# The Mass Attenuation Coefficients, Electronic, Atomic, and Molecular Cross Sections, Effective Atomic Numbers, and Electron Densities for Compounds of Some Biomedically Important Elements at 59.5 keV

Authors: Burcu Akça; Salih Z. Erzeneoğlu
Journal: Science and Technology of Nuclear Installations
 (2014)

---

## Abstract

The mass attenuation coefficients for compounds of biomedically important some elements (Na, Mg, Al, Ca, and Fe) have been measured by using an extremely narrow collimated-beam transmission method in the energy 59.5 keV. Total electronic, atomic, and molecular cross sections, effective atomic numbers, and electron densities have been obtained by using these results. Gamma-rays of241Am passed through compounds have been detected by a high-resolution Si(Li) detector and by using energy dispersive X-ray fluorescence spectrometer (EDXRF). Obtained results have been compared with theoretically calculated values of WinXCom and FFAST. The relative difference between the experimental and theoretical values are −9.4% to +11.9% with WinXCom and −11.8% to +11.7% FFAST. Results have been presented and discussed in this paper.


---

## Body

## 1. Introduction

The photon mass attenuation coefficient, effective atomic number, and electron density are the basic quantities required in determining the penetration of X andγ-ray in matter. The mass attenuation coefficient is a measure of the probability of the interaction that occurs between incident photons and the matter of the unit mass per unit area. The knowledge of the mass attenuation coefficients of X and γ-ray in biological and other important materials is of significant interest for industrial, biological, agricultural, and medical applications [1]. Additionally, the mass attenuation coefficient provides a wide variety of information about fundamental properties of the matter in the atomic and molecular level. Accurate values of the photon mass attenuation coefficients are required to provide essential data in diverse fields such as nuclear diagnostics (computerized tomography), radiation protection, nuclear medicine, radiation dosimetry, gamma ray fluorescence studies, and radiation biophysics. The mass attenuation coefficients are also widely used in the calculation of the photon penetration and the energy deposition in biological shielding and other dosimetric materials.Biomedically important elements are those that are required by an organism to maintain its normal physiological function. Without biomedically important elements, the organism cannot complete its normal life cycle or achieve normal healthy growth; such elements are the key components of the metalloenzymes and are involved in crucial biological functions, such as oxygen transport, free radical scavenging, and hormonal activity. Biomedically important elements deficiency or excess with respect to the human physiological level are found in the patients with certain diseases, including cancer [2–4].In the literature, a variety of experimental data relevant to the measurement of the mass attenuation coefficients of different samples is available. The mass attenuation coefficients, effective atomic numbers, and electron densities of some amino acids in the energy range 0.122–1.330 MeV have been carried out [5]. The mass attenuation coefficients for mono- and disaccharides at photon energies 8.136, 13.596, 17.781, 22.581, and 32.890 keV have been measured [6]. The photon mass energy absorption coefficient for biological samples in the energy range 200–1500 keV has been measured [7]. The measured values have been compared with the computed values obtained using personal computer software package WinXCom [7].In the present work, we have measured the mass attenuation coefficients, total electronic, atomic, and molecular cross sections, and effective atomic numbers and the electron densities have been obtained by using these results for Al, AlCl3, Al(NO3)3, Ca, CaSO4, CaF2, CaHPO4, CaO6C6H10, Fe, FeCl2, FeCl3, Fe2(SO4)3, Mg(NO3)2, MgO, NaO2C2H3, Na2CO3, NaF, NaNO3, Na2SO4, NaCl, and Na2SO3 in the energy 59.5 keV. The measured values have been compared with the theoretical ones calculated by using WinXCom and FFAST.


## 2. Theory

Whenγ-ray beam passes through an absorber, it is attenuated. The degree of attenuation depends on the scattering and various absorption processes. The absorption coefficient μ can be derived from the Lambert-Beer law
(1)I=I0e-μt,
where I0 is the incident γ-ray intensity when measured without sample, I is γ-rays intensity transmitted through the sample, and t is the sample thickness (cm). The experimental mass-absorption coefficient (μ/ρ) of elements is given by
(2)μρ=1ρtln⁡⁡(I0I),
where ρ is the material density (g/cm3). The theoretical mass-absorption coefficient μ/ρ (cm2/g) for any chemical compound or mixture of elements is given by mixture rule [1]
(3)(μρ)=∑iwi(μρ)i,
where wi and (μ/ρ)i are the weight fraction and mass attenuation coefficient of the ith constituent element, respectively. (μ/ρ) does not depend on the particular phase (gas, liquid, or solid) of the material; therefore, it is useful to define the mass attenuation coefficient. For a chemical compound, the fraction by weight (wi) is given by
(4)wi=niAi∑iniAi.
Mass attenuation coefficients of the given materials have been calculated by the WinXCom program. This program which is based on the DOS-based compilation XCom [11] provides the total mass attenuation coefficient and the total attenuation cross-section data for about 100 elements as well as partial cross sections for incoherent and coherent scattering, photoelectric absorption, and pair production at energies from 1 keV to 100 GeV [12]. The values of the mass attenuation coefficients can be used to determine the total molecular cross section, σt,m, by the following relation [13]:
(5)σt,m=(μρ)MNA,
where M is the molecular weight and NA is Avogadro’s number. The total atomic cross-section σt,a can be easily determined from the following equation [13]:
(6)σt,a=1NA∑ifiAi(μρ)i=σt,m∑ini,
where fi is the fractional abundance of element i with respect to the number of atoms; ni and Ai are the number of formula units and the atomic weight, respectively, of the constituent element i. The total electronic cross-section σt,el for the individual element is expressed by the following formula [14]:
(7)σt,el=1NA∑ifiAiZi(μρ)i=σt,aZeff.
The total atomic and electronic cross sections are related to the effective atomic number (Zeff) through the following relation:
(8)Zeff=σt,aσt,el.
The effective electron number or electron density, Ne (number of electrons per units mass), can be derived from [14–17]
(9)Ne=(μ/ρ)σt,el=NAMZeff∑ini=NAZeff〈A〉.
The average atomic weight or average atomic mass is the ratio of the molecular weight of the sample divided by the total number of the atoms of all types presented in the compound. 〈A〉 can be derived from [14]
(10)〈A〉=M∑ini.


## 3. Experimental Setup

The schematical arrangement of the experimental setup used in this study is shown in Figure1. It consists of a 3.7 × 109 Bq (100 mCi) 241Am point source, which essentially emits monoenergetic (59.5 keV) γ-rays. The powder samples have been compressed into pellets for 10 s at 15 ton by using a manual hydraulic press. Target has had a diameter of 13 mm. The powder samples have been prepared for four different mass that the best mass attenuation coefficients to obtain. ln⁡I-t graphs have been drawn by using Origin Pro8. Slope of graphs has obtained linear attenuation coefficients and later the mass attenuation coefficients have obtained the linear attenuation coefficients of the samples divided by density of the samples. Sample graph for Al(NO3)3 is shown in Figure 2.Figure 1
Experimental arrangement.Figure 2
A sample graph for Al(NO3)3.The intensities ofγ-rays have been measured using a high-resolution Si(Li) detector (FWHM of 160 eV at 5.96 keV) and the data were collected into 4096 channels of a multichannel analyzer. The spectra have been collected for a period of 1000 s. The counting electronics have included a pile-up rejection circuit and a live-time clock used for dead time correction. The dead time has been observed for all the channels which vary at minimum 1.32% and at maximum 11.10%. A typical spectrum of 59.5 keV gamma ray transmissions through MgO is shown in Figure 3.Figure 3
Spectrum of 59.5 keV gamma rays obtained with absorber (MgO).Theoretical values of mass attenuation coefficients for Al, AlCl3, Al(NO3)3, Ca, CaSO4, CaF2, CaHPO4, CaO6C6H10, Fe, FeCl2, FeCl3, Fe2(SO4)3, Mg(NO3)2, MgO, NaO2C2H3, Na2CO3, NaF, NaNO3, Na2SO4, NaCl, and Na2SO3 have been obtained using WinXCom [12] and FFAST [18].In this study, effort has been made to reduce the error sources in transmission measurements. In an ideal transmission experiment, all photons must be sent on absorber sample with a parallel beam. But in real experimental studies, there is the same errors. The errors in the present measurements are mainly due to counting statistics, nonuniformity of the absorber, impurity content of the samples, and scattered photons reaching the detector. These errors are attributed to the deviation from the average value in theI and I0 (<1.3%), sample thickness (<0.7%), the mass of sample (<0.2%), and systematic errors (<0.8%). Also, the ratio of theoretical (T) and experimental (E) values is ≤1.1% The maximum errors in the mass attenuation coefficients have been calculated from errors in incident (I0) and transmitted (I) intensities and areal density (t) by using the propagation of error formula
(11)Δ(μρ)=1t(ΔI0I0)2+(ΔII)2+(ln⁡⁡I0I)2(Δtt)2,
where ΔI0, ΔI, and Δt are the errors in the intensities I0, I, and thickness t of the sample, respectively.


## 4. Results and Discussion

The theoretical mass attenuation coefficients, total electronic, atomic, and molecular cross-sections, effective atomic numbers, and electron densities have been investigated by using WinXCom and FFAST. WinXCom is a program or dataset based on the mixture rule. The values in the FFAST dataset have been calculated by different methods and may produce different results. The experimental results are in good agreement with the theoretical values, calculated by WinXCom and FFAST. This study and other several studies have been compared in Table1. To the best of our knowledge there are no experimental data reported in the literature other than those shown in Table 1 for these compounds at 59.5 keV γ-rays.Table 1
Comparison of this study and other several studies.
Samples
Some atomic parameters
[8]
[9]
[10]
This study
Al
σ
t
,
m
—
12.4
—
12.6
σ
t
,
a
—
12.4
—
12.6
Z
eff
13.0
13.0
—
13.0
Fe
σ
t
,
m
—
119.3
—
117.8
σ
t
,
a
—
119.3
—
117.8
Z
eff
26.0
26.0
—
26.8
MgO
σ
t
,
m
—
—
—
15.3
σ
t
,
a
—
—
—
7.6
Z
eff
—
—
10.2
10.0
Na2CO3
σ
t
,
m
—
—
—
38.6
σ
t
,
a
—
—
—
6.4
Z
eff
—
—
9.5
9.5The theoretical and experimental mass attenuation coefficients, total electronic, atomic, and molecular cross-sections, effective atomic numbers, and electron densities for compounds of biomedically important elements are listed in Tables2, 3, and 4. It is clearly seen that the mass attenuation coefficient depends on chemical content.Table 2
The experimental mass attenuation coefficients (cm2/g), total atomic (barn/atom) and molecular (barn/atom) cross sections, effective atomic numbers, and electron densities (electrons/g) for compounds of biomedically important some elements.
Samples
μ/ρ
σ
t
,
a
σ
t
,
m
Z
eff
N
e  ×  1023
Al
0.282 ± 0.026
12.638 ± 1.165
12.638 ± 1.165
13.029 ± 1.201
2.907 ± 0.268
AlCl3
0.375 ± 0.010
20.765 ± 0.554
83.061 ± 2.215
14.832 ± 0.396
2.679 ± 0.071
Al(NO3)3
0.207 ± 0.005
5.633 ± 0.136
73.231 ± 1.769
8.535 ± 0.206
3.136 ± 0.076
Ca
0.647 ± 0.011
43.076 ± 0.732
43.076 ± 0.732
19.317 ± 0.328
2.901 ± 0.049
CaF2
0.401 ± 0.051
17.337 ± 2.205
52.010 ± 6.615
14.569 ± 1.853
3.370 ± 0.429
CaHPO4
0.354 ± 0.033
11.430 ± 1.066
80.009 ± 7.458
12.290 ± 1.146
3.806 ± 0.355
CaO6C6H10
0.267 ± 0.007
4.208 ± 0.110
96.785 ± 2.537
6.474 ± 0.170
4.108 ± 0.108
CaSO4
0.429 ± 0.035
16.169 ± 1.319
97.017 ± 7.915
15.698 ± 1.281
4.165 ± 0.340
Fe
1.270 ± 0.225
117.823 ± 23.657
117.823 ± 23.657
26.839 ± 5.389
2.893 ± 0.581
FeCl2
0.785 ± 0.043
55.093 ± 3.018
165.280 ± 9.054
22.126 ± 2.040
3.153 ± 0.291
FeCl3
0.689 ± 0.024
46.413 ± 1.617
185.652 ± 6.467
20.537 ± 0.715
3.049 ± 0.106
Fe2(SO4)3
0.485 ± 0.056
18.950 ± 2.188
322.154 ± 37.197
15.661 ± 1.808
4.008 ± 0.463
Mg(NO3)2
0.191 ± 0.005
5.228 ± 0.137
47.052 ± 1.232
7.921 ± 0.207
2.894 ± 0.076
MgO
0.228 ± 0.031
7.632 ± 1.038
15.263 ± 2.075
10.042 ± 1.365
3.000 ± 0.408
NaO2C2H3
0.208 ± 0.005
3.543 ± 0.085
28.343 ± 0.681
5.808 ± 0.140
3.410 ± 0.082
Na2CO3
0.219 ± 0.015
6.426 ± 0.440
38.558 ± 2.641
9.450 ± 0.647
3.221 ± 0.221
NaF
0.210 ± 0.040
7.324 ± 1.395
14.648 ± 2.790
9.897 ± 1.885
2.838 ± 0.541
NaNO3
0.189 ± 0.011
5.337 ± 0.311
26.683 ± 1.553
8.086 ± 0.471
2.864 ± 0.167
Na2SO3
0.287 ± 0.020
10.015 ± 0.698
60.089 ± 4.187
12.364 ± 0.862
3.543 ± 0.247
Na2SO4
0.237 ± 0.023
9.202 ± 0.775
64.413 ± 5.427
11.648 ± 0.981
3.456 ± 0.291
NaCl
0.343 ± 0.026
16.649 ± 1.262
33.297 ± 2.524
14.230 ± 1.079
2.932 ± 0.222Table 3
The theoretical (WinXCom) mass attenuation coefficients (cm2/g), total electronic (barn/atom), atomic (barn/atom), and molecular (barn/atom) cross sections, effective atomic numbers, and electron densities (electrons/g) for compounds of biomedically important some elements.
Samples
μ/ρ
σ
t
,
el
σ
t
,
a
σ
t
,
m
Z
eff
N
e  ×  1023
Al
0.281
0.970
12.597
12.594
12.983
2.897
AlCl3
0.413
1.400
22.869
91.477
16.335
2.950
Al(NO3)3
0.201
0.660
5.470
71.108
8.288
3.046
Ca
0.671
2.230
44.674
44.674
20.033
3.009
CaF2
0.438
1.190
18.936
56.809
15.913
3.681
CaHPO4
0.371
0.930
11.979
83.851
12.880
3.989
CaO6C6H10
0.281
0.650
4.429
101.860
6.813
4.323
CaSO4
0.384
1.030
14.473
86.840
14.052
3.728
Fe
1.230
4.390
114.112
114.112
25.994
2.802
FeCl2
0.792
2.490
55.585
166.754
22.324
3.181
FeCl3
0.717
2.260
48.299
193.197
21.371
3.173
Fe2(SO4)3
0.535
1.210
20.904
355.366
17.276
4.421
Mg(NO3)2
0.201
0.660
5.502
39.515
8.336
3.045
MgO
0.233
0.760
7.799
15.998
10.143
3.030
NaO2C2H3
0.202
0.610
3.441
27.525
5.640
3.311
Na2CO3
0.206
0.680
6.045
36.269
8.889
3.029
NaF
0.213
0.740
7.428
14.857
10.038
2.878
NaNO3
0.200
0.660
5.647
28.236
8.556
3.030
Na2SO3
0.261
0.810
9.108
54.645
11.244
3.222
Na2SO4
0.253
0.790
8.528
59.695
10.795
3.203
NaCl
0.361
1.170
17.522
35.045
14.976
3.085Table 4
The theoretical (FFAST) mass attenuation coefficients (cm2/g), total electronic (barn/atom), atomic (barn/atom), and molecular (barn/atom) cross sections, effective atomic numbers, and electron densities (electrons/g) for compounds of biomedically important some elements.
Samples
μ/ρ
σ
t
,
el
σ
t
,
a
σ
t
,
m
Z
eff
N
e  ×  1023
Al
0.289
0.996
12.952
12.952
13.004
2.902
AlCl3
0.425
1.441
23.534
94.135
16.332
2.949
Al(NO3)3
0.208
0.678
5.660
73.584
8.348
3.068
Ca
0.681
2.267
45.340
45.340
20.000
3.004
CaF2
0.448
1.225
19.369
58.106
15.811
3.657
CaHPO4
0.379
0.960
12.237
85.659
12.747
3.948
CaO6C6H10
0.287
0.672
4.523
104.035
6.731
4.271
CaSO4
0.393
1.053
14.813
88.875
14.067
3.732
Fe
1.260
4.496
116.895
116.895
26.000
2.802
FeCl2
0.812
2.559
56.988
170.965
22.270
3.173
FeCl3
0.735
2.316
49.512
198.047
21.378
3.174
Fe2(SO4)3
0.549
1.243
21.451
364.665
17.257
4.417
Mg(NO3)2
0.206
0.676
5.639
50.747
8.342
3.048
MgO
0.236
0.768
7.899
15.799
10.285
3.073
NaO2C2H3
0.208
0.628
3.543
28.343
5.642
3.312
Na2CO3
0.212
0.702
6.221
37.325
8.862
3.020
NaF
0.220
0.759
7.673
15.345
10.109
2.899
NaNO3
—
—
—
—
—
—
Na2SO3
0.269
0.837
9.387
56.320
11.215
3.214
Na2SO4
0.261
0.812
8.797
61.582
10.834
3.214
NaCl
0.371
1.203
18.008
36.015
14.969
3.084The effective atomic number is a useful parameter for low and medium-Z materials, encountered in biological and medical applications. It should be remembered that the concept of the effective atomic number is based on an underlying theory of X-ray and γ-ray interactions with matter [19]. In composite materials like alloys, soil, plastic, biological material, and so forth, for photon interactions, the atomic number cannot be represented uniquely across the entire energy region, as in the case of elements, by a single number. This number in composite materials is called “effective atomic number,” and it varies with energy [20]. The energy absorption in a given medium can be calculated if certain constants are known. These necessary constants are Zeff and electron density (Ne) of the medium. Therefore, the study of the effective atomic numbers of the biological samples is so useful for many technological applications. The effective atomic numbers are also useful in medical radiation dosimetry for the calculation of dose in radiation therapy and medical imaging [21]. The experimental effective atomic numbers are listed in Table 2. The effective atomic number for gamma ray interactions in materials composed of various elements cannot be expressed by a single number and for each of the partial processes the number has to be weighted differently [22]. A large Zeff generally corresponds to inorganic compounds and metals, while a small Zeff≤10 is an indicator of the organic substances [23]. Experimental determination of effective atomic number is important, and effective atomic number is studied as the only interpolation procedures and semiempirical expressions [16, 20, 22, 24–26]. The significant variation in effective atomic number is due to the relative dominance of the partial photon interaction processes. This confirms that effective atomic number depends on the number of elements and the range of atomic numbers in a compound. References [27, 28] confirm that the effective atomic numbers almost tend to be constant as a function of energy and attributes to the dominance of incoherent scattering and pair production in their respective energy region. But we have not confirmed this state, for our energy is below 100 keV (single energy 59.5 keV) and photoelectric cross sections are more dominant in respective energy region. [22, 29], especially, up to 50 keV. That is, the effective atomic number is affected by energy at <100 keV. The variation of effective atomic number with energy may be attributed to the relative domination of the partial processes, such as photoelectric effect, coherent scattering, incoherent scattering, and pair production. But at low energy, <100 keV, the photoelectric effect is dominant and so, the photoelectric effect is responsible for the change in the energy of effective atomic number.The present experimental results are in accordance with the theoretical results. But the experimental results give better agreement with results of WinXCom. So, the present experimental work upholds the suitability of the WinXCom that estimated values by using the mixture rule. Such results have been observed by earlier investigators [30–32]. It is evident from Tables 2, 3, and 4 that the experimental values are in accord with the WinXCom values within the estimated error −9.4% to +11.9% and FFAST −11.8% to +11.7%. This may be attributed to the effects of chemical environment on μ/ρ value. The μ/ρ values are believed to be affected by the chemical, molecular, and thermal environments. These phenomena led to the deviation of the experimental μ/ρ value from that of the theoretical value, since the calculation of the theoretical value has been done by considering the cross section for an isolated atom. This deviation is termed as the breakdown or no validity of the mixture rule. Such effects have been observed by earlier investigators [33–38]. It is observed that the experimental value deviates by WinXCom +7.9% and FFAST +4.6% for Na2SO4, in order of −4.9% and −7.3% for Mg(NO3)2, +2.9 and −0.5% for Al(NO3)3, −9.3% and −11.7% for Fe2(SO4)3, and −4.9% and −6.9% for CaO6C6H10. In this case, we have concluded that these deviations may not be directly explained by the number of the atoms increasing or decreasing in a compound. We have not confirmed that when the number of atoms in a compound increases, the significant differences between experimental and theoretical values are observed for these compounds. In this respect, the validity of the mixture rule cannot be interpreted according to the number of atoms in a composition. It is important for compounds that the chemical environmental effect and molecular bonding are neglected by mixture rule. Such effects have been observed by earlier investigators [33, 34, 39, 40]. According to relative differences, there are the adaptation between experimental and theoretical (WinXCom) values for Al and FeCl2. The differences between experimental and theoretical results may be attributed to chemical composition variations of the samples and mixture rule neglects present composition. Present results clearly reveal that the incapability of the mixture rule supports the new and sensitive experimental methods more than the semiempirical expressions and interpolation processes. The total experimental uncertainty of the measured quantity depends on the uncertainties of the thickness and the mass, while the uncertainty of the I0 and I measurement scarcely influences the results since both I0 and I have been measured with very good statistics (<1.3%). It is observed from Tables 2, 3, and 4 that the mass attenuation coefficients, total electronic, atomic, and molecular cross sections, effective atomic numbers, and electron densities are closely related to FeCl2 and FeCl3 compounds. As seen in Tables 2, 3, and 4, the mass attenuation coefficients, total electronic, atomic, and molecular cross sections, effective atomic numbers, and electron densities for Na compounds do not change. Sodium is low-Z, so its compounds will not see a significantly large change in average Z. At low energies such as this, 60 keV, the main effects in photon absorption are the photoelectric effect and Compton scattering; these are dominated by the presence of the electrons in the material and the effects from the nuclei are only a perturbation, largely in the different binding energy of the electrons; inner electrons in higher-Z materials have a higher binding energy. So really one will expect that the dominant effect in absorption and scattering will be the electron density in the material, which is calculable with knowledge of the stoichiometric ratio of the elements in the compound or mixture and the density.Further experimental studies on measurements of the mass attenuation coefficients, molecular, atomic, and total electronic cross sections, effective atomic numbers, and electron densities for compounds of biomedically important some elements will be useful to confirm, understand, and interpret the observed differences between the measured and calculated results. Also in order to reach more definitive conclusions on measurements, we project to extend these measurements for various compounds and different primer energies.



---

*Source: 901465-2014-11-12.xml*