CASL MPO- Hydrogen. Ms. Jennifer Jarvis (PhD Thesis, Defense 5/12/15) Ron Ballinger

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1 CASL MPO- Hydrogen Ms. Jennifer Jarvis (PhD Thesis, Defense 5/12/15) Ron Ballinger

2 Overview Introduction Water Chemistry: Dose rates and local chemistry Electrochemistry: Atomistic Simulations Conclusions Potential Future Work

3 The Coolant/Cladding/CRUD System Porous CRUD Deposit Solid: Ni,Fe,O, 50% by volume Coolant enriched in B, Li boiling Coolant Coolant Water at 15.5 MPa, K ppm B, ppm Li ph T = ppm H 2 Porous Oxide Layer Cracks and Pores Interconnected porosity near surface (still primarily solid!) nm at surface, 1-3 nm Primarily Monoclinic Dense Barrier Oxide Layer ~ 1 µm thick Monoclinic, Tetragonal ZrO 2 Suboxides Metal Zircaloy-4 Matrix Overall composition Zr,( )Cr, ( ) Fe, ( ) Sn Second Phase Particles ~ nm diameter, depending on manufacturing Delayed oxidation Metallic: Zr(Fe,Cr) 2 laves phase Oxidized: May Contain ZrO 2, Cr 2 O 3, Fe 2 O 3, Fe 3 O 4, (Cr x,fe x-1 ) 2 O 3

4 Corrosion and the Hydrogen Split Near-Surface Coolant O 2 2 ad O ab Bulk Coolant H 2 O O 2 + ad + 2H ad H + + ad H ab 2H + ad + 2e H 2 Two pathways for hydrogen: Recombination + Desorption Absorption O 2- H + e - Oxide Metal Zr O 2 ZrO 2 Zr Zr e Rather than consider hydrogen pickup from the absorption perspective: we can consider it in terms of recombination, i.e. How much hydrogen produced by corrosion is not absorbed by the cladding?

5 Objectives of Work Develop a radiolysis model for water chemistry in a PWR Including the effects of CRUD Use water chemistry results to provide supporting information to CASL research activities: Water chemistry (concentrations) for CRUD chemistry models Chemical Potentials in the coolant- to support corrosion modeling at the atomic level Corrosion potentials, redox potentials Better Understanding of the hydrogen split and the role of the oxidized second phase particles Do the precipitates act as a window for hydrogen? (Probably Not) Can the oxidized precipitates serve as recombination sites? [Cr 2 O 3 (maybe), Fe 2 O 3 (Not so Much)] Metallic SPPs (Not studied here but general consensus-yes)

6 Water Chemistry and Radiolysis Modeling Radiolysis is the breakdown of water molecules under irradiation Non-equilibrium chemistry From a corrosion perspective we are interested in: H 2, O 2, and H 2 O 2 (also ph) Water chemistry calculations performed with RADICAL code: Steady state, 1-D Chemistry in a loop under irradiation Radiolysis effects Chemical Reactions Mass transfer between liquid and vapor (for BWRs) ECP models e - H 2 O 2 HO 2 H 2 O H H + n, α, β-, γ H 2 OH HO

7 RADICAL and Water Chemistry Modeling Input : TH profile (mass flux,temperature, or power profile) Geometry (flow areas, hydraulic diameters) Component/Loop Mapping Reaction sets G-values Dose Profile Initial Concentrations ph routine: calculate ph based on B and Li addition Calculate Concentrations based on mass balance Concentration Profiles MPM : Alloy 600 (PWR) MPM : Alloy 690 (PWR) Mixed Potential Model: 304SS* (BWR+ PWR) EPRI empirical correlation (BWR) ECP Profile * New Mixed Potential Model Developed for 304SS D.D. Macdonald et al., Electrochemistry of Water-Cooled Nuclear Reactors (2006) H.S. Kim, A Study for Modeling Electrochemistry in Light Water Reactors (2007) C.C. Lin et al, Corrosion. Vol. 52, No. 8, pp (1996)

8 The PWR Radiolysis Model 4 Loop PWR at 15.5 MPa 193 fuel assemblies, 3587 MWth Upper Plenum Hot Leg Temperature: 599 K Cold Leg Temperature 569 K Models the entire primary loop Ave Core: 30% CRUD Bypass 2x pin Hot Pin 1x pin CRUD: Top 1/3 of active fuel Active Fuel Single channel analysis within the core- isolated individual fuel pins Core Plate Lower Plenum

9 Coolant Chemistry in PWR Cycle Burnup (MWd/kgU) Boron (ppm) Lithium (ppm) ph at 310 C Beginning of Cycle Max. Boron Middle of Cycle End of Cycle Boron Concentration, ppm BOC Max. Boron MOC EOC Cycle Burnup, MWd/kgU [EPRI PWR Primary Water Chemistry Guidelines. Volume 1, Revision 4, TR V1R4]

10 Coolant Dose Rates: Estimated using MCNP for fuel with and without CRUD A database of dose-to-lhgr ratios Interpolate for: Boron in the coolant Coolant density Fuel burnup Scale by LHGR Dose Rate = f (burnup, boron, density) LHGR UO 2 Fuel: composition changes with burnup Clad Gap Coolant ppm B g/cc CRUD µm thick 50% by volume solid CRUD 0.05 void fraction in coolant Enriched in boron

11 Coolant Dose Rates with CRUD can be quantified with a dose enhancement factor dose enhancment factor = dose with CRUD Bulk Boron, Burnup, ρ H2O, CRUD thickness + boron clean fuel dose Bulk Boron, Burnup, ρ H2O Dose enhancement factors are independent of bulk boron, burnup, and coolant density Dose to confined coolant depends on fraction of energy deposited to the coolant in the CRUD volume (solid CRUD + coolant) Dose enhancement factors for fuel with CRUD Bulk Coolant Confined Coolant Gamma Fast Neutron Alpha 1.21 function of boron 9.5% gamma dose to coolant (MCNP heating tally) 77-81% fast neutron dose (MCNP heating tally) 25% alpha dose (stopping power estimate)

12 Alpha dose rates to confined coolant in CRUD vary linearly with boron enrichment α dose confined coolant α dose in clean core increasing CRUD thickness CRUD to Bulk Coolant Boron ratio A relatively small change in the energy division between solid CRUD and confined coolant has a significant impact on alpha dose rates The solid CRUD reduces the alpha dose deposited to the confined coolant: For low boron enrichment in the CRUD (less than 3x bulk), dose rates are smaller than in the adjacent coolant

13 Calculated dose rates are in good agreement with literature Plant Gamma Dose [Rad/s] Fast Neutron Dose [Rad/s] Boron Concentration [ppm] Alpha Dose [Rad/s] Ringhals E E E+05 Tsuruga E E Model: PWR- 2.86E E E+04 ECP 3 Model: RADICAL (average dose in average core) 5.47E E E+04 [1] Christensen, Nucl. Tech. Vol 109. No 3. pg (1995) [2] Takiguchi et al., J Nucl. Sci. and Tech. Vol. 41, No. 5 pg (2004) [3]Urquidi-Macdonald et al., J Nucl. Matl. Vol 362, No. 1 pg 1-13 (2007)

14 CRUD effects on bulk water chemistry: Peroxide with and without CRUD at Middle of Cycle (1000 ppm B) Axial offset in Power Profiles Start of CRUDincrease in dose rates Coolant conditions are more oxidizing near CRUDparticular compared to the clean core average

15 Corrosion Potential at MOC with CRUD ECP Increase due to CRUD layer Start of Active Core

16 CRUD Effects Bulk coolant results indicate that conditions may be more oxidizing in the bulk adjacent to fuel with CRUD. Exception: top ~ 0.5 m of the active fuel if there is significant AOA Local radiolysis effects within the CRUD deposit will add to oxidizing conditions: Best Case Scenario: Coolant moves relatively easily through the depositsradiolysis estimates show that Gamma dose rates will be the same as in the bulk; fast neutron dose rates slightly higher, alpha dose rates If the 25% stopping power estimate is correct, then if the boron concentration is less 3x greater- then alpha dose rates are actually smaller. Worst Case Scenario: Limited coolant flow rate through CRUD and stopping power estimate is low-alpha dose contribution much higher leading to higher ECP. RADICAL needs additional updating to handle this situation.

17 Link Between Water Chemistry and Electrochemical Effects Chemical Potentials Provide estimates of phase stability Can be used to estimate defect concentrations in the oxide Electrochemical Energy levels: Determine electron transfer behavior

18 The hydrogen chemical potential in PWR coolant can be estimated from temperature and H 2 concentration 4.46 ppm H 2 (50 scc H 2 /kg H 2 O) (high end of EPRI recommendation) 2.23 ppm H 2 (25 scc H 2 /kg H 2 O) (low end of EPRI recommendation)

19 Oxygen chemical potentials are influenced by radiolysis Lower power assemblies: lower exit temperature Fresh fuel: high exit temperature

20 The energy level comparison: electron transfer can only occur when energy levels in the electrode and solution align Oxide band positions: Obtain from literature Band edges change with ph Conduction Band E C E F E V Oxide J c Valence Band E (ev) λ λ Coolant H+ (unoccupied states) Franck Condon splitting of H+/H energy, treated by Marcus theory Energy levels given by Gaussian distribution E o redox: Redox Energy, calculated from water chemistry + Nernst Equation H (occupied states)

21 Energy level comparison for PWR coolant conditions: if conduction band aligns with the proton energy level Cr 2 O 3 + SnO 2 : possible site if reorientation energy is small ZrO 2 : likely site, especially if reorientation energy is large Fe 2 O 3 : unlikely site, conduction band is below E o H/H+ Reorganization energy for metal Reorganization energy for oxide

22 Density Functional Theory Studies

23 Goal : Understand hydrogen interactions at the oxide/coolant interface Specifically consider the role of oxidized precipitates: Fe 2 O 3 and Cr 2 O 3 are two of the compounds found in the Oxidized Zr(Fe,Cr) 2 SPPs in Zircaloy-4 Can the precipitates serve as a site for hydrogen evolution recombination? Are the precipitates likely easy entry pathways for hydrogen?

24 Cr 2 O 3 and Fe 2 O 3 Corundum structure (space group R3c, group 167) Crystal Structure: Primitive unit cell: Rhombohedral (10 atoms) Hexagonal cell (30 atoms) 2 internal lattice parameters Antiferromagnetic, different spin ordering Wide gap semiconductors/insulators Cr 2 O 3 band gap: 3.4 ev Fe 2 O 3 band gap: 2.2 ev The rhombohedral cell (left) and hexagonal cell (right) of Cr 2 O 3. Oxygen atoms are shown in red, and Cr in blue. The (1,1,1) direction in the rhombohedral cell aligns with the (0001) direction in the hexagonal cell

25 Density Functional Theory Electronic Structure calculation- (quantum) Born-Oppenheimer Approximation: nuclei move much slower than electrons, we can treat the electrons as acting in a field of fixed nuclei and neglect the KE of nuclei. Hohenberg and Kohn Theorems The ground state energy from Schrodinger s equation is a unique functional of the electron density Variational Principle: The energy computed from a guessed wavefunction is an upper bound to the true ground state energy => We can find the ground state by minimizing the energy Kohn-Sham Equations

26 Calculation Details VASP Surface calculations: Valence electrons modeled: 3p 6 4s 1 3d 5 for Cr, 4s 1 3d 7 for Fe, and 2s 2 2p 4 for O (1x1) hexagonal surface model 3x3x1 gamma centered k-point grid 6 stoichiometric units in the surface model- bottom 2 fixed 15 A vacuum layer Dipole corrections applied to energies Projector Augmented Wave (PAW) Perdew-Burke-Ernzerhof (PBE) pseudopotentials Spin Dependence : both Cr 2 O 3 and Fe 2 O 3 are antiferromagnetic Simplified rotationally invariant DFT+U method of Duderev et al. Plane wave cutoff energy of 520 ev Ionic Force convergence of 0.01 ev/a Electronic Convergence criteria 1E-4 ev Gaussian Smearing with σ=0.05 ev Bader charge analysis performed with the Henkelman group s code Climbing Image Nudged Elastic Band (CI-NEB) calculations performed with Henkelman group s code VESTA was used for visualization

27 DFT Modeling Path Short distance Long distance Short distance Bulk Calculations: benchmark properties, Select appropriate method: (spin dependent PAW PBE + U corrections) Surface energy calculations: Benchmark surface relaxations against available data, Determine likely surface termination in PWR core Adsorption calculations: Determine sites, energies, use results for recombination and incorporation

28 Hydrogen adsorption on (0001) Fe 2 O 3 and Cr 2 O 3 Surface DFT calculations must be performed in an electronically neutral supercell : we add neutral hydrogen atoms to the simulation cell Bader charge analysis can be used to find the charge state of hydrogen (proton, neutral hydrogen, hydride) Surface models dotted lines show cell boundary Crs-1 O s b Cr s O s c O s a Cr s-2 O s b O s c Cr s-2 Cr s-1 O s a Cr s Adsorption Sites found by first performing an energy scan over the surface model- then relaxations were run at the lowest energy configurations

29 Hydrogen can adsorbs as either a proton or hydride on Fe 2 O 3 and Cr 2 O 3 : the sites are the same for both Adsorbed Proton: Bader charge: +0.6e O-H Bond length ~ 1 A Proton adsorbs to one of three equivalent surface oxygen ion sites Adsorbed Hydride: Bader charge: e Cr-H Bond length ~ 1.7 A Hydride adsorbs to the top most surface metal ion Smaller Red atoms: oxygen Large atoms (blue, black, yellow): Chromium Proton Hydride

30 Hydrogen Adsorption Energies E ads = E slab+ adsorbed H atoms E clean slab N H 2 E H 2 Adsorption energies relative to H 2 energy 1 ML = 1 H atom per cell. Negative energy is exothermic Hydrogen adsorption energies are more negative for Fe 2 O 3 Case Cr 2 O 3 Fe 2 O 3 (coverage + adsorption sites) (ev/atom) (ev/atom) 1 ML: O s ML: O s, O s ML: O s, M s ML: O s, O s, M s ML: O s, O s, O s On Cr 2 O 3, the 2 nd hydrogen prefers to adsorb to Cr- as a metal hydride. Adsorption at 2 ML is not stable with respect to the H 2 energy

31 The first step of the hydrogen recombination pathway is proton reduction + hydride formation: Shown Fe 2 O 3 Starting configuration: 2 adsorbed protons One proton is transferred from an oxygen ion to the surface Fe atom Charge is transferred between surface and this hydrogen Initial Charge: Final Charge: Intermediate state: Proton + hydride 2.21 ev 1.05 ev 1.16 ev 0 ev

32 The second step of hydrogen recombination is H 2 formation from the adsorbed proton-hydride pair Intermediate step: proton + hydride Transition state 2 Final State: H 2 adsorbed at surface Fe 2.21 ev 1.05 ev 0.72 ev 1.88 ev 0.62 ev 1.16 ev 1.27 ev 0 ev

33 Hydrogen Recombination on Cr 2 O 3 At 2 ML coverage- the lowest energy configuration is the H+ H- pair Small energy barrier : 0.28 ev Final State is H 2 adsorbed between surface O and Cr ions Recombination is exothermic at this coverage (hydrogen adsorption at 2 ML coverage was not favorable) 0 ev 0.28 ev 0.40 ev ev

34 Subsurface Hydrogen and Hydrogen incorporation At the perfect (0001) surface hydrogen is found in the unoccupied octahedral site below the surface metal ion Proton adsorbed at surface Proton in unoccupied octahedral Energy change and barrier for surface to subsurface migration at 1 ML coverage Energy Change Energy Barrier Cr 2 O ev 0.93 ev Fe 2 O ev 1.05 ev

35 Recombination or Adsorption? Coolant Water chemistry results: Chemical potential is ~ -0.9 ev Desorption DFT results: H 2 very weakly bound to surface < 0.1 ev DFT results: energy barrier ~ 1 ev H 2 formation H ad+ H ad- H 2 ads DFT results: Low energy barrier ~ ev Subsurface Migration H ad+ H sub + Adsorbed Protons at surface H ad + Proton Reduction H ad+ H ad - Oxide Inward Diffusion Stability determined by chemical potentials Energy barrier related to Fermi level in surface - DFT results had a high energy barrier for Fe 2 O 3 - Marcus theory predicts that Fe 2 O 3 is not a site for reduction

36 Recombination or Adsorption? Coolant Water chemistry results: Chemical potential is ~ -0.9 ev Desorption DFT results: H 2 very weakly bound to surface < 0.1 ev DFT results: energy barrier ~ 1 ev Oxide H 2 formation DFT results: Low energy barrier ~ ev Likely that proton reduction is the limiting step for the H ad+ hydrogen H ad- H 2 ads recombination step Fe 2 O 3 seems to be an unlikely site for proton reduction (according to Marcus theory) Cr 2 O 3 may be involved in hydrogen recombination Subsurface Adsorbed Protons at surface Proton Reduction Migration H + H ad+ H + H ad+ H - ad The (0001) surface of Cr sub ad 2 O 3 or Fe 2 O 3 provides some protection against hydrogen ingress: Hydrogen is more stable Stability above determined the surface than below Barrier it. related to fermi by chemical potentials Inward level in surface Diffusion High energy barrier for Fe 2 O 3

37 Summary Developed a detailed radiolysis model for PWRs that can be used to study steady state coolant chemistry in the core under a variety of conditions Realistic coolant chemistry, axial power profiles, dose rates Created a database of dose rate profiles for PWRs Estimated dose rates to confined coolant in CRUD Based on DFT calculations, identified Cr 2 O 3 as a possible site for hydrogen evolution, identified Fe 2 O 3 as an unlikely site Water Chemistry results: Support CRUD chemistry modeling Chemical Potential calculations support CASL corrosion work

38 Potential Future Work Radiolysis Modeling Add capability to model more appropriate flow conditions in porosity in CRUD RADICAL has capability for 2 phase flow (originally written for BWR). Directly to Moose? Do better job at estimation of alpha energy partitioning. DFT (Hydrogen Modeling) Rationalize/Combine SPP and ZrO 2 Results Build Dynamic Model for Evolution of SPPs/Oxide During Irradiation Take Shot at 1 st Generation Hydrogen Split Model (In the End-Stick with Empirical Correlation)

39 Thank You!

40 extras- supporting information

41 Work function (energy to move an electron from a vacuum to the electrode)- changes with hydrogen adsorption as follows: - decreases when hydrogen adsorbs as a proton ( the Fermi energy increases) - increases when hydrogen adsorbs as a hydride Case (coverage + adsorption sites) Adsorption energy (ev/atom) Cr 2 O 3 Fe 2 O 3 Work Function (ev) Adsorption energy (ev/atom) Work Function (ev) Clean Surface ML: O s ML: O s, O s ML: O s, M s ML: O s, O s, M s ML: O s, O s, O s Bottom line: Calculated adsorption energies include these potential changes. To arrive at H+ /H- energies, we d need to extrapolate to get the energy when the potential change is zero.

42 Radiolysis results- with CRUD at MOC

43 Reorganization Energy ( ) In a one-electron transfer reaction A + D A. - + D.+ Reorganization energy is the energy required for all structural adjustments (in the reactants and in the surrounding solvent molecules) which are needed in order that A and D assume the configuration required for the transfer of the electron.

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