Predicting the Effect of Fission Products in UO2

Kaajal H. Desaia, David Parfitta, Scott L. Owensb, Robin W. Grimesa

a Department of Materials, Imperial College, Prince Consort Road, London, UK

b Nexia Solutions, Hinton House, Risley, Warrington, Chesire UK

Imperial CollegeOF SCIENCE, TECHNOLOGY AND MEDICINE

Presentation at the VERCORS meeting

Aim: demonstrate what atomic scale computer simulation can provide, that is useful for developing a better understanding of the behaviour of nuclear fuels (particularly as they relate to fission product behaviour).

What can simulations do for you?

• Correlate experimental data with existing physical models (fill in the gaps and work out what’s missing).

• Generate data for known physical processes (point the way to better hunting grounds for experimental work).

• Develop new physical models that underpin phenomena (work out what science actually matters).

First – Correlate experimental data with physical models

• Use fission product inventories to investigate fuel swelling.

• Lattice swelling/contraction due to accommodation of soluble fission products as a function of fission product concentration.

• Affect on mechanical properties – elastic constants and bulk moduli as a function of fission product concentration.

First – Correlate experimental data with physical models

• The Physical process is well established.

• No new “science” is being suggested.

• Checking existing data and correlating it.

• Hence: fillng in the gaps and working out what’s missing.

Swelling Calculation Defect volume, VD, is calculated by:

KT (Å3 eV-1) is the isothermal compressibility,

V0 (Å3) initial unit cell volume

f (eV) the internal defect formation energy calculated within the Mott-Littleton approximation

Mechanical constants are calculated using:

Bulk Modulus

1211 2

3

ccKT

TTD dV

dfVKV

0

TKB

1

Range of Fission Products (FP) Different solution sites – U and O

substitution, interstitial octahedral site, cluster sites

Fuel Stoichiometry

Zr4+, Ce4+ - sites: , Sr2+ - sites: Isolated Clustered Isolated Clustered or

Y3+, La3+, Pr3+, Nd3+, Sm3+, Eu3+, Gd3+, Dy3+ sites: Isolated Clustered or Isolated Clustered

Model Considerations

XUZr

XUCe

OU VSr '' XOU VSr :''

UU USr 2'' UUU UUSr''' : XUU USr 2:''

OU VLa '2 '' : UOU LaVLa XOU VLa :2 '

UU ULa ' XUU ULa :'

Results I: Zr accommodation

Results II: Ce accommodation

FP Accommodation: Sr Number of ways Sr can be accommodated in lattice UO2 - substitution on U site is energetically favoured Charge compensated in 2 ways

VO··

Oxygen vacancy formationUU

·

Uranium oxidation, U5+ formation

Similarly for the trivalent, Y and lanthanide fission products

Results III: Sr accommodation

Results IV: La accommodation

Results V: Pr accommodation

Results VI: Nd accommodation

Results VII: Sm accommodation

Results VIII: Eu accommodation

Results IX: Gd accommodation

Results X: Dy accommodation

Results XI: Predicted Change in Bulk Modulus due to Sr

Results XIII: Predicted Change in Bulk Modulus due to Zr and Ce

Summary

A specific burnup yields a specific fission product inventory. This work aims to provide data from which it is possible to determine a change of lattice parameter or change in mechanical property of the UO2 lattice as a consequence of the dissolved fraction of those fission products. For example,

Sr2+ --> Increased lattice parameter Zr4+ --> Decreased lattice parameter

Second – Generate data for known physical processes

• The aim is to help to direct experimental work.

• The physical process is well established, but the significance to fuels not necessarily realised.

• Appropriate experimental data does not yet exist.

• Classic example: compositional changes due to segregation.

Aim of Segregation Study

• Computer simulation is used to investigate the accommodation and segregation of fission products to the (111), (110) and (100) surfaces of UO2

Fission products considered: Ce4+, Zr4+, Ba2+, Sr2+, Kr0 and Xe0

Ba2+ and Sr2+ are charge compensated by a single oxygen vacancy

Kr0 and Xe0 are compensated by two oxygen vacancies

• Important results concern:

Segregation dependence on the surface type

Defect cluster orientation with respect to a given surface

Anion termination configuration for dipolar surfaces

• This work provides information regarding the anisotropic release of fission products.

see Stanek et al. Mat. Res. Symp. Proc. 654 (2001) AA 3.32.

Methodology

• Computational codes CASCADE and MARVIN are used.

• A defect (isolated or clustered) is introduced to a characteristic lattice and moved stepwise through the bulk.

• The total energy of Region 1 is calculated for each step and the energies are compared with respect to when the cluster is furthest from the surface (i.e. in the bulk).

Divalent ClusterConfigurations: (111)• The nearest neighbour {(Ba/SrU)’’:(VO)..} configuration is preferred.

• There are four unique nearest neighbour cluster configurations with respect to the (111) surface, shown below.

• Each of these configurations must be modelled.

• The Zr4+ segregation energy, ES = 0.26eV, the trap energy, ET = 0.35eV, which suggests

that Zr4+ remain trapped just beneath the (111) surface.

• For Ce4+, ES = 0.23eV, which suggests that Ce4+ does not segregate to the (111) surface.

• (ET - ES) is negligible, which suggests that the trapping observed with Zr4+ is not present.

Ce4+ and Zr4+ (111) Segregation

Ba2+ and Sr2+ (111) Segregation

• The segregation energy ES = -2.71eV for Ba2+, thus Ba2+ will segregate to the (111) surface.

• A similar trend is observed for Sr2+, where ES = -1.60eV, though the driving force is reduced.

• In the bulk ( 10Å) there is little cluster configuration preference.

• Near to the surface, there is a dependence on defect cluster configuration.

Ce4+ and Zr4+ (110) Segregation

• The Zr4+ segregation energy, ES = 0.14eV, which suggests that Zr4+ will not segregate to the (110) surface.

• The nonlinear change in energy is due to alternating compression and dilation of atomic layers.

• For Ce4+ ES = 0.67eV which suggests that Ce4+ does not segregate to the (110) surface, more strongly than Zr4+.

• The trend for Ce4+ and Zr4+ not segregating to the (110) surface is similar to the trend observed for the (111).

Ba2+ and Sr2+ (110) Segregation

• The Ba2+, segregation energy, ES = -2.84eV, suggests that Ba2+ will segregate to the (110) surface.

• A similar trend is observed for Sr2+ where ES = -1.67eV; clearly the driving force is reduced.

• The segregation of Ba2+ and Sr2+ is very similar to that observed with the (111); similar segregation energies and cluster dependence nearer to the surface.

Conclusions Concerning Segregation

• Computer simulation calculations suggest that Ce4+ and Zr4+ show no tendency to segregate to the (111) or (110) surfaces of UO2.

• Zr4+ demonstrates a tendency to segregate to the (100)A surface, which suggests segregation is a function of surface.

• Ba2+ and Sr2+ display a tendency to segregate to the (111) and (110) surfaces, with cluster configuration becoming important near the surface in both cases.

• Segregation is not only a function of fission product chemistry and surface, but also cluster configuration with respect to surface and anion termination in the case of Type 3 surfaces.

• Fission product release will be highly anisotropic.

Third – identify new physical processes

Aims of the study Develop a robust computational model that can

simulate UO2 and fission gasses. It must replicate:

High temperature behaviour and defect energies

Good core-core repulsion for high energy collisions

Apply this model to predict the evolution of bubbles with respect to: Bubble size

Fission gas pressure

Temperature of material

Recoil energy

Transgranular fracture showing internal void, smaller gas bubbles and larger bubbles at grain boundaries

Transgranular fracture showing aligned metal

particles leading to a grain boundary

All micrographs courtesy of Ian Ray ITU

Intergranular and Transgranular Fracture

Molecular dynamics of radiation enhanced helium re-solution

Helium in bubbles can return to the crystal lattice via radiation-enhanced re-solution rather than thermal resolution

...But how does this actually work in practice?

It is thought that high-energy fission fragments 'knock out' helium atoms from bubbles leading to resolution.

What Bubbles?

Several different bubble sizes and shapes have been investigated: Octahedra constructed from (111) surfaces

Infinite pores from (110) surfaces

Spheres

Larger 'infinite' slab surfaces

In UO2 the morphology of the bubbles is roughly spherical but (111) surfaces are observed (which also dominate equilibrium voids).

MD Simulation of 5 keV U <111> Recoil

Event sequence:

•Ballistic phase.

•Thermal spike.

•Displacement damage interacts with the He bubble disrupting the bubble/lattice interface.

•Beginning of recovery phase.

MD Simulation of 5 keV U <111> Recoil

Event sequence:

•Ballistic phase and thermal spike are not seen.

•Displaced lattice ions interacts with the He bubble disrupting the bubble/lattice interface.

•He “leaks” into the damaged (partly disordered) lattice.

MD Simulation of 5 keV U <111> Recoil

Event sequence:

•Ballistic phase.

•Thermal spike.

•Lattice ions are displaced into the bubble.

•UO2 units are relocated across the bubble facilitating the overall movement of the bubble.

Why is this exciting?

• Physics behind this mode of radiation enhanced resolution is fundamentally different to what has been proposed previously.

• May explain some 'anomalous' terms in bubble migration models.

• More accurate and confident modelling leads to less conservatism in fuel performance codes.

Directions of Further Work

• Long timescale dynamics of bubble migration.

• He migration along dislocations.

• 'Phase diagram' of the bubbles as a function of temperature, He pressure and displacement cascade energy.

• Examine Xe gas behaviour as well – Xe adopts solid structures in fission gas bubbles.

• Aim to aid in reducing conservatism.

Summary

• A simple computational model has been used to generate structure (and defect structure) property composition relationships.

• Correlated experimental data with physical models (filled in some gaps and work out what’s missing).

• Identified computational variations close to surfaces (pointed the way for experimental investigations).

• Developed new physical models that underpin phenomena (worked out what bit actually matters).

• Need to use a range of computational techniques to underpin and generate the defect property relationships.

Imperial CollegeOF SCIENCE, TECHNOLOGY AND MEDICINE