Chapter-5
Measurement of linear attenuation coefficient of irregular
shaped FaL-G (flyash-lime-gypsum) samples using
‘Simplified Two media’ method
5.1
Introduction
Measurement of linear and mass attenuation coefficient of regular and irregular
shaped FaL-G (flyash-lime-gypsum) samples employing ‘Simplified Two media’
method are presented in this Chapter. Seven different liquid materials plus air have been
used as media to measure attenuation coefficient of these samples. Obtained results
have been compared with those for regular shaped samples. Experimental values have
also been compared with theoretical values calculated from FFAST (Chantler et al.,
2005) and XCOM (Berger and Hubbell, 1987). A good agreement has been observed
between experimental and theoretical values.
Gamma-ray transmission method utilizes the application of Lambert-Beer law
for the measurement of the linear attenuation coefficient ( of the sample under
investigation. But the accuracy of the method demands that the sample thickness should
to be known precisely. However many samples of archaeological type (such as rocks,
construction material, flyash materials etc.) have irregular shapes. The precise thickness
of such samples can not be measured with a micrometer or a vernier calliper, which, in
Part of this work has been published in
Appl. Radiat. Isotopes 69 (2011) 1516-1520
120
turn, limits the direct application of Lambert-Beer law for the determining of their linear
attenuation coefficient. The ‘Two media’ method (Silva and Appoloni, 2000) provides a
solution to this problem. This method utilizes standard Lambert-Beer law in such a way
that thickness of sample under study is not required.
However, Silva and Appoloni (2000), in their conclusions suggested that the
accuracy of the method depends upon the difference in the values of linear attenuation
coefficient of the pair of media used. Thus larger the different in the values of linear
attenuation coefficient, greater the accuracy of method. Secondly, the media should be
preferably homogenous.
Keeping in view of above suggestion, Elias (2003) theoretically proposed a
simple procedure to introduce some new combinations by considering air as one of the
media. This modified ‘Two media’ method is called ‘Simplified Two media’ method.
This procedure not only simplifies experimental work, but at the same time, it also
allows a greater number of repetitions as well as introduces larger difference in the
values of attenuation coefficient of the pair of media used. Further, the resulting linear
attenuation coefficient value is an absolute value and not a relative one referred to the
linear attenuation values of the media.
In present work, attempt has been made for the first time to check experimental
reliability and accuracy of this method by measuring the linear attenuation coefficient of
both regular as well as irregular shaped FaL-G (fly ash, lime and gypsum) bricks. Seven
different materials namely water, glycerin, mobile oil, machine oil, cottonseed oil,
ethanol and methanol plus air have been used as media in the procedure of
measurements.
121
5.1.1 FaL-G:
An eco-friendly building material
Increasing use of thermal power plants for electricity production in developing
countries like India, results in production of huge amount of fly ash, disposal of which
poses significant challenges for the power plants. Production of building materials,
particularly FaL-G (flyash-lime-gypsum) bricks is considered to be one of the effective
solutions to the ever increasing fly ash disposal problem. Besides this, it offers a viable,
energy efficient and environment friendly alternative over traditional burnt bricks used
for construction. As production of FaL-G bricks does not involve sintering, thus
eliminating the burning of fossil fuels required in the clay brick production process and
ultimately contributes to the reduction of greenhouse gas emissions. Therefore,
increasing use of flyash materials as a substitute of burnt bricks in construction section
demands proper knowledge of gamma ray spectroscopic parameter such as linear and
mass attenuation coefficient. This forms the basis of selecting FaL-G bricks as target
samples in present investigation.
5.2
Theoretical formulation of ‘Simplified Two media’ method
A collimated beam of gamma-ray having initial intensity Io is attenuated in
absorber of thickness ‘x’ of absorber according to the Lambert-Beer law:
I  I o e  x
(5.1)
Where I is transmitted bean intensity of unaffected primary photons.
‘Simplified Two media’ method utilizes this standard Lambert-Beer law in such
a way that it is possible to measure linear attenuation coefficient of any shaped sample
without using its thickness. In this method, the gamma-ray transmission intensity
through the sample under study is measured by immersing it, turn wise, into two
different media with known linear attenuation coefficients. Figure 5.1 illustrates
122
‘Simplified Two media’ method. Irregular shape sample of unknown thickness of which
linear attenuation coefficient is to be measured is placed inside an acrylic box of known
internal dimensions. The empty space inside the box and around sample is filled with
some medium of known attenuation coefficient. Gamma ray beam intensity is measured
through that medium. This procedure is repeated for at least two media with known but
different attenuation coefficients. Following mathematical expression is obtained for
resultant transmitted beam intensity, when the sample under study was immersed in
medium 1 which is air in present case:

I1  I o (e   x e  a a )
(5.2)
Where I 1 represents transmitted beam intensity by the assembly of sample, medium 1
and acrylic box, Io is incident beam intensity. and a represent linear attenuation
coefficients of sample and acrylic box respectively. While ‘a’ represents total thickness
of acrylic box.
Now expression of resultant beam intensity without sample becomes:
I1  I o (e   a a )
(5.3)
I1 is transmitted beam intensity of medium 1 and acrylic box
Similarly by immersing the sample in medium 2 we get:

I 2  I o (e  2 ( D  x ) e  x e  a a )
(5.4)
Where I 2 represents transmitted beam intensity by the assembly of sample, medium 1
and acrylic box,  2 is the linear attenuation coefficient of medium 2, ‘D’ is the internal
dimension of acrylic box and other parameters have the same meaning as describes
above. In the absence of sample expression (5.4) can be rewritten as:
I 2  I o (e  2 D e  a a )
123
(5.5)
a1
a2
a= a1+a2
D=d1+d2
Io
d1
d2
I
X
Media
Sample
Acrylic
Box
D - Internal width of acrylic box
a - total width of walls of acrylic box
X - Unknown thickness of sample
Fig. 5.1:
Schematic diagram of ‘Simplified Two media’ method.
124
where, I2 is transmitted beam intensity of medium 2 and acrylic box
Performing the proper substitutions of above equations, we get the following equation
which determine linear attenuation coefficient of irregular shape sample of unknown
thickness

Where C1 
2
 ln(C 2 ) 

1  
 ln(C1 ) 
(cm-1)
(5.6)


I
I1
and C2  2
I2
I1
Thus, we get the equation that determines the linear attenuation coefficient of
sample even without the knowledge of its thickness. In present measurement, values of
linear attenuation coefficient for both irregular as well as regular shaped samples of
FaL-G(flyash ,lime and gypsum) were obtained using expression (5.6).
5.2.2 Error
Linear attenuation coefficient  measured using ‘Simplified Two media’ method
using expression (5.6) is a function of different variables such as C1 and C2 i.e.
  f ( 2 , C1 , C2 ) .
Thus estimated error associated with is the resultant of uncertainties involved with the
measurement of each variable is given by following relation (Singh et. al, 2008):
  V 2  C2
(5.7)
where Variance term V is given by
2
2
2
  
  
  
V     22     C21     C22
 2 
 C1 
 C2 
2
125
where  2 corresponds to the independent uncertainty over each variable and the
Covariance term C is given by
    
    
 ' COV ( I1 I1' )  2
 ' COV ( I 2 I 2' )
C 2  2
 I1  I1 
 I 2  I 2 
Where COV(x,y) corresponds to the covariance for the variable x and y, which
measures the correlation among the uncertainties of each one of them and it is defined
as:
COV ( x, y ) 
1 n
 ( xi  x )( yi  y )
n i 1
(5.8)
While the maximum error linked with linear attenuation coefficient measured
employing standard transmission geometry has been calculated from the errors
associated with different physical parameters such intensities without sample (Io),
intensities with sample (I) and thickness (x) using the following relation:
1  I o   I   I o   x 
   ln   
  

 
x  I   I   I   x 
2
2
2
2
(5.9)
where I o , I and x are errors linked with the intensities Io, I and thickness of the
samples respectively.
5.3
Sample preparation
Two types of FaL-G (flyash-lime-gypsum) samples has been used in present
study; regular shaped as well as irregular shaped. Both types of samples have been
prepared in laboratories of Physics Department of Sant Longowal Institute of
Engineering and Technology, Longowal, Punjab, India. Flyash used in samples has
been procured from Guru Hargobind Thermal Plant Lehra, Bathinda, India. While lime
and gypsum has been procured from LOBA CHEMIE and MERCK chemical Pvt. Ltd.
126
Table 5.1:
Sample
Code
Chemical composition, thickness and density of regular as well as
irregular samples.
Category
Thickness
(cm)
Density
(g/cm3)
Percentage by weight(%)
composition
of flyash-lime-gypsum
Flyash
Lime
Gypsum
RS-1
Regular
0.60
1.15
70
20
10
RS-2
Regular
0.60
1.16
65
20
15
RS-3
Regular
0.60
1.18
60
20
20
RS-4
Regular
0.60
1.19
55
20
25
RS-5
Regular
0.60
1.21
50
20
30
IRS-1
Irregular
unknown
1.17
70
20
10
IRS-2
Irregular
unknown
1.18
65
20
15
IRS-3
Irregular
unknown
1.20
60
20
20
IRS-4
Irregular
unknown
1.19
55
20
25
IRS-5
Irregular
unknown
1.22
50
20
30
RS-regular shaped sample of FaL-G
IRS-irregular shaped sample of FaL-G
127
India respectively.
In order to standardized ‘Simplified Two media’ method for measuring linear
attenuation coefficient of odd shaped samples, initially the results obtained for
attenuation coefficient of regular shaped samples employing this method has to be
compared with those incurred using standard narrow beam transmission method. For
this, five regular discs shaped samples have been formed using the procedure as given
below:
Appropriate amount of flyash, lime and gypsum were weighted using an
electronic balance having an accuracy of 0.0001g. The materials were then thoroughly
mixed in pestle mortar for half an hour and sieved through mesh (-200) to achieved
particle size homogeneity. Some water was added to the mixture and the paste so
formed was poured into a specially designed disc shaped cylindrical mould and pressed
gently. Disc shaped samples so obtained were taken out from the mould and were kept
in sunlight for about 25-30 hours to completely remove the moisture content.
Further to check the validity and reliability of method for irregular shaped
samples, five odd shaped samples were prepared using the same procedure as described
above except the mould was of irregular shape.
The detailed description of all the regular as well as irregular shaped samples
has been given in Tables 5.1.
5.4
Experimental details and method of measurement
100 mCi
241
Am (59.54 keV) point source along with Ortec (3x3-in) NaI
scintillation detector coupled to EG&G Ortec multichannel analyzer has been used in
present measurements. Three collimators of aperture 4mm, 3mm and 2mm have been
used as source, sample and detector collimators respectively. Schematic diagram of the
128
experimental setup used in present investigation has been shown in figure 5.2.
To avoid the scattered radiations from reaching the detector, it was properly
surrounded with lead. The ray diagram (figure 5.3) represents the total scatter
acceptance angle (θsc) which is the sum of the incidence beam divergence (θin) and
angle subtended by exit collimation (θout). For present dimensions the total scatter
acceptance angle (θsc) was 2.79o, which is 30. Therefore for this acceptance angle,
scattered radiations reaching the detector can produce a ray sum error of (0.5-1.0) %,
which is within acceptable limit (Midgley, 2006). Incident (Io) and transmitted beam
intensity (I) for each sample were measured for sufficiently large fixed preset time so
that the statistical uncertainty could be kept below 0.5%. Stability and reproducibility of
the procedure was tested before and after each run. Acrylic box of dimensions of 5cm ×
5 cm × 9 cm has been used to hold sample and liquid media in ‘Simplified Two media’
method.
Experimental procedure for measuring linear attenuation coefficient of aforesaid
samples has been divided into three phases.
In first phase, linear attenuation coefficient of regular shaped FaL-G samples as
well as aforesaid liquids used as media has been measured by using standard
transmission method by adopting narrow beam geometry as shown in figure 5.2. In
second and third phase of experiment, linear attenuation coefficient of both regular and
irregular shaped samples has been measured by using ‘Simplified Two media’ method
adopting the procedure described as follow:
Firstly the sample under study has been immersed in medium 1 which is air in

present case. Transmitted beam intensity I1 has been measured through the whole
assembly (sample, medium 1 and acrylic box). Then the transmission beam intensity I 1
129
10 mm
10 mm
C1
4 mm
10 mm
C2
3 mm
C3
a
2 mm
D
S
270 mm
Amplifier ORTEC 272A
C1, C2 and C3- Collimators
a-Acrylic Box
Multi Channel Analyzer ORTEC
A64-BI
S-Source
H.V Power Supply
ORTEC 556
D-Detector
Fig. 5.2:
Experimental setup of standard transmission geometry.
130
S
in
C
T
sc
C
T-Target
S-Source
C-Collimator
D-Detector
out
D

Fig. 5.3:
Schematic diagram representing the incident beam divergence and
scattered radiations reaching the detector.
131

without sample has been measured. Similarly transmission beam intensities I 2 and
I 2 have been measured for medium 2 with same sample. Then by applying expression
(5.6), linear attenuation coefficients of given sample has been obtained for that
particular pair of media (i.e. air plus liquid media). Same procedure has been repeated
for all other media as well as for regular and irregular shaped samples.
5.5
Result and discussion
In first phase of experiment linear attenuation coefficients of seven different
materials; glycerin, water, cottonseed oil, Mobile oil, machine oil, ethanol and methanol
have been measured employing narrow beam transmission geometry. Similarly linear
attenuation coefficients of regular shaped samples of FaL-G have been measured by
using same geometry and have been shown in Table 5.2 along with theoretical values
obtained from XCOM (Berger and Hubbell, 1987) and FFAST (Chantler et. Al.,2005).
It has been observed from tables that measured values were in good agreement with
theoretical values within experimental uncertainties, which is ~2%.
In second phase of experiment, linear attenuation coefficients of same regular
shaped samples of FaL-G were measured employing ‘Simplified Two media’ method.
For this, following combinations of seven different materials with air have been used;
Glycerine-air, water-air, ethanol-air, methanol-air, cottonseed oil-air, machine oil-air
and mobile oil-air. Each of these above pairs acts as two media in ‘Simplified Two
media’ method. For each pair of media, a set of five different values of linear
attenuation coefficient of a given sample have been obtained. Same procedure has been
repeated with all other combinations of seven media and samples. Average value of
linear attenuation coefficient thus obtained for each sample has been depicted in Table
5.3. For standardization of this method, results have also been compared with those
132
obtained from standard transmission geometry as well as from FFAST (Chantler et al.,
2005) and XCOM (Berger and Hubbell, 1987). The maximum experimental error
associated with linear attenuation coefficient measured using ‘Simplified Two media’
method is ≤ 3%. Measured values have been found to be in good agreement with
theoretical values within experimental uncertainties.
In third phase of experiment, linear attenuation coefficients of irregular shaped
samples of FaL-G of same composition (as of regular shape samples) were measured
employing ‘Simplified Two media’ method. The procedure of measurement is same as
described in second phase. Obtained experimental results along with theoretical values
calculated from programme FFAST (Chantler et al., 2005) and XCOM (Berger and
Hubbell, 1987) have been shown in Table 5.4. It can be observed from the Table that
the measured values are in good agreement with calculated values within experimental
uncertainties.
To compare the results of regular and irregular shaped samples directly obtained
using ‘Simplified Two media’ method, their corresponding mass attenuation coefficient
has been measured. This is because; all mass attenuation coefficients are independent of
the actual density and physical state (gas, liquid or solid).
To obtain the values of mass attenuation coefficient of both regular and irregular
shaped FLaG samples, linear attenuation coefficient values of samples measured using
Simplified Two media method have been divided by their corresponding densities.
Densities of regular shaped samples have been measured using standard mass/volume
formula, whereas densities of irregular shaped samples have been measured using
standard Archimedes principle formula adopting the same procedure as describe
elsewhere (Kirdsiri et al., 2009). Table 5.5 shows a the comparison of mass attenuation
coefficient values of irregular shaped samples obtained using ‘Simplified Two media’
133
method and of regular shaped samples obtained using standard transmission geometry.
A good agreement between the values obtained using both methods has proved that the
‘Simplified Two media’ methodology has a potential application for the determination
of the linear and mass attenuation coefficient of irregularly shaped samples.
134
Table 5.2:
a
b
Comparison of measured values of linear attenuation coefficient
cm-1) of regular shaped samples obtained employing standard
transmission geometry with calculated values.
S.No.
Sample
code
Experimental values
Theoretical values
1.
RS-1
0.399
0.397a
0.393b
2.
RS-2
0.405
0.404a
0.400b
3.
RS-3
0.410
0.414a
0.410b
4.
RS-4
0.419
0.420a
0.416b
5.
RS-5
0.429
0.431a
0.427b
XCOM ( Berger and Hubbell,1987) values
FFAST (Chantler et al., 2005) Values
135
Table 5.3:
Comparison of the average experimental value of linear
attenuation coefficient (cm-1) of regular shaped samples
measured employing ‘Simplified Two media’ method with
calculated values.
S.No.
Sample
Code
1.
RS-1
2.
Average
experimental values
Theoretical
Values
Experimental values c
0.401
0.397a
0.393b
0.399
RS-2
0.406
0.404a
0.400b
0.405
3.
RS-3
0.413
0.414a
0.410b
0.410
4.
RS-4
0.424
0.420a
0.416b
0.419
0.428
0.431a
0.427b
0.429
5.
RS-5
a
XCOM ( Berger and Hubbell,1987) values
FFAST ( Chantler et al., 2005) Values
c
Obtained using linear transmission geometry
b
136
Table 5.4:
a
Comparison of the average experimental value of linear
attenuation coefficient (cm-1) of irregular shaped samples
measured employing ‘Simplified Two media’ method with
calculated values.
Average experimental
values
S.No.
Sample
Code
1.
IRS-1
0.404
0.403a
0.400b
2.
IRS-2
0.410
0.411a
0.406b
3.
IRS-3
0.418
0.421a
0.416b
4.
IRS-4
0.421
0.420a
0.417b
5.
IRS-5
0.430
0.434a
0.431b
XCOM ( Berger and Hubbell,1987) values
FFAST ( Chantler et al.(2005) Values
b
137
Theoretical
Values
Table 5.5:
Comparison of the average experimental values of mass attenuation
coefficient  /  (gm/cm2) of irregular and regular shaped FaL-G
(flyash-lime-gypsum) samples obtained using both the ‘Simplified
Two media’ method and standard transmission geometry
respectively
Average experimental
values
Sample Code
of mass attenuation
a
a
Measured using ‘Simplifiedcoefficient
Two media method’.
Sample
S.No
Code
b
a
b
Mass attenuation
coefficient value b
Measured using standard transmission geometry.
1.
IRS-1
0.345
RS-1
0.347
2.
IRS-2
0.347
RS-2
0.349
3.
IRS-3
0.348
RS-3
0.347
4.
IRS-4
0.354
RS-4
0.352
5.
IRS-5
0.352
RS-5
0.355
Obtained using ‘Simplified Two media’ method.
Obtained using standard transmission geometry.
138