1 Fundamentals of Void Swelling in Metal Alloys L. K. Mansur Workshop on Characterization of Advanced Materials under Extreme Environments for Next Generation Energy Systems Brookhaven National Laboratory September 25, 2009

2 Radiation-induced Swelling Introduction Background on radiation effects Importance of swelling Fundamentals Theory, experiments and characterization to understand swelling—many successes, many years to get there –Critical radius & critical no. of gas atoms –Dose dependence of swelling –Irradiation variable shifts –Approaches for swelling resistant alloys Conclusions and Recommendations

3 Origins of Radiation Effects in Materials Displacement of atoms (nuclear stopping) –Dominant damage process for metals –Significant for ceramics, semiconductors, polymers –Dose unit--displacement per atom, dpa –One dpa is the dose at which on average every atom in the material has been energetically displaced once Ionization and excitation (electronic stopping) –Generally can be neglected for metals –Important for polymers, ceramics, semiconductors –Dose unit--Gray, Gy, the dose for absorption of 1 J/Kg Transmutation reactions –Transmutation products, especially He and H from proton- and neutron- induced reactions, exacerbate damage –Customary unit of measure is appm transmutant per dpa, e.g., appm He/dpa, appm H/dpa

4 High Energy Accelerator Radiation Damage Comparison to Fission or Fusion Neutrons Highest particle energies –GeV vs. less than ~ 20 MeV for fission or fusion Instantaneous damage rates –10 -2 (time average ~ dpa/s) vs dpa/s for fission or fusion –He and H transmutation rates for GeV protons 500 appm H/dpa 100 appm He/dpa Fusion 10“ Fission 0.2 “ –Wide range of other transmutations

5 Time and Energy Scales for Radiation Effects by Displacement Damage Time Cascade Creation s Unstable Matrix s Interstitial Diffusion s Vacancy Diffusion 10 0 s Microstructural Evolution 10 6 s Energy Neutron or Proton eV Primary Knock-on Atom eV Displaced Secondary eV Unstable Matrix 10 0 eV Thermal Diffusion kT

6 Length Scales and Reaction Hierarchy for Property Changes in Structural Materials Evolution of Microstructure (…to hundreds μm) Displacement of Atoms (…nm) Diffusion and Aggregation of Defects (…to hundreds nm) Embrittlement, Swelling, Irradiation Creep (…mm to human scale…) What is it? Why is it important?

7 Displacement Damage Occurs in Cascades Particle (e.g., beam proton or spallation neutron) transfers its energy to the primary knock-on atom (pka) High energy particles, e.g., GeV protons or fusion neutrons may produce atomic recoils at much higher energies than fission neutrons Large-scale atomic simulations demonstrate that subcascade formation leads to similar defect production Molecular Dynamics Simulations of peak damage state in iron cascades at 100 K, R. E. Stoller, ORNL Many experimental confirmations in basic and fusion R&D. 10 nm 50 keV ~ avg. fusion 10 keV ~ avg. fission 200 keV pka energy

8 Theory, Modeling and Simulation Methods to Understand Radiation Effects Collision leading to pka s Cascade Creation s Unstable Matrix s Interstitial Diffusion s Vacancy Diffusion 10 0 s Microstructural Evolution 10 6 s Binary collision approximation (intuitive if you have played pool) Molecular dynamics Kinetic Monte Carlo Cascade Diffusion Theory Reaction Rate Theory

9 Historical Perspective on Swelling First observations published in 1967 by Cawthorne and Fulton Reaction in the community Swelling responsible for restructuring of the US and international fast reactor materials programs Intensive research and development devoted to fuel cladding and duct alloys in the period through early 1980’s; some applied work into early 1990’s Continuing level of more basic work Theory, modeling and critical experiments have led to understanding of mechanisms and design of swelling resistant alloys

10 Dimensional Instability Swelling is one of a class of phenomena collected under the term “dimensional instability” Other examples of dimensional instability –radiation creep (all materials) –radiation growth (anisotropic materials) –swelling by gas bubbles, cracks, … (nuclear fuels) –growth of and changes in type of pores and cracks (graphite) –shrinkage due to mass loss (polymers) Primary concern--swelling may cause substantial changes in dimensions of engineering components

11 Background Nucleation of a new phase--empty space--in the form of a distribution of nanoscale cavities Volume increase during displacive irradiation that typically occurs between 0.3 and 0.6 T m Pure metals may swell at low doses, < 1 dpa; Complex alloys require ~ dpa and higher Excess interstitials absorbed at dislocations and at other microstructural sinks; excess vacancies absorbed at cavities

12 Importance of Swelling Overall dimensional increase of components Sensitivity to gradients in dose, dose rate and temperature can lead to strong distortions Fabricated sizes and shapes not preserved May affect particle transport and thermal hydraulics, especially for small and tight cores of fast reactors Cavity distributions possible easy paths for fracture Could limit lifetime in advanced nuclear systems and high power accelerator components

13 Classic Defect Structure in Fe-Cr-Ni Alloy Irradiated to Moderate Dose J. O. Stiegler, 1974 Transmission electron microscopy after irradiation: dislocations, phase changes, cavities

14 Swelling of 20% CW Stainless Steel in EBR-II Garner and Gelles, 1990

15 Large Reductions in Swelling Can be Attained by Alloying Additions L. K. Mansur and E. H. Lee

16 Cluster Approach to Swelling Discrete Master Equation Fokker-Planck Approximation

17 Radial Growth Rate Cavity Growth Dislocation Loop Growth

18 Bias-driven Swelling Requires Accumulation of Critical No. of Gas Atoms, n g * Critical radius and critical number of gas atoms, keys to understanding swelling, a result of combined theory and critical experiments

19 Critical Radius Concept Discovered and Developed via Theoretical Modeling V. F. Sears, 1971 K. C. Russell, 1978 M. R. Hayns, et al, 1978 L. K. Mansur and W. A. Coghlan, 1983 H. Trinkaus, 1983 R. E. Stoller and G. R. Odette, 1985 L. K. Mansur, et al., exact solutions for van der Waals and higher pressure EOS gas

20 Concepts for Control of Swelling Derived from Critical Radius Critical quantities vary with composition –Move toward compositions that produce larger critical quantities, i.e., higher doses before swelling For a given critical size or critical number of gas atoms, dilute gas over a large number of cavities –Slow gas accumulation rate in each cavity and delay the attainment of critical number of gas atoms and therefore delay bias driven swelling

21 Controlled Variable Experiment to Investigate Critical Radii in Low and High Ni Alloys -Sequenced gas injection and heavy-ion irradiation -Gas injection established cavity distribution spanning critical number of gas atoms -Results confirmed critical number of gas atoms for bias-driven growth larger for high Ni alloy E. H. Lee, L. K. Mansur, Phil. Mag. A 52 (1985) 493

22 Calculated Map of Swelling with Cavity and Helium Concentrations Cavities have accumulated critical number of gas atoms Cavities have not accumulated critical number of gas atoms

23 Early Nanostructured Material For Swelling Resistance Austenitic Stainless Steel Precipitate-matrix interfaces allow nucleation of so many cavities that critical number of gas atoms cannot be accumulated in any one Number of cavities is low so that critical number of gas atoms is quickly accumulated in each E. H. Lee, L. K. Mansur, Phil Mag. A 61 (1990) 733

24 Dose Dependence of Swelling Depends on Balance of Sink Strengths Observed over wide dose range Low to medium dose or low N c High dose or high N c Simplest case: dislocations and cavities only

25 Relative Swelling as a Function of Dislocation-Cavity Sink Strength Ratio

Broad range of experiments in many alloys gives results consistent with low swelling for Q >>1 and Q <<1 and high swelling for Q ~ 1

27 Requiring Invariance in Key Quantities Leads to Irradiation Variable Shifts Highly Useful Relationships Obtainable Analytically Temperature shift to reach same total point defect absorption at sinks for different dose rates Temperature shift to reach same swelling (same net vacancy absorption at cavities) for different dose rates Dose shift to reach same total point defect absorption at sinks for different dose rates Dose shift to reach same swelling for different dose rates Temperature shift to reach same total point defect absorption at sinks for different doses

28 Concentrations and Cumulative Losses of Defects for Limiting Conditions

29 More General Relations for Irradiation Variable Shifts Temperature shift with dose rate for invariant swelling with arbitrary differences in sink strength and primary mode of defect loss

30 Simplest Relations for Irradiation Variable Shifts Temperature shift with dose rate for invariant net absorption at voids, i.e., invariant swelling For recombination dominated conditions

31 Comparison of Temperature Shift Theory with Experiments in Nickel

32 Alloy Design for Swelling Resistance Guided by Theory and Mechanistic Experiments High concentration nanostructures impart swelling (and embrittlement) resistance –Devise compositions so that desired nanostructures emerge at moderate doses –Fine initial nanostructures may be irrelevant –Sabilize structures for high doses or long times at lower doses Increase the required critical number of gas atoms, n g * –Tailor composition for low bias –Maximize overall concentration of point defect sinks Lower rate of approach to critical number of gas atoms, n g * –Dilute gas over as many bubbles as possible –Reduce residual gas content –Lower He transmutation gas (composition, isotopic tailoring) Avoid precipitate point defect collector effect –Eliminate coarsely distributed large precipitates

33 Comprehensive Publications on Theory and Modeling L. K. Mansur, "Void Swelling in Metals and Alloys under Irradiation: An Assessment of the Theory," Nucl. Technol. 40 (1978) 5-34 L. K. Mansur, "Mechanisms and Kinetics of Radiation Effects in Metals and Alloys," A chapter in the book, Kinetics of Non- Homogeneous Processes, edited by G. R. Freeman, Wiley- Interscience, New York 1987, pp L. K. Mansur, "Theory and Experimental Background on Dimensional Changes in Irradiated Alloys," International Summer School on the Fundamentals of Radiation Damage, Urbana, Illinois, August 1993, J. Nucl. Mater. 216 (1994) Compilation of Experimental Results on Stainless Steels F. A. Garner, “Irradiation Performance of Cladding and Structural Steels in Liquid Metal Reactors,” Chapter 6, Volume 10A, Nuclear Materials, Part 1, B. R. T. Frost, ed., Materials Science and Technology: A Comprehensive Treatment, R. W. Cahn, P. Haasen, and E. J. Kramer, eds., VCH publishers, Germany, Cavity Swelling

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