Multiscale Computer Simulations and Predictive Modeling of RPV Embrittlement Naoki Soneda Central Research Institute of Electric Power Industry (CRIEPI), Japan MATGEN-IV Cargese, Corsica September 29, 2007

Multiscale Modeling of RPV Embrittlement Naoki Soneda Central Research Institute of Electric Power Industry (CRIEPI), Japan MATGEN-IV Cargese, Corsica September 29, 2007

3 2007/09/29 Irradiation Embrittlement of LWR RPV Steels The accurate prediction of the transition temperature shift is very important in ensuring the structural integrity of reactor pressure vessels. PWR RPV Goal: Development of an accurate embrittlement correlation method to predict the transition temperature shifts

4 2007/09/29 Current Embrittlement Correlation Equation – Prediction of Transition Temperature Shift – US NRC  Regulatory Guide 1.99 Rev.2 JEAC , Japan  Statistical analysis was performed to identify chemical elements (Cu, Ni, Si and P) to be used in the equations.  Both the surveillance data of commercial reactors and test reactor irradiation data were used. The equations were developed based on the knowledge in the 80’s. Base Metal Weld Metal

5 2007/09/29 Activities in the 90’s and 00’s New information and new findings  Surveillance data at higher fluences became available.  New understandings on the embrittlement mechanisms have been obtained by state-of-the-art experiments and simulations. New projects have started in the US  Development of mechanism guided correlation US NRC, NUREG/CR-6551 (1998) & revised version (2000) ASTM, ASTM Standard E 900–02 (2002) US NRC, Regulatory Guide 1.99 Rev.3 (2007?) Plant Life Management for 60-years operation is necessary  2 plants will be 40 years old in 2010, and more than 10 plants are now older than 30 years in Japan  Accurate prediction of embrittlement is very important for safe and economical operation of the plants

6 2007/09/29 Surveillance Data In the commercial light water reactors, some surveillance capsules containing surveillance specimens are installed at the vessel inner wall to irradiate the same RPV material at a very similar irradiation condition to the vessel. Surveillance capsules are retrieved according to the schedule of the surveillance program. The surveillance specimens irradiated in the capsule are tested to measure the transition temperature shift. This data is called surveillance data.

7 2007/09/29 Activities in the 90’s and 00’s New information and new findings  Surveillance data at higher fluences became available.  New understandings on the embrittlement mechanisms have been obtained by state-of-the-art experiments and simulations. New projects have started in the US  Development of mechanism guided correlation US NRC, NUREG/CR-6551 (1998) & revised version (2000) ASTM, ASTM Standard E 900–02 (2002) US NRC, Regulatory Guide 1.99 Rev.3 (2007?) Plant Life Management for 60-years operation is necessary  2 plants will be 40 years old in 2010, and more than 10 plants are now older than 30 years in Japan  Accurate prediction of embrittlement is very important for safe and economic operation of the plants

8 2007/09/29 Analysis of the Recent Surveillance Data Transition Temperature Shift Neutron Fluence (n/cm 2, E>1MeV) 6x10 19 n/cm 2 (40years, PWR) 1x10 20 n/cm 2 (60years, PWR) High Cu material Irradiated at low flux Low Cu material Irradiated to high fluences Current prediction Surveillance data <3x10 18 n/cm 2 (60years, BWR)

9 2007/09/29 Embrittlement Mechanism – General Consensus – Formation of Cu-enriched clusters (CEC)  in high Cu materials  CEC is associated with Ni, Mn and Si  2~3 nm in diameter  obstacle to dislocation motion  dose rate effect exists Formation of matrix damage (MD)  point defect clusters such as dislocation loops or vacancy clusters, or point defect – solute atom complexes.  main contributor to the embrittlement in low Cu materials Phosphorus segregation on grain boundary  P segregation weakens grain boundaries.  not very important for relatively low P materials

/09/29 ASTM E Are the formation of SMD(MD) and CRP(CEC) independent? No effect of chemical composition? Is an exponential function appropriate? Is it product-form dependent? Is the threshold value appropriate Is there any other effect such as dose rate and other elements? Is the linear sum approximation appropriate? Dose it saturate at high fluences? TT f 1/2 SMD CRP Total

/09/29 Issues to be studied Do CEC and MD cause embrittlement?  What is the nature of MD?  What is the nature of CEC? Are CEC and MD formed independently? Does the contribution of CEC saturate? What is the effect of temperature? What is the effect of dose rate?

/09/29 Approach Mechanical property tests of neutron irradiated RPV steels Nano-structural characterization Multi-scale computer simulation

/09/29 Nano-structural Characterization 3-Dimensional Atom Probe Positron Annihilation (Coincidence Doppler Broadening) Cu-enriched clusters formed by neutron irradiation ~40 nm ~300 nm LEAP (Local Electrode Atom Probe) 50nm Transmission Electron Microscope (TEM)

/09/29 Multi-scale Computer Simulation Molecular Dynamics Dislplacement cascade Kinetic Monte Carlo Microstructural evolution during irradiation Dislocation Dynamics Dislocation behavior during deformation Detailed analysis of microstructure Point defect production Cu atoms Vacancies Dislocation loop Dislocation Radiation damage Molecular Dynamics Stress (MPa) Strain (%) ~ sec ~10 -8 m ~10 9 sec ~10 -7 m ~10 0 sec ~10 -4 m Dislocation Dynamics Prediction of mechanical property ~10 0 m Unirradiated Irradiated Interaction between dislocation and damage

/09/29 Issues to be studied Do CEC and MD cause embrittlement?  What is the nature of MD?  What is the nature of CEC? Are CEC and MD formed independently? Does the contribution of CEC saturate? What is the effect of temperature? What is the effect of dose rate?

/09/29 Damage accumulation in bcc-Fe – Kinetic Monte Carlo (KMC) simulation – Database of displacement cascades for a wide range of PKA energies Diffusion kinetics such as diffusivities and diffusion modes (1D, 3D…) of point defects and clusters Thermal stabilities (binding energies) of point defect clusters Defect production Clustering Formation and growth of loops Microstructure evolution m ～ s ～ m m Diffusion Cluster diffusion m s Dissociation KMC tracks all the events. Most of the data can be obtained from molecular dynamics simulations. Input Data

/09/29 Primary Knock-on Atom (PKA) Energy Spectrum Displacement cascade simulation results are necessary for different PKA energies to simulate the PKA energy spectrum. Molecular dynamics simulations have done for the PKA energies of 100eV, 200eV, 500eV, 1keV, 2keV, 5keV, 10keV, 20keV and 50keV. L.R. Greenwood, JNM 216 (1994) 29.

/09/29 Displacement Cascade Simulation Molecular Dynamics Inter-atomic potential  Ackland Potential  ZBL pair potential is used for the short distance interaction Constant volume at a temperature of 600K  Thermal bath at the periphery of the computation box Periodic boundary condition Automatic time step control Number of atoms ： 12,000 atoms for 100eV PKA cascade ~4,000,000 atoms for 50keV PKA cascade

/09/29 MD Simulation of Displacement Cascade Volume : (28.6nm) 3 2,000,000 atoms PKA energy: 50keV Wide variety of defect production is observed in high energy cascades of 50keV, which is not be observed in lower energy cascades. SIA Vacancy

/09/29 Small SIA & Small Vacancy Cluster Black dots : vacancies White circles : SIAs Case 45 Isolated subcascade formation

/09/29 Large SIA & Small Vacancy Cluster Black dots : vacancies White circles : SIAs Case 09 Overlapped subcascade formation (similar size subcascades)

/09/29 Large SIA & Large Vacancy Cluster (1) Case 28 Overlapped subcascade formation (large & small subcascades) Black dots : vacancies White circles : SIAs

/09/29 Large SIA & Large Vacancy Cluster (2) Case 39 One large cascade is formed, and then … 234 vacancies 70 SIAs 93 SIAs Black dots : vacancies White circles : SIAs

/09/29 Large SIA & large vacancy cluster (3) Black dots : vacancies White circles : SIAs Case 39 Large SIA loop b = a 0 /2 Large vacancy loop b = a 0 Cascade collapse occurred in  -Fe [110] [001] [010]

/09/29 Channelling Black dots : vacancies White circles : SIAs Case 31 direction Direction50keV20keV  011  20  133  10  233  20  111  01  112  11  337  10  113  10  114  10  115  01  116  12  001  70 All the events occur on (110) plane. PKA is always the channeling particle in 20keV cascades. Periodic boundary condition

/09/29 Dispersed defect production Black dots : vacancies White circles : SIAs Gray : replaced atoms Case 42 Direction50keV20keV  011  10  111  10  113  20  001  10 Similar direction to channeling, but associated with many interactions Did not occur in 20keV cascades Periodic boundary condition

/09/29 Summary of Cascade Database 53%17%10%15% 5%5% 50keV (100runs) 20keV (50runs) 80%8%10% 2%2% Small clusters Channeling Dispersed defect formation Large SIA clusters Large SIA & V clusters 100eV, 200eV, 500eV, 1keV, 2keV, 5keV, 10keV, 20keV, 50keV

/09/29 Diffusivity Diffusion simulation of a point defect by MD Calculate D o and E m by MD U x

/09/29 Diffusion Kinetics – Molecular Dynamics – 1D motion of SIA clusters Diffusivity Rotation frequency Migration energy, E m N. Soneda, T. Diaz de la Rubia, Phil. Mag. A, 81 (2001), 331.

/09/29 MD Simulation of SIA Cluster (I 3 ) 1D motion + rotation1D motion (lattice unit) 1000K

/09/29 Diffusivities of SIA Clusters – I 1 ~ I 20 – 1D motion is a common feature for the SIA cluster migration Migration energies of large SIA clusters are as low as 0.06eV, which means that SIA clusters are highly mobile. 1/T (K -1 ) Diffusivity (cm 2 /s)

/09/29 Migration Energies of SIA Clusters

/09/29 Rotation Frequency of Small Clusters Activation energy of rotation for the I 3 cluster is high.

/09/29 Binding Energies of Point Defect Clusters N. Soneda, T. Diaz de la Rubia, Phil. Mag. A, 78 (1998), 995.

/09/29 Algorithm of KMC Simulation Set all the possible events Calculate event frequency Choose one event Update time Do event DiffusionE m DissociationE b +E m Disp. cascadedose rate P =  N i P i i R = Random()*P t = -log(R) / P Calculate interaction between the neighboring particles (clustering, annihilation, etc.) Repeat until target dose or time is reached Bigmac (LLNL) KineMon (CRIEPI / Univ. Tokyo)

/09/29 Accumulation of Point Defect Clusters in Neutron Irradiated bcc-Fe 350K600K

/09/29 Microstructural evolution at different dose rates Stable SIA clusters are always produced, but the stability of vacancy clusters depends on the dose rate. Threshold dose rate exists between dpa/s and dpa/s, below which no dose rate effect is observed in defect cluster formation. Vacancy SIA dpa/s dpa/s No stable vacancy cluster is formed below dpa/s dpa/s dpa/s dpa/s dpa/s

/09/29 Experimental observation of SIA loops – TEM observation – 50nm B=[011] 、 3g (g=21-1) B=[133] 、 3g (g=-110) 0.12Cu/0.58Ni 4x10 19 n/cm Cu/0.59Ni 6x10 19 n/cm 2 Dislocation loops are observed in the RPV materials irradiated in commercial reactors. Number densities of the loops are relatively low. Mean size: 2.6 nm Number density: 1.8x10 22 m -3 Mean size: 2.3 nm Number density: 1.9x10 22 m -3

/09/29 Box size : 37×16×35nm (~1.7million atoms) Potential : EAM potential (Ackland et.al.) Burgers vector: Edge dislocation[111] SIA loop[111] SIA loop size : ~2nm Applied shear stress : 50MPa ~ 650MPa Temperature : 300K   b=[111] Dislocation – Loop interaction

/09/29 Dislocation Loop – Edge Dislocation Interaction Molecular Dynamics Simulation I IIIIIII’ IV  = 150MPa  = 250MPa  = 300,350,500MPa  = 650MPa  = 50MPa Repulsion PinningSuperjog (I)Superjog (I’) Superjog (II)

/09/29 Dislocation reacts with SIA loop Superjog formation Vacancies are left behind. 150MPa Dislocation is pinned. No bowing-out of the dislocation is observed at this applied stress Type II Interaction

/09/29 Details of Loop – Dislocation Interaction b=1/2[1 -1 1] b=1/2[-1 1 1] Formation of Bridge Dislocation b= [0 0 1] (=1/2[-1 1 1]+1/2[1 –1 1]) Trailing Bridge Dislocation b=1/2[ ] Leading Bridge Dislocation b=1/2[1 1 1] b= [0 0 1] Pinning occurs at this stage.

/09/29 Contribution of vacancy-type defects to embrittlement Low Cu, BWR Irradiation Recoveries of  Hv and  S occur at different temperatures indicating that the vacancy type defect is not responsible for the  Hv. Recovery of Hardness during PIA Recovery of  S during PIA  S is a measure of total amount of open volume. EPRI/CRIEPI Joint Program

/09/29 Summary of matrix damage CandidatesAnswer Dislocation loop of interstitial typeYes Vacancy clusterNo Point defect – solute atom complexSee the followings

/09/29 Issues to be studied Do CEC and MD cause embrittlement?  What is the nature of MD?  What is the nature of CEC? Are CEC and MD formed independently? Does the contribution of CEC saturate? What is the effect of temperature? What is the effect of dose rate?

/09/29 3D Atom Probe Time of flight Y X Z Fast = light Needle tip Pulse voltage Detection position Element 3D position Slow = heavy Detector 500  m Optical Microscope TEM 50nm 0.3x0.3x10mm Electro-polish

/09/29 Formation of Cu-enriched Clusters ~200nm ~40nm High Cu (0.25wt.%) RPV steel irradiated in a test reactor was examined. Cu-enriched clusters are formed with very high density, and they are associated with Ni, Mn, Si and, sometimes, P. The primary mechanism in high Cu content materials is the precipitation of Cu atoms beyond the solubility limit. Cu Si What is the formation process? What happens in medium – low Cu materials?

/09/29 Thermal ageing of Fe-Cu-Ni-Mn-Si alloys Clusters consist of Cu, Ni, Mn and Si. Amount of Si is very small. Ageing time (hour) Increase in Vickers Hardness (  H v ) CuNiMnSiC HL – HM – HH – HHC aged at 350 o C Distribution of Cu atoms 49 x 65 x 270 nm M atoms LEAP measurement

/09/29 Computer simulation of the thermal ageing – Kinetic Lattice Monte Carlo (KLMC) simulation – Consider all the atoms in the crystal Diffusion by vacancy mechanism + regular solution approximation for complex alloys Jump probability Activation energy Total energy of the crystal Vacancy migration energy & vacancy binding energy Choose one of the possible sites Energy change by vacancy jump Migration energy Pair interaction energy Ordering parameter Solubility

/09/29 Determination of KLMC parameters Binding energies between a vacancy and a solute atom in pure iron are obtained from first principles calculations using the VASP code. Vacancy – Solute Atom Binding Energy (eV) Vacancy – Solute Atom Binding Volume (A 3 )

/09/29 Process of precipitation : KLMC result ~40nm 673K573K

/09/29 (a) 1.6x10 7 sec (b) 3.2x10 7 sec (c) 7.9x10 7 sec (d) 7.9x10 8 sec Cu Ni Mn Si :::::::: or (at.%) Effect of Ni on cluster formation 8760hrs = 3.15x10 7 sec N d ~ 6.8x10 23 m -3 (a) 1.6x10 7 sec (b) 3.2x10 7 sec (c) 7.9x10 7 sec (d) 7.9x10 8 sec 1.8at.% Ni 1.0at.% Ni Cu : 0.3, Mn 1.4, Si 0.9 (at.%) Ni enhances the nucleation of clusters.

/09/29 Comparison between simulations and experiments Volume fraction (at.%) Ageing time (sec) SimulationExperiment 0.3Cu, 1.8Ni Direct and quantitative comparison of the microstructural changes with experiments can be made.

/09/29 Calculation Conditions Potential : Ackland potential Edge dislocation :b=a/2[111] Cu precipitate size : 1.5 ～ 5nm Box size :  50×24×56nm( ～ 6.0x10 6 atoms) for small Cu  50×36×56nm( ～ 8.5x10 6 atoms) for large Cu Applied shear stress : 350MPa Temperature : 300K b=a/2[111] Edge dislocation Cu precipitate τ τ x y z

/09/29 Hardening due to Cu precipitates – Molecular Dynamics – Diameter of Cu ppt (nm) Maximum bow-out distance (nm) 4nm Cu ppt 350MPa shear stress bow-out distance

/09/29 Interaction Process (Small Precipitate) Simple Shear

/09/29 Atom stacking below/on/above the slip plane changes from bcc to fcc-like structure. (011) Interaction Process (Large Precipitate)

/09/29 Dislocation Motion at Break-out Original slip plane Motion of screw dislocation Super jog formation Pure edge Pure screw Top view

/09/29 What is the difference between the thermal ageing and irradiation? Si content is much larger in the irradiated material than in the thermally aged materials. Low Si content in thermally aged materials is also seen by simulations aged for much longer time. Composition Cluster number Neutron irradiationThermal ageing

/09/29 Cluster diameter (nm) Counts 0.12Cu 4x10 19 n/cm 2 RGGuinier DComposition (at.%) (nm) FeMnFeNi58NiCuSiP V-weighted average Simple average x 41 x 491 nm M atoms Cu P N d 2.24 x m -3 V f 4.16 x d G 3.07 nm Cluster ID Composition (at.%) Fe Mn Ni Cu Si

/09/29 RGGuinier DComposition (at.%) (nm) FeMnFeNi58NiCuSiP V-weighted average Simple average x 38 x 284 nm 3 8.1M atoms Cu P Si Cluster ID Composition (at.%) Counts Guinier diameter (nm) N d 1.21 x m -3 V f 2.87 x d G 3.40 nm Fe Mn Ni Cu Si 0.07Cu 6x10 19 n/cm 2

/09/29 RGGuinier DComposition (at.%) (nm) FeMnFeNi58NiCuSiP V-weighted average Simple average Cluster ID Composition (at.%) 41 x 49 x 264 nm M atoms Cluster diameter (nm) Counts N d 5.61 x m -3 V f 1.13 x d G 3.14 nm Fe Mn Ni Cu Si 0.03Cu 6x10 19 n/cm 2 Cu P Si

/09/ Cu 3x10 19 n/cm 2 RGGuinier DComposition (at.%) (nm) FeMnFeNi58NiCuSiP V-weighted average Simple average Cluster ID Composition (at.%) 43 x 52 x 194 nm 3 9.6M atoms Cluster diameter (nm) Counts N d 2.31 x m -3 V f 4.51 x d G 3.10 nm Fe Mn Ni Cu Si Cu P Si

/09/29 Are the Ni-Si-Mn clusters responsible for embrittlement (hardening)? 35x45x300 nm M atoms 50x60x158 nm M atoms 31x39x238 nm 3 6.6M atoms 400 o C450 o C500 o C600 o C 31x42x299 nm 3 8.6M atoms 24x33x272 nm 3 5.1M atoms As irrad. Temperature ( o C)  Hv Holding time: 30min Recovery of hardness occurs at 500 ℃. Clusters becomes very diffuse at the same temperature.

/09/29 r ： <5nm  r ： 0.1nm Spacial Distribution Function, SDF(r) Mean concentration of the element of interest as a function of the distance from an atom of the element. SDF rr Uniform distributionclustering

/09/29 Analysis of clustering using SDF Slope becomes very weak at 500 o C in good correspondence with the diffuse clustering. Ni-Si-Mn clusters cause hardening. As Irrad. 400 ℃ 450 ℃ 500 ℃ 550 ℃ SDF (atoms/nm 3 ) Distance (nm)

/09/29 Answer to “What is the nature of CEC?” CEC is a Cu-Ni-Si-Mn cluster. The Cu content in the cluster is affected very much by the bulk Cu content, while Ni, Si and Mn contents are not affected by their bulk contents and it can be a Ni-Si-Mn cluster without Cu at very low Cu material. Thus it will be more appropriate to call such clusters as “Solute-atom Clusters (SC)”. The number density of SC becomes larger when Cu content is high. SC causes hardening, and thus embrittlement. Further question: Why do Ni, Si and Mn form clusters even though their solubility is very high in Fe-matrix? (cf: Cu form clusters because of its low solubility.)  One possible answer: It is the irradiation induced segregation of Ni, Si and Mn atoms on point defect clusters. (heterogeneous nucleation) Interaction between SC (CEC) and MD

/09/29 Issues to be studied Do CEC and MD cause embrittlement?  What is the nature of MD?  What is the nature of CEC? Are CEC and MD formed independently? Does the contribution of CEC saturate? What is the effect of temperature? What is the effect of dose rate?

/09/29 Are SC (CEC) and MD formed independently? Cu atoms beyond the solubility limit form precipitates in high Cu materials.  This mechanism is independent of the MD formation. Formation of Ni-Si-Mn clusters may be caused by solute-atom segregation to point-defect clusters What is the interaction between Cu and point defect clusters?

/09/29 Precipitation of Cu on dislocations in Fe LEAP analysis of irradiated RPV steel Clustering of Cu atoms on dislocations is evident. KLMC results of thermal ageing of Fe-Cu crystal at 823K using the lattice sites including two edge dislocations. KLMC

/09/29 Interaction between Cu atoms and point defect clusters Computer simulations show strong binding between the Cu atoms and point defect clusters of both vacancy and SIA. 100 Vac & 100 Cu vacancy Cu atom 20 SIA & 20 Cu SIA Cu atom KLMC, with Metropolis algorithm, + MD results of the lowest energy configuration of point defect – Cu atom clusters.

/09/29 Cu-vacancy clusters 100 Vac. & 10 Cu atoms100 Vac. & 100 Cu atoms 10 Vac. & 10 Cu atoms10 Vac. & 100 Cu atoms Vacancy Cu atom Cu atoms and vacancies form stable clusters. Central vacancy cluster + Cu shell

/09/29 Cu-SIA clusters 4 SIAs & 1 Cu atoms4 SIAs & 8 Cu atoms 4 SIAs & 16 Cu atoms20 SIAs & 20 Cu atoms Fe atom Cu atom Lattice site A row of four Cu atoms is a stable configuration.

/09/29 Mechanism Cu-SIA cluster formation Binding energy of the Cu precipitate and the SIA loop ~1.7eV Fe atom Cu atom Lattice site

/09/29 Issues to be studied Do CEC and MD cause embrittlement?  What is the nature of MD?  What is the nature of CEC? Are CEC and MD formed independently? Does the contribution of CEC saturate? What is the effect of temperature? What is the effect of dose rate?

/09/29 Issues to be studied Do CEC and MD cause embrittlement?  What is the nature of MD?  What is the nature of CEC? Are CEC and MD formed independently? Does the contribution of CEC saturate? What is the effect of temperature? What is the effect of dose rate?

/09/29 Temperature effect on MD R.B. Jones, T.J. Williams, Effects of Radiation on Materials: 17th International Symposium, ASTM STP 1270, American Society for Testing and Mateirals, 1996, 569. (T : 100 ~ 350 o C) Kinetic Monte Carlo Simulation Experimental correlation 227 ℃ 307 ℃ ASTM E Jones & Williams (T in o F)

/09/29 Issues to be studied Do CEC and MD cause embrittlement?  What is the nature of MD?  What is the nature of CEC? Are CEC and MD formed independently? Does the contribution of CEC saturate? What is the effect of temperature? What is the effect of dose rate?

/09/29 Dose Rate Effect in Low Cu Material Increase in yield stress (MPa) Dose rate (n/cm 2 -s) Transition temperature shift ( o C) Fluence (x10 19 n/cm 2 ) Comparison of French surveillance data and test reactor irradiation data Comparison of test reactor data irradiated at different fluxes No clear dose rate effect is observed in low Cu materials. P. Petrequin, ASMES:1996. Report Number 6 EUR EN CRIEPI/UCSB Joint Program Fluence Low High

/09/29 Dose Rate Effect in High Cu Material Low Dose RegionHigh Dose Region Dose rate effect is evident in high Cu materials T.J. Williams, P.R. Burch, C.A. English, and P.H.N. Ray, 3rd Int. Symp. on Environmental Degradation of Materials in Nuclear Power Systems – Water Reactors (1988), 121. High Cu Low Cu G.R. Odette, E.V. Mader, G.E. Lucas, W.J. Phythian, C.A. English, ASTM STP 1175 (1994), 373.

/09/29 Detailed Comparison of Surveillance Data and Test Reactor Irradiation Data of High Cu Material 0.24 wt.%Cu Very clear dose rate effect is observed in the material irradiated at very low dose rates. Dose Rate (n/cm 2 -s) ~1x10 9 ~2x x10 11

/09/29 SP1 Composition (at.%) Cluster ID 41 x 48 x 149 nm 3 6.3M atoms Cu P N d 4.32 x m -3 V f 4.39 x d G 2.58 nm Fe Mn Ni Si Cu Cu content Bulk:0.18at.% Matrix:0.11at.%

/09/29 SPT1 N d 2.94 x m -3 V f 1.25 x d G 1.96 nm Cluster ID Composition (at.%) Guinier diameter (nm) Count Fe Mn Ni Si Cu TG1-L : 24.1x28.6x175nm 3 2.7M atoms Cu P

/09/29 SPT2 N d 6.37 x m -3 V f 2.94 x d G 2.01 nm Cluster ID Composition (at.%) Guinier diameter (nm) Count Fe Mn Ni Si Cu TG1-L : 27.7x32.1x259nm 3, 5.1M atoms Cu P

/09/29 Estimation of the Number of Vacancy Jumps Diffusion of vacancies leads to the diffusion of solute atoms such as copper. We have two types of vacancies in the irradiated metals:  Irradiation-induced vacancy  Thermal vacancy Effect of dose rate on the number of vacancy jumps can be a measure of the dose rate effect on the solute diffusion (and clustering).  In KMC, we can count the number of vacancy jumps. The number of thermal vacancy jumps can be estimated as:

/09/29 Dose rate effect on the number of vacancy jumps - KMC study - At low dose rates, it is likely that the diffusion due to thermal vacancy may contribute to solute atom clustering. BWRPWR

/09/29 Dose rate effect at high dose region Dislocation Dynamics Simulations Obstacle strength of SIA loops (MD)

/09/29 DD simulations of flux effect in Fe

/09/29 Summary of Understanding on Embrittlement Mechanism Hardening due to the formation of solute atom clusters (SCs) and dislocation loops (MD) is the primary mechanism of embrittlement. Formation of SC depends on the formation of MD.  Irradiation induced solute clustering model Formation of MD is temperature dependent. Dose rate effect exists in high Cu materials especially at very low dose rates.

/09/29 Development of Embrittlement Correlation Method Two step modeling  Step 1: modeling of microstructural changes  Step 2: modeling of mechanical property change Approach  To formulate the microstructural changes by rate equations.  To optimize the coefficients of the equations using surveillance data.

/09/29 Modeling of Microstructural Changes Irradiation induced SCIrradiation enhanced SC Effect of Ni Effect of T irrad Cu available to form clusters decreases. Thermal vacancy plays a role. : amount of Cu in the matrix : amount of Cu beyond the solubility in the matrix SC depends on MD

/09/29 Transition temperature shift is almost proportional to V f 1/2 of solute atom clusters. Correlation between microstructure and mechanical property

/09/29 Modeling of Mechanical Property Change Model of cluster size Cu effect Ni effect Total shift is NOT a simple sum of the two contributions. SC contribution does not saturate at least under test reactor irradiation      one set of coefficients is determined.

/09/29 Comparison between the measured value and the prediction プラント補正なし プラント補正あり MethodStd. Dev.Mean Error JEAC RG1.99 ｒ EWO E CRIEPI CRIEPI adj Prediction ( o C) Measured value ( o C) w/o adjustment w adjustment

/09/29 Summary The mechanisms of neutron irradiation embrittlement of RPVs are studies using multi-scale computer simulations and experiments. A new embrittlement correlation method to predict transition temperature shifts is developed, in which the understandings of the mechanisms were formulated using the rate equations. The above approach will be adopted in the revision of JEAC4201 this year.