Effect of EXAFS on the dosimetric related parameters

doi:10.4236/ns.2011.35056

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Vol.3, No.5, 414-418 (2011) Natural Science

http://dx.doi.org/10.4236/ns.2011.35056

Effect of EXAFS on the dosimetric related parameters

Chitralekha Alur, Sharanabasappa Patil, Manjunath Apparao, Basavaraj Kerur*

Department of Physics, Gulbarga University, Gulbarga, India; *Corresponding Author: [email protected]

Received 4 March 2011; revised 22 March 2011; accepted 27 March 2011.

ABSTRACT

Mass attenuation coefficients have been meas-

ured for rare earth compounds at photon ener-

gies 8.041, 8.907 and 13.347 keV. The measured

values are compared with theoretical calcula-

tions. The agreement between experiment and

theory is more than the experimental error when

the incident photon energy is around the edge

of the element present in the compound and

agreeing with the theoretical values elsewhere.

The difference in agreement between the theo-

retical values and experimental values is attrib-

uted to the EXAFS effects on the mass attenua-

tion coefficient values.

Keywords: Mass Attenuation Coefficient;

Near Absorption Edge; Cross Section;

Resonance Raman Scattering; EXAFS

1. INTRODUCTION

In medical physics, it is important to measure the

amount of radiation delivered by the ionizing radiation,

in composite substances. For photon interactions in

composite substances a single number cannot represent

the atomic number uniquely across the entire energy

region. This number in composite substances is called

the effective atomic number and it varies with energy

and is denoted here by Zeff. On the other hand, the con-

cept of z-dependence of photon attenuation has led to

many applications in radiation studies. For example pre-

cise knowledge of effective atomic numbers is very im-

portant in medical radiation dosimetry and medical im-

aging, where the cross-sectional anatomy is generated by

computer-assisted tomography (CAT) scans [1]. It is a

common practice to verify the validity of calculation

algorithms by comparing the generated doses with the

measured doses in tissue equivalent phantom substances.

Similarly, tissue-equivalent phantoms are specifically

designed to study the image quality and performance of

the CAT scanners. In both instances, a precise knowl-

edge of the effective atomic number and electron density

of the composite substances is necessary in the low en-

ergy region and have proved to be a convenient parame-

ter for interpretation of x-ray attenuation by a complex

medium like a biological tissue and particularly for the

calculation of dose in radiography and radiation do-

simetry etc.

The x-ray mass attenuation coefficient,





, for any

material are usually estimated from Bragg’s additivity

law or more commonly called mixture rule. Thus





for any chemical compound/material is given by







 ,

where









is the mass attenuation coefficient of the

ith element and



i is the fraction by weight of the ith ele-

ment. For a compound/material with chemical formula

(Z1)a1, (Z2)a2, ···, (Zn)an the weight factor for the ith ele-

ment is given by



 





iii ii

aA aA



,

where Ai is the atomic weight of the ith element. Hence

an attempt has been in this regard to determine the





of x-rays for the dosimetric materials (sulphides of Mg,

Ca, Mn Fe and Zn elements) and then determined the Zeff

of these materials by LSF method from







Vs lnZ

graph. These values are compared with the theoretical

values. The so determined value of Zeff has been used in

the expression

eAeffi

NNZ nA





to calculate the electron density.

In the present measurement the validity of Bragg’s

law is studied for rare earths compounds of L edges. The

selection of the compounds was dictated by the incident

photon energy and the by the limitations of our experi-

mental facilities such that thin foils from the compounds.

The former factor determined the region of the atomic

numbers, wherein the absorption edges energy are close

to the incident photon energy, and the latter determined

the selection of particular compounds in this region. We

have used 241Am (VEC) radioactive x-ray source with

weighted average energy of Kα of 8.041 and 13.347 keV

energy respectively and the compounds of rare earths

C. Alur et al. / Natural Science 3 (2011) 414-418

415

having the elements in the region 57 ≤ Z ≤ 70.

2. EXPERIMENTAL ARRANGEMENT

The good-geometry experimental arrangement used

for the determination of the mass attenuation coefficient

is similar to the one described in detail by us earlier [2];

and is shown in Figure 1. Briefly, photons from a vari-

able energy x-ray source S passed through a collimator

C1 and were incident on the specimen A in the form of a

thin foil kept normal to the photon beam. The transmit-

ted beam passed through another collimator C2 and

reached a HPGe x-ray detector system D. The transmit-

ted photon spectrum was recorded using a PC based

multichannel analyzer.

The collimators C1 and C2 were 40 mm thick lead

discs that collimated respectively the incident and trans-

mitted beam to 6 mm dia. The scatter acceptance angle

equal to the sum of the incident beam divergence and

acceptance angle at the detector is found to be  3˚ de-

grees. This thickness of the collimator would reduce the

intensity of scattered photons of 300 keV by a factor of

107.

The variable energy x-ray source consisted of 10 mCi

(370 MBq) 241Am as the primary source of excitation

radiation Copper and Rubidium targets were selected to

produce fluorescence x-ray with characteristic energy of

the target i.e., 8.041 and 13.347 keV. The inner bremss-

trahlung intensity was found to be negligible compared

to the x-ray intensity in the region of interest. No no-

ticeable impurities were found in the source spectra.

The Dosimetric compounds viz., rare earth sulphate

compounds of 99.5% purity were obtained from SD fine

chemicals Mumbai, India. The Dosimetric samples of

required thickness in the range of 10 to 30 mg/cm2 were

prepared by using blotting paper technique. The area

density (mass per unit area) of each foil sample was de-

termined by weighing it using a single pan electronic

balance with an accuracy of 0.01 mg and measuring its

dimensions using a traveling microscope with an accu-

racy of 0.001 cm. Thus the measured areal density ex-

pressed in mg/cm2 had an uncertainty.

The x-ray spectrometer consist of an n-type x-ray de-

tector of area 500 mm2 × 100 mm thick High Purity

Germanium detector connected to DSA-1000 16K MCA.

The spectrometer was operated by Genie 2000 software.

The detector is connected directly to a preamplifier

through a cooled FET device, and mounted over a rigid

cryostat with Dewar to accommodate the liquid Nitrogen.

DSA-1000 allows independent of rise time and flat top

selection, which optimizes the performance of the de-

tector, spectral energy, count rate and resolution. HPGe

detector along with DSA-1000 has resulted with a reso-

lution of 191 eV at 5.895 keV as against 200 eV by the

Figure 1. Experimental arrangement.

manufacturers.

The advantage of the high resolution HPGe detector

system is its wide operating energy range from 3 keV to

500keV and very good energy resolution, 241Am source

with different target the photo peaks of Kα and Kβ of

were well resolved. As a result of this, the energies of

the photons with degrade in energy due to small angle

scattering and multiple scattering, if at all present, could

be observed in the source spectrum, but in the present

case no such degraded photo peak were observed except

the Kβ and Kβ and gamma photons of 241Am source.

Therefore,





value obtained in such configuration

is purely corresponding to the respective energies only

i.e., Kα and Kβ gamma-rays.

The error involved in each measurement is taken care

by following the procedure counting time conditions as

stated in [3]; viz., background to signal background to

foil thickness and signal to foil thickness, systematic

errors due to the detection of forward scattered radiation,

beam hardening when higher atomic number absorber is

used. Ray-sum method has been adopted in the present

measurement for calculation for the random errors which

arises from all aspects of the measurement, further is has

also suggested a method for the calculation called the

ray-sum error. In the present measurements ray-sum

method is applied to all the observation since the random

errors arises from all aspects of measurement, in the ex-

ponential law of attenuation. The errors are calculated by

using the formula provided by [4]; and are presented in

C. Alur et al. / Natural Science 3 (2011) 414-418

416

the tables.

No dead time corrections are found for photon inten-

sity measurements considered area under photopeak.

However, in the present case we have selected the live

time of the MCA for sources. With these conditions, the

transmitted intensity of x-rays for various combinations

of specimen thickness is recorded and corrected for

background intensity [5,6]. A plot of logarithm of trans-

mission as a function of specimen thickness yielded a

straight line for the entire transmission region, verifying

the validity of the Beer-Lambert’s law. This is confirmed

for different materials also.

3. RESULTS AND DISCUSSION

The plots of the logarithm of transmitted intensity

versus specimen thickness were linear for all the samples

and the





was obtained from the plots by linear

regression over the 50% - 2% transmission range [7].

The





obtained for the all dosimetric compounds at

three different photon energies are presented in Table 1.

The theoretical estimated errors are between 1% and

2% taken from the WinXCom. The error involved in

over all experimental values is about 2% to 3% for the

dosimetric samples.

In Table 1 the second column represent L shell Bind-

ing energies EL of the element present in the compound,

third column represents difference, (Ex − EL) between the

incident photon energy Ex (viz., 8.041, 8.907 and 13.347

keV) and L shell binding energy EL. The fourth column

represents experimental





value, fifth column repre-

sents theoretical





value (WinXom), and the per-

centage difference (PD) between experiment and theory

is given in the last column of the table. The positive and

negative sign indicates that the interested element L shell

binding energy is above or below the incident photon

energy, and the binding energies are taken from Kor-

tright et al. [8].

Further from Table 1, there is a good agreement be-

tween theoretical and experimental value for all the

compounds at 13.347 keV, it is confirmed fact that when

the incident photon energy is far away from the absorp-

tion edge, there is good agreement between experimental

value with theoretical value within 4%. On the other

hand, the same mixture rule can’t be applicable for

Neodymium and Europium sulphate with Ex-EL ranging

from 0.915 to 0.429. Here, the experimental value devi-

ates from the theoretical value by −7.7% and −16.2%

and next, in case of Europium and Terbium sulphate at

8.907 keV with Ex-EL in range from 1.295 and 0.655 keV

for L edge shows a deviation in the mass attenuation

Table 1. Experimental and theoretical mass attenuation coefficient.

Mass attenuation coefficient (cm2/kg)

Name of the Sample EL binding energy in keVE = Ex − EL (keV)

Expt. value WinXcom

P.D in %

Ex = 8.041 keV

Nd2(SO4)3·8H2O 7.126 0.915

165.3  1.7 179.2 −7.7

Eu2(SO4)3·8H2O 7.612 0.429

150.5  1.5 179.6 −16.2

Tb2(SO4)3·8H2O 8.252 −0.211 152.8  1.6 147.8 +3.3

Yb2(SO4)3·8H2O 9.978 −1.937 80.32  0.9 79.62 +0.8

Ex = 8.907 keV

Nd2(SO4)3·H2O 7.126 1.781

140.2  1.6 137.2 +2.2

Eu2(SO4)3·H2O 7.612 1.295

168.4  1.8 157.8 +6.7

Tb2(SO4)3·H2O 8.252 0.655

193.4  2.0 171.6 +12.7

Yb2(SO4)3·H2O 9.978 −1.071 59.76  0.8 60.97 −1.6

Ex = 13.347 keV

Nd2(SO4)3·H2O 7.126 6.221

47.21  0.5 46.89 +0.8

Eu2(SO4)3·H2O 7.612 5.735

55.43  0.6 54.62 +1.5

Tb2(SO4)3·H2O 8.252 5.095

59.01  0.7 59.84 −1.3

Yb2(SO4)3·H2O 9.978 3.369

75.23  0.6 74.81 +0.5

PD = Percent difference = [(Experimental mean μ/ρ − Computed μ/ρ)/Computed μ/ρ] × 100

C. Alur et al. / Natural Science 3 (2011) 414-418

417

Figure 2. Experimental and Theoretical estimated values of mass attenuation coefficient of rare earth sulphates.

coefficient between the experimental and theoretical by

6.7%, and 12.7% respectively. Thus mixture rule cannot

be applicable for the rare earths compounds where L

edge energy is close to the incident photon energy. This

deviation is also shown in Figure 2 by plotting mass

attenuation coefficient (Experimental and Theoretical)

Vs rare earths compound. The experimental and theo-

retical mass attenuation coefficient value for Neodym-

ium and Europium sulphates at 13.347 shows a good

agreement within the 2% and other hand the same com-

pound at 8.041 and 8.907 keV shows a deviation with

theoretical value. This results purely the mixture rule

can’t be applicable in both the cases otherwise it can be

applicable provided that the edge effects/chemical ef-

fects are taken into account.

In the Table 2 effective atomic number are estimated

using the least squares formula by ploting the mass at-

tenuation coefficient versus the elements for each ener-

gies. From the said graph the estimated value of effec-

tive atomic number of the dosimetric materials found to

vary from 10% to 18% for all the suphides. The theo-

retical values of the Zeff are also calculated using the for-

mula given by Jackson and Hawkes [1] and these values

are discussed in the light of the dosimetry point of view

and as discussed in the introduction. The experimental

Table 2. Determined and estimated values of effective atomic

number and electron density of the rare earths compounds.

Effective Atomic Number (Zeff)

Name of the

Sample Expt Jackson 1981

Electron Density

Ne (1024 elec g–1)

8.041 keV

Nd2(SO4)3·8H2O48.14 41.41 1.649

Eu2(SO4)3·8H2O46.58 43.79 1.562

Tb2(SO4)3·8H2O46.83 45.63 1.542

Yb2(SO4)3·8H2O37.37 49.91 1.185

8.907 keV

Nd2(SO4)3·8H2O45.44 41.41 1.557

Eu2(SO4)3·8H2O48.45 43.79 1.625

Tb2(SO4)3·8H2O50.87 45.63 1.674

Yb2(SO4)3·8H2O37.69 49.91 1.196

13.347 keV

Nd2(SO4)3·8H2O31.02 41.41 1.063

Eu2(SO4)3·8H2O32.82 43.79 1.101

Tb2(SO4)3·8H2O33.55 45.63 1.104

Yb2(SO4)3·8H2O36.53 49.91 1.159

C. Alur et al. / Natural Science 3 (2011) 414-418

418

and theoretical Zeff values are agreeing within 5% except

the edge region. It is important to mention that the theo-

retical/calculated values have not considered the edge

effects and since the effective atomic numbers are un-

der/over estimated when any element falls below the

absorption edge.

In the present work, there is a good indication that

even in the low photon energy region say that up to 15 keV

the effective atomic number can be determined with

greater accuracy but one should take into account of

edge effects.The electron density of the dosimetric mate-

rials is calculated using the experimental Zeff values and

found to vary 0.478 to 0.676 (1024 electrons g–1). In con-

clusion, the determined Zeff value is agreeing with the

theoretical values within 5% at this energy range and

one should also take care of effects if high atomic num-

ber dosimeters are involved.

4. ACKNOWLEDGEMENTS

One of the authors BRK is expressed sincere thanks since this work

is financially support by UGC New Delhi.

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