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 Composed of titanium-oxide mineral phases Based on TiO 6 octahedral framework Many different cations, varying valences & sizes Charge-compensating defects Varying radiation resistance –Composition –Structure –Defects

(Sr 1-3x/2 La x )TiO 3 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 Many different cation sublattices Partially ionic, partially covalent Oxygen is a problem… Previous work in oxides: –14 displacement cascade studies in oxides since 2000: ZrSiO 4 (5), SiO 2 (3), UO 2 (2), CaZrTi 2 O 7 (2), La 2 Zr 2 O 7, Gd 2 (Ti,Zr) 2 O 7. –A small number of other studies on threshold displacement energies –A large number of studies on defect formation and migration –Many inadequate models…

Strategy Study TiO 2 rutile: –Model development; behaviour of titanate systems –Radiation resistance Develop models for (Sr,La)TiO 3 Study short-range ordering as a function of La concentration Study radiation resistance as a function of La concentration and short-range order TiO 2 SrTiO 3 (Sr 1-3x/2 La x )TiO 3 Model Applications

Rutile TiO 2

Lessons from rutile Ockham’s razor: the simplest possible model to describe the broadest range of situations. Use partial charge (not formal or variable) –Determine using ab initio data (Mulliken analysis) 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,  ) for each atom type, plus charges.

Perovskite (Sr,La)TiO 3 Vacancy SrTiO 3 Sr La 0.25 TiO 3

Model development for SrTiO 3 Charges –ab initio (CRYSTAL, GGA, Mulliken) –Sr: 1.84, Ti: 2.36, O: Cubic: high symmetry –3 experimental parameters (a, c 11, c 12 = c 44 ) –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

2 layers SrTiO layer SrO Ruddlesden-Popper Sr 3 Ti 2 O 7 Unique fit (GULP) Good elastic & thermodynamic properties

Model development for (Sr,La)TiO 3 Fit La-O model (2 params) to (Sr,La)TiO 3 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)TiO 3 supercell configurations (VASP) –Fit La-O model to La=0.25 structure data (6) –Test La-O model using La=0.5 data (16)

(Sr La 0.25 )TiO 3 supercells

(Sr 0.25 La 0.5 )TiO 3 supercells

Relative energies (La=0.5)

Summary of model development For TiO 2 –Simplified functional form –Validated Mulliken charges For SrTiO 3 –Computed Sr, Ti and O ab initio Mulliken charges –Fitted Sr-O, Ti-O and O-O pair terms (6 parameters) to experimental data (SrTiO 3 and Sr 3 Ti 2 O 7 ) For (Sr,La)TiO 3 –Fitted La-O pair term to ab initio data for 6 Sr 5 La 2 Ti 8 O 24 configurations –Tested against 16 Sr 2 La 4 Ti 8 O 24 configurations –Checked Mulliken charge for La (not a parameter)

Radiation damage in rutile and SrTiO 3 Threshold displacement energies (< 100 eV) –Molecular dynamics (DL_POLY) –SRIM: binary collision approximation Defect structures, energies and migration Displacement cascades ( keV)

50 eV displacement in rutile, 160 K Ti O

Radiation damage in rutile Anisotropy, focus/defocus collisions Implications for SRIM calculations –Defect formation –Recombination distance Low energy O interstitial migration mechanisms –split-interstitials & channel sites Threshold Displacement Energy ± 5 eV (160 K) (001)(100)(110)(101)(111) O Ti

Oxygen migration in 800 K Ti O

5 keV displacement cascade in rutile

Radiation damage in SrTiO 3 Channeling important for Sr Oxygen and strontium interstitial migration energies higher Threshold Displacement Energy ± 10 eV (300 K) (100)(110)(111) O 3040 Sr Ti > 11080> 110

5 keV displacement cascade in SrTiO 3 Ti O Sr

Radiation damage in (Sr,La)TiO 3 (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?