Self-absorption correction in determining the 238U activity of soil samples via 63.3 keV gamma ray using MCNP5 code

Applied Radiation and Isotopes 71 (2013) 11–20

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Self-absorption correction in determining the via 63.3 keV gamma ray using MCNP5 code

238

U activity of soil samples

Ngo Quang Huy a,n, Do Quang Binh b, Vo Xuan An a, Truong Thi Hong Loan c, Nguyen Thanh Can c a

Ho Chi Minh City University of Industry, 12 Nguyen Van Bao Street, Go Vap District, Ho Chi Minh City, Vietnam Ho Chi Minh City University of Technical Education, 1 Vo Van Ngan, Thu Duc Street, Ho Chi Minh City, Vietnam c Ho Chi Minh City University of Natural Sciences, 227 Nguyen Van Cu Street, District 5, Ho Chi Minh City, Vietnam b

H I G H L I G H T S c c c c

Determination of the 238U activity via 63.3 keV gamma rays. Self-attenuation factors of 63.3 keV gamma rays for cylindrical sample container. The density, chemical composition and geometry effects are taken into account. Determination of the 238U activity in three soil types: grey, alluvial and red soils.

a r t i c l e i n f o

abstract

Article history: Received 27 January 2012 Received in revised form 5 September 2012 Accepted 6 September 2012 Available online 23 September 2012

The essential issue in analyzing the activity of 238U in an HPGe detector based gamma spectrometer via 63.3 keV line is relating to the strong self-absorption of this weak gamma ray in sample material. The present work suggests a method of the self-absorption corrections for 63.3 keV gamma rays by a combination of experimental measurements and Monte Carlo MCNP5 calculations. The effects of sample chemical composition, density and geometry were calculated in terms of self-attenuation factors. The method, developed for a cylindrical sample geometry, accounted for variable sample heights and densities. The analysis of 238U activity was applied for three main soil types in Vietnam, which are grey, alluvial and red soils. The results obtained with the above outlined method were in good agreement with those derived by other methods. & 2012 Elsevier Ltd. All rights reserved.

Keywords: Self-absorption Self-attenuation factor 238 U activity 63.3 keV MCNP5 code HPGe detector

1. Introduction The activity of 238U is commonly determined in an HPGe detector based gamma spectrometer by indirect methods. The direct analysis of the 238U activity is impossible because it emits two gamma rays with very weak intensities, namely 49.55 keV (0.0697%) and 113.5 keV (0.0174%), which lie in a large Compton scattering background of gamma spectrum. The indirect analysis of 238U is accomplished by means of the measurement of gamma rays emitted from daughter nuclides in uranium decay chains. The daughter nuclides often used are: 234 Th (T1/2 ¼24.1 days), 234mPa (T1/2 ¼1.17 min), 214Pb (T1/2 ¼ 26.8 min) and 214Bi (T1/2 ¼19.9 min). Among them, 214Pb and 214 Bi are widely applied because of large intensities of gamma

n

Corresponding author. Mob.: þ 84 908 394 813. E-mail addresses: [email protected], [email protected] (N.Q. Huy).

0969-8043/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.apradiso.2012.09.004

rays emitted from these nuclides. They are 241.9 keV (7.268%), 295.2 keV (18.5%), 351.9 keV (35.6%) gamma lines emitted from 214 Pb and 609.3 keV (45.49%), 768.4 keV (4.891%) and 1120.3 keV (14.909%) gamma lines emitted from 214Bi. The analysis of 238U activity by using 214Pb and 214Bi faces with two disequilibria. The first is a disequilibrium between 226Ra and 214Pb, 214Bi due to a leakage of 222Rn (T1/2 ¼3.825 days), which is a noble gas and is the decay product of 226Ra. To overcome this disequilibrium, samples are sealed for a month to attain the equilibrium between 226Ra and 222Rn. Then, the average activity of 214Pb and 214Bi can be assigned to that of 226Ra as reported in Huy and Luyen (2006). This value is not considered to be 238U activity because there is still a second geochemical disequilibrium between 226Ra and 238 U. The disequilibrium is caused by the different chemical properties of 238U and 226Ra in soil environment and a long lifetime of 1620 years for 226Ra. So, the 238U activity obtained by indirect analysis via 214Pb and 214Bi is only approximate when neglecting the geochemical disequilibrium.

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234 Th and 234mPa are the nearest daughters of 238U and are very short-lived nuclides compared to 238U, so radioactive equilibrium is quickly established. As a result, the geochemical disequilibrium between these nuclides and 238U can be ignored and the activities obtained for these nuclides can be assigned to that of 238U. The gamma rays preferably used for 238U analysis are 63.3 keV (4.8%) and 92.6 keV (5.58%) emitted from 234Th, and 766.4 keV (0.316%) and 1001.0 keV (0.839%) from 234mPa (Yucel et al., 1998, 2009; Huy and Luyen, 2004; Dowdall et al., 2004; De Corte et al., 2005; Kaste et al., 2006). However, from the point of view of analysis of 238U activity in soil samples with low specific activities, the measurement of 766.4 keV and 1001.0 keV gamma rays can give activities with large uncertainties because of their weak intensities and low efficiencies of germanium detectors at high energies. Gamma ray of 92.6 keV is a doublet, consisting of 92.4 keV (2.81%) and 92.8 keV (2.77%) and is interfered by other K-X- and gamma peaks, including 93.3 keV. So, in practice, the 92.6 keV peak cannot be separated from the multiplet of about 93 keV. The remaining 63.3 keV gamma ray includes contributions from the 63.3 keV gamma ray (4.8%) emitted from 234Th, 63.9 keV gamma ray (0.023%) from 231Th and 63.9 keV gamma ray (0.255%) from 232Th, but the contributions of 231Th and 232Th can be neglected (Kim and Burnett, 1985; Huy and Luyen, 2004). Therefore, the 63.3 keV gamma ray is a preferred candidate for determination of 238U activity in environmental soil samples. The important problem in the use of 63.3 keV line for analysis of 238U activity is the strong self-absorption of this weak gamma ray in sample material. As reported in Hasan et al. (2002), the values of the self-absorption correction factor for the IAEA reference samples of 1.0 g/cm3 and 1.4 g/cm3 densities, packed in 5 cm3 tube geometry and measured with a well-type HPGe detector, are approximately 13%, 5% and 2% for the energy ranges of 40–160 keV, 200–600 keV and 4600 keV, respectively. Therefore, the self-absorption corrections must be taken into account when the 63.3 keV gamma ray is used. For the volumetric sample with a homogeneous distribution of the attenuating material and the radioactive source, the influencing factors on self-absorption are composed of chemical composition, density and geometry effects. The self-absorption correction factor for a sample under study with given chemical composition, density and geometrical dimension was determined by calculating the ratio between its counting efficiency and that of a standard reference sample with known self-absorption property. Some works have made corrections for only density and geometry effects neglecting the composition effect (Kitto, 1991; Melquiades and Appoloni, 2001; Abbas, 2001; Vargas et al., 2002; Huy and Luyen, 2004). The selfabsorption corrections for all three effects, including the composition one, were conducted in the works of Hasan et al. (2002), San Miguel et al. (2002), Nachab et al. (2004) and Carrazana Gonzalez et al. (2010). An approach to perform the selfabsorption corrections is to calculate the self-attenuation factor suggested by Debertin and Helmer (1988) and developed by Korun (1999, 2000), Korun and Vidmar (2003), Boshkova and Minev (2001) and Boshkova (2003). This factor describes the probability of interaction between the photons and the sample material and is given by the ratio between the counting efficiency for the actual sample eV(m,E), where m, E and V denote the attenuation coefficient, the energy of photon and the sample volume, respectively, and the counting efficiency for the same sample-detector geometry but without self-attenuation eV(0,E) (Korun, 1999):

F V ðm,EÞ ¼

eV ðm,EÞ eV ð0,EÞ

ð1Þ

The advantage of the self-attenuation factor is that the detector properties enter the expression via both efficiencies

and cancel out to a large extent in the ratio. Therefore, the selfattenuation factor is given as a function of sample parameters, disregarding the detector properties. The aim of present work is to develop a method to analyze 238 U activity in soil samples via 63.3 keV by a combination of experimental measurement and Monte Carlo MCNP5 calculation. The corrections of all chemical composition, density and geometry effects were carried out by application of the self-attenuation factor. The method, developed for a cylindrical sample geometry, accounted for variable sample heights and densities. The analysis of 238U activity was applied for three main soil types in Vietnam, which are grey, alluvial and red soils.

2. Experimental The measuring system used in the study was the Canberra HPGe GC1518 p-type detector based gamma spectrometer installed at the Center for Nuclear Techniques Ho Chi Minh City, Vietnam. It has a relative efficiency of 15% and an energy resolution of 1.8 keV at 1332 keV line. The geometry dimensions and material compositions of the lead shield and the GC1518 detector were described in Huy et al. (2007). An important parameter of the HPGe GC1518 p-type detector is its thickness of dead layer, which was 0.35 mm of germanium equivalent as provided by the manufacturer in 1996 and grown over operation time to 0.65 mm in 1999, 1.15 mm in 2005 and 1.46 mm in 2009 (Huy and Ngo Quang, 2010). The sample container used in the measurement had cylindrical form of 7.2 cm diameter and 5 cm height. The height of sample material depended on its mass and density.

3. Reliability of MCNP5 calculation of self-absorption corrections for 63.3 keV gamma rays The reliability of MCNP5 calculation of self-absorption corrections for 63.3 keV gamma rays was controlled by using a 238U standard sample and a 238U water solution, chemical compositions of which are presented in Table 1. The 238U standard was supplied by Institute of Nuclear Science and Technology in Hanoi (INST sample) with a specific activity of 1296 712 Bq/kg. The 238 U water solution was prepared by addition of an amount of [238U]uranyl-acetate to water with an activity of 119397 126 Bq/kg. Different samples of heights between 0.2 cm and 2.4 cm with 0.1 cm increments for INST sample and between 0.2 cm and 1.8 cm with 0.1 cm increments for water solution were measured in the spectrometer. With the model of detector, lead shield and sample cylindrical container as described in Huy et al. (2007) we simulated gamma spectra by the MCNP5 calculation. The experiment of measuring the efficiencies of INST and water samples were carried out in 2003, therefore the dead layer thickness of GC1518 detector was taken to be 0.9 mm. The F8 tally of the MCNP5 code is a pulse height tally, which provides the energy distribution of pulses created in a detector by radiation. It was used to extract the pulse height distribution of gamma spectra, and the 63.3 keV full energy peak efficiency was determined. Simulation relative error was kept under 0.3% with a total of 3,000,000 source gamma-rays. The densities, chemical compositions and geometries of INST and water samples included in the input data of the MCNP5 code are presented in Table 1. From the gamma spectra measured in the GC1518 detector based gamma spectrometer, the experimental efficiencies of 63.3 keV full energy peaks were determined with relative uncertainties of less than 5% and plotted in Fig. 1 against the sample height. From Fig. 1 it is seen that the curves calculated by the MCNP5 code describe well experimental data. Besides, the ratios

N.Q. Huy et al. / Applied Radiation and Isotopes 71 (2013) 11–20

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Table 1 Densities, chemical compositions and geometries of INST sample and water solution. Sample

Density (g/cm3)

Chemical composition

Range of sample height (cm)

INST sample Water solution

1.513 1.000

CaCO3 (71.33%), MgCO3 (24.84%), H2O (3.83%) H2O (100%)

0.2–2.4 (23 samples) 0.2–1.8 (17 samples)

Fig. 1. Experimental and calculated efficiencies of 63.3 keV full energy peaks for INST sample and water solution versus sample heights.

Fig. 2. The efficiencies of 63.3 keV full energy peaks plotted against the heights of the INST samples. (2.1) Narrow beam experiment: (a) measurement and its fitting curve. (2.2) Cylindrical container: (b) measurement and its fitting curve and (c) MCNP5 calculation and its fitting curve.

ecal/eexp, averaged over the height ranges of 0.2–2.4 cm for INST sample and 0.2–1.8 cm for water solution are equal to 0.97670.049 and 0.990 70.024, respectively. It is clear that these ratios are very close to unity, which confirms the reliability of efficiency calculation by using MCNP5 for different sample densities, chemical compositions and geometries. 4. Self-attenuation factors of 63.3 keV gamma rays for different soil types 4.1. Formulation of the self-attenuation factor The self-attenuation factor F V ðm,EÞ ¼ ðeV ðm,EÞÞ=ðeV ð0,EÞÞ of 63.3 keV gamma rays was applied for the INST sample with the chemical composition included in Table 1 and the density r ¼1.513 g/cm3, containing in the cylindrical container of 7.2 cm diameter. Two measurements with the INST material were performed. The first was a direct transmission measurement of a narrow 59.5 keV gamma beam from an 241Am source with the INST attenuating material containing in the cylindrical container. The counts of gamma rays after the absorber were plotted versus

the sample heights varied from 0.2 cm to 4.4 cm with 0.2 cm increments (Fig. 2(2.1)). The experimental data were fitted with an exponential function of the height:

eðm,hÞ ¼ eðm,0Þ expðmhÞ

ð2Þ

where m is the linear attenuation coefficient, which is equal to 0.3696 cm  1 obtained from the fitting curve (curve a). The curve a was normalized so that it is equal to the efficiency of the INST cylindrical sample measurement at the height zero, i.e., e(m,0)¼0.0433. The second measurement was carried out with the INST samples containing in the cylindrical container of the sample heights from 0.2 cm to 2.4 cm with 0.1 cm increments. The sample in this measurement played two roles, namely the radioactive source and the attenuating material. The experimental counting efficiencies were plotted against the height (Fig. 2(2.2)) and fitted with an exponential function (curve b). The MCNP5 calculation results performed for this measurement at five height values of 0.5 cm, 1.0 cm, 1.5 cm, 2.0 cm and 2.5 cm were presented in Fig. 2(2.2) and fitted with an exponential function (curve c). These two fitting curves were used for purely mathematical description of the experimental and MCNP5

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calculation data. They showed that the data of the cylindrical sample experiment were also described by an exponential function, similar to one in the narrow beam experiment (curve a). The exponential function in this case has the following form:

eðmeff ,hÞ ¼ eð0,hÞ expðmeff hÞ

ð3Þ

where e(0,h) is the efficiency without self-attenuation and meff is the effective attenuation coefficient. It should be noted that e(m,0) in Eq. (2) represents the efficiency in the case of a height zero, whilst e(0,h) in Eq. (3) is the efficiency obtained at effective attenuation coefficient zero. Furthermore, the linear attenuation coefficient m in Eq. (2) having dimension of cm  1 expresses the attenuation in the sample matrix only because the point radioactive source is located behind the absorber, whilst the effective attenuation coefficient meff having also dimension of cm  1 reflects two effects, the first of which is the attenuation in the sample matrix and the second is the volumetric distribution of radioactive source. As a result, the effective attenuation coefficient meff can be defined as follows:

meff ðr,hÞ ¼ aðhÞr

ð4Þ

where a(h) is a mass attenuation coefficient having dimension of (g/cm2)  1. In the narrow beam measurement, it depends only on material matrix of the sample. In the experiment of cylindrical radioactive and attenuating samples, a(h) is dependent of the sample matrix and the height. So Eq. (3) becomes:

eðmeff ,hÞ ¼ eð0,hÞ exp½meff ðh, rÞh ¼ eð0,hÞ exp½aðhÞhr

ð5Þ

where e(0,h) is determined at r ¼0, i.e., at meff ¼0. The MCNP5 code was used for calculating the counting efficiencies as functions of the INST densities from 0.2 g/cm3 to 1.8 g/cm3 with 0.2 g/cm3 increments for the sample heights from 0.5 cm to 2.5 cm with 0.5 cm increments (Fig. 3). The calculated data of counting efficiencies were fitted with exponential function (5), from which the values of e(0,h) and a(h)h were determined (Table 2, rows 1 and 2). The values of a(h) and meff ¼a(h)r at r ¼1.513 g/cm3 were calculated and reported in rows 3 and 4

of Table 2. It is noted that e(0,h) was obtained at r ¼0, i.e., at meff ¼0 according to Eq. (4). From rows 1 and 4 of Table 2 it is revealed that e(0,h) and meff ¼a(h)r decrease with the increasing height, whilst e(m,0) and m are constant in the narrow beam experiment. The calculated counting efficiencies ecal(meff,h) for five h values from 0.5 cm to 2.5 cm were obtained (Table 2, row 5), which are in good agreement with the experimental ones eexp(meff,h) (Table 2, row 6). Based on the good agreement of the counting efficiency calculated by Eq. (5) with the experimental data, the attenuation factor can be expressed as follows: Fðmeff ,hÞ ¼

    eðmeff ,hÞ ¼ exp meff ðr,hÞh ¼ exp aðhÞhr eð0,hÞ

ð6Þ

It is noted that the effective attenuation coefficients meff of 0.2717 cm  1, 0.2495 cm  1, 0.2306 cm  1, 0.2148 cm  1 and 0.2006 cm  1 at the heights of 0.5 cm, 1.0 cm, 1.5 cm, 2.0 cm and 2.5 cm, respectively (Table 2, row 4), are less than the linear attenuation coefficient m ¼0.3696 cm  1. This difference results from the difference of the two experiments, where the linear attenuation coefficient m was obtained in an experiment with a collimated gamma beam from the point radioactive source placed behind the attenuating material, whilst the effective attenuation coefficient meff was obtained in the case, when the attenuating material of cylindrical form is also radioactive source. Because the cylindrical radioactive source of a given height is placed close to detector, its counting efficiency is larger than that of the point radioactive source in the narrow beam measurement with the attenuating material of the same height placed between the source and the detector. Then the effective product (mh)eff of cylindrical container measurement should be less than the product mh of the narrow beam experiment. The first product can be written as (mh)eff ¼ meffh¼ mheff, where meff is the effective attenuation coefficient and heff is the effective height or the photons average path length (Korun, 1999). The inequality (mh)eff o mh leads to meff o m if the height h is fixed or heff oh if the linear attenuation coefficient m is kept unchanged. In the experiment with the INST samples, m ¼0.3696 cm  1 and meff ¼0.2717 cm  1, 0.2495 cm  1,

Fig. 3. The counting efficiencies calculated for the INST material densities from 0.2 g/cm3 to 1.8 g/cm3 and the sample heights from 0.5 cm to 2.5 cm.

Table 2 MCNP5 calculation results of counting efficiencies for the INST sample with r ¼ 1.513 g/cm3. No.

h (cm)

0.5

1.0

1.5

2.0

2.5

1 2 3 4 5 6

e(0,h)

0.0431 0.0898 0.1796 0.2717 0.0376 0.0361

0.0406 0.1649 0.1649 0.2495 0.0316 0.0330

0.0381 0.2286 0.1524 0.2306 0.0270 0.0279

0.0358 0.2839 0.1419 0.2148 0.0233 0.0241

0.0336 0.3314 0.1326 0.2006 0.0204 0.0220

a(h)h a(h) meff ¼ a(h)r (r ¼1.513 g/cm3) ecal(meff,h) eexp(meff,h) (75%)

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0.2306 cm  1, 0.2148 cm  1 and 0.2006 cm  1, so the ratios between the photons average path lengths and the geometrical thicknesses are heff/h¼ meff/m ¼0.735, 0.675, 0.624, 0.581, and 0.543 at the heights of 0.5 cm, 1.0 cm, 1.5 cm, 2.0 cm and 2.5 cm, respectively. For comparison purpose, we consider the self-attenuation factor obtained by Debertin and Helmer (1988). For a plane source of thickness h with a homogeneous distribution of the attenuating material and the activity, placed coaxially with the detector at a far distance, it has the following form: F 0 ðm,hÞ ¼

1emh mh

ð7Þ

The function F0 (m,h) was calculated for the INST sample with the linear attenuation coefficient m ¼0.3696 cm  1 and the sample heights of 0.01 cm, 0.5 cm, 1.0 cm, 1.5 cm, 2.0 cm and 2.5 cm (Fig. 4). Because the source plane is placed at a far distance from the detector, we can consider the effective attenuation coefficient meff independent of the height. In this case, the obtained data of self-attenuation factor F0 (m,h) could be fitted with the function F(meff,h)¼ exp( meffh) with a constant value of meff. The fitting result showed that meff ¼0.1707 cm  1 with R2 ¼ 0.9994. So, we can conclude that the self-attenuation factor (7), obtained by Debertin and Helmer (1988) with a given linear attenuation coefficient m, can be expressed by Eq. (6) with an appropriate effective attenuation coefficient meff. It is seen that heff/h¼ meff/m ¼ 0.46270.046. This value is in good agreement with the ratio of 0.46170.027 between the average path sðmÞ and the geometrical thickness h for a slab-shape sample, obtained from the formula (Korun, 1999)   1 mhemh sðmÞ ¼ 1 ð8Þ m 1emh and averaged over the heights from 0.5 cm to 2.5 cm with m ¼0.3696 cm  1. 4.2. Application of the self-attenuation factor to some soil types of Vietnam The self-attenuation factor (6) was applied for determining the self-absorption corrections of some soil types of Vietnam. According to the soil classification of Vietnam based on the method of FAO-UNESCO classification, Vietnam has three main soil types, which encompass 93.3% soil area of Vietnam (Ton That Chieu et al., 1991; Vietnam Soil Scientific Society, 1996; Pham Quang Khanh, 1995). They are grey soil (63.8%), alluvial soil (19.9%) and red soil (9.6%). The key chemical compositions of these soil types were reported in Pham Quang Khanh (1995). The main compositions of grey soil and alluvial soil are SiO2 and Al2O3 with their

15

total percentage of about 85–95%. Whilst the main compositions of red soil are composed of two groups, the first consists of SiO2 and Al2O3 with their total percentage of about 55–65%, and the second consists of Fe2O3, FeO and TiO2 with their total percentage of about 25–35%. Other compositions have negligible contributions. Table 3 presents the chemical compositions of four soil samples, collected in Southern Vietnam and measured by the South Vietnam Geological Mapping Division. From Table 3 it is noted that the measured composition percentages are close to those given in Pham Quang Khanh (1995). The self-attenuation factor was calculated by MCNP5 code using Eq. (6) for four samples of grey soil 1, grey soil 2, alluvial soil and red soil. Then the effective attenuation coefficient depends on chemical composition (c), sample height (h) and sample density (r):

meff ðc,h, rÞ ¼ aðc,hÞr

ð9Þ

The counting efficiency has the following form:

eðmeff ,c,h, rÞ ¼ eð0,c,h,0Þ exp½meff ðc,h, rÞh ¼ eð0,c,h,0Þ exp½aðc,hÞhr ð10Þ where e(0,c,h,0) is the counting efficiency without selfattenuation obtained at r ¼0, i.e., at meff ¼ 0. The self-attenuation factor can be described by the expression: F 1 ðmeff ,c,h, rÞ ¼

    eðmef f ,c,h, rÞ ¼ exp meff ðc,h, rÞh ¼ exp aðc,hÞhr eð0,c,h,0Þ

ð11Þ The counting efficiencies were calculated for 5 values of the sample heights of 0.5 cm, 1.0 cm, 1.5 cm, 2.0 cm and 2.5 cm, and Table 3 The measured chemical compositions of grey soil 1, grey soil 2, alluvial soil and red soil samples, collected in Southern Vietnam. Chemical composition

SiO2 Al2O3 Fe2O3 FeO TiO2 MnO MgO CaO Na2O K2O P2O5 Loss of ignition

Percentage (%) Grey soil 1

Grey soil 2

Alluvial soil

Red soil

83.16 5.34 0.84 1.59 0.82 – 1.07 0.37 0.12 0.15 0.13 4.98

89.32 4.42 0.5 0.97 0.50 – 0.04 0.74 0.12 0.21 0.04 2.96

83.30 4.90 2.83 3.55 0.69 0.05 0.49 0.68 0.48 1.04 0.10 1.58

33.08 25.46 18.06 2.32 4.52 0.22 0.49 0.11 0.14 0.08 14.56

Fig. 4. Function F0 (m,h) ¼ð1emh Þ=mh calculated for the INST sample with m ¼ 0.3696 cm  1 depending on the height. The calculated data are fitted with function F(meff,h) ¼exp(  meffh).

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9 density values from 0.2 g/cm3 to 1.8 g/cm3 with 0.2 g/cm3 increments. They are expressed as functions of the density for different values of the sample height. As an example, in Fig. 5 the calculated efficiencies for the height of 2 cm are plotted versus the density for grey soil 1, grey soil 2, alluvial soil and red soil. From Fig. 5 the values of e(0,c,h,0), a(c,h)h and a(c,h) are obtained and presented in Table 4. It is revealed from Table 4 that the efficiencies without self-attenuation e(0,c,h,0) have almost the same values for the three soil types at a given thickness. It is because that these values are obtained at r ¼0, i.e., they are independent of soil types. From Fig. 5 it is seen that three curves for the grey soil 1, grey soil 2 and alluvial soil are close each to other, which clearly differ from the curve for the red soil. The average values of a(c,h)h and a(c,h) for the grey and alluvial soils are 0.2476 and 0.1239 with their relative uncertainties of 5.65%, whilst the relative differences between these average values compared to the corresponding values of red soil of 0.3477 and 0.1738 are 28.8%. So, three soil types can be categorized into 2 groups, one is the group of grey and alluvial soils and another is the red soil one. The similar calculations were performed for four remaining height values of 0.5 cm, 1.0 cm, 1.5 cm and 2.5 cm. The MCNP5 calculation data were plotted versus the density and fitted with the Eq. (10). From the fitting results, the values e(0,c,h,0), a(c,h)h and a(c,h) were obtained and presented in Table 5. From Table 5 it is revealed that e(0,c,h,0) have the similar values for the red soil (column 2) and the average of grey soil and alluvial soil (column 3) at a given height. The average value for 4 soil samples is reported in column 4 of Table 5, plotted in Fig. 6 versus the height and fitted with a linear function of the sample height:

eð0,c,h,0Þ ¼ 0:004843h þ0:045442

ð12Þ

The values of a(c,h)h and a(c,h) were presented in Table 5, which are different for the red soil and the average of grey soil and alluvial soil. In Fig. 7 the values of a(c,h) are plotted versus the sample height and are fitted with the functions: 2

aðc,hÞ ¼ ph þ qh þr

ð13Þ

where p, q and r depend on soil types and are equal to: p ¼ 0:00467,

q ¼ 0:04587,

r ¼ 0:24639

q ¼ 0:02738,

r ¼ 0:16825

meff ðc,h, rÞ ¼ aðc,hÞr ¼ ðph2 þ qh þrÞr

ð16Þ

where p, q and r depend on chemical compositions.

5. Propagation of uncertainties in chemical composition, sample height and sample density to the uncertainty of the self-attenuation factor The self-attenuation factor is expressed by the exponential function (11), explicitly depending on the sample height (h) and the sample density (r). However, the self-attenuation factor is an implicit function of the chemical composition (c). In order to determine the propagation of the uncertainties in chemical composition, sample height and sample density to the uncertainty of the self-attenuation factor we suggest an explicit function of the self-attenuation factor depending on the chemical composition, sample height and sample density as follows: F 2 ðmeff ,c,h, rÞ ¼

11 X

ai ðcÞ  f i ðmef f ,h, rÞ

ð17Þ

i¼1

where 11 is the number of oxides, ai denotes the percentage of ith oxide and fi is the self-attenuation factor of the sample containing only ith oxide. Note that ai depends on the chemical composition of soil, whilst fi depends on the sample height and the sample density. The correctness of Eq. (17) is checked by comparison of the self-attenuation factor calculated by the expression P F 2 ¼ 11 i ¼ 1 ai f i (row 12 of Table 6) and that calculated for the real matrix of sample, expression F1 ¼exp[  meff(c,h,r)h] (row 13 of Table 6). From Table 6, it is evident that these two values match for grey, alluvial and red soils. So Eq. (17) can be used for determining the propagation of uncertainties instead of Eq. (11). The relative uncertainty of the self-attenuation factor F2 is described via the relative uncertainties sai =ai and sf i =f i as Table 4 The values of e(0,c,h,0), a(c,h)h and a(c,h) in Eq. (10) for grey soil 1, grey soil 2, alluvial soil and red soil in the case of sample height h ¼2 cm.

ð14Þ

Sample

e(0,c,h,0) a(c,h)h

a(c,h) ¼ a(c,h)h/h

ð15Þ

Grey soil 1 (GS1) Grey soil 2 (GS2) Alluvial soil (AS) Red soil (RS) Average for GS1, GS2 and AS (RS-Average)/RS

0.0359 0.0359 0.0358 0.0355

0.1212 0.1185 0.1317 0.1738 0.1239 (75.65%) 28.80%

for the red soil; and p ¼ 0:00254,

uncertainty of a(c,h). Then the effective attenuation coefficient is expressed by the formula:

for the average of grey and alluvial soils. The relative uncertainties of the parameters p, q, r are about 5% as estimated for

0.2424 0.2369 0.2634 0.3477 0.2476 (7 5.65%) 28.80%

Fig. 5. The calculated efficiencies plotted versus the density for grey soil 1, grey soil 2, alluvial soil and red soil in the case of 2 cm height.

N.Q. Huy et al. / Applied Radiation and Isotopes 71 (2013) 11–20

17

Table 5 The values e(0,c,h,0), a(c,h)h and a(c,h) for red soil and the average of grey and alluvial soils. Note: RS, GS and AS denote the red soil, grey soil and alluvial soil, respectively. h (cm)

e(0,c,h,0)

(1)

RS (2)

Average of GS and AS (3)

Average of GS, AS and RS (4)

RS (5)

Average of GS and AS (6)

RS (7)

Average of GS and AS (8)

0.5 1.0 1.5 2.0 2.5

0.0431 0.0405 0.0379 0.0355 0.0332

0.0431 0.0407 0.0382 0.0359 0.0337

0.0431 0.0406 0.0381 0.0357 0.0335

0.1124 0.2049 0.2819 0.3477 0.4017

0.0776 0.1436 0.1990 0.2476 0.2892

0.2248 0.2049 0.1879 0.1739 0.1607

0.1551 0.1436 0.1327 0.1238 0.1157

a(c,h)h

a(c,h)

Fig. 6. The average value e(0,c,h,0) for 4 soil samples plotted versus the sample height.

Fig. 7. The values a(c,h) for the red soil (curve a) and the average of grey soil and alluvial soil (curve b) plotted versus the sample height.

follows: 

sF 2 F2

P11

2 ¼

2 i ¼ 1 ðf i

P 11

s2ai þ a2i s2f i Þ

j¼1

aj f j

2

¼

11 X i¼1

ai f i aj f j

!2 "

P11

j¼1

sai ai

2

 þ

sf i

2 #

fi

ð18Þ The calculation based on the MCNP5 code shows that the function fi has an exponential form f i ðmeff,i ,h, rÞ ¼ exp½meff,i ðh, rÞh ¼ exp½ai ðhÞrh

ð19Þ

where meff,i is the effective attenuation coefficient of ith oxide, which is expressed by a function of density, similar to Eq. (16):

meff,i ðh, rÞ ¼ ai ðhÞr ¼ ðpi h2 þqi h þr i Þr

ð20Þ

The parameters pi, qi and ri are calculated for 5 main oxides SiO2, Al2O3, Fe2O3, FeO and TiO2 (Table 7).

Taking into account Eqs. (19) and (20), Eq. (18) becomes: !2 (    2 11 spi sF 2 2 X sai 2 ai f i 3 ¼ þ ðpi h rÞ2 P11 F2 ai pi i¼1 j ¼ 1 aj f j  2  2 h sqi sri 2 3 2 þ ðr i hrÞ2 þ ð3pi h r þ 2qi h r þ ðqi h rÞ2 qi ri is 2 3 2 h g ð21Þ þ r i hrÞ2 þðpi h r þ qi h r þ r i hrÞ2 h



According to Pham Quang Khanh (1995), the grey and alluvial soils are mainly composed of SiO2 and Al2O3 with the relative uncertainties of their percentages sai =ai E0.05 and the red soil of SiO2, Al2O3, Fe2O3, FeO and TiO2 with sai =ai E0.10. The relative uncertainties of the parameters pi, qi, ri are spi =pi  sqi =qi  sri = r 3i  0.05 as stated in Section 4. The sample heights were measured with the uncertainty of 0.05 cm. Then the maximal relative uncertainties sF 2 =F 2 obtained from Eq. (21) are equal to

18

N.Q. Huy et al. / Applied Radiation and Isotopes 71 (2013) 11–20

Table 6 The measured chemical compositions of grey 1, alluvial and red soil samples, collected in Southern Vietnam (columns 4, 6, 8). The self-attenuation factor fi (column 3) calculated for the sample containing only ith oxide with 2 cm height and 1 g/cm3 density. The products aifi for grey 1, alluvial and red soils are presented in columns 5, 7, 9, respectively. i

Oxide

fi

Grey soil 1

(1)

(2)

(3)

(4)

1 2 3 4 5 6 7 8 9 10 11 12

SiO2 Al2O3 Fe2O3 FeO TiO2 MnO MgO CaO Na2O K2O P2O5 11 P F2 ¼ ai f i

0.8033 0.8454 0.6328 0.6982 0.7616 0.6693 0.8715 0.7175 0.8692 0.7266 0.8493

0.8932 0.0442 0.0050 0.0097 0.0050 0.0000 0.0004 0.0074 0.0012 0.0021 0.0004

13

F1 ¼ exp(  meff h)

Alluvial soil

ai

aifi (5)

ai (6)

0.7175 0.0374 0.0032 0.0068 0.0038 0.0000 0.0003 0.0053 0.0010 0.0015 0.0003 0.7772

0.8330 0.0490 0.0283 0.0355 0.0069 0.0005 0.0049 0.0068 0.0048 0.0104 0.0010

Red soil

aifi (7) 0.6692 0.0414 0.0179 0.0248 0.0053 0.0003 0.0043 0.0049 0.0042 0.0076 0.0008 0.7806

ai (8) 0.3308 0.2546 0.1806 0.0232 0.0452 0.0022 0.0049 0.0000 0.0011 0.0014 0.0008

aifi (9) 0.2657 0.2153 0.1143 0.0162 0.0344 0.0015 0.0043 0.0000 0.0010 0.0010 0.0007 0.6543

i¼1

0.7847

Table 7 Parameters pi, qi and ri of Eq. (20) for 5 main soil oxides SiO2, Al2O3, Fe2O3, FeO and TiO2. i

Oxide

pi

qi

ri

1 2 3 4 5

SiO2 Al2O3 Fe2O3 FeO TiO2

0.00198 0.00106 0.02218 0.02427 0.00733

 0.02434  0.02053  0.16327  0.18011  0.06979

0.15051 0.14152 0.50819 0.54579 0.30469

5.2% for grey and alluvial soils and 5.9% for red soil. In summary, we consider that the maximal relative uncertainties of the selfattenuation factors are about 6% for all soil types.

6. Determination of the

238

U activity for soil samples

Specific activity A (Bq/kg) of efficiency e as follows: A ðBq=kgÞ ¼

S

eITm

238

U is determined through the

0.7684

0.7063

6.1. Grey, alluvial and red soils Grey, alluvial and red soils were added with amounts of [238U]uranyl-acetate to enhance their counting statistics. The measurement was carried out for two grey soil samples with the densities of 1.077 g/cm3 and 1.347 g/cm3, one alluvial soil sample with the density of 1.069 g/cm3 and one red soil sample with the density of 0.918 g/cm3. For each sample, 4 configurations with the height values of 0.5 cm, 1.0 cm, 1.5 cm and 2.0 cm were measured and calculated. In Table 8, the parameters S, T, m and e are presented for each sample with 4 height values. Here the efficiency was determined according to formula e  e(meff,c,h,r)¼ e(0,h)exp(  meffh), in which e(0,h)  e(0,c,h,0) are taken from column 4 of Table 5 and meff(h,r)  meff(c,h,r)¼ a(h)r, where a(h)  a(c,h) are taken from columns 7 and 8 of Table 5 for the red soil and the average of grey and alluvial soils, respectively. From Table 8 it is revealed that average activities over 4 sample heights are in good agreement with reference activities, which were determined by quantities of [238U]uranyl-acetate added to soil samples. The activity of the sample matrix is neglected in comparison to that of [238U]uranyl-acetate.

ð22Þ

where S, I, T and m denote the area of the 63.3 keV experimental full energy peak, intensity of 63.3 keV gamma emission I¼0.0484 70.0048 (Firestone and Shirley, 1996; Yucel et al., 2009), measuring time in second and sample mass in kg, respectively. The determination of 238U activity was validated for some soil samples and an IAEA reference sample. The efficiency is determined from Eq. (10), in which e(0,c,h,0) from Eq. (12), a(c,h) from Eqs. (13)–(15) and meff(c,h,r) from Eq. (16). The relative uncertainty of the activity A is determined from Eq. (22): s 2 s 2 s 2 s 2 s 2 s 2 e m I T S A ¼ þ þ þ þ ð23Þ A S e I T m qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi where sS =S ¼ 5%; se =e ¼ ðseð0,c,h,0Þ =eð0,c,h,0ÞÞ2 þðsF 1 =F 1 Þ2  qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðseð0,c,h,0Þ =eð0,c,h,0ÞÞ2 þ ðsF 2 =F 2 Þ2 ¼ 0:012 þ 0:062 ¼ 6%;

sI =I ¼10%; sT =T and sm =m are less than 1% and can be neglected. So, the relative uncertainty of the activity is: rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s 2 s 2 s 2 sA e I S ¼ þ þ ¼ 0:052 þ 0:062 þ0:102  12:7%: A S e I

6.2. IAEA reference sample The reference sample IAEA-368 of 31 Bq/kg 238U activity, 1.291 g/cm3 density, 0.4 cm height and 0.021 kg mass was measured for 40 h. The area of 63.3 keV full energy peak was 169 717. Chemical composition of IAEA-368 marine sediment is close to that of grey and alluvial soils. The values e(0,h)¼0.0435 and a(h)¼0.1577 were taken from Eqs. (12) and (13), so the effective attenuation coefficient meff ¼a(h)r ¼0.2036 cm  1 and the efficiency e ¼ e(0,h)exp(  meffh)¼0.0401. The specific activity of this sample was equal to 29.1 74.4 Bq/kg according to Eq. (22). This value is in good agreement with that of 31 Bq/kg ranged within 25.0–33.0 Bq/kg for the IAEA-368 reference sample.

7. Conclusion The present work assumes a method for analyzing the 238U specific activity in soil samples via the 63.3 keV gamma rays by experimental measurement in the HPGe GC1518 p-type detector based gamma spectrometer and calculation with using MCNP5 code. In order to complete this analysis, it is important to make

N.Q. Huy et al. / Applied Radiation and Isotopes 71 (2013) 11–20

Table 8 Specific activities of

238

19

U for 2 grey soils, 1 alluvial soil and 1 red soil.

Height (cm)

0.5

Grey soil 1 r ¼1.077 g/cm3 S 3212 T (h) 6 m (kg) 0.0219 0.0396 e ¼ e(0,h)emef f h

1.0

938 1 0.0439 0.0348

A(Bq/kg) 3568.1 Grey soil 2 r ¼1.347 g/cm3 S 19102 T (h) 36 m (kg) 0.0275 0.0388 e ¼ e(0,h)emef f h

3555.0

A(Bq/kg) 2876.0 Alluvial soil r ¼ 1.069 g/cm3 S 532 T (h) 0.5 m (kg) 0.0218 0.0397 e ¼ e(0,h)emeff h

2951.9

A(Bq/kg) 7119.8 Red soil r ¼0.918 g/cm3 S 7849 T (h) 13 m (kg) 0.0187 0.0382 e ¼ e(0,h)emef f h

6434.0

A(Bq/kg)

5101.2

4888.7

937 1 0.0549 0.0335

844 0.5 0.0436 0.0348

359 0.333 0.0375 0.0326

1.5

2.0

1318 1 0.0659 0.0307

1573 1 0.0879 0.0273

3764.1

3787.4

1173 1 0.0824 0.0291

1435 1 0.1099 0.0256

2827.1

2954.5

1208 0.5 0.0654 0.0308 6941.6 396 0.333 0.0562 0.0282 4344.1

self-absorption corrections, which consist of chemical composition, geometry and density effects of these weak gamma rays in sample materials. The study of the above-mentioned effects was performed by application of self-attenuation factor, which is defined as the ratio between the counting efficiency for the actual sample and the counting efficiency for the same sample-detector geometry in the absence of self-attenuation. This factor was expressed by an exponential function F(meff,c,h,r)¼exp[ meff(c,h,r)h], where meff, c, h and r are the effective attenuation coefficient, chemical composition, sample height and sample density in the cylindrical container, respectively. The effective attenuation coefficient meff ¼ (ph2 þqhþr)r reflects the self-attenuation property of volumetric radioactive and attenuating samples. The self-attenuation factor F(meff,c,h,r)¼exp[ meff(c,h,r)h] and the counting efficiency e(meff,c,h,r)¼ e(0,c,h,0)F(meff,c,h,r), where e(0,c,h,0) is the efficiency without self-attenuation, were calculated by MCNP5 code for the main soil types of Vietnam, which are grey, alluvial and red soils. The efficiency e(meff,c,h,r) was applied for determining the 238U activities in some soil samples via 63.3 keV gamma rays. The obtained 238U activities were in good agreement with those derived by other methods.

Acknowledgments The authors express their thanks to Mr. Nguyen Van Mai and Mr. Ninh Duc Tuyen for their help in use of the GC1518 detector based gamma spectrometer. This work is completed with the financial support from the Vietnam’s National Foundation for Science and Technology Development (NAFOSTED), code 103.04.01.09. References Abbas, M.I., 2001. HPGe detector photopeak efficiency calculation including selfabsorption and coincidence corrections for Marinelli beaker sources using compact analytical expressions. Appl. Radiat. Isot. 54, 761–768. Boshkova, T., Minev, L., 2001. Corrections for self-attenuation in gamma-ray spectrometry of bulk samples. Appl. Radiat. Isot. 54, 777–783.

Average activity (Bq/kg)

Reference activity (Bq/kg)

3668.67 249.5

3664

2902.4 7 197.4

2963

6843.77 465.4

7137

5058.7 7 645.6

4896

28401 10 0.0872 0.0274 6879.5 626 0.333 0.0749 0.0246 5900.7

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