Determination of in situ detection efficiency for IM-NAA of non-standard geometrical samples
Nuclear Science and Technology, Vol.9, No. 4 (2019), pp. 27-33
Determination of in situ detection efficiency for IM-NAA of
non-standard geometrical samples
Nguyen Duy Quang1, Trinh Van Cuong1, Tran Tuan Anh1,
Ho Van Doanh1, Nguyen Thi Tho1, Ho Manh Dung2
1 Dalat Nuclear Research Institute, 01 Nguyen Tu Luc Street., Da Lat, Lam Dong.
2 Center For Nuclear Techniques, 217 Nguyen Trai street, District 1, HCM City.
(Received 29 November 2019, accepted 30 December 2019)
Abstract: The k0-based internal mono-standard (IM) method was first proposed for the concentration
analysis of samples of non-standard geometry in the 2000s. The method has demonstrated several
advantages such as the elimination of gamma-ray self-attenuation and geometrical effects. On the
other hand, the accuracy of the method principally depends on the in situ relative detection efficiency,
which requires to be obtained in each measurement. Therefore, the relative detection efficiency is
always under consideration for the improvement of the analysis results. The present paper describes a
simple and automatic procedure for the determination of the relative efficiency using one or more
activation products emitting gamma rays over a considered range of the spectrum. The procedure can
be applied for INAA and PGNAA analysis.
Keywords: INAA, PGNAA, internal mono-standard method, relative efficiency, non-standard
geometry samples.
and then used for elemental concentration
analysis. The in situ relative detection
efficiency plays a key role in the analysis as it
is valuable to the correction of sample
geometry effects [6]. In this study, a computer
code for the determination of the in situ
relative efficiency has been developed. Using
Prompt Gamma NAA (PGNAA) and
Instrumental NAA (INAA) nuclear data, the
software requires only a peak area report file
for calculation of relative efficiency and
perform further analysis. Results from
measurements of standard reference materials
have been found to be in good agreement with
certified values.
I. INTRODUCTION
Neutron activation analysis (NAA) is a
sensitive multi-element analytical technique
used for both qualitative and quantitative
analysis of elements in a vast amount of
materials. The technique has applications in
chemistry, geology, archeology, medicine,
environmental monitoring and even in forensic
science [1-4]. However, there are limitations
due to sample size for application in bulk
analysis, in particular for archaeology and
cultural art artifacts, forensic materials as well
as geological studies . For example, large and
non-standard geometry samples give rise to
problems of neutron self-shielding, gamma
rays attenuation and certain geometrical
effects. Therefore, the internal mono-standard
analysis method has been proposed to
overcome the mentioned difficulties [5]. In this
method, the in situ relative detection efficiency
is required to be obtained in each measurement
II. CONTENT
A. Subjects and methods
In INAA using k0 approach, consider
two arbitrary elements x and y presented in an
activated sample which emits two series of
©2019 Vietnam Atomic Energy Society and Vietnam Atomic Energy Institute
DETERMINATION OF IN SITU DETECTION EFFICIENCY FOR IM-NAA OF NON-STANDARD...
characteristic gamma rays Ex,i and Ey,j (i, j = 1,
2,...), respectively. The mass ratio of element x
to y can be expressed as follow [5]:
As clearly seen in eq. (3), the relative
concentration of element x to y can be
determined by the ratio of full peak detection
efficiencies. This leads to the need for using
relative detection efficiency which can be
determined straightforwardly from eq. 3 using
a fitting procedure. The relation of detection
efficiencies is as follow:
P
k
0,Ey, j
(SDC( f Q0 ()))y
mx
Ex,i Ey, j
(1)
my (SDC( f Q0 ()))x P
k
Ey, j Ex,i 0,Ex,i
Where S is the saturation factor, D is
the decay factor, C is the measurement
factor, f is the ratio of the thermal to
epithermal neutron fluxes, Q0() is the ratio
of the resonance integral-to-thermal neutron
cross-section corrected for the non-ideal
epithermal neutron flux distribution (α), P is
the peak area and ε is the full energy peak
detection efficiency. In case of high f, the
cE
m
x,i
(6)
E
x E
y, j
x,i
cE my
y, j
Hence,
cE
cE
mx
my
x,i
ln(E ) ln
ln
ln(E )
x,i
(7)
y, j
y, j
The efficiencies at different gamma
energies of each element are derived from
eq. (6)
value of
in eq.
( f Q0 ()))y / ( f Q0 ()))x
(1) tends to unity and therefore, eq. (1) can
be simplified as:
cE
cE
x,1
x,i
(8)
ln(E ),i 2,3,...
ln(E ) ln
P
k
0,Ey, j
x,i
x,1
(SDC)y
mx
Ex,i Ey, j
(2)
my (SDC)x P
k
0,Ex,i
Ey, j Ex,i
cE
cE
y,1
ln(E ) ln
ln(E ), j 2,3,... (9)
y, j
y,1
The situation is very simple in case of
PGNAA where the correction factors S, D and
C can be eliminated. Though, it should be
noted that the k0 databases for two different
techniques are different. Having it in mind, the
mass ratio in both INAA and PGNAA can be
rewritten as:
y, j
Thus, relative efficiency curves in
logarithmic scale constructed individually
from each element are expected to be differed
by constant factors, say t. Because of using
relative efficiency, an arbitrary positive value
can be firstly assigned to one detection
efficiency of each element, e.g.
E
ArbE 10%
cE
mx
my
y, j
k ,1
x,i
(3)
c
Ey, j
Ex,i
for any k-th element where “Arb” indicates
the first choice of detection efficiency. The
relative detection efficiencies are then
corrected by t-factors:
Where c is the coefficient calculated
using k0 database and experimental data
P
Ex,i
(4)
c
Ex,i
(10)
In general, the expression for the relative
ln(RelE ) ln(ArbE ) tk
(SDC)x ( f Q0 ()))x k0,E
k ,i
k ,i
x,i
and in some cases can be simplified as
efficiency curve is
P
Ex,i
n
(5)
cE
ln(Rel(E)) a (ln E)i
x,i
(11)
(SDC)x k0,E
i
x,i
i0
28
NGUYEN DUY QUANG et al.
Where ai is the coefficient and n is the
order of the polynomial that can be chosen
depending on the energy range of interest.
After the relative efficiency calibration curve
(11) is constructed, the relative concentrations
can be calculated from eq. (3) and converted to
absolute concentration using a well-know mass
fraction of an element presented in the sample.
If the concentration of m elements are required
to be analysed there will be m+n+1 parameters
needed to be optimized in fitting procedure,
including ai, i=0,1,..n and tk, k=1,2,...m. The
iteration loop for determination of all
mentioned parameters is presented in Fig. 1.
of experimental relative detection efficiency at
different energies of all elements, i.e.
calculation of all characteristic factors t in eq.
10 (see Fig. 2). In the next step, least-square
fitting is performed to construct a new
efficiency curve. The Goodness Of Fit (GOF)
in the fitting step is used for stop condition.
The loop is forced to stop whenever the GOF
starts to increase. On the other hand, it will
stop if the number of the loop is large enough
and the GOF is almost saturated. A typical
curve corresponding to the detector used for
spectrum acquisition may be chosen as the
original reference efficiency curve. It has been
found that the employment of different original
reference efficiency curves gives a very small
divergence on final analysis results.
The loop starts with a reference efficiency
curve which is then used for the correction
Fig.1. Iteration for optimization of fitting parameters
Fig. 2. Illustration of relative efficiency correction for iron by tFe-factor.
(a) before correction, (b) after correction
29
DETERMINATION OF IN SITU DETECTION EFFICIENCY FOR IM-NAA OF NON-STANDARD...
For evaluation of the method
performance uscore test was implemented. uscore
factor was calculated as follow:
The detector solution is 1.90 keV for 1332.5
keV (60Co).
mx my
(12)
uscore
m2 m2
x
y
In this study, the limiting value for uscore
has been set to 2.58 for a level of probability at
99% to determine if a result passes the
evaluation. The uscore values less than 1.96
mean that the result probably does not differ
significantly from the certified value while
uscore less than 1.64 that means the result does
not differ significantly from the certified value.
B. Results and discussion
In experiments, standard reference
materials, BIR-1 and SMELS-III, were used
for quality verification of the element
concentration for PGNAA and INAA,
respectively. BIR-1 sample had been
irradiated and analyzed by KFKI lab using k0
approach. The acquired spectrum was re-
used to construct a relative efficiency curve
for internal monostandard analysis. In case
of INAA, the SMELS III sample was sealed
in a polyethylene bag and irradiated for 09
hours at the Rotary Rack channel of Dalat
research reactor. The ratio f between thermal
and epithermal neutron flux is 37.3 and
epithermal neutron spectrum factor α is
0.073 [7]. The measurement was carried out
for about ~18 hours after ~5 days of decay.
To assess the feasibility of the method,
analysis of large samples has been attempted.
Two NIST-679 samples of different sizes and
weights were prepared and irradiated. The
small one (103.25mg) was analyzed by k0
approach while the large (1.365g) were
studied by IM-method using both optimized
and non-optimized efficiency curves. Gamma
spectrum was acquired by an HPGe detector.
Fig. 3. Construction of in situ relative efficiencies.
(A) BIR-1 sample, original curve 1,
(B1) SMELS-III sample, original curve 1,
(B2) SMELS-III sample, original curve 2.
In situ relative efficiency for each
sample has been constructed using the
mentioned fitting procedure. Fig. 3 indicates
the improvement of efficiency curves before
and after fitting steps. As for the BIR-1 sample,
the efficiency curve demonstrates a small
30
NGUYEN DUY QUANG et al.
change at high energy region while in the low
the BIR-1 sample. A majority of IM’s
element sconcentration has been found in
good agreement with certified values,
excluding results for Cr, Mn and Co.
However, k0 approach shows a very similar
pattern in case of Cr and Co when the
results are about 2 times greater than the
certified values.
energy region the divergence becomes large.
To assess the feasibility of the procedure,
two different original efficiency curves were
used in the study of the SMELS-III sample.
As clearly seen, the obtained relative
efficiency curves are very similar, showing
the differ from each other by nearly a
constant factor of about 1.3 in the logarithm
of relative efficiency.
The situation becomes better when using
IM’s method in the INAA study of the
SMELS-III sample (see Table. II). Despite
using different original efficiency curves, the
results are convergent and very close to
assigned values.
Analysis of element concentration in
the samples has been implemented using the
orresponding efficiency curve. Table I
shows the mass fraction of 15 elements in
Table I. Concentration found in BIR-1 sample (unit: Oxide form – wt%, Element – ppm)
Certified values
k0-approach (KFKI)
Conc. Rel. Unc. (3) Conc.
IM-approach
Note
No. El
Conc. (1)
+/- (2)
+/-
u-score
1
2
3
4
5
6
7
8
9
Na
Mg
Al*
Si
Ca
Sc
Ti
1.82
9.7
15.5
47.96
13.3
44
0.96
310
370
0.175
11.3
52
0.045
0.079
0.15
0.19
0.12
1
0.01
11
8
0.003
0.12
2
6
-
1.82
10
15.0
48
12.8
56
1.01
401
516
0.175
11.2
104
180
0.80
1.6
1.9
5.
1.82
9.4
0.06
0.6
0.9
1.47
0.4
3.4
0.03
40
47
0.010
0.4
8
0.00
0.50
0.00
1.75
1.92
1.61
0.63
0.63
5.37
2.68
0.48
7.76
0.80
-
Oxide form
Oxide form
Oxide form
Oxide form
Oxide form
Element
Oxide form
Element
Element
Oxide form
Oxide form
Element
Element
Element
2.6
1.4
3.0
2.7
2.6
3.5
5.
2.4
2.4
4.0
7.
15.5
45.37
12.5
49.7
0.98
336
V
Cr
626
10 Mn
11 Fe
12 Co
13 Ni
14 Sm
15 Gd
0.203
11.5
116
200
0.78
1.82
170
1.1
1.8
37
0.04
0.11
3.6
5.
0.4
0.05
Element
Table II. Concentration found in SMELS III sample (unit: ppm)
IM-approach, original
curve 2
IM-approach, original
curve 1
Assigned values k0-approach
No. El.
Conc.
1.140
86.7
+/-
0.031
2.6
190
0.33
11
Conc. +/- Conc.
1.21 0.01 1.136 0.039
90.01 3.79 83.5
8655 357 8200
25.45 1.04 23.9
+/-
u-score
Conc.
+/-
0.039
3
190
0.8
21
u-score
1
2
3
4
5
6
7
8
9
Sc
Cr
0.08
0.82
-
0.46
0.42
0.32
1.13
1.67
0.94
1.91
1.15
88.8
8200
23.9
610
0.2
0.53
-
0.46
0.34
1.54
0.05
0.81
1.96
3.6
2.9
190
0.8
21
4.9
272
0.7
1.2
0.8
Fe* 8200
Co
Zn
Se
Sr
Cs
Tm
24.3
618
131
8150
20.80
23.3
20.7
660
144
27
6
608
133.5
6
143
5
200
0.34
0.7
8891 374 7767
22.53 0.92 19.5
8132
20.1
26.2
24.1
286
0.8
1.3
0.8
25
22.5
1
0.9
24.6
22.5
10 Yb
0.5
11 Au
0.901
0.016
-
-
0.832 0.028
2.14
0.879
0.03
0.65
31
DETERMINATION OF IN SITU DETECTION EFFICIENCY FOR IM-NAA OF NON-STANDARD...
Table III. Concentration found in NIST-679 samples (unit: Fe-wt%, others-ppm)
IM approach
Non-optimized efficiency, Optimized efficiency,
Large sample Large sample
Conc. +/-
IM-approach
Datasheet
Value's
k0-approach,
Small sample
u-
score
No. El.
Conc. +/-
Conc.
+/-
Conc.
+/-
1
2
3
4
5
6
7
8
9
Sc
Cr
22.5
109.7
9.05
26
150
190
9.6
105
1.9
4.6
-
4.9
0.21
-
-
-
-
-
-
-
22.4
120.2
8.95
24.9
163
201
9.4
118
1.6
4.3
0.5
5.5
2.2
0.8
15
17
0.5
4
23.3
107.5
9.05
26.3
130.4
211.7
9.6
98.1
1.62
4.54
0.6
2.7
0.21
0.6
3.5
6.1
0.3
2.6
0.04
0.13
23.4
106.7
9.05
0.7
3.3
0.21
0.7
3.8
6.6
0.36
3.7
0.06
0.16
-
0.51
-
-
-
-
-
-
-
-
Fe*
Co
Zn
Rb
Cs
Ce
Eu
Hf
26.1
130.4
211.8
9.54
105.4
1.65
0.1
0.2
10
4.53
(1) Concentration, (2) Absolute Uncertainty, (3) Relative Uncertainty (%).
*Reference Element
The study of samples of different sizes
and weights has been attempted. Table III
compares mass fractions of 10 elements
presented in NIST-679 samples with
certified and informative values. As clearly
seen, the difference in sample size and
weight gives rise to some variation in
obtained relative concentrations of Cr, Zn,
Rb, Ce to Fe. If the optimized efficiency
curve is employed it can help to correct the
results for Ce. However, the difference in
sample size and weight gives an
insignificant change in the relative
efficiency curve. Therefore, it is desired for
further verification of the method using
large samples of various shape and size.
various geometry is required to verify and
optimize the method.
ACKNOWLEDGMENT
The authors are thankful to the Ministry
of Science and Technology of Vietnamese
government for financial support through the
ministerial-level
VNCHN.
project
DTCB-01/18-
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III. CONCLUSIONS
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NGUYEN DUY QUANG et al.
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