Computational Theory and Modeling Relevant to Fusion Reactor Materials Roger E. Stoller in collaboration with: Yuri Osetskiy, Haixuan Xu, Stanislav Golubov, Alexander Barashev Materials Science and Technology Division Oak Ridge National Laboratory ICFRM-17 Tutorial Session: Fusion Reactor Materials Aachen, Germany 11 October 2015 ornl Why do we care about modeling radiation damage in structural materials? • Although irradiation experiments cannot be replaced by modeling alone, a purely experimental approach to understanding the effects of irradiation is also not practicable . costs for design and execution of reactor irradiations . costs of post-irradiation examination of radioactive materials . declining facilities for both irradiation and examination . combinatorial problem: broad range of materials, phenomena, and irradiation conditions - coolants, temperature, loading conditions, dose rate, i.e. because we have to … . dose because we have to • Recent advances in computational hardware, computational materials science, ... make it more feasible than ever to aggressively pursue the contribution of modeling see relevant chapters in: Comprehensive Nuclear Materials, R. J. M. Konings, T. R. Allen, R. E. Stoller, and S. Yamanaka, Editors, Elsevier (2012) ornl Components of Primary Radiation Damage Source Term • incident particles of different types and energies produce different displacement production types of primary damage from elastic collisions – neutrons, heavy charged particles, electrons, photons • produce differences in secondary damage accumulation • need to know both energy spectrum and absolute flux level nuclear transmutation nuclear transmutation from from thermal neutrons, high-energy neutrons, E<1 eV threshold reactions, E>2 MeV ornl What is unique about modeling the fusion environment? • the DT fusion reaction source term, unique aspect is 14.1 MeV neutrons higher energy atomic recoils for displacement damage production • higher levels of He and H from transmutation via threshold reactions, e.g. ~12 appm He/dpa and 50 appm H/dpa in AISI-316 for typical first note: many lower energy wall spectrum neutrons as well ornl Early mechanistic models used to anticipate role of transmutant helium on swelling: potential fission-fusion difference • Helium production higher in fusion than LMFBR (FFTF) environment – experiments with isotopic tailoring of Ni in austentitic steel used to obtain intermediate and high helium in water moderated reactors (ORR and HFIR) – experiments confirmed model predictions of possible non- monotonic behavior Stoller and Odette, 1982 ornl Relevant phenomena with related computational and experimental methods ornl Provide brief examples from various aspects of the multiscale modeling scheme • ab initio (VASP), development of interatomic potentials, He-Fe potential to account for He defects in iron • primary damage formation, molecular dynamics and atomistic kinetic Monte Carlo • mesoscale (reaction rate theory) model of microstructural evolution – illustrate loosely coupled multiscale modeling (parameter passing) – 2D cluster dynamics – compare alternate kinetic models • molecular dynamics (atomistic) simulation of dislocation- defect interactions • displacement rate effects and ion vs. neutron irradiation presentation focuses on bulk radiation effects, other unique aspects for plasma-facing materials ornl Application of ab initio calculations: Development of He-Fe potential • Wilson’s He-Fe pair potential developed in 1960s, Defects Fitted still extensively used Unrelaxed Heint oct • A new He-Fe inter-atomic potential has been Unrelaxed Heint tet developed at ORNL Unrelaxed He • Extensive fitting to first-principles calculations of sub He octahedral point defects and clusters int • First-principles calculations in VASP Heint tetrahedral • Fitted to both relaxed and unrelaxed defects Heint midpoint oct-tet – Both forces and energies fitted Hesub • Must predict tetrahedral site as most stable site for He-He-V cluster He – Not possible with pair or EAM-style functional forms He-He-He-V cluster – Hence 3-body potential needed Heint-Heint pair • Large clusters e.g. He3V – Up to 128 atoms in VASP ornl ORNL three-body He-Fe potential • Considerable effort invested to properly understand and implement 3-body potential: complex dependence Energy of Fe-He-Fe triplet as a function of angle Qjik and rik where rij is equal to 1.8 Angstrom 2 Y(rij ,rik ,Qijk ) cos Qijk 0.44fcut rij fcut rik j,kFe ornl Interstitial He diffusion 6x10-8 • Fe Potentials: – AM: Ackland-Mendelev /s) – A97: Ackland-Bacon 2 – FS: Finnis-Sinclair 10-8 • He-Fe Potentials – OR: ORNL 3-body – JN: Juslin-Nordlund – W: Wilson Fe Fe-He E (eV) D (10-8 m2/s) m 0 • Results with ORNL Fe-He AM JN 0.062 9.64 -9 FS ORS 0.065 3.15 potential lies between those of 10 A97 ORS 0.073 3.27 other Fe-He potentials He diffusion coeficient (m AM ORS 0.043 2.23 AM W 0.107 4.69 5x10-10 • ORNL potential shows 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 consistent results with different T /T (K-1) Fe potentials m ornl Formation of Interstitial clusters • Yellow atoms are He, BCC Fe lattice not shown. • He-He in Fe has strong binding – This leads to formation of interstitial clusters • Mobility decreases with size • When cluster is large enough, it creates Frenkel pair, emitting SIA – new He-vacancy cluster immobile – He and He-v clusters are new source of Frenkel pair – SIA formation leads to formation of small loops ornl Comparison of potentials: He clustering • He diffusion and clustering properties • Behavior of different He-Fe potentials – Wilson potential creates FP (SIA emission) more quickly than ORNL potential, higher He binding energy. – Juslin-Nordlund potential does not form He clusters or create FP above ~400°C. • Provide parameters for mesoscale microstructural models ornl He transport with ORNL potential • Single interstitial helium atoms are very mobile – but easily captured by vacancies • SIA can recombine with HexV if x small – creates mobile interstitial helium • Interstitial helium tends to form clusters • Small He clusters are mobile – The smaller, the more mobile • Large He clusters create Frenkel pair to increase local volume, reduce pressure – transformation to He-vacancy cluster, nascent bubble – He-vacancy cluster is immobile – ejected interstitials trapped by the He-V cluster and combine to form dislocation loops ornl Molecular dynamics simulation of primary damage • MD simulations provide opportunity to investigate displacement cascade evolution, e.g. effects of lattice, PKA energy, T, etc. • Classical molecular dynamics, typical implementations: – many millions of atoms, solve Newton’s equation of motion – constant pressure or volume, periodic boundary condition – system may or may not be thermostated to prevent PKA from heating system – no electronic losses or electron-phonon coupling, energy of cascade simulation, hence for:, • to compare with standard NRT displacement model: nNRT = 0.8Tdam /(2 Ed), Tdam= kinetic energy lost in elastic collisions – EMD ~ Tdam (NRT) < EPKA – e. g. for Tdam = 100 keV, EPKA = 175.8 keV and nNRT = 1000 (see appendix on use of SRIM for dpa calculations) ornl Comparison of representative neutron and corresponding PKA energy spectra • differences in neutron flux level lead to different atomic displacement rates • neutron energy spectrum differences lead to different PKA energy spectra – different coolants, water for HFIR and PWR vs. sodium for FFTF alter neutron energy spectrum, primarily influence lower energy – high energy influenced by neutron source, c.f. all fission with ITER fusion ornl MD cascade database for iron • an extensive cascade database has been developed that covers a broad range of cascade energy and temperature – up to 200 keV at 100, 600, and 100 keV at 900K • this database includes a sufficient number of simulations at each condition to provide a good statistical measure of average cascade behavior – total number of point defects produced – in-cascade clustering fractions for both interstitials and vacancies – in-cascade cluster size distributions – Note: nature of cascade event leads to better statistics for defect production than for clustering • common use of Finnis-Sinclair potential provides basis for comparison other investigations: – pre-existing damage (relevant to cascade overlap) using 10 keV cascades – free surfaces (relevant to in situ experiments) using 10 and 20 keV cascades – nanograined iron using 10 and 20 keV cascades ornl Time dependence of defect evolution in atomic displacement cascades Movies 10keV 50keV ornl Cascade-induced shock wave • Three distinct phases in cascade evolution: – Supersonic – Transonic – Sonic Calder, et al. (Phil. Mag. 90, 2010) ornl The role of shock waves in defect cluster formation February 27-March 3, 2011 – San Diego, ornl California Angular dependence of displacement threshold energy: effect of crystalline lattice on defect formation classical MD Fe V Zepeda-Ruiz, PRB 67, 2003 Bacon, et al., JNM 205, 1993 ab initio MD, P. Olsson, C. Domain, EDF R&D, unpublished ornl ornl If normalized to NRT displacements, MD results show reduced defect survival as cascade energy increases - some of curve structure is significant, related to cascade morphology and subcascade formation - note small standard errors, measure of mean behavior - effect of temperature, 100 to 900K, is systematic but not strong ornl Many of surviving defects are in clusters formed during the cascade event 20 keV, 600K Note: poorer statistics, larger standard errors,