Thermodynamic Modeling of Uranium and Oxygen Containing Ternary Systems with Gadolinium, Lanthanum, and Thorium
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University of Tennessee, Knoxville TRACE: Tennessee Research and Creative Exchange Doctoral Dissertations Graduate School 12-2014 Thermodynamic Modeling of Uranium and Oxygen Containing Ternary Systems with Gadolinium, Lanthanum, and Thorium Jacob Wesley McMurray University of Tennessee - Knoxville, [email protected] Follow this and additional works at: https://trace.tennessee.edu/utk_graddiss Part of the Ceramic Materials Commons, Nuclear Engineering Commons, and the Thermodynamics Commons Recommended Citation McMurray, Jacob Wesley, "Thermodynamic Modeling of Uranium and Oxygen Containing Ternary Systems with Gadolinium, Lanthanum, and Thorium. " PhD diss., University of Tennessee, 2014. https://trace.tennessee.edu/utk_graddiss/3152 This Dissertation is brought to you for free and open access by the Graduate School at TRACE: Tennessee Research and Creative Exchange. It has been accepted for inclusion in Doctoral Dissertations by an authorized administrator of TRACE: Tennessee Research and Creative Exchange. For more information, please contact [email protected]. To the Graduate Council: I am submitting herewith a dissertation written by Jacob Wesley McMurray entitled "Thermodynamic Modeling of Uranium and Oxygen Containing Ternary Systems with Gadolinium, Lanthanum, and Thorium." I have examined the final electronic copy of this dissertation for form and content and recommend that it be accepted in partial fulfillment of the requirements for the degree of Doctor of Philosophy, with a major in Energy Science and Engineering. Theodore M. Besmann, Major Professor We have read this dissertation and recommend its acceptance: Claudia J. Rawn, Brian D. Wirth, James R. Morris Accepted for the Council: Carolyn R. Hodges Vice Provost and Dean of the Graduate School (Original signatures are on file with official studentecor r ds.) Thermodynamic Modeling of Uranium and Oxygen Containing Ternary Systems with Gadolinium, Lanthanum, and Thorium A Dissertation Presented for the Doctor of Philosophy Degree The University of Tennessee, Knoxville Jacob Wesley McMurray December 2014 Copyright © 2014 by Jacob W. McMurray All rights reserved ii Dedicated to my wife Perla McMurray my children Audrey and Samuel McMurray and my parents. Ron and Teddi McMurray iii ACKNOWLEDGEMENTS “No man is an island entire of itself; every man is a piece of the continent, a part of the main; if a clod be washed away by the sea, Europe is the less, as well as if a promontory were, as well as any manner of thy friends or of thine own were; any man's death diminishes me, because I am involved in mankind. And therefore never send to know for whom the bell tolls; it tolls for thee.” – John Donne The words of John Donne, the epigraph for Ernest Hemingway’s 1940 novel For Whom the Bell Tolls and likely the inspiration for the title, still stirs my spirit and embodies my philosophy on life; we all need one another, we are all in this thing together. To believe that any one person can create anything of value in a vacuum is hubris of the gods. I am therefore, profoundly grateful to Dr. Lee Riedinger, Dr. Mike Simpson, Dr. Jim Roberto, and the Bredesen Center for Interdisciplinary Research and Graduate Education for this remarkable opportunity to contribute to science and potentially impact energy issues. I am eternally grateful to Dr. Theodore M. Besmann, my mentor, for his instruction, patience and confidence in the skills I developed under his tutelage. A special thanks to Stewart Voit for fabricating samples, sharing laboratory expertise, and at – length discussions on the science behind our experimental measurements and Dr. Dongwon Shin for impromptu thermodynamic modeling lectures. I am grateful to Dr. Jaime Morris, Dr. George Pharr, Dr. Brian Wirth, and Dr. Claudia Rawn for their contribution to my education and agreeing to take part as members of my dissertation committee. The cooperation of my classmates, to whom I owe much gratitude for many hours of study, was instrumental in my success as a student. Finally, I must acknowledge my family for their advice, moral, emotional, and financial support. iv Research supported by the US Department of Energy, Office of Nuclear Energy, Fuel Cycle Technology Program. v ABSTRACT The CALPHAD method is used to assess the thermodynamic properties and phase relations in the U-M-O system where M = Gd, La, and Th. A compound energy formalism (CEF) model for fluorite UO2±x [urania] is extended to represent the complex U1-yMyO2±x [urania solid solution] phases. The lattice stabilities for fictive GdO2 [gadolinia] and LaO2 [lanthana] fluorite structure compounds are calculated from density functional theory (DFT) for use in the CEF for U1-yMyO2±x [urania solid solution phase] while U6+ [uranium 6 plus cation] is introduced into the cation sublattice of the CEF for U1-yMyO2±x [urania solid solution phase] to better reproduce phase relations in U-Ln-O systems at high fixed trivalent Ln [lanthanide] compositions. Tentative Gibbs functions and CEF representations for the fluorite derivative rhombohedral phases were developed and the two-sublattice liquid model (TSLM) was used to describe the melt. Equilibrium oxygen pressures over U1-yThyO2±x [urania thoria solid solution] were obtained from thermogravimetric measurements and used together with those reported in the literature, phase relations, and other experimentally determined thermodynamic values to fit adjustable parameters of the CEF and TSLM along with the standard state enthalpy and entropy of the Gibbs functions representing the stoichiometric compounds. The models can be extended to include other actinides and fission products to develop higher order multi-component system assessments to support further experimental efforts and the development of multi-physics fuel performance simulation codes. vi TABLE OF CONTENTS Chapter 1 Introduction 1 1.1 Nuclear power 4 1.2 Fuel and fission product chemistry 5 1.3 Computational thermodynamics coupled fuel 9 performance simulations 1.4 Goals of research 14 Chapter 2 Thermodynamic modeling of complex 15 crystalline phases and ionic liquids 2.1 CALPHAD methodology 16 2.2 Computational thermodynamics codes 18 2.3 Sublattice models 18 2.4 Excess functions 22 2.5 Summary 22 Chapter 3 Crystal chemistry of urania and urania solid 24 solutions 3.1 The UO2 crystal 24 3.2 Oxygen defect clustering in UO2 26 3.3 Dissolution of La and Gd in UO2±x 28 3.3.1 Lattice stabilities from DFT 32 3.3.2 Lattice parameter 33 3.3.3 Ionic radii 37 3.3.4 Oxidation state of uranium in fluorite solid 39 solutions 3.4 Oxygen order-disorder transition 46 vii Chapter 4 Thermodynamic data for the U-M-O systems 51 4.1 Thermodynamic data 52 4.2 Gadolinium 52 4.3 Lanthanum 56 4.4 Thorium 59 Chapter 5 Experimental 70 5.1 Sample preparation 70 5.2 Measurements 71 5.3 Approach to error analysis 85 5.4 Experimental results 89 Chapter 6 Modelling and assessments 92 6.1 The gas phase 94 6.2 Pure elements and stoichiometric phases 94 6.3 The UO2±x phase 95 6.4 The U-O liquid phase 98 6.5 The rhombohedral UGd6O12 101 6.6 The rhombohedral ULa6O12-x phase 101 6.7 The rhombohedral U2La6O15 phase 102 6.8 The rhombohedral (U,La)8O16 phase 103 6.9 Th-U solution phases 103 6.10 The ThUO5 phase 104 6.11 The (U1-yThy)4O9 solution phase 104 6.12 The U-M-O liquid phases 105 6.13 Fluorite-structure U1-yMyO2±x phases 107 6.14 Parameter optimization 112 6.14.1 The U–Gd–O system 112 viii 6.14.2 The U–La–O system 113 6.14.3 The U–Th–O system 113 6.15 Results for the U–Gd–O system 115 6.15.1 The Gd–O binary 115 6.15.2 The U–Gd binary 117 6.15.3 The U–Gd–O ternary 117 6.16 The U–La–O system 120 6.16.1 The La–O binary 120 6.16.2 The U–La binary 126 6.16.3 The U–La–O ternary 126 6.17 The U–Th–O system 132 6.17.1 The Th–O binary 132 6.17.2 The U–Th binary 133 6.17.3 The U–Th–O ternary 138 6.18 Defect chemistry 146 Chapter 7 Summary and conclusions 153 Chapter 8 Recommendations 158 8.1 Short range ordering 158 8.2 Order – disorder transition 160 8.3 Oxygen clustering 160 8.4 Experimental studies 162 8.4 Conclusions 162 List of References 164 Appendix 181 A Tabulated experimental results 182 B U–Gd–O Thermodynamic Functions 185 ix C U–La–O Thermodynamic Functions 189 D U–Th–O Thermodynamic Functions 194 Vita 198 x LIST OF TABLES Table 3.1 Defects proposed by Park and Olander [33] for their UO2±x thermochemical model using Kröger-Vink for point defects and a new notation for clustering….29 Table 3.2 Host metal empirical constants after Kim [53]….35 Table 3.3 Percent difference between U4+ radius and the effective ionic radius of an Ln3+….41 Table 4.1 Compositional and temperature ranges of equilibrium oxygen pressure over U1-yGdyO2±x by author….53 Table 4.2 Method, composition and temperature range of authors reporting heat capacity data for U1-yGdyO2. …55 Table 4.3 Compositional and temperature ranges of equilibrium oxygen pressure over U1-yLayO2±x by author….60 Table 4.4 Compositional, temperature ranges, and methods of equilibrium vapor pressure measurements over U1-yThyO2+x by author….66 Table 4.5 Method, composition and temperature range of authors reporting heat capacity data for U1-yThyO2….66 Table 5.1 Comparison of the calculated and measured oxygen partial pressure associated with different flow settings through the EGMS unit….76 Table 5.2 Flow combinations corresponding to the log p values used to measure the mass change of U Th O O2 0.95 0.05 2+x at 1573 K in Fig.