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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 . . . . . . . . . . . . . . 2 2 3 . . . . . . . . . . . 4 4 4 4 5 6 7 7 9 10 11 11 3 Designing of the Irradiation Device 3.1 The Irradiation Device Design . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 13 4 Conclusion 13 References 14 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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