Thermodynamic Modeling of Uranium and Oxygen Containing Ternary Systems with Gadolinium ...

216 Pages·2016·7.19 MB·English

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Doctoral Dissertations Graduate School
12-2014
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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
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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
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[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 student records.)
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

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A
CKNOWLEDGEMENTS

“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.
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Research supported by the US Department of Energy, Office of Nuclear Energy, Fuel
Cycle Technology Program.

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A
BSTRACT

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 UO [urania] is extended to represent the complex
2±x
U M O [urania solid solution] phases. The lattice stabilities for fictive GdO
1-y y 2±x 2
[gadolinia] and LaO [lanthana] fluorite structure compounds are calculated from density
2
functional theory (DFT) for use in the CEF for U M O [urania solid solution phase]
1-y y 2±x
while U6+ [uranium 6 plus cation] is introduced into the cation sublattice of the CEF for
U M O [urania solid solution phase] to better reproduce phase relations in U-Ln-O
1-y y 2±x
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 U Th O [urania thoria solid solution] were
1-y y 2±x
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.

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T C
ABLE OF ONTENTS
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 UO crystal 24
2
3.2 Oxygen defect clustering in UO 26
2
3.3 Dissolution of La and Gd in UO 28
2±x
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
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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 UO phase 95
2±x
6.4 The U-O liquid phase 98
6.5 The rhombohedral UGd O 101
6 12
6.6 The rhombohedral ULa O phase 101
6 12-x
6.7 The rhombohedral U La O phase 102
2 6 15
6.8 The rhombohedral (U,La) O phase 103
8 16
6.9 Th-U solution phases 103
6.10 The ThUO phase 104
5
6.11 The (U Th ) O solution phase 104
1-y y 4 9
6.12 The U-M-O liquid phases 105
6.13 Fluorite-structure U M O phases 107
1-y y 2±x
6.14 Parameter optimization 112
6.14.1 The U–Gd–O system 112
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