Australian Nuclear Science & Technology Organisation Simulating radiation damage in quaternary oxides Bronwyn Thomas, Nigel Marks, Bruce Begg, Ren Corrales, Ram Devanathan Synroc-type titanates for radioactive waste

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

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 Ockhams razor: the simplest possible model to describe the broadest range of situations.

kqiq j Cij V ( r) = + Aij exp(rij / ij ) 6 rij rij Use partial charge (not formal or variable) Determine using ab initio data (Mulliken analysis) Dont 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)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?