Universities Nuclear Technology Forum
University of Huddersfield
11th - 13th April 2011
Computer Modelling of Thoria:
Determining the Suitability of Thoria
for a Next Generation Nuclear Fuel.
Dr Paul Martin, Dr David Cooke, Prof. Bob Cywinski
(Hudds) and Prof. S.C. Parker (Bath).
Contents
•
Why Thoria ? Background and the Thoria Fuel Cycle
•
Computational methods and results
- Potential model validation
- Modelling the of bulk material & Calculations of thermo-physical
properties:
1. Internal structure - MD
2. Thermal expansion - MD
3. Defect Chemistry – Static modelling
4. Oxide ion diffusion - MD
5. Heat Capacity – MD
6. Uranium clustering at surfaces and bulk - LD
•
Conclusions
Why Study Thoria ?
Background and the Thoria Fuel
Cycle
Experts propose a new future
for low carbon energy
production :
Nuclear power from Thoria
• Thorium is four times more plentiful than uranium in the earth's crust
• All of the thorium dug from the ground
can be usefully burnt
• ThO2 produces little Plutonium
∴ doesn’t contribute to proliferation
When used in an energy amplifier
• Thorium produces far less nuclear waste
• The process can ‘eat’ spent waste from
conventional reactors
Professor Bob Cywinski (right)
with Nobel Laureate Professor Carlo Rubbia, former Director of CERN
Thorium Cycle
Spallation
Absorbs neutron to become Th 233
Stop neutron bombardment
= cycle stops
Energy released
By Nuclear fission
and
Neutrons freed to
continue process
Thorium is not fissile
Electron loss
Further Decay
Electron loss
Computational methods
and Results
2 main methods: QM v MM
Quantum Mechanics
Very Accurate But very slow
Molecular Mechanics
Can study larger systems
But needs reliable
potential parameters
Shell model calculations
Water on CaO {100} surface
Force dominated by electrostatic
interactions, but include repulsion,
van der Waals and polarisability
Potentials and Static Simulations
• Model Validation – 3 parameter sets used to optimise geometry of
bulk Thoria.
• Values from atomistic calcs ALL fall in range produced by DFT and
experimental (which vary widely). (eg) Latt. Param. Within 0.03 Å of
expt. determined structure.
Cell
Parameter
a/Å
Elastic constants
/GPa
C11
C12
C44
Moduli
Bulk
/GPa
Shear
/GPa
Lewis A
Lewis B
Balducci
5.61
5.62
5.59
431
430
435
91.7
91.7
92.3
205
204
207
114
103
114
399
398
403
Terki (DFT)
Shein (DFT)
Shein (Expt.)
5.59
5.62
5.59
355
315
339
106 54
73.1 75.7
71.0 77.0
82
94.5
82-106
215
244
215-261
86.4
72.9
86.3
193
193
175-290
Youngs
/GPa
• Lewis B & Balducci : shell model parameters. Lewis A: rigid ion –
Use for subsequent MD – computationally less expensive
Molecular Dynamic (Bulk)
Using Lewis A potential (Rigid Ion) – less expensive
Simulations
Timestep = 0.001 ps
Simulation time = 106 steps
1 ns
NB. If use shell model, timestep = 0.0001
ps
Ensemble : nst
constant temperature, stress. Number of
atoms (allow shape change)
Pure cell : 500 Th 1000 O
U Doped Cells : 1.0 %
2.0 %
5.0 %
10.0 %
Similar dopant levels to those
found in fuel rods of ThO2 based
reactor – then more extreme
levels
Full Radial Distribution Function
Analysis
RDF (Th - O) Pure Thoria Temperature Range (1500K - 3600K)
6
5
5
1500 K
2700 K
3600 K
4
RDF - Density
RDF - Density
RDF (Th - O) 1% U Temperature Range 1500K- 3600 K
6
Temps : 1500K – 3600K
U levels: 1% U - 10 % U
3
2
1500 K
2700 K
3600 K
4
3
2
1
1
0
0
0
2
4
6
8
10
Distance (Å)
0
12
6
2
4
6
8
10
12
Distance Å
RDF (Th - O) 10% U Temperature Range (1500K - 3600K)
RDF- Density
5
1500 K
2700 K
3600 K
4
3
2
RDF (Th - O) 5% U Temperature Range 1500K - 3600K
6
RDF - (TH - O) 2% U Temperature Range 1500K - 3600K
6
1
5
5
0
RDF - Density
2
4
6
8
Distance (Å)
3
2
10
12
14
RDF - Density
0
1500 K
2700 K
3600 K
4
1500 K
2700 K
3600 K
4
3
2
1
1
0
0
2
4
6
8
10
12
0
0
2
4
6
Distance (Å)
-1
Distance (Å)
ThO2 Supports no phase change over the full range of temperatures.
8
10
12
Thermal Expansion
ThO2 has favourable thermophysical properties because of the higher thermal conductivity and
lower co-efficient of thermal expansion compared to UO2 [5] - Better fuel performance
Lattice Parameter of Uranium/Thoria Solid Solutions as a Function of
Temperature
0.585
0.583
Lattice Parameter /nm
0.581
0.579
0.577
0.575
0.00%
0.01%
0.05%
0.10%
0.573
0.571
0.569
0.567
1400
1900
2400
2900
3400
3900
4400
Temperature / K
[6] Rao et al. Thermal expansion and XPS of U-Thoria Solid Solutions. Journ. Nuc. Mat. 281 (2000)
[NB] Exptl. Experimental
Work involves much higher % doping and lower temperatures.
Coefficient of Thermal Expansion of
Uranium/Thoria Solid Solutions as a Function
of Temperature.
fractional change in size per degree change in temperature at a constant pressure
1.00E-05
Uranium does not effect low thermal expansion
10 % U – Extreme Levels
-1
Coefficient of Thermal Expansion (K )
9.90E-06
1%, 2%, 0% U
9.80E-06
0.00%
0.01%
0.05%
0.10%
– Normal operational levels
9.70E-06
9.60E-06
9.50E-06
9.40E-06
9.30E-06
9.20E-06
9.10E-06
1800
2000
2200
2400
2600
2800
3000
3200
3400
3600
3800
Temperature (K)
Lit. Value for average linear thermal expansion coefficients = 9.04 x 10-6 K-1 [7]
Journ. Nuc. Mat. 288, 1, 2001, 83-85.
Plot of Average Coefficient of Linear Expansion
against % Uranium content over temp. range
(1500 – 3220 K)
9.50E-06
-1
Average Coefficient of Linear Expansion (K )
9.48E-06
9.46E-06
Exptl. Lit. Value= Average lattice thermal expansion
coefficient (293 to 1473 K) of pure thoria = 9.58 ×
10−6 K-1 [8] (Ceramics. Int. 31, 6, 2005, 769-772.)
9.44E-06
9.42E-06
9.40E-06
9.38E-06
9.36E-06
9.34E-06
9.32E-06
9.30E-06
9.28E-06
0
0.0
1.0
0.01
1.0
2.0
0.02
0.03
0.04
0.05
0.06
5.0
% Uranium
% Uranium
0.07
0.08
0.09
10.00.1
10.0
Statics: Defect Chemistry
1. Because of high energy fission products and initial neutron bombardment,
fuel rods contain vacancies and interstitials.
2. We Calculate energy required to form vacancies, interstitials and to
substitute U4+ into the crystal lattice
Super Cell /eV
(periodic boundary
conditions)
Mott-Littleton /eV
(2 region approach)
O2- Vacancy
Th4+ Vacancy
O2- Interstitial
Th4+ Interstitial
U4+ Interstitial
13.97
81.34
-7.79
-56.80
-59.41
14.43
81.01
-7.81
-57.43
-59.98
U4+ on Th4+ site
-1.59
-1.59
Schottky Trio ThO2
Anion Frenkel
Cation Frenkel
3.01
3.08
12.27
3.21
3.31
11.79
Calcs predict substitution of U4+ onto Th4+ site costs only -1.59 eV, suggesting that
doping the crystal with U will not adversely affect the stability of bulk Thoria.
Oxide Ion Diffusivity – Activation Free
Energy of Migration Predictions
[NB] Th ion – diffusion so small, the errors involved would be bigger than the value
Our calculated values agree with experiment
Both pure ThO2 and U doped ThO2
Eact = approx 360-380 kJ. Mol-1
= approx 3.6 – 3.9 eV
Therefore, little or no diffusion
~0.5 eV
~0.7 eV
Heat Capacity (Cp) – compares well
with
Th
doped
LiF
Temperature (K)
-4.68E+06
1500
-4.69E+06
-4.70E+06
Enthalpy kJ/mol
-4.71E+06
-4.72E+06
2000
2500
3000
Pure Thoria
0.01% U in Thoria
Linear (Pure Thoria)
Linear (0.01% U in Thoria)
3500
y = 40.491x - 5E+06
-4.73E+06
Cp = (dH/dT)p
-4.74E+06
-4.75E+06
-4.76E+06
Pure ThO2
y = 40.924x - 5E+06
Slope = 40.942 kJ/mol/K
= 40942 J/mol/K
-4.77E+06
= 0.3100 kJ/g/K
-4.78E+06
= 310.031 J/Kg/K
-4.79E+06
Temperature /K
Th doped LiF 400 – 700 J/Kg/K
Effect of Lattice Uranium, Defects
and Interstitials on Heat Capacity
High energy fission products and initial neutron bombardment
means fuel rods contain vacancies and interstitials.
345
Uranium +
Oxygen
Interstitials
-density increase
340
Cp (J/kg/K)
U5+
U3+
U4+
335
Uranium alone
- little change
330
Uranium +
oxygen defects
-Less dense
325
320
0%
2%
4%
6%
%U
8%
10%
12%
Conclusions
•
We use atomistic simulation to help determine suitability of thoria as a next
generation nuclear fuel
– Involves similar dopant levels to those found in fuel rod, and higher levels too
– Full range of temperatures from ambient to the extreme working conditions
•
The 3 ThO2 potentials give very similar optimal bulk geometries – so we use
rigid-ion Lewis A model – computationally less demanding
•
ThO2 has favourable thermophysical properties – low coefficient of thermal
expansion, (1500 – 3200 K). Uranium doping at levels found in fuel rods
and well above this level, does increase expansivity, but not greatly.
•
Doping at the levels found in fuel rods does not effect stability of Bulk ThO2,
over the temperature range under test.
•
Very Low Ion Diffusivity.
Even for Oxide ion Eact (diffusion) = approx. 3 - 4 eV
•
Our work does point towards thoria being a suitable next generation fuel
•
Future work includes effect of defects and other dopants and effect of
neutron bombardment at the {111} surface to calculate recoil energies for
ThO2
Acknowledgements
1. The Science and Technology Facilities Council for
funding
2. National Grid Service (NGS) for computing resource.
3. CCP 5 for travel/collaboration grant between Huddersfield
and Bath.
4. Many thanks go to the following for useful
discussions/collaborations regarding science, lattice and
molecular dynamics simulations or NGS use:
Prof. Bob Cywinski
Dr D.J. Cooke
Dr. P. Martin
University
of Bath:
Prof. S.C. Parker
Tom Shapley
Dr. Marco Molinari
Jennifer Crabtree
Mofuti Mehlape
References
1.
2.
3.
4.
5.
6.
7.
8.
Lewis G., Catlow C. Journal Physics C – Solid State Physics 18, 1149, (1985).
Balducci et al. Chemistry of Materials 12, 677, (2000).
Terki et al. Computational Materials Science 33, 44, (2005).
Shein et al. J. Nucl. Mater., 361, No. 1, 69-77 (2007).
Thorium Fuel Cycle. Potential Benefits and Challenges. I.A.E.A.-tec-doc-1450 May
2005.
Rao et al. Thermal expansion and XPS of U-Thoria Solid Solutions. Journ. Nuc.
Mat. 281 (2000)
Journ. Nuc. Mat. 288, 1, 2001, 83-85.
Ceramics. Int. 31, 6, 2005, 769-772