Comprehensive nuclear materials 1 06 the effects of helium in irradiated structural alloys

Comprehensive nuclear materials 1 06 the effects of helium in irradiated structural alloys Comprehensive nuclear materials 1 06 the effects of helium in irradiated structural alloys Comprehensive nuclear materials 1 06 the effects of helium in irradiated structural alloys Comprehensive nuclear materials 1 06 the effects of helium in irradiated structural alloys Comprehensive nuclear materials 1 06 the effects of helium in irradiated structural alloys Comprehensive nuclear materials 1 06 the effects of helium in irradiated structural alloys

Y Dai

Paul Scherrer Institut, Villegen PSI, Switzerland

G R Odette and T Yamamoto

University of California, Santa Barbara, CA, USA

ß 2012 Elsevier Ltd All rights reserved.

1.06.2 Experimental Approaches to Studying He Effects in Structural Alloys 146

1.06.3 A Review of Helium Effects Models and Experimental Observations 151

1.06.3.3 Void Swelling and Microstructural Evolution: Mechanisms 1551.06.3.4 The CBM of Void Nucleation and RT Models of Swelling 1561.06.3.5 Summary: Implications of the CBM to Understanding He Effects on Swelling and

1.06.4.2.1 Helium effects on tensile properties and He-induced hardening effects 1721.06.4.2.2 Helium effects on fracture properties and He-induced embrittlement effects 174

1.06.4.4 Summary of Effects of Irradiation on Tensile and Fracture Properties 178

1.06.5.4 Master Models of He Transport, Fate, and Consequences 182

1.06.6 Radiation Damage Tolerance, He Management, Integration of Helium Transport

1.06.6.1 ISHI Studies and Thermal Stability of Nanofeatures in NFA MA957 1831.06.6.2 Master Models of He Transport Fate and Consequences: Integration of

Abbreviations

APT Accelerator Production of Tritium

CBM Critical bubble model

EELS Electron energy-loss spectroscopy

embrittlement

IFMIF International Fusion Material

Irradiation Facility

ISHI In situ He implantation

KMC/KLMC Kinetic Monte Carlo–lattice Monte

Carlo

LANSCE Los Alamos Neutron Science Center

embrittlement

NFA Nanostructured ferritic alloys

ODE Ordinary differential equation

OEMS (Positron) orbital electron

momentum spectra

PAS Positron annihilation spectroscopy

REP Radiation enhanced precipitation

RIP Radiation-induced precipitation

SANS Small-angle neutron scattering

SIA Self-interstitial atom

SINQ Swiss Spallation Neutron Source

irradiations STIP SINQ Target Irradiation Program

1.06.1 Introduction and OverviewThis chapter reviews the profound effects of He onthe bulk microstructures and mechanical properties

of alloys used in nuclear fission and fusion energysystems Helium is produced in these service envir-onments by transmutation reactions in amounts rang-ing from less than one to thousands of atomic partsper million (appm), depending on the neutron spec-trum, fluence, and alloy composition Even higheramounts of H are produced by corresponding n,preactions In the case of direct transmutations, theamount of He and H are simply given by the contentweighted sum of the total neutron spectrum averagedenergy dependent n,a and n,p cross-sections for allthe alloy isotopes (hsn,ai) times the total fluence (ft).The spectral averaged cross-sections for a specifiedneutron spectrum can be obtained from nuclear data-base compilations such as SPECTER,1LAHET,2andMCNPX3 codes He and H are also produced incopious amounts by very high-energy protons andneutrons in spallation targets of accelerator-basednuclear systems (hereafter referred to as spallationproton–neutron (SPN) irradiations, SPNI).4,5 TheD–T fusion first wall spectrum includes 14 MeVneutrons (20%), along with a lower energy spec-trum (80%) The 14 MeV neutron energy is farabove the threshold for n,a (5 MeV) and n,

p (1 MeV) reactions in Fe.6

Note that some tant transmutations also take place by multistepnuclear reactions For example, thermal neutrons(nth) generate large amounts of He in Ni-bearingalloys by a 58Ni(nth,g)59Ni(nth,a) reaction sequence.These various irradiation environments also produce

impor-a rimpor-ange of solid trimpor-ansmutimpor-ation products

High-energy neutrons also produce induced displacement damage in the form of vacancyand self-interstitial atom (SIA) defects Vacancies andSIA are the result of a neutron reaction and scattering-induced spectrum of energetic primary recoiling

radiation-atoms with energies ranging from less than 1 keV, in

neutron irradiations, up to several MeV in SPN

irra-diations.7 The high-energy primary recoils create

cascades of secondary displacements of atoms from

their crystal lattice positions, measured in a

calcu-lated dose unit of displacements per atom (dpa)

As in the case of n,a transmutations, dpa production

can also be evaluated using spectral averaged

dis-placement cross-sections8 that are calculated using

the codes and nuclear database compilations cited

above

Typical operating conditions of various fission,

fusion, and spallation facilities are summarized in

Table 1 Notably, He (and H) generation in fast fission

(He/dpa<< 1), fusion (He/dpa  10), and spallation

proton–neutron (He/dpa up to 100) environments

differs greatly and this is likely to have significant

effects on the corresponding microstructural and

mechanical property evolutions

The primary characteristic of He, which makes it

significant to a wide range of irradiation damage

phenomena, is that it is essentially insoluble in solids

Hence, in the temperature range where it is mobile,

He diffuses in the matrix and precipitates to initially

form bubbles, typically at various microstructural

trapping sites The bubbles can serve as nucleation

sites of growing voids in the matrix and creep cavities

on grain boundaries (GBs), driven by displacement

damage and stress, respectively While He effects are

primarily manifested as variations in the cavities, all

microstructural processes taking place under

irradia-tion are intrinsically coupled; hence, difference in the

He generation rate can also affect precipitate,

dislo-cation loop, and network dislodislo-cation evolutions as

well (seeSection 1.06.3)

Figure 1, adopted from Molvik et al.,9

schemati-cally illustrates the effects of high He as a function

of lifetime-temperature limits in a fusion first wall

structure for various irradiation-induced

degrada-tion phenomena At high temperatures, lifetimes

(green curve) are primarily dictated by chemical

compatibility, fatigue, thermal creep, creep rupture,

and creep–fatigue limits In this regime, He can

fur-ther degrade the tensile ductility and the ofur-ther

high-temperature properties, primarily by enhancing grain

boundary cavitation, in some cases severely In

aus-tenitic stainless steels (AuSS), high-temperature

He embrittlement (HTHE) has been observed at

concentrations as low as 1 appm.10,11 In contrast,

9Cr ferritic–martensitic steels (FMS), which are

cur-rently the prime candidate alloy for fusion structures,

are much more resistant to HTHE.12,13

At intermediate temperatures (blue curve), growingvoids form on He bubbles, and He accumulationlargely controls the incubation time prior to theonset of rapid swelling (see Section 1.06.3) FMSare also much more resistant to swelling than stan-dard austenitic alloys,14,15 although the microstruc-tures of the latter can be tailored to be more resistant

to void formation by He management schemes.16High He concentrations can also extend irradiationhardening and fast fracture embrittlement to inter-mediate temperatures.17

At lower temperatures (red curve), where irradiationhardening and loss of tensile uniform ductility aresevere, high He concentrations enhance large positiveshifts in the ductile-to-brittle transition temperature(DBTT) in bcc (body-centered cubic) alloys.18–20This low-temperature fast fracture embrittlementphenomenon is believed to be primarily the result of

He embrittlement, thermal creep, corrosion

Dimensional instability irradiation creep and swelling

Window

Hardening, fracture

Temperature

Figure 1 Illustration of the materials design window for the fusion energy environment, as a function of temperature Reproduced from Molvik, A.; Ivanov, A.; Kulcinski, G L.;

et al Fusion Sci Technol 2010, 57, 369–394.

Table 1 Typical dpa, He, and H production in nuclear fission, fusion, and spallation facilities

Irradiation facility Fission

reactor

Fusion reactor first wall

Spallation targets

dpa range (in Fe) <200–400 50–200 <35

He per dpa (in Fe) <1 10 <100

H per dpa (in Fe) <1 40 <500 Temperature (C) 270–950 300–800 50–600 Source: Dietz, W.; Friedrich, B C In Proceedings of the OECD NEA NSC Workshop on Structural Materials for Innovative Nuclear Systems, 2007, p 217; Mansur, L K.; Gabriel, T A.; Haines, J R.; Lousteau, D C J Nucl Mater 2001, 296, 1; Vladimirov, P.; Moeslang, A J Nucl Mater 2006, 356, 287–299.

He-induced grain boundary weakening, manifested by

a very brittle intergranular (IG) fracture path,

inter-acting synergistically with irradiation hardening.20,21

High concentrations also increase the irradiation

hardening at dpa levels that would experience

satu-ration in the absence of significant amounts of He.17

A significant concern for fusion is that the

dpa-temperature window may narrow, or even close, for

a practical fusion reactor operating regime

What is sketched above is only a very broad-brush,

qualitative description of some of the important He

effects The quantitative effects of He, displacement

damage, temperature and stress, and their interactions,

which control the actual positions of the schematic

curves shown inFigure 1, depend on the combination

of all the irradiation variables, as well as details of the

alloy type, composition, and starting microstructure

(material variables) The effects of a large number of

interacting variables, the complex interactions of a

plethora of physical mechanisms, and the

implica-tions to the wide range of properties of concern are

not well understood; and even if they were, such

complexity would beg easy description Therefore, afirst priority is to develop a good understanding ofand models for the transport and fate of He at thepoint when it is effectively immobilized in bubblesand voids, often at various microstructural sites Suchinsight provides a basis for developing microstruc-tures that can manage He and thus mitigate its dele-terious effects To this end we next briefly outline keyradiation damage processes, including the role of He

Figure 2 schematically illustrates the combinedeffects of He and displacement damage on irradiation-induced microstructural evolutions.22 Figure 2(a)

shows a molecular dynamics simulation of primarydisplacement damage produced in displacement cas-cades Most of the initially displaced atoms return to alattice site (self-heal) Residual cascade defects includesingle and small clusters of vacancies and SIA Inthe temperature range of interest, vacancies (red cir-cles) and SIA (green dumbbells) are mobile SIAclusters, in the form of dislocation loops, are alsobelieved to be mobile in some cases, undergoingone-dimensional diffusion on their glide prisms

SIA

Vacancy Cascade

However, the cascade loops may also be trapped by

interactions with solutes Small cascade vacancy

clus-ters may coarsen in the cascade region by Ostwald

ripening and diffusion coalescence mechanisms Both

isolated and clustered defects interact with alloy

solutes forming cascade complexes The cascade

vacancy clusters dissolve over a time associated with

cascade aging, which depends strongly on

tempera-ture The concentration of cascade vacancy clusters,

which act as sinks (or recombination centers) for

migrating vacancies and SIA, scales directly with the

damage rate Thus, the overall defect production

microstructures can be viewed as being composed of

steady-state concentrations of diffusing defects, small

loops, and cascade vacancy clusters; the latter are

important if the irradiation time is much less than

the cluster annealing time Vacancy–SIA

recombina-tion at clusters, in the matrix and at vacancy trapping

sites, can give rise to important damage rate, or flux,

effects

Figure 2(b) shows that SIA can recombine with

diffusing and trapped vacancies, in this case one

trapped on a precipitate interface.Figure 2(b) also

shows that both bubbles (blue part circle) and voids

(orange part circle) often form on precipitates

Figure 2(c) shows that dislocation loops (green

hexagon) nucleate and grow due to preferential

absorption of SIA (bias) Preferential accumulation

of SIA also takes place at network dislocation

segments (inverted green T), causing climb Loop

growth and dislocation climb can lead to creation

(loops and Herring–Nabarro sources) and annihilation

(of oppositely signed network segments) of

disloca-tions, ultimately leading to quasi-steady-state

densi-ties, as is observed in the case of AuSS

Figure 2(d) shows that He precipitates to formbubbles (larger blue circles) at various sites, in thiscase in the matrix Small bubbles are stable since theyabsorb and emit vacancies in net numbers thatexactly equal the number of SIA that they absorb;thus bubbles grow only by the addition of diffusing

He atoms (small blue circle) However, Figure 2(e)

shows that when bubbles reach a critical size theyconvert to unstably growing underpressurized voids(large orange circle containing blue He atoms) due to

an excess flux of vacancies over SIA arising from thedislocation bias for the latter defect Figure 2(e)

shows the corresponding growing creep cavitiestransformed from critical He bubbles on stressedGBs Designs of microstructures that mitigate, oreven fully suppress, these various coupled evolutionsare described in Section 1.06.6 and discussed inreferences.22,23

Therefore, a master overarching framework formeasuring, modeling, and managing He effects must

be based on developing and understanding the nant mechanisms controlling its generation, trans-port, fate, and consequences, as mediated by theirradiation conditions and the detailed alloy micro-structure Figure 3illustrates such a framework for

domi-He generation, transport, and fate In this framework,experiments and models can be integrated to estab-lish how He is transported to various microstructuraltrapping (-detrapping) features and how He locallyclusters to form bubbles at these sites, as well as in thematrix The master models must incorporate para-meters that describe He diffusion coefficients underirradiation, binding energies for trapping at the vari-ous sites and He–vacancy cluster and other interac-tion energies

Matrix transport of He by various mechanisms and partitioning to subregion sinks controlled by vacancy and SIA defects, matrix properties,

and trap-sink microstructures – Nucleation and growth of matrix cavities Generate mobile He by transmutation and emission from traps

Other precipitates Grain

boundaries

Fine-scale precipitates

Dislocation substructures Transport of He within and between interconnected subregions Emission of He from subregions Formation of subregion cavities

Internal region structure Multiscale modeling-experiment framework

sub-Figure 3 Illustration of a multiscale master modeling–experiment framework for He generation, transport, and fate.

Given the length and comprehensive character of

this chapter, it is useful to provide the reader a guide

to what follows Notably, we have tried to develop

useful semi-standalone sections

Section 1.06.2describes the various experimental

approaches to studying He effects in structural alloys

including both neutrons and various types of

charged-particle irradiations (CPI)

Section 1.06.3 reviews the historical knowledge

base on He effects, which has been developed over

the past 40 years, with emphasis on bubble evolution,

void swelling, and HTHE processes While less

of current interest, the examples included here

pri-marily pertain to standard AuSS, discussions of

experiment and modeling are closely integrated to

emphasize the insight that can be derived from such

coupling Particular attention is paid to the critical

bubble mechanism for the formation of growing voids

and grain boundary cavities and the corresponding

consequences to swelling and creep rupture The

implications of the coupled models and experimental

observations to designing irradiation-tolerant alloys

that can manage He are discussed in some detail

Section 1.06.4focuses on a much more recent body

of observations on He effects in SPNI The emphasis

here is on descriptions of defect and cavity

microstruc-tures in both FMS and AuSS irradiated at low to

intermediate temperatures and the corresponding

effects on their strength, ductility, and fast fracture

resistance Similarities and differences between the

SPNI effects and those observed for fission

irradia-tions are drawn where possible

Section 1.06.5summarizes some key examples of

atomistic modeling of He behavior, which has been

the focus of most recent modeling efforts Insight into

mechanisms and critical parameters provided by

these models will form the underpinning of the

com-prehensive master models of He transport, fate, and

consequences

Section 1.06.6 builds on the discussion in

Section 1.06.3regarding managing He by trapping it

in a population of small stable bubbles A specific

example comparing FMS to a new class of

high-temperature, irradiation-tolerant nanostructured

fer-ritic alloys (NFA) irradiated in a High-Flux Isotope

Reactor (HFIR) at 500C to 9 dpa and 380 appm He is

described The results of this study offer proof in

principle of the enormous potential for developing

irradiation-tolerant NFA that could turn He from a

liability to an asset Section 1.06.6 again couples

these experimental observations with a master

multi-scale model of the transport and fate of He in both

FMS and NFA The predictions of the master model,that is both microstructurally informed and parame-terized by atomistic submodels, are favorably com-pared to the HFIR data

Section 1.06.7 briefly summarizes the status ofunderstanding of He effects in structural alloys andconcludes with some outstanding issues Reading thissummary first may be helpful to general readers whothen can access the more detailed information at theirown discretion

1.06.2 Experimental Approaches to Studying He Effects in Structural Alloys

1.06.2.1 Single, Dual, and Triple-Beam CPISingle (He), dual (typically heavy ions to producedpa and He), and triple (typically heavy ions, Heand H) beam CPI have been extensively used tostudy He effects for a wide variety of materials andconditions The number of facilities worldwide, bothcurrent and historically, and the large resulting liter-ature cannot be fully cited and summarized in thischapter, but some examples are given in Section1.06.3 A more complete overview of these facilitiescan be found in a recent Livermore National Labo-ratory Report.24 Extensive high-energy He implan-tation studies of creep properties were carried out atForschungszentrum Ju¨lich using a 28 MeV He cyclo-tron.25 Major dual- and triple-beam studies werepreviously carried out at Oak Ridge National Labo-ratory (180 keV H, 360 keV He, 3.5 MeV Fe)26 andmany other facilities around the world.24 The newJANNUS facility at Saclay couples a 3 MV Pelletronwith a multicharged ion source and a 2.5 MV singleVan de Graaff and a 2.25 MeV tandem accelerator.27Another multibeam facility at Orsay couples a 2 MVcouple, a tandem accelerator, and a 190 kV ion im-planter to a 200 kV transmission electron microscope(TEM) to allow simultaneous co-irradiation andobservation.27

The advantages of He implantation andmultibeam ion irradiations include the following:(a) conditions can be well controlled and in manycases selectively and widely varied; (b) high dpa, He,and H levels can be achieved in short times; (c) thespecimens are often not, or only minimally, acti-vated; and (d) in situ TEM observations are possible

in some cases The disadvantages include the ing: (a) highly accelerated damage rates comparedwith neutron irradiations; and in the case of

follow-multibeam ion irradiations, (b) shallow damage

depths and the proximity of free surfaces; (c)

non-uniform damage production and the deposition of

foreign ions; and (d) inability to measure bulk

prop-erties High-energy He implantation can be used

on bulk specimens tested, either in situ or

post-implantation, to measure tensile, creep, and creep

rupture properties The corresponding disadvantages

are that He implantation results in high He/dpa

ratios (6000 appm He/dpa).28

The differences tween CPI and neutron irradiation can significantly

be-affect microstructural evolution

Thus, it must be emphasized that He implantation

and multibeam CPI do not simulate neutron

irradia-tions Although it has been argued that CPI reveal

general trends and that corrections, like temperature

adjustments, allow extrapolations to neutron-irradiation

conditions, both assertions are problematic The proper

role of He implantation and multibeam CPI is to help

inform and calibrate models and to identify and

quantify key processes based on carefully designed

mechanism experiments

1.06.2.2 Neutron Irradiations with B or

Ni Doping

The effects of high He levels on microstructure and

mechanical properties have been extensively studied

in mixed fast–thermal spectrum fission reactor

irradia-tions of alloys naturally containing, or doped with, Ni

and B In these cases, high He levels are produced

by thermal neutron nth,a reactions, either by (a) the

two-step reaction with58Ni(nth,g) (68% of elemental

Ni with a nth,g cross-section of0.7 barns) and59

Ni

(nth,a) (bred from 58Ni with a n,a cross-section

of 10 barns) cited inSection 1.06.1; (b) or by the10

Bþ nth!7

Liþ a reaction (20% of elemental Bwith a cross-section of 4010 barns) (1 barn ¼10–24 cm2) Significant quantities of He can also begenerated by epithermal–fast spectrum neutron reac-tions with B as well as prebred59Ni.29

Figure 4(a) shows calculated and measured Heproduction in natural Ni in the HFIR target capsuleposition.30 Figure 4(b) shows the correspondingHe/dpa ratio for a Fe alloy doped with 2% natural Ni.Two Ni doping characteristics are evident: (a) there is

a transient phase in He production regime prior to aHe/dpa peak at about 20 dpa in HFIR; (b) if thealloy contains more than a few percent Ni, like inAuSS, the He/dpa is much higher than that for fastfission and higher than that for fusion spectra but

is comparable to, or slightly less than, the He/dpafor SPNI

Modifying the amounts of58Ni and60Ni (isotopetailoring) can control and target He/dpa ratios(e.g., to fusion).29,31,32 An approximately constant

He generation rate can be obtained by using diated Ni pre-enriched in59Ni.29,31Various amounts

irra-of58Ni,59Ni, and60Ni can also be used to control theHe/dpa ratio in fast spectrum reactors, like the FastFlux Test Facility (FFTF), as well as in mixed spec-trum reactors, like HFIR.29,31,32

Boron is not normally added to steels used fornuclear applications, but it has been used in a number

of doping studies.33,34A major advantage of B doping isthat significant amounts of He are produced by the10

B, but not the11B, isotope Thus, the effect of dopingwith10B versus11B can be used to isolate this effect of

(b)

0

2 4 6 8 10 12 14

dpa

0

5 (a)

34

Thermal neutron fluence (10 22 n cm –2 )

Total Incremental

Figure 4 (a) Measured and calculated He production from Ni irradiated in HFIR The solid line is calculated using the evaluated58Ni and59Ni cross-sections (b) The He/dpa ratio in Fe-based 2% Ni alloy for accumulated total (solid red line) and incremental (dashed blue line) He Reproduced from Greenwood L R.; ASTM STP 1490 and the data provided by Greenwood L R.

He, in a B-containing alloy However, the issues

asso-ciated with B doping are even more problematic

than those for Ni In mixed spectrum reactors, all the

10

B is quickly converted to He and Li by the thermal

neutrons In this case, the He is initially introduced

at much too high a rate per dpa but then saturates at

the10B content The other major limitations are that

B is virtually insoluble in steels and primarily resides

in Fe and alloy boride phases.35Boron also segregates

to GBs Thus, He from B reactions is not

homo-geneously distributed Recently, nitrogen additions

to FMS steels to form fine-scale BN phases have

been used to increase the homogeneity of B and He

distributions.36

Varying the He/dpa ratio in Ni- and B-containing

alloys can also be achieved by attenuating thermal

neutron fluxes (spectral tailoring) in mixed spectrum

reactors as well as selecting appropriate fast reactor

irradiation positions.31,37,38 Spectral tailoring, either

by attenuating thermal neutrons or irradiating in

epithermal–fast reactor spectra, is especially helpful

in B doping.33,39,40

However, doping alloys that do not normally

con-tain Ni or B can affect both their properties and

microstructures, including their response to He and

displacement damage For example, transformation

kinetics during heat treatments (hardenability) and

the baseline properties of FMS are strongly affected

by both Ni and B Ni also has a strong effect on refining

irradiation-induced microstructures and enhancing

irradiation hardening.20,41–44As noted previously, to

some extent these confounding factors can be

evalu-ated by comparing the effects of various amounts of

10

B/11B45 and 58Ni/60Ni However, doped alloys are

inherently ‘different’ from those of direct interest

Note that excess dpa due to n,a reaction recoils must

be accounted for,46and in the case of B doping the Li

reaction product may play some role as well

1.06.2.3 In Situ He Implantation

In situ He implantation (ISHI) in mixed spectrum

fission reactors is a very attractive approach to assess

the effects of He–dpa synergisms in almost any

mate-rial that avoids most of the confounding effects of

doping The basic idea is to use an implanter layer,

containing Ni, Li, B, or a fissionable isotope, to inject

high-energy a-particles into an adjacent sample

simultaneously undergoing neutron-induced

dis-placement damage Early work proposed implanting

He using the decay of a thin layer of a-emitting

isotope adjacent to the target specimen.47 However,

the isotope decay technique produces few dpa at

a very high He/dpa The first proposal ISHI in

a mixed fast (dpa)–thermal (He) spectrum proposedusing235U triple fission reactions to inject16 MeVa-particles uniformly in steel specimens up to 50 mmthick; the 50 mm thickness permits tensile and creeptesting as well as microstructural characterization andmechanism studies at fusion relevant dpa rates andHe/dpa ratios.31 The triple fission technique wasapplied to implanting ferritic steel tensile specimen,albeit without complete success.48A much more prac-tical approach is to use thin Ni-bearing implanter foils

to uniformly deposit He up to a depth of8 mm in Fe

in a thick specimen at controlled He/dpa ratios.49

As illustrated in Figure 5(a)–5(c), there are atleast three basic approaches to implanter design.Here we will refer to thin and thick, specificallymeaning a specimen (ts) or implanter layer (ti) thick-ness that is less than or greater than the corre-sponding a-particle range, respectively Ignoringeasily treated difference in the a-particle range (Ra)and atom densities in the injector and specimens forsimplicity, thick implanter layers on one side of athick specimen produce linearly decreasing He con-centration (XHe) profiles, with the maximum concen-tration at the specimen surface that is one half theconcentration in the bulk injector material, XHeo¼

XHei/2 (Figure 5(a)) If a thin specimen is implantedfrom both sides by thick layers, the He concentration

is uniform and equal to one half that in the bulk

injector material (Figure 5(b)) In contrast, a thin

layer implants a uniform concentration of He to a

depth of the Ra ti In this case, the He concentration

in both the implantation layer and specimen is equal

and lower than in the bulk (XHei) as XHes¼ tiXHei/

2Ra (Figure 5(c)) Thus, the He/dpa ratio can be

controlled by varying the concentration of the

iso-tope that undergoes n,a reactions with thermal

neu-trons, ti, and the thermal to fast flux ratio

ISHI experiments were, and continue to be, carried

out in HFIR using thin (0.8–4 mm) NiAl coating layers

on TEM disks for a large matrix of Fe-based alloys for

a wide range of dpa, He/dpa (<1–40 appm He/dpa),

and irradiation temperatures In this case, 4.8 MeV

a-particles produce uniform He concentration to a

depth of 5–8 mm (Figure 5(c)) Further details are

given elsewhere.50 The first results of in situ

implan-tation experiments in HFIR have been reported and

are discussed inSection 1.06.6.23,51–53The technique

has also been used to implant SiC fibers irradiated

in HFIR.50 More recently, the two-sided thick Ni

implanter method was used to produce He/dpa

ratios 25 appm/dpa in thin areas of wedge-shaped

specimen alloys irradiated in the advanced test reactor

to7 dpa over a range of high temperatures.54

1.06.2.4 Spallation Proton–Neutron

Irradiations, SPNI

High fluxes of neutrons can be generated by

high-energy and current (power) proton beams via

spall-ation reactions that fragment the atomic nuclei

heavily in a heavy metal target (like W, Pb, and

Hg) At 500 MeV, these reactions produce10

neu-trons per proton Applications of spallation sources

include neutron scattering, nuclear waste

transmu-tation, and driving subcritical fission reactors A key

challenge to developing advanced high-power,

long-lived spallation source targets is the ability of

structural alloys to withstand severe radiation

dam-age, corrosive fluids, and mechanical loading Most

notably, radiation damage in spallation source

irradia-tions, produced by the neutrons and protons, results

in both high dpa and concentrations of transmutation

products, including He and H (see Table 1) As a

consequence, there have been and continue to be

international programs on radiation effects in SPNI

environments, beginning with a large program in

Los Alamos Neutron Science Center (LANSCE)

in 1996 and 1997,55 followed by a continuing

SINQ (Swiss Spallation Neutron Source) Target

Irradiation Program – STIP, started in 1998, that tinues to this day, at the Paul Sherrer Institute, inSwitzerland, involving an international collaboration

con-of ten institutions in China, Europe, Japan, and theUnited States.56,57

Because of the accelerator production of tritium get application, the irradiation temperature LANSCEexperiment was up to164C The highest damagelevels, mostly produced by protons, were 12 dpaand 180 appm He/dpa.4

tar-About 20 materials wereirradiated in a variety of specimen configurations inthis study

The maximum damage levels in the STIP-I to -IVirradiations56,57 were  25 dpa and 2000 appm He.The corresponding temperatures ranged from 80 to

800C, but most specimens were nominally diated between 100 and 500C The temperaturesdirectly depend on the high nuclear heating rates

irra-in the target, and both varied by 15% during the2-year irradiation; and, in the case of STIP-I and-IV,some capsules experienced a significant overtem-perature transient The high heating rates also result

in fairly large uncertainties in the temperatures ofindividual specimens Note that the temperaturecontrol in the most recent STIP-V experiment wassignificantly better than that in previous studies.Over 60 elemental metals and alloys, ceramics, andcomposites have been irradiated in the STIP-I to -V,

in the form of miniaturized specimens for both structural studies and mechanical testing, includingtensile, fatigue, fracture toughness, and CharpyV-notch (CVN) measures of the DBTT Some speci-mens were irradiated in contact with stagnant liquid

micro-Hg, PbBi eutectic, and Pb The STIP database isdiscussed inSection 1.06.4

1.06.2.5 Proposed FutureNeutron-Irradiation FacilitiesThe proposed International-Fusion-Material-Irradiation-Facility (IFMIF) is an accelerator-drivenneutron source that is based on the proton-strippingreaction.58,59 Neutrons are generated by a beam of

40 MeV deuterons that undergo a proton-strippingreaction when they interact with a flowing liquidlithium jet target The resulting neutron beam has

a spectrum with a high-energy tail above a peakaround 14.60 As in the case of D, T, and spallationreactions, these neutrons are well above the thresh-old energy for n,a reactions; thus, IFMIF producesfusion like He/dpa ratios at high dpa rates Thenuclear reaction kinematics and limited neutron

target source dimensions result in an IFMIF

irradia-tion volume with large gradients over a high-flux

region just behind the target Two 125 mA beams

on the Li target produce an 500 cm3

region withdpa rates of 20–50 fpy1 (full power year) at He/

dpa 12 appm dpa1

The medium flux region,from 1.0 to 20 dpa fpy1, is much larger with a

volume of6000 cm3

.The Materials Test Station is a new spallation

neutron source, proposed by Los Alamos National

Laboratory, that is primarily intended to irradiate

fast reactor materials and fuels.61 The LANSCE

linear accelerator will produce a 1-MW proton

beam to drive the spallation neutron source with a

fast reactor like spectrum and a high-energy tail up

to 800 MeV The high-energy tail neutrons produce

a He/dpa 6–13 appm dpa1 close to that for a

fusion first wall The dpa rates are 7.5–15 fpy1

in a 200 cm3irradiation volume and 2.5–12.5 fpy1in

an additional volume of 450 cm3 An accelerator

upgrade to 3.6 MW would increase these dpa rates to

20–40 fpy1and 5–16 fpy1, respectively

In both cases, the limited volume for high-flux

accelerated irradiations presents a great challenge to

developing small specimen mechanical test

meth-ods62,63 and experimental matrices64 that can

pro-duce the database needed for materials qualification

The database will require irradiations over a range

of temperatures for tensile, fracture toughness,

fatigue, and creep property characterization Indeed,

it is clear that qualifying materials for fusion

ap-plications will require a new paradigm of linking

comprehensive microstructural characterization and

physically based predictive modeling tools to

multi-scale models and experiments of structure-sensitive

properties as input into engineering models of

mate-rials performance

A variety of proposals have been made to develop

volumetric D–T fusion devices such as the Fusion

Nuclear Science Facility (FNSF), which would

pro-vide a basis to test components and materials.65

In some cases, these devices would address a much

broader array of issues, such as tritium breeding and

extraction In most cases, the fusion source would be

driven by external energetic D beams Discussing the

details of such proposed devices is far beyond the

scope of this chapter However, we note that from a

materials development perspective, such devices

would be useful to the extent that they are steady

state, operate with very high-duty factors, and

pro-duce sufficient wall loading to deliver high He and

dpa exposures

1.06.2.6 Characterization of He and

He BubblesThe primary techniques used to characterize thebehavior of He and He bubbles in materials includeTEM, small-angle neutron scattering (SANS), posi-tron annihilation spectroscopy (PAS), and thermaldesorption spectroscopy (TDS) All of these techni-ques, and their numerous variants, have individuallimitations Complete and accurate characterization

of He transport and fate requires a combination ofthese methods; however, such complementary toolsare seldom employed in practice Note that there arealso a variety of other methods of studying helium insolids that cannot be discussed due to spacelimitations

TEM, with a practical resolution limit of about

1 nm, is the primary method for characterizing Hebubbles Bubbles and voids are most frequentlyobserved by bright field (BF) ‘through-focus’ imaging

in thin regions of a foil The Fresnel fringe contrastchanges from white (under) to black (over) as a func-tion of the focusing condition The bubble size isoften taken as the mid diameter of the dark underfocus fringe Two critical issues in such studies areartifacts introduced by sample preparation, whichproduce similar images and determine the actualsize, especially below 2 nm.66–68 Electron energy-loss spectroscopy (EELS) can be used to estimatethe He pressure in bubbles.69,70

SANS provides bulk measures of He bubblemicrostructures In ferromagnetic steels, both nuc-lear and magnetic scattering cross-sections can bemeasured by applying a saturating magnetic field(2T) perpendicular to the neutron beam Thecoherent scattering cross-section variations with thescattering vector are fit to derive the bubble sizedistribution, with a potential subnanometer resolu-tion limit.71 The magnitude of the scattering cross-section is proportional to the square of the scatteringlength density contrast factor between the matrix andthe bubble times the total bubble volume fraction.Since the magnetic scattering factor contrast is known(He is not magnetic), the bubble volume fraction,and corresponding number densities, can be directlydetermined by SANS The nuclear scattering cross-section provides a measure of the He density in thebubbles Thus, the variation in the ratio of the nuclear(He dependent) to magnetic (He independent) scat-tering cross-sections with the scattering vector can beused to estimate the He pressure (density) as a func-tion of the bubble size.71,72Some studies have shown

that SANS bubble size distributions are in good

agreement with TEM observations,73,74while others

show considerable differences for small (<2 nm)

bubbles.72 Limitations of SANS include

distin-guishing the bubble scattering from the contributions

of other features; note that, in many cases, these

features may be associated with the bubbles Other

practical issues include measurements over a

suffi-cient range of scattering vectors and handling of

radioactive specimens Note that small-angle X-ray

scattering studies can also be used to characterize He

bubbles, and this technique is highly complementary

to SANS measurements

PAS is a powerful method for detecting cavities

that are smaller than the resolution limits of TEM

and SANS Indeed, positrons are very sensitive to

vacancy type defects, and even single vacancies can

be readily measured in PAS studies.75,76PAS can also

be used to estimate the He density, or He/vacancy

ratio, in bubbles.77In the case of He-free cavities, the

positron lifetime increases with increasing the

nano-void size, saturating at several tens of vacancies

How-ever, in the case of bubbles, the lifetime decreases

with increasing He density In principle, positron

orbital electron momentum spectra (OEMS) can also

provide element-specific information about the

anni-hilation site.78Thus, for example, OEMS might detect

the association of a bubble with another

microstruc-tural feature Limitations of positron methods include

that they generally do not provide quantitative and

unique information about the cavity parameters

The application of PAS to studying He in steels has

been very limited to date

TDS measures He release from a sample as a

function of temperature during heating or as a

function of time during isothermal annealing The

time–temperature kinetics of release provides

indi-rect information about He transport and trapping/

detrapping processes For example, isothermal

anneal-ing experiments on low-dose (<2 appm) a-implanted

thin Fe and V foils showed that substitutional helium

atoms migrate by a dissociative mechanism, with

dissociation energies of about 1.4 eV, and that

dihe-lium clusters are stable up to 637 K in Fe and up to

773 K in V.79 At higher concentrations in irradiated

alloys, He can be deeply trapped in cavities (bubbles

and voids); in this case, He is significantly released

only close to melting temperatures.80,81 Given the

complexity and multitude of processes encountered

in many studies, it is important to closely couple

TDS with detailed physical models.82,83Techniques

that can quantify He concentrations at small levels

used in TDS can also be used to measure the total Hecontents in samples that are melted.81

In summary, a variety of complementary ques can be used to characterize He and He bubbles

techni-in structural materials A good general reference forthese techniques and He behavior in solids can befound in Donnelly and Evans.84TEM and SANS canmeasure the number densities, size distributions, andvolume fractions of bubbles, subject to resolutionlimits and complicating factors The correspondingdensity of He in bubbles can be estimated byTEM–EELS, SANS, and PAS TDS can provideinsight into the He diffusion and trapping/detrappingprocesses Unfortunately, there have been very lim-ited applications in which various methods have beenapplied in a systematic and complementary manner.Major challenges include characterizing subnan-ometer bubbles in complex structural alloys, includ-ing their association with various microstructuralfeatures

1.06.3 A Review of Helium Effects Models and Experimental

Observations1.06.3.1 BackgroundClearly, it is not possible to cite, let alone describe

in detail, the extensive literature on He effects inirradiated alloys This literature encompasses bothmechanical properties, especially HTHE, and theeffects of He on microstructural evolutions, particu-larly void swelling There is also a more limitedliterature on fundamental processes and propertiesrelated to He in solids, like desorption measurementsand He solution, binding, and diffusion activationenergies Much of previous work pertains to fcc(face-centered cubic) AuSS, which is one of interestfor fast reactor cladding applications However, stan-dard AuSS, like AISI 316 (Fe–0.17Cr–0.12Ni–bal

Mo, Si, Mn, ) are highly prone to both HTHEand void swelling Thus, advanced AuSS and bccFMS have supplanted conventional AuSS as theleading candidates for nuclear applications Never-theless, conventional AuSS alloys nicely illustratethe damaging effects of He (see Section 1.06.3.2

and following), which are both subtle and cantly mitigated in advanced steels Swelling andHTHE resistance are largely due to microstructuraldesigns that manage He

signifi-Particular emphasis in this section is placed onthe critical bubble model (CBM) concept of the

transition of stable He bubbles to unstably growing

voids, both under irradiation-driven displacement

damage, and stress-driven growth of grain boundary

creep cavities We believe this focus is appropriate,

since it seems that many current modeling efforts

have lost connection with the basic

thermody-namic–kinetic foundation for understanding He

effects provided by the CBM concept and the large

body of earlier related research

The organization of this section is as follows

Section 1.06.3.2 outlines the historical motivation

for concern about He effects in structural alloys,

including examples of HTHE and void swelling

Section 1.06.3.3describes the mechanisms of swelling

and its relation to He and He bubbles, especially

in AuSS.Section 1.06.3.4presents a quantitative CBM

for void nucleation and a simple rate theory (RT)

model of swelling Section 1.06.3.5 summarizes the

implications of the experimental observations and

models, and the development of irradiation-resistant

alloys Sections 1.06.3.6 and 1.06.3.7 discuss the

application of the CBM to HTHE and corresponding

experimental observations, respectively

1.06.3.2 Historical Motivation for

He Effects Research

The primary motivation for the earliest research was

the observation that even a small concentration of

bulk He, in some cases in the range of one appm or

less, generated in fission reactor irradiations of AuSS,

could lead to HTHE, manifested as significant

re-ductions in tensile and creep ductility and creep

rupture times The degradation of these properties

coincided with an increasing transition from

trans-granular to intertrans-granular rupture.10,85–89 HTHE is

attributed to stress-driven nucleation, growth, and

coalescence of grain boundary cavities formed on the

He bubbles The early studies included mixed

spec-trum neutron irradiations that produce large amounts

of He in alloys containing Ni and B.Figure 6shows

one extreme example of the dramatic effect of HTHE

on creep rupture times for a 20% cold-worked (CW)

316 stainless steel tested at 550C and 310 MPa

following irradiations between 535 and 605C in the

mixed spectrum HFIR that produced up to 3190 appm

He and 85 dpa.88At the highest He concentration, the

creep rupture time is reduced by over four orders of

magnitude, from several thousand to less than 0.1 h

A comprehensive review of the large early body of

research on He effects on mechanical properties

of AuSS can be found in Mansur and Grossbeck.11

The early fission reactor irradiations research

on HTHE was later complemented by extensiveaccelerator-based He ion implantation experiments,primarily carried out in the 1980s (see Schroeder andBatfalsky90and Schroeder, Kesternich and Ullmaier91asexamples) but that have continued to recent times.92HTHE models were developed during this period,primarily in conjunction with the He ion implanta-tion experiments.93–100The He implantation studiesand models are discussed further inSections 1.06.3.6and 1.06.3.7 A more general review of He effects,again primarily in AuSS, can be found in Ullmaier99and a comprehensive model-based description of thebehavior of He in metals in Trinkaus.96

Research on He effects was also greatly stimulated

by the discovery of large growing voids in irradiatedAuSS.101 As an example,Figure 7(a) shows swellingcurves for a variety of alloys used in reactor applica-tions.102–104Figure 7(b)illustrates macroscopic conse-quences of this phenomenon in an AuSS.105Figure 8

shows a classical micrograph of a solution annealed (SA)AuSS with dislocation loops and line segments, preci-pitates, precipitate-associated and matrix voids, andpossibly He bubbles (the small cavities) RT-basedmodeling studies of void swelling began in the early1970s,106,107peaking in the 1980s, and continuing up torecent times.108Most of the earliest models emphasizedthe complex effects of He on void swelling.109,110

As discussed in more detail below, these and latermodels rationalized many observed swelling trendsand also suggested approaches to developing moreswelling-resistant AuSS, largely based on trapping

Figure 6 Creep rupture time for CW 316 AuSS for various

He contents following HFIR irradiation Reproduced from Bloom, E E.; Wiffen, F W J Nucl Mater 1975, 58, 171.

He in small bubbles at the interfaces of fine-scale

precipitates Reviews summarizing mechanisms and

modeling of swelling carried out during this period,

including the role of He, can be found in Odette,111

Odette, Maziasz and Spitznagel,112 Mansur,113

Mansur and Coghlan,114Freeman,115and Mansur.116

Reviews of experimental studies of void swelling can

be found in later studies by Maziasz16 and Zinkle,Maziasz and Stoller.117

Further motivation for understanding He effectswas stimulated by a growing interest in the effects ofthe very high transmutation levels produced in fusionreactor spectra (see Section 1.06.1).89,99,111,112,118Experimental studies comparing microstructuralevolutions in AuSS irradiated in fast (lower He) andmixed spectrum (high He) reactors provided keyinsight into the effects of He.16,119,120Helium effectswere also systematically studied using dual-beamHe–heavy ion CPI.26,121–129

Beginning in the mid-1970s, a series of studiesspecifically addressed the critical question of how touse fission reactor data to predict irradiation effects

in fusion reactors,15,109–112,118,130–133 and this topicremains one of intense interest to this day An indica-tion of the complexity of He effects is illustrated in

Figure 9, showing microstructures in a dual-beamHe–heavy ion irradiation of a SA AuSS to 70 dpa and

625C at different He/dpa.123In this case, voids donot form in the single heavy ion irradiation without

He At intermediate levels, of 0.2 appm/dpa, largevoids are observed, resulting in a net swelling of3.5% At even higher levels of 20 appm/dpa, thevoids are more numerous, but smaller, resulting

in less net swelling of 1.8% These observationsshow that some He promotes the formation ofvoids, but that higher amounts can reduce swelling

Figure 10shows the effect of various conditions for

2 1/4Cr–1Mo PCA 316SS

Unirradiated fuel cladding

Figure 7 (a) Typical swelling versus dpa curves for standard 316 AuSS (316SS), a swelling-resistant AuSS (PCA), and various ferritic–martensitic steels (HT9, 9C–1Mo, and 21/4C–1Mo) Reproduced from Gelles, D S J Nucl Mater 1996,

233, 293; Garner, F A.; Toloczko, M B.; Sencer, B H J Nucl Mater 2000, 276, 123; Klueh, R L.; Harries, D.R.

High-Chromium Ferritic and Martensitic Steels for Nuclear Applications; American Society for Testing and Materials: Philadelphia, 2001 (b) Illustration of macroscopic swelling Reproduced from Straalsund, J L.; Powell, R.W.;

Chin, B A J Nucl Mater 1982, 108–109, 299.

Figure 8 Typical microstructures observed in irradiated

solution annealed (SA) AuSS composed of dislocation

loops, network dislocations, precipitates, and voids,

including both those in the matrix and associated with

precipitates (by courtesy of J Stiegler).

introducing 1400 appm He coupled with a 4 MeV Ni

ion irradiation of a swelling-prone model SA AuSS to

70 dpa at 625C.125In this case, the swelling is largest

(18% due to voids) with no implanted He and

smallest (1%) with He preimplanted at ambient

temperature due to the very high density of

bub-bles These results also show that voids can form

at sufficiently high CPI damage rates without

He, probably assisted by the presence of impuritieslike oxygen and hydrogen Most notably, however,the swelling decreases with increasing bubble num-ber densities

The emphasis of more recent experimentalwork has been on SPNI that generate large amounts

100 nm

Figure 9 The effects of the He/dpa ratio on void swelling in a dual ion-irradiated AuSS at 70 dpa and 625C The void volume is largest at the intermediate He/dpa ratio of 0.2 appm dpa1, which falls between the limits of 0 and 20 appm dpa1 Reproduced from Kenik, E A.; Lee, E H In Irradiation Effects on Phase Stability; Holland, J R., Mansur, L K., Potter, D I., Eds.; TMS-AIME, Pittsburgh PA, 1981; p 493.

(d) (c)

He cold preimplanted at 20C (1%) Reproduced from Packan, N H.; Farrell, K J Nuc Mat 1979, 85–86, 677–681.

of He, compared with fission reactors, as well as

dis-placement damage (seeSection 1.06.4) The SPNI

studies have focused on mechanical properties and

microstructures, primarily at lower irradiation

tem-peratures, nominally below the HTHE regime In

addition, as discussed inSection 1.06.2, a previously

proposed in situ He injection technique31,49 has

recently been developed and implemented to study

He–displacement damage interactions in mixed

spec-trum reactor irradiations (e.g., HFIR) at

reactor-relevant dpa rates.23,51–53 As discussed in Section

1.06.5, recent modeling studies have emphasized

electronic and atomistic evaluations of the energy

parameters that describe the behavior of He in solids,

including interactions with point and extended

defects134–136 (and see Section 1.06.5) The refined

parameters are being used in improved RT and Monte

Carlo models of He diffusion and clustering to form

bubbles on dislocations, precipitates, and GBs, as well

as in the matrix, as discussed inSection 1.06.6

It is again important to emphasize that the broad

framework for predicting He effects is an

under-standing and modeling of its generation, transport,

and fate, as well as the multifaceted consequences of

this fate We begin with a discussion of the role of

He in void swelling and other microstructural

evo-lution processes We then return to the issue of

HTHE

1.06.3.3 Void Swelling and Microstructural

Evolution: Mechanisms

The previous section included examples of void

swelling Voids result from the clustering of vacancies

produced by displacement damage, as characterized

by the number of dpa Atomic displacements produce

equal numbers of vacancy and SIA defects As noted

previously, descriptions of swelling mechanisms,

including the role of He, can be found in excellent

reviews.113–116Early RT models showed that swelling

is due to an excess flux of vacancies to voids, which is

a consequence of a corresponding excess flux of

SIA to biased dislocation sinks.106,107 Typical

dis-placement rates (Gdpa) in high-flux reactors (HFR)

are 10–6

–10–7dpa s1 Hence, an irradiation time

of 108s (3 years) produces up to 100 dpa Only

about 30% of the primary defects survive

short-time cascade recombination.137The residual defects

undergo long-range migration and almost all either

recombine with each other or annihilate at sinks

However, a small fraction of SIA and vacancies

cluster to form dislocation loops and cavities,

respectively Ultimate survival of only 0.1% of thedpa in the form of clustered vacancies leads to 10%swelling at 100 dpa

Classical models138,139 demonstrated that for thelow Gdpain neutron irradiations, homogeneous voidnucleation rates are very low at temperatures in thepeak swelling regime for AuSS between about 500and 600C However, heterogeneous void nucleation

on He bubbles is much more rapid than homogeneousnucleation.109Indeed, nucleation is not required whenthe He bubbles reach a critical size (r*) and He content(m*) The CBM concept has provided a great deal ofinsight into the effects of He on swelling.15,109–

112,114,118,130–133,140–151

In particular, the CBM lized the extended incubation dpa in fast reactorirradiations prior to the onset of rapid swelling Aspreviously shown in Figure 2(d) and 2(e), here weclearly distinguish between bubbles, which shrink orgrow only by the addition of He, from larger voids,which grow unstably by the continuous accumulation

rationa-of vacancies In the case rationa-of bubbles, the gas pressure (p)plus a chemical stress due to irradiation (seeSection1.06.3.4) just balances the negative capillary stress 2g/

rb, where g is the surface energy and rb the bubbleradius By definition drb/dt ¼ 0 for bubbles, while thegrowth rate is positive and negative for cavities thatare slightly smaller and larger than rb, respectively Inthe case of voids (v), drv/dt is positive at all rvgreaterthan the critical radius Voids are typically underpres-surized with p<< 2g/rv More generally, cavitiesinclude both bubbles and voids and can contain anarbitrary number of vacancies (n) and He atoms (m).The evolution of the number of discrete vacancy(n)–He (m) cavities, N(n,m), in a two-dimensionalnm space can be numerically modeled using clusterdynamics (CD) master equations In the simplest case

of growth or shrinkage by the absorption or emission

of the monomer diffusing species (He, vacancies, andSIA), an ordinary differential equation (ODE) foreach n,m cluster, dN(n,m)/dt, tracks the transitionsfrom and to all adjacent cluster classes (n  1 and

m  1), as characterized by He, vacancy, and SIArates of being absorbed (bHe,v,i) and the vacancyemission (av) rate, as

He may be dynamically resolutioned by

displace-ment cascades.152,153There are a total of nmax mmax

such coupled ODEs The rate coefficients, a and b,

are typically computed from solutions to the

diffu-sion equation, to obtain cavity sink strengths,107,113–116

along with the concentrations of the various

spe-cies in the matrix and vacanspe-cies in local

thermody-namic equilibrium with the cavity surface The local

vacancy concentrations are controlled by the surface

energy of the void, g, via the Gibbs Thomson effect,

and the He gas pressure.109,139,141Conservation

equa-tions are used to track the matrix concentraequa-tions of

the mobile He, vacancies, and SIA based on their

rates of generation, clustering, loss to all the sinks

present, and, for the point defects, vacancy–SIA

recombination.144

Similar RT CD methods can also be used to

simultaneously model SIA clustering to form

dislo-cation loops, as well as climb driven by the excess flux

of SIA to network dislocations.111,144In AuSS, loop

unfaulting produces network dislocations, and

net-work climb results in both production and

annihila-tion of the network segments with opposite signs

Thus, dislocation structures evolve along with the

cavities

However, the a and b rate coefficients depend on a

number of defect and material parameters that were

not well known during the period of intense research

on swelling in the 1970s and 1980s, and integrating

a very large number of nmax mmaxcoupled ODEs

was computationally prohibitive at the time these

models were first proposed One simplified approach,

based on analytically calculating the rate of void

nucleation on an evolving distribution of He bubbles,

coupled to a void growth model provided

consider-able insight into the role of He in void swelling.109,111

These early models, which also included parametric

treatments of void and bubble densities,110–112 led

to the correct, albeit seemingly counterintuitive,

predictions that higher He may decrease, or even

totally suppress, swelling in some cases, while in

other cases swelling is enhanced, or remains

unaf-fected These early models also predicted the

forma-tion of bimodal cavity size distribuforma-tions, as confirmed

by subsequent modeling studies and many

experi-mental observations.111,112,114,118,131,133,134,148,151

Most aspects of void formation and swelling

incubation can be approximately modeled based

on the CBM concept A critical bubble is one that

has grown to a radius (r*) and He content (m*),

such that, upon the addition of a single He atom

or vacancy, it immediately transforms into an

unstably growing void (see Figure 2(d) and 2(e))without the need for statistical nucleation Notethat while a range of n and m clusters are energeti-cally highly favorable compared with equal numbers

of He atoms and vacancies in solution, bubbles resent the lowest free energy configuration in thevacancy-rich environments, characteristic of mate-rials experiencing displacement damage That is,

rep-in systems that can swell due to the presence ofsink bias mechanisms that segregate excess fractionsSIA and vacancies to different sinks and at lowreactor relevant damage rates, cavities primarilyevolve along a bubble path that can ultimately end

in a conversion to voids

1.06.3.4 The CBM of Void Nucleation and

RT Models of SwellingFor purposes of discussion and simplicity, the effects

of cascade defect clustering and recombination areignored, and we consider only single mobile vacan-cies and SIA defects in the simplest form of RT toillustrate the CBM At steady state, isolated vacanciesand SIA are created in equal numbers and annihilate

at sinks at the same rate Dislocation–SIA interactionsdue to the long-range strain field result in an excessflow of SIA to the ‘biased’ dislocation sinks and, thus,leave a corresponding excess flow of vacancies toother neutral (or less biased) sinks, (DvXv DiXi).Here, D is the defect diffusion coefficient and X thecorresponding atomic fraction Assuming that thedefect sinks are restricted to bubbles (b), voids (v),and dislocations (d), the DX terms are controlled bythe corresponding sink strengths (Z): Zb (4prbNb),

Zv(4prvNv) for both vacancies and SIA; Zd(r) forvacancies and Zdi(r [1 þ B]) for SIA Here, r and Nare the size and number densities of bubbles andvoids, r is the dislocation density, and B is a biasfactor At steady state,

DvXv DiXi¼½GdpaZdi=fðZbþ Zvþ ZdÞ

ðZbþ Zvþ Zd½1 þ BÞg þ DvXve ½2Here, DvXve represents thermal vacancies that exist

in the absence of irradiation and (1/3) is the ratio

of net vacancy to dpa production In the absence

of vacancy emission, the excess flow of vacanciesresults in an increase in the cavity radius (r) at arate given by

dr=dtþ¼ ðDvXv DiXiÞ=r ½3

However, cavities also emit vacancies, resulting in

shrinkage at a rate given by the capillary

approxi-mation as

dr=dt¼ DvXveexp½ð2g=r  pÞO=kT=r ½4

The Xveexp[(2g/r  p)O/kT] term is the

concentra-tion of vacancies in local equilibrium at the cavity

surface, and O is the atomic volume Thus, the net

cavity growth rate is

dr=dt ¼ Df vXv DiXi DvXve

exp½ð2g=rc pÞO=kTg=r ½5

Growth stability and instability conditions occur at

the dr/dt ¼ 0 roots ofeqn [5], when

DvXv DiXi DvXveexp½ð2g=r  pÞO=kT ¼ 0 ½6a

Note that DvXveis approximately the self-diffusion

coefficient, Dsd The He pressure is given by

Here, k is the real gas compressibility factor

Equa-tion [6a]can be expressed in terms of the effective

vacancy supersaturation,

L¼ ðDvXv DiXiÞ=Dsd ½6c

The bubble and critical radius occur at

L exp½ð2g=r  pÞO=kT ¼ 0 ½6d

In the absence of irradiation (or sink bias), L¼ 1 and

all cavities are bubbles in thermal equilibrium, at

p ¼ 2g/rb Assuming an ideal gas, k¼ 1,eqn [6d]can

be written as

2g=r  ð3mkTÞ=ð4pr3Þ  kT lnðLÞ=O ¼ 0 ½7a

Note that kT ln(L)/O is equivalent to a chemical

hydrostatic tensile stress acting on the cavity

Rear-ranging eqn [7a] leads to a cubic equation with

the form,

rc3þ c1r2þ c2¼ 0 ½7b

c1¼ ½2gO=½kT lnðLÞ ½7c

c2¼ ½3mO=½4p lnðLÞ ½7d

As shown inFigure 2(d) and 2(e),eqn [7b]has up to

two positive real roots The smaller root is the radius

of a stable (nongrowing) bubble containing m He

atoms, rb, and the larger root, rv, is the

corresponding critical radius of a (m*,n*) cavity

that transforms to a growing void Voids can, and

do, also form by classical heterogeneous nucleation

on bubbles between rband rv.109,132,141However, asshown in Figure 2(d) and 2(e), as m increases, rbincreases and rvdecreases, until rb¼ rv¼ r* at thecritical m* An example of the dr/dt curves assumingideal gas behavior taken from Stoller133is shown in

Figure 11 for parameters typical of an irradiatedAuSS at 500C with L¼ 4.57 The corresponding r*and m* are 1.50 nm and 931, respectively

The critical bubble parameters can be evaluatedfor a realistic He equation of state using mastercorrection curves, y1(ln L) for m* and y2(ln L) forr*, based on high-order polynomial fits to numericalsolutions for the roots ofeqn [7b].143A simpler ana-lytical method to account for real gas behavior based

on a Van der Waals equation of state can also beused.151The results of the two models are very simi-lar.143 Voids often form on critical bubbles located

at precipitate interfaces at a smaller m* than in thematrix.142 This is a result of the surface–interfacetension balances that determine the wetting angle be-tween the bubble and precipitate interface (see

Figure 20(b)) Formation of voids on precipitatescan be accounted for by a factor Fv 4p/3, reflectingthe smaller volume of a precipitate-associated critical

1.25

Figure 11 The CBM predictions of radial growth rate of cavities as a function of their He content, m, normalized by the critical He content for conversion of bubbles to growing voids, m* The effective supersaturation is (L ¼ 4.57), temperature is (T ¼ 500  C), and surface energy is (g ¼ 1.6 J m 2 ) The two roots in the case of m < m* are for bubbles and voids, respectively Cavities can transition from bubbles to voids by classical nucleation or reach a m* by He additions The effect of He on the growth of voids is minimal

at sizes larger than about 2.5 nm in this case.

bubble at r*, compared with a spherical bubble in the

matrix, with Fv¼ 4p/3 Note that the critical matrix

and precipitate-associated bubble have the same r*

The m* and r* are given by

m ¼ ½32Fvy1g3O2=½27ðkTÞ3ðlnðLÞ2Þ ½8a

r ¼ ½4y2gO=½3kT lnðLÞ ½8b

Figure 12shows m*, r* as a function of temperature

for typical parameters for SA AuSS steels taken from

Stoller.133More generally, L can simply be related to

Dsd, , Gdpa, B, and the sink’s various strengths

Assuming Zv 0 during the incubation period,

Thus, to a good approximation, the primarymechanism for void formation in neutron irradiations

is the gradual and stable, gas-driven growth of bles by the addition of He up to near the critical m*

Figure 13 Critical bubble predictions of m* and r* as a function of the bubble density (N b ) at 773 and 873 K for

parameters typical of a solution annealed AuSS taken from Stoller.133At low N b the bubble sink strength is lower than that for dislocations, hence bubbles have little effect on m* and r* However, at higher bubble densities the bubbles become the dominant sink resulting in rapid increases in m* and r*.

Although nucleation is rapid on bubbles with m close

to m*, modeling void formation in terms of evaluating

the conditions leading to the direct conversion of

bubbles to voids is a good approximation.132 The

corresponding incubation dpa (dpa*) needed for Nb

bubbles to reach m* is given by

dpa ¼ m½ Nb= He=dpa½  ½10

Figure 14 shows dpa* for He/dpa¼ 10 appm dpa1

and the same AuSS parameters used in Figure 13

Clearly high Nbincreases the dpa*, both by

increas-ing the neutral sink strength, thus decreasincreas-ing L,

and partitioning He to more numerous bubble sites

Indeed, in the bubble-dominated limit, Zb>> Zdand

Zv, the dpa* scales with Nb

5

!The CBM also predicts bimodal cavity size dis-

tributions, composed of growing voids and stable

bubbles Once voids have formed, they are sinks for

both He and defects, and thus slow and eventually

stop the growth of the bubbles to the critical size and

further void formation.Figure 15shows a bimodal

cavity versus size distribution histogram plot for

a Ni–He dual ion irradiation of a pure stainless

steel,114 and many other examples can be found in

the literature111,112,114,133,153Figure 16(a)shows low

He favors the formation of large voids in a CWstainless steel irradiated in experimental breederreactor-II (EBR-II) to 40 dpa at 500C and 43 appm

He, resulting in12% swelling, whileFigure 16(b)

shows that the same alloy irradiated in HFIR at 515–

540C to 61 dpa and 3660 appm He has a muchhigher density of smaller cavities, resulting in only2% swelling.16

Thus, while He is generally necessary for voidformation, very high bubble densities can actuallysuppress swelling for the same irradiation conditions

as also shown previously inFigures 9 and 10 Thiscan lead to a nonmonotonic dependence of swelling

on the He/dpa ratio One example of a model diction of nonmonotonic swelling is shown in Fig-ure 17.154 Note that unambiguous interpretations ofneutron-irradiation data are often confounded byuncertainties in irradiation temperatures and complextemperature histories.155,156However, the suppression

pre-of swelling by high Nbis clear even in these cases.Bubble sinks can also play a significant role in thepost-incubation swelling rates Neglecting vacancyemission from large voids, and using the same assump-tions described above, leads to a simple expressionfor the overall normalized swelling rate _S, the rate of

Figure 14 Predicted incubation dpa* for the onset of void

swelling as a function of the density (N b ) of 1 nm at 773 and

873 K for parameters typical of a solution annealed AuSS

taken from Stoller 133 The dpa* increases linearly with N b at

lower bubble densities, simply because the He partitions to

more sites However, in the bubble sink dominated regime,

dpa* scales with N 5 The horizontal dashed line shows a

a Ni–He dual ion-irradiated AuSS at 670C, 10 dpa, and a

20 appm He/dpa Reproduced from Mansur, L K.; Coghlan, W A J Nucl Mater 1983, 119, 1.

increase in total void volume per unit volume divided

by the displacement rate as

S_ ¼ ½BZdZv= Z½ð bþ Zvþ ZdÞ Zð dð1þ BÞ þ Zvþ ZbÞ

½11

Figure 18 shows _S for B ¼ 0.15 and  ¼ 0.3 as a

function of Z/Z , with a peak at Z ¼ Z and

Zb 1, representing the case when nearly all thebubbles have converted to voids and balanced voidand dislocation sink strengths The _S decreases athigher and lower Zv/Zd.Figure 18also shows _S as

a function of Zv/Zdfor a range of Zb/Zv Increasing

Zbwith the other sink strengths fixed reduces the _S

in the limit scaling with 1=Z2 These results againshow that significant swelling rates require some

50

SA FFTF ORR HFIR Model predictions

550 ⬚C, 75 dpa CW 316

He/dpa ratio (appm He/dpa)

PCA, 500–520 ⬚C, 11–13 dpa

Figure 17 Data for irradiations at 500–520C of CW and SA AuSS suggesting that swelling peaks at an intermediate He/dpa ratio, reasonably consistent with the trend of model predictions (lines) at higher temperature and dpa.

Reproduced from Stoller, R E J Nucl Mater 1990, 174(2–3), 289.

bubbles to form voids with a sink strength of Zvthat is

not too small (or large) compared with Zd However, a

large population of unconverted bubbles, with a high

sink strength Zb, can greatly reduce swelling rates

A significant advantage of the CBM is that it

requires a relatively modest number of parameters,

and parameter combinations, that are generally

rea-sonably well known, including for defect production,

recombination, dislocation bias, sink strengths,

inter-face energy, and Dsd Potential future improvements

in modeling bubble and void evolution include better

overall parameterization using electronic–atomistic

models, a refined equation of state at small bubble

sizes, and precipitate specific estimates of Fvbased on

improved models and direct measurements Further, it

is important to note that the CBM parameters can be

estimated experimentally as the pinch-off size between

the small bubbles and larger voids.114,124,157

Application of CBM to void swelling requires

treatment of the bubble evolution at various sites,

including in the matrix, on dislocations, at precipitate

interfaces, and in GBs Increasing the He generation

rate (GHe) generally leads to higher bubble

concen-trations, scaling as Nb/ Gp

He.111,112,131–133,140,144,172The exponent p varies between limits of 0, for

totally heterogeneous bubble nucleation on a fixed

number of deep trapping sites, to >1 when the

dominant He fate is governed by trap binding gies, large He bubble nucleus cluster sizes (mostoften assumed to be only two atoms), and loss of He

ener-to other sinks Assuming the dominant fate of He is ener-toform matrix bubbles, p has a natural value of  1=2for the condition that the probability of diffusing He

to nucleate a new matrix bubble as a di-He cluster isequal to the probability of the He being absorbed in apreviously formed bubble.158

Bubble formation is also sensitive to temperatureand depends on the diffusion coefficient and mech-anism, as well as He binding energies at varioustrapping sites Substitutional He (Hes) diffuses byvacancy exchange with an activation energy of

Ehs 2.4 eV.159

For bimolecular nucleation of matrixbubbles, Nb scales as exp(Ehs/2kT ) Helium canalso diffuse as small n 2 and m 1 vacancy–Hecomplexes, but bubbles are essentially immobile atmuch larger sizes Helium is most likely initiallycreated as interstitial He (Hei), which diffuses sorapidly that it can be considered to simply partition

to various trapping sites, including vacancy traps,where Heiþ V ! Hes Note that, for interstitial dif-fusion, the matrix concentrations of Hei are so lowthat migrating Hei–Hei reactions would not beexpected to form He bubbles Thermal detrapping of

Hesfrom vacancies to form Heiis unlikely because ofthe high thermal binding energy160 and see Section1.06.5for other references) but can occur by a HesþSIA! Heireaction, as well as by direct displacementevents.152,161If Heiand Hesmaintain their identities attrapping sites, they can detrap in the same configura-tion Clustering reactions between Hes, Hei, andvacancies form bubbles at the trapping sites

Thus, He binding energies at traps are also critical

to the fate of He and the effects of temperature and

GHe Traps include both the microstructural sitesnoted above as well as deeper local traps withinthese general sites, such as dislocation jogs andgrain boundary junctions136(and seeSection 1.06.5

for other references) If the trapping energies are low,

or temperatures are high, He can recycle betweenvarious traps and the matrix a number of times before

it forms or joins a bubble However, once formedbubbles are very deep traps, and at a significant sinkdensity, they play a dominant role in the transportand fate of He

In principle, the binding energies of He clustersare also important to bubble nucleation Recent

ab initio simulations have shown that even small ters of Heiin Fe are bound, although not as strongly

clus-as He–V complexes Indeed, the binding energies of

Figure 18 Predicted swelling rate ( _ S) for various bubble

to void sink strength ratios (Z b /Z v ) as a function of the void

to dislocation sink ratio (Z v /Z d ) The highest _ S is for a low

Z b /Z v at a balanced void and dislocation sink strengths

Z v  Z b _ S decreases with increasing Z b /Z v and the

corresponding peak rate shifts to lower Z b /Z v

small HemVn complexes with n m are large (2.8–

3.8 eV),134,135suggesting that the bi- or trimolecular

bubble nucleation mechanism is a good approximation

over a wide range of irradiation conditions Further,

for neutron-irradiation conditions with low GHe and

Gdpathat create a vacancy-rich environment, it is also

reasonable to assume that He clusters initially evolve

along a bubble-dominated path

As discussed previously, the effects of higher bubble

densities on overall microstructural evolutions are

complex The observation that Nbscales as GHep relation

has been used in many parametric studies of the effects

of varying bubble and void microstructures Bubble

nucleation and growth and void swelling are

sup-pressed at very low GHe However, as noted above,

swelling can sometimes decrease beyond a critical

GHe due to higher Nb Indeed, void formation and

swelling can be completely suppressed by a very high

concentration of bubbles High bubble concentrations

can also suppress the formation of dislocation loops and

irradiation-enhanced, induced, and modified

precipi-tation associated with solute segregation, by keeping

excess concentrations of vacancies and SIA very

low.16,26,111,112,162

1.06.3.5 Summary: Implications of the

CBM to Understanding He Effects on

Swelling and Microstructural Evolution

Void swelling is only one component of

microstruc-tural and microchemical evolutions that take place in

alloys under irradiation In addition to loops and

network dislocations, other coevolutions include

sol-ute segregation and irradiation–enhanced–induced–

altered precipitation In the mid-1980s, CBM and RT

models of dislocation loop and network evolution

were self-consistently integrated in the computer

code MicroEv, which also included a parametric

treatment of precipitate bubble–void nucleation

sites.133,144Later work in the 1990s further developed

and refined this code.163A major objective of much of

this research was to develop models to make

quanti-tative predictions of the effect of the He/dpa ratios

on void swelling for fusion reactor conditions

CBMs have been used to parametrically evaluate

the effects of many irradiation variables and

ma-terial parameters15,114,118,128,129,140,149,150 as well as

to model swelling as a function of temperature, dpa

and dpa rates, and the He/dpa ratio (see both Stoller

and Odette references) The CBMs have also been

both informed by and compared with data from

experiments in both fast and mixed thermal–fast

spectrum test reactors, including EBR-II (fast), FFTF(fast), and HFIR (mixed),16,119complemented by exten-sive dual ion CPI results.26,124,125,128,129,157,164a,164–171The semiempirical CBM models and concepts ratio-nalize a wide range of seemingly complex and some-times disparate observations, including the following:

He/dpa dependence of the number densities ofbubbles and voids

including the effects of temperature and stress

tions of small He bubbles and larger voids

interfaces

by increasing GHe, depending on the combination

of other irradiation and material variables

ber of densities of bubbles

microstructural features, resulting in weaker trendtoward refinement of precipitate and loop struc-tures at higher GHeand, in the limit of very high

Nb, suppression of loops and precipitation

history of He implantation in CPI

associated with corresponding influence on cipitation, solute segregation, and the self-diffusioncoefficient

pre-scale precipitates that trap He in small interfacebubbles

compared with fcc AuSSThe concept of trapping He in a high number den-sity of bubbles to enhance the swelling and HTHEresistance (and creep properties in general) was imple-mented in the development of AuSS containingfine-scale carbide and phosphide phases Figure 19

shows the compared cavity microstructures resulting

in 6% void swelling in a conventional AuSS(Figure 19(a)) to an alloy modified with Ti andheat treated to produce a high density of fine-scaleTiC (Figure 19(b)) phases with less than 0.2%bubble swelling following irradiation to 45 dpa and

2500 appm He at 600C.172 There are many otherexamples of swelling-resistant AuSS that were suc-cessful in delaying the onset of swelling to much

higher dpa than in conventional AuSS However, as

illustrated in Figure 7, these steels also eventually

swell This has largely been attributed to

thermal-irradiation instability and coarsening of the fine-scale

precipitates that provide the swelling resistance.172

FMS are much more resistant to swelling than

advanced AuSS.15,102,104,116,128,129,162,169,174,175 The

swelling resistance of FMS, compared with AuSS,

can be attributed to a combination of their (a) lower

dislocation bias; (b) higher sink densities for

parti-tioning He into a finer distribution of bubbles, thus

increasing m*; (c) low void to dislocation sink ratios;

(d) a higher self-diffusion coefficient that increases

m*; and (e) lower He/dpa ratios.15,176However, void

swelling does occur in FMS, as well as in unalloyed

Fe,177 and is clearly promoted by higher He/dpa

ratios Higher He can decrease incubation times for

void formation and increase Zv/Zdratios closer to 1,

resulting in higher swelling rates.52,157,168–171Recent

models predict significant swelling in FMS,178and the

potential for high postincubation swelling rates in

these alloys remains to be assessed Swelling in

FMS clearly poses a significant life-limiting

chal-lenge in fusion first wall environments in the

temper-ature range between 400 and 600C

NFA, which are dispersion strengthened by a high

density of nanometer-scale Y–Ti–O-enriched features,

are even more resistant to swelling and other

mani-festations of radiation damage than FMS.22,23,51,179,180

Irradiation-tolerant alloys will be discussed in

Section 1.06.6

1.06.3.6 HTHE Critical Bubble Creep

Rupture Models

The CBM concept can also be applied to the effects

of grain boundary He on creep rupture properties

Stress-induced dislocation climb also results in

gen-eration excess vacancies that can accumulate at

growing voids In particular, tensile stresses normal

to GBs (s) generate a flux of vacancies to boundarycavity sinks, if present, and an equal, but opposite,flux of atoms that plate out along the boundary asillustrated inFigure 20(a) The simple capillary con-dition for the growth of empty cavities is the s> 2g/

r In this case of cavities containing He, the growthrate is given by

dr=dt ¼ ½ðDgbdÞ=ð4pr2Þ

f1  exp½ð2g=r  P  sÞO=kTg ½12Here Dgb and d are the grain boundary diffu-sion coefficient and thickness, respectively Thecorresponding dr/dt ¼ 0 conditions also lead to

a stable bubble (rb) and unstably growing creepcavity (r*) roots As noted previously, a vacancysupersaturation, L, produces a chemical stress that

is equivalent to a mechanical stress s¼ kT ln(L)/O.Thus, replacing ln(L) in eqn [8a] and [8b] withsO/kT directly leads to expressions for m* and r*for creep cavities

m ¼ ½32Fvpg3=½27kTs2 ½13a

This simple treatment can also be easily modified toaccount for a real gas equation of state Note that it isusually assumed that GBs are perfect sinks for bothvacancies and SIA Thus, it is generally assumed thatdisplacement damage does not contribute to the for-mation of growing creep cavities

Understanding HTHE requires a correspondingunderstanding of the basic mechanisms of creep rup-ture in the absence of He At high stresses and shortrupture times, the normal mode of fracture in AuSS

is transgranular rupture, generally associated withpower law creep growth of matrix cavities.181,182However, at lower stresses IG rupture occurs in a

0.25 mm

Figure 19 Comparison of a conventional AuSS (a) to a swelling-resistant (b) Ti-modified alloy for HFIR irradiations

at 600C to 45 dpa and 2500 appm He Reproduced from Maziasz, P J.; J Nucl Mater 1984, 122(1–3), 472.

wide range of austentic and ferritic alloys Although

space does not permit proper citation and review, it is

noted that a large body of literature on IG creep

rupture emerged in the late 1970s and early 1980s

Briefly, this research showed that under creep

condi-tions a low to moderate density of grain boundary

cavities forms (1010–1012m2), usually in

associa-tion with second-phase particles and triple-point

junctions.183–184a Grain boundary sliding results in

transient stress concentrations at these sites, and

interface energy effects at precipitates also reduce

the critical cavity volume (Fv 4p/3) relative to

matrix voids, as illustrated inFigure 20(b)

Once formed, however, creep cavities can rapidly

grow and coalesce if unhindered vacancy diffusion

and atom plating take place along clean GBs Such

rapid cavity growth rates lead to short rupture times

in low creep strength, single-phase alloys Thus,

use-ful high-temperature multiphase structural alloys

must be designed to constrain creep cavity

nucle-ation and growth rates by a variety of mechanisms

For example, grain boundary phases can inhibit

dis-location climb and atom plating.185

As illustrated inFigure 20(a), growth cavities, which

are typically not uniformly distributed on all grain

boundary facets, can be greatly inhibited by the

con-straint imposed by creep in the surrounding cage of

grains, which is necessary to accommodate the cavity

swelling and grain boundary displacements.186 Creep

stresses in the grains impose back stresses on the GBsthat result in compatible deformation rates Thus, it is theaccommodating matrix creep rate that actually controlsthe rate of cavity growth, rather than grain boundarydiffusion itself Creep-accommodated, constrained cav-ity growth rationalizes the Monkman–Grant relation187between the creep rate (e0), the creep rupture time (tr),and a creep rupture strain (ductility) parameter (er) as

Thus, in high-strength alloys, low dislocation creeprates (e0) lead to long tr The typical form of e0

e0¼ AsrexpðQcr=kTÞ ½14bThe effective stress power r for dislocation creep istypically much greater than 5 for creep-resistantalloys, and the activation energy for matrix creep of

Q cr 250–350 kJ mol1 is on the order of the bulkself-diffusion energy.181These values are much higherthan those for unconstrained grain boundary cavitygrowth, with r  1–3 and Q gb 200 kJ mol1

A number of creep rupture and grain boundarycavity growth models were proposed based on theseconcepts.186,188,189Note that there are also conditions,when grain boundary vacancy diffusion and atomplating are highly restricted and cavities are wellseparated, where matrix creep enhances, rather thanconstrains, cavity growth As noted above, power lawcreep controls matrix cavity growth at high stress,

(b) (a)

so that the deformation processes come to a steady-state balance, where the creep rate controls the cavity growth rate (b) A schematic illustration of the differences in the volume of cavities with the same radius of curvature that are located in the matrix, on grain boundaries, and on grain boundary particles Smaller volumes reduce the critical m* for conversion of bubbles to creep cavities due to the applied stress The same mechanism occurs for bubble to void conversions associated with chemical stresses due to irradiation-induced vacancy supersaturation.

leading to transgranular fracture.181,182Models of the

individual, competing, and coupled creep and cavity

growth processes have been used to construct creep

and creep rupture maps that delineate the boundaries

between various dominant mechanism regimes

How-ever, further discussion of this topic is beyond the

scope of this chapter

Accumulation of significant quantities of grain

boundary He has a radical effect on creep rupture,

at least in extreme cases First, at high He levels, the

number density of grain boundary bubbles (Ngb) and

creep cavities (Nc) is usually much larger than the

corresponding number of creep cavities in the absence

of He; the latter is of the order 1010–1012m2.181,190

Figure 21shows the evolution of He bubbles and grain

boundary cavities under stress.191Indeed, Ngbof more

than 1015m2 have been observed in high-dose He

implantation studies.100,192 Although Ngbis not well

known for neutron-irradiated AuSS, it has been

esti-mated to be of the order 1013m2or more.193,194

At high He levels, a significant fraction of the

grain boundary bubbles convert to growing creep

cavities, resulting in high Nc Of course, both Ngb

and Nc depend on stress as well as many material

parameters and irradiation variables, especially those

that control the amount of He that reaches and

clus-ters on GBs As less growth is required for a higher

density of cavities to coalesce, creep rupture strains,

er, roughly scale with Nc1=2 Bubble-nucleated creepcavities are also generally more uniformly distributed

on various grain boundary facets More uniformdistributions and lower er decrease accommodationconstraint, thus, further reducing rupture times asso-ciated with cavity growth

Equation [13a]suggests that m* scales with 1/s2

If the GB bubbles nucleate quickly and once formedthe creep cavities rapidly grow and coalesce, thencreep rupture is primarily controlled by gas-drivenbubble growth to r* and m*.93–95,97In the simplest case,assuming a fixed number of grain boundary bubbles

Ngb and flux of He to the grain boundary, JHe, thecreep rupture time, tr, is approximately given by

tr¼ f½Fv32pg3=½27kTs2g½Ngb=JHe  Ngb=½GHes2 ½15Note that this simple model, predicting tr/1/s2scal-ing, is a limiting case primarily applicable at (a) lowstress; (b) when creep rupture is dominated by Hebubble conversion to creep cavities by gas-driven bub-ble growth to r*; and (c) when diffusion (or irradiation)creep-enhanced stress relaxations are sufficient to pro-duce compatible deformations without the need forthermal dislocation creep in the grains More gener-ally, scaling of tr/1/sr, r 2 is expected for bubblescontaining a distribution of m He atoms For example,

if Ngbscales as mq, then Ncwould scale ass2q.194,195Further, at higher s, hence lower tr, there is lesstime for He to collect on GBs Thus in this regime,intragranular dislocation creep, with a larger stresspower, r, may return as the rate-limiting mechanismcontrolling the tr–srelations

Equation [15]also provides important insight intothe effect of both the grain boundary and matrixmicrostructures Helium reaches the GBs (JHe) only

if it is not trapped in the matrix Matrix bubbles are,

by far, the most effective trap for He.95,97 If it isassumed that the number of matrix bubbles, Nb, isproportional to√GHewhile the grain boundary bub-ble number density (Ngb) is fixed, a scaling relationfor trcan be approximated as

con-YE-11611

YE-11560

0.1 mm 0.1 mm

Figure 21 The growth of grain boundary bubbles and

their conversion to creep cavities in an AuSS: (a) bubbles on

grain boundaries of a specimen injected with 160 appm and

annealed at 1023 K for 6.84 10 4 s; (b) the corresponding

cavity distribution for an implanted specimen annealed at

1023 K for 6.84 10 4

s under a stress of 19.6 MPa.

Reproduced from Braski, D N.; Schroeder, H.; Ullmaier, H.

J Nucl Mater 1979, 83(2), 265.

gas-driven constrained growth of grain boundary

cavities.198 The HTHE models developed by

Trinkaus and coworkers were closely integrated with

the extensive He implantation and creep rupture

studies discussed further below It should be

empha-sized that the HTHE models cited above are only

qualitative and primarily represent simple scaling

concepts that must be validated and calibrated using

microstructural, creep rate, and creep rupture data

For example, more quantitative models require

detailed treatment of He accumulation and

redistri-bution at the GBs into a stably growing population

of bubbles, with a time-dependent fraction that

ultimately converts to growing creep cavities

1.06.3.7 Experimental Observations

on HTHE

The results of experimental studies on He

embrittle-ment of AuSS are broadly consistent with the concepts

described here However, the literature for neutron

irradiations is much more limited than in the case

of microstructural evolution and matrix swelling,

especially for the most pertinent data from reliable

in-reactor creep rupture tests Indeed, there is little

quan-titative characterization of grain boundary cavity and

other microstructures for neutron-irradiated alloys

The most consistent trend for neutron irradiations

is that high-temperature postirradiation tensile tests

show significant to severe reductions in tensile ductility

and creep rupture times and IG rupture along GBs.11

As noted above, there is a much more significantbody of work for well-characterized high-energy Heion implantation studies Helium can be preimplanted

at various temperatures and further subjected to ous postimplantation annealing treatments, prior totensile or creep testing, or simultaneously with creeptesting The different modes of He implantation result

vari-in very different creep rupture behavior.90 Heliumimplantation during high temperature in-beam creep

is perhaps the most relevant, controlled, and systematicapproach to studying HTHE A series of implantationstudies carried out at the Research Center Ju¨lich inGermany, coupled with the models described above,are the most comprehensive and insightful examples

of this research.90,91,99,100,192,199–201 Figure 22(a)

shows the mean trend lines for trversus applied stressfor SA 316SS at 1023 K for in-beam creep, at animplantation rate of 100 appm He/h, compared withunimplanted controls.90 Clearly, HTHE leads to avery large reduction in the trespecially at lower stress.The stress power is r  4 for the in-beam creepcondition, compared with  9 for the unimplantedcontrol.Figure 22(b)shows a corresponding plot for

a Ti-modified AuSS (DIN 1.4970) in-beam creeptested at 1073 K.90HTHE is observed, but the magni-tude of the reduction in tris less in this case The stresspower in-beam creep condition is r  2.85 comparedwith 5.7 for the control As expected, HTHE alsoreduces er; in the case of Ti-modified steel, erdecreases from10% to 1%90

and for the annealed316SS from more than 30% to 1% or less.99Similar

0.1

80 100 120 140 160 180 200 1

10 100

Figure 22 (a) The creep rupture time versus stress for a 316 AuSS tested at 1023 K under He implantation at a rate

of 100 appm h 1 and the corresponding unimplanted control showing severe HTHE (b) The creep rupture time versus stress for a Ti-modified AuSS tested at 1073 K also under He implantation at a rate of 100 appm h 1 and the corresponding unimplanted control Data for He preimplantation to 100 appm at 1073 K is also shown.90Note that the Ti-modified AuSS is much stronger than the 316 alloy in spite of the higher test temperature and that the effect of HTHE is mitigated at lower stresses in this alloy.

corresponding number of creep cavities in the absence

of He; the latter is of the order 10 10 ? ?10 12 m2.18 1 ,19 0

Figure 21shows the evolution of. .. swelling resistance.17 2

FMS are much more resistant to swelling than

advanced AuSS.15 ,10 2 ,10 4 ,11 6 ,12 8 ,12 9 ,16 2 ,16 9 ,17 4 ,17 5 The

swelling resistance of FMS,... results.26 ,12 4 ,12 5 ,12 8 ,12 9 ,15 7 ,16 4a ,16 4? ?17 1The semiempirical CBM models and concepts ratio-nalize a wide range of seemingly complex and some-times disparate observations, including the following: