Modeling of Radiation-induced Dimensional Instability of Metals and Alloys in Nuclear Systems: Improved Understanding of the Stress and Alloying Elements Effects by Rate Theory

Department of Nuclear EngineeringHistorically a rate theory is one of the most favorite modeling methodologies to simulate the radiation effects on structural materials for nuclear reactors. The easy usability of rate theory, caused by various simplification, could help many researchers to grasp fundamental the understanding. However, simplification in rate theory gives not only easy accessibility but also inaccurate information. Various effect such as alloying element, stress, and cascade effect were neglected because lattice distortion could not be directly considered. Hence, in this paper, to overcome the simplification of rate theory, two approaches had been applied to enhance the performance of the rate theory. In the first approach, detail behavior of defect, which is derived by the state of art simulation tools, were adopted in diffusion coefficient under the stress and alloying element condition. In the second, cascade effect on sink annihilation was considered by a fitting method from the experimental observation. The stress effect on interstitial diffusivity also recently studied by MD simulations. C. Kang and M. Banislaman show that migration energy of interstitial and its clusters is reduced by applied stress in iron. Hence in this study, irradiation swelling, and creep is predicted by considering the recent calculation result. In ultra-long fuel cycle condition, hoop stress could be nearly up to 600 MPa. By MD simulation it was observed that diffusivity of interstitial has 8.437??10-5 cm2 /s at 873 K. This value was 11 times higher than non-stress applied condition (7.414??10-6 cm2 /s). In detail, M. Christensen reveals that Nb decreases the interstitial diffusivity nearly 1/5.64 at 500 K and 1/5.88 at 700 K with 0.5 % Nb in zirconium. Also, the same method was applied to account the Sn effect. Sn shows the high dependency with temperature and relatively less effect than Nb. Interstitial diffusivity is decreased about 1/4.05 at 500 K and 1/1.38 at 700 K with 2.5 Sn. This information was adopted in rate theory and then irradiation growth was predicted. By adding 0.5 % Nb in cold-worked zirconium, 0.2 % strain is obtained whilst cold-worked pure zirconium shows nearly 0.3 % strain at 10 dpa. Since there was no experiment about irradiation growth of Zr-0.5Nb, Zr-2.5Nb experimental result was compared with simulation results. In case of cascade annihilation of sinks, there is no study including theoretical method. However, by F. Garner, it was experimentally observed that network dislocation density of iron-based alloy is saturated nearly 1011 cm2 no matter how fabrication process is applied to the specimen. Hence by the fitting method, sink annihilation rate by cascade is adopted in rate theory. As results, irradiation swelling rate is decreased by nearly 30 % compared with non-considering the cascade annihilation of sink case. Until now, three representative types of rate theory were developed in the research area of radiation VI effectthese are SRT, CDM, and PBM. In case of SRT and CDM, there is no big difference except the consideration of cluster number density. However, there is a large gap between PBM and SRT/CDM because 1-D reaction kinetics, caused by mobile interstitial cluster, is accounted in PBM. Since the purpose of this dissertation is an improvement of scientific understanding of the RIDI behavior within rate theory frames, there was attempting to verify the stress and alloy element effect between SRT and PBM in zirconium, and between CDM and PBM in iron. However, unfortunately, in case of zirconium, PBM could not be carried out because many parameters for cluster such as migration, formation, and binding energy are not discovered. Hence, stress and alloy element effect were verified only in SRT. In case of an iron-based alloy, since there was significant progress about study of defect behavior, stress and alloy effect could be examined in between CDM and PBM. There was also a conventional way to account the stress and alloy element effect. To improved scientific understanding, the result of the conventional method and results of this work are compared in the discussion chapter. Therefore, the result of this study could enhance the fundamental understanding of radiation effect on structural materials because various effects were considered within various rate theory frame.ope

Classification of real Bott manifolds and acyclic digraphs

We completely characterize real Bott manifolds up to affine diffeomorphism in terms of three simple matrix operations on square binary matrices obtained from strictly upper triangular matrices by permuting rows and columns simultaneously. We also prove that any graded ring isomorphism between the cohomology rings of real Bott manifolds with $\mathbb Z/2$ coefficients is induced by an affine diffeomorphism between the real Bott manifolds. Our characterization can also be described in terms of graph operations on directed acyclic graphs. Using this combinatorial interpretation, we prove that the decomposition of a real Bott manifold into a product of indecomposable real Bott manifolds is unique up to permutations of the indecomposable factors. Finally, we produce some numerical invariants of real Bott manifolds from the viewpoint of graph theory and discuss their topological meaning. As a by-product, we prove that the toral rank conjecture holds for real Bott manifolds.Comment: 27 pages, 5 figures. It is a combination of arXiv:0809.2178 and arXiv:1002.4704, including some new result

Irradiation Growth Modeling of Zirconium in Nuclear Reactors

Department of Nuclear EngineeringZirconium and zirconium alloys are extensively used as nuclear core material due to their excellent ability to withstand reactor conditions including corrosion and neutron irradiation. Despite their excellent properties as structure material, radiation-induced phenomena (growth, hardening, creep, and amorphization) are still main concerns at structure materials. Among them, irradiation growth is main concern in zirconium base alloy. In nuclear reactor condition, main design criteria of zirconium alloys is corrosion. Therefore history of zirconium alloy development has been done to develop it which has better corrosion resistant properties. Representative zirconium alloy in nuclear society such as Zircaloy-1, Zircaloy-2, Zircaloy-4 and Zirlo are materials which show high corrosion resistant property. So far, irradiation growth was not main concern of nuclear plant safety criteria because of corrosion phenomenon. Therefore irradiation growth research is still insufficient compare with corrosion research filed. Nowadays, however, commercial reactor life extension is needed and research reactor is received more neutron flux than commercial thing. Therefore, safety analysis of irradiated materials is become important. Irradiation growth combine with irradiation hardening could induce materials failure. Therefore this is the timing to analysis of irradiated materials. So far, to recognize environment and material parameter effects on growth, extensive experiments have been done and some important experiments were completed. In the extensive research, to figure out the individual sink effects (grain boundary and dislocation loop and line, texture) on the growth mechanism, irradiation growth of single crystal experiments had been done. After single crystal growth data were analyzed, polycrystalline and zircaloy were also researched systemically. From these experiments, major parameter effect on irradiation growth was conformed. After growth experiment, specimen was analyzed by microstructure morphology such as sink density and size. From microstructure change, researcher could analyze irradiation growth mechanism. In 1980s, a lot of research had been done irradiated materials. Eventually, in rate of 1980s, research about irradiation growth, microstructure and growth theory are published. However, recently, microstructure morphology change and fundamental parameter are updated and anisotropy diffusion difference concept was developed. Former research does not contain these developed. Recently theoretical modeling, which contain new developed concept, has been done in single modeling. However irradiation growth of polycrystalline and zircaloy do not developed. Therefore this research object is modeling of irradiation growth from single crystal to zircaloy. To modeling of irradiation growth, in the literature study, microstructure change morphology and growth experiment were systemically reviewed by organization from single crystal to zircaloy. Also theoretical analysis, which conducted various authors are reviewed. At lastly, defect rate theory, which could explain microstructure change fundamentally, is reviewed for theoretical modeling. In the results, based on the defect rete theory, improved theoretical modeling are suggested and growth results are presented from single to zircaloy. Before to growth modeling in research reactor, growth modeling are conducted at commercial reactor condition because there are more extensive research results are exist in commercial reactor condition. These results also conducted systemically form single to zircaloy for represent individual sink effect on growth. Individual parameters effects on irradiation growth are analyze by growth modeling results. Many metallurgical conditions eventually change the material parameters hence texture, grain size, dislocation density effect on growth are analyzed and also experimental conditions effect on growth are reviewed. In case of single crystal and cold worked polycrystalline, the growth result show well agreement with experimental result. For the fundamental understanding of these case, the behavior of the defect flux and sink strength behavior are analyzed. From this analysis, it was clear that the growth modeling are well established. However, in case of annealed polycrystalline case, the results was not well matched with experimental results because in case of polycrystalline case, the sinks behavior are more complex than single and cold worked case. Unfortunately, irradiation growth modeling of annealed polycrystalline was disagreement of experiment result. However, from the detail analysis in result and discussion, it was clear that limitation of the modeling and improvement direction. Therefore, in the future work, assumption of defect rate equation will be extended to cluster and grain boundary sink strength modeling will be conducted. Also irradiation growth equation will be modified to contain axis shortening. Diffusion coefficient is most important parameter in the modeling result. Therefore, defect induced diffusion coefficient change also will be treated. This specific work will be done with MD simulation.ope