Reports
MURJ
Volume 40, Fall 2020
Improving Thermal Neutron Scattering Simulation Data Charlotte Wickert Student Contributor, MIT Department of Physics, Cambridge, MA 02139
1. Introduction Safe operation and design of nuclear systems require accurate simulations that can predict neutron fluxes and power distribution in nuclear reactors. However, the trustworthiness of simulation output is limited by the quality of the input nuclear data. Despite the importance of thermal neutrons, which are more likely to result in fissions than fast neutrons, data regarding their scattering behaviour has been historically neglected. In order to provide the most accurate data for thermal neutron scattering it is essential to have access to a flexible range of materials at various temperatures. One of the most common data processing tools is a modular code known as NJOY (Macfarlane, Muir, Boicourt, Kahler III, & Conlin, 2017), where two of the modules (LEAPR and THERMR) are dedicated to preparing thermal neutron data. However, while these modules can often prepare data for abitrary materials, there are other calculations for which LEAPR and THERMR are limited to hard-coded values in the source code. This reliance on hardcoded values restricts NJOY to only six materials for coherent elastic scattering1. Furthermore, these hard-coded values are sourced from various papers from the 1960s and are now outdated. Graphing the coherent elastic scattering cross sections results in “Bragg peaks” which are sharp jumps in the cross sections that occur at various energies. Comparing the graphs generated from the original and modern physical constants reveals that updating the scattering constant values scales the height of the Bragg peaks and updating the lattice constants shifts the Bragg peaks on the energy axis. These corrections constitute an improved representation of the coherent elastic scattering process. Implementing these corrections allows for more accurate predictions of thermal neutrons and more reliable technology.
2. Technical Background Thermal neutrons can interact with materials in one of four ways, each collision is either elastic or inelastic and coherent or incoherent. An elastic collision means that total kinetic energy is conserved during the interaction. Since thermal neutrons do not have sufficient energy to break molecular bonds, they typically scatter off of much larger targets than fast neutrons (i.e., a full lattice as opposed to a single atom). Thus, the size of the target is much larger than that of the neutron, causing the neutron to lose little to no energy in an elastic collision. In an inelastic collision, the total amount of kinetic energy is not conserved, but is instead lost or gained in the creation or destruction of phonons in the
target material. Each elastic and inelastic collision has a coherent and incoherent contribution. Material composition and material structure dictate whether coherent or incoherent scattering will dominate. Some nuclides have inherent preference towards coherent or incoherent scattering. Those with preference towards coherent scattering have a larger bound coherent scattering cross section, σcoh, and a smaller incoherent bound scattering cross section, σinc. These material properties are used when computing both the elastic and the inelastic scattering cross sections. Whether a neutron will scattering coherently or incoherently also depends on material structure. Coherent scattering is more likely to occur when the target atoms are arranged in such a way that the scattering causes the resulting waves to constructively amplify or destructively cancel each other. Incoherent scattering is more likely to take place when the atoms are not arranged in a regular way and the resulting waves are more chaotic. When the coherent bound scattering cross section σcoh is sufficiently large and the material structure is ordered, then computing the coherent elastic thermal neutron scattering cross section is desired. This data can be prepared using the NJOY nuclear data processing code. The LEAPR module outputs the Bragg vector associated with a specific material. This vector contains weights and energies that can then be used to plot the Bragg peaks for the material with this equation. The coherent elastic cross section (integrated over all angles) is
where σcoh is the material scattering constant and fi are the weights of each Bragg peak,
The weights are computed as a function of τ2, the reciprocal lattice vector lengths. The reciprocal lattice vector lengths for a Body Centered Cubic (BCC) Lattice are
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