Download Utilization of Thermal Neutrons

University of Ljubljana
Faculty of Mathematics and Physics
Aljaž Kolšek
Utilization of Thermal Neutrons
Seminar IV
Abstract:
The neutrons produced in the fission reactions emerge with the average
energy being around 2 MeV, therefore neutron moderation is required to
achieve well thermalized neutron flux. Their usage is spread over various
science fields with applications exploiting several physical processes like
neutron capture, elastic and inelastic scattering, upscattering, etc. The
MCNP Monte Carlo neutron transport code is used to calculate the
neutron fluxes and spectra in the TRIGA Mark-II MCNP model.
MENTOR: doc. dr. Andrej Trkov
CO-MENTOR: dr. Luka Snoj
Ljubljana, 2012
Contents
1 Introduction
1.1 Neutron Thermalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Moderating Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2 Utilization of Thermal Neutrons
2.1 Neutron Activation Analysis . . . . . . . .
2.1.1 Physical Aspect . . . . . . . . . . .
2.1.2 Detection . . . . . . . . . . . . . .
2.1.3 Calculating Element Concentration
2.1.4 FT-TIMS . . . . . . . . . . . . . .
2.2 Neutron Scattering Techniques . . . . . .
2.2.1 Elastic Neutron Scattering . . . . .
2.2.2 Inelastic Neutron Scattering . . . .
2.3 Ultracold Neutrons . . . . . . . . . . . . .
2.3.1 Production . . . . . . . . . . . . .
2.3.2 Utilization . . . . . . . . . . . . . .
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3 Designing of the Irradiation Device
3.1 The Irradiation Device Design . . . . . . . . . . . . . . . . . . . . . . . . . . .
12
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4 Conclusion
13
References
14
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1
Introduction
The study of thermal neutrons is a very important part of reactor physics. As the
neutrons are produced in neutron induced fission of a fissile material, they have to be
slowed down to the thermal energies due to the absorption cross section being inversely
proportional to the velocity. This property makes them suitable for measuring the
cross sections of the different isotopes. Their usage is spread over various science fields
with applications exploiting several physical processes like neutron capture, elastic and
inelastic scattering, upscattering, etc. Neutron moderators, such as light water, heavy
water and graphite, are used for neutron thermalization to achieve well thermalized
neutron flux, required for these applications.
1.1
Neutron Thermalization
The neutrons produced in the fission reactions emerge with a distribution (Figure
1) of energies, with the average fission neutron energy being around 2 MeV. This
distribution depends on incident neutron energy and nuclear isotope involved, however
it also differs for prompt and delayed neutrons. On Figure 1 is function χ(E) defined
so that χ(E)dE is the fraction of the prompt neutrons with energies between E and
dE.
0,4
[E]
0,3
0,2
0,1
0,0
0
1
2
3
4
5
6
E [MeV]
Figure 1: Fission spectrum for thermal neutron induced fission in
235
U
As we can see most of the fission neutrons are produced in the fast region, but the
fuel absorption cross section has 1/v dependence in the low-energy region (Figure 2).
Therefore neutron thermalization is desirable to sustain nuclear chain reaction in nuclear reactors. Neutron thermalization is the process that utilizes inelastic collisions in
the fuel and elastic collisions in the moderator to slow down high energy (fast) neutrons
to thermal equilibrium with the moderator nuclei. The spectrum of the thermal neutrons is Maxwellian characterized by the moderator temperature. Their temperature
is around ET = 0.025 eV) at room temperature 293 K and velocity 2.2 · 105 cm/s.[1]
2
Cross Section [b]
Energy [MeV]
Figure 2: Energy dependence of the absorption cross section.[14]
1.2
Moderating Power
Some applications and experimental methods require high thermal to fast neutron
flux ratio, therefore neutron moderation is necessary. Cross sections are highly dependant on the type of nuclide in the moderator. The number of collisions necessary to
slow down a neutron to thermal energies is inversely proportional to ξ, which is defined
as the mean lethargy gain per collision. Lethargy is defined as
E0
(1.1)
u = ln ,
E
where E0 is chosen to be maximum energy that neutrons can achieve in the problem.
Better moderators will thus have larger values of ξ. Moderating or slowing down power
of a moderator is defined as ξΣs . This definition does not take into account neutron
s
absorption, therefore more appropriate quantity is moderating ratio ξΣ
.
Σa
Table 1: Slowing down parameters of typical moderators.[1]
Moderator
ξ
No. of collisions from 2 MeV to 1 eV ξΣs [cm−1 ]
H2 O
0.920
16
1.35
D2 O
0.509
29
0.176
C
0.158
91
0.060
238
U
0.008
1730
0.003
ξΣs
Σa
71
5670
192
0.0092
The moderating ratio and moderating power is given for few materials in Table 1. In
this comparison it is apparent that D2 O is better moderator than others. Its advantage is a very low neutron absorption with still sufficiently large moderating power.
However, using heavy water as a moderator is also very expensive with prices being
around $300/kg.[1]
3
2
Utilization of Thermal Neutrons
Thermal neutrons are invaluable tools for applications in fundamental, engineering and medical science, as their physical properties allow scientists to conduct nondestructive testing techniques. They have wavelength similar to atomic distances in
crystal lattices, which means these neutrons can produce interference patterns and give
information about material structures. Penetration can be deep into the material, as
they have no electric charge and the neutron-matter interaction is weak. Presence of
the neutron magnetic moment can also help with the research on magnetic structures
of magnetic materials. Moreover, testing of the lattice vibrations can be conducted,
as thermal neutrons have kinetic energy similar to vibration energy of atoms in solids
and liquids.[16]
2.1
Neutron Activation Analysis
Neutron Activation Analysis is a sensitive analytical technique used for quantitative
and qualitative multi-element analysis of major, minor, trace and rare elements in
different types of samples.
2.1.1
Physical Aspect
The sample is bombarded with neutrons, causing one of the most common neutronmatter nuclear reactions (n,γ) or neutron capture, where a neutron interacts with the
target nucleus via non-elastic interaction and compound nucleus is formed in an excited
state. The excitation energy of the compound nucleus is due to the binding energy of
the neutron with the nucleus.
The compound nucleus almost instantaneously de-excite into a more stable nucleus
through emission of characteristic prompt gamma rays with short half lives in the
order of milliseconds. Frequently can this new configuration also include radioactive
nucleus which also de-excites and emits characteristic delayed gamma rays, but with
much longer half lives that can ranger from part of a second to several years. Therefore
Neutron Activation Analysis splits into two categories: Prompt Gamma-Ray Neutron
Activation Analysis (PGNAA) and Delayed Gamma-Ray Neutron Activation Analysis
(DGNAA).[17]
2.1.2
Detection
Measurements of gamma rays are usually performed with semiconductor detectors,
associated electronics and a computer-based multi-channel analyser. Typical semiconductor detector is HPGe (intrinsic germanium) which operates at liquid nitrogen
temperatures (77 degrees K) by mounting the germanium crystal in a vacuum cryostat, thermally connected to a copper rod. Most frequently used type of detector can
4
measure gamma-rays with energies from 60 KeV to 3.0 MeV. Figure 3 shows typical
gamma-ray spectra from an irradiated pottery specimen.[17]
Most common and efficient neutron sources are nuclear reactors, that can produce
thermal neutron flux of around 1012 − 1014 neutrons/cm2 s at maximum power. Highly
sensitive analysis is possible, because the cross section of neutron activation is high
in thermal region for the majority of the elements. However, interfering reactions
must also be considered, as there is a wide distribution of neutron energy in nuclear
reactor. To take this reactions into account, the neutron spectrum in the channels of
irradiation should be known exactly. For this application, mostly thermal neutron flux
is desired.[19]
Figure 3: Gamma-ray spectrum showing several short-lived elements measured in a
sample of pottery irradiated for 5 seconds, decayed for 25 minutes, and counted for 12
minutes with an HPGe detector.[17]
2.1.3
Calculating Element Concentration
The usual procedure to calculate concentration (in units ppm) of an element in the
unknown sample is to irradiate the unknown sample and a comparator with known
amount of the element of interest together in the reactor. If the activities of sample and
standard are measured on the same detector, it is necessary to correct the difference in
decay between the two. Measured counts are usually corrected for both samples using
the half-life of the measured isotope. Equation 2.1 is used to calculate the mass of an
element in the unknown sample relative to the comparator standard.
msam (e−λTd )sam
Asam
=
Astd
mstd (e−λTd )std
(2.1)
where A is the activity of sample (sam) and standard (std), m is mass of the element,
λ equals decay constant for the isotope and Td is decay time.
5
Table 2: Estimated Detection limits for NAA using decay gamma rays. Assuming
irradiation in a reactor neutron flux of 1013 neutrons/cm2 s.[17]
Sensitivity [picograms]
1
1 − 10
10 − 100
100 − 103
103 − 104
104 − 105
105 − 106
107
Elements
Dy, Eu
In, Lu, Mn
Au, Ho, Ir, Re, Sm, W
Ag, Ar, As, Br, Cl, Co, Cs, Cu, Er, Ga, Hf, I, La,
Sb, Sc, Se, Ta, Tb, Th, Tm, U, V, Yb
Al, Ba, Cd, Ce, Cr, Hg, Kr, Gd, Ge, Mo, Na, Nd, Ni,
Os, Pd, Rb, Rh, Ru, Sr, Te, Zn, Zr
Bi, Ca, K, Mg, P, Pt, Si, Sn, Ti, Tl, Xe, Y
F, Fe, Nb, Ne
Pb, S
The sensitivity of Neutron Activation Analysis is dependent on the irradiation parameters (neutron flux, irradiation and decay times), measurement conditions (measurement
time, detector efficiency) and nuclear parameters of the elements being measured (isotope abundance, neutron cross-section, half-life and gamma-ray abundance). Table 2
lists the approximate sensitivities for determination of elements assuming irradiation
in a reactor flux of 1013 neutrons/cm2 s and interference free spectra.[17]
2.1.4
FT-TIMS
Fission Track-Thermal Ionization Mass Spectrometry (FT-TIMS) is ultra-sensitive
particle analysis technique that uses high thermal flux from nuclear reactors for sample
irradiation. Firstly, particles are removed from a filter or a swipe by ultra-soneration.
Collodion is added to the suspension in ethanol and all the particles are spread on
polycarbonate disks (Lexan). Each disk is covered with a solid state nuclear track
detector made of another Lexan disk. Well thermalized neutron flux is then applied
that activates fissile atoms and their tracks can be revealed after chemical etching of
the detector. Largest fission tracks correspond to the biggest particles or the highest
enrichment in 235 U or 239 P u. Figure 4 shows 100 µm tracks that come from 1 µm
particles and contain a few picograms of uranium or plutonium.[9]
Figure 4: Fission tracks for uranium particles in Lexan after 1 min irradiation.[9]
6
2.2
Neutron Scattering Techniques
Neutron scattering referring to the experimental technique is a scattering of free
neutrons by matter. It is used in biophysics, physics, chemistry, crystallography, materials research and many other areas. Depending on the neutron-matter interaction,
two main physical processes are used: neutron diffraction (elastic scattering) for determining structures and inelastic neutron scattering for the study of atomic vibrations
and other excitations.
The Fermi Golden Rule (Equation 2.4) is a base for single-scattering theory that
describes the s-wave scattering. The result applies to elastic, quasielastic and inelastic
scattering. If the spin coupling term is included in the interaction potential, Eq. 2.2
can also be applied for magnetic scattering.
E2
ks D m d2 σ
=
V
(Q)
s
i δ(E − Es + Ei ),
2
dEdΩ
ki
2π~
(2.2)
with m being the neutron mass, Es and Ei are the energy states of the nucleus after
and before the scattering and V(Q) is the Fermi pseudo-potential formed of a series of
Dirac Delta functions due to the short-ranged neutron-nucleus interactions.
V (Q) =
2π~2
m
X
N
~
bj e−iQr~j ,
(2.3)
j
with bj being the scattering length for nucleus j and N is the number of scattering
nuclei in the sample.
2.2.1
Elastic Neutron Scattering
Elastic Neutron Scattering consists of measuring the scattered intensity with varying scattering angle. This is a way of solving the scattering Equation 2.4
4π
Θ
sin
λ
2
(2.4)
~ = k~s − k~i ,
Q
(2.5)
Q=
with Q being
λ is the neutron wavelength and Θ is the scattering angle. Angle variation is performed
by step-scanning or using a position-sensitive detector. Two main types of neutron
scattering methods are used: Neutron Diffraction is using mostly single scattering
events, while Neutron Reflectometry operates in the refraction mode and it involves
a large number of incremental scattering events that completely reflect the incident
neutron beam.
One of the most used techniques is SANS or Small-Angle Neutron Scattering that
uses elastic neutron scattering at small angles from 0.2◦ to 20◦ to investigate structures
7
from the near Angstrom sizes to the near micrometer sizes. Figure 5 shows four
basic steps used in this technique. Monochromation is performed mostly by using a
velocity selector, collimation is achieved through the use of source and sample aperture
placed far apart, scattering is done mainly on liquid or solid samples and detection is
performed using a neutron area detector inside an evacuated scattering vessel.
Figure 5: Schematics of the SANS technique.[5]
SANS advantage over other small-angle scattering methods (like small-angle xray scattering) is the deuteration method. This method is done by using deuterium
labelled components in sample in order to enhance their contrast, so SANS can measure
density fluctuations and also composition fluctuations. However, low neutron flux is
the disadvantage comparing to the SAXS (Small-Angle X-Ray Scattering).[5]
Figure 6: Single crystal diffraction pattern obtained from highly packed silica particles
under gentle shear and in D2O.[5]
Figure 6 shows highly packed silica particles in D2 O solution with a 6-fold symmetry
pointing to a body centered cubic structure. Four orders of diffraction spots are visible
before the instrumental smearing becomes overwhelming.[5]
8
2.2.2
Inelastic Neutron Scattering
Inelastic Neutron Scattering techniques are used for the study of thermodynamical,
optical, dielectrical and magnetic properties of materials, which are closely related to
lattice vibrations and crystal field excitations. Equations 2.6 and 2.7 are energy and
momentum conservation equations for one phonon process:
~ =K
~0 − K
~ ′ = 2π K
~ ± ~q
Q
(2.6)
E0 − E ′ = ±hν
(2.7)
~ 0 (K
~ ′)
where E0 and E ′ are respectively the incident and scattered neutron energy, K
~ is the momentum transfer vector, m is the
is the incident (scattered) wave vector, Q
mass of the neutron, ν is the frequeny and ~q is the propagation vector of the normal
~ is the reciprocal lattice vector. The plus or
mode to which the phonon belongs and K
minus sign refers to creation or annihilation of the phonon.[6]
Most common application utilizing and measuring one-phonon inelastic scattering
is Triple Axis Spectrometry (TAS), shown on Figure 7.
Figure 7: Triple Axis Spectrometer (TAS).[11]
Triple Axis Spectrometer is neutron application, where thermal neutrons from the
reactor core pass through the primary collimator and are reflected on the monochromator crystal (first axis) according to the Bragg Law. Monoenergetic neutrons then
fall on sample (second axis) and are inelastically scattered through an angle Φ. Analyser crystal (third axis) is used as the energy analyser for the inelastically scattered
neutrons and also diffracts neutrons to the position sensitive detector.[6]
9
2.3
Ultracold Neutrons
Ultracold Neutrons (UCN) are those neutrons which have an energy lower than the
average Fermi potential (Eq. 2.9) formed by the scattering length density of constituent
nuclei in matter.[8] They experience special physical properties comparing to the cold,
thermal or fast neutrons under certain velocities, so UCN can be totally reflected at any
angle of incidence from surfaces of most materials. The behaviour of ultracold neutrons
can be described as gas, filling the available volume in material. Their trajectories are
parabolic due to the small kinetic energy and the effect of the potential energy in
Earth’s gravitational field.
Energy of the ultracold neutrons is usually below 300 neV. That corresponds to a
maximum velocity of a few metres per second or a minimum wavelength of a few tens
of nanometres. If their velocity exceeds the critical velocity (i.e. threshold velocity of
a material, over which UCN are no longer totally reflected on the materials surfaces),
neutrons can escape from the traps. However, because the cross section is inversely
proportional to the neutron velocity (Subsection 1.1) and becomes huge for the UCN
energy range, escaped neutrons would be absorbed in a few nanometres of a surface.[20]
Figure 8: Ultracold Neutron Traps.[20]
Figure 8 shows simple schematic of the two different types of ultracold neutron
traps, one using the total reflection mentioned in the paragraph above, and the second
one with the magnetic trap. In a magnetic trap the magnetic field increases in all
directions from its center, thus forcing neutrons with their magnetic moment in the
direction parallel to the magnetic field gradient. A magnetic barrier of 1 T completely
reflects the neutrons with velocities below 3.4 m/s.[13]
Equation 2.8 represents the customary definition of ultracold neutrons as neutrons
with energies E lesser than effective potential V in the medium.
E<V =
2π~2 X
~
Ni ai ± ~µ · B
m i
(2.8)
where Ni is the number density of nuclei of type i in the material, ai is the coherent
scattering length of a type i nucleus, and V is the effective potential for the neutrons
in the medium. In practical units the effective potential V can be written as
10
157 · ρg/cm3 · af m
± 6.03 · Bkilogauss [neV ]
(2.9)
A
where ρg/cm3 is the density in g/cm3 , a and B are measured in fm and kG, respectively,
and A si the atomic mass of the element in the medium.[7]
V =
2.3.1
Production
Fission neutrons are produced with energies around 2 MeV, so they have to be
cooled down for about 13 orders of magnitude to achieve ultra-cold region. First, their
energy is reduced by reactor moderator usually being light or heavy water. The process
is called thermalization, as they reach thermal equilibrium with their environment.
Thermal neutrons can then be cooled down by entering solid methane at temperature
around 45 K and become cold neutrons. At the end they enter solid deuterium, where
some of neutrons loose all of their kinetic energy at once. This type of resonance effect
happens when the kinetic energy of the neutron matches one of the possible excitation
energies of the deuterium crystal. Neutron excites the molecules of solid deuterium
and becomes ultracold with reduced energy by five orders of magnitude. UCN effective
temperature is about 1 mK in comparison to the solid deuterium temperature of 5 K,
so they have to be extracted as quickly as possible, or else they can be heated back up
by next collision.[20]
2.3.2
Utilization
Ultracold neutron storage experiments have improved the production, transportation and storage of UCN and thus broaden their usefulness on many scientific fields.
Studies of condensed matter utilize ultracold neutrons in reflection and tunneling studies (UCN Reflectometry), elastic scattering, inelastic scattering and also upscattering.
Absorption cross section vary as 1/v for low energy neutrons, thus making UCN perfect
for measuring absorption in rare isotopes or for making high-accuracy measurements
of absorption cross sections.
Due to the total reflection at any angle of incidence and UCN trapping capabilities,
ultracold neutrons can also be used for measuring neutron lifetime and neutron β-decay
observables to provide fundamental information on the parameters characterizing the
weak interaction of the nucleon. Results can be used to extract a value for the CKM
quark-mixing matrix element Vud , the spin content of the nucleon and tests of the
Goldberger-Treiman relation.[4]
The observation of a non-zero neutron electric dipole moment would provide the
first evidence for Time-Reversal violation and related CP violation as an explanation
for the matter-antimatter asymmetry observed in the universe. This violation is a result
of a photon interaction with the permanent electric dipole moment of the neutron, as
it violates both parity and T invariance.[12]
11
3
Designing of the Irradiation Device
The TRIGA Mark II research reactor at the Jozef Stefan Institute features several ex-core irradiation facilities that can be used for different applications, e.g. neutron radiography, radiation damage studies, etc. Recently a few test irradiations were
performed for the Fission Track-Thermal Ionization Mass Spectrometry (FT-TIMS)
method, which requires a well thermalized neutron spectrum for sample irradiation.
The percentage of fast neutrons must be very low, in the range of 0.01 % and the
thermal neutron fluence should be about 1015 neutrons/cm2 . The MCNP Monte Carlo
neutron transport code is used to calculate the neutron fluxes and spectra in the major
TRIGA ex-core irradiation facilities (Figure 9).
The Radial Beam Port (RBP) and the Radial Piercing Port (RPP) extend radially
from the outer and inner boundaries of the graphite reflector, while the Tangential
Channel (TangCh) and the Elevated Piercing Port (EPP) are tangential to the reactor
core. EPP is marked on Fig. 9 with the dashed line, as it’s not on the same level as
other three. The Thermal Column, a graphite stack that extends from the graphite
reflector to the outer concrete wall of the reactor, thermalizes the neutrons leaking
from the reactor core.
The results of MCNP calculations and data visualization are used in diploma thesis,
that consists of the designing and optimization of an irradiation device, placed in one
of the TRIGA reactor’s ex-core irradiation facilities. Calculations of neutron flux and
energy spectra were made in the irradiation facilities to optimize the position of the
device. Optimal conditions were found in the thermal column, while the irradiation
channels can’t be used for this application.
Figure 9: TRIGA Mark-II top view.
12
3.1
The Irradiation Device Design
The irradiation device is placed in the thermal column. The design consists of an
aluminium vessel filled with heavy water and with the opening for sample insertion.
Inside the vessel is cylindrical opening where the polyethylene capsule can be placed.
Irradiation facilities, several neutron tracks and the irradiation device on Figure 10 are
visualized with Amira, software platform for visualizing and manipulating data.
Figure 10: Side view of the canister filled with heavy water and the capsule placement.
4
Conclusion
Nuclear research reactors such as TRIGA Mark-II are ideal as a source of thermal
neutron flux used in many different applications presented in the seminar. Current
results of MCNP calculations show that with minor modifications sample irradiation for
desired application can be possible. Using the proposed irradiation device, approximate
700:1 thermal to fast neutron ratio was calculated with thermal neutron fluence of
1015 neutrons/cm2 .
13
References
[1] J. J. Duderstadt and L. J. Hamilton, Nuclear Reactor Analysis, John Wiley & Sons, 1976
[2] J. R. Lamarsh and A. J. Baratta, Introduction to Nuclear Engineering, Prentice Hall, 2001
[3] G. I. Bell and S. Glasstone, Nuclear Reactor Theory, Van Nostrand Reinhold Company, 1970
[4] A. Frei et al., First Measurement of the Neutron β Asymmetry with Ultracold Neutrons, Physical
Review Letters 102, 012301, 2009
[5] B. Hammouda, Probing Nanoscale Structures - The SANS Toolbox, National Institute of Standards and Technology
[6] A. A. Z. Ahmad, Thermal Neutron Scattering: Principles & Applications, BRAC University
Journal, Vol. I, No. 1, 2004
[7] R. Golub, Ultracold neutrons: Their role in studies of condensed matter, Reviews of Modern
Physics, Vol. 68, No. 2, 1996
[8] Y. Masuda, Ultra-cold neutron production with superfluid helium and spallation neutrons, Nuclear Instruments and Methods in Physics Research A 440, 2000
[9] S. Baude, M.C. Larriere, O. Marie, R. Chiappini, Micrometric particle’s isotopics: An ultrasensitive tool to detect nuclear plant discharge in the environment, Radioprotection-Colloques,
Vol. 37, C1, 2002
[10] R. Golub, J. M. Pendlebury, Ultra-cold Neutrons, Rep. Prog. Phys., Vol. 42, 1979
[11] M. C. Rheinstaedter, Triple-Axis Spectrometry, CINS Summer School 2011
[12] R. Alarcon, Fundamental physics with cold and ultracold neutrons, Revista Mexicana de Fisica
S53 (3) 125-127, 2007
[13] V. F. Ezhov et al., First Ever Storage of Ultracold Neutrons in a Magnetic Trap Made of Permanent Magnets, Journal of Research of the National Institute of Standards and Technology,
Volume 110, Number 4, July-August 2005
[14] http://atom.kaeri.re.kr/cgi-bin/endfplot.pl
[15] http://www.coursehero.com/file/1251057/ch3neutrons/
[16] http://www.ndt.net/article/v07n08/guidez/guidez.htm
[17] http://archaeometry.missouri.edu/naa_overview.html
[18] http://www.ne.ncsu.edu/nrp/naa.html
[19] http://www.reak.bme.hu/Wigner_Course/WignerManuals/Budapest/NEUTRON_ACTIVATION_
ANALYSIS.htm
[20] http://www.ne.ncsu.edu/nrp/ucns.html
14