949 – 3.160 0.500 0.124 4.570 0.420 – – 6.90
52.791 0.816 5.100 3.280 16.392 0.437 9.080 0.440 0.382 3.500 0.360 0.137 – 6.160
Composition Composition Composition Composition Composition
of of of of of
Martian Martian Martian Martian Martian
soil, Meridiani, taken from Economou [25]. soil, Gusev, taken from Economou [25]. soil, MPF, taken from Economou [25]. soil taken from Economou [25]. soil, Guadalupe, taken from Economou [25].
materials composed of multi elements are the sum of the (lm)i values of each constituent element by the following mixture rule [8];
l¼
X
wi ðlm Þi
ð2Þ
where wi is the weight fraction and (lm) is mass attenuation coefficient of the ith element. The theoretical lm values for present samples were calculated by WinX-Com program [26].
44
A. Un, Y. Sahin / Nuclear Instruments and Methods in Physics Research B 288 (2012) 42–47
Fig. 1. Cross sections of different scatterings and sum of them versus energy for the world soils S9.
Fig. 3. Variation of effective atomic numbers versus photon energy for the Earth and Martian soils.
Fig. 2. Variation of total mass attenuation coefficients versus photon energy for the Earth and Martian soils.
More detailed information about the Zeff and Neff calculated for some soils used in this work have been given in some previous studies [17,18].
Absorbed dose is defined as the limiting value of the mean of the energy imparted by ionizing radiation per unit mass. The quantity Kerma can be easily computed, but its value can be over-or underestimated depending on the final-state energy taken for the induced charged particles. A quantity related to the kerma, termed the collision kerma, has long been in use as an approximation to absorbed dose when radiative losses are not negligible. The collision kerma excludes the radiative losses by the liberated charged particles. Kerma and absorbed dose are nearly equal in magnitude when radiation equilibrium is established [27,28]. The kerma is feasible to photons (x- and c-rays etc.) and neutrons and has unit J kg1 = Gy, as the absorbed dose. Therefore, kerma is the resultant of the energy fluence and mass energyabsorption coefficient, ðlen =qÞ. More info for Kerma has been given in previous work [21]. Kerma relative to water of the soil can be expressed as
ðlen =qÞs ðlen =qÞw
ð3Þ
In order to calculate kerma relative to water, the values of mass energy-absorption coefficients for liquid water have been taken from the compilation of Hubbel and Seltzer [8].
A. Un, Y. Sahin / Nuclear Instruments and Methods in Physics Research B 288 (2012) 42–47
45
Fig. 4. Comparison of effective atomic numbers (a) and effective atomic numbers (b) for Martian soils with effective atomic and electron number of world soils S9.
3. Results and discussion The chemical content of the Earth and Martian soils are tabulated in Tables 1–3. It can be seen from Tables 1–3 that the chemical contents of the Martian soils resembles to the chemical contents of the Earth soils. The contributions of the different effects and the total mass attenuation coefficients for the median value of world soils S9 are shown in Fig. 1. In addition, the total mass attenuation coefficients via energy of the Earth and Martian soils are presented in Fig. 2. Although the soils have a wide variety of elements, the main influence on the results in this work is the amount of iron in the soils. The higher concentration of iron in the chemical composition of the Martian soil MS3 in comparison to that of the other Martian soils and the higher concentration of iron in the chemical composition of Earth soil S1 in comparison to that of other Earth soils as seen in the Tables 1–3 explain the greater value of lm for the Martian soil MS3 in comparison to values of lm for other Martian soils and the greater value of lm for Earth soil S1 in comparison to values of lm for other Earth soils as shown in Fig. 2.
The experimental lm values of soil S2 for energies 60, 356 and 662 keV are 0.298, 0.102 and 0.081 cm2/g, respectively [2]. The lm values of Martian soils MS1, MS2, MS3, MS4, MS5 in this work are 0.457, 0.421, 0.473, 0.451, 0.435 for 60 keV, 0.1079, 0.1077, 0.1078, 0.1080, 0.1080 for 300 keV and 0.0798, 0.0799, 0.0797, 0.0800, 0.0800 for 600 keV, respectively. Because of the Z dependency of Compton scattering (for energies 300 and 600 keV), the lm values of Martian soils are very close to the experimental values lm of soil S2. But, for the energy 60 keV, because of the Z4 dependency of photoelectric interaction, high difference in the amount of the iron (Z = 26) between the Martian soils and S2 soil explains why the greater values of lm values of Martian soils are greater than the lm values of the soil S2. The Z eff values of soils were determined by using the values of lm. The variations of Z eff values versus photon energy for Earth and Martian soils are shown in Fig. 3. In Fig. 3, three energy regions E < 0.01 MeV, 0.05 MeV < E < 10 MeV and E > 100 MeV can be clearly seen. In the low energy, main interaction is photoelectric interaction which is proportional to Z4. Because of the Z4 dependency of photoelectric interaction, for the soil samples, the
46
A. Un, Y. Sahin / Nuclear Instruments and Methods in Physics Research B 288 (2012) 42–47
Fig. 5. Variation of effective electron numbers versus photon energy for the Earth and Martian soils.
maximum values of Z eff have been found in low-energy range. Because of the Z4 dependence of photoelectric interaction and the photoelectric interaction near the K- edge of the elements with the high Z numbers, Z eff values of S1 and MS3 is higher than the other soil samples as seen in Fig. 3. The iron concentration values in the Martian soils are very close to each other and the iron concentration values in the Earth soils are different from each other as seen in Tables 1–3. Because of that, the Z eff values of Martian soils are more close to each other and the Z eff values of Earth soils are different from each other as shown in Fig. 3. At the intermediate energies, Compton scattering is main photon interaction. In this energy range, Z eff values are almost constant for a given samples. Because of the Compton scattering proportional to Z, minimum value of Z eff is found for the soils in this energy range. The value of Z eff is also constant in the high energy range in which the pair production is the main interaction. Because of proportionality of the pair production with Z2, the value of Z eff for high energy region smaller than the value obtained for photoelectric interaction and higher than the value obtained for Compton scattering.
Fig. 6. Variation of kerma values versus photon energy for the Earth and Martian soils.
In Fig. 4, the Martian soils are compared with Earth soil S9. It is clearly seen Fig. 4 that the Z eff values of Martian soils higher than the Z eff value the soil S9. However, because the elemental content of soil S9 more similar to the elemental content of soil MS2 in comparison to the other Martian soils, the Z eff value of soil MS2 is closer to the Z eff value of soil S9 than the other Martian soils. The variation of Nel values versus photon energy for Earth and Martian soils is shown graphically in Fig. 5, respectively. In Fig. 5, three energy regions are clearly seen. The energy dependence of the effective electron number, Nel, is similar to the effective atomic numbers, Z eff . The effective electron numbers for the Martian soils are compared with the Nel value of the median value of world soils S9 in Fig 4. As can be seen in Fig 4, the Nel value of soil MS2 is closer to the Nel value of soil S9 than the other Martian soils. Explanation for values of Z eff and Nel of Earth and Martian soils as shown in Fig. 2 is almost the same mentioned above in the case of the values of lm for Earth and Martian soils.
A. Un, Y. Sahin / Nuclear Instruments and Methods in Physics Research B 288 (2012) 42–47
The energy dependence of kerma relative to water is presented in Fig. 6 for Earth and Martian soils, respectively. Two energy regions can be clearly seen in Fig. 6. In the low energy region, main interaction is photoelectric interaction, and, in the other energy region, the Compton scattering is the main interaction. Because of the photoelectric interaction near the K-edge of the elements with the high Z number, kerma relative to water values in the low energy region higher than the other energy region as seen in Fig. 6. Because of elemental composition and the higher concentration of iron in the soil S1 in comparison to the other soils, the kerma value of soil S1 higher than the other soils.
4. Conclusions The effective atomic number, Zeff, the effective electron number, Nel and kerma depends on the elemental compositions of the soils. The iron concentration of the soil is more effective than the other elemental concentrations on the results analyzed. Although the Zeff, and Nel values of Martian soils higher than the Zeff, and Nel values of the median of the world soils, the Martian soils very similar to the Earth soils. To our best knowledge, the investigation of the Zeff, Nel and kerma relative to water for Earth and Martian soils in the studied energies are not available in the literature. It is expected that the present work can lead to other studies such as radiation shielding and understanding of the extraterrestrial materials.
References [1] R. Cesareo, J.T. de Assis, S. Crestana, Attenuation coefficients and tomographic measurements for soil in the energy range 10–300 keV, Appl. Radiat. Isot. 45 (1994) 613. [2] D. Demir, A. Ün, M. Özgül, Y. Sßahin, Determination of photon attenuation coefficient, porosity and field capacity of soil by gamma-ray transmission for 60, 356 and 662 keV gamma rays, Appl. Radiat. Isot. 66 (2008) 1834. [3] A.F. Baytas, S. Akbal, Determination of soil parameters by gamma-ray transmission, Radiat. Meas. 35 (2002) 17. [4] L.F. Pires, O.O.S. Bacchi, K. Reichardt, Soil water retention curve determined by gamma-ray beam attenuation, Soil & Till. Res. 82 (2005) 89. [5] J.H. Hubbell, Review of photon interaction cross section data in the medical and biological context, Phys. Med. Biol. 44 (1999) R1. [6] A. Un, D. Demir, Y. Sßahin, Determination of density and volumetric water content of soil at multiple photon energies, Radiat. Phys. Chem. 80 (2011) 863. [7] J.H. Hubbell, Photon mass attenuation and energy-absorption coefficients, Int. J. Appl. Radiat. Isot. 33 (1982) 1269.
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[8] J.H. Hubbell, S.M. Seltzer, Tables of X-ray mass attenuation coefficients and mass energy-absorption coefficients from 1 keV 20 MeV for elements Z = 1 to 92 and 48 additional substances of dosimetric interest, NISTIR (1995) 5632. [9] M.J. Berger, J.H. Hubbell, XCOM: Photon cross section on a personal computer, NBSIR (1987) 87. [10] D.C. Wang, L.A. Ping, H. Yang, Measurements of the mass attenuation coefficients for SiH4 and Si, Nucl. Instrum. Methods, B 95 (1995) 161. [11] K. Singh, H. Singh, G. Sharma, L. Gerward, A. Khanna, R. Kumar, R. Nathuram, H.S. Sahota, Gamma ray shielding properties of CaO–SrO–B2O3 glasses, Radiat. Phys. Chem. 72 (2004) 225. [12] G.J. Hine, The effective atomic numbers of materials for various gamma ray interactions, Phys. Rev. 85 (1952) 725. [13] M. Kurudirek, M. Buyukyildiz, Y. Ozdemir, Effective atomic number study of various alloys for total photon interaction in the energy region of 1 keV– 100 GeV, Nucl. Instrum. Methods, A 613 (2010) 251. [14] I. Han, L. Demir, Mass attenuation coefficients, effective atomic and electron numbers of Ti and Ni alloys, Radiat. Meas. 44 (2009) 289. [15] L. Demir, I. Han, Mass attenuation coefficients, effective atomic numbers and electron densities of undoped and differently doped GaAs and InP crystals, Ann. Nucl. Energy 36 (2009) 869. [16] M. Kurudirek, Estimation of effective atomic numbers of some solutions for photon energy absorption in the energy region 0.2–1.5 MeV: an alternative method, Nucl. Instrum. Methods, A 659 (2011) 302. [17] S.R. Manohara, S.M. Hanagodimath, Studies on effective atomic numbers and electron densities of essential amino acids in the energy range 1 keV–100 GeV, Nucl. Instrum. Methods, B 258 (2007) 321. [18] S.R. Manohara, S.M. Hanagodimath, Effective atomic numbers for photon energy absorption of essential amino acids in the energy range 1 keV–20 MeV, Nucl. Instrum. Methods, B 264 (2007) 9. [19] A. Un, Y. Sahin, Determination of mass attenuation coefficients, effective atomic and electron numbers, mean free paths and kermas for PbO, barite and some boron ores, Nucl. Instrum. Methods, B 269 (2011) 1506. [20] ICRU, International Commission on Radiation Units and Measurements, Radiation Quantities and Units, ICRU Report 33, International Commission on Radiation Units and Measurements, Bethesda MD, 1980. [21] S.R. Manohara, S.M. Hanagodimath, L. Gerward, Studies on effective atomic number, electron density and kerma for some fatty acids and carbohydrates, Phys. Med. Biol. 53 (2008) N377–N386. [22] L. Wielopolski, Z. Song, I. Orion, A.L. Hanson, G. Hendrey, Basic considerations for Monte Carlo calculations in soil, Appl. Radiat. Isot. 62 (2005) 97. [23] C.E. Miller, L.M. Turk, Fundamentals of Soil Science, Chapman&Hall Limited, London, 1951. [24] M.E. Medhat, Application of gamma-ray transmission method for study the properties of cultivated soil, Ann. Nucl. Energy 40 (2012) 53. [25] N. Singh, K.J. Singh, K. Singh, H. Singh, Comparative study of lead borate and bismuth lead borate glass systems as gamma-radiation shielding materials, Nucl. Instrum. Methods, B 225 (2005) 305. [26] L. Gerward, N. Guilbert, K.B. Jensen, H. Levring, X-ray absorption in matter. Reengineering XCOM, Radiat. Phys. Chem. 60 (2001) 23. [27] ICRU, International Commission on Radiation Units and Measurements, Fundamental quantities and units for ionizing radiation (revised), ICRU Report 85a, J. ICRU 11, Oxford University Press, Oxford, 2011. [28] M.S. Singh, Kerma Factors for Neutron and Photons with Energies below 20 MeV, University of California, Carifornia, 1979.
Contents lists available at SciVerse ScienceDirect
Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Determination of mass attenuation coefficients, effective atomic numbers, effective electron numbers and kermas for Earth and Martian soils A. Un a,⇑, Y. Sahin b a b
_ Ag˘rı Ibrahim Çeçen University, Faculty of Arts and Sciences, Department of Physics, 04100 Ag˘rı, Turkey Atatürk University, Faculty of Sciences, Department of Physics, 25240 Erzurum, Turkey
a r t i c l e
i n f o
Article history: Received 2 May 2012 Received in revised form 21 July 2012 Available online 7 August 2012 Keywords: Mass attenuation coefficient Effective atomic and electron number Kerma Earth soil and Martian soil
a b s t r a c t Total mass attenuation coefficients, effective atomic numbers, effective electron numbers and kerma values for Earth and Martian soils are calculated in the energy range from 1 keV to 100 GeV. The values of mass attenuation and absorption coefficients used in calculations are taken from the WinXCOM program and correct data base. Contributions of different scatterings on the total mass attenuation coefficients of the soils are presented. In addition, the obtained results for Martian soils are compared with the results for Earth soils. The similarities of Earth and Martian soils are also investigated. Crown Copyright Ó 2012 Published by Elsevier B.V. All rights reserved.
1. Introduction Soil is an important natural and cheap material for radiation shielding. Although many types of it, soils have chemical composition characterized by the presence of SiO2, Al2O3, Fe2O3, CaO, MgO, B2O3 and others in variable concentrations [1,2]. Due to the widespread use of soil, determination of soil properties and physical parameters is important. The gamma-rays are often used for the soil researches [3,4]. The most relevant parameter determining the photon interaction in the soil and the other materials is the mass attenuation coefficient. The mass attenuation coefficient lm is a measure of probability of interactions of incident photons with the thickness (g/cm2) of target material [5]. The mass attenuation coefficients of different soils are determined by some works [1– 3,6]. There are a great number of experimental and theoretical investigations of lm values [7–11]. For composite materials such as soil, it is related to effective atomic number, Zeff. Since partial interaction cross-section depends on the composite material of elements, a single atomic number being a characteristic of element will not describe the atomic number of composite material in the all energy range. This new number for composite materials is called to be Zeff that varies with energy and theoretical expressions to evaluate Zeff values for the individual partial photon interaction processes have been suggested by Hine [12]. Some works to determine the Zeff values of composite materials various alloys [13,14], GaAs and InP crystals [15], some
⇑ Corresponding author. Tel.: +90 472 215 11 88; fax: +90 472 215 11 82. E-mail address: [email protected] (A. Un).
solutions and amino acids [16–18] and boron ores [19] have been reported in the literature. The other important physical parameter is kerma on radiation interaction with matter. Kerma (Kinetic energy released per unit mass) is defined as the initial kinetic energy of all secondary charged particles released per unit mass at a point of interest by uncharged radiation [20]. Kerma, effective atomic number and effective electron density Neff for some boron ores and some fatty acids have been reported by Un and Sahin [19] and Manohara et al. [21], respectively. The knowledge of the interaction of radiation with matter in a wide energy range is important. Therefore, in this work, the calculation of the total mass attenuation coefficient, Zeff, Neff and KERMA is aimed for energies in the range from 1 keV to 100 GeV. In the present work, the total mass attenuation coefficient, Zeff, Neff and KERMA of 5 different Martian and 14 different Earth soils have been reported. The calculated values of Martian and Earth soils have been compared. The chemical compositions of Earth soils are taken from the works of Baytas and Akbal [3] (labeled S1-Ankara, S3-Konya, S4-Fatsa, S5-Bergama, S6-Batman), Demir et al. [2] (labeled S2-Erzurum), Wielopolski et al. [22] (labeled S7, S9-the median value of world soils), Miller and Turk [23] (labeled S8) and Medhat [24] (labeled S10–14). In the soils, bulk density, moisture content, porosity and field capacity are very important parameters. For the soils S1–S6 bulk density, moisture content, porosity and field capacity have been determined in previous works [2,3,6]. The bulk density and porosity of the soils S7, a carbon rich loam soil S8 and S9 have been determined [22]. Moisture, bulk density, porosity and field capacity of the soil samples from five different agricultural zones in Egypt with different
0168-583X/$ - see front matter Crown Copyright Ó 2012 Published by Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.nimb.2012.07.031
43
A. Un, Y. Sahin / Nuclear Instruments and Methods in Physics Research B 288 (2012) 42–47 Table 2 Elemental composition of Earth soils S8–S14.
Table 1 Elemental composition of Earth soils S1–S7.
a b c d e f g
Element
S1a
S2b
S3c
S4d
S5e
S6f
S7g
Element
S8a
S9b
S10c
S11d
S12e
S13f
S14g
H Li B C N O F Na Mg Al Si P S Cl K Ca Sc Ti V Cr Mn Fe Co Ni Cu Rb Y Zr Ba Nd Sm Hf Pb Bi Th
– – – – – 41.920 6.560 0.850 0.630 3.720 15.990 10.250 0.270 – 1.400 8.720 – – – – – 8.550 – – – – – – – – – – – – –
– – 0.714 5.960 – 54.716 – 1.559 1.736 7.310 20.250 0.109 0.026 0.009 1.438 2.579 – 0.881 – 0.014 0.098 2.351 – 0.010 0.005 0.007 – 0.018 0.031 – – – – – –
– – – – – 33.118 8.854 0.307 1.872 4.000 17.118 14.446 0.124 – 1.344 16.096 – – – – – 0.941 – – – – – – – – – – – – –
– – – – – 44.400 2.980 1.980 0.570 10.080 24.650 4.860 0.070 – 3.710 2.680 – – – – – 2.310 – – – – – – – – – – – – –
– – – – – 44.410 2.880 1.660 1.134 8.520 26.610 4.700 0.110 – 2.170 3.580 – – – – – 1.660 – – – – – – – – – – – – –
– – – – – 44.850 3.660 1.100 2.240 6.960 27.140 5.980 0.090 – 1.800 3.900 – – – – – 2.010 – – – – – – – – – – – – –
0.2100 0.0013 0.0013 0.1950 0.0032 53.0032 0.0046 0.2450 0.0881 1.0960 43.7600 0.0128 – 0.0108 0.2250 0.1180 0.0005 0.1228 0.0035 0.0029 0.0151 0.7240 0.0007 0.0009 0.0012 0.0058 0.0035 0.0545 0.0540 0.0063 0.0012 0.0029 0.0050 0.0051 0.0037
H Li B C N O F Na Mg Al Si P Cl K Ca Sc Ti V Cr Mn Fe Co Ni Cu Rb Y Zr Ba Hf Pb Th
2.81 – – 14.43 0.001 49.64 – 0.82 – 8.93 21.32 – – 0.56 0.54 – – – – – 0.96 – – – – – – – – – –
– 0.0030 0.0010 2.0000 0.1000 48.8700 0.0200 0.6300 0.5000 7.1000 33.3000 0.0650 0.0100 1.4000 1.3700 0.0007 0.5000 0.0100 0.1000 0.0850 3.8000 0.0008 0.0040 0.0020 0.0100 0.0050 0.0300 0.0500 0.0006 0.0010 0.0005
– – – – – 49.803 – 1.558 1.272 5.988 31.336 – – 3.875 2.370 – 0.600 – – – 2.839 – – – – – – – – – –
– – – – – 50.039 – 2.389 1.134 2.571 37.033 – – 3.651 1.185 – 0.582 – – – 1.253 – – – – – – – – – –
– – – – – 49.784 – 1.729 1.596 9.939 24.457 – – 2.855 3.113 – 0.540 – – – 5.023 – – – – – – – – – –
– – – – – 51.952 – 1.743 0.858 8.920 28.104 – – 2.763 2.663 – 0.546 – – – 4.795 – – – – – – – – – –
– – – – – 48.897 – 2.515 1.656 10.408 21.094 – – 2.705 2.435 – 0.600 – – – 6.363 – – – – – – – – – –
Composition Composition Composition Composition Composition Composition Composition
of of of of of of of
a b c d e
Ankara soil taken from Baytas and Akbal [3]. Erzurum soil taken from Demir et al. [2]. Konya soil taken from Baytas and Akbal [3]. Fatsa soil taken from Baytas and Akbal [3]. Bergama soil taken from Baytas and Akbal [3]. Batman soil taken from Baytas and Akbal [3]. Earth soil taken from Wielopolski et al. [22].
f g
a b
2. Theory
c d
The mass attenuation coefficients of the different materials can be determined by the transmission. This process can be described by the following equation
I ¼ I0 e
of of of of of of of
Earth soil taken from Miller and Turk [23]. Earth soil taken from Wielopolski et al. [22]. Egypt soil taken from Medhat [24]. Egypt soil taken from Medhat [24]. Egypt soil taken from Medhat [24]. Egypt soil taken from Medhat [24]. Egypt soil taken from Medhat [24].
Table 3 Elemental composition of Martian soils MS1–MS5.
fractions of sand, coarse silt, fine silt, coarse clay and fine clay have been also determined by Medhat [24]. The chemical compositions of Earth soils considered were carried out using wavelength dispersive X-ray fluorescence (WDXRF) spectrometer, set of chemical reactions and conventional methods [2,3,24]. The chemical compositions of five Martian soils are taken from the work of Economou [25] (labeled MS1-Meridiani, MS2-Gusev, MS3-MPF, MS4-Viking and MS5-Guadalupe). The elemental contents of Martian soils were determined by the Alpha Scattering Instrument (ASI). A beam of alpha particles from 242Cm of homogenous energy of 6.1 MeV was used and the scattered alpha particles were detected by solid-state Si detector.
lmt
Composition Composition Composition Composition Composition Composition Composition
ð1Þ
where I0 denotes the number of photons incoming in unit time with energy E, incoming intensity; I the number of outgoing in unit time photons with energy E, outgoing intensity after attenuation; lm = l/ q (cm2/g) is the mass attenuation coefficient and t (g/cm2) is sample mass thickness (the mass per unit area). The total lm values for
e
Element
MS1a
MS2b
MS3c
MS4d
MS5e
O Na Mg Al Si P S Cl K Ca Ti Cr Mn Fe
51.084 1.558 5.136 5.327 20.702 0.389 1.884 0.510 0.174 4.855 0.300 0.335 0.271 6.993
50.411 2.656 5.904 5.829 20.898 0.445 2.467 0.620 0.141 4.040 0.120 0.192 0.217 5.558
51.778 2.003 4.020 5.237 20.174 0.262 2.080 0.800 0.580 3.927 0.480 0.205 0.232 8.120
51.060 – 3.840 4.232 21.949 – 3.160 0.500 0.124 4.570 0.420 – – 6.90
52.791 0.816 5.100 3.280 16.392 0.437 9.080 0.440 0.382 3.500 0.360 0.137 – 6.160
Composition Composition Composition Composition Composition
of of of of of
Martian Martian Martian Martian Martian
soil, Meridiani, taken from Economou [25]. soil, Gusev, taken from Economou [25]. soil, MPF, taken from Economou [25]. soil taken from Economou [25]. soil, Guadalupe, taken from Economou [25].
materials composed of multi elements are the sum of the (lm)i values of each constituent element by the following mixture rule [8];
l¼
X
wi ðlm Þi
ð2Þ
where wi is the weight fraction and (lm) is mass attenuation coefficient of the ith element. The theoretical lm values for present samples were calculated by WinX-Com program [26].
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A. Un, Y. Sahin / Nuclear Instruments and Methods in Physics Research B 288 (2012) 42–47
Fig. 1. Cross sections of different scatterings and sum of them versus energy for the world soils S9.
Fig. 3. Variation of effective atomic numbers versus photon energy for the Earth and Martian soils.
Fig. 2. Variation of total mass attenuation coefficients versus photon energy for the Earth and Martian soils.
More detailed information about the Zeff and Neff calculated for some soils used in this work have been given in some previous studies [17,18].
Absorbed dose is defined as the limiting value of the mean of the energy imparted by ionizing radiation per unit mass. The quantity Kerma can be easily computed, but its value can be over-or underestimated depending on the final-state energy taken for the induced charged particles. A quantity related to the kerma, termed the collision kerma, has long been in use as an approximation to absorbed dose when radiative losses are not negligible. The collision kerma excludes the radiative losses by the liberated charged particles. Kerma and absorbed dose are nearly equal in magnitude when radiation equilibrium is established [27,28]. The kerma is feasible to photons (x- and c-rays etc.) and neutrons and has unit J kg1 = Gy, as the absorbed dose. Therefore, kerma is the resultant of the energy fluence and mass energyabsorption coefficient, ðlen =qÞ. More info for Kerma has been given in previous work [21]. Kerma relative to water of the soil can be expressed as
ðlen =qÞs ðlen =qÞw
ð3Þ
In order to calculate kerma relative to water, the values of mass energy-absorption coefficients for liquid water have been taken from the compilation of Hubbel and Seltzer [8].
A. Un, Y. Sahin / Nuclear Instruments and Methods in Physics Research B 288 (2012) 42–47
45
Fig. 4. Comparison of effective atomic numbers (a) and effective atomic numbers (b) for Martian soils with effective atomic and electron number of world soils S9.
3. Results and discussion The chemical content of the Earth and Martian soils are tabulated in Tables 1–3. It can be seen from Tables 1–3 that the chemical contents of the Martian soils resembles to the chemical contents of the Earth soils. The contributions of the different effects and the total mass attenuation coefficients for the median value of world soils S9 are shown in Fig. 1. In addition, the total mass attenuation coefficients via energy of the Earth and Martian soils are presented in Fig. 2. Although the soils have a wide variety of elements, the main influence on the results in this work is the amount of iron in the soils. The higher concentration of iron in the chemical composition of the Martian soil MS3 in comparison to that of the other Martian soils and the higher concentration of iron in the chemical composition of Earth soil S1 in comparison to that of other Earth soils as seen in the Tables 1–3 explain the greater value of lm for the Martian soil MS3 in comparison to values of lm for other Martian soils and the greater value of lm for Earth soil S1 in comparison to values of lm for other Earth soils as shown in Fig. 2.
The experimental lm values of soil S2 for energies 60, 356 and 662 keV are 0.298, 0.102 and 0.081 cm2/g, respectively [2]. The lm values of Martian soils MS1, MS2, MS3, MS4, MS5 in this work are 0.457, 0.421, 0.473, 0.451, 0.435 for 60 keV, 0.1079, 0.1077, 0.1078, 0.1080, 0.1080 for 300 keV and 0.0798, 0.0799, 0.0797, 0.0800, 0.0800 for 600 keV, respectively. Because of the Z dependency of Compton scattering (for energies 300 and 600 keV), the lm values of Martian soils are very close to the experimental values lm of soil S2. But, for the energy 60 keV, because of the Z4 dependency of photoelectric interaction, high difference in the amount of the iron (Z = 26) between the Martian soils and S2 soil explains why the greater values of lm values of Martian soils are greater than the lm values of the soil S2. The Z eff values of soils were determined by using the values of lm. The variations of Z eff values versus photon energy for Earth and Martian soils are shown in Fig. 3. In Fig. 3, three energy regions E < 0.01 MeV, 0.05 MeV < E < 10 MeV and E > 100 MeV can be clearly seen. In the low energy, main interaction is photoelectric interaction which is proportional to Z4. Because of the Z4 dependency of photoelectric interaction, for the soil samples, the
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A. Un, Y. Sahin / Nuclear Instruments and Methods in Physics Research B 288 (2012) 42–47
Fig. 5. Variation of effective electron numbers versus photon energy for the Earth and Martian soils.
maximum values of Z eff have been found in low-energy range. Because of the Z4 dependence of photoelectric interaction and the photoelectric interaction near the K- edge of the elements with the high Z numbers, Z eff values of S1 and MS3 is higher than the other soil samples as seen in Fig. 3. The iron concentration values in the Martian soils are very close to each other and the iron concentration values in the Earth soils are different from each other as seen in Tables 1–3. Because of that, the Z eff values of Martian soils are more close to each other and the Z eff values of Earth soils are different from each other as shown in Fig. 3. At the intermediate energies, Compton scattering is main photon interaction. In this energy range, Z eff values are almost constant for a given samples. Because of the Compton scattering proportional to Z, minimum value of Z eff is found for the soils in this energy range. The value of Z eff is also constant in the high energy range in which the pair production is the main interaction. Because of proportionality of the pair production with Z2, the value of Z eff for high energy region smaller than the value obtained for photoelectric interaction and higher than the value obtained for Compton scattering.
Fig. 6. Variation of kerma values versus photon energy for the Earth and Martian soils.
In Fig. 4, the Martian soils are compared with Earth soil S9. It is clearly seen Fig. 4 that the Z eff values of Martian soils higher than the Z eff value the soil S9. However, because the elemental content of soil S9 more similar to the elemental content of soil MS2 in comparison to the other Martian soils, the Z eff value of soil MS2 is closer to the Z eff value of soil S9 than the other Martian soils. The variation of Nel values versus photon energy for Earth and Martian soils is shown graphically in Fig. 5, respectively. In Fig. 5, three energy regions are clearly seen. The energy dependence of the effective electron number, Nel, is similar to the effective atomic numbers, Z eff . The effective electron numbers for the Martian soils are compared with the Nel value of the median value of world soils S9 in Fig 4. As can be seen in Fig 4, the Nel value of soil MS2 is closer to the Nel value of soil S9 than the other Martian soils. Explanation for values of Z eff and Nel of Earth and Martian soils as shown in Fig. 2 is almost the same mentioned above in the case of the values of lm for Earth and Martian soils.
A. Un, Y. Sahin / Nuclear Instruments and Methods in Physics Research B 288 (2012) 42–47
The energy dependence of kerma relative to water is presented in Fig. 6 for Earth and Martian soils, respectively. Two energy regions can be clearly seen in Fig. 6. In the low energy region, main interaction is photoelectric interaction, and, in the other energy region, the Compton scattering is the main interaction. Because of the photoelectric interaction near the K-edge of the elements with the high Z number, kerma relative to water values in the low energy region higher than the other energy region as seen in Fig. 6. Because of elemental composition and the higher concentration of iron in the soil S1 in comparison to the other soils, the kerma value of soil S1 higher than the other soils.
4. Conclusions The effective atomic number, Zeff, the effective electron number, Nel and kerma depends on the elemental compositions of the soils. The iron concentration of the soil is more effective than the other elemental concentrations on the results analyzed. Although the Zeff, and Nel values of Martian soils higher than the Zeff, and Nel values of the median of the world soils, the Martian soils very similar to the Earth soils. To our best knowledge, the investigation of the Zeff, Nel and kerma relative to water for Earth and Martian soils in the studied energies are not available in the literature. It is expected that the present work can lead to other studies such as radiation shielding and understanding of the extraterrestrial materials.
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