Comprehensive nuclear materials 1 07 radiation damage using ion beams

1.07

Radiation Damage Using Ion Beams

G. S. Was
University of Michigan, Ann Arbor, MI, USA

R. S. Averback
University of Illinois at Urbana-Champagne, Urbana, IL, USA

ß 2012 Elsevier Ltd. All rights reserved.

1.07.1
1.07.2
1.07.3
1.07.3.1
1.07.3.2
1.07.3.3
1.07.3.4
1.07.4
1.07.4.1
1.07.4.1.1
1.07.4.1.2
1.07.4.2
1.07.4.2.1
1.07.4.2.2
1.07.4.2.3
1.07.4.2.4
1.07.4.2.5
1.07.4.2.6
1.07.4.3

1.07.5
1.07.5.1
1.07.5.2
1.07.5.3
1.07.6
References

Introduction
Motivation for Using Ion Beams to Study Radiation Damage
Review of Aspects of Radiation Damage Relevant to Ion Irradiation
Defect Production
Primary and Weighted Recoil Spectra
Damage Morphology
Damage Rate Effects
Contributions of Ion Irradiation to an Understanding of Radiation Effects
Electron Irradiations
Displacement threshold surfaces
Point defect properties
Ion Irradiations
The damage function
Freely migrating defects
Alloy stability under ion irradiation
Mechanical properties
Multiple ion beams
Swift ions
Comparison with Neutrons
Advantages and Disadvantages of Irradiations using Various Particle Types
Electrons
Heavy Ions
Light Ions

Practical Considerations for Radiation Damage Using Ion Beams

Abbreviations
AES
APT
bcc
BWR
dpa
fcc
FMD
FP
IASCC
IGSCC
LWR
MD
NRT

Auger electron spectroscopy
Atom probe tomography
Body-centered cubic
Boiling water reactor
Displacements per atom
Face-centered cubic
Freely migrating defect
Frenkel pair
Irradiation assisted stress corrosion
cracking
Intergranular stress corrosion
cracking
Light water reactor

Molecular dynamics
Norgett–Robinson–Torrens

NWC
PKA
RCS
RIS
SCC
STEM/EDS

TEM

195
196
197
197
199
200
202
204
204
204
205
206
206
207
207
209
209
209

211
215
216
217
219
219
221

Normal water chemistry
Primary knock-on atom
Recoil collision sequence
Radiation induced segregation
Stress corrosion cracking
Scanning transmission electron
microscopy/energy dispersive
spectrometry
Transmission electron microscopy

1.07.1 Introduction
Radiation effects research has been conducted using
a variety of energetic particles: neutrons, electrons,
protons, He ions, and heavy ions. Energetic ions
195


196

Radiation Damage Using Ion Beams

can be used to understand the effects of neutron

irradiation on reactor components, and interest in
this application of ion irradiation has grown in recent
years for several reasons including the avoidance of
high residual radioactivity and the decline of neutron
sources for materials irradiation. The damage state and
microstructure resulting from ion irradiation, and thus
the degree to which ion irradiation emulates neutron
irradiation, depend upon the particle type and the
damage rate. This chapter will begin with a summary
of the motivation for using ion irradiation for radiation
damage studies, followed by a brief review of radiation damage relevant to charged particles. The contribution of ion irradiation to our understanding of
radiation damage will be presented next, followed by
an account of the advantages and disadvantages of
the various ion types for conducting radiation damage
studies, and wrapping up with a consideration of practical issues in ion irradiation experiments.

1.07.2 Motivation for Using Ion
Beams to Study Radiation Damage
In the 1960s and 1970s, heavy ion irradiation was
developed for the study of radiation damage processes in materials. As ion irradiation can be
conducted at a well-defined energy, dose rate, and
temperature, it results in very well-controlled experiments that are difficult to match in reactors. As such,
interest grew in the use of ion irradiation for the
purpose of simulating neutron damage in support of
the breeder reactor program.1–3 Ion irradiation and
simultaneous He injection were also used to simulate
the effects of 14 MeV neutron damage in conjunction
with the fusion reactor engineering program. The
application of ion irradiation (defined here as irradiation by any charged particle, including electrons)
to the study of neutron irradiation damage caught

the interest of the light water reactor community to
address issues such as swelling, creep, and irradiation
assisted stress corrosion cracking of core structural
materials.4–6 Ion irradiation was also being used to
understand the irradiated microstructure of reactor
pressure vessel steels, Zircaloy fuel cladding, and
materials for advanced reactor concepts.
There is significant incentive to use ion irradiation
to study neutron damage as this technique has the
potential for yielding answers on basic processes
in addition to the potential for enormous savings in
time and money. Neutron irradiation experiments
are not amenable to studies involving a wide range

of conditions, which is precisely what is required for
investigations of the basic damage processes. Simulation by ions allows easy variation of the irradiation
parameters such as dose, dose rate, and temperature
over a wide range of values.
One of the prime attractions of ion irradiation is
the rapid accumulation of end of life doses in short
periods of time. Typical neutron irradiation experiments in thermal test reactors may accumulate damage at a rate of 3–5 dpa yearÀ1. In fast reactors, the
rates can be higher, on the order of 20 dpa yearÀ1. For
low dose components such as structural components
in boiling water reactor (BWR) cores that typically
have an end-of-life damage of 10 dpa, these rates are
acceptable. However, even the higher dose rate of a
fast reactor would require 4–5 years to reach the peak
dose of $80 dpa in the core baffle in a pressurized
water reactor (PWR). For advanced, fast reactor concepts in which core components are expected to
receive 200 dpa, the time for irradiation in a test

reactor becomes impractical.
In addition to the time spent ‘in-core,’ there is an
investment in capsule design and preparation as well
as disassembly and allowing for radioactive decay, adding additional years to an irradiation program. Analysis
of microchemical and microstructural changes by
atom probe tomography (APT), Auger electron spectroscopy (AES) or microstructural changes by energy
dispersive spectroscopy via scanning transmission
electron microscopy (STEM-EDS) and mechanical
property or stress corrosion cracking (SCC) evaluation can take several additional years because of the
precautions, special facilities, and instrumentation
required for handling radioactive samples. The result
is that a single cycle from irradiation through microanalysis and mechanical property/SCC testing may
require over a decade. Such a long cycle length does
not permit for iteration of irradiation or material
conditions that is critical in any experimental research
program. The long cycle time required for design and
irradiation also reduces flexibility in altering irradiation programs as new data become available. The
requirement of special facilities, special sample
handling, and long irradiation time make the cost
for neutron irradiation experiments very high.
In contrast to neutron irradiation, ion (heavy,
light, or electrons) irradiation enjoys considerable
advantages in both cycle length and cost. Ion irradiations of any type rarely require more than several
tens of hours to reach damage levels in the 1–100 dpa
range. Ion irradiation produces little or no residual
radioactivity, allowing handling of samples without


Radiation Damage Using Ion Beams

the need for special precautions. These features
translate into significantly reduced cycle length and
cost. The challenge then is to verify the equivalency
between neutron and ion irradiation in terms of
the changes to the microstructure and properties
of the material. The key question that needs to be
answered is how do results from neutron and charged
particle irradiation experiments compare? How, for
example, is one to compare the results of a component
irradiated in-core at 288  C to a fluence of 1 Â 1021 n
cmÀ2 (E > 1 MeV) over a period of one year, with an ion
irradiation experiment using 3 MeV protons at 400  C
to 1 dpa (displacements per atom) at a dose rate of
10À5 dpa sÀ1 ($1 day), or 5 MeV Ni2þ at 500  C to
10 dpa at a dose rate of 5 Â 10À3 dpa sÀ1 ($1 h)?
The first question to resolve is the measure of radiation effect. In the Irradiation assisted stress corrosion
cracking (IASCC) problem in LWRs, concern has centered on two effects of irradiation: radiation-induced
segregation of major alloying elements or impurities to
grain boundaries, which may cause embrittlement or
enhance the intergranular stress corrosion cracking
(IGSCC) process, and hardening of the matrix that
results in localized deformation and embrittlement.
The appropriate measure of the radiation effect in the
former case would then be the alloy concentration at
the grain boundary or the amount of impurity
segregated to the grain boundary. This quantity is
measurable by analytical techniques such as AES, APT,
or STEM-EDS. For the latter case, the measure of the
radiation effect would be the nature, size, density, and
distribution of dislocation loops, black dots, and the

total dislocation network, and how they impact
the deformation of the alloy. Hence, specific and measurable effects of irradiation can be determined for
both neutron and ion irradiation experiments.
The next concern is determining how ion irradiation translates into the environment describing neutron irradiation. That is, what are the irradiation
conditions required for ion irradiation to yield the
same measure of radiation effect as that for neutron
irradiation? This is the key question, for in a postirradiation test program, it is only the final state of
the material that determines equivalence, not the
path taken. Therefore, if ion irradiation experiments
could be devised that yielded the same measures
of irradiation effects as observed in neutron irradiation
experiments, the data obtained in postirradiation
experiments will be equivalent. In such a case, ion
irradiation experiments can provide a direct substitute
for neutron irradiation. While neutron irradiation will
always be required to qualify materials for reactor

197

application, ion irradiation provides a low-cost and
rapid means of elucidating mechanisms and screening
materials for the most important variables.
A final challenge is the volume of material that can
be irradiated with each type of radiation. Neutrons
have mean free paths on the order of centimeters
in structural materials. One MeV electrons penetrate
about 500 mm, 1 MeV protons penetrate about 10 mm,
and 1 MeV Ni ions have a range of less than 1 mm.
Thus, the volume of material that can be irradiated
with ions from standard laboratory-sized sources

(TEMs, accelerators), is limited.

1.07.3 Review of Aspects of Radiation
Damage Relevant to Ion Irradiation
1.07.3.1

Defect Production

The parameter commonly used to correlate the damage produced by different irradiation environments is
the total number of displacements per atom (dpa).
Kinchin and Pease7 were the first to attempt to determine the number of displacements occurring during
irradiation and a modified version of their model
known as the Norgett–Robinson–Torrens (NRT)
model8 is generally accepted as the international
standard for quantifying the number of atomic displacements in irradiated materials.9 According to the
NRT model, the number of Frenkel pairs (FPs),
nNRT(T ), generated by a primary knock-on atom
(PKA) of energy T is given by
nNRT ðT Þ ¼

kED ðT Þ
2Ed

½1Š

where ED(T ) is the damage energy (energy of the
PKA less the energy lost to electron excitation), Ed is
the displacement energy, that is, the energy needed to
displace the struck atom from its lattice position, and k
is a factor less than 1 (usually taken as 0.8). Integration

of the NRT damage function over recoil spectrum and
time gives the atom concentration of displacements
known as the NRT displacements per atom (dpa):
ðð
½2Š
dpa ¼ fðEÞvNRT ðT ÞsðE; T ÞdT dE
where f(E) is the neutron flux and s(E,T ) is the probability that a particle of energy E will impart a recoil
energy T to a struck atom. The displacement damage is
accepted as a measure of the amount of change to the
solid due to irradiation and is a much better measure
of an irradiation effect than is the particle fluence.
As shown in Figure 1, seemingly different effects of


198

Radiation Damage Using Ion Beams

300
LASREF, 40 ЊC
RTNS-II, 90 ЊC
OWR, 90 ЊC

250

Yield stress change (MPa)

Yield stress change (MPa)

300

200
150
100
50
0

1017

1018

1019

LASREF, 40 ЊC
RTNS-II, 90 ЊC
OWR, 90 ЊC

250
200
150
100
50

0

1020

10−3

Neutron fluence, E > 0.1 MeV

10−2

DPA

Figure 1 Comparison of yield stress change in 316 stainless steel irradiated in three facilities with very different neutron
energy flux spectra. While there is little correlation in terms of neutron fluence, the yield stress changes correlate well
against displacements per atom (dpa). Reprinted, with permission, from ASTM, copyright ASTM International, 100 Barr
Harbor Drive, West Conshohocken, PA 19428.

7.5 MeV tantalum
10−15

1012

5 MeV nickel
1010
Protons
ITER be first wall
HFIR target
FFTF mid-core
PWR 1/4-T RPV

108
106
104 −9
10

10−7

10−5
10−1
10−3
Particle energy (MeV)

10

Figure 2 Energy spectrum for neutrons from a variety
of reactor types and a monoenergetic proton beam.
Reproduced from Stoller, R. E.; Greenwood, L. R.
J. Nucl. Mater. 1999, 271–272, 57–62.

Calculated dpa/(incident particle) (cm2)

Neutron flux/lethergy (n cm−2 s−1)
proton flux (ions cm−2 s−1)

10−14
1014

10−16

20 MeV carbon

10−17
1.3 MeV hydrogen

10−18

10−19

14 MeV neutrons
−20

1 MeV neutrons

10

irradiation on low temperature yield strength for the
same fluence level (Figure 1(a)) and disappear when
dpa is used as the measure of damage (Figure 1(b)).
A fundamental difference between ion and neutron irradiation effects is the particle energy spectrum
that arises because of the difference in the way the
particles are produced. Ions are produced in accelerators and emerge in monoenergetic beams with
very narrow energy widths. However, the neutron
energy spectrum in a reactor extends over several
orders of magnitude in energy, thus presenting a
much more complicated source term for radiation
damage. Figure 2 shows the considerable difference
in neutron and ion energy spectra and also between
neutron spectra in different reactors and at different
locations within the reactor vessel.

10−21

0

2

4
6

8
Distance into solid (m)

10

12

Figure 3 Displacement–damage effectiveness for various
energetic particles in nickel. Reproduced from Kulcinski,
G. L.; Brimhall, J. L.; Kissinger, H. E. In Proceedings of
Radiation-Induced Voids in Metals; Corbett, J. W.,
Ianiello, L. C., Eds.; USAEC Technical Information Center:
Oak Ridge, TN, 1972; p 453, CONF-710601.

Another major difference in the characteristics of
ions and neutrons is their depth of penetration. As
shown in Figure 3, ions lose energy quickly because
of high electronic energy loss, giving rise to a spatially nonuniform energy deposition profile caused


Radiation Damage Using Ion Beams

where Rd is the number if displacements per unit volume per unit time, N is the atom number density, and f
is the particle flux (neutron or ion). In the case of
neutron–nuclear interaction described by the hardsphere model, eqn [3] becomes
 
Rd
gE
ss
¼

½4Š
Nf
4Ed
where g ¼ 4mM/(m þ M)2, M is the target atom mass, m
is the neutron mass, E is the neutron energy, and ss is
the elastic scattering cross-section. For the case of ion–
atom interaction described by Rutherford scattering,
eqn [3] becomes
 
Rd
pZ2 Z2 e4 M1
gE
¼ 1 2
ln ;
½5Š
NI
4EEd
M2
Ed
where e is the unit charge, M1 is the mass of the ion, and
M2 is the mass of the target atom. As shown in Figure 3,
for comparable energies, 1.3 MeV protons cause over
100 times more damage per unit of fluence at the
sample surface than 1 MeV neutrons, and the factor
for 20 MeV C ions is over 1000. Of course, the damage
depth is orders of magnitude smaller than that for
neutron irradiation.
1.07.3.2 Primary and Weighted
Recoil Spectra
A description of irradiation damage must also consider the distribution of recoils in energy and space.

The primary recoil spectrum describes the relative
number of collisions in which the amount of energy
between T and T þ dT is transferred from the primary

recoil atom to other target atoms. The fraction of
recoils between the displacement energy Ed, and T is
ð
1 T
sðE; T 0 ÞdT 0
½6Š
PðE; T Þ ¼
N Ed
where N is the total number of primary recoils and
s(E,T ) is the differential cross-section for a particle
of energy E to create a recoil of energy T. The recoil
fraction is shown in Figure 4, which reveals only a
small difference between ions of very different masses.
Figure 5 shows the difference in the types
of damage that are produced by different types of
1.0

0.8
Fraction of recoils

by the varying importance of electronic and nuclear
energy loss during the slowing down process. Their
penetration distances range between 0.1 and 100 mm
for ion energies that can practically be achieved by
laboratory-scale accelerators or implanters. By virtue
of their electrical neutrality, neutrons can penetrate

very large distances and produce spatially flat damage profiles over many millimeters of material.
Further, the cross-section for ion–atom reaction is
much greater than for neutron–nuclear reaction giving
rise to a higher damage rate per unit of particle fluence.
The damage rate in dpa per unit of fluence is proportional to the integral of the energy transfer cross-section
and the number of displacements per PKA, nNRT(T):
ð gE
Rd
¼ sðE; T ÞnNRT ðT ÞdT
½3Š
Nf
Ed

199

He
H
Kr
Ar

0.6
Ne
0.4

Fraction of recoils
with energy above
Ed and below T

0.2
1 MeV ions ® Cu

0
101

102

103

104

T (eV)
Figure 4 Integral primary recoil spectra for 1 MeV
particles in copper. Curves plotted are the integral fractions
of primary recoils between the threshold energy and recoil
energy, T from eqn [6]. Reproduced from Averback, R. S.
J. Nucl. Mater. 1994, 216, 49.

1 MeV electrons
T = 60 eV
e = 50−100%

106

E

105
104

1 MeV protons
T = 200 eV
e = 25%

Ti

103
102

1 MeV heavy ions
T = 5 keV
e = 4%

Tn

Ed

Tp
Te

101
E

1 MeV neutrons
T = 35 keV
e = 2%
Figure 5 Difference in damage morphology, displacement
efficiency, and average recoil energy for 1 MeV particles of
different types incident on nickel. Reproduced from
Was, G. S.; Allen, T. R. Mater. Char. 1994, 32, 239.


Radiation Damage Using Ion Beams

particles. Light ions such as electrons and protons
will produce damage as isolated FPs or in small
clusters while heavy ions and neutrons produce damage in large clusters. For 1 MeV particle irradiation of
copper, half the recoils for protons are produced with
energies less than $60 eV while the same number
for Kr occurs at about 150 eV. Recoils are weighted
toward lower energies because of the screened
Coulomb potential that controls the interactions of
charged particles. For an unscreened Coulomb interaction, the probability of creating a recoil of energy
T varies as 1/T2. However, neutrons interact as
hard spheres and the probability of creating a recoil
of energy T is independent of recoil energy.
In fact, a more important parameter describing the
distribution of damage over the energy range is a
combination of the fraction of defects of a particular
energy and the damage energy. This is the weighted
average recoil spectrum, W(E,T ), which weights the
primary recoil spectrum by the number of defects or
the damage energy produced in each recoil:
ðT
1
sðE; T 0 ÞED ðT 0 ÞdT 0
½7Š
W ðE; T Þ ¼
ED ðEÞ Ed
ED ðEÞ ¼

ð T^

sðE; T 0 ÞED ðT 0 ÞdT 0

½8Š

Ed

^ is the maximum recoil energy given by
where T
^
T ¼ gEi ¼ 4EiM1M2/(M1 þ M2)2. Ignoring electron
excitations and allowing ED(T ) ¼ T, then the
weighted average recoil spectra for Coulomb and
hard sphere collisions are
WCoul ðE; T Þ ¼

lnT À lnEd
^ À lnEd
lnT

½9Š

T 2 À Ed2
Ed2

½10Š

WHS ðE; T Þ ¼

Equations [9] and [10] are graphed in Figure 6 for
1 MeV particle irradiations of copper. The characteristic energy, T1/2 is that recoil energy below which

half of the recoils are produced. The Coulomb
forces extend to infinity and slowly increase as the
particle approaches the target; hence the slow
increase with energy. In a hard sphere interaction,
the particles and target do not interact until their
separation reaches the hard sphere radius at which
point the repulsive force goes to infinity. A screened
Coulomb is most appropriate for heavy ion irradiation. Note the large difference in W(E,T ) between
the various types of irradiations at E ¼ 1 MeV.

1.0
Copper
0.8

Protons

Ne

0.6

Kr

W (T)

200

0.4
Neutrons
0.2

0
101

102

103

104
T (eV)

105

106

107

Figure 6 Weighted recoil spectra for 1 MeV particles in
copper. Curves representing protons and neutrons are
calculated using eqns [9] and [10], respectively. W(T ) for other
particles were calculated using Lindhard cross-sections
and include electronic excitation. Reproduced from
Averback, R. S. J. Nucl. Mater. 1994, 216, 49.

While heavy ions come closer to reproducing the
energy distribution of recoils of neutrons than do
light ions, neither is accurate in the tails of the distribution. This does not mean that ions are poor simulations of radiation damage, but it does mean that
damage is produced differently and this difference
will need to be considered when designing an irradiation program that is intended to produce microchemical and microstructural changes that match those
from neutron irradiation.
There is, of course, more to the description of

radiation damage than just the number of dpa.
There is the issue of the spatial distribution of damage
production, which can influence the microchemistry
and microstructure, particularly at temperatures
where diffusion processes are important for microstructural development. In fact, the ‘ballistically’
determined value of dpa calculated using such a
displacement model is not the appropriate unit to
be used for dose comparisons between particle
types. The reason is the difference in the primary
damage state among different particle types.

1.07.3.3

Damage Morphology

The actual number of defects that survive the displacement cascade and their spatial distribution
in solids will determine the effect on the irradiated
microstructure. Figure 7 summarizes the effect of


Radiation Damage Using Ion Beams

201

Total dpa
Particle type
and energy
Loss to
displacement
cascades

Freely migrating
defects

Mutual
recombination
outside of cascade

Loss to sinks
in matrix

Loss at grain
boundaries

Void swelling
loop structure

Defect diffusion
matrix chemistry

Boundary
structure
and micro
chemistry
Radiation-induced
segregation

Figure 7 History of point defects after creation in the displacement cascade.

damage morphology from the viewpoint of the grain

boundary and how the defect flow affects radiationinduced grain boundary segregation. Of the total
defects produced by the energetic particle, a fraction
appears as isolated, or freely migrating defects, and the
balance is part of the cascade. The fraction of the
‘ballistically’ produced FPs that survive the cascade
quench and are available for long-range migration is
an extremely important quantity and is called the
migration efficiency, e. These ‘freely migrating’ or ‘available migrating’ defects10 are the only defects that will
affect the amount of grain boundary segregation,
which is one measure of radiation effects. The migration efficiency can be very small, approaching a few
percent at high temperatures. The migration efficiency, e, comprises three components:
gi,v: the isolated point defect fraction,
di,v: clustered fraction including mobile defect
clusters such as di-interstitials, and
z: fraction initially in isolated or clustered form
after the cascade quench that is annihilated during
subsequent short-term (>10À11 s) intracascade
thermal diffusion.
They are related as follows:
e ¼ di þ g i þ z i ¼ d v þ g v þ z v

½11Š

Figure 8 shows the history of defects born as vacancies and interstitials as described by the NRT model.

Displacement cascade efficiency
(x)
Intracascade thermal
recombination (z )
Surviving defect

fraction (QDF) (x – z )
Isolated point defect
fraction (IDF) (g i,v)

Clustered point defect
fraction (CDF) (d i,v)

Mobile
clusters

Immobile
clusters

Evaporating
defects
Available
defects (li,v)

Figure 8 Interdependence of isolated point defects,
mobile defect clusters, and thermally evaporating defect
clusters that contribute to the fraction of surviving defects
that are ‘available’ for radiation effects. Reproduced from
Zinkle, S. J.; Singh, B. N. J. Nucl. Mater. 1993, 199, 173.

Due to significant recombination in the cascade,
only a fraction ($30%) is free to migrate from the
displacement zone. These defects can recombine outside of the cascade region, be absorbed at sinks in the


202

Radiation Damage Using Ion Beams

matrix (voids, loops), or be absorbed at the grain
boundaries, providing for the possibility of radiationinduced segregation.
The fraction of defects that will be annihilated
after the cascade quench by recombination events
among defect clusters and point defects within the
same cascade (intracascade recombination), z, is
about 0.07, for a migration efficiency of 0.3 (see
below for additional detail).10 The clustered fraction,
d includes large, sessile clusters and small defect
clusters that may be mobile at a given irradiation
temperature and will be different for vacancies and
interstitials. For a 5 keV cascade, di is about 0.06 and
dv is closer to 0.18.10 Some of these defects may be
able to ‘evaporate’ or escape the cluster and become
‘available’ defects (Figure 8).
This leaves g, the isolated point defect fraction
that are available to migrate to sinks, to form clusters, to interact with existing clusters, and to participate in the defect flow to grain boundaries that
gives rise to radiation-induced segregation. Owing
to their potential to so strongly influence the irradiated microstructure, defects in this category, along
with defects freed from clusters, make up the freely
migrating defect (FMD) fraction. Recall that electrons
and light ions produce a large fraction of their
defects as isolated FPs, thus increasing the likelihood of their remaining as isolated rather than clustered defects. Despite the equivalence in energy
among the four particle types described in Figure 5,
the average energy transferred and the defect production efficiencies vary by more than an order of
magnitude. This is explained by the differences in
the cascade morphology among the different particle types. Neutrons and heavy ions produce dense

cascades that result in substantial recombination
during the cooling or quenching phase. However,
electrons are just capable of producing a few widely
spaced FPs that have a low probability of recombination. Protons produce small widely spaced cascades and many isolated FPs due to the Coulomb
interaction and therefore, fall between the extremes
in displacement efficiency defined by electrons and
neutrons.
The value of g has been estimated to range from
0.01 to 0.10 depending on PKA energy and irradiation temperature, with higher temperatures resulting
in the lower values. Naundorf12 estimated the freely
migrating defect fraction using an analytical treatment based on two factors: (1) energy transfer to
atoms is only sufficient to create a single FP, and
(2) the FP lies outside a recombination (interaction)

Table 1
Efficiency for producing freely migrating
defects, g, in nickel by different kinds of irradiations (Ed ¼ 40
eV, riv ¼ 0.7 nm) using Lindhard’s analytical differential
collision cross-section
Irradiation

(%)

1 MeV Hþ
2 MeV Hþ
2 MeV Liþ
1.8 MeV Neþ
300 keV Niþ
3 MeV Niþ
3.5 MeV Krþ

2 keV Oþ

24.0
19.2
16.9
8.7
2.3
3.8
3.0
9.8

Source: Naundorf, V. J. Nucl. Mater. 1991, 182, 254.

radius so that the nearby FPs neither recombine nor
cluster. The model follows each generation of the
collision and calculates the fraction of all defects
produced that remain free. Results of calculation
using the Naundorf model are shown in Table 1 for
several ions of varying mass and energy. Values of Z
range between 24% for proton irradiation to 3% for
heavy ion (krypton) irradiation. Recent results,13
however, have shown that the low values of FMD
efficiency for heavy ion or neutron irradiation cannot
be explained by defect annihilation within the parent
cascade (intracascade annihilation). In fact, cascade
damage generates vacancy and interstitial clusters
that act as annihilation sites for FMD, reducing the
efficiency of FMD production. Thus, the cascade
remnants result in an increase in the sink strength
for point defects and along with recombination in the

original cascade, account for the low FMD efficiency
measured by experiment.
1.07.3.4

Damage Rate Effects

As differences in dose rates can confound direct
comparison between neutron and ion irradiations, it
is important to assess their impact. A simple method
for examining the tradeoff between dose and temperature in comparing irradiation effects from different
particle types is found in the invariance requirements.
For a given change in dose rate, we would like to know
what change in dose (at the same temperature) is
required to cause the same number of defects to be
absorbed at sinks. Alternatively, for a given change
in dose rate, we would like to know what change in
temperature (at the same dose) is required to cause
the same number of defects to be absorbed at
sinks. The number of defects per unit volume, NR,
that have recombined up to time t, is given by Mansur14


Radiation Damage Using Ion Beams

ðt
NR ¼ Riv Ci Cv dt

½12Š

0

where Riv is the vacancy–interstitial recombination
coefficient and Ci and Cv are interstitial and vacancy
concentrations, respectively. Similarly, the number of
defects per unit volume that are lost to sinks of type j,
NSj, up to time t, is
ðt
NSj ¼ kSj Cj dt

½13Š

0

where kSj is the strength of sink j and Cj is the sink
concentration. The ratio of vacancy loss to interstitial
loss is
RS ¼

NSv
NSi

½14Š

where j ¼ v or i. The quantity NS is important in
describing the microstructural development involving
total point defect flux to sinks (e.g., RIS), while RS is the
relevant quantity for the growth of defect aggregates
such as voids that require partitioning of point defects
to allow growth. In the steady-state recombination dominant
regime, for NS to be invariant at a fixed dose, the following relationship between ‘dose rate (Ki) and temperature

(Ti)’ must hold:
 2  
kT1
K2
Evm ln K1


 
T2 À T1 ¼
½15Š
K2
1
ln
1 À kT
Evm
K1
where Evm is the vacancy migration energy. In the
steady-state recombination dominant regime, for RS to be

invariant at a fixed dose, the following relationship
between ‘dose rate and temperature’ must hold:

  
kT12
K2
Evm þ2Evf ln K1

  
½16Š
T2 À T1 ¼

K2
1
ln
1 À EvmkT
þ2Evf
K1
where Evf is the vacancy formation energy. In the steadystate recombination dominant regime, for NS to be invariant
at a fixed temperature, the following relationship
between ‘dose (F) and dose rate’ must hold:
 1=2
F2
K2
¼
½17Š
F1
K1
Finally, in the steady-state recombination dominant regime,
for NS to be invariant at a fixed dose rate, the following
relationship between ‘dose and temperature’ must hold:

  
À2kT12
2
ln F
Evm
F1
   
½18Š
T2 À T1 ¼
F2

1
ln
1 À kT
Evm
F1
Figure 9 shows plots of the relationship between the
ratio of dose rates and the temperature difference
required to maintain the same point defect absorption
at sinks (a), and the swelling invariance (b).
The invariance requirements can be used to
prescribe an ion irradiation temperature–dose rate
combination that simulates neutron radiation. We
take the example of irradiation of stainless steel
under typical BWR core irradiation conditions of
$4.5 Â 10À8 dpa sÀ1 at 288  C. If we were to conduct
a proton irradiation with a characteristic dose rate of
7.0 Â 10À6 dpa sÀ1, then using eqn [15] with a vacancy
formation energy of 1.9 eV and a vacancy migration

50

700

40

500

Em
ν = 0.5

400
300
200

1.0
1.5

100

(a)

DTemperature (ЊC)

DTemperature (ЊC)

600

0

203

1

10
100
Ratio of dose rates

Eνm = 0.5
30
1.0

1.5
20

10

0

1000

1

(b)

10
100
Ratio of dose rates

1000

Figure 9 Temperature shift from the reference 200  C required at constant dose in order to maintain (a) the same point
defect absorption at sinks, and (b) swelling invariance, as a function of dose rate, normalized to initial dose rate. Results are
shown for three different vacancy migration energies and a vacancy formation energy of 1.5 eV. Adapted from Mansur, L. K.
J. Nucl. Mater. 1993, 206, 306–323; Was, G. S. Radiation Materials Science: Metals and Alloys; Springer: Berlin, 2007.


204

Radiation Damage Using Ion Beams

energy of 1.3 eV, the experiment will be invariant in

NS with the BWR core irradiation (e.g., RIS) at a
proton irradiation temperature of 400  C. Similarly,
using eqn [16], a proton irradiation temperature of
300  C will result in an invariant RS (e.g., swelling
or loop growth). For a Ni2þ ion irradiation at a dose
rate of 10À3 dpa sÀ1, the respective temperatures are
675  C (NS invariant) and 340  C (RS invariant). In
other words, the temperature ‘shift’ due to the higher
dose rate is dependent on the microstructure feature
of interest. Also, with increasing difference in dose
rate, the DT between neutron and ion irradiation
increases substantially. The nominal irradiation temperatures selected for proton irradiation, 360  C and
for Ni2þ irradiation, 500  C represent compromises
between the extremes for invariant NS and RS.

1.07.4 Contributions of Ion
Irradiation to an Understanding of
Radiation Effects
Ion irradiations have been critical to the development
of both our fundamental and applied understanding
of radiation effects. As discussed in Sections 1.07.2
and 1.07.3, it is the flexibility of such irradiations and
our firm understanding of atomic collisions in solids
that afford them their utility. Principally, ion irradiations have enabled focused studies on the isolated
effects of primary recoil spectrum, defect displacement rate, and temperature. In addition, they have
provided access to the fundamental properties of
point defects, defect creation, and defect reactions.
In this section, we highlight a few key experiments
that illustrate the broad range of problems that can
be addressed using ion irradiations. We concentrate

our discussion on past ion irradiations studies that
have provided key information required by modelers
in their attempts to predict materials behavior in
existing and future nuclear reactor environments,
and particularly information that is not readily
available from neutron irradiations. In addition, we
include a few comparative studies between ion
and neutron irradiations to illustrate, on one hand,
Table 2

the good agreement that is possible, while on the other,
the extreme caution that is necessary in extrapolating
results of ion irradiations to long-term predictions
of materials evolution in a nuclear environment.
1.07.4.1

Electron Irradiations

The unique feature of electron irradiations in comparison to ions and neutrons is that they create defects in
very low-energy recoil events. As a consequence, nearly
all FPs are produced in isolation. This has been of
foremost importance in developing our understanding
of radiation damage, as it made studies of defect creation mechanisms as well as the fundamental properties
of FPs possible. Recall that the properties of vacancies
andvacancy clusters, for example, formation and migration energies, stacking fault energies, etc., could be
determined from quenching studies. It is not possible,
however, to quench in interstitials in metals. Very little
was therefore known about this intrinsic defect prior
to about 1955 when irradiation experiments became
widely employed. In this section, we highlight some of

the key findings derived from these past studies.
1.07.4.1.1 Displacement threshold surfaces

The creation of a stable FP requires that a lattice
atom receives an energy greater than Tm, which is
the minimum displacement energy. This value has
been determined experimentally in many materials
by measuring the change in some physical property,
such as electrical resistivity or length change, as a
function of maximum recoil energy of a target atom.
Such experiments are practical only for electron
irradiations for which recoil energies can be kept
low, but with the irradiation particles still penetrating
deeply into, or through, the specimen. Typical values
are shown in Table 2.
As a crystal is not homogeneous, the threshold
energy depends on the crystallographic direction in
which the knock-on atom recoils. The anisotropy of
the threshold energy surface has been mapped out in
various crystals by measuring the production rate of
defects as a function of both the electron energy, near
threshold, and the orientation of single crystalline

Minimum displacement energies in pure metals, semiconductors, and stainless steel (SS)

Materials

Al

Cgraph

Cu

Fe

Ge

Mo

Ni

W

Si

SS

Tm (eV)

16

25

19

17

15

33

23

41

13

18

Source: Lucasson, P. In Fundamental Aspects of Radiation Damage in Metals; Robibnson, M. T., Young, F. W., Jr., Eds.; ERDA Report
CONF-751006; 1975; p 42; Andersen, H. H. Appl. Phys. 1979, 18, 131.


Radiation Damage Using Ion Beams

specimens with respect to the electron beam direction.15,16 The total cross-section for FP production
rate is given by the expression
2ðp p=2
ð

sd ðY1 ; F1 ; E1 Þ ¼
0

0

dsðy2 ; E1 Þ df2
2p
dy2

½19Š

nðY2 ; F2 ; T Þdy2
where the subscripts 1 and 2 refer to incoming electron and recoiling ion, respectively, and Y1, F1, Y2,
F2 are the polar and azimuthal angles of the electron
beam relative to the crystal axis; y2, f2, are these
same angles relative to the beam direction; n is the
anisotropic damage function. Near threshold, n ¼ 1
for T > Tm, and 0 for T < Tm. By measuring the
production rate for many sample orientations and
energies, the damage function can be obtained using
eqn [19], although various approximations are required
in the deconvolution. The results are illustrated
in Figure 10 for Cu.17 It is noteworthy that the
minimum threshold energy is located in the vicinity
of close-packed directions. This is also true for bcc
metals. The anisotropy reflects the basic mechanism
of defect production, viz., replacement collision
sequences (RCSs), which had been identified by
molecular dynamics simulations as early as 1960.18
[111]
56

55
406

18
2

43
683

a
b
22
6

23
4
18
2

23
2

47
81
43

43
208

150
61

215

253

31

103
28
9

60

11

45
69

25
3

24
4
20
3

26
0
22
4

27
11

30
10

26
3

24
4

23
6

20
3

20
4

23
4

25
5

25
12

29
9

23
4

21
4

20

23
2

25
4

23
3

21
3

29
10

[100]

20
2

3
22
3
[110]

(a)
Figure 10 Displacement energy threshold surface for Cu.
The general anisotropy is typical of all fcc metals, although
specific values vary. bcc metals show similar behavior of
minima along close-packed directions. Reproduced from
King, W. E.; Merkle, K. L.; Meshii, M. Phys. Rev. B 1981,
23, 6319.

205

The primary knock-on atom in an RCS recoils in
the direction of its nearest neighbor, h110i in fcc
crystals, and replaces it, with the neighbor recoiling
also in the h110i and replacing its neighbor. A vacancy
is left at the primary recoil site, and an interstitial is
created at the end of the sequence. Replacement
sequences are the most efficient way to separate
the interstitial far enough from its vacancy, $2–3
interatomic spacings, for the FP to be stable. While
the lengths of these sequences are still debated, it is
clear that the mechanism results in both defect production and atomic mixing. For neutron irradiations,
higher energy recoils are numerous, and the average
displacement energy, Ed, becomes more relevant for
calculations of defect production (see eqn [1]). This
value, which can be obtained by averaging over the
threshold displacement energy surface, is usually difficult to determine experimentally. A rough estimate,
however, can be obtained from, Td % 1.4Tm in fcc
metals and 1.6Tm in bcc metals.19
1.07.4.1.2 Point defect properties

As FPs are produced in isolation during electron
irradiation, the properties of single point defects
and their interactions with impurities and sinks
can be systematically investigated. An example is
shown in Figure 11(a), where the results of lowtemperature isochronal annealing of Cu are shown
following 1.4 MeV electron irradiation at 6 K.20
Recovery is observed to occur in ‘stages.’ These studies have revealed that interstitial atoms become
mobile at very low temperatures, always below
100 K, in so-called Stage I, while vacancies become
mobile at higher temperatures, Stage III. The various
substages IA–IE seen in Figure 11(a) arise from the
interaction between interstitial–vacancy pairs, which
are produced in close proximity. Stage IE refers to
the free migration of interstitials in the lattice, away
from its own vacancy, and annihilation at distant
vacancies; these interstitials are freely migrating as
discussed earlier. For comparison, Stage I annealing
of Cu following neutron irradiation is shown in
Figure 11(b).21 Notice that the close pair substages
are suppressed during neutron irradiation, illustrating the dramatic difference in the defect production
process for these types of irradiation. Similarly,
annealing studies on electron-irradiated Al doped
with Mg or Ga impurities are shown in Figure 12.22
For these, it is observed that Stage I recovery is
suppressed as interstitials trap at impurities and do
not recombine. The recovery at higher temperature,
in Stage II, reveals distinct subannealing stages.


206

Radiation Damage Using Ion Beams

ID

IB

ID

IC
dDr (% K–1)
dT

7
dDr
(% K–1)
dT

40

6
5

IE
IA

3

30

20

1
− Dr
°

1
− Dr
°

4

Cu

IC

10

2

IB

IA

1
0

10

20

30

(a)

40
50
T (K)

60

70

0

80

(b)

10

20

40

30

50

60

70

T (K)

Figure 11 Low-temperature isochronal annealing of Cu following (a) electron (reproduced from Corbett, J. W.; Smith, R. B.;
Walker, R. M. Phys. Rev. 1959, 114, 1452) or (b) fast neutron irradiation (reproduced from Burger, G.; Isebeck, K.;
Volkl, J.; Schilling, W.; Wenzl, H. Z. Angew. Phys. 1967, 22, 452).

100
Dr [nW.cm]
°
2.5
2.7
Al-(99.995%pure) 3.3

90

Al-0.06° at.%Mg
Al-0.085 at.%Ga

Dr/Dr0 (%)

80
70
60
50
40
30

1.07.4.2.1 The damage function

20
10
0
10

30

100

300

T (K)

Figure 12 Recovery of electrical resistivity in Al,
Al–0.06 at.% Ga, and Al–0.085 at.% Ga following 1 MeV
electron irradiation. Reproduced from Garr, K. R.; Sosin,
A. Phys. Rev. 1969, 162, 669.

These annealing stages are generally attributed to
either the interstitial dissociating from the impurity,
or the interstitial–impurity complex migrating to a
vacancy or a defect sink. Migrating interstitial–solute
complexes lead to segregation. A compilation of the
properties of point defects for many metals, and their
interactions with impurities can be found in Ehrhart.23
This information has played a crucial role in developing an understanding of radiation damage in more
complex engineering alloys and under more complex
irradiation conditions.

1.07.4.2

threshold energies using low energy protons, to tens
of keV using MeV self-ions. In addition, defect production rates can be varied over many orders of
magnitude, reaching values over %0.1 dpa sÀ1. Moreover, by using more than one ion beam, the primary
recoil spectrum can be tailored to closely match that
produced by an arbitrary fission neutron spectrum.

Ion Irradiations

Ion irradiations are the most flexible method for
irradiating materials. As discussed in Section 1.07.2,
the primary recoil spectrum can be shifted from near

Calculations of defect production, eqn [2], require
knowledge of the damage function, n(T ). While it is
not possible to measure this function directly, as no
irradiation creates monoenergetic recoils except near
the surface, it can be obtained by measuring defect
production for a wide range of ion irradiations and
subsequently deconvoluting eqn [3]. Low-energy
light ions, for example, weight the recoil spectrum
near the threshold energy, %25–100 eV, while more
energetic heavy ions weight it at high energies.
Results are shown for Cu in Figure 13. Here, electrical resistivity measurements are employed to monitor
the absolute number of FPs produced per unit dose
of irradiation. Included in this figure are the damage
efficiency function, x(T1/2), deduced from the experiments and x(T ) calculated using molecular dynamics
computer simulation. The damage efficiency function
is defined as

nðT Þ ¼ xðT ÞnNRT ðT Þ;

½20Š

where nNRT(T ) is the NRT damage function defined
by eqn [1]. The good agreement between experiment
and simulations illustrates that the damage function
in Cu is now well understood. This is now true for
many other pure metals as well.24 In alloys and ceramic


Radiation Damage Using Ion Beams

207

Cu
H

Experiment
Calculation

0.8

He

x

Li
0.6

CN
O

0.4

Ne

Cu

Kr
Ar Fe
Ag Bi

1.0
Relative efficiency

1

1 MeV H

0.8
0.6
2 MeV He
0.4

2 MeV Li

FF
0.2
0

10

2

0.2

FN

MD simulation
3

10

10

4

5

10

T, T1/2 (eV)

Figure 13 Damage function efficiency factor of Cu
(see eqn [20]) showing the decrease in efficiency versus
cascade energy. The experimental data (solid squares)
represent efficiencies for different ion irradiations plotted
versus the characteristic cascade energy for the irradiation,
T1/2 (see text). The open triangles represent the efficiency

versus cascade energy, T, obtained by molecular dynamics
(MD) simulation. The open circles represent the calculated
efficiencies for the different irradiations using the MD
efficiency function and eqn [2]. Reproduced from Averback,
R. S.; de la Rubia, T. D. In Solid State Physics; Ehrenreich,
H., Spaepen, F., Eds.; Academic Press: New York, 1998; pp
281–402.

materials, however, the damage function remains
poorly known.
1.07.4.2.2 Freely migrating defects

The damage function refers to the number of FPs
created within the first several picoseconds of the
primary recoil event. At longer times, defects migrate
from their nascent sites and interact with other
defects and microstructural features. As noted earlier,
many radiation effects, such as radiation-enhanced
diffusion, segregation, and void swelling, depend more
strongly on the number of defects that escape their
nascent cascades and migrate freely in the lattice before
annihilating, trapping, or forming defect clusters. The
same general approach used to determine the damage
function has been employed to determine the relative
fraction of freely migrating defects, that is, e/nNRT, as
illustrated by Figure 14. Here, the relative number of
Si atoms segregating to the surface during irradiation,
per dpa, is plotted versus a characteristic energy of
the recoil spectrum, T1/2. It is seen that the fraction
decreases rapidly with increasing recoil energy. Similar experiments were performed using radiationenhanced diffusion, as described in Section 1.07.2.

While ion irradiation has proved extremely useful
in illustrating the spectral effects on freely migrating

0
102

3 MeV Ni
3.25 MeV Kr
103

104
105
T1/2 (eV)

106

107

Figure 14 Relative efficiencies for producing freely
migrating defects plotted as a function of the characteristic
recoil energy, T1/2. Reproduced from Rehn, L. E.;
Okamoto, P. R.; Averback, R. S. Phys. Rev. 1984,
B30, 3073.

defects, extracting quantitative information about
freely migrating defects from such experiments is
difficult. These measurements, unlike the damage
function, require very high doses, and several dpa;
the buildup of the sink structure must be adequately
taken into account. It is also difficult to estimate,

for example, how many interstitials are required to
transport one Si atom to the surface. We mention in
passing that experiments performed using ordering
kinetics in order–disorder alloys have provided a
more direct measure of the number of freely migrating defects (vacancies in this case), as these experiments require doses less than %10À7 dpa so that no
damage build-up can occur.25 These experiments
show similar effects of primary recoil spectrum on
the fraction of freely migrating defects, although the
fractions of such defects were found to be somewhat
higher in these experiments, %5–10%. These fractions are in good agreement with radiation-enhanced
diffusion experiments using self-ions on Ni, when the
effect of sink strength is taken into account.26
1.07.4.2.3 Alloy stability under ion irradiation

Irradiation of materials with energetic particles drives
them from equilibrium, and in alloys, this becomes
manifest in a number of ways. One of them concerns
nonequilibrium segregation. The creation of large
supersaturations of point defects leads to persistent
defect fluxes to sinks. In many cases, these point defect
fluxes couple with solutes, resulting in either the
enrichment or depletion of solutes at these sinks.
This effect was first discovered by using in situ electron


208

Radiation Damage Using Ion Beams

irradiations in a high voltage electron microscope,27

and it has been systematically investigated subsequently using ion irradiations,28 as the surface sink
provides a convenient location to measure composition changes. Unlike neutron irradiation, moreover,
the damage created by ions is generally inhomogeneous, reaching a peak level at some depth in the
sample. As a consequence, point defect fluxes emanate from these regions. An example of this effect is
shown in Figure 15 where a Ni–12.7 at.% Si alloy
was irradiated with protons. As the alloy is supersaturated with Si prior to irradiation, Ni3Si precipitates

Ni plating

Peak
damage
region

Ni3Si surface film
Bombarded surface

Figure 15 Behavior of silicon in a Ni–12.7 Si alloy
following irradiation with protons. Note the region depleted
of Ni3Si precipitates at the peak damage location and just
below the surface. Courtesy of P. R. Okamoto.

form in the sample. At the location of peak damage,
the concentration of interstitials is the highest, and
hence these defects flow outward from this region.
These interstitials form interstitial–solute complexes
with Si, resulting in a Si flux out of this area as well,
depleting the region of Si. As a consequence, a region
depleted of Ni3Si precipitates is observed at the
peak damage depth. Note too that the surface sink
for interstitials leads to enrichment of Si, resulting in

a surface layer of Ni3Si. The region just below the
surface accordingly becomes depleted of Si, leaving a
zone depleted of Ni3Si precipitates.
While irradiation induced segregation can lead to
nonequilibrium segregation and precipitation in single phase alloys, irradiation can also lead to dissolution of precipitates in nominally two-phase alloys.
An interesting example of this behavior concerns
Ni–12 at.% Al alloys irradiated with 300 keV Ni
ions.29 These alloys were first annealed at high temperatures to develop a two-phase structure of Ni3Al
(g0 ) and Ni–10.5 at.% Al (g). The initial precipitate
size, depending on the annealing time was 2.5 or
4.6 nm. As shown in Figure 16, the precipitates disorder during irradiation at room temperature, owing
to atomic mixing in cascades. The rate of disordering
depends on the size of the precipitates, being slowest
for homogeneous Ni3Al sample and fastest in the
alloy with the smallest precipitates. The authors

Ni3AI
NiAI (r = 4.6 nm)
NiAI (r = 2.5 nm)

0.8
0.6
0.4
0.2

Degree of LRO S/S0

Degree of LRO S/S0

1.0

1.0

Ni3AI
NiAI (r = 4.6 nm)

0.5

0.0
0.0
0.0
0.00 0.05 0.10 0.15 0.20 0.25 0.30
(b)
(a)
Irradiation dose F (dpa)

550 ЊC
450 ЊC
2.0
4.0
Irradiation dose F (dpa)

6.0

0.8

f(r )

0 dpa
0.4

0.0
0.0
(c)

5 dpa

2 dpa

4.0

8.0

0.0

4.0
8.0
Radius (nm)

0.0

4.0

8.0

Figure 16 (a) Disordering rate Ni3Al precipitates in two-phase Ni–12 at.% Al alloys and homogeneous Ni3Al during 300 keV
Ni bombardment at room temperature; (b) same as (a) but irradiation at 550  C; (c) size distribution of Ni3Al precipitates
after irradiation to two doses. After 5 dpa, a steady state size is obtained. Reproduced from Schmitz, G.; Ewert, J. C.;
Harbsmeier, F.; Uhrmacher, M.; Haider, F. Phys. Rev. B 2001, 63, 224113.

Radiation Damage Using Ion Beams

suggest that the reason for this dependence on precipitate size is that atomic mixing reduces the
concentration of Al in the precipitates, which
thereby accelerates the disordering. When the same
irradiation is performed at higher temperatures, and
radiation-enhanced diffusion takes place, the system
does not completely disorder, but rather remains
partially ordered, owing to a competition between
disordering in the displacement cascades and reordering by radiation-enhanced diffusion. Noteworthy,
however, is the size of the precipitate, as shown in
Figure 16(c), where it is observed that the precipitates initially shrink in size, but then reach a steady
state radius. Therefore, unlike in thermal aging, precipitates in irradiated alloys can reach a stable steady
state size that is a function of irradiation intensity and
temperature. Similar behavior has been observed in
two-phase immiscible alloys in which case a steady
state size of precipitates is formed.30 This so-called
‘patterning’ phenomenon has been explained on the
basis of a competition between disordering by atomic
mixing in energetic collision events and reordering
during thermally activated diffusion. For patterning,
however, it is required that the atomic relocation
distances during collisional mixing are significantly
larger than the nearest neighbor distance. An interesting consequence of this requirement in regard to
the present discussion of using ion irradiation to
simulate neutron damage is that electron and proton
irradiations, which do not produce energetic cascades
or long relocation distances, should not induce compositional patterning, but heavy ions and fast neutron
irradiation, which do produce cascades, will cause
patterning. Further details can be found in Enrique31

and Enrique et al.32
1.07.4.2.4 Mechanical properties

Measurements of mechanical properties on irradiated materials usually require bulk samples and
therefore neutron irradiation. Ion beams, however,
can be employed for some measurements, such as
plastic deformation. Typically, these experiments
employ high energy protons, E > % 2 MeV, or He
ions, E > 7 MeV, as these particles can penetrate
through thin foils, such as Fe or steel, that are greater
than 15 mm in thickness. Moreover, displacement
rates %10À5 dpa sÀ1 are obtainable without excessive
beam heating.33 Deformation experiments have also
been performed using GeV heavy ions, as these penetrate targets several microns in thickness. The displacement rates, however, are low as most of the beam
energy is lost through electronic excitations. Heavy

209

ions with lower energies, E % 1–4 MeV, have also
been used in deformation studies; for these, however,
specimen must be very thin, %200 nm, and effects of
the surface must be taken into account.34,35
1.07.4.2.5 Multiple ion beams

One of the difficulties in using ion beams to simulate
neutron irradiation damage is the potential for missing certain synergistic behaviors in the damage evolution. For example, neutron irradiation leads to
transmutation products and the generation of He
and fission gases in addition to displacement damage.
Generation of gas is particularly relevant to 14 MeV
neutron irradiation for which large amounts of

He and H are produced. Ion beams, however, offer
the opportunity of using two or even three beams
simultaneously and thus to tailor test irradiations to
meet expected reactor conditions; see, for example,
Serruys et al.36 This is often not possible in existing
test reactor facilities, and the building of new test
facilities for fusion machines has been formidably
expensive. The application of multiple ion beams is
illustrated in Figure 17 in a study of void swelling in
vanadium. Here, the synergistic effects of simultaneously implanting 350 keV H and 1 MeV He, while
irradiating with 12 MeV Ni ions are shown. Without
the He beam, swelling is negligible, even with the
implantation of H, but with it, the H greatly enhances
the swelling. H implantation, on the other hand, is
seen to reduce the density of cavities.
1.07.4.2.6 Swift ions

An important contribution to the damage in nuclear
fuels derives from fission fragments. There are two
groups of fission products: one group with atomic
number near 42 (Mo) and energy %100 MeV and
the other with atomic number near 56 (Ba) and
energy %70 MeV. The maximum electronic stopping
powers of these energetic particles, %18 keV nmÀ1
for the heavier and 22 keV nmÀ1 for the lighter, are
far greater than their respective nuclear stopping
powers. Similar to ion irradiation studies described
above, where the primary recoil spectrum can be
systematically varied, the masses and energies of
ions can be varied to examine effects of electronic

stopping power. An example is shown in Figure 18
where the electronic stopping power is plotted as a
function of energy (per nucleon) for different ion
irradiations of UO2. The two boxes in the figure
indicate stopping powers associated with the fission
fragments and the heavy particle recoils of a emitters. One of the questions addressed by such studies


Radiation Damage Using Ion Beams

Swelling (%)

20

10

20

0
20

10

Cavity density (1020 m−3)

210

20
15
10

20

5
15
0
10

pa
)d
pm
(ap
He

pa
)d
pm
(ap
He

20

10

5

10

0

0

0

0
0

–1

–1

0

(a)

20
10
a–1
p
d
)
m
p
p
H(a

(b)

20
10

pa–1
d
)
m
p
p
(a
H

dE/dx (keV nm–1)

70

60

20

1.4
1.2
Heavy FP

Light FP

1.0
0.8

10

0.6

238U

208Pb

0.4

50
U Fission

0
40

197Au

0.2

235

dE/dx (keV nm–1)

Energy (MeVamu–1)

Figure 17 Cavity volume fraction (a) and cavity density (b) in pure vanadium irradiated with 12 MeV Ni3þ ions to 30 dpa
at 873 K with and without simultaneous irradiation of He and H. Reproduced from Sekimura, N.; Iwai, T.; Arai, Y.; et al.
J. Nucl. Mater. 2000, 283–287, 224–228.

−8 −6 −4 −2 0 2 4
FPs range (μm)

0.0

8

6

129Xe

116Sn

30
GANIL
HMI

GSI
TASCC

106Cd
100Mo
127I

dE/dxFP

20

70Zn

Recoils
10

Zn70Zn
Efission

0
10−5

10−4

10−3

10−2

10−1

1

10

102

Energy (MeVamu–1)
Figure 18 Plot of dE/dx as a function of the energy for a series of ions. The circle indicates the conditions for 72 MeV
ions of 127I. The two large squares show dE/dx representative of fission products and for the heavy recoil atoms of
a-decaying actinides. The inset shows the energy loss and the remaining energy of typical light and heavy fission
products along their range of %7 mm length. Reproduced from Matzke, Hj.; Lucuta, P. G.; Wiss, T. Nucl. Instrum. Meth. B
2000, 166–167, 920.


Radiation Damage Using Ion Beams

1.07.4.3

Comparison with Neutrons

Proton irradiation has undergone considerable
refinement as a radiation damage tool. Numerous
experiments have been conducted and compared
to equivalent neutron irradiation experiments in
order to determine whether proton irradiations capture the effects of neutron irradiation on microstructure, microchemistry, and hardening. In some cases,
benchmarking exercises were conducted on the same
native alloy heat as neutron irradiation in order to
eliminate heat-to-heat variations that may obscure
comparison of the effects of the two types of irradiating particles. The following examples cover a number
of irradiation effects on several alloys in an effort to
demonstrate the capability of proton irradiation
to capture the critical effects of neutron irradiation.
Figures 19–23 show direct comparisons of the
same irradiation feature on the same alloy heats
(commercial purity (CP) 304 and 316 stainless steels)
following either neutron irradiation at 275  C or

8

24
CP-316 SS
Protons at 360 ЊC to 1.0 dpa
Neutrons at 275 ЊC to
1.1ϫ1021 n cm–2 (~1.5 dpa)

20

7
6

5

16

Cr
4
Ni

3

12

Measured Si (wt%)

Measured Cr or Ni (wt%)

has been the formation of fission fragment tracks.
Tracks have not yet been observed in the bulk of
UO2 due to fission; however, by using ion irradiation,
the stopping powers could be increased. The dashed
line at 29 keV nmÀ1 in Figure 18 represents the
threshold stopping power for track formation.37
This value is %30% greater than the maximum for
fission fragments, thus helping to explain why fission
fragment tracks are not seen in the bulk. Such tracks
are observed, however, close to the surface. They are
explained by fission products passing near or parallel
to the surface and creating shock waves which interact with the surface.38 These studies have also been
useful in gaining important data for understanding
fission gas evolution in nuclear fuels. For example,

72 MeV iodine ions (see Figure 18), approximate
very closely the stopping power of fission fragments.
Such studies have shown that 72 MeV I irradiations
cause Kr atoms preimplanted into UO2 to nucleate
into bubbles, and preformed bubbles to undergo resolution. A radiation-enhanced diffusion coefficient
for the Kr was estimated from these studies to be
D % 1.2 Â 10À30 cm5 Â F_ , where F_ is the fission rate
per cubic centimeter, and found independent of temperature below %500  C (see Matzke et al.37 for details).
The importance of such studies as these is that
the basic processes in complex nuclear fuels can be
elucidated by studies that carefully control singly
the irradiation conditions and materials parameters
in the fuel, such as fission gas concentration, damage, etc.

211

2
Si
1

8
−12

0
4
8
−8
−4
Distance from grain boundary (nm)

0
12

Figure 19 Comparison of grain boundary segregation of
Cr, Ni, and Si in commercial purity 16 stainless steel
following irradiation with either protons or neutrons to
similar doses. From Was, G. S.; Busby, J. T.; Allen, T.; et al.
J. Nucl. Mater. 2002, 300, 198–216.

3 MeV proton irradiation at 360  C to similar doses.
Figure 19 compares the RIS behavior of Cr, Ni, and
Si in a 316 stainless steel alloy following irradiation to
approximately 1 dpa. Neutron irradiation results are
in open symbols and proton irradiation results are in
solid symbols. This dose range was chosen as an
extreme test of proton irradiation to capture the
‘W’-shaped chromium depletion profile caused by
irradiation of a microstructure, which contained
grain boundaries that were enriched with chromium
prior to irradiation. Note that the two profiles track
each other extremely well, both in magnitude and
spatial extent. Good agreement is obtained for all
three elements.
Figure 20 shows a comparison of the dislocation
microstructure as measured by the dislocation loop
size distribution (Figure 20(a)) and the size and
number density of dislocation loops (Figure 20(b))
for 304 SS and 316 SS. The main features of the loop
size distributions are similar for the two irradiations,
viz. a sharply peaked distribution in the case of 304

SS and a flatter distribution with a tail in the case of
316 SS. The agreement in loop size is good for the
304 SS alloy, while loops are smaller for the protonirradiated 316 alloy. The loop density is about a
factor of 3 less for the proton-irradiated case than
the neutron-irradiated case, which is expected as the
proton irradiation temperature was optimized to
track RIS (higher temperature) rather than the


30

Fraction of loop population (%)

Radiation Damage Using Ion Beams

Fraction of loop population (%)

212

Protons at 360 ЊC
(1.0 dpa)
Neutrons at 275 ЊC
(0.7 dpa)

20

10

CP 304 SS
0

0

10
20
15
Loop diameter (nm)

5

(a)

25

30

12

50
Protons at 360 ЊC (1.0 dpa)

40

Neutrons at 275 ЊC (1.1 dpa)

30
20

CP 316 SS

10

0
0

5

10
15
20
Loop diameter (nm)

25

30

1024

Loop density (m−3)

Loop diameter (nm)

10
8
6
4
Protons at 360 ЊC

2

304

1023

1022

316

Protons at 360 ЊC

Neutrons at 275 ЊC

0

0

1

2

(b)

304

316

Neutrons at 275 ЊC

3
4
Dose (dpa)

5

1021

6

0

1

2

3
4
Dose (dpa)

5

6

Figure 20 Comparison of (a) loop size distributions and (b) loop diameter and loop number density for commercial
purity 304 and 316 stainless steels irradiated with neutrons or protons to similar doses. From Was, G. S.; Busby, J. T.;
Allen, T.; et al. J. Nucl. Mater. 2002, 300, 198–216.
1500

1500

1000

500

0

(a)

CP 316 SS

Yield strength (MPa)

Yield strength (MPa)

CP 304 SS

0

1

2

3
4
Dose (dpa)

5

1000

500

0

6

0

1

(b)

2

3
4
Dose (dpa)

5

6

Protons at 360 ЊC (hardness)
Neutrons at 275 ЊC (hardness)
Neutrons at 275 ЊC (shear punch)

Figure 21 Comparison of hardening in commercial purity 304 (a) and 316 (b) stainless steel irradiated with neutrons or
protons to similar doses. From Was, G. S.; Busby, J. T.; Allen, T.; et al. J. Nucl. Mater. 2002, 300, 198–216.

dislocation loop microstructure. That the loop sizes
and densities are even close is somewhat remarkable
considering that loop density is driven by in-cascade
clustering, and cascades from proton irradiation are

much smaller than those from neutron irradiation.
The surviving fraction of interstitial loops, however,
is greater for proton irradiation, partially compensating the greater loop formation rate under neutron


Radiation Damage Using Ion Beams

0

1.4

Fast neutron fluence (E > 1 MeV) ϫ1025 n m−2
0.5
1
1.5
2
2.5
3
3.5
4

Neutrons
With He
Without He

1.2

100

CP 304 SS

Protons at 360 ЊC
Neutrons at 275 ЊC

NWC

213

1
0.8
s/s0

Measured IG percentage

80

60

0.6
0.4

40

0.2

20
0

0

0

1

2

3
Dose (dpa)

4

5

6

Figure 22 Comparison of the extent of intergranular
stress corrosion cracking in commercial purity 304 stainless
steel following similar stress corrosion cracking tests of
either neutron- or proton-irradiated samples from the same
heat. From Was, G. S.; Busby, J. T.; Allen, T.; et al. J. Nucl.
Mater. 2002, 300, 198–216.

0.14
Ni+ irradiation
675 ЊC
140 dpa

70
60

0.13
0.12

Proton irradiation
400 ЊC
3.0 dpa

50
40
30

0.11
0.10
0.09

Neutron irradiation
510 ЊC
2.6 ϫ 1026 n m−2
E > 0.1 MeV

20

0.08

10
0

Swelling (%) protons

Swelling (%) neutron and Ni ion

80

0.07
0

20

40

60

80

0.06
100

Bulk nickel concentration (at.%)

Figure 23 Effect of bulk nickel concentration on swelling
resulting from irradiation with different particles: neutrons,
nickel ions, and protons. Reproduced from Allen, T. R.;
Cole, J. I.; Gan, J.; Was, G. S.; Dropek, R.; Al Kenik, E.
J. Nucl. Mater. 2005, 341, 90–100.

irradiation and resulting in loop densities that are
within a factor of 3.39
Figure 21 shows a comparison of irradiation hardening between the two types of irradiation. The results

0

0.5

1
1.5
Dose (dpa)

2

2.5

Figure 24 Comparison of relaxation in residual stresses
between neutron- and proton-irradiated stainless steel after
removing the effect of thermally-induced relaxation. From
Sencer, B. H.; Was, G. S.; Yuya, H.; Isobe, Y.; Sagasaka, M.;
Garner, F. A. J. Nucl. Mater. 2005, 336, 314–322.

are again similar, with proton irradiation resulting in
slightly lower hardness. Figure 22 shows the IASCC
susceptibility of CP 304 SS as measured by the %IG on
the fracture surface following constant load testing
(neutron-irradiated samples) and constant extension
rate testing (proton-irradiated samples) in BWR normal water chemistry (NWC). Despite the significantly
different testing mode, the results are in excellent
agreement in that both proton and neutron irradiation
result in the onset of IGSCC, at about 1 dpa.40
Figure 23 shows the swelling behavior in austenitic stainless steels as a function of nickel content
for proton, Ni ion, and neutron irradiation. While
these experiments were conducted on different sets
of alloys, and under highly disparate irradiation conditions, they all show the same dependence of nickel

on swelling. In the two commercial purity alloys,
no voids were formed in either neutron or protonirradiated samples.
As a last example of stainless steel alloys,
Figure 24 shows the relaxation of residual stress by
neutron and proton irradiation. Here again, results
are from different alloys and different types of
tests, but both show the same dependence of stress
relaxation on dose.
The next examples are from reactor pressure vessel
steel and Zircaloy. Figure 25 shows an experiment on
model reactor pressure vessel alloys in which the


214

Radiation Damage Using Ion Beams

500

300

Tin = 300 ЊC (all)

−7

Proton: 3–7 ϫ 10 dpa s–1
−10
Neutron: 3 ϫ 10
dpa s–1
−9

Electron: 7 ϫ 10 dpa s–1

280

Vickers hardness (Hv)

Change in yield strength (MPa)

400

300
VA, Fe, neutron
VA, Fe, proton
VA, Fe, electron
VD, Fe–0.9Cu–1.0 Mn, neutron
VD, Fe–0.9Cu–1.0 Mn, proton
VD, Fe–0.9Cu–1.0 Mn, electron
VH, Fe–0.9Cu, neutron
VH, Fe–0.9Cu, proton

200

100

0

−100
10−5

260

240
220
200

p - Zircaloy 4, 350 ЊC
n - Zircaloy 2, 350–400 ЊC
p - Zircaloy 4, 310 ЊC

180

10−4

10−3
Dose (dpa)

10−2

10−1

160

0

1

2

3

4

5
Dose (dpa)

6

7

8

Figure 25 Irradiation hardening in model reactor pressure
vessel steels following neutron, proton, and electron
irradiation at about 300  C. From Was, G. S.; Hash, M.;
Odette, G. R. Philos. Mag. 2005, 85(4–7), 703–722.

Figure 26 Hardening of Zircaloy-4 irradiated with 3 MeV
protons at 310 and 350  C and comparison to neutronirradiated Zircaloy-2. From Zu, X. T.; Sun, K.; Atzmon, M.;
et al. Philos. Mag. 2005, 85(4–7), 649–659.

same model alloy heats were irradiated with neutrons, electrons, or protons at %300  C to doses spanning two orders of magnitude. The alloys include a
high-purity Fe heat (VA) that hardens very little
under irradiation, an Fe–0.9Cu (VH) heat that hardens rapidly initially, followed by a slower hardening
rate above 0.1 mpda, and a Fe–0.9Ce–1.0Mn alloy
(VD) in which the hardening rate is greatest over
the dose range studied. Despite the very different
compositions and hardening rates, the results of the
three types of irradiation agree well.
Figure 26 shows hardening for Zircaloy-2 and
Zircaloy-4 irradiated with either neutrons or protons.
Although the irradiations were not conducted
on the same heats of material, or using similar

irradiation parameters, there is good agreement in
the magnitude and dose dependence of hardening.
Proton irradiation also induced amorphization of a
Zr(Fe,Cr)2 precipitate after irradiation to 5 dpa
at 310  C, similar to that observed in reactor. These
examples represent a comprehensive collection of
comparison data between proton and neutron irradiation and taken together serve as a good example for the
capability of charged particles to emulate the effect of
neutron irradiation on the alloy microstructure.
As a final example, to emphasize the care that
must be exercised in extrapolating the results of one
type of irradiation to make predictions for another,
we discuss a comparison of void swelling in Cu due to

2.5 MeV electrons, 3.0 MeV protons, and fission neutrons.41 An attempt was made to keep all irradiation
variables constant during the experiments, sample
purity, defect production rate, and temperature; only
the primary recoil spectrum was varied. The results
for nucleation rates of voids and void swelling are
shown in Figure 27(a) and 27(b), respectively.
Clearly observed is that void swelling and void
nucleation are significantly enhanced for neutron
irradiation in comparison to proton or electron
irradiation. This result is notably in strong contrast
to the efficiencies obtained for defect production and
radiation-induced segregation (or FMDs) for these
three types of irradiation. The reduced efficiency of
the production of FMDs was attributed to defect annihilation within the cascade core; these results for void
swelling, however, indicate that the defect clustering
process is also critical to microstructural evolution in

irradiated alloys. Singh and coworkers41,42 argue that
the clustering of interstitials in cascades, and their
collapse into dislocation loops, result in interstitial
migration by one-dimensional glide of loops, the
so-called production bias model.43 As a consequence,
interstitials and vacancies become efficiently separated. Swelling therefore is more severe for irradiations that produce energetic cascade, for example,
neutrons, than for those that do not, electrons. Proton
irradiation is intermediate; that is, small cascades are
produced.


Radiation Damage Using Ion Beams

215

100

Copper
523 K
10−1
1022

523 K
Void density (m−3)

Swelling (%)

Copper
10−2

10−3

10−4

10−5 −4
10

10−2
10−1
Dose (NRT dpa)

Fission neutrons
10

3 MeV protons

20

1019

Fission neutrons
3 MeV protons
2.5 MeV electrons
10−3

1021

2.5 MeV electrons

100

1018 −4
10

10−3
10−2
10−1
Dose (NRT dpa)

100

Figure 27 Void swelling as a function of dose in oxygen-free high conductivity (OFHC)-copper during irradiations with
electrons, protons, and fission neutron. Reproduced from Singh, B. H.; Eldrup, M.; Horsewell, A.; Ehrhart, P.; Dworschak,
F. Philos. Mag. A 2000, 80, 2629.

1.07.5 Advantages and
Disadvantages of Irradiations using
Various Particle Types

ton = 50 ms
50

toff = 2000 ms

40
K0/K0,avg

Each particle type has its advantages and disadvantages for use in the study of radiation effects or for
emulating neutron irradiation damage. Common disadvantages of charged particle beams are the lack of
transmutation reactions and the need to use a rasterscanned beam. With the exception of some minor

transmutation reactions that can occur with light
ion irradiation, charged particles do not reproduce
the types of transmutation reactions that occur in
reactor core materials due to the interaction with
neutrons. The most important of these is the production of He by transmutation, particularly in alloys
that contain elements such as Ni or B. But a second
consideration is that of a raster-scanned beam in
which any volume element of the target is exposed
to the beam for only a fraction of the raster-scan
cycle. For a typical beam scanner and beam parameters, the fraction of time that any particular volume element in the solid is being bombarded is
$0.025. Thus, the instantaneous dose rate during
the beam-on portion of the cycle is 40 times that of
the average, Figure 28. The result is that the defect
production rate is very high and defects can anneal
out in the remaining 0.975 portion of the cycle
before the beam again passes through the volume
element. As such, the effective defect production

60

30

20

10
K0,avg
0

0

1

2

3
4
Time (ms)

5

6

7

Figure 28 The effect of a raster-scanned beam on the
instantaneous production rate of point defects with the
same time averaged rate as a continuous source. From
Was, G. S.; Allen, T. R. In Radiation Effects in Solids, NATO
Science Series II: Mathematics, Physics and Chemistry;
Sickafus, K. E., Kotomin, E. A., Uberuaga, B. P., Eds.;
Springer: Berlin, 2007; Vol. 235, pp 65–98.

rate in raster-scanned systems will be less, and must
be accounted for.
One objective of ion irradiation is to emulate
the effect of neutrons, and a second is to understand
basic physical radiation damage processes, for which


216

Radiation Damage Using Ion Beams

neutron irradiation is often less well suited. While
ion irradiation can be conducted with great control
over temperature, dose rate, and total dose, such
control is a challenge to reactor irradiations. For
example, instrumented tubes with active temperature
control are expensive to design, build, and operate.
Even so, frequent power changes can be difficult
to handle as the flux–temperature relationship will
change and this can result in artifacts in the irradiated
microstructure.44 On the other hand, temperatures in
cheaper irradiation vehicles that use passive gas gaps
and gamma heating (such as ‘rabbit’ tubes) are known
with even less certainty. While neutron dosimetry
is used in some experiments, doses and dose rates
are often determined by neutronic models of the
core locations and are not verifiable. As such, ion
irradiations enjoy the advantage of better control
and verification of irradiation conditions as compared
to neutron irradiation. Table 3 provides a list for
each of three particle types: electrons, heavy ions,
and light ions (protons), and they are discussed in
detail in the following sections.
1.07.5.1

Electrons

Electron irradiation is easily conducted in a highvoltage transmission electron microscope using either

Table 3

a hot filament or a field emission gun as an electron
source. An advantage is that the same instrument
used for irradiation damage can be used to image
the damage. Another advantage is that the high dose
rate requires very short irradiation time, but will
also require a large temperature shift as explained
in the Section 1.07.3.
There are several disadvantages to electron irradiation using a TEM. First, energies are generally
limited to 1 MeV. This energy is sufficient to produce
an isolated FP in transition metals, but not cascades.
The high dose rate requires high temperatures that
must be closely monitored and controlled, which is
difficult to do precisely in a typical TEM sample
stage. Another drawback is that as irradiations are
often conducted on thin foils, defects are created in
close proximity to the surface and their behavior may
be affected by the presence of the surface. Perhaps
the most serious drawback is the Gaussian shape to
the electron beam that can give rise to strong dose
rate gradients across the irradiated region. Figure 29
shows the composition profile of copper around a
grain boundary in Ni–39%Cu following electron
irradiation. Note that while there is local depletion
at the grain boundary (as expected), the region adjacent to the minimum is strongly enriched in copper
because of the strong defect flux out of the irradiated

Advantages and disadvantages of irradiations with various particle types

Advantages
Electrons
Relatively ‘simple’ source – TEM
Uses standard TEM sample
High dose rate – short irradiation times

Heavy ions
High dose rate – short irradiation times
High Tavg
Cascade production

Light ions
Accelerated dose rate – moderate irradiation times
Modest DT required
Good depth of penetration
Flat damage profile over tens of microns

Disadvantages
Energy limited to $1 MeV
No cascades
Very high beam current (high dpa rate) leading to large temperature
shifts relative to neutrons
Poor control of sample temperature
Strong ‘Gaussian’ shape (nonuniform intensity profile) to beam
No transmutation
Very limited depth of penetration
Strongly peaked damage profile
Very high beam current (high dpa rate) leading to large temperature
shifts relative to neutrons

Potential for composition changes at high dose via implanted ion
No transmutation
Minor sample activation
Smaller, widely separated cascade
No transmutation

Source: Was, G. S.; Allen, T. R. In Radiation Effects in Solids, NATO Science Series II: Mathematics, Physics and Chemistry;
Sickafus, K. E., Kotomin, E. A., Uberuaga, B. P., Eds.; Springer: Berlin, 2007; Vol. 235, pp 65–98.


Radiation Damage Using Ion Beams

217

8

9
7

8
Si concentration (at.%)

6

494 ЊC

Cu concentration (at.%)

5
e-beam

diameter

4
6

400 ЊC

D+

7
6
8

e−

7

5

6
4

5
6

−4

400 ЊC
5
4

−6

0
2
4
−4
−2
Distance from grain boundary (μm)

6

Figure 29 Enrichment of copper surrounding a local
depletion at the grain boundary. The enrichment is caused
by the high defect flux away from the irradiated region
defined by the horizontal line. From Ezawa, T.; Wakai,
E. Ultramicroscopy 1991, 39, 187.

Solute concentration (wt%)

60

50
Iron
Chromium
Nickel

40

30

−3

0
1
2
3
−2
−1
Distance from grain boundary (μm)

4

Figure 31 Comparison of (a) deuteron and (b) electron
irradiation showing the greater amount of segregation and
the narrower profile for the deuteron irradiation. From
Wakai, E. Trans. J. Nucl. Mater. 1992, 33(10), 884.

zone defined by the horizontal line below the spectrum. This outward-directed defect flux causes a
reversal in the direction of segregation from that
caused by a defect flux to the sink. Another often
observed artifact in electron irradiation is very
broad grain boundary enrichment and depletion
profiles. Figure 30 shows that the enrichment profile
for Ni and the depletion profiles for Fe and Cr in
stainless steel have widths on the order of 75–100 nm,
which is much greater than the 5–10 nm widths
observed following neutron irradiation under similar
conditions and model simulations of radiationinduced segregation. A similar effect was observed
by Wakai45 using electron and Dþ irradiation of the
same alloy in which the segregation profile was much

higher and narrower around the grain boundary in
the deuteron-irradiated sample as compared to the
electron irradiation (Figure 31).

20

1.07.5.2
10

0

100

200
300
400
Distance (nm)

500

600

Figure 30 Broad grain boundary enrichment and
depletion profiles in Fe–20Cr–25Ni–0.75Nb–0.5Si following
irradiation with electrons at 420  C to 7.2 dpa. From
Ashworth, J. A.; Norris, D. I. R.; Jones, I. P. J. Nucl. Mater.
1992, 189, 289.

Heavy Ions

Heavy ions enjoy the benefit of high dose rates
resulting in the accumulation of high doses in short
times. Also, because they are typically produced in
the energy range of a few MeV, they are very efficient
at producing dense cascades, similar to those produced by neutrons. The disadvantage is that as with
electrons, the high dose rates require large


218

Radiation Damage Using Ion Beams

dpa versus depth for
various ions
incident on nickel

Ni

5

9
Al

4

6

3

8.1 MeV aluminum ions

(dpa per 1016 ions cm−2)

1.2
1.0
0.8
0.6

2

0.4

1

0.2

0

0

3

0

0

0.5

1

1.5

2

2.5

3

5 MeV carbon ions (dpa per 1016 ions cm−2)

C

12

Al
Ni
C

14 MeV nickel ions (dpa per 1016 ions cm−2)

15

Depth (μm)
Figure 32 Damage profiles for C, Al, and Ni irradiation of a nickel target at energies selected to result in the same
penetration depth. From Whitley, J. B. Ph.D. Thesis, University of Wisconsin-Madison, Madison, WI, 1978.

1.5

250

3.2

1.5

200
Swelling (%)

2.4

Observed

2

150

1.6
dpa

1.2
0.8

100

50

0.4
0
0
(a)

0.2 0.4 0.6 0.8 1

Depth (μm)

Displacement rate (10−3 dpa s–1)

5 MeV
2.8

1

0.5

0
0

0
1.2 1.4 1.6
(b)

Ni2+

on Ni

1

0.5

0
0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
Depth (μm)

þ

Figure 33 (a) Subsurface swelling resulting from 5 MeV Ni ion irradiation of Fe–15Cr–35Ni at 625  C and (b) displacement
rate and ion deposition rate calculated for 5 MeV Ni2þ on nickel. Adapted from Garner, F. A. J. Nucl. Mater. 1983, 117,
177–197; Lee, E. H.; Mansur, L. K.; Yoo, M. H. J. Nucl. Mater. 1979, 85&86, 577–581.

temperature shifts so that irradiations must be conducted at temperatures of $500  C in order to create
similar effects as neutron irradiation at $300  C.
Clearly, there is not much margin for studying neutron irradiations at higher reactor temperature
as higher ion irradiation temperatures will cause
annealing. Another drawback is the short penetration
depth and the continuously varying dose rate over
the penetration depth. Figure 32 shows the damage
profile for several heavy ions incident on nickel.
Note that the damage rate varies continuously and

peaks sharply at only 2 mm below the surface. As a
result, regions at a very well-defined depth from the
surface must be isolated and sampled in order to
avoid dose or dose rate variation effects from sample
to sample. Small errors (500 nm) made in locating the
volume to be characterized can result in a dose that
varies by a factor of 2 from the target value.
A problem that is rather unique to nickel ion irradiation of stainless steel or nickel-base alloys is that in
addition to the damage they create, each bombarding
Ni ion constitutes an interstitial. Figure 33(a) shows


Radiation Damage Using Ion Beams

that 5 MeV Ni2þ irradiation of a Fe–15Cr–35Ni alloy
resulted in high swelling in the immediate subsurface
region compared to that near the damage peak. As
shown in Figure 33(b), the Ni2þ ions come to rest at a
position just beyond the peak damage range. So even
though the peak damage rate is about 3Â that at the
surface, swelling at that location is suppressed by
about a factor of 5 compared to that at the surface.46
The reason is that the bombarding Ni2þ ions constitute interstitials and the surplus of interstitials near
the damage peak results in a reduction of the void
growth rate.47,48 In the dose rate–temperature regime
where recombination is the dominant point defect
loss mechanism, interstitials injected by Ni2þ ion
bombardment may never recombine as there is no
corresponding vacancy production.
1.07.5.3

Light Ions

In many ways, proton irradiation overcomes the
drawbacks of electron and neutron irradiation.
The penetration depth of protons at a few MeV can
exceed 40 mm and the damage profile is relatively flat
such that the dose rate varies by less than a factor
of 2 over several tens of micrometers. Further, the
depth of penetration is sufficient to assess such properties as irradiation hardening through microhardness
measurements, and stress corrosion cracking through
crack initiation tests such as the slow strain rate test.

219

Figure 34 shows schematics of 3.2 MeV proton and
5 MeV Ni2þ damage profiles in stainless steel. Superimposed on the depth scale is a grain structure with a
grain size of 10 mm. Note that with this grain size,
there are numerous grain boundaries and a significant
irradiated volume over which the proton damage rate
is flat. The dose rate for proton irradiations is 2–3
orders of magnitude lower than that for electrons or
ions, thus requiring only a modest temperature shift,
but as it is still 102–103 times higher than neutron
irradiation, modest doses can be achieved in reasonably short irradiation time.
The disadvantages are that because of the
small mass of the proton compared to heavy ions,
the recoil energy is smaller and the resulting damage
morphology is characterized by smaller, more widely
spaced cascades than with ions or neutrons. Also,
as only a few MeV are required to surmount the Coulomb barrier for light ions, there is also a minor amount
of sample activation that increases with proton energy.

1.07.6 Practical Considerations for
Radiation Damage Using Ion Beams
In the process of setting up an ion irradiation experiment, a number of parameters that involve beam

105
Ion
10−15
5 MeV Ni

10−17

Calculated range (μm)

dpa/(ion cm−2)

10−16

1000

2+

3.2 MeV protons

10−18
10−19
10−20

10

0.1
1 MeV neutrons

10−21
10−22
0

H
He
Ni

10

20
30
Depth (μm)

40

Figure 34 Damage profiles for 1 MeV neutrons, 3.2 MeV
protons, and 5 MeV Ni2þ ions in stainless steel. From Was,
G. S.; Allen, T. R. In Radiation Effects in Solids, NATO
Science Series II: Mathematics, Physics and Chemistry;
Sickafus, K. E., Kotomin, E. A., Uberuaga, B. P., Eds.;
Springer: Berlin, 2007; Vol. 235, pp 65–98.

Calculated by SRIM 2000
Stainless steel (Fe–20Cr–10Ni)

0.001
0.01

0.1

1

10

100

Energy (MeV)
Figure 35 Range of hydrogen, helium, and nickel ions in

stainless steel as a function of ion energy. From Was, G. S.;
Allen, T. R. In Radiation Effects in Solids, NATO Science
Series II: Mathematics, Physics and Chemistry; Sickafus,
K. E., Kotomin, E. A., Uberuaga, B. P., Eds.; Springer: Berlin,
2007; Vol. 235, pp 65–98.