Modeling Fusion Neutron Irradiated Microstructures (focus on Fe-Cr & W-based alloys)

Modeling Fusion Neutron Irradiated Microstructures (focus on Fe-Cr & W-based alloys) B.D. Wirth*,1,#, X. Hu1,#, A. Kohnert1, and D. Xu1, with significant contributions from G. Nandipati, R.J. Kurtz, W. Setyawam2, N. Ghoniem & J. Marian3, G. Samolyuk & R.E. Stoller#, and G.R. Odette4 Presented at the Fusion Materials PI meeting 26 July 2016 University of Tennessee, Knoxville 2 4 * bdwirth@utk.edu 3 1 # This work was partially supported by the U.S. Department of Energy, Office of Fusion Energy Sciences, along with partial support from the Office of Nuclear Energy.

Clad/Structural materials behavior is inherently multiscale Biggest long-term scientific challenge is understanding the kinetics of coupled defect – impurity evolution with a disparate range of kinetic rates --- this requires algorithmic improvements on both the physics and computing side Microstructural evolution driven by kinetics f(t,T,dose rate, microstructure) Radiation damage produces atomic defects and transmutants at the shortest time and length scales, which evolve over longer scales to produce changes in microstructure and properties through hierarchical and inherently multiscale processes

Generate mobile He by transmutation and emission from traps Matrix transport of He partitioning and nucleation and growth of matrix cavities Framework for modeling He(gas) – defect evolution Grain boundaries Fine scale precipitates Dislocation substructures Other precipitates Transport of He within and between interconnected sub-regions Emission of He from sub-regions Formation of sub-region cavities Internal sub-region structure

DFT efforts – focused on energetics of small clusters The properties of small vacancy clusters and their interaction with H/He in W have been investigated using a first principles approach, the density functional theory (DFT) method. Vacancy formation energy modeling cell size dependence Constant volume per atom Vacancy formation energy in eV: Constant lattice parameter Binding energy 6x6x6: V + He: 4.64 eV (4.5 eV [4] - 4x4x4 cell) vacancy L. Ventelon, F. Willaime, C.-C. Fu, M. Heran, I. Ginoux, JNM 425 (2012) 16 P. M. Derlet, D. Nguyen-Manh, and S. L. Dudarev, PRB 76 (2007) 54107 D. Kato, H. Iwakiri, K. Morishita, JNM 417 (2011) 1115 Becquart C S and Domain C JNM. (2009) 386

Modeling Cascade Damage in Bulk Tungsten • Spectrum of W PKAs due to 14-MeV neutrons shows a significant number of PKAs up to 280 keV of recoil energy or 196 keV of damage energy (EMD) • Previously, primary defect damage database includes EMD up to 100 keV • New displacement damage data generated at 150 and 200 keV for 300, 1025, and 2050 K • Data at 150 and 200 keV follow the trend of defect production curve (NF) for EMD > 30 keV • Transition in defect production observed & explained due to interacting shock waves 196 keV 0.18(EMD)1.40 31 keV 1.76(EMD)0.74 * Setyawan, Selby, Juslin, Stoller, Wirth and Kurtz, J. Phys. Cond. Matter 27 (2015) 225402; and Setyawan, Nandipati, Roch, Heinisch, Wirth and Kurtz, J. Nuc. Mater. 462 (2015)

Cascade defect production Snapshots of 75 keV cascades in W at 300K * Setyawan, et al, J. Nuc Mat 462 (2015) 329-337.

KMC simulations of neutron-irradiated W(-Re) Cluster expansion Hamiltonians that include solute plus defects Thermodynamics + Kinetics These simulations will provide a window to understanding RED/RIP of transmutation-induced Re precipitation in neutron irradiated- W Mechanism of self-interstitial Re transport discovered from DFT calculations: transition from 1D to 3D  swelling suppression and non-thermodynamic Re transport DFT calculations of W-Re structural energetics to capture thermodynamic driving forces Phase diagram calculations of out-of-equilibrium Re clustering for 0.01% vacancy population

Cluster dynamics approach • Mean field approach that calculates average concentration of a group of defects having the same size, but does not track the exact 3D coordinates of an individual defect – but includes a spatial dependence corresponding to thin film (thru thickness) geometry • One partial differential equation for each defect/cluster size • A sample equation: • How to describe reaction rates? • Capture Reactions: • C1+C2 C3; • Emission: C1C2+C4; • parameterization (based on ab initio, MD, previous experiments): • geometric size • migration energies • binding energies of Vn and In • Spatial derivative:

Finite-volume stochastic cluster dynamics (SCD) Recast deterministic ODE system into stochastic framework: ⇒ • Stochastic integrator (based on kMC) allows for treatment of arbitrary number of chemical species. • Statistical fluctuations of damage accumulations are captured naturally Defect size distributions from SCD Recent extension to spatially-resolved calculations (Dunne, Capolungo, Marian) First simulations of triple-species irradiation (Marian et al, JNM 2011)

Open questions about modeling interstitial clusters • MD simulations consistently show high mobility of interstitial clusters (crowdion bundles) in BCC materials with very low activation energies, which occurs 1-dimensionally. TEM observations, including at the IVEM, indicate such black dot clusters are mobile in 1D, but with much higher activation energies (~1.3 eV in Fe) or that is discrete and temperature independent when the ion beam is on (beam assisted diffusion). - Presumed mechanism is trapping and de-trapping of interstitial clusters with impurities (How best to model: effective D, explicit impurity interactions, beam-assisted?) • Loop geometry, and dimensionality of diffusion, has significant impact on the defect reaction kinematics Crowdion bundles diffuse in 3D, loops have spherical absorption volumes Crowdion bundles diffuse in 1D, loops have spherical absorption volumes Crowdion bundles diffuse in 1D, loops absorb on dislocations only

Temperature dependence of interstitial cluster density • Models, which include ‘beam-assisted’ mobility of interstitial clusters assumed trapped by impurity interactions capture observed T-dependence of black dot features Heavy Ion Irradiation Electron Irradiation Expt: Fe-12Cr - D. Kaoumi et al J. Nucl. Mater. 445 (2014) 12–19 NF616 - C. Topbasi et al J. Nucl. Mater. 425 (2012) 48–53 Modeling: Kohnert and Wirth, J. Appl. Phys. 117 (2015) 154305 Expt - K. Arakawa et al J. Nucl. Mater. 307-311(2002) 272-277

Impact of reaction kinetics • Mechanism for thermally activated motion impacts transition temperature • Stronger temperature dependence in thermal regime • Assumptions about reaction kinetics can strongly affect long term cluster growth Trapped loops migrate Loops dissociate from traps Kohnert and Wirth, J. Appl. Phys. 117 (2015) 154305

Impact of reaction kinetics • 1d kinetics allow long term survival of small loops • Loop cross section important to growth 1D kinetics Full cluster cross section 1D kinetics Dislocation cross section 3D kinetics Spherical volumes Kohnert and Wirth, J. Appl. Phys. 117 (2015) 154306

Modeling neutron irradiation of pure Fe 333K 373K Dose Dose Vn Vn In Modeling results of the yield strength increase at two neutron irradiation temperatures and the tensile test measurements for two neutron irradiation conditions for low purity iron samples In Dose Dose Dose (dpa) Hardening model predictions for high purity iron samples at 333 K and 373 K vs experimental data Hu, Xu, Byun, and Wirth, MSMSE 22 (2014) 065010.

Defect cluster evolution modeling in Tungsten Vacancy Cluster Evolution Loop Evolution X. Hu et al., J. Nucl. Mater. 470 (2016) 278 Estimates of cluster density from positron spectrum Experiments Modeling Expected positron spectrum from computed cluster densities Hu, Kohnert, Wirth, et al., in preparation

Handling the complexity of the cluster domain He bubbles Swelling Model • Generally too expensive to simulate the entire phase space • We employ three simulation geometries helium V I Loop Model voids <111> loops <100> loops dumbbells Node Positions Thin Film Bulk No spatial dependence Damage Ion-beam irradiation

Evaluating void swelling

Model predicted ‘micrographs’ Dual-beam ion Irradiation

Next steps in cluster dynamics modeling • Advances in grouped cluster dynamics utilized in modeling helium bubble nucleation & growth as well as loop populations One equation for each cluster size Spatial diffusion Loss at sinks Aggregation, recombination, and emissions Production in cascades Bubble Evolution Stability in Group Size Swelling Curves

• Materials behavior in extreme environments involves inherently multiscale phenomena -fundamental understanding of radiation damage requires multiscale modeling, closely coupled with theory & experiments • - Fusion materials has been at the forefront of multiscale materials modeling paradigm – now represented by the Materials Genome, etc… • • Highlighted some select examples of activities across a number of modeling scales, including extensive effort at ‘meso-scale’ • • Future challenges: • -> Addressing prismatic loop morphology, spatial/Elastic field driven interactions and defect reaction kinematics – further extend modeling to link defect cluster & chemical evolution (beyond a couple of species), as well as bubble evolution to fully evaluate swelling onset in prototypic fusion environment and evaluating He-H synergies • -> Modeling assumptions indicate impacts on experimental observables (e.g., size distributions), which require further high-resolution TEM Summary & Future Challenges

Modeling Fusion Neutron Irradiated Microstructures (focus on Fe-Cr & W-based alloys)