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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 LaboratorySeptember 25, 2009

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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

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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

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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 ~ 10-6 dpa/s) vs. 10-6 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

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Time and Energy Scales forRadiation Effects by Displacement Damage

TimeCascade Creation

10-13 s

Unstable Matrix10-11 s

Interstitial Diffusion10-6 s

Vacancy Diffusion100 s

MicrostructuralEvolution

106 s

EnergyNeutron or Proton

105 - 109 eV

Primary Knock-on Atom104 - 105 eV

Displaced Secondary102 - 103 eV

Unstable Matrix100 eV

Thermal DiffusionkT

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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?

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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

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Theory, Modeling and Simulation Methods to Understand Radiation Effects

Collision leading to pka10-18 s

Cascade Creation10-13 s

Unstable Matrix10-11 s

Interstitial Diffusion10-6 s

Vacancy Diffusion100 s

MicrostructuralEvolution

106 s

Binary collision approximation(intuitive if you have played pool)

Molecular dynamics

Kinetic Monte Carlo

Cascade Diffusion Theory

Reaction Rate Theory

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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

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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

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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 Tm

• Pure metals may swell at low doses, < 1 dpa; Complex alloys require ~ 10-100 dpa and higher

• Excess interstitials absorbed at dislocations and at other microstructural sinks; excess vacancies absorbed at cavities

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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

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Classic Defect Structure in Fe-Cr-Ni Alloy Irradiated to Moderate Dose

J. O. Stiegler, 1974

Transmissionelectronmicroscopyafter irradiation:dislocations,phase changes,cavities

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Swelling of 20% CW Stainless Steel in EBR-II

Garner and Gelles, 1990

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Large Reductions in Swelling Can be Attained by Alloying Additions

L. K. Mansur and E. H. Lee

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Cluster Approach to Swelling

Discrete Master Equation

Fokker-Planck Approximation

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Radial Growth Rate

Cavity Growth

Dislocation Loop Growth

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Bias-driven Swelling Requires Accumulation of Critical No. of Gas Atoms, ng*

Critical radius andcritical number ofgas atoms, keys to

understanding swelling,a result of combined

theory and criticalexperiments

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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., 1986--exact solutions for

van der Waals and higher pressure EOS gas

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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

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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 confirmedcritical number of gasatoms for bias-driven growth larger for high Ni alloy

E. H. Lee, L. K. Mansur, Phil. Mag. A 52 (1985) 493

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Calculated Map of Swelling with Cavity and Helium Concentrations

Cavities have accumulatedcritical number of gas atoms

Cavities have notaccumulated

critical numberof gas atoms

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Early Nanostructured MaterialFor Swelling Resistance

AusteniticStainless

Steel

Precipitate-matrix interfacesallow nucleation of so manycavities that critical number

of gas atoms cannot beaccumulated in any one

Number of cavities is lowso that critical numberof gas atoms is quickly

accumulated in each

E. H. Lee, L. K. Mansur,Phil Mag. A 61 (1990) 733

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Dose Dependence of Swelling Depends on Balance of Sink Strengths

Observed over wide dose range

Low to medium dose or low Nc

High dose or high Nc

Simplest case: dislocations and

cavities only

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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

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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

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Concentrations and Cumulative Losses of Defects for Limiting Conditions

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More General Relations for Irradiation Variable Shifts

Temperature shift with dose rate for invariantswelling with arbitrary differences in sinkstrength and primary mode of defect loss

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Simplest Relations for Irradiation Variable Shifts

Temperature shift with dose rate for invariantnet absorption at voids, i.e., invariant swelling

For recombination dominated conditions

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Comparison of Temperature Shift Theory with Experiments in Nickel

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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, ng*– Tailor composition for low bias– Maximize overall concentration of point defect sinks

• Lower rate of approach to critical number of gas atoms, ng*– 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

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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. 377-463.

• 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) 97-123.

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, 1994.

Cavity Swelling

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