ABSTRACT ZHU, YUWEI. Analysis of Neutron Thermalization in Liquid FLiBe. (Under the direction of Prof. Ayman I. Hawari). FLiBe, a liquid formed by fusing crystalline LiF and BeF2 salts at temperatures exceeding 732 K, has the chemical formula Li2BeF4. FLiBe demonstrates outstanding properties such as chemical stability at high temperatures, high moderating ratio, and high heat capacity. It has therefore been proposed as a coolant, moderator, and heat storage medium in thermal neutron driven nuclear reactors. In proposed reactor designs such as the thorium molten salt reactor (TMSR), and the small modular advanced high-temperature reactor (SmAHTR), liquid FLiBe can compose up to 70% volume of the fuel blanket. Neutronic simulations for the design of such thermal reactors require high fidelity thermal neutron scattering data for FLiBe. However, there is currently no available thermal neutron scattering law for liquid FLiBe. To date, proposed thermal neutron scattering cross sections for FLiBe are based on a crystalline solid model that fundamentally exhibits different thermal neutron scattering behavior from liquid FLiBe. In this work, the thermal neutron scattering law (i.e. 푆(훼, 훽) ) for liquid FLiBe is calculated. The process used a liquid FLiBe molecular dynamics (MD) model based on the Born-Mayer pair potential. Predicted physical properties from the MD model such as density, viscosity, heat capacity, and diffusion coefficient showed good agreement with experimental measurements. Velocity autocorrelation functions (VACF) as well as particle trajectories were generated from the model. With these data, two different methods were implemented to calculate the FLiBe thermal scattering law (TSL). The first method is used to evaluate the TSL of this molten salt liquid by separating the excitation DOS into the bound vibrational mode and the diffusional mode. The partial TSLs of the bound vibrational mode and the diffusional mode were evaluated separately, each using its respective partial DOS. The total TSL of FLiBe was calculated by convolving the partial TSLs. The differential and the total thermal scattering cross sections of FLiBe were subsequently evaluated. In the second method, MD trajectories were used to evaluate the TSL. This required introducing a quantum correction to the classical width function that appears in the intermediate scattering function. Subsequently, the classical width functions for each element in FLiBe were evaluated and quantum corrected. With the quantum width function, the corresponding TSLs for each element in FLiBe were evaluated at the representative reactor core temperatures of 873K, 923K, and 973K. Generally, good agreement was found between the quantum corrected self scattering law and the DOS evaluated self scattering law. However, in the MD based analysis, the distinct scattering law is included in the evaluation by enforcing the same quantum correction ratio as for the self scattering law. The inclusion of distinct scattering law, which is validated by thermal neutron scattering measurements using liquid lithium, relaxes the Gaussian and the incoherent approximations and allows capturing the angular aspects of the scattering cross section. Based on that, the total thermal scattering law for each element in FLiBe was generated at the temperatures listed above and all corresponding thermal scattering cross sections were evaluated in a form appropriate for addition to the Evaluated Nuclear Data File (ENDF) and for use in reactor design analysis. © Copyright 2018 by Yuwei Zhu All Rights Reserved Analysis of Neutron Thermalization in Liquid FLiBe by Yuwei Zhu A dissertation submitted to the Graduate Faculty of North Carolina State University in partial fulfillment of the requirements for the degree of Doctor of Philosophy Nuclear Engineering Raleigh, North Carolina 2018 APPROVED BY: _______________________________ _______________________________ Nam Dinh Paul Huffman _______________________________ _______________________________ Bernard Wehring Michael Zerkle _______________________________ Ayman I. Hawari Committee Chair DEDICATION This thesis is dedicated to the development of mankind’s knowledge. ii BIOGRAPHY Yuwei was born in a small town in southwest China. He spent his childhood in a neighborhood under significant planned economy. He became curious about how the universe governs itself since his childhood. In pursuit of science, he went to the University of Science and Technology of China (USTC) and graduated with Bachelor in Nuclear Engineering in 2012. He subsequently came to North Carolina State University (NCSU) for his graduate study. Yuwei began working with Dr. Ayman Hawari and got introduced into the field of thermal neutron scattering. He accomplished Master of Science in 2014 with the work on the thermal neutron scattering cross section of 3C- SiC. After that, he continued his effort in this field. Besides this thesis work, he has implemented the first version of the FLASSH code. He also published numerous thermal scattering law libraries in the ENDF/B-VIII.0 release. There is an old Chinese classic named《生于忧患死于安乐》. It would be quoted here to summarize this biography: 生于忧患，死于安乐。 One thrives and survives under suffering and hardships, and withers if left overly-protected and contented with current situation. 故天将降大任于斯人也， When the universe is about to confer a great responsibility on man, 必先苦其心志，劳其筋骨，饿其体肤， it will first fill his heart with suffering, toil his sinews and bones, exposes his body to huger, 空乏其身，行拂乱其所为，所以动心忍性， subjects him to extreme poverty, confounds his journey with setbacks and troubles, so as to stimulate his alertness, toughen his nature, 曾益其所不能。 eventually bridging his incompetence gap and prepare him for the task. iii ACKNOWLEDGMENTS I would like to give my wholehearted gratitude to Dr. Ayman Hawari for guiding me in this project. Without his patients and guidance, this project would be impossible. Dr. Hawari’s professional outlook and abundant knowledge always shed light on our discussion. I would also like to thank Jonathan Wormald from my research group. His ample knowledge in nuclear engineering and physics always gives me insight of problems in discussion. Many thanks to Cole Manring, Drew Antony, and Nina Colby Sorrell. They helped me proofread my thesis and gave me a lot of advices. Last but not least, my roommate Jun Fang and my friend Jinyong Feng gave me a lot of support during my study here. I would also like to thank my family and other friends. Their supports always encourage me to overcome obstacles in my life. iv TABLE OF CONTENTS LIST OF TABLES ....................................................................................................................... viii LIST OF FIGURES ...................................................................................................................... ix Chapter 1 Introduction .....................................................................................................................1 1.1 Advanced Nuclear Reactors ...................................................................................................1 1.2 Research and Development of Molten Salt ...........................................................................5 1.3 Chemistry of FLiBe ...............................................................................................................8 1.4 Status of FLiBe Thermal Scattering Law Libraries .............................................................14 Chapter 2 Thermal Neutron Scattering Physics .............................................................................18 2.1 General Theory of Thermal Neutron Scattering ..................................................................18 2.1.1 Background of Thermal Neutron Scattering Theory ....................................................18 2.1.2 The Dynamic Structure Factor 푆(풌, 휔) And the Thermal Scattering Law 푆(훼, 훽) ......22 2.1.3 The 퐺(풓, 푡) Function and the 퐼(풌, 푡) Function .............................................................25 2.1.4 The Self and Distinct Thermal Scattering Laws ...........................................................27 2.1.5 Thermal Neutron Scattering and the Incoherent Approximation .................................29 2.2 The Gaussian Approximation and the Width Function .......................................................30 2.2.1 The Gaussian Approximation and the Width Function for Solid and Gas Materials ...30 2.2.2 The Gaussian Approximation and the Width Function for Liquid Materials ...............32 2.3 The Separation of the Diffusive Thermal Scattering Law and the Bound Thermal Scattering Law ......................................................................................................36 2.4 Thermal Neutron Scattering Models for Liquid Materials ..................................................38 2.5 The Quantum Thermal Scattering Law and the Classical Thermal Scattering Law ............44 2.5.1 From the Quantum Thermal Scattering Law to the Classical Thermal Scattering Law – the Classical Approximation ..............................................44 2.5.2 From the Classical Thermal Scattering Law to the Quantum Thermal Scattering Law – the Quantum Correction .....................................................46 2.5.3 The Semiclassical Quantum Correction........................................................................47 2.5.4 The Quantum Correction on Distinct Thermal Scattering Law ....................................50 2.6 Computational