Determining photon energy absorption parameters for different soil samples.

The mass attenuation coefficients (μs) for five different soil samples were measured at 661.6, 1173.2 and 1332.5 keV photon energies. The soil samples were separately irradiated with (137)Cs and (60)Co (370 kBq) radioactive point gamma sources. The measurements were made by performing transmission experiments with a 2″ × 2″ NaI(Tl) scintillation detector, which had an energy resolution of 7% at 0.662 MeV for the gamma-rays from the decay of (137)Cs. The effective atomic numbers (Zeff) and the effective electron densities (Neff) were determined experimentally and theoretically using the obtained μs values for the soil samples. Furthermore, the Zeff and Neff values of the soil samples were computed for the total photon interaction cross-sections using theoretical data over a wide energy region ranging from 1 keV to 15 MeV. The experimental values of the soils were found to be in good agreement with the theoretical values. Sandy loam and sandy clay loam soils demonstrated poor photon energy absorption characteristics. However, clay loam and clay soils had good photon energy absorption characteristics.

INTRODUCTION

Soils have chemical composition characterized by the presence of major compounds, such as Si02, Al203, CaO, Fe2O3 and MgO, and have physical properties, including water holding capacity, moistness, particle density, appearance density, porosity, and the concentrations of sand, silt, clay and loam. Soils also contain microelements such as Zn, Cu, Fe and Mn.

The gamma-ray transmission method has been reported as the most accurate and convenient technique for non-destructive measurements of soil parameters, including the linear attenuation coefficient, field capacity, moisture content, bulk density and porosity [1]. In laboratory experiments, lead is used for shielding purposes. In field conditions, soil may be used as a radiation shielding material. The use of soil as the shielding is advantageous from the perspectives of cost and availability [2]. To interpret the behavior and performance of soils as radiation shielding materials, it is important to identify soil photon energy absorption parameters, such as the mass attenuation coefficients (µ), the effective atomic numbers (Z) and the effective electron densities (N).

The photon attenuation coefficient is an important parameter that characterizes the penetration and diffusion of gamma-rays in composite materials such as soils [3]. This coefficient is a measure of the average number of interactions that occur between gamma-rays and the matter mass per unit area. The μ depends on the chemical composition of the absorbing material and the incident photon energy. However, for the total photon interaction, the variation of µ with the soil composition is large below 50 keV, and negligible above 300 keV, up to 3 MeV [4]. Studies of Z provide conclusive information about the target related to the radiation interactions [5]. A commonly used method to determine the Z value for a composite material is based on the determination of the µ values for gamma-ray interactions using the transmission method. Z represents the interaction of radiation with the matter being studied, and is a convenient parameter to consider when designing radiation shields and computing the absorbed dose, energy absorption and exposure build-up factors. The Z and N values vary with energy, depending on the interaction processes involved. The energy absorption in a given medium can be calculated if certain constants are known. These necessary constants are the Z and N values of the medium. Consequently, these constants have been defined and computed in many different ways by various researchers [6-42]. However, only a limited amount of work has been reported in the literature on the photon energy absorption parameters for different soil samples [43-55]. Therefore, this work concentrates on the theoretical and experimental determination of the photon energy absorption parameters of different soils. Photon energy absorption parameters (i.e. µ, Z and N) were calculated for photon energies in the range 1 keV–15 MeV, and the results were compared with the measurements obtained with photon energies of 661.6, 1173.2 and 1332.5 keV for five different soil samples, i.e. Soils 1, 2, 3, 4 and 5. The soils under consideration were collected from Bursa (Turkey). The gamma-ray attenuation measurements were performed using 137Cs and 60Co radioactive sources.

MATERIALS AND METHODS

Theory

When a gamma-ray beam passes through a soil sample of thickness x (cm), the photons are transmitted according to Beer–Lambert's law [56]. This process is expressed as follows: where I is the initial intensity of the gamma-rays, I is intensity of the gamma-rays after attenuation through a soil column of length x, and μ (cm−1) is the linear attenuation coefficient of the dry soil. The linear attenuation coefficient can be described as follows: where µ = μ/ρ (cm2/g) is the mass attenuation coefficient and ρ is the density of the soil sample. Equation (1) can be rewritten as follows: where d (g/cm2) is the mass thickness of the dry soil sample. Equation (3) may be written in the following linear form: µ can be obtained from the measured values of and d. The total µ values for materials composed of multiple elements are the sums of the (µ) values of each constituent element according to the following mixture rule [57]: where W is the fractional atomic mass of the elements and (µ) is the mass attenuation coefficient of the ith element in the mixture. For materials composed of multiple elements, the fraction by atomic mass is given by where A is the atomic weight of the ith element and n is the number of formula units. The total atomic cross-sections (σt) for the sample can be obtained from the measured values of µ using the following relation [58]: where N is Avogadro's number. The total electric cross-section (σe) is given by the following formula [22]: where is the number fraction of the atoms of element i relative to the total number of the atoms of all elements in the mixture, and is the atomic number of the ith elements in the mixture. and are related to the Z of the material through the following expression [22]: The N (number of electrons per unit mass) can be written as following: The µ values of the materials have been calculated using the WinXCom program [59]. This well-known and widely used program provides the total mass attenuation coefficient and total attenuation cross-section data for approximately 100 elements, as well as the partial cross-sections for incoherent and coherent scattering, photoelectric absorption and pair production at energies from 1 keV to 100 GeV [59]. All computations in the present work have been performed using the WinXCom program.

Experimental details

The soil samples used in this study were taken from a soil tillage depth. The soils were classified as Entisol (Soil 1, Soil 2, and Soil 5), Inceptisol (Soil 3) and Alfisol (Soil 4), according to the Soil Taxonomy [60]. According to the results of the soil analysis, the soils were primarily medium-textured, had neutral or slightly alkaline pHs, contained different amounts of lime, and primarily had a low organic matter content. There was no salinity problem in the soils. The soil samples considered were analyzed for the percentage of clay, silt and sand using the hydrometer method [61]. Some physical characteristics of the soils, along with their sample codes, are presented in Table 1.

Table 1.

Some physical characteristics of the soils

Soil code	Geographic coordinate of the soils		Soil type	Particle size distribution (%)
	X(East)	Y (North)		Sand	Silt	Clay	TC	ρ (g/cm3)
Soil 1	599956	4449947	Entisol	35.3	42.0	22.7	L	1.38
Soil 2	598362	4451236	Entisol	58.6	22.0	19.4	SL	1.45
Soil 3	698495	4491031	Inceptisol	59.1	18.0	22.9	SCL	1.42
Soil 4	651463	4449239	Alfisol	29.3	18.0	52.7	C	1.24
Soil 5	633706	4425913	Entisol	30.0	42.0	28.0	CL	1.34

TC = Soil Texture Class, L = Loam, SL = Sandy Loam, SCL = Sandy Clay Loam, C = Clay, CL = Clay Loam. (The texture classes are based on USDA classification).

The soil samples were passed through a 2-mm sieve. Each soil was then dried in a 105ºC oven for 24 h and packed in a Perspex box. The chemical composition of the soil samples were analyzed using an energy-dispersive X-ray fluorescence (EDXRF) spectrometer from SPECTRO (X-LAB 2000), which had a 400 W Pd end-window X-ray tube, sample trays for 32 mm (20 positions) and 40 mm (12 positions) samples, 47 mm Teflon filters, and an N2-cooled Si (Li) detector with the required electronics (i.e. amplifier, ADC and multichannel analyzer). The EDXRF analyses (major-element compositions and trace-element analyses) were performed in the Bursa Test and Analysis Laboratory (BUTAL). The chemical compositions of these soil samples are given in Table 2. The soil samples studied have different chemical composition and different fractions (i.e. sand, silt and clay).

Table 2.

EDXRF analysis results of the dry soil samples

Soil code	Chemical components (%)
	Na2O	MgO	Al2O3	SiO2	P2O5	K2O	CaO	TiO2	Cr2O3	MnO	Fe2O3	LOI
Soil 1	1.39	2.442	14.62	63	0.170 3	2.79	6.78	0.595 1	0.017 81	0.073 3	4.312	3.6
Soil 2	2.02	1.3	12.75	78.4	0.321 05	2.51	1.76	0.503 1	0.010 97	0.073 535	2.79	<1
Soil 3	2.45	1.04	16.1	68.3	0.125 85	1.644	3.89	0.638 6	0.007 3	0.109 55	5.791	<1
Soil 4	0.230 5	1.94	13.14	55.9	0.112 55	1.91	11	0.599 55	0.027 095	0.096 44	4.53	10
Soil 5	0.11	9	10.66	39.62	0.221 4	0.379 45	15.9	0.413 1	0.037 78	0.053 13	4.38	19.2

LOI = Loss of Ignition

The schematic arrangement of the experimental set-up used in the present study is shown in Fig. 1. The soil samples were kept in a polyethylene box that was 6.5 cm high and 11 cm in diameter. The point sources were placed on the symmetry axis of the polyethylene box and over the soil level. The samples were separately irradiated with 137Cs (661.6 keV) and 60Co (1173.2 and 1332.5 keV) radioactive point sources. Each source had an activity of 10 µCi (370 kBq). The pulse-height spectra of the gamma-rays transmitted through the soil were measured using a 2″ × 2″ cylindrical NaI(Tl) detector connected to the Canberra Series 40 Multi-Channel Analyzer (MCA) system with 2048 channels. The detector was positioned on the symmetry axis of the box. The detector assembly was surrounded by lead shielding. Both the soil sample and the point source were also surrounded by lead collimators inside the lead castle.

Fig. 1.

The schematic arrangement of the experimental setup.

The measurements for all samples were taken to have good statistics and performed three times for each energy value to improve the statistical error. The transmitted spectra were recorded with the MCA for a time period that was sufficient to obtain the desired precision and accuracy of the results. The peak areas were calculated from the spectra obtained for each measurement. The µ values of the soils were calculated from Equation (4) for known physical densities using the gamma transmission measurements for the dry soil samples.

The maximum errors in the total mass attenuation coefficients were calculated from the errors in the intensities I (without sample) and I (with sample) and the errors in the physical densities, using the following relation: where χ is the sample thickness in centimeters, , and are the errors in the intensities and and the density , respectively. In these experiments, the net counts I0 and I were obtained for the same amount of time and under the same experimental conditions. The overall uncertainty ithe experimental measurements was < 3%. This uncertainty is mainly due to the counting statistics, the thickness measurements, the evaluation of the peak areas, and the scattered photons reaching the detector.

RESULTS AND DISCUSSION

The µ values for the different soil samples were also calculated for photon energies in the range of 1 keV–15 MeV. The results were plotted versus the photon energy with the measurement values for energies of 661.6, 1173.2 and 1332.5 keV in Fig. 2. The experimental and theoretical results are clearly in good agreement for all of the studied soil samples. Figure 2 shows that the µ values are large and show a decreasing trend, with strong energy dependence in the low incident photon energy range of 1–100 keV. In the intermediate (100 keV–1 MeV) and high (1–15 MeV) energy regions, the µ values show a less energy-dependent behavior and gradually decrease with the increasing incident photon energy. Fig. 3 shows the incident photon energy dependence of the measured µ values for all of the studied soils.

Fig. 2.

The calculated mass attenuation coefficients of the soil samples within the 1 keV–15 MeV photon energy range and a comparison between measurements and photon energies.

Fig. 3.

Measured mass attenuation coefficients of the soil samples at 661.6, 1173.2 and 1332.5 keV.

Note that µ depends on the incoming photon energies because the partial photon-matter interactions (such as photoelectric absorption, Compton scattering and pair production) in the nuclear and electric fields are different for different photon energies. Due to the dominant photoelectric absorption, the µ values show a strong incident photon energy dependence in the low energy range because µ is inversely proportional (1/E3.5 dependence) to the incident energy. The differences observed in the µ values for the soils in the low energy region can be attributed to the dominance of photoelectric absorption because the photoelectric cross-section is strongly dependent (Z4 or Z5 dependence) on the atomic number of the constituent elements [16, 62].

Compton (inelastic) scattering starts to dominate over the photoelectric absorption process when the incident photon energy exceeds ∼100 keV, up to ∼1 MeV. In this intermediate energy range, no significant differences in the behavior of the different soils are observed because the composition effects play a less significant role in Compton scattering (linear Z dependence) relative to photoelectric absorption.

In the high energy region, the pair production processes in the nuclear and electric fields come into prominence after certain thresholds above 1 MeV are exceeded. The energy dependence of µ thus changes its slope relative to the intermediate energy region.

The Z values for all soil samples have been calculated using Equation (9) for photon energies in the range of 1 keV–15 MeV in 36 energy steps. The results have been plotted against the photon energies, as shown in Fig. 4. In this figure, the theoretical results were also compared with the experimental results performed with photon energies of 661.6, 1173.2 and 1332.5 keV. A good agreement between the theoretical and measurement results has clearly been obtained. The Z values of the soil samples change with a change in the energy. However, the behavior of Z with respect to the energy is rather interesting. The Z values for all of the soil samples show a small decrease with increasing energy in the range of 1–1.5 keV and a sharp increase with increasing energy in the range of 1.5–2 keV. The Z values then sharply decrease again with increasing energy up to 8 keV (up to 10 keV for Soils 2 and 4). The Z values are nearly constant between 8 and 40 keV photon energies (in the energy region of 10–30 keV for Soils 2 and 4). Beyond this energy region, the Z values increase again with increasing energy in the range of 40–300 keV. The Z values are then nearly constant again in the energy region of 300 keV–5 MeV and decrease again with increasing energy, up to 15 MeV. This decrease in the Z values is small but continuous.

Fig. 4.

The effective atomic number of the soil samples as a function of photon energy.

This significant variation in the Z values for all of the soil samples is because of the relative domination of the partial photon interaction mechanism (e.g. photoelectric absorption, Compton scattering and pair production). This variation also depends on the range of the atomic numbers of soil constituent elements and the number of elements in the composite material. The atomic numbers of the elements of the selected soils vary from 8 (O2) to 26 (Fe), and a total of 12 elements are considered. As expected, the Z values of the soils lie within the range of the atomic numbers of their constituent elements (8 < Z <26).

The N values for all of the soil samples have been calculated using Equation (10) for photon energies in the range of 1 keV–15 MeV in 36 energy steps. The results have been plotted against photon energies, as shown in Fig. 5. In this figure, the theoretical results were also compared with the experimental results obtained with photon energies of 661.6, 1173.2 and 1332.5 keV. There are slight differences in the N values for different soils, where a higher value of the electron density would indicate an increased probability of a photon-electron energy transfer and an energy deposition into the material. The N values show a photon–energy dependence similar to that observed for Z. This is confirmed in Fig. 6, which shows the correlation of the Z and N values obtained from the theoretical calculation and experimental results.

Fig. 5.

The effective electron density of the soil samples as a function of photon energy.

Fig. 6.

Correlation between the effective atomic number and the electron density of the soils for the theoretical and experimental results.

Different proportions of sand, silt and clay give rise to the different types of loam soils: loam (L), sandy loam (SL), sandy clay loam (SCL), clay (C), clay loam (CL), silt loam and silt clay loam. Sandy loam, due to the larger size of its particles, feels gritty. Clay loam, due to the smaller size of its particles, feels sticky. Silt loam, being moderate in size, has a smooth or floury texture. From Table 1, it can be observed that Soils 1, 2, 3, 4 and 5 have the texture classes of L, SL, SCL, C and CL, respectively. Soils 2 (SL) and 3 (SCL) demonstrate poor photon energy absorption characteristics (i.e. low µ, Z and N). However, Soils 5 (CL) and 4 (C) soils have good photon energy absorption characteristics (i.e. high µ, Z and N). These results may be due to the compositional variation among the different types of the soils and the effects of the soil grain size on the gamma-ray attenuation. Furthermore, it can be observed from Table 2 that Soil 5 (CL) has the minimum percentage of SiO2 (39.62%) and the maximum contribution of CaO (15.9%), whereas Soil 2 (SL) has the minimum amount of CaO (1.76%) and the maximum percentage of SiO2 (78.4%). The photon energy-absorption parameters of the clay loam are higher where the CaO weight percentage is greater and that of SiO2 is smaller. The photon energy absorption parameters of sandy loam are also lower where the SiO2 weight percentage is greater and that of CaO is smaller.

CONCLUSION

It can be concluded from this work that the photon energy-absorption parameters depend on the photon energies and the chemical composition of the soil samples. A good agreement was observed between the theoretical calculations and experimental results. The dependence of µ on both the photon energy and soil composition is remarkable in the low incident energy range due to the dominant photoelectric absorption mechanism. The compositional effects and photon energy dependencies are reduced from the intermediate energy range to the high energy range because Compton scattering and pair production processes start to dominate the photon absorption process.

Among the investigated soil samples, the photon absorption effectively increases in the following order: Soil 5 (clay loam) > Soil 4 (clay) > Soil 1 (loam) > Soil 3 (sandy clay loam) > Soil 2 (sandy loam). The sandy loam and sandy clay loam soils demonstrate poor photon energy absorption characteristics (i.e. low µ, Z and N). However, the clay loam and clay soils have good photon energy absorption characteristics (i.e. high µ, Z and N).

FUNDING

This work was supported by the Commission of Scientific Research Projects of Uludag University, Project Number UAP(F)-2011/74.