1. Modelling and theory of systems relevant to nuclear waste processing
Kostya Trachenko
Queen Mary University of London

2. My research interests: - Theory (dynamics and thermodynamics) of liquids, liquid-glass transition and supercritical state Extension to field theory and cosmology - Modelling radiation damage effects (nuclear and fusion applications)
Today’s talk
Molecular dynamics of radiation damage in waste forms

3. Transport and diffusion in radiation-damaged zircon
Resistance of materials to amorphization by radiation damage
Properties of collision cascades
High-energy radiation damage in iron
Diffusion rates and activation energies in radiation-amorphized zirconolite

4. Modelling of high-energy radiation damage
Future of nuclear industry is linked to safe encapsulation of nuclear waste
Radiation damage in materials to be used to encapsulate highly radioactive nuclear waste: ceramic materials
2. Radiation damage in nuclear fuels in current and future nuclear reactors: metals
3. Radiation damage in future fusion reactors: metals

5. Crystalline ceramics as waste forms
Safe and more durable alternative to glasses: CaTiO3, CaZrTi2O7, BaAl2Ti6O16 and TiO2 - geochemically stable minerals which have immobilised uranium and thorium for billions of years. Can incorporate high-level radioactive waste (Pu, Sr, Ba, Cs)
Pyrochlore (Gd, Sm, Hf-based)-rich titanate phases for Pu encapsulation: high waste load plus criticality control (neutron absorbants)
Other potential “waste forms”: ZrSiO4, ZrO2, Gd2Zr2O7 and so on
What are the effects of radiation damage?
How do they affect performance of waste forms?

6. Effect of radiation-induced amorphization on diffusion
What are long-term (millions of years) effects of irradiation on the performance of waste forms?
Case study: zircon ZrSiO4 minerals are ~1 billion years old, completely amorphous yet intact
Absorbs large ions like Pu on Zr site
Can we learn from Nature?

8. What are the effects of radiation damage?
Processes are too fast and collision cascades are too small for experiments -> MD simulations
Challenge of large energy and large size:
Recoil energies: keV
Require very large MD boxes
Not achievable previously

9. Molecular dynamics simulation of radiation damage: challenge of large energy and large size
Details:
1. Empirical potentials; short-range ZBL potential at short <~1 Å distances
2. Perfectly scalable MD code based on domain decomposition strategy (DL_POLY MD package)
3. Parallel computers (Cambridge HPC, HPCx, HECToR, Archer)
4. Adapted MD code to handle out-of-equilibrium conditions (variable time step, boundary scaling)

10. High-energy U recoils in ZrSiO4
50 keV U recoil and their overlap
Density variations appeared inside cascades and during their overlap
Density variations later confirmed in diffuse X-ray scattering

11. (Geisler et al, Trachenko et al, 2003, 2004)
The value of percolation threshold in the continuum percolation is pc=0.3 (approx.)
(non-trivial because it is continuous percolation)
This gives channels of increased diffusion and explains percolation-type increases of transport
(Geisler et al, Trachenko et al, 2003, 2004)

12. A material is amorphizable if it is able to form a covalent network
Amorphizability
A material is amorphizable if it is able to form a covalent network

13. Resistant vs amorphizable materials
Some materials are easily amorphized (silicates and titanates)
Others are extremely resistant to amorphization (e.g., ZrO2, Gd2Zr2O7)
What is the nature of the process of resistance to amorphization by radiation damage?
The same question is relevant in other areas:
GaN and ZnO are considerably more resistant than GaAs, GaSb, Si etc

14. Understanding resistance to amorphization to radiation damage
Resistance is governed by activation barriers for damage recovery and the nature of the bond

15. Understanding resistance to amorphization
Many criteria do not generally work (review in JPCM 2004)
Out of ~10 criteria, Naguib&Kelly (1975) empirically noticed that for binaries, resistance increases with ionicity (Pauling ionicity scale). Many other followed.
Need: generality and applicability to all systems =>physical explanation
Way to quantify: need hard numbers. Neither Pauling nor Phillips scales work generally!
Trachenko et al, PRB 2005

16. Understanding resistance to amorphization
Trachenko et al, PRB 2005
Prediction, verified experimentally
Review paper in JPCM 2004: 115 complex materials with no exception to this rule: increased covalency (reduced ionicity) decreases resistance

17. Molecular dynamics: look at the process in detail
Rutile TiO2

18. Two types of damage relaxation:
1. Elastic reversible relaxation of crystalline lattice around the swollen cascade – large peak in Ndef
2. Irreversible topological damage
1-2 ps ps

19. Resistance to amorphization
50 keV U recoil
Poor recovery
Intermediate recovery
Good and perfect recovery
SiO2
GeO2
TiO2
MgO
Al2O3
t=1 ps
t=5, 50 ps
MD simulations reproduce experimental behaviour of resistance to amorphization.
Damage increases with the stiffness of O-O interaction

20. Why do empirical potentials reproduce activation barriers that govern damage recovery?

21. Resistance to amorphization
Classical MD simulations reproduce experimental behaviour of resistance to amorphization
MD simulations can be used to predict highly resistant materials where resistance to amorphization operates on the time scale of picoseconds. Successfully predicted resistance of series of pyrochlores.
Slower recovery processes are possible. Even then, predictions work if recovery is slow (cascade size in MD simulations on ps time scale=in billion-year-old samples from NMR experiments)

22. Radiation damage in iron
Simulate radiation damage in fusion reactors: ~1 Mev Fe recoil atoms from 14 MeV neutrons
Also relevant for nuclear fuels: fission products (many MeVs) These energies were not studied before, yet are important to simulate
Need up to 1 billion atoms in a MD box. The size of this system is about 0.2 micrometers – size where, for the first time, simulations and many experiments meet!

23. DL_POLY development work
(supported by the EPSRC grant)
Radiation damage-specific developments:
Identification of radiation damage and defects
Electronic energy loss mechanism (friction term and two-temperature models)
Tuning potentials to very non-equilibrium conditions

24. DL_POLY development work (supported by the current EPSRC grant)
General developments related to very large system sizes:
Calculation of properties on the fly (one configuration of 250 mln atoms is about 100 Gb, 10,000-frame history file is Petabyte in size)
Change the paradigm of how to run&analyze MD results – MD of the future
Relevant for many interested in phenomena operating on microscale: shock, fracture, initiation of micro-cracks, micro-structural changes, interfacial effects, macromolecules, biological systems and so on

25. These energies have not been simulated before
MeV Fe recoils in iron
These energies have not been simulated before
Many-body (embedded atom) potential optimized against several defect energies in alpha-iron
million atoms, system size ~ nm
24,000-60,000 parallel HeCTOR processors
Great PhD student!
1. What does the collision cascade actually look like? First visualization of high-energy cascades
2. Novel insights into the cascade structure: continuous damage morphology vs sub-cascade branching

26. 0.5 MeV recoils in Fe
Displaced atoms
Defect atoms

27. 0.5 MeV recoils in Fe
Displaced atoms
Defect atoms

28. Look at defects locally:
500 keV Fe recoils in iron
anharmonicity
displaced atoms
defect atoms
Look at defects locally:
Large (~100 atoms) clusters of interstitials and vacancies. Quantify and discuss their stability. News Story in JPCM 2013

29. Radiation damage at interfaces and effects of microstructure
Current work:
Radiation damage at interfaces and effects of microstructure
Gd2Zr2O7, Gd2Zr2O7 and CaZrTi2O7
interface

30. Radiation damage at interfaces and effects of microstructure
Current work:
Radiation damage at interfaces and effects of microstructure
Slab: defects
Spherical inclusion: defects
The number of displaced and defect atoms increases compared to the crystal
Presumably due to disorder at interfaces and grains

31. Current work: interfaces in Y2O3-ZrO2
Cubic phase
Orthorhombic (not monoclinic) phase

32. Current work: effect of shock waves
Can the damage due to shock waves be PERMANENT?

33. Diffusion in waste forms
What are the effects of amorphization and density decrease on diffusion?
Problem of long time scales
Several methods exist (search for transition states, temperature-accelerated dynamics and so on)
We simulate at high temperature and extract activation energy barriers

34. Yang et al, Journal of Applied Physics 2014
Solid-state diffusion in amorphous zirconolite ZrCaTi2O7
Under typical waste load, zirconolite becomes amorphous in about 1000 years
Most of radiation damage will take place in an amorphous system
Insert some U atoms. Prepare an amorphous structure by liquid quenching
Directly observe diffusion of atomic species
Calculate diffusion coefficient D from <r2>=6Dt at different temperature and density and calculate activation energy barrier U from D=D0exp(-U/T)
Disentangle effects of amorphization and density on diffusion (not possible in the experiment)
Yang et al, Journal of Applied Physics 2014

35. Diffusion of O atoms Disorder increases diffusion of O atoms
Density does not

36. Diffusion of cations
Smaller density increases diffusion of cations

37. Activation energy barriersCa
Activation energies for cations dramatically depend on disorder (no diffusion is seen in the crystal) but not on density – a surprise.
Activation energies of O atoms are not sensitive to disorder and density
Diffusion pre-factors increase at smaller density for cations by
Diffusion pre-factors for O do not depend on density and increase as a result of amorphization
not affected by density – a surp Zr Ti U

38. Activation energies and pre-factors enable us to predict diffusion of atomic species at long times and evaluate performance of a nuclear waste

39. Thank you