Determination of thermal neutron flux distribution at the rotary rack served for elemental concentration analysis using the k₀-INAA method
Nuclear Science and Technology, Vol.10, No. 1 (2020), pp. 11-20
Determination of thermal neutron flux distribution
at the rotary rack served for elemental concentration analysis
using the k0-INAA method
Nguyen Thi Tho1, Tran Tuan Anh1, Trinh Van Cuong1, Ho Van Doanh1,
Tran Quoc Duong1, Ho Manh Dung2
1Dalat Nuclear Research Institute, 01 Nguyen Tu Luc Street., Da Lat, Lam Dong.
2Center For Nuclear Techniques, 217 Nguyen Trai street, District 1, HCM City.
(Received 08 January 2020, accepted 24 February 2020)
Abstract: The accuracy of elements concentration determination using the k0-standardization method
directly depends on irradiation and measurement parameters including Non-1/E epithermal neutron
flux distribution shape (
), thermal-to-epithermal neutron flux ratio f, efficiency , peak
⁄
area… In the case of the irradiation position at the rotary rack of the Dalat Nuclear Research Reactor
(DNRR), the difference of thermal neutron flux between the bottom (3.541012 n.cm-2.s-1) and the top
(1.931012 n.cm-2.s-1) of the 15 cm aluminum container is up to 45%. Therefore, it is necessary to
accurately determine above-mentioned parameters in the sample irradiation position. The present
paper deals with the determination of the distribution of thermal neutron flux along the sample
irradiation container by using 0.1% Au–Al wire activation technique. The thermal neutron flux was
then used to calculate the concentration of elements in the Standard Reference Material 2711a and
SMELS type III using k0-INAA method at different positions in the container. The obtained results
with the neutron flux correction were found to be in good agreement with the certified values. In
conclusion, the proposed technique can be applied for activation analyses without sandwiching flux
monitors between samples during irradiations.
Keywords: K0-standardization method, Dalat nuclear research reactor, neutron spectrum parameters.
The advantages of k0-NAA in the applications
are a capability of the determination of multi-
element with high precision and accuracy as
well as a minimized sample preparation [1].
I. INTRODUCTION
Nuclear analytical techniques have been
developed for decades. It has been used to
solve
environmental
problems,
legal
investigations.... Since March 2012, the DNRR
has been continuously operated about 100130
hours per month at a nominal power of 500 kW
for radioisotopes production, activation
analysis and other researches. The k0-
standardization method (k0-NAA) has been
applied and developed at the DNRR over 17
years. Its main applications include the studies
in geology, bio-medicine, material, petroleum,
archaeology and environment among others.
At the DNRR, there are three irradiated
channels used for NAA (Fig.1): (1) The fast
pneumatic transfer system for very short
irradiation at the channel 13-2 and thermal
column (Tirr<45 sec); (2) The pneumatic
transfer system for short and medium
irradiations at the 7-1 channel (Tirr = 451200
sec); (3) The rotary rack with 40 irradiated
holes placed inside the graphite reflector for
long irradiation
(Tirr>20
min). The
©2020 Vietnam Atomic Energy Society and Vietnam Atomic Energy Institute
DETERMINATION OF THERMAL NEUTRON FLUX DISTRIBUTION AT THE ROTARY RACK ...
experiments for determination of thermal flux
were carried out at the sixth hole of the rotary
rack of the DNRR.
in NAA are parameters such as flux variation
within a sample and irradiation geometry in the
container. When the sample is irradiated with
neutrons, the activation rates depend on the
geometry effect due to the irradiation position
within the container, the variation and the
differences within the irradiation site [4].
In the determination of elemental
concentration in unknown samples using k0-
method, samples and flux monitors were
simultaneously irradiated together. The flux
monitors were usually positioned at the top,
middle and bottom of the containers.
Therefore, we proposed the technique that can
be applied for k0-method with suitable
accuracy without sandwiching flux monitors
between samples during irradiations. An
experimental determination of the thermal
neutron flux in the inner sample irradiation
container at the rotary rack of the DNRR
using foil activation technique was undertaken
in this work.
Fig. 1. Dalat research reactor cross-section.
The neutron spectrum parameters of the
DNRR were reported to be very stable which
permit the use of k0-NAA method [2].
Instrumental neutron activation analysis with
research
reactors
has
some
special
characteristics which makes it more attractive
to use for routine analysis. These include
multi-element capability, reproducibility of
the results and independence of the chemical
state of the element [3,4]. Thermal, epithermal
and fast neutron fluxes determination are
useful when characterizing the activation site
in instrumental neutron activation analysis. In
this perspective NAA using reactor neutrons
plays a vital role due to its high sensitivity
and detection limits for many elements in a
variety of matrices [5], but these could not be
achieved without proper knowledge of the
neutron flux [6].
II. CONTENT
A. Subjects and methods
In the absolute method, the thermal
neutron flux is given as [7]:
(1)
(2)
[
]
Where Asp is the specific activity, M is
It is necessary to measure thermal
neutron flux distribution at various points in
sample irradiation container and neutron flux
monitoring is, therefore, required to be carried
out regularly for any reactor for analytical
quality control. This is to guarantee continues
application of neutron activation analysis since
the main sources of measurement uncertainty
the atomic mass, is the isotopic abundance,
is the 2200 m.s-1 (n, γ) cross-section, γ is the
absolute gamma-intensity, Np is the number of
counts under the full-energy peak during the
counting time tm, w is the sample weight in
gram, S = l-exp(-tirr) is the saturation factor
with tirr being the irradiation time,
12
NGUYEN THI THO et al.
is the decay factor with td being decay time, C
= [l-exp(-tm) ]/tm is the measurement factor
correcting for decay during the measurement
time tm, is the decay constant, NA is the
[11]. This is due to the fact that the epithermal
flux is shown to deviate from the ideal situation
with a factor . Eq. (4) should, therefore, be
modified to take care of the flux-shaping factor
and thus we have a semi-empirical relationship
given as:
Avogadro’s number, p is the full energy peak
detection efficiency, f is the thermal to
epithermal neutron flux ratio, is the
epithermal neutron flux shape factor.
[ ]
(5)
Where is the characteristic of the
reactor irradiation position and was shown [11]
to be positive or negative depending on the
reactor epithermal spectrum. Eq.(5) was
proved to be satisfactory for instrumental
neutron activation analysis [6,11] and it
enables the correction of the resonance integral
to the deviating spectrum. Thus to preserve
accuracy in the k0-method, should be known
when calculating the concentration of an
element in a sample [6,12].
For ideal situation Q0 = I0/0, I0 -
resonance integral for an ideal (assumed 1/E)
epithermal neutron flux distribution.
For a non-ideal situation, the Q0(I0) need
to be modified with an -dependent term. The
conversions from the tabulated Q0(I0) values to
Q0() (or (I0()) are given by:
]
[
(3)
̅̅̅
The k0-standardization method was
Where ECd is the effective Cd cut-off
introduced in NAA [13]. In terms of the k0-
energy ( ECd=0.55 eV in standard conditions)
methodology,
adopting
the
Hødgdahl
and Er is the effective resonance energy,
convention [14], the concentration calculations
are based on the fundamental equation:
defined by Ryves [8]. The a term
(numerically unity) originates from the
definition of the epithermal neutron flux in a
1/E1+ distribution [9,10].
⁄
(6)
⁄
(
)
For an ideal reactor flux, the slowing
down neutrons after collision with the
moderator atoms, show an energy distribution
e(E) which varies as E-1. This means that the
epithermal neutron flux integrated over one
logarithmic energy interval can be represented
by a constant e since:
With k0 defined as:
(7)
SMELS type III [13] (a multi-element
synthetic material producing the long-lived
radionuclides when irradiated with neutrons)
and SRM-2711a (the certified reference
material from National Institute for Standard
and Technology - NIST) were used to calculate
the concentration of the elements at different
positions in the container using k0-INAA.
[ ]
(4)
However, it was found that applying a
single comparator method (k0-standardization)
with reactor neutrons, using Eq. (4) is
unacceptable from the standpoint of accuracy
13
DETERMINATION OF THERMAL NEUTRON FLUX DISTRIBUTION AT THE ROTARY RACK ...
In order to evaluate the laboratory
performance, the u-score test was used in
which the u-score is calculated according to the
following equation:
(9)
B. Experiment
For determination of the axial flux
distribution, the gold wire (Al-0.1%Au, =0.6mm)
was used. The 15 cm long Au wire was placed at
the center of the aluminum container. After
irradiation and suitable decay, it was cut in pieces
of 5 mm with the weight of about 2 - 6 mg. The
gold foils (Al-0.1%Au, d=0.1mm) and zirconium
foils (Zr-99.98%) were also placed at some
positions 1, 2, 6, 7, 12, 14 cm in order to determine
the thermal neutron flux and , f values.
(8)
√
Where xlab, ulab, xref, and uref are the
experimental and reference values and
uncertainties, respectively [2].
The relative bias between the
experimental result and the reference value is
calculated and expressed as a percentage:
Fig. 2. Typical aluminum sample irradiation container usually used at the rotary rack of the DNRR.
Table I. The irradiation, decay, counting times for Au wire/foil, Zr monitor, SRM-2711a, SMELS III.
Counting time
SRM/Monitor
Au wire
Irradiation time (tirr)
Decay time (td)
12d
(tm)
1739h
1h
1h/10h
1h
Au foil
34 d
10 15m
120m
Zr monitor
SRM-2711a
SMELS III
3d
1h/10h
10h
912d
215h
223h
1018d
After an appropriate decay time, the
Au wire was cut into sixteen pieces of 5mm
and measured on the HPGe coaxial detector
1.9 keV at 1332.5 keV. The full-peak
energy efficiency of the detector was
determined using standard gamma-ray
sources of 241Am, 133Ba, 109Cd, 137Cs, 60Co,
57Co and 152Eu.
(GMX30190), which has
a
relative
efficiency of 30% and energy resolution of
14
NGUYEN THI THO et al.
and the top (1.931012 n.cm-2.s-1) of the 15 cm
C. Results and discussion
aluminum container is up to 45%. The
measured results of and f at the rotary rack
of the DNRR were found of 0.088 and 39.5,
respectively. The values are in good agreement
with the previous measurements [16].
The thermal neutron flux distribution in
the sample irradiation container of the DNRR
was shown in Table II and Fig. 3. The
difference of thermal neutron flux between the
bottom (3.541012 n.cm-2.s-1) of the 0.75 cm
Table II. The axial thermal neutron flux profile in the sample irradiation container.
Thermal
neutron flux
(n.cm-2s-1)
Axial position in
the container
(cm)
Thermal
neutron flux
(n.cm-2s-1)
Axial position in the
container
Error
Error
(n.cm-2s-1)
(n.cm-2s-1)
(cm)
0.75
1.25
2.25
3.25
4.25
5.25
6.25
6.75
7.25
8.25
9.25
10.25
12.25
13.25
13.75
14.25
3.51E+12
3.43E+12
3.48E+12
3.28E+12
3.16E+12
3.08E+12
2.90E+12
2.86E+12
2.77E+12
2.71E+12
2.68E+12
2.55E+12
2.26E+12
2.13E+12
2.09E+12
1.98E+12
1.43E+11
1.39E+11
1.43E+11
1.32E+11
1.29E+11
1.25E+11
1.18E+11
1.17E+11
1.13E+11
1.15E+11
1.09E+11
1.04E+11
9.25E+10
8.63E+10
8.67E+10
8.16E+10
2(*)
7(*)
3.35E+12
2.84E+12
2.06E+12
3.51E+12
3.07E+12
2.27E+12
1.32E+11
1.13E+11
8.31E+10
1.38E+11
1.22E+11
9.11E+10
14(*)
1(**)
6(**)
12(**)
(*) Neutron flux in January 2019. (**) Neutron flux in February 2019.
4.0E+12
Thermal flux using Au wire
Thermal flux using Au foils *
3.5E+12
Thermal neutron using Au foils **
3.0E+12
2.5E+12
2.0E+12
1.5E+12
0
5
10
15
Position (cm)
Fig. 3. Thermal neutron flux distribution from the bottom to top of the container.
15
DETERMINATION OF THERMAL NEUTRON FLUX DISTRIBUTION AT THE ROTARY RACK ...
The thermal neutron flux distribution in
the sample irradiation container of the DNRR
also was simulated by MCNP code,
simulation results were shown in Fig. 4.
In this simulation (Fig. 5), it has been
shown that the difference of thermal neutron
flux within 2.4 cm of the diameter of the
aluminum container is about 20% and with
1.5 cm of the effection diameter of the sample
box is about 10%. This difference won’t affect
the accuracy of element analysis using k0-
INAA when irradiation samples are coaxially
arranged in the.
1.1
MCNP
1
Exp
0.9
0.8
0.7
0.6
0.5
0.4
The obtained neutron flux was then
used to calculate concentration of the
elements in the SRM-2711a and SMELS III
using k0-INAA method at different positions
in the container. The xlab/xref ratios, RB values
and u-scores were used to evaluate the
precision of data. The thermal neutron flux
distribution in the container were shown in
Table II and Fig. 3. The concentration of
elements Fe, Cr, Co, Sc in SRM-2711a were
compared with the reference values in which
the RB values are less than 5% in both cases
of sandwiching and linear interpolation at
difference positions in the container, except
for Cr were about 12% at the position of 14
cm. The u-score values were within ±1.64 for
all elements (see Tables III-IV).
0
5
10
Positon (cm)
15
20
Fig. 4. Obtained thermal neutron flux distribution
from the bottom to top of the container by
experiment and simulation.
Fig. 4 shows that within the error range
the obtained results from experiment are in
good agreement with simulation results.
The determination of thermal neutron
flux distribution along the diameter of the
container by experiment is quite difficult so
we have simulated this distribution by MCNP
code. Simulation result was seen in Fig. 5.
4.0E+12
3.9E+12
3.8E+12
3.7E+12
3.6E+12
3.5E+12
3.4E+12
3.3E+12
3.2E+12
3.1E+12
-1.8
-1.2
-0.6
0
0.6
1.2
1.8
Position (cm)
Fig. 5. Simulation of thermal neutron flux distribution along the diameter of the container by MCNP code.
16
NGUYEN THI THO et al.
Table III. The concentration of elements and uncertainties in mg/kg, xlab/xref ratios, RB and u-score values
for SRM-2711a at position 2cm in the container.
RB1 RB2
(%) (%)
1
2
1
2
Element
xlab±ulab
29621±1235 29258±1223 28200±400
54.2±3.2 53.5±3.2 52.3±2.9
10.31±0.55 10.19±0.54 9.89±0.18
8.6±0.4 8.5±0.3 8.5±0.1
xlab±ulab
xref±uref
xlab/xref xlab/xref
u-score1 u-score2
Fe
Cr
Co
Sc
1.05
1.04
1.04
1.01
1.04 5.04 3.75
1.02 3.63 2.29
1.03 4.25 3.03
1.00 1.18 0.00
1.09
0.44
0.73
0.24
0.82
0.29
0.52
-0.05
1 using sandwiching flux monitor
2 using linear interpolation
Table IV. The concentration of elements and uncertainties in mg/kg, xlab/xref ratios, RB and u-score values
for SRM-2711a at position 7 cm in the container.
RB1 RB2
(%) (%)
2.08 2.32 0.46
u-
u-
1
2
1
2
Element
xlab±ulab
xlab±ulab
xref±uref xlab/xref xlab/xref
1.02
1.00 -0.18 -4.06 0.47
score1 score2
Fe
Cr
Co
Sc
28786±1197 28854±1180 28200±400 1.02
0.53
0.5
54.1±2.6
10.25±0.47 9.85±0.44
8.6±0.4 8.3±0.3
52.0±2.5
54.2±2.6
9.89±0.18
8.6±0.4
1.00
1.04
1.00
1.00
0.97
3.64 -0.40 0.72
0.00 -3.49 0.32
0.78
0.38
Table V. The concentration of elements and uncertainties in mg/kg, xlab/xref ratios, RB and u-score values for
SRM-2711a at position 14 cm in the container.
RB1 RB2
u-
2
1
2
1
Element
xlab±ulab
xlab±ulab
xref±uref xlab/xrefxlab/xref
u-score2
score1
(%) (%)
28726±1234 28985±1223 28200±400 1.02 1.03 1.87 2.78
58.2±3.2 58.7±3.2 52.3±2.9
10.16±0.51 10.25±0.51 9.89±0.18 1.03 1.04 2.73 3.64
8.8±04 8.9±0.4 8.5±0.1 1.04 1.05 3.53 4.71
Fe
Cr
Co
Sc
0.41
0.61
1.49
0.67
0.95
1.11 1.12 11.28 12.24 1.37
0.49
0.73
Table VI. The concentrations of elements and uncertainties in mg/kg, xlab/xref ratios, and u-scores
for SMELS III at position 1 cm in the container.
RB1 RB2
(%) (%)
u-
u-
1
2
1
2
Element xlab±ulab
xlab±ulab
xref±uref
xlab/xref xlab/xref
score1 score2
Fe
Co
Cr
Sc
Cs
In
8672±358 8655±357
8200±190
1.06
1.05
1.04
1.06
1.05
1.04
1.06
1.08
1.10
1.07
1.10
1.09
1.11
1.07
1.09
1.07
5.76 5.55 1.16 1.12
4.94 4.73 1.09 1.05
4.04 3.81 0.76 0.72
6.14 6.14 1.16 1.12
8.56 8.32 1.80 1.76
10.28 10.17 1.69 1.66
7.03 6.64 1.37 1.33
10.69 9.92 1.61 1.57
9.31 9.09 1.79 1.75
10.69 10.69 1.88 1.84
7.30 7.30 1.40 1.36
9.18 8.70 1.76 1.72
6.96 6.80 1.49 1.44
25.50±1.04 25.45±1.04 24.3±0.33
90.2±3.79 90.0±3.8 86.7±2.6
1.21±0.05 1.21±0.01 1.140±0.031 1.06
22.58±0.92 22.53±0.92 20.80±0.34
1.09
1.10
1.07
1.11
1.09
1.11
1.07
1.09
1.07
510±21
54.8±2.2
145±6
509±21
54.6±2.2
144±6
462±19
51.2±1.3
131±6
Sb
Se
Sr
8909±375 8891±374
8150±200
26.2±0.9
23.3±0.7
20.7±0.5
618±11
Th
Tm
Yb
Zn
29±1
25±1
29±1
25±1
22.6±0.9
661±27
22.5±0.9
660±27
17
DETERMINATION OF THERMAL NEUTRON FLUX DISTRIBUTION AT THE ROTARY RACK ...
Table VII. The concentrations of elements and uncertainties in mg/kg, xlab/xref ratios, and u-scores for
SMELS III at position 6 cm in the container.
RB1 RB2
u-
u-
1
2
1
2
Element xlab±ulab
xlab±ulab
xref±uref
xlab/xref xlab/xref
score1
score2
(%) (%)
1.57 6.06
0.41 4.94
4.96 9.57
0.88 5.26
0.96 5.77
5.63 10.39
1.56 7.42
5.34 9.92
3.73 8.33
7.25 12.21
9.87 9.68
9.18 14.01
0.81 5.18
Fe
Co
Cr
Sc
Cs
In
8329±485 8697±505
8200±190
24.3±0.33
86.7±2.6
1.02
0.96
1.05
1.01
1.01
1.06
1.02
1.05
1.04
1.07
1.10
1.09
1.01
1.06
1.05
1.10
1.05
1.06
1.10
1.07
1.10
1.08
1.12
1.10
1.14
1.05
0.25
0.07
0.82
0.20
0.19
0.91
0.42
0.77
0.64
1.29
1.62
1.53
0.14
0.92
0.90
1.49
0.95
1.02
1.62
1.17
1.42
1.37
2.06
1.77
2.24
0.91
24.4±1.2
91±5
25.5±1.3
95±5
1.15±0.06 1.20±0.06 1.140±0.031
21±1
488±22
52±3
22±1
510±23
55±3
20.80±0.34
462±19
Sb
Se
Sr
51.2±1.3
131±6
138±7
144±7
8454±433 8829±453
28.1±1.2 29.4±1.3
25.6±1.3 22.7±1.02
8150±200
26.2±0.9
23.3±0.7
20.7±0.5
618±11
Th
Tm
Yb
Zn
22.6±1.2
623±32
23.6±1.2
650±34
Tables VI and VII show elements
concentration and uncertainties in mg/kg for
SMELS III sample along with xlab/xref ratios,
RB values and u-scores at different placed
sample positions in the container with
sandwiching flux monitors and with linear
interpolation of thermal neutron flux. These
results were compared with the obtained results
by the other authors [18] in which the RB
values for all elements were within ±5%.
Generally, most u-score values were within
±1.96 except for Th, Yb (the second method
was marked 2, at position 6 cm in the
container) were bigger than this value (Table
VII). If we increase the limiting value for the
u-score to 2.58 for a level of probability at
99%, all our analytical results will pass. So we
see that determination of concentration of
elements using k0-INAA method with or
without sandwiching flux monitors are
acceptable. It means that we can get the precise
of thermal neutron flux at each position of the
sample from the linear interpolation instead of
sandwiching the monitor as usual.
III. CONCLUSIONS
The axial thermal neutron flux
distribution in the sample irradiation container
at the rotary rack of the DNRR was determined
by gold wire activation analysis. The
difference of thermal neutron flux within 0.5
cm of the aluminum container length is about
2%, 1 cm is about 4%, 2 cm is about 10% and
between the bottom and the top of the
aluminum container is up to 45%. The
accuracy of element analysis using k0-INAA
method strongly depends on the thermal
neutron flux. Hence, the proposed technique
can be applied for the determination of
concentration of elements without sandwiching
flux monitors.
18
NGUYEN THI THO et al.
[6]. Ahmed, Y.A., Ewa, I.O.B., Umar, I.M.
ACKNOWLEDGMENT
“Effective resonance energy and nonideality of
epithermal neutron flux distribution in neutron
activation analysis”, Nigerian Journal of
Physics, 14(1), 82-85, 2002.
The authors are thankful to the
Ministry of Science and Technology of
Vietnamese government for financial
support through the ministerial-level project
DTCB-01/18-VNCHN.
[7]. H.M Dung. “Study for development of k-zero
Neutron Activation Analysis for multi-element
characterization”, PhD thesis, the Natural
Science University, Hochiminh city, 2003.
REFERENCE
[8]. T.B. Ryves. “A new thermal neutron flux
convention”, Metrologia, 5(4), 119-124, 1969.
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