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Measurement of the Effective Atomic Number
of Some Transition and Rare Earth Compounds
Using the Rayleigh to Compton Scattering Ratio of
Gamma Radiation
Mutturaj Hosamani, S. Ramesh Babu, Santosh Mirji & N. M. Badiger
To cite this article: Mutturaj Hosamani, S. Ramesh Babu, Santosh Mirji & N. M. Badiger (2017):
Measurement of the Effective Atomic Number of Some Transition and Rare Earth Compounds
Using the Rayleigh to Compton Scattering Ratio of Gamma Radiation, Spectroscopy Letters, DOI:
10.1080/00387010.2017.1332650
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Date: 31 May 2017, At: 03:18
Measurement of the Effective Atomic Number of Some Transition and Rare Earth
Compounds using the Rayleigh to Compton Scattering Ratio of Gamma Radiation
Mutturaj Hosamani1, S. Ramesh Babu2, Santosh Mirji1, N. M. Badiger1
1
Department of Studies in Physics, Karnatak University, Dharwad, India 2Karnatak
University, Dharwad, India
Abstract
The Effective Atomic Number of some transition and rare earth compounds have been
determined by measuring the ratio of Rayleigh to Compton scattering signal using 59.5
kilo electron Volt gamma radiation from americium-241 radioactive source. The
scattered gamma photons from the elements and compounds at an angle 90 degree were
detected using an ORTEC make High Purity Germanium detector coupled with 16 kilo
Multi Channel Analyzer. By measuring the ratio of Rayleigh to Compton scattered signal
(momentum transfer 3.38 Å-1) the Effective Atomic Number of the transition and rare
earth compounds have been determined and compared with theoretical values predicted
by Autozeff, Power law and Direct method.
KEYWORDS: Effective atomic number; Coherent to Incoherent ratio; composite
materials; gamma photons; Rayleigh to Compton scattering ratio
INTRODUCTION
The effective atomic number (Zeff), is a single number which can visualize many
characteristics of a composite systems such as shielding materials in nuclear reactor,
superconducting materials and biological objects such as normal and cancer tissues [1–3]
1
The effective atomic number (Zeff) of composite materials can be determined by various
methods such as gamma ray transmission method, ratio of Rayleigh to Compton
scattering method, backscattering of gamma ray method [2–5]. In the gamma ray
transmission method, gamma ray photons are allowed to transmit through a target at zero
degree and transmitted photons are measured. By knowing incident and transmitted
gamma ray photons, the mass attenuation coefficient (μ/ρ) of the target is determined and
from this value, the Zeff of the target is determined. Using this method various
investigators have determined the Zeff of compound targets, biological samples, alloys
and etc [6]. It is well known that gamma photon undergoes the photoelectric effect which
is proportional to fourth power of the atomic number of the target, by Compton effect
which is proportional to atomic number of target and by pair production which is
proportional to square of atomic number of target (Z). Hence, Zeff of composite material
for photon interaction depends on energy of the incident photon. However in the case of
ratio of Rayleigh to Compton scattering method, intensities of Rayleigh scattered
photons and Compton scattered photons are measured for various atomic number of
elemental targets. Plot of Rayleigh to Compton scattering ratio versus the Z value gives
the calibration curve and from this calibration curve, the effective Z value of composite
material is determined. Using this method, recently several investigators have determined
the effective Z values of alloys [7–10], compounds, biological samples and cancer tissues
[11]
. The backscattering method in which back scattered photons by electrons of the target
at 180o are measured for elemental and compound targets. The signal of the backscattered
photon saturates above at certain thickness. By knowing the saturated signal and
saturated thickness, the Zeff of the composite target is determined. Using this method
2
many investigators have measured Zeff of the various materials as well as compounds
[4,12]
.
In this work determined the Zeff of some transition and rare earth compounds by adopting
Rayleigh to Compton scattering ratio method. The transition and rare earth composite
materials are being used in the fields like consumer electronics, computer and networks,
generation of clean energy, health care, advance transportation and defense. Therefore
study of the properties of these materials has been subject of experimental and theoretical
investigations. These materials have unique properties such as magnetic, luminescent,
electrochemical, mixing capacity, conductivity and also their malleable, ductile, lustrous
properties. Hence the study of interaction of radiation with these materials is very
important for technology development. With the best knowledge of authors the Zeff of
these compounds have not been determined using Rayleigh to Compton scattering ratio
method by keeping high resolution gamma detector at 90o. The experimentally measured
Zeff values have been compared with theoretically predicted values using AutoZeff
computational code [13], Power law [6] and Direct method [14]. Details of various methods
for determining Zeff of some tissue substitutes by AutoZeff, Power law, Interpolation and
Direct method are given in reference [3].
THEORY
In present work, measured the elastically scattered gamma photon which is known as
Rayleigh scattering and the inelastic scattered gamma photon which is known as
Compton scattering. Rayleigh scattering is a phenomenon of scattering of gamma photon
3
by bound atomic electrons, without disturbing the atom state (neither ionized nor
excited). In this scattering there is no transfer of energy to struck electron and it is
significant at low energy and for high atomic number targets. The Rayleigh scattering
cross section is given by..
dσ R
dΩ
ro2
1 cos 2θ F q, Z
2
2
(1)
Where F q, Z is the atomic form factor. The square of this atomic form factor
F q, Z
2
is the probability that the atomic number electrons of an atom take up the
recoil momentum ‘q’ without absorbing any energy. The scattered signal depends on the
cross section; therefore Rayleigh scattering cross section is proportional to the Z2. The
values of F(q, Z) have been tabulated by Hubbell 1975 [15] for Z from 1 to 100 over a
range of q. The atomic form factor, F(q, Z), accounts for the effects that atomic structure
has on the scattering cross-sections.
In Compton scattering, gamma photons interacting with an atomic electrons can undergo
deflection with energy varying from the incident to the backscattered energies. The cross
section for Compton scattering is given by..
dσ CKN
θ
dΩ
dσ C
dΩ
S q, Z
Where
dσ CKN
θ is the Klein-Nishina cross section per electron for un-polarized incident
dΩ
(2)
photons and it assumes that the interaction takes place between a free electron at rest, and
is valid if E >> Bi, where ‘Bi’ is binding energy of an electron in ith energy level. The
atomic binding effects are taken into account by using S(q, Z), incoherent scattering
4
function. The ‘q’ is a momentum transfer which depends on energy and deflection angle
and Z is atomic number of target. Therefore Compton scattering cross section is
proportional to atomic number, Z, of the target material.
In the existing literature there are some methodologies to calculate the Zeff of several
element composed materials. Here some methods are highlighted to determine the Zeff
with Rayleigh to Compton scattering signal ratio. Harding et al [16] has measured the Zeff
by assuming the ratio between Rayleigh to Compton scattering is a function power of
effective atomic number..
R
K
(Zeff ) A
(3)
Where, K is representing the Thomson to Klein-Nishina [15] cross section ratio and A,
represents a power of Zeff. But by assuming Rayleigh and Compton scattering are
proportional to Z3 and Z respectively, the Zeff will be [17].
Wi
Zeff
Wi
1/2
Ai
Ai
Z
3
i
(4)
Zi
Where Wi is the weight fraction composition and Ai is the atomic mass of the
contaminated elements.
Duvauchelle et al [18], have also measured the Zeff. They used the atomic form factor F(x,
z) and incoherent scattering function S(x, z), as depend on the atomic number and the
momentum transfer. For each value of the momentum transfer, there is a discrete function
fx, that gives the..
5
Z
F2
S
f xD
(5)
For a target formed by several elements, consider that the function fx are continuous and
allow to calculate the Zeff..
Zeff
Zeff
Σ F x, zi
fx
2
(6)
Σ S x, zi
F2
S
fx
(7)
eff
Tsai and Cho [19] suggested the following empirical formula which is valid for incident
energies below 150 keV..
1/3.4
α
Zeff
e
i
Z
3.4
i
(8)
i
Where,
Wi
α
Ai
Wi
Ai
e
i
Zi
Zi
Using atomic percentage α iat , the expression for Zeff is [20].
Wi
Ai
Wi
Ai
α iat
αiat
Zeff
(9)
Zi
(10)
i
And also, can obtain the Zeff using some empirical relations like..
6
1/2.94
Zeff
fi
Zi
2.94
(11)
i
Here, fi is the fraction of total number of electrons associated with each element and Zi is
atomic number of each element. It is called the Power law method [20]. The effective
atomic number can also be calculated using Direct method [14].
Zeff
Where, f i
fi
Ai
μm
i
fi
Ai
Zi
μm
i
(12)
ni
and Zi are fractional composition and atomic number of constituent
ni
elements, respectively; ni is the total number of atoms of the constituent element; Σ ni is
the total number of atoms presents in the molecular formula.
Experimental Technique
The total experimental setup to measure the effective atomic number of some transition
and rare earth compounds (having purity ~99.99%) is shown in the Fig. 1. In the present
experiment the signal ratio of the Rayleigh to Compton scattered photons are measured
for elemental as well as compound targets. The americium (Am-241) radioactive source
(S) which emits 59.5 keV gamma radiation has been used in the present experiment. The
activity of the source is 100 milli Curie (mCi) and therefore it was placed in a lead
container. Effective atomic number of the composite materials depends on the type of
particles as well as its energy. The selection of energy of the incident particle is very
important; if it is near the K shell binding energy the effects such as Extended X-ray Fine
Absorption Structure (EXFAS) and Resonance Rayleigh Scattering (RRS) may also
7
contribute to the Zeff. In the present investigations, the energy of the incident particle far
away from K shell binding energy of the composite materials is selected. The gamma
radiation is collimated using graded collimators which are made up of lead and
aluminum. The lead X-rays emitted from the lead target are stopped by the aluminum
target by using appropriate thickness. The graded collimator C1 has thickness of 2 cm
thick lead and 1.5 cm thick aluminum, the collimator acceptance size is 7 mm diameter.
When photons are scattered from the target there will undergo elastic as well as inelastic
scattering and such scattered photons are allowed to enter into the detector. In order to
prevent the multiple scattered photons from entering into the detector from the target, one
more graded collimator C2 has been placed between target and detector. The collimator
size is 1.15 cm diameter with same thicknesses of lead and aluminum as mentioned
above respectively. The elastically scattered as well as inelastically scattered photons are
detected using an ORTEC make High Purity Germanium (HPGe) semiconductor detector
(GMXIOP). The detector of crystal diameter of 49.6 mm, length 47.1 mm with beryllium
window of thickness 0.5 mm is coupled to computer based ORTEC Mastreo 16K Multi
Channel Analyzer (MCA). The detector has been calibrated using standard
monoenergetic gamma energies of 59.5 keV, 661.6 keV, 511 keV, 1276 keV, 1172 keV
and 1333 keV. The energy resolution of the detector is 564 eV at1.8 keV and 1.77 keV at
1.33 MeV.
RESULT AND DISCUSSION
The signal ratio of the Rayleigh to Compton scattered gamma photons is measured to
determine the Zeff of some transition and rare earth compounds targets. The gamma
8
photons of 59.5 keV emitted from Am-241 radioactive source are allowed to interact with
the elemental as well as compound targets through collimator C1. The elastically and in
elastically scatted photons from the targets are allowed to pass through collimator C2.
The energy and signal of the scatted photons are measured by keeping high resolution
detector at an angle 90o to direction of incident radiation. Typical recorded spectrum from
copper element target is shown in Fig. 2. The figure shows two peaks at higher energy
region; one peak corresponds to Rayleigh scattering and the other one is the Compton
scattering. The area under peak, after correcting for attenuation of scattered photons in
air medium and in target, efficiency of the detector, and etc, would give signal of the
scattered photons through Rayleigh scattering and Compton scattering. The correction
factor β for gamma ray attenuation in air medium and also in target is calculated using the
following [20].
μ in
1 exp
β
μ in
cosθ
cosθ
μ scat
μ scat
cos
ρt
cos
(13)
ρt
Where μin is the linear attenuation coefficient of material at incident energy, μscat is the
linear attenuation coefficient of material at scattered energy. The θ and
are the
incident and scattered angles respectively and ‘ρt’ is the areal density of the medium or
material. Therefore, by knowing measured signal ‘Nmeasured’, the actual signal ‘Ntrue’ is
determined by using the following equation..
N True
εγ
N Measured
β Air βTarget
(14)
By knowing the Ntrue for Rayleigh scattering and Compton scattering, the ratios are
determined for elemental targets whose Z values are variable from 6 to 82. Using these
9
values the calibration curve has been obtained which is given in Fig. 3. The following
equation is used to fit the experimental data.
Y
0.0658 exp
x
22.363
0.0299
(15)
Have also measured the scattered signal ratio for the some transition and rare earth
compounds targets like; Silver Chloride(AgCl), Silver Iodide (AgI), Silver Oxide (Ag2O),
Silver Sulphide (Ag2S), Cadmium Acetate (Cd(CH3COO)2.2H2O), Cadmium Carbonate
(CdCO3), Cadmium Oxide (CdO), Cerium Oxide (Ce2O3), Lanthanum Oxide (La2O3),
Neodymium Oxide (Nd2O3), Lead Acetate (Pb(C2H3O2)2), Lead Nitrate (Pb(NO3)2), Lead
Oxide (PbO), Praseodymium Carbonate (Pr2(CO3)3), Antimony Oxide (Sb2O3),
Samarium Carbonate (Sm2(CO3)3), Tin Bromide (SnBr4), Tin Chloride (SnCl4), Tin
Oxide (SnO2) and Yttrium Carbonate (Y2(CO3)3). Table 1 gives the effective atomic
number and corresponding signal ratio for above mentioned composite materials. The
experimentally determined effective atomic number from Rayleigh to Compton ratio and
theoretical values of Zeff predicted by AutoZeff simulation code, Power law semiempirical methods and Direct method are given in Table 2. This work motivates to
continue the same concept with electron beam interaction and heavy ion interaction for
these industrially important materials. No data existed regarding this.
CONCLUSION
In the present investigations the measured effective atomic number of some transition and
rare earth compounds have been determined using Rayleigh to Compton ratio by keeping
the detector at 90o. The measured Zeff values are compared with theoretical values
predicted by three models namely; AutoZeff model, Power law model, Direct model.
10
From the data it is important to notice that the measured values are closely agree with
theoretical values predicted by AutoZeff model within 3% except Pb(C2H3O2)2.
However, present experimental values are less than the values predicted by Direct
method. Therefore for accurate measurement of Zeff for transition and rare earth
compounds, the Rayleigh to Compton scattering ratio technique can be used. If
experiment values are not available, the values predicted by AutoZeff may be used. Many
investigators have estimated the effective atomic number of several composite materials
using various techniques. With best knowledge of the authors the effective atomic
number of transition and rare earth compounds have not been studied using Rayleigh to
Compton scattering ratio technique. Normally the techniques like Total reflection X-Ray
Fluorescence (TXRF), Micro X-Ray Fluorescence (μXRF) as well as synchrotron base
experiments have been adopted for measuring the Zeff [21,2]. In the present investigations a
simple technique has been adopted to measure the Zeff of transition and rare earth
compounds. The method can also be extended for measurement of Zeff of normal and
cancer tissues.
ACKNOWLEDGEMENT
The authors would like to thank University Science Instrument centre (USIC) Karnatak
University, Dharwad and the Department of Science and Technology (DST), New Delhi
for providing the financial support under the DST-PURSE-Phase II-Program (Contract
No. SR/PURSE Phase 2/13(G)) to carry out the above experiment. One of the authors
(MMH) would like to thanks the IUAC New Delhi for the financial support under the
project UFR-51312.
11
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14
Table 1. Experimentally determined effective atomic number and Rayleigh to Compton
ratio for some composite materials.
Composite material
Molecular formula
Measured Rayleigh to
Experimental
Compton scattered
Zeff
Photon signal
(This work)
ratio
Cadmium Acetate
Cd(CH3COO)2.2H2O 0.1215
20.13
Yttrium Carbonate
Y2(CO3)3
0.1577
22.98
Lead Acetate
Pb(CH3COO)2
0.2895
34.16
Lead Nitrate
Pb(NO3)2
0.2579
31.80
Cadmium Carbonate
CdCO3
0.2531
32.88
Tin Chloride
SnCl4
0.2599
33.14
Praseodymium
Pr2(CO3)3
0.2939
35.24
Samarium Carbonate
Sm2(CO3)3
0.2559
34.20
Tin Oxide
SnO2
0.2029
30.04
Silver Chloride
AgCl
0.2026
30.01
Tin Bromide
SnBr4
0.2575
34.72
Antimony Oxide
Sb2O3
0.3408
39.40
Cadmium Oxide
CdO
0.3725
41.22
Silver Oxide
Ag2O
0.3324
39.66
Silver Sulphide
Ag2S
0.3986
44.34
Lanthanum Oxide
La2O3
0.3653
41.74
Carbonate
15
Cerium Oxide
Ce2O3
0.4152
44.54
Neodymium Oxide
Nd2O3
0.4733
47.19
Lead Oxide
PbO
0.4738
47.20
Silver Iodide
AgI
0.5237
49.01
16
Table 2. Comparison of experimentally determined Zeff with theoretical values
Composite material
Experimental Zeff
Theoretical Zeff [3,6]
(This work)
AutoZeff
Power law
Direct
Code
method
method
Cadmium Acetate
20.13±0.60
21.43
20.22
46.60
Yttrium Carbonate
22.98±0.68
23.54
30.83
37.60
Lead Acetate
34.16±1.0
26.33
70.34
80.78
Lead Nitrate
31.80±0.95
30.16
69.92
80.72
Cadmium Carbonate
32.88±0.98
32.01
31.53
47.44
Tin Chloride
33.14±0.99
33.14
38.91
47.84
Praseodymium
35.24±1.05
34.80
49.90
58.49
34.20±1.02
36.37
52.87
61.55
Tin Oxide
30.04±0.90
37.25
46.12
49.73
Silver Chloride
30.01±0.90
39.25
42.9
46.34
Tin Bromide
34.72±1.04
39.32
40.19
42.43
Antimony Oxide
39.40±1.18
39.82
47.98
50.80
Cadmium Oxide
41.22±1.23
39.85
45.88
47.84
Silver Oxide
39.66±1.18
42.16
45.87
46.92
Silver Sulphide
44.34±1.33
42.25
44.93
46.60
Lanthanum Oxide
41.74±1.25
44.26
44.00
56.85
Cerium Oxide
44.54±1.33
44.99
44.97
57.86
Carbonate
Samarium
Carbonate
17
Neodymium Oxide
47.19±1.42
46.44
46.94
49.58
Lead Oxide
47.20±1.42
48.72
79.95
81.83
Silver Iodide
49.01±1.47
50.18
50.41
50.70
18
Figure 1.
19
Figure 2.
20
Figure 3.
21