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

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.

1.06.1
1.06.2
1.06.2.1
1.06.2.2
1.06.2.3
1.06.2.4
1.06.2.5
1.06.2.6
1.06.3
1.06.3.1
1.06.3.2
1.06.3.3
1.06.3.4
1.06.3.5
1.06.3.6
1.06.3.7
1.06.4
1.06.4.1
1.06.4.2

1.06.4.2.1
1.06.4.2.2
1.06.4.3
1.06.4.4
1.06.5
1.06.5.1
1.06.5.2
1.06.5.3
1.06.5.4
1.06.5.5
1.06.6
1.06.6.1
1.06.6.2
1.06.7
References

Introduction and Overview
Experimental Approaches to Studying He Effects in Structural Alloys
Single, Dual, and Triple-Beam CPI
Neutron Irradiations with B or Ni Doping
In Situ He Implantation
Spallation Proton–Neutron Irradiations, SPNI
Proposed Future Neutron-Irradiation Facilities
Characterization of He and He Bubbles
A Review of Helium Effects Models and Experimental Observations
Background
Historical Motivation for He Effects Research
Void Swelling and Microstructural Evolution: Mechanisms
The CBM of Void Nucleation and RT Models of Swelling
Summary: Implications of the CBM to Understanding He Effects on Swelling and

Microstructural Evolution
HTHE Critical Bubble Creep Rupture Models
Experimental Observations on HTHE
Recent Observations on Helium Effects in SPNI
Microstructural Changes
Mechanical Properties of FMS After SPNI
Helium effects on tensile properties and He-induced hardening effects
Helium effects on fracture properties and He-induced embrittlement effects
Mechanical Properties of AuSS After SPNI
Summary of Effects of Irradiation on Tensile and Fracture Properties
Atomistic Models of He Behavior in Fe
He Energetics and He–Defect Complex Interactions
He Interactions with Other Defects
Helium Migration
Master Models of He Transport, Fate, and Consequences
Dislocation–Cavity Interactions
Radiation Damage Tolerance, He Management, Integration of Helium Transport
and Fate Modeling with Experiment
ISHI Studies and Thermal Stability of Nanofeatures in NFA MA957
Master Models of He Transport Fate and Consequences: Integration of
Models and Experiment
Summary and Some Outstanding Issues

Abbreviations
ANL
appm
APT

Argon National Laboratory
Atomic parts per million

Accelerator Production of Tritium

AT
AuSS
bcc
BF

142
146
146
147
148
149
149
150
151
151
152
155
156
162
163
166
168
168
172
172
174
177
178

178
179
180
180
182
182
183
183
185
186
189

As tempered
Austenitic stainless steels
Body-centered cubic
Bright field

141


142

CBM
CD
CPI
CT
CVN
CW
DBTT

The Effects of Helium in Irradiated Structural Alloys

Critical bubble model
Cluster dynamics
Charged-particle irradiations
Compact-tension
Charpy V-notch
Cold-worked
Ductile-to-brittle transition
temperature
DDBTT
Shifts in DBTT
DFT
Density functional theory
dpa
Displacement per atom
EAM
Embedded atom method
EELS
Electron energy-loss spectroscopy
fcc
Face-centered cubic
FFTF
Fast Flux Test Facility
FMS
Ferritic–martensitic steels
FNSF
Fusion Nuclear Science Facility
FZJ
Forschungscentrum Ju¨lich

GB
Grain boundary
HFIR
High Flux Isotope Reactor
HFR
High Flux Reactor (Petten)
HTHE
High temperature helium
embrittlement
IFMIF
International Fusion Material
Irradiation Facility
IG
Intergranular
ISHI
In situ He implantation
KMC/KLMC Kinetic Monte Carlo–lattice Monte
Carlo
LANSCE
Los Alamos Neutron Science Center
LBE
Liquid lead-bismuth eutectic
LTHE
Low temperature hardening-helium
embrittlement
MD
Molecular dynamics
MS
Molecular statics
NF

Nanofeatures
NFA
Nanostructured ferritic alloys
ODE
Ordinary differential equation
OEMS
(Positron) orbital electron
momentum spectra
ORNL
Oak Ridge National Laboratory
PAS
Positron annihilation spectroscopy
PIE
Postirradiation examination
RED
Radiation-enhanced diffusion
REP
Radiation enhanced precipitation
RIP
Radiation-induced precipitation
RIS
Radiation-induced segregation
RT
Rate theory
SANS
Small-angle neutron scattering
SIA
Self-interstitial atom
SINQ
Swiss Spallation Neutron Source

SP
SPN
SPNI
STIP
TDS
TEM
TMS
V

Small punch
Spallation proton–neutron
Spallation proton–neutron
irradiations
SINQ Target Irradiation Program
Thermal desorption spectroscopy
Transmission electron microscopy
Tempered martensitic steels
Vacancy

1.06.1 Introduction and Overview
This chapter reviews the profound effects of He on
the bulk microstructures and mechanical properties
of alloys used in nuclear fission and fusion energy
systems. Helium is produced in these service environments by transmutation reactions in amounts ranging from less than one to thousands of atomic parts
per million (appm), depending on the neutron spectrum, fluence, and alloy composition. Even higher
amounts of H are produced by corresponding n,p
reactions. In the case of direct transmutations, the
amount of He and H are simply given by the content
weighted sum of the total neutron spectrum averaged

energy dependent n,a and n,p cross-sections for all
the alloy isotopes (hsn,ai) times the total fluence (ft).
The spectral averaged cross-sections for a specified
neutron spectrum can be obtained from nuclear database compilations such as SPECTER,1 LAHET,2 and
MCNPX3 codes. He and H are also produced in
copious amounts by very high-energy protons and
neutrons in spallation targets of accelerator-based
nuclear systems (hereafter referred to as spallation
proton–neutron (SPN) irradiations, SPNI).4,5 The
D–T fusion first wall spectrum includes 14 MeV
neutrons (%20%), along with a lower energy spectrum (%80%). The 14 MeV neutron energy is far
above the threshold for n,a (%5 MeV) and n,
p (%1 MeV) reactions in Fe.6 Note that some important transmutations also take place by multistep
nuclear reactions. For example, thermal neutrons
(nth) generate large amounts of He in Ni-bearing
alloys by a 58Ni(nth,g)59Ni(nth,a) reaction sequence.
These various irradiation environments also produce
a range of solid transmutation products.
High-energy neutrons also produce radiationinduced displacement damage in the form of vacancy
and self-interstitial atom (SIA) defects. Vacancies and
SIA are the result of a neutron reaction and scatteringinduced spectrum of energetic primary recoiling


The Effects of Helium in Irradiated Structural Alloys

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)
He per dpa (in Fe)
H per dpa (in Fe)
Temperature ( C)

<200–400
<1
<1
270–950

50–200
$10
$40
300–800

<35
<100
<500
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.

Dimensional
instability
irradiation creep
and swelling

Life time

atoms with energies ranging from less than 1 keV, in
neutron irradiations, up to several MeV in SPN irradiations.7 The high-energy primary recoils create
cascades of secondary displacements of atoms from
their crystal lattice positions, measured in a calculated dose unit of displacements per atom (dpa).
As in the case of n,a transmutations, dpa production
can also be evaluated using spectral averaged displacement 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 irradiation are intrinsically coupled; hence, difference in the
He generation rate can also affect precipitate, dislocation loop, and network dislocation evolutions as
well (see Section 1.06.3).
Figure 1, adopted from Molvik et al.,9 schematically illustrates the effects of high He as a function
of lifetime-temperature limits in a fusion first wall
structure for various irradiation-induced degradation 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 further degrade the tensile ductility and the other hightemperature properties, primarily by enhancing grain
boundary cavitation, in some cases severely. In austenitic 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 currently the prime candidate alloy for fusion structures,
are much more resistant to HTHE.12,13

143

He embrittlement,
thermal creep,
corrosion

Hardening,
fracture

Window

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.

At intermediate temperatures (blue curve), growing
voids form on He bubbles, and He accumulation
largely controls the incubation time prior to the
onset of rapid swelling (see Section 1.06.3). FMS
are also much more resistant to swelling than standard austenitic alloys,14,15 although the microstructures of the latter can be tailored to be more resistant
to void formation by He management schemes.16
High He concentrations can also extend irradiation
hardening and fast fracture embrittlement to intermediate temperatures.17
At lower temperatures (red curve), where irradiation
hardening and loss of tensile uniform ductility are
severe, high He concentrations enhance large positive
shifts in the ductile-to-brittle transition temperature
(DBTT) in bcc (body-centered cubic) alloys.18–20
This low-temperature fast fracture embrittlement
phenomenon is believed to be primarily the result of


144

The Effects of Helium in Irradiated Structural Alloys

He-induced grain boundary weakening, manifested by
a very brittle intergranular (IG) fracture path, interacting synergistically with irradiation hardening.20,21
High concentrations also increase the irradiation
hardening at dpa levels that would experience saturation in the absence of significant amounts of He.17
A significant concern for fusion is that the dpatemperature 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 in Figure 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 implications to the wide range of properties of concern are
not well understood; and even if they were, such

complexity would beg easy description. Therefore, a
first priority is to develop a good understanding of
and models for the transport and fate of He at the
point when it is effectively immobilized in bubbles
and voids, often at various microstructural sites. Such
insight provides a basis for developing microstructures that can manage He and thus mitigate its deleterious effects. To this end we next briefly outline key
radiation damage processes, including the role of He.
Figure 2 schematically illustrates the combined
effects of He and displacement damage on irradiationinduced microstructural evolutions.22 Figure 2(a)

shows a molecular dynamics simulation of primary
displacement damage produced in displacement cascades. Most of the initially displaced atoms return to a
lattice site (self-heal). Residual cascade defects include
single and small clusters of vacancies and SIA. In
the temperature range of interest, vacancies (red circles) and SIA (green dumbbells) are mobile. SIA
clusters, in the form of dislocation loops, are also
believed to be mobile in some cases, undergoing
one-dimensional diffusion on their glide prisms.

Recombination

Precipitate – void
(b)
Growing SIA loop/
climbing dislocation

Cascade
(a)

Vacancy

SIA
(c)

Stably growing
matrix bubble

He
GB
h

+

Unstably growing
matrix void

m = m*

drc /dt

rc

0
rb
−

sn

(e)

r c* (m*)

(f)

Jv

Stress-driven grain
boundary cavity growth

r*v
m < m*

(d)
Figure 2 Illustration of the combined effects of He and displacement damage on irradiation-induced microstructural
evolutions.


The Effects of Helium in Irradiated Structural Alloys

However, the cascade loops may also be trapped by
interactions with solutes. Small cascade vacancy clusters 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 temperature. 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 recombination 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 dislocations, ultimately leading to quasi-steady-state densities, as is observed in the case of AuSS.

Figure 2(d) shows that He precipitates to form
bubbles (larger blue circles) at various sites, in this
case in the matrix. Small bubbles are stable since they
absorb and emit vacancies in net numbers that
exactly 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 they
convert to unstably growing underpressurized voids
(large orange circle containing blue He atoms) due to
an excess flux of vacancies over SIA arising from the
dislocation bias for the latter defect. Figure 2(e)
shows the corresponding growing creep cavities
transformed from critical He bubbles on stressed
GBs. Designs of microstructures that mitigate, or
even fully suppress, these various coupled evolutions
are described in Section 1.06.6 and discussed in
references.22,23
Therefore, a master overarching framework for
measuring, modeling, and managing He effects must
be based on developing and understanding the dominant mechanisms controlling its generation, transport, fate, and consequences, as mediated by the

irradiation conditions and the detailed alloy microstructure. Figure 3 illustrates such a framework for
He generation, transport, and fate. In this framework,
experiments and models can be integrated to establish how He is transported to various microstructural
trapping (-detrapping) features and how He locally
clusters to form bubbles at these sites, as well as in the
matrix. The master models must incorporate parameters that describe He diffusion coefficients under
irradiation, binding energies for trapping at the various sites and He–vacancy cluster and other interaction energies.

Multiscale modeling-experiment framework
Generate mobile He by transmutation and emission from traps
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

Grain
boundaries

Internal subregion structure

Fine-scale
precipitates

145

Dislocation
substructures

Other
precipitates

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

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


146

The Effects of Helium in Irradiated Structural Alloys

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 1.06.2 describes 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 primarily 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 1.06.4 focuses on a much more recent body
of observations on He effects in SPNI. The emphasis
here is on descriptions of defect and cavity microstructures 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 irradiations are drawn where possible.
Section 1.06.5 summarizes 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 comprehensive master models of He transport, fate, and
consequences.
Section 1.06.6 builds on the discussion in
Section 1.06.3 regarding managing He by trapping it
in a population of small stable bubbles. A specific
example comparing FMS to a new class of hightemperature, irradiation-tolerant nanostructured ferritic alloys (NFA) irradiated in a High-Flux Isotope
Reactor (HFIR) at 500  C 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 multiscale 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 parameterized by atomistic submodels, are favorably compared to the HFIR data.
Section 1.06.7 briefly summarizes the status of
understanding of He effects in structural alloys and
concludes with some outstanding issues. Reading this
summary first may be helpful to general readers who
then can access the more detailed information at their
own discretion.

1.06.2 Experimental Approaches to
Studying He Effects in Structural
Alloys
1.06.2.1

Single, Dual, and Triple-Beam CPI

Single (He), dual (typically heavy ions to produce
dpa and He), and triple (typically heavy ions, He
and H) beam CPI have been extensively used to
study He effects for a wide variety of materials and
conditions. The number of facilities worldwide, both
current and historically, and the large resulting literature cannot be fully cited and summarized in this
chapter, but some examples are given in Section
1.06.3. A more complete overview of these facilities
can be found in a recent Livermore National Laboratory Report.24 Extensive high-energy He implantation studies of creep properties were carried out at
Forschungszentrum Ju¨lich using a 28 MeV He cyclotron.25 Major dual- and triple-beam studies were
previously carried out at Oak Ridge National Laboratory (180 keV H, 360 keV He, 3.5 MeV Fe)26 and
many other facilities around the world.24 The new
JANNUS facility at Saclay couples a 3 MV Pelletron
with a multicharged ion source and a 2.5 MV single
Van de Graaff and a 2.25 MeV tandem accelerator.27

Another multibeam facility at Orsay couples a 2 MV
couple, a tandem accelerator, and a 190 kV ion implanter to a 200 kV transmission electron microscope
(TEM) to allow simultaneous co-irradiation and
observation.27
The advantages of He implantation and
multibeam ion irradiations include the following:
(a) conditions can be well controlled and in many
cases selectively and widely varied; (b) high dpa, He,
and H levels can be achieved in short times; (c) the
specimens are often not, or only minimally, activated; and (d) in situ TEM observations are possible
in some cases. The disadvantages include the following: (a) highly accelerated damage rates compared
with neutron irradiations; and in the case of


The Effects of Helium in Irradiated Structural Alloys

(nth,a) (bred from 58Ni with a n,a cross-section
of %10 barns) cited in Section 1.06.1; (b) or by the
10
B þ nth ! 7Li þ a reaction (%20% of elemental B
with a cross-section of %4010 barns) (1 barn ¼
10–24 cm2). Significant quantities of He can also be
generated by epithermal–fast spectrum neutron reactions with B as well as prebred 59Ni.29
Figure 4(a) shows calculated and measured He
production in natural Ni in the HFIR target capsule
position.30 Figure 4(b) shows the corresponding
He/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 a
He/dpa peak at about %20 dpa in HFIR; (b) if the

alloy contains more than a few percent Ni, like in
AuSS, the He/dpa is much higher than that for fast
fission and higher than that for fusion spectra but
is comparable to, or slightly less than, the He/dpa
for SPNI.
Modifying the amounts of 58Ni and 60Ni (isotope
tailoring) 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 irradiated Ni pre-enriched in 59Ni.29,31 Various amounts
of 58Ni, 59Ni, and 60Ni can also be used to control the
He/dpa ratio in fast spectrum reactors, like the Fast
Flux Test Facility (FFTF), as well as in mixed spectrum reactors, like HFIR.29,31,32
Boron is not normally added to steels used for
nuclear applications, but it has been used in a number
of doping studies.33,34 A major advantage of B doping is
that significant amounts of He are produced by the
10
B, but not the 11B, isotope. Thus, the effect of doping
with 10B versus 11B can be used to isolate this effect of

multibeam ion irradiations, (b) shallow damage
depths and the proximity of free surfaces; (c) nonuniform damage production and the deposition of
foreign ions; and (d) inability to measure bulk properties. High-energy He implantation can be used
on bulk specimens tested, either in situ or postimplantation, 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 between CPI and neutron irradiation can significantly
affect microstructural evolution.
Thus, it must be emphasized that He implantation
and multibeam CPI do not simulate neutron irradiations. 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 irradiations 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 with 58Ni(nth,g) (%68% of elemental
Ni with a nth,g cross-section of %0.7 barns) and 59Ni

(a)

14
12

59 dpa

Helium (appm/dpa)

Helium production (appm)

40 000

44

30 000
34
20 000

10 000

10
8
6
4
Total
Incremental

2
0

147

0

5
10
Thermal neutron fluence (1022 n cm–2)

0

15
(b)

0

20

40

60

80

100

dpa

Figure 4 (a) Measured and calculated He production from Ni irradiated in HFIR. The solid line is calculated using the
evaluated 58Ni and 59Ni 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.


148

The Effects of Helium in Irradiated Structural Alloys

He, in a B-containing alloy. However, the issues associated 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
the 10B content. The other major limitations are that
B is virtually insoluble in steels and primarily resides
in Fe and alloy boride phases.35 Boron also segregates
to GBs. Thus, He from B reactions is not homogeneously 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 contain 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.20,41–44 As noted previously, to
some extent these confounding factors can be evaluated 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,46 and in the case of B doping the Li

reaction product may play some role as well.

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 proposed
using 235U triple fission reactions to inject %16 MeV
a-particles uniformly in steel specimens up to 50 mm
thick; the 50 mm thickness permits tensile and creep
testing as well as microstructural characterization and
mechanism studies at fusion relevant dpa rates and
He/dpa ratios.31 The triple fission technique was
applied to implanting ferritic steel tensile specimen,
albeit without complete success.48 A much more practical approach is to use thin Ni-bearing implanter foils
to uniformly deposit He up to a depth of %8 mm in Fe
in a thick specimen at controlled He/dpa ratios.49
As illustrated in Figure 5(a)–5(c), there are at
least three basic approaches to implanter design.
Here we will refer to thin and thick, specifically
meaning a specimen (ts) or implanter layer (ti) thickness that is less than or greater than the corresponding a-particle range, respectively. Ignoring
easily treated difference in the a-particle range (Ra)
and atom densities in the injector and specimens for
simplicity, thick implanter layers on one side of a
thick specimen produce linearly decreasing He concentration (XHe) profiles, with the maximum concentration at the specimen surface that is one half the
concentration in the bulk injector material, XHeo ¼
XHei/2 (Figure 5(a)). If a thin specimen is implanted
from both sides by thick layers, the He concentration

XHe

XHe

Xmax =

2

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 material 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 displacement damage. Early work proposed implanting
He using the decay of a thin layer of a-emitting
isotope adjacent to the target specimen.47 However,

XHei Ri
2 Ra

Ra

x
0

1.06.2.3

XHe =

XHei Ri

(a)

x

0

Rα

Rα

(b)
XHe

XHe = tiXHei/2Ra

ti

x
0

Xu Ra

(c)
Figure 5 Illustration of three basic approaches to the ISHI
design.


The Effects of Helium in Irradiated Structural Alloys

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 À ti. In this case, the He concentration
in both the implantation layer and specimen is equal
and lower than in the bulk (XHei) as XHes ¼ tiXHei/
2Ra (Figure 5(c)). Thus, the He/dpa ratio can be
controlled by varying the concentration of the isotope that undergoes n,a reactions with thermal neutrons, 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 implantation experiments in HFIR have been reported and
are discussed in Section 1.06.6.23,51–53 The 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
to %7 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 highenergy and current (power) proton beams via spallation reactions that fragment the atomic nuclei
heavily in a heavy metal target (like W, Pb, and
Hg). At 500 MeV, these reactions produce %10 neutrons per proton. Applications of spallation sources
include neutron scattering, nuclear waste transmutation, and driving subcritical fission reactors. A key
challenge to developing advanced high-power, longlived spallation source targets is the ability of

structural alloys to withstand severe radiation damage, corrosive fluids, and mechanical loading. Most
notably, radiation damage in spallation source irradiations, 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

149

Irradiation Program – STIP, started in 1998, that continues to this day, at the Paul Sherrer Institute, in
Switzerland, involving an international collaboration
of ten institutions in China, Europe, Japan, and the
United States.56,57
Because of the accelerator production of tritium target application, the irradiation temperature LANSCE
experiment was up to %164  C. The highest damage
levels, mostly produced by protons, were %12 dpa
and %180 appm He/dpa.4 About 20 materials were
irradiated in a variety of specimen configurations in
this study.
The maximum damage levels in the STIP-I to -IV
irradiations56,57 were % 25 dpa and 2000 appm He.
The corresponding temperatures ranged from 80 to
800  C, but most specimens were nominally irradiated between 100 and 500  C. The temperatures
directly depend on the high nuclear heating rates
in the target, and both varied by Æ15% during the
2-year irradiation; and, in the case of STIP-I and-IV,

some capsules experienced a significant overtemperature transient. The high heating rates also result
in fairly large uncertainties in the temperatures of
individual specimens. Note that the temperature
control in the most recent STIP-V experiment was
significantly better than that in previous studies.
Over 60 elemental metals and alloys, ceramics, and
composites have been irradiated in the STIP-I to -V,
in the form of miniaturized specimens for both microstructural studies and mechanical testing, including
tensile, fatigue, fracture toughness, and Charpy
V-notch (CVN) measures of the DBTT. Some specimens were irradiated in contact with stagnant liquid
Hg, PbBi eutectic, and Pb. The STIP database is
discussed in Section 1.06.4
1.06.2.5 Proposed Future
Neutron-Irradiation Facilities
The
proposed
International-Fusion-MaterialIrradiation-Facility (IFMIF) is an accelerator-driven
neutron source that is based on the proton-stripping
reaction.58,59 Neutrons are generated by a beam of
40 MeV deuterons that undergo a proton-stripping
reaction when they interact with a flowing liquid
lithium jet target. The resulting neutron beam has
a spectrum with a high-energy tail above a peak
around 14.60 As in the case of D, T, and spallation
reactions, these neutrons are well above the threshold energy for n,a reactions; thus, IFMIF produces
fusion like He/dpa ratios at high dpa rates. The
nuclear reaction kinematics and limited neutron


150

The Effects of Helium in Irradiated Structural Alloys

target source dimensions result in an IFMIF irradiation 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 with
dpa rates of 20–50 fpyÀ1 (full power year) at He/
dpa %12 appm dpaÀ1. The medium flux region,
from 1.0 to 20 dpa fpyÀ1, is much larger with a
volume of %6000 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 dpaÀ1 close to that for a
fusion first wall. The dpa rates are %7.5–15 fpyÀ1
in a 200 cm3 irradiation volume and 2.5–12.5 fpyÀ1 in
an additional volume of 450 cm3. An accelerator
upgrade to 3.6 MW would increase these dpa rates to
20–40 fpyÀ1 and 5–16 fpyÀ1, respectively.
In both cases, the limited volume for high-flux
accelerated irradiations presents a great challenge to
developing small specimen mechanical test methods62,63 and experimental matrices64 that can produce 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 applications will require a new paradigm of linking
comprehensive microstructural characterization and
physically based predictive modeling tools to multiscale models and experiments of structure-sensitive
properties as input into engineering models of materials 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 provide 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 produce sufficient wall loading to deliver high He and
dpa exposures.

1.06.2.6 Characterization of He and
He Bubbles
The primary techniques used to characterize the
behavior of He and He bubbles in materials include
TEM, small-angle neutron scattering (SANS), positron annihilation spectroscopy (PAS), and thermal
desorption spectroscopy (TDS). All of these techniques, and their numerous variants, have individual
limitations. Complete and accurate characterization
of He transport and fate requires a combination of
these methods; however, such complementary tools
are seldom employed in practice. Note that there are
also a variety of other methods of studying helium in
solids that cannot be discussed due to space

limitations.
TEM, with a practical resolution limit of about
1 nm, is the primary method for characterizing He
bubbles. Bubbles and voids are most frequently
observed by bright field (BF) ‘through-focus’ imaging
in thin regions of a foil. The Fresnel fringe contrast
changes from white (under) to black (over) as a function of the focusing condition. The bubble size is
often taken as the mid diameter of the dark under
focus fringe. Two critical issues in such studies are
artifacts introduced by sample preparation, which
produce similar images and determine the actual
size, especially below 2 nm.66–68 Electron energyloss spectroscopy (EELS) can be used to estimate
the He pressure in bubbles.69,70
SANS provides bulk measures of He bubble
microstructures. In ferromagnetic steels, both nuclear and magnetic scattering cross-sections can be
measured by applying a saturating magnetic field
(%2T) perpendicular to the neutron beam. The
coherent scattering cross-section variations with the
scattering vector are fit to derive the bubble size
distribution, with a potential subnanometer resolution limit.71 The magnitude of the scattering crosssection is proportional to the square of the scattering
length density contrast factor between the matrix and
the 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 directly
determined by SANS. The nuclear scattering crosssection provides a measure of the He density in the
bubbles. Thus, the variation in the ratio of the nuclear
(He dependent) to magnetic (He independent) scattering cross-sections with the scattering vector can be
used to estimate the He pressure (density) as a function of the bubble size.71,72 Some studies have shown

The Effects of Helium in Irradiated Structural Alloys

that SANS bubble size distributions are in good
agreement with TEM observations,73,74 while others
show considerable differences for small (<$2 nm)
bubbles.72 Limitations of SANS include distinguishing 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 sufficient 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.75,76 PAS can also
be used to estimate the He density, or He/vacancy
ratio, in bubbles.77 In the case of He-free cavities, the
positron lifetime increases with increasing the nanovoid size, saturating at several tens of vacancies. However, 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 annihilation site.78 Thus, for example, OEMS might detect
the association of a bubble with another microstructural 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 indirect information about He transport and trapping/
detrapping processes. For example, isothermal annealing 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 dihelium 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.82,83 Techniques
that can quantify He concentrations at small levels

151

used in TDS can also be used to measure the total He
contents in samples that are melted.81
In summary, a variety of complementary techniques can be used to characterize He and He bubbles
in structural materials. A good general reference for
these techniques and He behavior in solids can be
found in Donnelly and Evans.84 TEM and SANS can
measure the number densities, size distributions, and
volume fractions of bubbles, subject to resolution
limits and complicating factors. The corresponding
density of He in bubbles can be estimated by
TEM–EELS, SANS, and PAS. TDS can provide

insight into the He diffusion and trapping/detrapping
processes. Unfortunately, there have been very limited applications in which various methods have been
applied in a systematic and complementary manner.
Major challenges include characterizing subnanometer bubbles in complex structural alloys, including their association with various microstructural
features.

1.06.3 A Review of Helium Effects
Models and Experimental
Observations
1.06.3.1

Background

Clearly, it is not possible to cite, let alone describe
in detail, the extensive literature on He effects in
irradiated alloys. This literature encompasses both
mechanical properties, especially HTHE, and the
effects of He on microstructural evolutions, particularly void swelling. There is also a more limited
literature on fundamental processes and properties
related to He in solids, like desorption measurements
and He solution, binding, and diffusion activation
energies. Much of previous work pertains to fcc
(face-centered cubic) AuSS, which is one of interest
for fast reactor cladding applications. However, standard AuSS, like AISI 316 (%Fe–0.17Cr–0.12Ni–bal
Mo, Si, Mn, . . .) are highly prone to both HTHE
and void swelling. Thus, advanced AuSS and bcc
FMS have supplanted conventional AuSS as the
leading candidates for nuclear applications. Nevertheless, conventional AuSS alloys nicely illustrate
the damaging effects of He (see Section 1.06.3.2
and following), which are both subtle and significantly mitigated in advanced steels. Swelling and

HTHE resistance are largely due to microstructural
designs that manage He.
Particular emphasis in this section is placed on
the critical bubble model (CBM) concept of the


The Effects of Helium in Irradiated Structural Alloys

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 thermodynamic–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 1.06.3.3 describes the mechanisms of swelling
and its relation to He and He bubbles, especially
in AuSS. Section 1.06.3.4 presents 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 reductions in tensile and creep ductility and creep
rupture times. The degradation of these properties
coincided with an increasing transition from transgranular to intergranular 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 spectrum neutron irradiations that produce large amounts
of He in alloys containing Ni and B. Figure 6 shows
one extreme example of the dramatic effect of HTHE
on creep rupture times for a 20% cold-worked (CW)
316 stainless steel tested at 550  C and 310 MPa
following irradiations between 535 and 605  C in the
mixed spectrum HFIR that produced up to 3190 appm
He and 85 dpa.88 At 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

104
1000
100
tr (h)

152

10
1
0.1
0.01

0

20
48
He (appm)

3190

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.

The early fission reactor irradiations research
on HTHE was later complemented by extensive
accelerator-based He ion implantation experiments,
primarily carried out in the 1980s (see Schroeder and
Batfalsky90 and Schroeder, Kesternich and Ullmaier91 as
examples) but that have continued to recent times.92
HTHE models were developed during this period,
primarily in conjunction with the He ion implantation experiments.93–100 The He implantation studies
and models are discussed further in Sections 1.06.3.6
and 1.06.3.7. A more general review of He effects,
again primarily in AuSS, can be found in Ullmaier99

and a comprehensive model-based description of the
behavior of He in metals in Trinkaus.96
Research on He effects was also greatly stimulated
by the discovery of large growing voids in irradiated
AuSS.101 As an example, Figure 7(a) shows swelling
curves for a variety of alloys used in reactor applications.102–104 Figure 7(b) illustrates macroscopic consequences of this phenomenon in an AuSS.105 Figure 8
shows a classical micrograph of a solution annealed (SA)
AuSS with dislocation loops and line segments, precipitates, precipitate-associated and matrix voids, and
possibly He bubbles (the small cavities). RT-based
modeling studies of void swelling began in the early
1970s,106,107 peaking in the 1980s, and continuing up to
recent times.108 Most of the earliest models emphasized
the complex effects of He on void swelling.109,110
As discussed in more detail below, these and later
models rationalized many observed swelling trends
and also suggested approaches to developing more
swelling-resistant AuSS, largely based on trapping


The Effects of Helium in Irradiated Structural Alloys

153

16
HT-9
9Cr–1Mo
2 1/4Cr–1Mo
316SS
PCA

Void swelling (%)

14
12

Unirradiated
fuel cladding
tube

1 cm

10
8
6
4
2
0

(a)

0

50

100
150
200
Displacement dose (dpa)

250

(b)

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).

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,114 Freeman,115 and 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 effects
was stimulated by a growing interest in the effects of
the very high transmutation levels produced in fusion
reactor spectra (see Section 1.06.1).89,99,111,112,118

Experimental studies comparing microstructural
evolutions in AuSS irradiated in fast (lower He) and
mixed spectrum (high He) reactors provided key
insight into the effects of He.16,119,120 Helium effects
were also systematically studied using dual-beam
He–heavy ion CPI.26,121–129
Beginning in the mid-1970s, a series of studies
specifically addressed the critical question of how to
use fission reactor data to predict irradiation effects
in fusion reactors,15,109–112,118,130–133 and this topic
remains one of intense interest to this day. An indication of the complexity of He effects is illustrated in
Figure 9, showing microstructures in a dual-beam
He–heavy ion irradiation of a SA AuSS to 70 dpa and
625  C at different He/dpa.123 In this case, voids do
not form in the single heavy ion irradiation without
He. At intermediate levels, of 0.2 appm/dpa, large
voids are observed, resulting in a net swelling of
3.5%. At even higher levels of 20 appm/dpa, the
voids are more numerous, but smaller, resulting
in less net swelling of 1.8%. These observations
show that some He promotes the formation of
voids, but that higher amounts can reduce swelling.
Figure 10 shows the effect of various conditions for


154

The Effects of Helium in Irradiated Structural Alloys

100 nm

(a)

(b)

(c)

Figure 9 The effects of the He/dpa ratio on void swelling in a dual ion-irradiated AuSS at 70 dpa and 625  C. The void
volume is largest at the intermediate He/dpa ratio of 0.2 appm dpaÀ1, which falls between the limits of 0 and 20 appm dpaÀ1.
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.

(a)

100 nm

S = 18%

(b)

S = 11%

(c)

(d)

S = 4%

S = 1%

Figure 10 The effects of He and He implantation conditions on the cavity microstructure in ion-irradiated pure Fe–Ni–Cr SA

AuSS (note that this is a different alloy from the one in Figure 9) at 70 dpa and 625  C, where the swelling is given in :
(a) no He (18%); (b) 1400 appm He co-implanted (11%); (c) 1400 appm He hot preinjected at 900 K (4%); and (d) 1400 appm
He cold preimplanted at 20  C (1%). Reproduced from Packan, N. H.; Farrell, K. J. Nuc. Mat. 1979, 85–86, 677–681.

introducing 1400 appm He coupled with a 4 MeV Ni
ion irradiation of a swelling-prone model SA AuSS to
70 dpa at 625  C.125 In 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 bubbles. These results also show that voids can form

at sufficiently high CPI damage rates without
He, probably assisted by the presence of impurities
like oxygen and hydrogen. Most notably, however,
the swelling decreases with increasing bubble number densities.
The emphasis of more recent experimental
work has been on SPNI that generate large amounts


The Effects of Helium in Irradiated Structural Alloys

of He, compared with fission reactors, as well as displacement damage (see Section 1.06.4). The SPNI
studies have focused on mechanical properties and
microstructures, primarily at lower irradiation temperatures, nominally below the HTHE regime. In
addition, as discussed in Section 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 spectrum reactor irradiations (e.g., HFIR) at reactorrelevant 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 RTand Monte
Carlo models of He diffusion and clustering to form
bubbles on dislocations, precipitates, and GBs, as well
as in the matrix, as discussed in Section 1.06.6.
It is again important to emphasize that the broad
framework for predicting He effects is an understanding 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 evolution 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.113–116 Early 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 displacement rates (Gdpa) in high-flux reactors (HFR)
are %10–6–10–7 dpa sÀ1. Hence, an irradiation time
of 108 s (%3 years) produces up to %100 dpa. Only
about 30% of the primary defects survive shorttime cascade recombination.137 The 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,

155

respectively. Ultimate survival of only 0.1% of the
dpa in the form of clustered vacancies leads to 10%
swelling at 100 dpa.
Classical models138,139 demonstrated that for the
low Gdpa in neutron irradiations, homogeneous void
nucleation rates are very low at temperatures in the
peak swelling regime for AuSS between about 500
and 600  C. However, heterogeneous void nucleation
on He bubbles is much more rapid than homogeneous
nucleation.109 Indeed, nucleation is not required when
the He bubbles reach a critical size (r*) and He content
(m*). The CBM concept has provided a great deal of
insight into the effects of He on swelling.15,109–
112,114,118,130–133,140–151
In particular, the CBM rationalized the extended incubation dpa in fast reactor
irradiations prior to the onset of rapid swelling. As
previously shown in Figure 2(d) and 2(e), here we
clearly distinguish between bubbles, which shrink or
grow only by the addition of He, from larger voids,
which grow unstably by the continuous accumulation
of vacancies. In the case of bubbles, the gas pressure (p)
plus a chemical stress due to irradiation (see Section
1.06.3.4) just balances the negative capillary stress 2g/
rb, where g is the surface energy and rb the bubble

radius. By definition drb/dt ¼ 0 for bubbles, while the
growth rate is positive and negative for cavities that
are slightly smaller and larger than rb, respectively. In
the case of voids (v), drv/dt is positive at all rv greater
than the critical radius. Voids are typically underpressurized with p << 2g/rv. More generally, cavities
include both bubbles and voids and can contain an
arbitrary 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-dimensional
nÀm space can be numerically modeled using cluster
dynamics (CD) master equations. In the simplest case
of growth or shrinkage by the absorption or emission
of the monomer diffusing species (He, vacancies, and
SIA), an ordinary differential equation (ODE) for
each n,m cluster, dN(n,m)/dt, tracks the transitions
from and to all adjacent cluster classes (n Æ 1 and
m Æ 1), as characterized by He, vacancy, and SIA
rates of being absorbed (bHe,v,i) and the vacancy
emission (av) rate, as
dN ðn; mÞ=dt ¼ bHe ðn; m À 1ÞN ðn; m À 1Þ
þ bv ðn À 1; mÞN ðn À 1; mÞ À av ðn þ 1; mÞN ðn þ 1; mÞ
þ bi ðn þ 1; mÞN ðn þ 1; mÞ À ½bHe ðn; mÞ À bv ðm; nÞ
À bi ðn; mފN ðn; mÞ

½1Š

Note that thermal SIA and He emission rates are
low and need not be included in eqn [1]. However,

156

The Effects of Helium in Irradiated Structural Alloys

He may be dynamically resolutioned by displacement cascades.152,153 There are a total of nmax  mmax
such coupled ODEs. The rate coefficients, a and b,
are typically computed from solutions to the diffusion equation, to obtain cavity sink strengths,107,113–116
along with the concentrations of the various species in the matrix and vacancies in local thermodynamic 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.109,139,141 Conservation equations are used to track the matrix concentrations 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 dislocation loops, as well as climb driven by the excess flux
of SIA to network dislocations.111,144 In AuSS, loop
unfaulting produces network dislocations, and network climb results in both production and annihilation 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  mmax coupled 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 considerable 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 unaffected. These early models also predicted the formation of bimodal cavity size distributions, as confirmed
by subsequent modeling studies and many experimental 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. Note
that while a range of n and m clusters are energetically highly favorable compared with equal numbers
of He atoms and vacancies in solution, bubbles represent the lowest free energy configuration in the
vacancy-rich environments, characteristic of materials experiencing displacement damage. That is,
in systems that can swell due to the presence of
sink bias mechanisms that segregate excess fractions
SIA and vacancies to different sinks and at low
reactor relevant damage rates, cavities primarily
evolve 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 Swelling
For purposes of discussion and simplicity, the effects

of cascade defect clustering and recombination are
ignored, and we consider only single mobile vacancies and SIA defects in the simplest form of RT to
illustrate the CBM. At steady state, isolated vacancies
and SIA are created in equal numbers and annihilate
at sinks at the same rate. Dislocation–SIA interactions
due to the long-range strain field result in an excess
flow of SIA to the ‘biased’ dislocation sinks and, thus,
leave a corresponding excess flow of vacancies to
other neutral (or less biased) sinks, (DvXv À DiXi).
Here, D is the defect diffusion coefficient and X the
corresponding atomic fraction. Assuming that the
defect sinks are restricted to bubbles (b), voids (v),
and dislocations (d), the DX terms are controlled by
the corresponding sink strengths (Z): Zb (%4prbNb),
Zv (%4prvNv) for both vacancies and SIA; Zd (%r) for
vacancies and Zdi (%r [1 þ B]) for SIA. Here, r and N
are the size and number densities of bubbles and
voids, r is the dislocation density, and B is a bias
factor. At steady state,
Dv Xv À Di Xi ¼ ½Gdpa Zdi Š=fðZb þ Zv þ Zd Þ
ðZb þ Zv þ Zd ½1 þ BŠÞg þ Dv Xve ½2Š
Here, 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 vacancies
results in an increase in the cavity radius (r) at a
rate given by
dr =dtþ ¼ ðDv Xv À Di Xi Þ=r

½3Š

The Effects of Helium in Irradiated Structural Alloys

However, cavities also emit vacancies, resulting in
shrinkage at a rate given by the capillary approximation as

m/m*=
0.60
0.75

½4Š

The Xve exp[(2g/r À p)O/kT] term is the concentration of vacancies in local equilibrium at the cavity
surface, and O is the atomic volume. Thus, the net
cavity growth rate is
dr =dt ¼fDv Xv À Di Xi À Dv Xve
exp½ð2g=rc À pÞO=kT Šg=r

10

½5Š

5

dr/dt (10-5 nm s-1)

dr =dtÀ ¼ ÀDv Xve exp½ð2g=r À pÞO=kT Š=r

157

1.0
1.25

0

-5

Growth stability and instability conditions occur at
the dr/dt ¼ 0 roots of eqn [5], when
Dv Xv À Di Xi À Dv Xve exp½ð2g=r À pÞO=kT Š ¼ 0 ½6aŠ
Note that DvXve is approximately the self-diffusion
coefficient, Dsd. The He pressure is given by
p ¼ 3kmkT =4pr 3

½6bŠ

Here, k is the real gas compressibility factor. Equation [6a] can be expressed in terms of the effective
vacancy supersaturation,
L ¼ ðDv Xv À Di Xi Þ=Dsd

½6cŠ

The bubble and critical radius occur at
L À exp½ð2g=r À pÞO=kT Š ¼ 0

½6dŠ

In the absence of irradiation (or sink bias), L ¼ 1 and
all cavities are bubbles in thermal equilibrium, at

p ¼ 2g/rb. Assuming an ideal gas, k ¼ 1, eqn [6d] can
be written as
2g=r À ð3mkT Þ=ð4pr 3 Þ À kT lnðLÞ=O ¼ 0

½7aŠ

Note that kT ln(L)/O is equivalent to a chemical
hydrostatic tensile stress acting on the cavity. Rearranging eqn [7a] leads to a cubic equation with
the form,
rc3 þ c1 r 2 þ c2 ¼ 0

½7bŠ

c1 ¼ À½2gOŠ=½kT lnðLފ

½7cŠ

c2 ¼ ½3mOŠ=½4p lnðLފ

½7dŠ

As shown in Figure 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, rvà , 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

-10

0.8 0.9 1

2

3

rc (nm)
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 mÀ2) . 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.

on bubbles between rb and rvà .109,132,141 However, as
shown in Figure 2(d) and 2(e), as m increases, rb
increases and rv decreases, until rb ¼ rv ¼ r* at the
critical m*. An example of the dr/dt curves assuming
ideal gas behavior taken from Stoller133 is shown in
Figure 11 for parameters typical of an irradiated
AuSS at 500  C with L ¼ 4.57. The corresponding r*
and m* are 1.50 nm and 931, respectively.
The critical bubble parameters can be evaluated
for a realistic He equation of state using master
correction curves, y1(ln L) for m* and y2(ln L) for
r*, based on high-order polynomial fits to numerical

solutions for the roots of eqn [7b].143 A simpler analytical method to account for real gas behavior based
on a Van der Waals equation of state can also be
used.151 The results of the two models are very similar.143 Voids often form on critical bubbles located
at precipitate interfaces at a smaller m* than in the
matrix.142 This is a result of the surface–interface
tension balances that determine the wetting angle between the bubble and precipitate interface (see
Figure 20(b)). Formation of voids on precipitates
can be accounted for by a factor Fv 4p/3, reflecting
the smaller volume of a precipitate-associated critical


158

The Effects of Helium in Irradiated Structural Alloys

L % f½Gdpa BZd Š=½ðZb þ Zd Þ

bubble at r*, compared with a spherical bubble in the
matrix, with Fv ¼ 4p/3. Note that the critical matrix
and precipitate-associated bubble have the same r*.
The m* and r* are given by
Ã

3

2

m ¼ ½32Fv y1 g O Š=½27ðkT Þ ðlnðLÞ ÞŠ
3

2

ðZd ð1 þ BÞ þ Zb ފ=Dsd g þ 1

Figure 13 shows the corresponding m* and r* as a
function of the concentration of 1 nm bubbles, Nb, at
500 and 600  C again using the AuSS parameters
given in Stoller.133 Clearly, high Nb can lead to large
critical bubble sizes requiring high He contents for
void formation.
Thus, to a good approximation, the primary
mechanism for void formation in neutron irradiations
is the gradual and stable, gas-driven growth of bubbles by the addition of He up to near the critical m*.

½8aŠ

r à ¼ ½4y2 gOŠ=½3kT lnðLފ

½9Š

½8bŠ

Figure 12 shows m*, r* as a function of temperature
for typical parameters for SA AuSS steels taken from
Stoller.133 More generally, L can simply be related to
Dsd, , Gdpa, B, and the sink’s various strengths.
Assuming Zv % 0 during the incubation period,
107

103

106
102
rc* (nm)

m*He

105
104

101

103
100

Ideal gas
102

HSEOS

101
300

400

500

HSEOS
Ideal gas

600

700

10-1
300

400

500

600

700

Temperature (ЊC)

Temperature (ЊC)

Figure 12 Critical bubble model predictions of m* and r* as a function of temperature for parameters typical of an AuSS
modified from Stoller.133

10−4

1013

1011

773 K
873 K

10−5
10−6

rc* (m)

m*

109

107

10−7

105

10−8

103

10−9

101 20
10

773 K
873 K

1021

1022

Nb (m−3)

1023

1024

10−10 20
10

1021

1022

1023

1024

Nb (m−3)

Figure 13 Critical bubble predictions of m* and r* as a function of the bubble density (Nb) at 773 and 873 K for
parameters typical of a solution annealed AuSS taken from Stoller.133 At low Nb 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*.


The Effects of Helium in Irradiated Structural Alloys

20

1013
1011

773 K
873 K

109
Voids per interval (%)

15

dpa*

107
105
103

159

400 dpa

101

10

5

10−1
10−3

1020

1021

1022

1023

1024

Nb (m−3)
Figure 14 Predicted incubation dpa* for the onset of void
swelling as a function of the density (Nb) 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 Nb at
lower bubble densities, simply because the He partitions to
more sites. However, in the bubble sink dominated regime,
dpa* scales with N5b . The horizontal dashed line shows a
dose of 400 dpa.

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
dpaà ¼ ½mà Nb Š=½He=dpaŠ

½10Š

Figure 14 shows dpa* for He/dpa ¼ 10 appm dpaÀ1
and the same AuSS parameters used in Figure 13.
Clearly high Nb increases the dpa*, both by increasing the neutral sink strength, thus decreasing L,
and partitioning He to more numerous bubble sites.
Indeed, in the bubble-dominated limit, Zb >> Zd and
Zv, the dpa* scales with N5b!
The CBM also predicts bimodal cavity size distributions, 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 15 shows 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

0

0

20

40
60
Void diameter (nm)

80

Figure 15 A typical example of a bimodal cavity size
distribution composed of small bubbles and large voids in
a Ni–He dual ion-irradiated AuSS at 670  C, 10 dpa, and a

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

the literature111,112,114,133,153 Figure 16(a) shows low
He favors the formation of large voids in a CW
stainless steel irradiated in experimental breeder
reactor-II (EBR-II) to 40 dpa at 500  C and 43 appm
He, resulting in %12% swelling, while Figure 16(b)
shows that the same alloy irradiated in HFIR at 515–
540  C to 61 dpa and 3660 appm He has a much
higher density of smaller cavities, resulting in only
2% swelling.16
Thus, while He is generally necessary for void
formation, very high bubble densities can actually
suppress swelling for the same irradiation conditions
as also shown previously in Figures 9 and 10. This
can lead to a nonmonotonic dependence of swelling
on the He/dpa ratio. One example of a model prediction of nonmonotonic swelling is shown in Figure 17.154 Note that unambiguous interpretations of
neutron-irradiation data are often confounded by
uncertainties in irradiation temperatures and complex
temperature histories.155,156 However, the suppression
of swelling by high Nb is clear even in these cases.
Bubble sinks can also play a significant role in the
post-incubation swelling rates. Neglecting vacancy
emission from large voids, and using the same assumptions described above, leads to a simple expression
_ the rate of
for the overall normalized swelling rate S,


160

The Effects of Helium in Irradiated Structural Alloys

0.25 mm

0.10 mm

(b)

(a)

Figure 16 Comparison of swelling in a 20% CW AuSS irradiated in fast spectrum Experimental Breeder Reactor-II
(EBR-II, low He) and the mixed spectrum HFIR (high He) reactors: (a) the EBR-II irradiation at 510  C to 69 dpa and 43 appm
He produced %12% swelling; (b) the HFIR irradiation at 515–540  C to 61 dpa an appm He/dpa ratio %60 produced %2%
swelling. Reproduced from Maziasz, P. J. J. Nucl. Mater. 1993, 205, 118.

50

5
PCA, 500–520 ЊC,
11–13 dpa

Swelling (DV/VO, %)

3

SA CW
FFTF
ORR
HFIR

Model predictions
550 ЊC, 75 dpa CW
316

40

30

2

20

1

10

0
0

20
40
60
He/dpa ratio (appm He/dpa)

Swelling (DV/V, %)

Fusion range

4

0
80

Figure 17 Data for irradiations at 500–520  C 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.

increase in total void volume per unit volume divided
by the displacement rate as
S_ ¼ ½BZd Zv =½ðZb þ Zv þ Zd ÞðZd ð1 þ B Þ þ Zv þ Zb ފ
½11Š
Figure 18 shows S_ for B ¼ 0.15 and  ¼ 0.3 as a
function of Zv/Zd, with a peak at Zd ¼ Zv and

Zb ( 1, representing the case when nearly all the
bubbles have converted to voids and balanced void
and dislocation sink strengths. The S_ decreases at
higher and lower Zv/Zd. Figure 18 also shows S_ as
a function of Zv/Zd for a range of Zb/Zv. Increasing
Zb with the other sink strengths fixed reduces the S_
in the limit scaling with 1=Zb2 . These results again
show that significant swelling rates require some


The Effects of Helium in Irradiated Structural Alloys

10-1
10-2
10-3

·
S

10-4
10-5
10-6

Zb/Zv = 0.1
Zb/Zv = 1

10-7

Zb/Zv = 10
Zb/Zv = 100

10-8
10-3

10-2

10-1

100

101

102

103

Zv / Zd
_ for various bubble
Figure 18 Predicted swelling rate (S)
to void sink strength ratios (Zb/Zv) as a function of the void
to dislocation sink ratio (Zv/Zd). The highest S_ is for a low
Zb/Zv at a balanced void and dislocation sink strengths
Zv % Zb. S_ decreases with increasing Zb/Zv and the
corresponding peak rate shifts to lower Zb/Zv.

bubbles to form voids with a sink strength of Zv that 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 reasonably well known, including for defect production,
recombination, dislocation bias, sink strengths, interface 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 Fv based 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 concenp

trations, scaling as Nb / GHe .111,112,131–133,140,144,172
The exponent p varies between limits of %0, for
totally heterogeneous bubble nucleation on a fixed
number of deep trapping sites, to >1 when the

161

dominant He fate is governed by trap binding energies, large He bubble nucleus cluster sizes (most
often assumed to be only two atoms), and loss of He
to other sinks. Assuming the dominant fate of He is to
form matrix bubbles, p has a natural value of % 1=2
for the condition that the probability of diffusing He
to nucleate a new matrix bubble as a di-He cluster is
equal to the probability of the He being absorbed in a
previously formed bubble.158
Bubble formation is also sensitive to temperature
and depends on the diffusion coefficient and mechanism, as well as He binding energies at various
trapping sites. Substitutional He (Hes) diffuses by
vacancy exchange with an activation energy of
Ehs % 2.4 eV.159 For bimolecular nucleation of matrix
bubbles, Nb scales as exp(ÀEhs/2kT ). Helium can
also diffuse as small n ! 2 and m ! 1 vacancy–He
complexes, but bubbles are essentially immobile at
much larger sizes. Helium is most likely initially
created as interstitial He (Hei), which diffuses so
rapidly that it can be considered to simply partition
to various trapping sites, including vacancy traps,
where Hei þ V ! Hes. Note that, for interstitial diffusion, the matrix concentrations of Hei are so low
that migrating Hei–Hei reactions would not be
expected to form He bubbles. Thermal detrapping of

Hes from vacancies to form Hei is unlikely because of
the high thermal binding energy160 and see Section
1.06.5 for other references) but can occur by a Hes þ
SIA ! Hei reaction, as well as by direct displacement
events.152,161 If Hei and Hes maintain their identities at
trapping sites, they can detrap in the same configuration. Clustering reactions between Hes, Hei, and
vacancies 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 sites
noted above as well as deeper local traps within
these general sites, such as dislocation jogs and
grain boundary junctions136 (and see Section 1.06.5
for other references). If the trapping energies are low,
or temperatures are high, He can recycle between
various traps and the matrix a number of times before
it forms or joins a bubble. However, once formed
bubbles are very deep traps, and at a significant sink
density, they play a dominant role in the transport
and fate of He.
In principle, the binding energies of He clusters
are also important to bubble nucleation. Recent
ab initio simulations have shown that even small clusters of Hei in Fe are bound, although not as strongly
as Hes–V complexes. Indeed, the binding energies of


162

The Effects of Helium in Irradiated Structural Alloys

small HemVn complexes with n ! m are large (2.8–
3.8 eV),134,135 suggesting 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
Gdpa that 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
p
complex. The observation that Nb scales as GHe 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 suppressed 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 precipitation 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 microstructural and microchemical evolutions that take place in
alloys under irradiation. In addition to loops and
network dislocations, other coevolutions include solute 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.133,144 Later work in the 1990s further developed
and refined this code.163 A major objective of much of
this research was to develop models to make quantitative 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 material 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),16,119 complemented by extensive dual ion CPI results.26,124,125,128,129,157,164a,164–171
The semiempirical CBM models and concepts rationalize a wide range of seemingly complex and sometimes disparate observations, including the following:
 Void nucleation on bubbles
 The general trends in the temperature, dpa, and
He/dpa dependence of the number densities of
bubbles and voids
 Incubation dpa and postincubation swelling rates,
including the effects of temperature and stress
 The occurrence of bimodal cavity size distributions of small He bubbles and larger voids
 Bubble nucleation on dislocations and precipitate
interfaces
 Swelling that is increased, decreased, or unaltered
by increasing GHe, depending on the combination

of other irradiation and material variables
 Suppression of void swelling by a very high number of densities of bubbles
 Highly coupled concurrent evolutions of all the
microstructural features, resulting in weaker trend
toward refinement of precipitate and loop structures at higher GHe and, in the limit of very high
Nb, suppression of loops and precipitation
 Strong effects of the schedule and temperature
history of He implantation in CPI
 Effects of alloying elements on swelling incubation
associated with corresponding influence on precipitation, solute segregation, and the self-diffusion
coefficient
 Swelling resistance of AuSS that have stable finescale precipitates that trap He in small interface
bubbles
 The much higher swelling resistance of bcc FMS
compared with fcc AuSS
The concept of trapping He in a high number density of bubbles to enhance the swelling and HTHE
resistance (and creep properties in general) was implemented in the development of AuSS containing
fine-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 and
heat treated to produce a high density of fine-scale
TiC (Figure 19(b)) phases with less than 0.2%
bubble swelling following irradiation to 45 dpa and
2500 appm He at 600  C.172 There are many other
examples of swelling-resistant AuSS that were successful in delaying the onset of swelling to much


The Effects of Helium in Irradiated Structural Alloys

(a)

(b)

163

0.25 mm

Figure 19 Comparison of a conventional AuSS (a) to a swelling-resistant (b) Ti-modified alloy for HFIR irradiations
at 600  C to 45 dpa and 2500 appm He. Reproduced from Maziasz, P. J.; J. Nucl. Mater. 1984, 122(1–3), 472.

higher dpa than in conventional AuSS. However, as
illustrated in Figure 7, these steels also eventually
swell. This has largely been attributed to thermalirradiation 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 partitioning 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.15,176 However, 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/Zd ratios closer to 1,
resulting in higher swelling rates.52,157,168–171 Recent
models predict significant swelling in FMS,178 and the
potential for high postincubation swelling rates in

these alloys remains to be assessed. Swelling in
FMS clearly poses a significant life-limiting challenge in fusion first wall environments in the temperature range between 400 and 600  C.
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 manifestations 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 generation excess vacancies that can accumulate at

growing voids. In particular, tensile stresses normal
to GBs (s) generate a flux of vacancies to boundary
cavity sinks, if present, and an equal, but opposite,
flux of atoms that plate out along the boundary as
illustrated in Figure 20(a). The simple capillary condition for the growth of empty cavities is the s > 2g/
r. In this case of cavities containing He, the growth
rate is given by
dr =dt ¼ ½ðDgb dÞ=ð4pr 2 ފ
f1 À exp½ð2g=r À P À sÞO=kT Šg

½12Š

Here Dgb and d are the grain boundary diffusion coefficient and thickness, respectively. The
corresponding dr/dt ¼ 0 conditions also lead to
a stable bubble (rb) and unstably growing creep
cavity (r*) roots. As noted previously, a vacancy
supersaturation, L, produces a chemical stress that

is equivalent to a mechanical stress s ¼ kT ln(L)/O.
Thus, replacing ln(L) in eqn [8a] and [8b] with
sO/kT directly leads to expressions for m* and r*
for creep cavities
mà ¼ ½32Fv pg3 Š=½27kT s2 Š

½13aŠ

r à ¼ 0:75g=s

½13bŠ

This simple treatment can also be easily modified to
account for a real gas equation of state. Note that it is
usually assumed that GBs are perfect sinks for both
vacancies and SIA. Thus, it is generally assumed that
displacement damage does not contribute to the formation of growing creep cavities.
Understanding HTHE requires a corresponding
understanding of the basic mechanisms of creep rupture in the absence of He. At high stresses and short
rupture times, the normal mode of fracture in AuSS
is transgranular rupture, generally associated with
power law creep growth of matrix cavities.181,182
However, at lower stresses IG rupture occurs in a


164

The Effects of Helium in Irradiated Structural Alloys

sa

sb
Plating atoms
Jv

Ja

Creeping grain cage

Matrix

sn

Cavities

GB

sn
sb

GB particle

sa

(a)

(b)

Figure 20 (a) A schematic illustration of cavity growth by vacancy diffusion and atom plating when subject to an applied
stress, sa. The surrounding cage of uncavitated grains must creep to accommodate the displacements caused by the
cavitated grain boundary. This results in a back stress, sb, that reduces the net stress, sn, on the grain boundary (sn ¼ sa À sb)

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.

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 conditions a low to moderate density of grain boundary
cavities forms (1010–1012 mÀ2), usually in association 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 in Figure 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, useful high-temperature multiphase structural alloys
must be designed to constrain creep cavity nucleation and growth rates by a variety of mechanisms.
For example, grain boundary phases can inhibit dislocation climb and atom plating.185
As illustrated in Figure 20(a), growth cavities, which
are typically not uniformly distributed on all grain
boundary facets, can be greatly inhibited by the constraint 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 GBs
that result in compatible deformation rates. Thus, it is the
accommodating matrix creep rate that actually controls
the rate of cavity growth, rather than grain boundary
diffusion itself. Creep-accommodated, constrained cavity growth rationalizes the Monkman–Grant relation187
between the creep rate (e0 ), the creep rupture time (tr),
and a creep rupture strain (ductility) parameter (er) as
e0 tr ¼ er

½14aŠ

Thus, in high-strength alloys, low dislocation creep
rates (e0 ) lead to long tr. The typical form of e0
e0 ¼ Asr expðÀQcr =kT Þ

½14bŠ

The effective stress power r for dislocation creep is
typically much greater than 5 for creep-resistant
alloys, and the activation energy for matrix creep of
Q cr % 250–350 kJ molÀ1 is on the order of the bulk
self-diffusion energy.181 These values are much higher
than those for unconstrained grain boundary cavity
growth, with r % 1–3 and Q gb % 200 kJ molÀ1.
A number of creep rupture and grain boundary
cavity growth models were proposed based on these
concepts.186,188,189 Note that there are also conditions,
when grain boundary vacancy diffusion and atom
plating are highly restricted and cavities are well
separated, where matrix creep enhances, rather than

constrains, cavity growth. As noted above, power law
creep controls matrix cavity growth at high stress,


The Effects of Helium in Irradiated Structural Alloys

leading to transgranular fracture.181,182 Models 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. However, 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 1010–1012 mÀ2.181,190
Figure 21 shows the evolution of He bubbles and grain
boundary cavities under stress.191 Indeed, Ngb of more
than 1015 mÀ2 have been observed in high-dose He
implantation studies.100,192 Although Ngb is not well
known for neutron-irradiated AuSS, it has been estimated to be of the order 1013 mÀ2 or 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 clusters on GBs. As less growth is required for a higher

density of cavities to coalesce, creep rupture strains,

YE-11560

YE-11611

(a)

(b)
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 Â 104 s; (b) the corresponding
cavity distribution for an implanted specimen annealed at
1023 K for 6.84 Â 104 s under a stress of 19.6 MPa.
Reproduced from Braski, D. N.; Schroeder, H.; Ullmaier, H.
J. Nucl. Mater. 1979, 83(2), 265.

165

er, roughly scale with NcÀ1=2 . Bubble-nucleated creep
cavities are also generally more uniformly distributed
on various grain boundary facets. More uniform
distributions and lower er decrease accommodation
constraint, thus, further reducing rupture times associated with cavity growth.
Equation [13a] suggests that m* scales with 1/s2.

If the GB bubbles nucleate quickly and once formed
the creep cavities rapidly grow and coalesce, then
creep rupture is primarily controlled by gas-driven
bubble growth to r* and m*.93–95,97 In the simplest case,
assuming a fixed number of grain boundary bubbles
Ngb and flux of He to the grain boundary, JHe, the
creep rupture time, tr, is approximately given by
tr ¼ f½Fv 32pg3 Š=½27kT s2 Šg½Ngb =JHe Š $ Ngb =½GHe s2 Š ½15Š

Note that this simple model, predicting tr / 1/s2 scaling, is a limiting case primarily applicable at (a) low
stress; (b) when creep rupture is dominated by He
bubble conversion to creep cavities by gas-driven bubble growth to r*; and (c) when diffusion (or irradiation)
creep-enhanced stress relaxations are sufficient to produce compatible deformations without the need for
thermal dislocation creep in the grains. More generally, scaling of tr / 1/sr, r ! 2 is expected for bubbles
containing a distribution of m He atoms. For example,
if Ngb scales as mÀq, then Nc would scale as s2q.194,195
Further, at higher s, hence lower tr , there is less
time for He to collect on GBs. Thus in this regime,
intragranular dislocation creep, with a larger stress
power, r, may return as the rate-limiting mechanism
controlling the tr – s relations.
Equation [15] also provides important insight into
the effect of both the grain boundary and matrix
microstructures. 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 is
assumed that the number of matrix bubbles, Nb, is
proportional to √GHe while the grain boundary bubble number density (Ngb) is fixed, a scaling relation
for tr can be approximated as
pffiffiffiffi

tr / Ngb =½ G He s2 Š
½16Š
if the number of grain boundary bubbles also scales
À1=4
with √JHe, tr scales with GHe . At the other extreme,
if Nb and Ngb are both independent of the He conÀ1
(eqn [15]). Thus, microcentration, tr scales with GHe
structures with high Nb (and Zb) that are resistant to
void swelling are also likely to be resistant to HTHE.
HTHE models for AuSS were developed
based on these concepts and various elaborations93–96,182,190,194,196,197 as well as methane