Australian Nuclear Science & Technology Organisation
Simulating radiation damage in
quaternary oxides
Bronwyn Thomas, Nigel Marks, Bruce Begg,
René Corrales, Ram Devanathan
Synroc-type titanates for radioactive waste
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Composed of titanium-oxide mineral phases
Based on TiO6 octahedral framework
Many different cations, varying valences & sizes
Charge-compensating defects
Varying radiation resistance
–Composition
–Structure
–Defects
(Sr1-3x/2Lax)TiO3 perovskite
• Charge compensation via cation vacancies, one
vacancy per two La ions
• Maximum radiation resistance at x ≈ 0.2
• Phase transitions at x ≈ 0.2 (tilt) and 0.55 (layer)
• Short-range order observed from x ≈ 0.25
• How do we simulate partially disordered solids?
• What causes the radiation resistance anomaly?
–Cation vacancies?
–Ordering?
Challenges in simulating complex oxides
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Many different cation sublattices
Partially ionic, partially covalent
Oxygen is a problem…
Previous work in oxides:
–14 displacement cascade studies in oxides since
2000: ZrSiO4 (5), SiO2 (3), UO2 (2), CaZrTi2O7 (2),
La2Zr2O7, Gd2(Ti,Zr)2O7.
–A small number of other studies on threshold
displacement energies
–A large number of studies on defect formation and
migration
–Many inadequate models…
Strategy
TiO2
SrTiO3
(Sr1-3x/2Lax)TiO3
Model
Applications
• Study TiO2 rutile:
–Model development; behaviour of titanate systems
–Radiation resistance
• Develop models for (Sr,La)TiO3
• Study short-range ordering as a function of La
concentration
• Study radiation resistance as a function of La
concentration and short-range order
Rutile TiO2
Lessons from rutile
• Ockham’s razor: the simplest possible model to
describe the broadest range of situations.
kqiq j
Cij
V r 
 Aij exp rij / r ij  6
rij
rij
• Use partial charge (not formal or variable)
–Determine using ab initio data (Mulliken analysis)
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• Don’t include atomic polarisation (shell model)
–Added complexity for little gain
• No dispersion terms
• No cation-cation Born-Mayer terms
• Simplest: Two parameters (A, r) for each atom
type, plus charges.
Perovskite (Sr,La)TiO3
Vacancy
SrTiO3
Sr0.625La0.25TiO3
Model development for SrTiO3
• Charges
–ab initio (CRYSTAL, GGA, Mulliken)
–Sr: 1.84, Ti: 2.36, O: -1.40
• Cubic: high symmetry
–3 experimental parameters (a, c11, c12 = c44)
–6 Born-Mayer parameters
–Not enough data! Fit is not unique
• Other data?!
–Binary oxides? Other structures? Ab initio data?
–Need to separate Sr-O and Ti-O interactions
Ruddlesden-Popper Sr3Ti2O7
2 layers SrTiO3
+
1 layer SrO
• Unique fit (GULP)
• Good elastic &
thermodynamic
properties
Model development for (Sr,La)TiO3
• Fit La-O model (2 params) to (Sr,La)TiO3 data
–Data: Experimental crystallographic structures,
volume varies linearly with La content
• Problems:
–Atomic-level structures unknown; local cation
ordering increases with La concentration
–“Random” cation configurations have wide range of
energies and volumes
• Solution: Ab initio calculations of (Sr,La)TiO3
supercell configurations (VASP)
–Fit La-O model to La=0.25 structure data (6)
–Test La-O model using La=0.5 data (16)
(Sr0.625La0.25)TiO3 supercells
(Sr0.25La0.5)TiO3 supercells
Relative energies (La=0.5)
Summary of model development
• For TiO2
–Simplified functional form
–Validated Mulliken charges
• For SrTiO3
–Computed Sr, Ti and O ab initio Mulliken charges
–Fitted Sr-O, Ti-O and O-O pair terms (6 parameters)
to experimental data (SrTiO3 and Sr3Ti2O7)
• For (Sr,La)TiO3
–Fitted La-O pair term to ab initio data for 6
Sr5La2Ti8O24 configurations
–Tested against 16 Sr2La4Ti8O24 configurations
–Checked Mulliken charge for La (not a parameter)
Radiation damage in rutile and SrTiO3
• Threshold displacement energies (< 100 eV)
–Molecular dynamics (DL_POLY)
–SRIM: binary collision approximation
• Defect structures, energies and migration
• Displacement cascades (1 - 10 keV)
50 eV displacement in rutile, 160 K
Ti
O
Radiation damage in rutile
Threshold Displacement Energy ± 5 eV (160 K)
(001)
(100)
(110)
(101)
(111)
O
65
30
55
30
35
Ti
75
110
95
105
115
• Anisotropy, focus/defocus collisions
• Implications for SRIM calculations
–Defect formation
–Recombination distance
• Low energy O interstitial migration mechanisms
–split-interstitials & channel sites
Oxygen migration in rutile @ 800 K
Ti
O
5 keV displacement cascade in rutile
Radiation damage in SrTiO3
Threshold Displacement Energy ± 10 eV (300 K)
(100)
(110)
(111)
O
30
40
40
Sr
30
60
70
Ti
> 110
80
> 110
• Channeling important for Sr
• Oxygen and strontium interstitial migration
energies higher
5 keV displacement cascade in SrTiO3
Sr
Ti
O
Radiation damage in (Sr,La)TiO3 (future work)
• Monte Carlo simulation of short-range order
• Oxygen interstitial/vacancy migration vs La
content
–Effects of cation vacancies
–Effects of short-range order
• Displacement cascades
• Why maximum radiation resistance at x ≈ 0.2?