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).

Universities Nuclear Technology ForumUniversity of Huddersfield11th - 13th April 2011

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 - MD2. Thermal expansion - MD3. Defect Chemistry – Static modelling4. Oxide ion diffusion - MD5. Heat Capacity – MD6. Uranium clustering at surfaces and bulk - LD

• Conclusions

Why Study Thoria ?Background and the Thoria Fuel Cycle

• 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

Experts propose a new future for low carbon energy

production :Nuclear power from Thoria

Professor Bob Cywinski (right) with Nobel Laureate Professor Carlo Rubbia, former Director of CERN

Thorium CycleSpallation

Stop neutron bombardment = cycle stops

Absorbs neutron to become Th 233

Electron loss

Electron loss

Energy releasedBy Nuclear fission

andNeutrons freed to continue process

Further Decay

Thorium is not fissile

Computational methods and Results

2 main methods: QM v MM

Molecular MechanicsQuantum Mechanics

Water on CaO {100} surface

Force dominated by electrostaticinteractions, but include repulsion,van der Waals and polarisability

Can study larger systems

But needs reliable potential parameters

Very Accurate But very slow

Shell model calculations

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.

• Lewis B & Balducci : shell model parameters. Lewis A: rigid ion – Use for subsequent MD – computationally less expensive

Cell Parameter

a / Å

Elastic constants /GPa

C11 C12 C44

Moduli

Bulk Shear Youngs

/GPa /GPa /GPa

Lewis A

Lewis B

Balducci

5.61

5.62

5.59

431 91.7 86.4

432 91.7 72.9

435 92.3 86.3

205 114 399

206 103 398

207 114 403

Terki (DFT)

Shein (DFT)

Shein (Expt.)

5.59

5.62

5.59

355 106 54

315 73.1 75.7

339 71.0 77.0

193 82 215

193 94.5 244

175-290 82-106 215-261

Molecular Dynamic (Bulk) Simulations

Timestep = 0.001 psSimulation time = 106 steps

1 nsNB. If use shell model, timestep = 0.0001 ps

Ensemble : nstconstant temperature, stress. Number of atoms (allow shape change)

Pure cell : 500 Th 1000 OU Doped Cells : 1.0 %

2.0 % 5.0 % 10.0 %

Using Lewis A potential (Rigid Ion) – less expensive

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)

0

1

2

3

4

5

6

0 2 4 6 8 10 12

Distance (Å)

RD

F -

De

ns

ity

1500 K

2700 K

3600 K

RDF (Th - O) 1% U Temperature Range 1500K- 3600 K

0

1

2

3

4

5

6

0 2 4 6 8 10 12

Distance Å

RD

F -

Den

sity

1500 K

2700 K

3600 K

RDF - (TH - O) 2% U Temperature Range 1500K - 3600K

-1

0

1

2

3

4

5

6

0 2 4 6 8 10 12

Distance (Å)

RD

F -

Den

sity

1500 K

2700 K

3600 K

RDF (Th - O) 5% U Temperature Range 1500K - 3600K

0

1

2

3

4

5

6

0 2 4 6 8 10 12

Distance (Å)

RD

F -

Den

sity

1500 K

2700 K

3600 K

RDF (Th - O) 10% U Temperature Range (1500K - 3600K)

0

1

2

3

4

5

6

0 2 4 6 8 10 12 14

Distance (Å)

RD

F-

Den

sity

1500 K

2700 K

3600 K

ThO2 Supports no phase change over the full range of temperatures.

Temps : 1500K – 3600KU levels: 1% U - 10 % U

Thermal Expansion

Lattice Parameter of Uranium/Thoria Solid Solutions as a Function of Temperature

0.567

0.569

0.571

0.573

0.575

0.577

0.579

0.581

0.583

0.585

1400 1900 2400 2900 3400 3900 4400

Temperature / K

Latt

ice P

ara

mete

r /n

m

0.00% 0.01%

0.05% 0.10%

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

[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.

9.10E-06

9.20E-06

9.30E-06

9.40E-06

9.50E-06

9.60E-06

9.70E-06

9.80E-06

9.90E-06

1.00E-05

1800 2000 2200 2400 2600 2800 3000 3200 3400 3600 3800

Temperature (K)

Co

effi

cien

t o

f T

her

mal

Exp

ansi

on

(K-1

)

0.00% 0.01%

0.05% 0.10%

Coefficient of Thermal Expansion of Uranium/Thoria Solid Solutions as a Function

of Temperature.

Uranium does not effect low thermal expansion

fractional change in size per degree change in temperature at a constant pressure

Lit. Value for average linear thermal expansion coefficients = 9.04 x 10-6 K-1 [7] Journ. Nuc. Mat. 288, 1, 2001, 83-85.

10 % U – Extreme Levels

1%, 2%, 0% U

– Normal operational levels

Plot of Average Coefficient of Linear Expansion against % Uranium content over temp. range

(1500 – 3220 K)

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.)

1.0 2.0 10.00.0 1.0 5.0 10.0

% Uranium

Statics: Defect Chemistry1. 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

U4+ on Th4+ site

13.97

81.34

-7.79

-56.80

-59.41

-1.59

14.43

81.01

-7.81

-57.43

-59.98

-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

Both pure ThO2 and U doped ThO2

Eact = approx 360-380 kJ. Mol-1

= approx 3.6 – 3.9 eVTherefore, little or no diffusion

~0.5 eV

~0.7 eV

Our calculated values agree with experiment

y = 40.924x - 5E+06

y = 40.491x - 5E+06

-4.79E+06

-4.78E+06

-4.77E+06

-4.76E+06

-4.75E+06

-4.74E+06

-4.73E+06

-4.72E+06

-4.71E+06

-4.70E+06

-4.69E+06

-4.68E+06

1500 2000 2500 3000 3500

Temperature /K

En

thal

py

kJ/

mo

l

Pure Thoria

0.01% U in Thoria

Linear (Pure Thoria)

Linear (0.01% U in Thoria)

Heat Capacity (Cp) – compares well with Th doped LiF

Cp = (dH/dT)p

Slope = 40.942 kJ/mol/K

= 40942 J/mol/K

= 0.3100 kJ/g/K

= 310.031 J/Kg/K

Pure ThO2

Th doped LiF 400 – 700 J/Kg/K

Temperature (K)

Effect of Lattice Uranium, Defects and Interstitials on Heat Capacity

320

325

330

335

340

345

0% 2% 4% 6% 8% 10% 12%

%U

Cp

(J/k

g/K

)

U5+ U3+ U4+

Uranium alone - little change

Uranium +Oxygen

Interstitials-density increase

Uranium + oxygen defects

-Less dense

High energy fission products and initial neutron bombardmentmeans fuel rods contain vacancies and interstitials.

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

Acknowledgements1. 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 CywinskiDr D.J. CookeDr. P. Martin

Prof. S.C. ParkerTom ShapleyDr. Marco MolinariJennifer CrabtreeMofuti Mehlape

University of Bath:

References

1. Lewis G., Catlow C. Journal Physics C – Solid State Physics 18, 1149, (1985).

2. Balducci et al. Chemistry of Materials 12, 677, (2000).

3. Terki et al. Computational Materials Science 33, 44, (2005).

4. Shein et al. J. Nucl. Mater., 361, No. 1, 69-77 (2007).

5. Thorium Fuel Cycle. Potential Benefits and Challenges. I.A.E.A.-tec-doc-1450 May 2005.

6. Rao et al. Thermal expansion and XPS of U-Thoria Solid Solutions. Journ. Nuc. Mat. 281 (2000)

7. Journ. Nuc. Mat. 288, 1, 2001, 83-85.

8. Ceramics. Int. 31, 6, 2005, 769-772