thesis

EPFL - ETHZ joint Master in Nuclear
Engineering
Master Thesis
Determination of helium implantation
induced swelling in ODS steels
Loïc Fave
Master thesis performed in PD Dr. W. Hoﬀelner HT-Mat group of the
Laboratory for Nuclear Materials at the Paul Scherrer Institut
Supervisors
Dr. Manuel A. Pouchon
Paul Scherrer Institut
Prof. Rakesh Chawla
École polytechnique fédérale de Lausanne
PD. Dr. Wolfgang Hoﬀelner
Paul Scherrer Institut
June 2012

Abstract
A study of the irradiation induced swelling in two ODS steel is presented in this master
thesis. The main focus is put on the effect of helium in these materials. Samples of the
experimental 15CRA-3 alloy are irradiated with He+
ions from room temperature up to
800◦
C, to a dose of 0.84 dpa with a helium content of around 4000 appm/dpa. Mesh
400 TEM Gilder grid are put on top of the surface, resulting in an irradiated surface
featuring periodical steps, whose heights of a few nanometre are measured by white light
interferometry. This method has been shown to be very fast and effective at measuring
these surface features.
A fast working and efficient image analysis program was coded with the aim of fa-
cilitating and guaranteeing the reproducibility of the surface displacement evaluation.
Additionally to this the swelling of PM2000 samples, a commercial ODS steel, previously
irradiated under similar conditions, is reassessed using this new method. Low swelling is
found in both alloys, although the PM2000 shows a lower resistance, with a peak swelling
of ∼ 0.8%·dpa−1
at 600◦
C, whereas the 15CRA-3 presents an almost constant swelling of
around 0.3%·dpa−1
throughout the temperature range.
This higher swelling resistance of the experimental ODS is attributed to the very fine
distribution of coherent-interfaced Y2O3 nanoparticles, which act as sites of enhanced
point defect recombination as well as traps for the implanted helium.
i

Contents
List of ﬁgures vi
List of tables vii
List of symbols viii
List of abbreviations x
1 Introduction 1
2 Theoretical background 7
2.1 Interactions of radiation and matter . . . . . . . . . . . . . . . . . . . . . . 7
2.1.1 Light ions scattering . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.1.2 Stopping powers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.1.3 Simulation of neutron irradiation eﬀect with ions . . . . . . . . . . 16
2.1.4 Interactions modelling in SRIM . . . . . . . . . . . . . . . . . . . . 18
2.2 Radiation damage in metals . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.2.1 General considerations . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.3 Irradiation induced swelling - basics . . . . . . . . . . . . . . . . . . . . . . 21
2.3.1 Void swelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.3.2 Bubble swelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3 Experimental 33
3.1 Sample preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.2 Irradiation simulation with SRIM . . . . . . . . . . . . . . . . . . . . . . . 34
3.3 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.3.1 Irradiation station . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.3.2 Tandem accelerator . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.4 White light interferometer . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.5 Image analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
iii

4 Results 45
4.1 Surface displacement measures . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.2 Surface features at high temperature . . . . . . . . . . . . . . . . . . . . . 49
4.2.1 Optical microscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.2.2 Roughness mapping . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.2.3 SEM imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.2.4 SEM-EDX elemental maps - Copper content . . . . . . . . . . . . . 53
5 Discussion 59
6 Conclusion 63
Bibliography 67
A SEM-EDX elemental mappings 73
iv

List of Figures
2.1 ρ/a ratio for different ions . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2 Collision orbits in the CM system . . . . . . . . . . . . . . . . . . . . . . . 11
2.3 Sketch of an ion penetrating into a material . . . . . . . . . . . . . . . . . 16
2.4 Trajectories of He, Fe and U ions in the 15CRA-3 . . . . . . . . . . . . . . 18
2.5 316 stainless steel showing a large irradiation induced swelling . . . . . . . 21
2.6 Event sequence in radiation damage . . . . . . . . . . . . . . . . . . . . . . 22
2.7 Swelling peak temperature versus dose rate . . . . . . . . . . . . . . . . . . 28
2.8 Typical swelling behaviour of nickel . . . . . . . . . . . . . . . . . . . . . . 29
3.1 Example of a grid used for the irradiation experiments . . . . . . . . . . . 33
3.2 Screenshots of a TRIM simulation . . . . . . . . . . . . . . . . . . . . . . . 34
3.3 Irradiation profile simulated with the actual experiment parameters - 7
energies case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.4 Irradiation profile simulated with the actual experiment parameters - 8
energies case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.5 Irradiation station with z-shift unit schematics . . . . . . . . . . . . . . . . 38
3.6 Schematics of the furnace used for the experiments . . . . . . . . . . . . . 39
3.7 Schematic view of ETH tandem accelerator . . . . . . . . . . . . . . . . . . 39
3.8 Layout of an interference microscope . . . . . . . . . . . . . . . . . . . . . 40
3.9 Typical white light interferometry image before image processing . . . . . . 41
3.10 Topographical information after processing of the WLI data . . . . . . . . 43
3.11 WLI image height profile with sought steps . . . . . . . . . . . . . . . . . . 43
3.12 Example of a roughness map . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.1 Swelling as function of temperature in the 15CRA-3 ODS steel . . . . . . . 46
4.2 Swelling as function of temperature in the PM2000 ODS steel . . . . . . . 47
4.3 Normalised swelling in the 15CRA-3 and PM2000 ODS steels . . . . . . . . 48
4.4 Topography of the 15CRA-3 sample irradiated at 800◦
C . . . . . . . . . . 48
4.5 Optical microscopy of irradiated 15CRA-3 samples - 1 . . . . . . . . . . . . 50
4.6 Optical microscopy of irradiated 15CRA-3 samples - 2 . . . . . . . . . . . . 50
4.7 Roughness mapping of irradiated 15CRA-3 samples -1 . . . . . . . . . . . . 51
v

4.8 Roughness mapping of irradiated 15CRA-3 samples -2 . . . . . . . . . . . . 51
4.9 SEM pictures of 15CRA-3 samples irradiated at 600◦
C and 700◦
C . . . . . 52
4.10 SEM pictures of a 15CRA-3 sample irradiated at 800◦
C . . . . . . . . . . . 53
4.11 SEM-EDX elemental mapping of a 15CRA-3 sample irradiated at 600◦
C . 54
C . 54
C . 54
4.14 SEM-EDX elemental mapping of a PM2000 sample irradiated at 700◦
C . . 55
4.15 Backscattering SEM micrograph of 15 CRA-3 samples . . . . . . . . . . . . 57
A.1 Elemental mapping of a 15CRA-3 sample irradiated at 600◦
C . . . . . . . 74
C . . . . . . . 75
C . . . . . . . 76
A.4 Elemental mapping of a PM2000 sample irradiated at 700◦
C . . . . . . . . 77
vi

List of Tables
1.1 Irradiation conditions met in various facilities . . . . . . . . . . . . . . . . 2
1.2 Composition of the 15CRA-3 ODS steel . . . . . . . . . . . . . . . . . . . . 3
1.3 Composition of the PM2000 ODS steel . . . . . . . . . . . . . . . . . . . . 4
2.1 ASTM recommended Td values . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2 Relevant ˆT, Ť and ¯T values for the 15CRA-3 ODS steel . . . . . . . . . . 12
2.3 Ion and neutron irradiation characteristics . . . . . . . . . . . . . . . . . . 19
2.4 Time and energy scales in radiation damage events . . . . . . . . . . . . . 20
4.1 Conditions under which the 15CRA-3 samples were irradiated . . . . . . . 45
vii

List of symbols
Td : Lattice dependent threshold energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1
Ei Initial energy of a colliding particle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1
¯Te Average recoil energy in elastic collisions with neutrons . . . . . . . . . . . . . .2.1
¯T(n,γ) Average recoil energy in (n, γ) reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1
Z1 Atomic number of the colliding atom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.1
Z2 Atomic number of the target atom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1
a0 Bohr radius . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.1
re Lattice spacing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1
b Collision parameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1
T Recoil energy in ion-atom interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.1
φ Asymptotic scattering angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.1
ρ(b) Distance of closest approach in ion-atom interactions . . . . . . . . . . . . . . . .2.1
a Screening radius in ion-atom interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.1
M1 Light ion mass (M1 ∈ [1, 4]) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.1
b0 Collision parameter of a head-on collision . . . . . . . . . . . . . . . . . . . . . . . . . .2.1.1
x Inverse of the distance separating a light ion and its target . . . . . . . . 2.1.1
σs Scattering cross-section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.1
ˆT Total energy involved in a ion-atom collision . . . . . . . . . . . . . . . . . . . . . . 2.1.1
Ť Energy threshold to trigger displacements in ion-atom collisions . . . 2.1.1
N Target (M2) number density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.1.2
Sn, Se, Sr Elastic, electronic and radiative stopping powers . . . . . . . . . . . . . . . . . . .2.1.2
λ Mean-free path between successive collisions . . . . . . . . . . . . . . . . . . . . . . .2.1.2
Ťb Recoil energy in the b = a case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.2
χ(r) Screening function accounting for interactions between atoms . . . . . .2.1.2
∈ Dimensionless energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.1.2
t Parameter characterising the depth of penetration into an atom . . . 2.1.2
σ Diﬀerential energy transfer cross-section . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.2
f(t1/2
) Scalling function characterising σ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.1.2
χU Universal screening function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.1.2
Sn(Ei)ZBL ZBL universal nuclear stopping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.1.2
∈ZBL ZBL dimensionless energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.2
viii

me Mass of an electron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.2
¯I Mean electron excitation level of a target . . . . . . . . . . . . . . . . . . . . . . . . . .2.1.2
R Average total range of an ion in a material . . . . . . . . . . . . . . . . . . . . . . . . 2.1.2
ρ Target density, in g/cm3
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.2
Rp Average projected range of an ion in a material . . . . . . . . . . . . . . . . . . . .2.1.2
∆Rp Straggling of the average projected range . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.2
N(x) Implanted ion concentration as function of the target depth . . . . . . . 2.1.2
Np Peak concentration of an implanted ion . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.1.2
Ns Number of implanted ions per target unit area . . . . . . . . . . . . . . . . . . . . 2.1.2
Ed Displacement energy, same as Td . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.4
Eb Binding energy in a given material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.4
Ef Recoil energy below which an atom is considered stopped . . . . . . . . . .2.1.4
M2 Target atom mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.2
ψ Scattering angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2
Dv, Di Vacancies and interstitials diffusion coefficients . . . . . . . . . . . . . . . . . . . . 2.3.1
Cv, Ci Vacancies and interstitials concentrations . . . . . . . . . . . . . . . . . . . . . . . . . .2.3.1
kv, ki Mean travelling distance of a free defect before being trapped . . . . . 2.3.1
K1 Effective strength of neutral sinks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1
Cs1 Neutral sinks average concentration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1
¯c1 Concentration characterising the thermal emission rate of sinks . . . .2.3.1
ce Sink concentration a thermal equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . .2.3.1
Cp Coherent precipitate concentration in the medium . . . . . . . . . . . . . . . . . 2.3.1
Cm
i , Cm
v Defect concentration in the medium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1
Yi, Yv Probabilities of occupation of trapping sites found in the medium . .2.3.1
ρd Dislocations total density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1
ρN
d Density of dislocations in networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1
¯cvL Thermal emission parameter of dislocations loops . . . . . . . . . . . . . . . . . .2.3.1
¯cvN Thermal emission parameter of dislocations in networks . . . . . . . . . . . 2.3.1
Zi, Zv Scaling factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1
Ki, Kv Effective defect generation rates in the medium . . . . . . . . . . . . . . . . . . . .2.3.1
α Defect recombination coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1
F(η) Function characterising the swelling dependence on temperature . . .2.3.1
x Factor characterising the dominant type of sinks . . . . . . . . . . . . . . . . . . .2.3.1
Ts Swelling onset temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.3.1
Tp Peak swelling temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1
Tf Final swelling temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1
Q Vacancy mechanism self-diffusion activation energy . . . . . . . . . . . . . . . . 2.3.1
ix

List of abbreviations
LFR Lead-bismuth fast reactor
SFR Sodium fast reactor
VHTR Very-high temperature reactor
SCWR Super-critical water reactor
DEMO Demonstration power plant
LWR Light water reactor
BWR Boiling water reactor
PWR Pressurised water reactor
VVER Water-water power reactor, Russian type PWR
ODS Oxide dispersion strengthening
PKA Primary knocked-on atom
EDX Energy dispersive X-ray spectroscopy, also known as EDS
ASTM American Society for Testing and Materials
CM Centre of mass
ZBL Ziegler-Biersack-Littmark
dpa Displacement per atom, radiation damage unit
SDA Secondary displaced atom
SEM Scanning electron microscopy
WLI White light interferometry
IFMIF International Fusion Materials Irradiation Facility
ESS European Spallation Source
XADS Experimental Accelerator Driven System
HFR High Flux Reactor, a multi-purpose materials testing LWR
BOR60 Sodium-cooled fast spectrum test reactor
FFTF Fast Flux Test Facility, a 400 MW sodium cooled test reactor
MOTA Materials Open Test Assembly, a facility used in the FFTF reactor
ICP-MS Inductively coupled plasma mass spectrometry
AFM Atomic force microscopy
TEM Transmission electron microscopy
x

Chapter 1
Introduction
Structural materials research is essential when the development of future nuclear appli-
cations is considered. By future applications are meant advanced fission reactors, also
known as Generation IV[1]
, and nuclear fusion reactors. In both cases, researchers aim at
finding new ways to safely produce electricity in quantities that will meet the demand of
the next decades, without making use of fossil resources such as oil or natural gas.
Advanced fission reactor designs share common characteristics that are high to very
high temperatures, corrosive coolants and very hard radiation fields. Examples of such
systems could be liquid lead-bismuth eutectic cooled (LFR), liquid sodium cooled (SFR),
very-high temperature gas cooled (VHTR) or super-critical pressurised water cooled re-
actors (SCWR). Fusion applications also share these characteristics as super critical pres-
surised water is also being considered as a coolant for DEMO reactors[2]
.
These particular environments put extremely high requirements on structural mate-
rials such as reactor vessels, fuel rods or fusion blankets. Temperature, one of the three
main issues, would range from ∼500 ◦
C (SCWR) to 1000 ◦
C (VHTR) at the outlet of
advanced fission reactors, whereas plasma facing walls would see temperatures between
500 and 3200 ◦
C[3]
in fusion reactors. Another important point is corrosion: several of the
considered coolants, liquid metals such as lead-bismuth eutectic or liquid sodium or super
critical pressurised water are very aggressive media. The last big problem that scientists
are faced with is radiation damage; these advanced systems would use fast fission or fu-
sion neutrons, i.e. neutrons with energies ranging from the keV to several MeV, combined
with high flux densities. As a result, radiation damage such as helium embrittlement,
irradiation induced segregation or swelling would occur much faster and be more intense
than in current light water reactors.
1

CHAPTER 1. INTRODUCTION 2
Quantification of radiation damage is done with help of the displacement per atom
unit (dpa). Damage rates are often given in displacement per atom per full power year
(dpa·fpy−1
), or simply per second (dpa·s−1
). Other relevant quantities are the amount of
helium introduced in the bulk of the material by (n, α) and direct bombardment. The
amount of helium introduced is measured in atomic parts per million, usually linked to
the dose in terms of He appm/dpa. Typical dose rates and helium amounts found in
fusion (DEMO), stripping (IFMIF), spallation (ESS), ADS systems (XADS) as well as
fast (e.g. BOR60), mixed and thermal fission (e.g. HFR) spectra are presented in Tab.1.1
below. The conditions under which samples were irradiated with He+
ions in the ETH
Hönggerberg tandem accelerator in this work are also presented.
parameter
DEMO
first wall
IFMIF ESS XADS
fast
spectrum
mixed
spectrum
thermal
spectrum
tandem
dpa/s 9.5 · 10−7 1.75·10−6 3 · 10−7 1.2 · 10−6 0.6−3·10−6 1 − 4 · 10−7 8 · 10−8 4 · 10−5
He/dpa 11 10-12 5-6 35 0.15-0.5 4-40 0.3 ∼ 4000
Table 1.1: Overview of the irradiation conditions in various test facilities having thermal
to fast fission, spallation, stripping and fusion spectra. The parameters under
which samples of the experimental 15CRA-3 ODS steel were irradiated are
presented in the last column. These irradiations took place in the tandem
accelerator of the AMS facility at ETH Hönggerberg[4]. More detailed values
can be found in the litterature[5,6,7].
The specific conditions met inside fast spectrum reactors rule out most of the currently
used structural materials such as Zircalloy, normal ferritic steels and stainless steels used
in LWRs. Good candidates would have to have very good mechanical properties at el-
evated temperatures and be able to cope with the high radiation doses. Research lead
to the conclusion that austenitic steels have a better creep behaviour than ferrite-based
alloys: the creep compliances of these systems typically differ by a factor of two[8]
. Nev-
ertheless, it has also be found that ferritic/martensitic steels are less prone to irradiation
damage such as dimensional changes than austenite-based steels: steady-state swelling
rates of ferritic/martensitic steels are typically lower to those of austenitic alloys by a
factor of two to four[8]
.
Developments of high-temperature applications in other industries such as that of gas
turbines have lead to extensive research on materials strengthened with dispersed oxide
particles, known as ODS materials. In the 1970s and 1980s, it was found that ODS
nickel-based superalloys could provide significative improvement to the lifetime of gas
turbines[9]
.
ODS stands for "Oxide dispersion strengthened". Hence, in its most general definition,
an ODS material is made of a matrix that is reinforced by the addition of a dispersion
of ceramic particles. Matrices that can be strengthened in such a way can be of any

material class. However, matrices of technological relevance for nuclear applications are
metallic, more speciﬁcally based on the iron-carbon system, i.e. steels. The introduction
of small ceramic particles such as TiO2 or Y2O3 in the metallic matrix results in improved
mechanical properties. Since these oxide particles are very hard, almost insoluble in the
metallic matrix and non-shearable, they act as pinning points for dislocations, i.e. they
block the movement of dislocations, thus increasing the strength of the material[10]
.
Several types of ODS steels, either austenitic- or ferritic/martensitic, have been ex-
tensively studied during the last decade for their potential use as structural materials in
future nuclear applications[11,12,13,14]
. As this type of alloys display very good properties
in nuclear reactor environments, i.e. high temperature creep rupture resistance, excellent
neutron irradiation resistance and low activation[11,14]
, ODS ferritic/martensitic steels
have been identiﬁed as serious candidates for future nuclear applications[15]
. Studies car-
ried out in the past decade have shown that ferritic/martensitic ODS alloys have a good
resistance to irradiation induced swelling[14,16]
; it appears that the interfaces between
nano-scaled oxide particles and the ferritic matrix locally enhances the recombination
of point defects and might also act as sinks for Helium, what hinders the formation of
bubbles within the bulk of the material. In addition to this, strengthening by oxide dis-
persion gives ferritic/martensitic steels the level of creep strength required for the high
temperatures met in Gen IV systems[11]
.
Two high chromium content ODS alloys are studied in the present work, the 15CRA-
3, a ferritic/martensitic steel and the PM2000 alloy, which is ferritic. This work focuses
on the 15CRA-3 alloy, one of the latest development made by Japanese researchers and
has been obtained from Prof. Akihiko Kimura, head of the Advanced Energy Conversion
Division of the Institute of Advanced Energy, Kyoto University[17]
. This alloy is an Iron-
Chromium-Tungsten-Titanium alloy strengthened with 2 to 4 nm Y2O3 particles. It has
a yield strength of 1165 MPa at room temperature and 358 MPa at 700 ◦
C. The detailed
chemical composition of this alloy is presented in Tab.1.2:
Alloying elements Particles
C Si Mn P S Ni Cr W Ti Y O N Y2O3 Ex.O
wt.% 0.02 <0.01 <0.01 <0.005 0.002 <0.01 14.9 2.0 0.20 0.27 0.16 0.009 0.34 0.09
at.% 0.093 <0.020 <0.010 <0.009 0.003 <0.009 15.933 0.605 0.232 0.253 1.182 0.036 N.A. N.A.
Table 1.2: Chemical composition of the 15CRA-3 as obtained from professor A. Kimura.
The balance is completed with the iron content.
The 15CRA-3 alloy has been designed in order to meet several requirements of Gen
IV systems. Chromium has been put to a high enough content so that it guarantees
a good corrosion resistance (> 14 wt.%) but avoids ageing embrittlement through the
formation of secondary phases rich in chromium (< 16 wt.%)[18]
. Addition of nickel
would grant better corrosion resistance but as this steel is meant for nuclear application,

this alloying element is out of question: Nickel containing alloys are quite sensitive to
helium embrittlement because nickel can capture a thermal neutron:
58
28Ni +1
0 nth
→59
28 Ni + γ
59
28Ni +1
0 nth
→56
26 Fe +4
2 He
For this the 15CRA-3 nickel content is kept as low as possible (<0.01 wt.%). The other
main alloying elements, tungsten and titanium are added to guarantee good mechanical
properties at high temperatures. First, adding tungsten to a maximum of 2 wt.% increases
creep rupture time at 600 ◦
C without losing martensite to ferrite. Second, small additions
of Ti has the effect of favouring a high density of small oxide particles[18]
. It also appears
that titanium forms complex oxides such as Y2Ti2O7 and Y2TiO5, that are stable under
irradiation[19]
.
Finally, it should be noted that 15CRA-3 is an aluminium-free ODS steel: Reason for
this is the strive to avoid activation of materials as much as possible - aluminium can
undergo a (n,2n) reaction leading to the β+
emitting radioisotope 26
13Al[20]
. Additionally
to this, aluminium decreases the strength of the alloy as it increases the size of the oxide
particles, hence decreasing their number density. Nevertheless one should keep in mind
that adding aluminium can significantly improve corrosion resistance of ODS steels as it
forms a thin film of alumina at the surface of the material[18]
.
The PM2000 is a commercial ODS alloy produced by the Plansee Group[21]
used
in several industrial components like combustion parts for engines, stirrers in the glass
industry or even honey comb structures for aerospace. It is a highly oxidation resistant
and creep resistant ferritic iron-chromium-aluminium based alloy, strengthened with finely
dispersed Y2O3 particles that have a typical size of 20 to 50 nm[22]
. It has a density of
7.18 g·cm−3
. The composition of this alloy is shown in Tab.1.3:
Alloying elements
Cr Al Ti C O N Y Fe
wt.% 18.6 5.2 0.54 0.04 0.09 0.006 0.0391 75.385
at.% 18.6 10.021 0.587 0.173 0.292 0.022 0.023 70.282
Table 1.3: Chemical composition of the PM2000 ODS alloy as determined by XR fluores-
cence[23].

This alloy has remarkable properties against creep up to 1300◦
C thanks to the Y2O3
particles. It is also highly resistant to corrosion up to 1100◦
C[24]
because an aluminium
oxide layer forms at its surface. For data concerning the PM2000 mechanical properties,
the MatWeb database[22]
can be consulted. This alloy has been used as a basis for the
preparatory phases of this work as well as for comparison with the 15CRA-3 properties.

Chapter 2
Theoretical background
2.1 Interactions of radiation and matter
Most of the radiations present in nuclear applications, neutrons, α and β+/−
particles and
γ quanta, are able to interact with materials what generally results in damaging them.
However, when radiation damage of structural materials is considered, neutrons are of
the highest relevance: the other particles having a large damage potential, α particles
and fission products, are stopped within the fuel. Radiation damage always begins with
displacements at the atomic level, i.e. damage of the lattice and microstructure and can
have consequences up to macro scales.
Although the topic of this thesis is a particular type of radiation damage, basics on
the interactions between radiation and matter shall be presented before going into details
on the topic of radiation damage.
When a particle goes through an infinitesimal distance dx in a solid, it will lose en-
ergy because of elastic e, or inelastic i, scattering or nuclear reactions, n. This be can
summarised as follows:
dE
dx
=
dE
dx e
+
dE
dx i
+
dE
dx n
The first mechanism, elastic collisions, is the main source for atomic displacements as
the bombarding ion transfers part of its energy to a target atom. The first atom to be
struck by the incoming ion or particle is called primary knocked-on atom (PKA). If the
energy transferred to the PKA is higher than a lattice dependent threshold energy Td, it
will leave its original lattice position, hereby creating a so called Frenkel pair (vacancy-
interstitial). As threshold energies are typically on the order of tens of eV and radiations
to which the materials are exposed in a nuclear reactor have energies going from parts of
eV to MeV, the PKA itself will have enough energy to displace neighbouring atoms thus
creating a so called displacement cascade.
7

CHAPTER 2. THEORETICAL BACKGROUND 8
Td values recommended by the ASTM for the metals contained in the 15CRA-3 alloy
(Tab. 1.2, p. 3) are presented in Tab.2.1:
Metal Tmin
eV Td eV
Fe 20 40
Cr 28 40
W 40 90
Ti 19 30
Table 2.1: recommended Td values from ASTM E521-96[26].
Secondly, inelastic interactions between the incoming particle and the electrons of
the target can lead to ionization, transfer or exchange of electrons. These processes are
basically competing with the elastic interactions as they reduce the energy available for
atomic displacements. They can nonetheless create some displacements as the energy
imparted to the recoiled nucleus is often larger than Td.
The third type of interactions are those in which the bombarding particles interact
with the target nucleus. On the contrary to the former two types of reactions, where
the energy losses are on the same order of magnitude as the energy deposited by the
bombarding particle, nuclear reactions often have a far higher energy output than that
of the incoming particle or ion. Example of such a reaction is nuclear fission: induced by
a neutron having an energy going from less than an eV to a few MeV, it yields neutrons
and fission products having a total energy of about 200 MeV. Nuclear reactions are of
highest relevance when one studies radiation damage.
The way in which these reactions occur within solids depends on several factors such
as the material, the type and the energy of the radiation.
Neutrons
The interactions between neutrons and target atoms can be modelled as collisions between
hard spheres. Indeed neutrons do not interact with the electron cloud due to their elec-
trical neutrality. When a neutron collides with an atom nucleus it can either be scattered
or induce nuclear reactions. Scattering can be inelastic or elastic, i.e. with or without
loss of kinetic energy in the system. In the first case, that of a neutron of mass m with
an initial energy Ei elastically scattered by an atom of mass M, the average recoil energy,
i.e. the one which is transferred to the collided atom, is expressed by:
¯Te =
γEi
2
with γ =
4Mm
(M + m)2 (2.1)
Computing this value for the case of an iron atom struck by 1 MeV neutron yields
¯T = 35 keV TFe
d = 40 eV, see Tab. 2.1, meaning that the PKA would have more than

enough energy to trigger a displacement cascade.
In the case of inelastic scattering, the reaction outcome is different. First, the nucleus
absorbs the incoming neutron to form a compound that in turn emits a neutron and a γ
quanta[27]
. The emission of more than one γ-ray is possible since the struck nucleus may
be left in an excited state after the emission of the neutron and first γ. These reactions are
usually written down in the following form: A
Z X(n, n )A
Z X∗
. In such reactions, the recoiled
energy depends on several parameters such as its cross-section or the neutron energy.
Furthermore, nuclear reactions, such as (n, 2n), which are triggered by neutrons within
the material, are relevant. They produce additional neutrons that can increase the extent
of radiation damage. Transmutation is also crucial as it leads to composition changes that
can be followed by segregation, phase transformations and lattice deformations. Further-
more, (n, α) or (n, γ) reactions are also of importance: gas atoms are produced in the first
case and the energy imparted to the recoiling nucleus is sufficient for displacing the struck
atom in the second. An expression similar to Eq. 2.1 can be derived for (n, γ) reactions:
¯T(n,γ)
E2
γ
4 (M + m) c2
(2.2)
Ions
Interactions between ions and atoms or between two atoms are of high relevance when
radiation damage is studied, as ions are very often used to simulate neutron irradiation and
displacement cascades induced either by neutrons or ions involve atom-atom interactions.
These interactions are governed by the so-called interatomic potentials. These func-
tions describe the forces acting on neighbouring atoms as a function of the distance r
separating them. Atoms are made of a negatively charged electron cloud and a positive
nucleus. At this scale the governing forces are electrostatic. These functions have similar
forms to that of the well-known simple Coulomb potential:
V =
Z1Z2ε2
r
, r a0 (2.3)
and are defined for a0 < r < re where a0 and re are the Bohr radius and a lat-
tice spacing, respectively. Determining the energy transferred between colliding atoms
or ions requires selecting an appropriate potential, determining the collision parame-
ter b as a function of the asymptotic scattering angle φ, which is a function of the
recoil energy T and obtaining the energy transfer cross-section. This process is case
dependent since the usually used potentials (e.g. Born-Mayer[28]
or Brinkman[27]
poten-
tials) have applicability limits. A thorough treatment of this question can be found in

Fundamentals of Radiation Materials Science - Metals and Alloys by Gary S. Was[27]
.
The energy transferred in atom-ion collisions also depends on the ion type: Light
energetic ions such as protons do not interact in the same way as fission fragments would,
i.e. different potentials shall be used to describe the situation. The ratio of ρ
a
(T), where
ρ is the distance of closest approach and a the screening radius and T the recoil energy,
is the parameter allowing one to select an appropriate potential. Figure 2.1 shows the
different regimes that this ratio characterises as a function of T.
1.2 Interactions Between Ions and Atoms 31
Classification of Ions
There are three important classes of ions in ion–atom collisions. The first is light en-
ergetic ions with Ei > 1MeV. The second is highly energetic (Ei ∼ 102 MeV) heavy
ions such as fission fragments (M ∼ 102). The third is lower energy heavy ions that
may be produced by an accelerator or appear as a recoil that result from an earlier
high-energy collision. The energy of these recoils is generally less than 1MeV.
For each of these interactions, we must decide on the most appropriate potential
function. A convenient guide is ρ/a, the ratio of the distance of closest approach
to the screening radius as a function of the recoil energy, T. A rough graph of ρ
vs. T is provided in Fig 1.12 to aid in the selection of the most appropriate poten-
tial. The three curves represent ions of each of the three classes just discussed: (1)
20MeV protons, (2) 70MeV fission fragments, and (3) 50keV Cu ions. Curve (1)
collisions apply to the regime where ρ a and the simple Coulomb potential is ad-
equate. Curve (2) collisions that are head-on will have ρ a also. But for glancing
collisions, ρ ∼ a and the screened Coulomb potential is most appropriate. Curve
(3) represents the region where a < ρ 5a and the inverse square potential or
Brinkman potential would apply since both the Born–Mayer and screened Coulomb
terms must be accounted for.
Fig. 1.12. Distance of closest approach r, as a function of T for (1) 20MeV protons in Cu, (2)
70MeV Xe+ ions in Cu, and (3) 50keV Cu+ recoils in Cu (from [12])Figure 2.1: ρ/a ratio as a function of T for energetic protons and heavy (Xe+
) ions as well
as for low energy heavy ions (Cu+
). From a book by Gary S. Was[27]
2.1.1 Light ions scattering
From Fig.2.1 it can be seen that only the simple Coulomb potential (Eq.2.3) is of relevance
in this study since He+
ions with energies of 800 keV to 2 MeV are used for the irradiations.
Collisions of light ions (M1 ∈ [1, 4]) are described by Rutherford scattering, i.e. pure
elastic scattering due to Coulomb static forces. A schematic view of a collision between
two particles is shown on Fig.2.2.
As mentioned before, determining the energy transfer cross-section requires ψ, φ and
b to be determined. Hence the following definitions are needed:
η =
M2
M1 + M2
and b0 =
Z1Z2ε2
ηEi
and ρ(b) =
b0
2
1 + 1 +
4b2
b2
0
1/2
where b0 is the smallest collision parameter to which head-on collision correspond. ρ(b)
is the aforementioned distance of closest approach as a function of the impact parameter.
With these parameters the asymptotic scattering angle can be determined as a function
of the impact parameter:

b
M1
M2
CM
ф
ψr1
r2
Figure 2.2: Representation of collision orbits in the centre of mass system. ψ is the scat-
tering angle of the struck atom, φ the asymptotic value of this angle and b the
collision parameter. Figure after an illustration from Gary. S. Was[27].
φ/2
π/2
dψ =
1/ρ
0
1
b2
1 −
V (x)
ηEi
− x2
−1/2
dx =
0
1/ρ
1
b2
−
b0
b2
x − x2
−1/2
dx
φ = π − 2
φ/2
π/2
dψ → sin−2 φ
2
= 1 +
4b2
b2
0
→ b =
b0
2
cot
φ
2
Where x = 1/r. Now the sought cross-section can be determined from its very deﬁni-
tion:
σs(Ei, T)dT = σs(Ei, φ)dΩ = 2πbdb → σs(Ei, φ) =
b0
4
2
1
sin4 φ
2
σs(Ei, T) = σs(Ei, φ)
dΩ
dT
=
πb2
0
4
Eiγ
T2
(2.4)
Here ˆT = γEi, the energy that is involved on the collision and Ť = Ed = Tmin, the
energy required to trigger a displacement. Finally, using its deﬁnition, the average energy
loss ¯T can be determined:
¯T =
ˆT
Ť
Tσs(Ei, T)dT
ˆT
Ť
σs(Ei, T)dT
≈ Ed ln
γEi
Ed
(2.5)
Applying these relations to the case of the 15CRA-3 alloy is rather complex as an

incoming particle has chances to hit any of the alloying and trace elements. However,
without introducing these probabilities in the hereby discussion - this is done later when
the irradiations are simulated with the SRIM software[29]
- values of ˆT, Ť and ¯T computed
for 2 MeV and 800 keV helium ions colliding the most signiﬁcant alloying elements. These
are displayed on Tab. 2.2
Element Ť eV
2 MeV He ions 800 keV He ions
ˆT keV ¯T EV ˆT keV ¯T EV
Fe 40 499.2 377 199.7 341
Cr 40 530.9 379 212.4 343
W 90 166.8 677 66.7 595
Ti 30 569.6 295 227.8 268
Table 2.2: ˆT, Ť and ¯T values for the main alloying elements found in the 15CRA-3 ODS
steel - for 2 MeV and 800 keV He ions. Ť values are these recommended by the
ASTM[26].
2.1.2 Stopping powers
Up to this point, only collisions have been considered as sources of energy losses. This,
however, does not describe reality: the stopping of an ion may be due to additional
processes, namely ionisation, electronic excitation and Bremsstrahlung as it goes through
the target material. Hence, the total energy loss is described by Eq. 2.6:
−
dE
dx tot
=
dE
dx n
+
dE
dx e
+ −
dE
dx r
= N (Sn + Se + Sr) (2.6)
N is the target number density and S’s are the so-called stopping powers in units of
energy times squared distance. Energy losses can be elastic, n, electronic, e or radiative,
r. This last process is neglected because it is small in cases inspected here[27]
.
The ratio of Se to Sn is of importance since it decides whether a given interaction can
be treated like a pure Coulomb collision, this is the case at high energies where ρ a and
Se Sn, or if it has to be treated diﬀerently, for example at low energies, where ρ ≈ a
and Sn > Se. In either cases, Eq.2.6 holds and the average energy loss per collision can be
determined with Eq. 2.7, provided that the corresponding energy transfer cross-sections
are known.
dE
dx
=
¯T
λ
=
¯T
N
σ = N
ˆT
Ť
Tσ(Ei, T)dt (2.7)
where λ = σ/N is the mean-free path between two successive collisions.

Elastic collisions
Energy losses by elastic collisions, also referred to as nuclear stopping (whence the n
subscript) are described by ignoring interactions between nuclei, i.e. each nucleus acts
independently from the others on the stopping of an ion. Here, high energy elastic col-
lisions will be discussed for describing the stopping of He ions as the lowest energy used
for irradiation is 800 keV, which is high enough to be treated as pure Coulomb collisions.
The energy transfer cross-section valid in such cases is presented in Eq.2.4: regarding
this the nuclear stopping power is expressed by:
dE
dx n
= NSn(Ei) = N ·
πZ1Z2ε4
Ei
M1
M2
log
γEi
Ťb
(2.8)
Where Ťb is the value of T for which a = b, i.e. Ťb = (ε2
γE2
a)/(4Ei) and Ea the
value of Ei that yields ρ0 = a, i.e. Ea = 2Er(Z1Z2)7/6
(M1 + M2) /(M2e). Equation 2.8
can be simplified for collisions in which identical atoms collide with each other. How-
ever, in the case of this study only the helium ions are energetic enough to have pure
Coulomb collisions, this case will not be discussed here. More details can be found in
Fundamentals of Radiation Materials Science - Metals and Alloys[27]
.
As it can be seen in Tab. 2.2, the average energy loss is in the eV scale, meaning
that atom-atom collisions cannot be described with a simple Coulomb potential as the
nuclear charges are screened by the charge of the innermost electron shells that enter the
internuclear space. More simply put, electrons play a role in these situations while they
do not when MeV ions are bombarding the target atoms. Such situations are described
with help of "screened" Coulomb potentials that have the following form:
V (r) =
Z1Z2ε2
r
· χ(r) (2.9)
where χ(r) is a screening function that moderates the simple Coulomb potential from
Eq. 2.3, in the sense that it describes how atoms interact at all distances. χ(r) values are
comprised between zero for large distances and unity at very small r’s. Determination
of stopping powers appropriate to these situations is done with help of the differential
energy transfer cross-section proposed by Lindhard et al.[30]
:
σ =
−πa2
2
f(t1/2
)
t3/2
(2.10)
σ only depends on t, defined as: t =∈2 T
ˆT
, where ∈ is the dimensionless energy[31]
. t
characterises the penetration depth into an atom during a collision[27]
, i.e. it is small at
low energies and growth with increasing energies:

∈=
aM2
Z1Z2ε2 (M1 + M2)
Ei (2.11)
f(t1/2
) is a scaling function that has various analytical expressions, i.e. polynomials
or power law among others. The general trend is that the cross-section depends on t1/6
at low energies, is independent of ∈ at intermediate energy levels and varies with t−1/3
at
high collision energies.
With these considerations an expression similar to Eq. 2.8 can be written for screened
Coulomb collisions:
dE
dx n
=
−Nπa2 ˆT
∈2
ˆT
0
f(t1/2
)dt1/2
→ Sn(∈) =
∈
πa2γEi
Sn(E) =
1
∈
∈
0
f(t1/2
)dt1/2
(2.12)
Equation 2.12 can be further developed in cases where a power-law function is used
for f(t1/2
). However, for practical applications, the actual stopping power has to be
computed by numerical integration. This is done with help of the "universal screening
function", χU , proposed by Ziegler et al.[27,32]1
. This yields the so-called ZBL universal
nuclear stopping[32]
:
Sn(Ei)ZBL =
8.462 · 10−15
Z1Z2M1Sn (∈ZBL)
(M1 + M2) (Z0.23
1 + Z0.23
2 )
(2.13)
where Sn(∈ZBL), the "ZBL" version of Eq. 2.12 is:
Sn(∈ZBL) =
0.5 log (1 + 1.1383 ∈)
(∈ +0.01321 ∈0.21226 +0.19593 ∈0.5)
and ∈ZBL=
32.53M2Ei
Z1Z2 (M1 + M2) (Z0.23
1 + Z0.23
2 )
and ∈ZBL is the ZBL dimensionless energy[27]
. These three last relations are the ones
that are eﬀectively implemented in the SRIM software[29]
used to simulate the irradiation
experiments.
The last type of ion stopping mechanism is due to electrons. It is much more complex
than that of nuclear stopping. The energy loss dE/dx can be fairly well approximated by
the Bethe-Bloch formula:
−
dE
dx e
=
2NπZ2
1 Z2ε4
Ei
M
me
log
γeEi
¯I
(2.14)
1
ZBL stands for Ziegler-Biersack-Littmark, the names of those who developed this model

With me the electron mass, γe being the result of Eq. 2.1 for electrons and ¯I the
mean excitation-ionisation level of the target, given by ¯I ≈ Z2 · 11.5 eV, i.e. the lower
energy limit for ion-electron interactions[27]
. The exact analytical model describing these
interactions was developed by Lindhard, Scharﬀ and Schiott (LSS), details can be found
in Gary S. Was book’s[27]
. The main result of the LSS treatment is that as long as an
ion has an energy E greater than the Fermi energy of the target, the electronic stopping
power goes with E1/2
.
Range of ions in matter
Provided the results of the last subsection, the range or stopping distance of ions in matter
can now be determined. The basic assumption behind the following development is that
the energy loss mechanisms presented in subsection 2.1.2 (page 13) are independent from
one another. Thus the total stopping power is the sum of both the electronic and nuclear
stopping powers, multiplied by the target number density N.
From the very deﬁnition of the energy loss, the so-called average total range is simply
determined by:
dE
dx tot
= N [Sn(E) + Se(E)] → R =
R
0
dx =
1
N
Ei
0
dE
[Sn(E) + Se(E)]
(2.15)
This quantity is not the one sought in range calculations however; the important
quantity that one wants to determine when planning irradiation experiments is the actual
depth that the ion reach in the direction perpendicular to the sample surface, i.e. parallel
to the beam. Hence, the sought quantity is the average projected range, Rp. Fig.2.3 gives
a good representation of the various parameters found in range calculations.
Details on the derivation of Rp can be found in books by Nastasi and Mayer[33]
and
by Was[27]
. The result of the mathematical treatment is the following:
R[nm] =
6EM1(M1 + M2) Z
2/3
1 + Z
2/3
2
1/2
ρZ1Z2M2
(2.16)
where ρ is the target density in g·cm−3
, E is given in keV and 2 subscripts stand for
the target atoms. Additionally to this, the average projected range and its straggling are
expressed as:
Rp
R
1 + (M1/3M2)
and ∆Rp
1.1Rp
2.5


2 (M1 + M2)1/2
M1 + M2


Rp
2.5
(2.17)
The range distribution follows a Gaussian with a standard deviation which is the

α
incident ion
surface plane
y
z
x
Rr - radial range
Rp - projected
range
xs - depth
(penetration)
(xs, ys, zs)
R - path length
(range)
Figure 2.3: Schematic view of an ion penetrating in a material with an angle of incidence.
After an illustration from M. Nastasi and J.W. Mayer[33].
straggling calculated in Eq. 2.17. With these results, the concentration of implanted ions
can be calculated as a function of the target depth, x:
N(x) = Np exp
1
2X2
(2.18)
Here, Np is the peak concentration at Rp and X = (x−Rp)/∆Rp. Integrating Eq. 2.18
over x yields the number of ions implanted per unit area Ns:
Ns =
∞
−∞
N(x)dx = ∆RpNp
√
2π


2
π
∞
0
exp −
1
2X2
dX

 (2.19)
2.1.3 Simulation of neutron irradiation effect with ions
Using ions to simulate radiation damage caused by neutrons is advantageous because
of several factors such as easiness of handling, rareness of neutron sources and time.
These motivations are simple to understand: neutron irradiation of materials triggers
transmutation by neutron capture. This means that neutron irradiated samples will
practically always be radioactive, thus requiring very careful handling and use of adapted
facilities like hot cells. This difficulty is avoided in the frame of the present work as
He ions with energies of 2 MeV or less are used to irradiate the samples: activating the
material would require He ions with energies of at least 5 MeV.
Another important incentive to use ions instead of neutrons is the time needed for an
experiment: in order to reach high enough neutron fluences, i.e. damage levels, one to

three years of in-core exposure2
are required whereas similar damage can be introduced
within a day if a material is irradiated by ions in an accelerator[27]
. The experiments
carried out in this work take around 8 hours per sample in ETH Hönggerberg tandem
accelerator (see section 3.3.2, p.37).
Finally, the number of neutron sources is a significant issue. Very few facilities where
neutron irradiation experiments could be carried out are found in Switzerland. As a
matter of fact, three research reactors are located in the country: Crocus at EPFL, AGN-
211-P at the University of Basel and Protheus at PSI. However, only two of these are
still in operation as Protheus was shut down and set for dismantling in 2011. Aside from
these small facilities, the spallation source SINQ located at PSI and the four Swiss nuclear
power plants[34]
are the only other neutron sources found in the country.
These three points are the main reasons for which ion irradiation is preferred when
basic radiation phenomena are studied. Nevertheless, a crucial question arises from this:
are the effects of ion irradiation representative of damages caused by neutrons?
When radiation experiments are carried out, the important thing is the final state
in which the sample is, i.e. the irradiation history is not of much relevance as long as
the radiation damage is the same. The problem is that although some processes like
irradiation induced swelling mostly depend on the dose, others such as irradiation creep
take a long time to become significant. It means that in spite of the fact that a given dpa
level can be reached rather quickly, ion irradiation might not yield the same damage as
in-core exposure. As a reminder dpa stands for displacement per atom, the standard unit
of radiation damage.
Further differences may arise from the very nature of ion irradiation, energetic ions
are created in accelerators and obtained as mono-energetic beams, i.e. only a given depth
will be damaged according to Eq.2.17 whereas neutrons cover a spectrum that spans from
sub-eV to MeV energies. This can be overcome by the use of multiple beams in order to
distribute radiation effects over the sample depth like it is done in this study.
The most substantial difference between neutrons and ions of different masses is how
the material is damaged by the irradiation, more specifically how the ions or neutron
energy is deposited as a function of the particle mass. On one hand bombarding a target
with neutrons or heavy ions produces damage in large clusters (displacement cascades).
On the other hand, the damage structure produced by using light ions such as protons
or He ions consists of Frenkel pairs or small clusters[27]
. Last, it has been reported that
due to the higher dpa rates achieved by electron or heavy ion irradiation, the point at
which swelling peaks is shifted a 100 or 150◦
C towards higher temperatures[35]
. Although
light ions (He) are used in the frame of this study, a similar shift of the peak swelling
temperatures is also to be expected in this case since the damage rate is much higher than
2
in a thermal spectrum reactor

in a neutron irradiation experiment.
Projections of the ion distribution with recoils created by different ions being stopped
in the 15CRA-3 are displayed on Fig.2.4. These give a clear example of the influence of
the ion mass on its range and damage structures that it creates.
Figure 2.4: Projections of the ion distribution and recoils created by 2 MeV He ions (white
tracks on top), 10 MeV Fe ions (blue tracks in the middle) and 20 MeV U
ions (orange tracks at the bottom) in the 15CRA-3 ODS steel. These were
simulated by SRIM.
The main positive and negative characteristics of irradiation experiments carried out
with neutrons and light or heavy ions are summarised in Tab. 2.3.
2.1.4 Interactions modelling in SRIM
SRIM[29]
is a software used to simulate the irradiations that are carried out in the ex-
perimental part of this thesis. By using SRIM, one can perform range and transport of
ions calculations. SRIM stands for "Stopping and Range of Ions in Matter" and TRIM
for "TRansport of Ions and Matter". The actual irradiation experiments are simulated by
TRIM calculations in order to determine the depth of penetration of the He ions as well
as irradiation profiles in the sense of plots displaying the level of dpa versus the sample
depth, like those presented on Fig.3.3 and 3.4, p.35.
TRIM calculates how energetic ions interact with matter by Monte Carlo simulation.
This software lets one predict the effect of a given matrix irradiation with a chosen type
of ions. The bombarding ions can be given any energy and angle of incidence with respect
to target.
SRIM simulates collisions with screened Coulomb collisions, including exchange and
correlation interactions between the overlapping electronic shells[32]
. The algorithm con-
siders that the ions jump from one collision to another and averages the collision results
over the gap that separates these collisions. The ions also have long range interactions by

Advantages Disadvantages
neutrons
• obtention of real damage
data
• displacement cascades
• transmutation
• very long irradiation time
• high sample activation
• scarcity of sources
light ions
• moderate dose rates
• reasonable irradiation time
• good penetration depth
• low activation level (high E)
• minor cascades
• no transmutation
heavy ions
• high dose rates
• short irradiation time
• displacement cascades
• no activation
• very small penetration
• no transmutation
• composition changes (im-
plantation)
• high dpa rate (annealing)
Table 2.3: Summary of the most important characteristics of irradiation experiments using
neutrons, light ions and heavy ions. From the book of Gary S. Was[27].
electron excitation and plasmons in the target material: these interactions are simulated
by taking into account the target collective electronic and interatomic bond structures.
In order to simulate future irradiations and their resulting damage, the SRIM input
was set up with ”Detailed calculation and full damage cascades”: this option follows every
recoiling atom until its remaining energy is lower than the energy required to displace any
of the target atoms. In this respect, all collisional damage is accounted for and fully
analysed.
The physics behind the creation of vacancies is modelled as follows:
Vacancies = Interstitials + Atoms leaving the target volume
The collision cascades resulting from the knock-on of incident atoms or ions, having a
mass Z1 and a given energy E0 with target atoms of mass Z2 are calculated as follows:
• All target species are given a speciﬁed displacement energy Ed, binding energy of
the atoms to their lattice position Eb and the ﬁnal energy below which a recoiled
atom is considered as stopped Ef .

• After a collision, the incoming atom Z1 has an energy E1 and the struck atom Z2
has an energy E2.
• Displacements occur in cases where E2 > Ed, i.e. the atom is given enough energy
to leave its lattice position. A vacancy is however not necessarily created in this
case: the creation of a vacancy requires both E1 > Ed and E2 > Ed, i.e. both atom
have enough energy to leave said position after the collision. In the latter case, the
atoms become moving atoms of the displacement cascade and the struck atom will
lose Eb when it leaves its lattice position.
• In cases where E1 < Ed and E2 > Ed, two possibilities are present: either Z1 = Z2
or Z1 = Z2, i.e. the incident atom is identical or different from its target. In the first
case, the collision is called a replacement collision and the incident atom remaining
energy E1 is released as phonons. In the second case (incident atom is different from
its target), Z1 is stopped as an impurity.
• The last possible case is that of E1 < Ed and E2 < Ed in which case Z1 becomes an
interstitial and the remaining energy E1 + E2 is released as phonons.
2.2 Radiation damage in metals
2.2.1 General considerations
Radiation damage of materials is principally due to energy losses by elastic collisions. The
time scales and energy levels involved in radiation damage events are very large: typical
times are spanning over more than fifteen orders of magnitude and energies are comprised
in a eV to MeV range. These scales are presented in Tab. 2.4
Characteristic time and energy scales
for radiation damage processes
Event Time Energy carrier Energy
cascade creation 10−13
s bombarding particle 106
eV
unstable matrix 10−11
s PKA 104
eV
interstitial diffusion 10−6
s SDA 102
eV
vacancy diffusion 1s unstable matrix 1 eV
microstructure evolution 104
s thermal diffusion kT
Table 2.4: Characteristic time and energy scales involved in the radiation damage of ma-
terials, taken from[36]. PKA and SDA stand for primary knocked-on atom and
secondary displaced atoms, respectively.
Here, one can see that the time between the creation the vacancy-interstitial pair and
the diffusion of these point defects to microstructural features acting as sinks is much
longer than the time needed by the matrix to stabilize past the bombardment.

The diffusion of these point defects is at the core of the radiation damage mechanisms
affecting the dimensional stability of irradiated materials. These mechanisms are the
following: swelling, shrinkage, creep and growth - the first two phenomena induce volume
changes whereas the two last are volume-conserving shape alterations[36]
.
2.3 Irradiation induced swelling - basics
Irradiation induced swelling is defined as the isotropic volume expansion of a solid without
an external stress[27]
. Cawthorne and Fulton were the first to report this phenomenon
back in 1967 by inspecting stainless steel irradiated in a fast reactor: they showed that the
cavities found in their samples could not be Helium bubbles produced by (n, α) reactions
but were clusters of irradiation induced vacancies[36]
. An example of a highly swollen
stainless steel rod irradiated in the EBR-II reactor is displayed on Fig.2.5. This photo-
graph shows that irradiation induced swelling can induce deformation of several percent
in alloys that are not designed with the specific purpose of being swelling resistant.
Figure 2.5: 316 stainless steel rods before and after irradiation at 533◦C under a fluence
of 1.5 · 1023 n·m−2, taken form a paper by L.K. Mansur[36].
First mentions of extensive theoretical and experimental investigations on irradiation
induced swelling date back to the early seventies[37,38]
. Brailsford and Bullough set the
actual kinetic rate theory of swelling in 1972[39]
. The main features of this theory are
presented in subsections 2.3.1 and 2.3.2.
A comprehensive theoretical treatment of irradiation induced swelling starts with the
description of how point defects gather, migrate and cluster in a material. Voids and
bubbles share common characteristics in the sense that both defect types are cavities
within the material bulk. The difference between a void and a bubble is mainly depends
on the amount of gas found in a given cavity. A usual distinction criteria is the shape of
a given cavity: voids will tend to be faceted shaped cavities, whereas bubbles are usually
spherical[27]
. Reason for this shape difference is the following: on one hand, because of the

lattice periodicity, voids show facets that lie along the close-packed planes. On the other
hand when the surface energy of the bulk/cavity interface is changed by the presence
of gas or if the gas pressure is sufficiently high, the gas-filled cavities tend to become
spherical.
2.3.1 Void swelling
The kinetic theory of point defects[36,39]
was developed with the purpose of making a
precise description of the interactions of point defects with one another, clusters and
point defect sinks such as dislocation loops located within the matrix possible.
A flowchart presenting the different "routes" that point defects can take from their creation
due to exposure to radiation to effective irradiation damage is displayed on Fig.2.6:
Displacement
Available Deffects
Diffusion of vacancies
and interstitials
Formation of
extended deffects
Absorption at
existing sinks
Bulk
recombination
In matrix At traps In matrix At traps
Recombination at
sinks
Recombination at
sinks
Damage
accumulates
Damage
annihilated
Hardening,
swelling,
growth, creep,
solute
redistribution
No change in
properties
Figure 2.6: Diagram showing the sequence of events implicated in irradiation damage of
materials. After a diagram from Was[36].
The hypothesis which is at the very basis of this theory is that growth of voids is driven
by the existence of sinks, such as dislocations, that have a preference for interstitials over
voids[39]
. Voids will grow in such situations because the steady state concentrations of
point defects result in a net flux of vacancies drifting towards voids. For this reason, ki-
netics involved in void growth, and hence in irradiation induced swelling, strongly depend
on the sink type concentrations, e.g. that of precipitates, particles, dislocation and void

densities all influence the rate at which a metal will swell under irradiation.
As mentioned above, the presence of defect sinks is at the very heart of the present
theory: in the rate theory the material in which the actual sinks are discrete and randomly
distributed is modelled as a medium containing a continuous distribution of sinks densities
to which respective defect capture strengths are assigned[36]
. This means that each point of
this medium has both a defect recombination and absorption character, i.e. the modelled
medium has the same generation and loss terms as the material, in a volume-averaged
sense.
In this framework, rate at which vacancies and interstitials are lost within the medium
can be written as:
Dv/iCv/ik2
v/i (2.20)
Where D’s are diffusion coefficients, Cv/i stands for the vacancy or interstitial concen-
tration and kv/i has dimensions of cm−2
, i.e. k−1
v/i is a distance that represent the mean
distance that free defects can travel within the medium before being trapped[39]
.
The next step of the rate theory of swelling is the determination of the sink strengths,
i.e. how efficient they are at capturing defects. These strengths are analytically deter-
mined by considering that a sink can be modelled as a small sphere of radius rs1 found
in the medium. A sink-free spherical region of radius R1 is defined around the sinks - it
is better suited to randomly distributed sinks than zero flux conditions[39]
.
Sinks are categorized in three different types: neutral, variable-bias and fixed-bias
sinks. The first type is defined as having no preference for vacancies or interstitials. Sinks
of this kind are voids or incoherent precipitates and have the ability to accept point defects
without limitation. The effective strength of such sinks can be written as:
k2
1 = 4πrs1Cs1 (2.21)
Here, Cs1 is the average concentration of neutral sinks in the body, i.e. the void
or incoherent precipitate volume concentration. Additionally to this, the rate at which
defects are effectively emitted into the medium from such sinks, K1, is expressed by
Eq. 2.22:
K1 = 4πrs1Cs1D¯c1 = k2
1 · D¯c1 (2.22)
where ¯c1 characterises the sink thermal emission rate by D/re · ¯c1, given by: ¯c1 =
ce · exp(F1r3
e/kT), a function of the thermal equilibrium concentration ce of the defect,
F1r3
e the variation in the sink energy when said defect leaves the sink and re is a lattice
spacing.

The other class of sinks are referred to as biased: they show a preference for a given
type of defects. Such a preference can either be intrinsic (fixed-bias) or adaptive to
the amount of neutral sinks (variable-bias). The bias is to be understood as follows: a
interstitial preferring sink will cause an accumulation of vacancies at neutral sinks. In
order to counteract this accumulation, sinks that have only a limited ability to absorb
vacancies must adopt a bias, i.e. favour the capture of interstitials. This bias is variable
in that its magnitude depends on the amount of neutral sinks available for trapping the
excess of vacancies. This type of biased sinks play an important in irradiation induced
swelling because they act as recombination centres[39]
. Coherent precipitates are a typical
example of variable-bias sinks as they try to maintain local order trough their interface
with the matrix.
For such sinks, noting the precipitates radius rp, their volume concentration Cp, Cm
i/v
the defect concentration in the medium and defining the trapping sites occupation prob-
abilities Yi/v, the loss rate of defects is given by Eq. 2.23
Yi/vDi/vCm
i/v4πrpCp with YiDiCm
i = YvDvCm
v (2.23)
It should be noted that there is no thermal activation of the defect emission from such
sinks.
The last category of sinks are those having a fixed-bias towards the capture of intersti-
tials over that of vacancies. Network dislocations due to prior deformation and dislocation
loops created by the condensation of interstitials belong to this category. This constant
bias is caused by the interaction of dislocations with interstitials which is stronger than
that with vacancies. As a result, there is an attraction term (energy) going as 1/r for
interstitials drifting towards dislocations[39]
.
Provided the total density of dislocations ρd and that of those in networks ρN
d and the
respective thermal emission parameters for dislocation loops and network ¯cvL and ¯cvN ,
the rate at which defects are lost to dislocations is expressed by:
ZiρdDiCm
i and ZvDv ρdCm
v − ρL
d ¯cvL − ρN
d ce
v (2.24)
Here, the Zi/v terms are scaling factors depending on the number of sites n at which a
defect can get attached to a dislocation loop and b the lattice spacing introduced earlier.
By combining equations 2.21 to 2.24 yields expressions for the mean k2
i and k2
v param-
eters:

k2
i = Ziρd + 4πrsCs + 1 +
(Zi − Zv) ρd
Zvρd − 4πrsCs
4πrpCp (2.25)
k2
v = Zvρd + 4π (rsCs + rpCp) (2.26)
With these results, the effective rates at which defects are generated in the medium K
can be determined. These rates are crucial for both the swelling rate and the temperature
dependence of swelling are function of these rates.
The thermal emission of interstitials is ruled out because their formation energy is too
large[39]
, i.e. Ki − K = 0. As a reminder, K is the number of displacement per atom, in
other words, the dose in dpa. On the contrary, the emission of vacancies does not require
much energy - hence:
Kv − K = Dv Zv ρL
d ¯cvL + ρN
d ce
v + 4πrsCs¯cvS (2.27)
where ¯cvS ≡ ¯c1 used in equation 2.22. Here, the role of the different types of sinks is
identified and will be used to determine the thermal dependence of swelling.
With these first results, the actual defect concentrations within the medium can be
computed with:
K − DiCik2
i − αCiCv = 0 → Ci =
Dvk2
v
2α
−(1 + µ) + (1 + µ)2
+ η
1/2
(2.28)
K − DvCvk2
v − αCiCv = 0 → Cv =
Dik2
i
2α
−(1 + µ) + (1 + µ)2
+ η
1/2
(2.29)
where α is a coefficient characterising defect recombination and η and µ are factors
given by:
η =
4αK
DiDvki2k2
v
and µ =
(K − K) η
4K

Effect of dose
Further steps consist into determining the rate of accumulation of excess vacancies at
voids and incoherent precipitates, i.e. the volume swelling rate. At this step, the swelling
rate variation with respect to time is dropped as it would lead to obscure expressions and
lose the general character of the present treatment[39]
. In regard to these conditions the
volumetric swelling can be written as:
∆V
V
∆V
V 0
F(η) (2.30)
where F(η) and ∆V
V 0
are large algebraic expressions presented in a paper by A.
Brailsford[39]
. The most important feature of Eq. 2.30 is that the swelling behaviour is
given by two expressions, ∆V
V 0
, which mostly depends on metallurgical properties and
F(η) that characterises the temperature dependence of swelling.
(∆V/V )0 is given by:
∆V
V 0
=
K (t − t0) (Zi − Zv) ρd4πrsCs
(ρd + 4πrsCs) (ρd + 4πrsCs + 4πrpCp)
(2.31)
Eq. 2.31 is inversely proportional to ρd, Cs and Cp, what shows that sinks mainly
serve as recombination centres. It is also directly proportional to (Zi −Zv)ρd and 4πrsCs,
i.e. swelling needs biased as well as neutral sinks. In the case where no coherent pre-
cipitates are found in the medium, further simplifications of Eq. 2.31 yield the following
relationship:
∆V
V 0
= K(t − t0)(Zi − Zv)
x
(1 + x)2 (2.32)
where K(t − t0) is the dose actually contributing to the swelling - Kt0 is the so-called
incubation dose, defined as the dpa level, or cumulative dose, required for the material
to swell by one percent[40]
. x ≡ 4πrsCs/ρd whose values are comprised between zero and
one. The upper boundary value of x yields an upper bound for the swelling as a function
of dose:
∆V
V
% ≤
1
4
· dose in dpa (2.33)
The factor x characterises the dominant type of sinks, x > 1 holds for precipitates
dominant recombination, whereas x < 1 is valid for a medium in which the dislocations
are assuming this role. Hence, it defines the effect of cold work on swelling: in the case
where dislocations serve as recombination centres, an increase of the dislocation density
leads to a decreasing swelling while cases in which dislocations provide a sufficient bias,
i.e. x > 1, an increased level of cold work would also increase the swelling.

Further details on the effect of precipitates sizes can be deduced from ∆V
V 0
. Since
it is proportional to 4πrsCs ≡ 4π (r0Cip + RvCv) with rv the radius of voids and Cip and
Cv being the densities of incoherent precipitates and voids, respectively, the role of neu-
tral sinks on swelling can be measured by the sinks radii multiplied by their densities[39]
.
Thus, a fine distribution of small precipitates would lead to the least swelling when re-
combination is dominant at this type of sinks whereas a case in which recombination is
favoured at dislocations (x < 1) requires big precipitates coarsely dispersed to guarantee
a minimum level of volume swelling.
Finally, the swelling of coherent precipitates containing media would be dominated by
these particular sinks and lead to a different situation, in which cold work always decreases
the swelling[39]
. A more detailed discussion on the topic of precipitate-matrix interfaces,
i.e. coherent and incoherent precipitates, is presented in another paper by Brailsford[41]
.
Effect of temperature
As mentioned earlier, the dependence of void swelling on temperature is described by
F(η):
F(η) =
2
η
− (1 + µ) + (1 + µ)2
+ η
1/2
− ζη (2.34)
Where η, µ and ζ are rather large algebraic expressions depending on most problem
parameters, such as D’s, Z’s, C’s and others. More details can be found in Brailsford’s
paper[39]
. These parameters, however, tend to follow trends. First, η ∝ exp Ev
m/kT with
Em
v being the vacancy motion activation energy. Secondly, ζη ∝ ce
v/(Zi − Zv), i.e. plays
a role only at high temperatures and finally, µ ∝ ce
v and is not relevant if ζ = 0[39]
.
The general trend is the following:
F(η)



2
η1/2
at low temperatures
1 at intermediate temperatures
0 at high temperatures
Figure 2.7 presented below displays the result of numerical evaluations of F(η) made
by Brailsford[39]
. The variation of F(η) with temperature clearly illustrates how the
temperature at which swelling reaches its maximum shifts towards high temperatures as
the dose rate increases.
Important temperatures found in Fig.2.7 are these at which the swelling starts, Ts,
peaks, Tp and meet an upper bound Tf . These temperatures can be determined with the
help of algebraic expressions, which contribute to set some parameters like α/Di or D0
v
are set. Brailsford wrote a paper in which examples of such treatment can be found[39]
.

Temperature [°C]
200 300 400 500 600 700 800
1.0
0.8
0.6
0.4
0.2
0
F(η)
K=10 dpa·sec
-6 -1
K=10 dpa·sec
-3 -1
Figure 2.7: Swelling peak temperature shift as a function of dose rate. values used for
these curves are the following: Cp = 0, ρL
d = (ρL
d + ρN
d )10−2 = 109 cm−2,
¯CvL = 0, ¯CvL = Ce
v = exp (−1.6 eV/kT), Zi − Zv = 0.01, Zv = 4πrsCs =
1011 cm−2, α/Di = 1017 cm−2 and Dv = 0.6 exp (−1.4 eV/kT) cm2·s−1. After
A. Brailsford’s paper[39].
Starting temperature is usually defined as that at which a 10% of the maximum swelling is
reached, whereas the final temperature Tf is naturally that at which swelling terminates.
Considering this, both η and ζ can be rewritten as exponential functions:
η = 400 exp
−Em
v
k
1
Ts
−
1
T
ζ =
1
2
exp
−Q
k
1
T
−
1
Tf
where Q is the activation energy of self-diffusion by the vacancy mechanism. Having
these parameters as well as S and F(η) defined as:
F(η) =
2
η
(1 + η)1/2
− 1 −
1
2
η exp −
Q
k
1
T
−
1
Tf
S =
ρd4πrsCs
(ρd + 4πrsCs) (ρd + 4πrsCs + 4πrdCd)
A "swelling formula" can then be written as follows:
∆V
V
% = S · K(t − t0) · F(η) (2.35)

For steels, Brailsford[39]
suggests values of Em
v = 1.4 eV, Q = 3.0 eV and S 0.17,
whereas Ts and Tf shall be adjusted. This concludes the main aspects of the rate theory
of swelling as it was developed by Brailsford in 1972. In the case of the high chromium
ODS steels, it has been found that particles tend to be either semi-coherent or coherent
depending upon the extrusion temperature. Dou et al.[42]
have reported that aluminium
containing high chromium steels extruded at 1150 ◦
C show around 78% of semi-coherent
precipitates, while samples extruded at 1050 ◦
C have more than 85% of their ODS par-
ticles that show interfaces coherent with the matrix. It appears that in the case of such
alloys, the extrusion temperature can be a way of controlling the irradiation induced
swelling as point defect trapping at coherent matrix-precipitate interfaces is recognized
for being an effective mean to reduce swelling of irradiated materials[43]
.
The effects of temperature and dose on the void swelling behaviour of a given material
can be summarised as follows: Mansur[36]
showed that the swelling goes as dn
, where d
stands for the dose and n is an integer with values typically between 3/5 and 3. The ratio
of dislocation to cavity sink strength, Q, is the factor governing the dose dependence of
swelling rate. If Q ≥ 1, then the rate is low and the exponent n is large, whereas Q ≤ 1
leads to situations in which both the swelling rate and the exponent n are small.
Qualitatively, the temperature dependence can be resumed with three temperature
regimes to which the previously introduced temperatures Ts, Tp and Tf correspond. On
Fig.2.7, it can be seen that F(η) shows a humped curve when plotted against temperature
and since this function determines the thermal behaviour of swelling, actual swelling
curves are similar to that displayed on Fig.2.8:
378 8 Irradiation-Induced Voids and Bubbles
Fig. 8.16. Swelling in nickel as a function of irradiation temperature for a fluence of 5 ×
1019 n/cm2 (after [17])
Figure 2.8: Swelling in nickel as a function of irradiation temperature. Fluence of the
irradiation: 5 · 1019n·cm−2. Figure from G.S. Was book’s[27].

Reason for these regimes where pointed out earlier when the variation of F(η) and ζ
with temperature were discussed. It can be put in simple words as follows: On one hand,
the swelling is minor at rather low temperatures because the vacancies are practically
immobile allowing their concentration to build up, which facilitates the recombination
with interstitials. On the other hand, when temperature is high enough, cavities emit
vacancies at a rate that is sufficienbtly high to counterbalance the vacancy influx caused
by the irradiation[36]
, resulting in minor swelling levels as well. Finally, between these two
thermal regimes, swelling peaks at an intermediate temperature because neither of the
aforementioned processes can compete with the generation of radiation induced vacancies.
2.3.2 Bubble swelling
For quite a long time, helium has been known for having a detrimental effect on the
behaviour of materials under irradiation. Glasgow et al.[44]
, as well as Ghoniem et al.[45]
,
proposed theoretical models for the formation of helium bubbles and for the transport
and clustering of helium atoms in metals under irradiation.
As soon as a material is being irradiated, helium transport does not follow the same
mechanics as it usual does, i.e. it does not only diffuse by occupying interstitial, substitu-
tional or vacant sites of the lattice. In addition to these mechanisms, helium transport in
materials under irradiation is complicated by three main factors[45]
. First, helium atoms
and self-interstitials tend to compete regarding reactions with vacancies. Secondly, ther-
mal and irradiation induced vacancies act as traps where He atoms are predisposed to
agglomerate and finally, collisions due to displacement cascade can be energetic enough
to "free" He atoms that were agglomerated, what add additional mobile atoms to those
introduced either by the irradiation itself or by (n, α) reactions.
The helium effects on irradiation induced swelling are rather complex. Glasgow et
al.[44]
reported terminal void number densities in neutron irradiated austenitic stainless
steels not to be dependent on the helium concentration. However, the time to reach this
final density gets shorter with high He concentration because it increases the rate at which
voids nucleate. This effect also increases with temperature as reported by Farrell and
Packan[46]
(in austenitic steels): cavity nucleation increases by a factor of 2 to 5 between
840 and 950 K and by factors of thousands when temperature reaches 1100 K. In addition
to this, the size of the cavities themselves varies with temperature and consequently so
does the swelling: Farrell et al. reported reduced swelling at temperatures below 750 ◦
C
and increasing above 1100 K were reported[46]
. This is explained as follows: at high
temperatures the rate at which cavities nucleate is higher than that of their size reduction
due to thermal emission of defects, what leads to increased swelling.

Farrell and Packan[46]
also reported that bubble swelling does not depend on the
irradiation dose. Gases have the most eﬀect at low doses, speciﬁcally below 1 dpa as cavity
nucleation takes place at this stage of the irradiation. At high doses, bubble swelling is
governed by the growth of the cavities themselves, a thermal mechanism independent of
the dose.
Ferritic-martensitic steels are also prone to bubble swelling. Chernov et al.[47]
found
larger gaseous bubbles in ferritic grains of such steels than in nickel and austenitic steels.
Moreover, it appears that the ferrite and martensite grains do not behave similarly with
regard to bubble swelling: martensitic grains showed minimal swelling levels compared to
the ferritic regions investigated. This peculiarity of ferritic-martensitic steels is surprising
since it is known that void swelling is minimised in this materials; the low activation energy
required for vacancies to migrate results in an enhanced point defect recombination, thus
leading to minor swelling compared to austenitic steels. However, in the presence of
helium, vacancy clusters act like capture points for He atoms the recombination rate
decreases. Furthermore, as helium-vacancies complexes (bubbles) have a large binding
energy and because of the high mobility of these complexes in bcc metals, bubble swelling
is enhanced in the ferritic grains of ferritic-martensitic steels[47]
.

Chapter 3
Experimental
A large portion of this work consists of its experimental part: preparing the samples,
irradiating these in ETH Hönggerberg tandem particle accelerator and measuring sur-
face displacement using a white light interferometer. Moreover, a program was coded to
ease the data analysis and guarantee the reproducibility of the results. Details on these
procedures are given in the next sections.
3.1 Sample preparation
Samples of 7 × 7 × 1 mm3
are cut from the piece of 15CRA-3 obtained by Dr. M.A.
Pouchon from Prof. A. Kimura. These were ground with SiC papers grades 1200 to 4000
and polished with solutions containing diamonds of 3 and 1 µm to obtain satisfactory
surface quality.
Additionally to this, the other side of the samples are engraved so that they can be
identiﬁed and TEM parallel bar type G400P-N3 gilder grids are placed on top of the
sample surface, prior to any irradiation.
Figure 3.1: Type G400P-N3 TEM parallel bar
gilder grid[48].
The parallel bar grids are made of
40 µm wide bands of nickel, with a peri-
odicity of 22 µm, this results in a striped
pattern with a 62 µm periodicity. These
enable the recognition between irradiated
and non-irradiated regions of the sample
surface. The actual eﬀect of those grids is
a surface featuring periodically distributed
steps of a few nanometres.
33

CHAPTER 3. EXPERIMENTAL 34
3.2 Irradiation simulation
with SRIM
As introduced in section 2.1.4, SRIM, a Monte Carlo simulation software, is used to
simulate the irradiation experiments and determine the depth reached by the He ions while
bombarding the target. Simulations were set according to the 15-CRA-3 composition
presented in Tab.1.2 and run with 104
particles.
SRIM has a very user-friendly interface and is rather easy to use. The ﬁrst window
presents several choices, such as stopping and range tables, tutorials or TRIM calculation.
Choosing TRIM calculation starts the input interface presented in Fig.3.2a:
(a) TRIM input (b) TRIM simulation
Figure 3.2: (a) screenshot of the TRIM input interface
(b) running simulation of 1.8 MeV He ions irradiating a PM2000 sample
The red boxes shown here highlight the input parameters that the user has to give
to set a simulation; these are the type, energy and angle of incidence of the bombarding
particles, number of particles, layers composition and last number and depth of these
layers. The layer composition has to be given in atomic percent, as TRIM does not
accept input in weight %.
At this point, it is also important to select "detailed calculation with full damage
cascades" when choosing how the damage is simulated. The simulation can then be
started and the user has to wait for the results. Figure 3.2b shows a screenshot of a
running simulation of He ion irradiating a piece of PM2000.
By selecting this type of calculations, the output we are interested in is the number of
vacancies created per ion per Ångström for each type of atom found in the matrix, this
as a function of the sample depth. The layer thickness is set to 4 µm since 2 MeV helium
ions are stopped by ∼3.5 µm of 15-CRA-3 and less energetic ions will undoubtedly be
stopped closer to the sample surface.
Obtaining the actual level of damage created in the material is simple provided that

the fluence Φ and the atomic density ρat are known. The damage function fdam is then
simply given by;
fdam = Nvac
Φ
ρat
with units of:
vac
ion × Å
×
ion
cm2
÷
at
cm3
=
vac
at
≡ dpa (3.1)
The dpa level as a function of the sample depth, i.e. an irradiation profile, is obtained
by applying the formula above. Finally the average damage level is obtained by numerical
integration of the profile:
dpa =
1
xmax − xmin
xmax
0
dpa(x)dx
Following this methodology, the plots displayed on Fig.3.3 and 3.4 have been made:
they present two irradiation possibilities. The first plot corresponds to an irradiation
carried out with seven energies spanning from 800 to 2000 keV, while the second has an
additional irradiation with 600 keV He ions. Motivation for an additional low energy
irradiation would be to extend the damaged zone closer to the sample surface.
0 0.5 1
0
0.5
1
1.5
depth [µm]
dpa
Damage profile as function of depth
average dose
0.8357 dpa
dpa
1.5 2 2.5 3 3.5
Figure 3.3: TRIM simulated irradiation profile with 7 energies going from 800 keV to
2 MeV with an energy step of 200 keV. Energy of the ions goes up as the
stopping distance increases, i.e. the peak on the left corresponds to 800 keV
ions and the last on the right to 2 MeV ions. Fluences were tuned from low
to high energy with 55%, 60%, 60%, 65%, 70%, 75% and 100% of the nominal
fluence. The total fluence is 9.7 · 1016 ions·cm−2. The dashed lines represent
the damage created by the single implantations.
Out of these two options, the first was chosen for two reasons: first, setting a stable
600 keV beam would have been very difficult and secondly, irradiating with eight energies

Damage profile as function of depth
average dose
0.8357 dpa
0 0.5 1
0
0.5
1
1.5
dpa
dpa
1.5 2 2.5 3 3.5
depth [µm]
Figure 3.4: Similar profile to that displayed above except for the addition of a 600 keV
irradiation to damage the matrix closer to the sample surface. Fluences were
tuned from low to high energy with 55%, 55%, 60%, 60%, 65%, 70%, 75% and
100% of Φnom. The total fluence is 1.08 · 1017 ions·cm−2. The dashed lines
represent the damage created by the single implantations.
with the desired fluence would not have been possible to do within a single day - seven
energies irradiations took up to 11 hours, a number that does not account for the fact
that the samples had to be cooled down and changed subsequently.

3.3 Experimental setup
The experimental setup employed in the frame of this thesis consists of the irradiation
station used to position the samples in the beam line and to heat them up with help of
a resistance furnace and of the tandem particle accelerator itself. Additionally to this,
surface displacement is measured by white light interferometry, a technique discussed in
section 3.4.
3.3.1 Irradiation station
A sketch of the irradiation station that will be used for the future irradiations is shown in
Fig.3.5. The position of the furnace is controlled with a motor from Nanotech Electronics
GmbH & Co; its step resolution is very ﬁne and allows displacements of 25 µm.
A detailed view of the furnace is presented in Fig.3.6, with the following main elements;
the grey element is the furnace holder made of stainless steel, the blue elements are
Tantalum plates hindering radiative heat transfer to the outside of the furnace. The pink
part is the heating element itself.
In addition to this, a Ni-Cr-Ni thermocouple is put in contact with the heating element
through the casing shown in black. The furnace was designed to reach temperatures going
as high as 1’000 ◦
C.
The experiments related to the irradiation station aimed at getting familiar with the
positioning control system and determining the parking and irradiation positions; as one
cannot see the sample position in the irradiation chamber at ETH Hönggerberg, the exact
location had to be determined prior to any irradiation.
3.3.2 Tandem accelerator
As mentioned before, the irradiations took place in the ETH Hönggerberg particle accel-
erator. The equipment found at this facility is a tandem accelerator designed for acceler-
ating ion beams to energies of 0.6 to 60 MeV[4]
which is mainly used for accelerated mass
spectrometry (AMS) investigations. A top view of the facility is presented on Fig.3.7.

Beam
Furnace
Figure 3.5: Schematics of the irradiation station used for He implantation in the ETH
Hönggerberg tandem accelerator. The irradiation station can be seen on the
upper part of the picture, the furnace can be seen as the purple rectangle.
The lower part of the picture, below the "HUB" inscription, is the irradiation
chamber of the particle accelerator. A detailed view of the furnace can be seen
in Fig.3.6. The numbers on the side of the sketch express dimensions of the
various irradiation station parts in mm.

Figure 3.6: Schematics of the furnace used to vary the irradiation temperature and for
holding the sample.
Figure 3.7: top view of the tandem particle accelerator facility located at ETH Höngger-
berg. The red circle highlights the position at which the irradiation station is
located for the irradiation experiments.
3.4 White light interferometer
White light interferometry measurements were carried out using a Fogale Nanotech Mi-
crosurf 3D optical proﬁle interferometer.
White Light Interferometry (WLI) is a technique that makes use of the interference
principle. Thus, a light beam is collimated from its source and then split into two beams.
One of them goes to the observed object, while the other serves as reference beam. Both
beams will be reﬂected, either by the object itself or by a reference mirror and then
captured and recombined at the beam splitter. After the recombination, the superimposed
beams are imaged by a CCD camera for further processing.
The basic principle is the following: if both optical paths are identical, the beams

interfere in a constructive way, resulting in a high intensity pixel. On the contrary, if
the optical paths are diﬀerent, destructive interferences occur and less intense pixels will
be captured. As a consequence, the relative height of each point can be determined
by varying the object distance and by processing all the corresponding image pixels. A
topographic map of the object can be reconstructed.
The image displayed in Fig.3.8 presents a schematic diagram of a white light interfer-
ometry setup:
Figure 3.8: Schematic layout of an interference microscope[49].
In this, a series of moving interference fringes will be created as the objective lens is
moved vertically. To obtain a 3D mapping of the surface, the point at which the maximum
constructive interference occurs has to be found for each pixel; once this is achieved the
topography is acquired by tracking the vertical movement of the objective lens.
This measurement technique is a very attractive alternative to atomic force microscopy
(AFM): it is very fast and accurate; resolution of 0.1 Å can be reached[49]
.

3.5 Image analysis
In the preparatory phase of this thesis, an irradiated PM2000 sample was measured by
WLI and analysed. The image analysis required several tedious and hardly reproducible
steps. First, by using the interferometer built-in software, the image was "flattened" by
three arbitrary selected points and levelled with respect to the mean plane enclosing these
points. Secondly, Gwyddion, a free scanning probe microscopy (SPM) data visualisation
and analysis software, was used to remove peaks and crevasses found at the sample surface
by "painting" these by hand. In this manner a surface profile could be obtained. The
problem was that the analysed region was rather small: it could cover the image width
(∼140 µm) but only "heights" of around 20 µm only. The sample surface curvature had
then to be removed by processing the data in spreadsheets. At this point, the locations of
the steps due to irradiation induced swelling had to be guessed as good as possible, once
these were found, a third order polynomial was used to fit the aforementioned curvature
and remove it from the profile data.
One can clearly realise that this method faced significant reproducibility issues as all
steps included guesses and decisions made by the analyst. For this reason a program was
coded in order to ensure that the results obtained in the present work could be reproduced
in potential future studies. A detailed documentation of this program can be found in
the TM-46-12-03 PSI technical report[50]
: only the main ideas behind it are given here.
Figure 3.9 shows an example of what an actual WLI topography measurement looks like
without processing. The treatment of this image is explained in the next lines.
Figure 3.9: starting WLI topographical information - the sought surface displacement fea-
tured by 10 to 15 nm steps are not visible yet.

This script runs several routines whose roles can be grouped in two parts: one that
finds and removes peaks and undesired surface features and another which corrects the
sample curvature. The peaks are found according to their physical characteristics, i.e.
peak width and height difference between successive points. The peak finding routine
scans the image twice: first, the absolute value of height differences between a given point
elevation and taht of the n, n is a "typical peak width", previous and next points along the
x and y directions are stored in vectors. When these differences are larger than a given
threshold along x or y, a peak has been found and a binary true is stored in a matrix of
identical dimensions to that of the scanned image. The second level of filtering inspects
only points for which peaks have already been found and scans their nearest neighbours
in a similar fashion to that of the first scan. The difference here is that the threshold
value is lowered to 50%, 25% or 12.5% depending on the distance between the located
peak and its nth
neighbour. The result of these scans is that the peaks are localised and
can be removed from the original image without leaving "stumps" around their locations.
The second main procedure has been coded so that the height of the steps due to
the irradiation induced swelling is found and the image is flattened. This is done by
removing the sample curvature from the surface measurement obtained by white-light
interferometry. First, the average height along each matrix column is computed and
these lines are also fitted with fourth order polynomials. This operation provides a first
modelling of the curvature as well as an average height profile are obtained. Secondly,
because the exact location of these steps is unknown, a first routine restructures the data
so that it matches the expected topography, i.e. flat dips having a width of around 35 µm
and plateaus of ∼17 µm separated by steep ascents of around 10 µm. The data used
at this point is that of the average height profile, since the correction along the y axis
is already known. Additionally to this, a matrix identifying the non-irradiated from the
swollen regions is created. It contains either 1’s at irradiated regions, −1’s at regions
covered by the TEM gilder grid or NaN’s where ascents are located. This information is
then used to fit the data with the following function;
f(xi,j) = ax3
i,j + bx2
i,j + cxi,j + d +
h
2
[1 + sign (zi,j)] (3.2)
where h is the actual step-height, i.e. the value sought for determining the irradiation
induced swelling. The fitting procedure is carried out over all the possible cases and the
one having the best R-squared value corresponds to the actual position of the steps.
The curvature correction can then be defined as the surface obtained by fitting the
lines with fourth order polynomials and adding the fitting function f(x), which describes
the curvature along x. The average height profile is removed to this surface so that the
correction is zero on average, i.e. the signal is not lost.

An example for an image processing output is displayed in Fig.3.10: the surface pre-
sented here is that of a 15CRA-3 sample irradiated with He ions at 500◦
C.
Figure 3.10: View of the post-processing region imaged by WLI.
Finally, height profile of the flattened and filtered surface can be computed by numer-
ical integration over the lines along y. Such a profile is shown on Fig.3.11. Additionally
to the profile, shown in black, the corresponding steps found during the fitting procedure
are shown in red. The blue curves represent the 1σ intervals in which the data is found
- these errors are those arising from the averaging procedures, not from the measuring
technique itself.
20 40 60 80 100 120
−20
−15
−10
−5
0
5
10
15
20
25
30
Height[nm]
hbest
= 12.7338 nm
ascents= 5 µm
P
hh
= 34.6 nm
dist= 10 %
part= 5.3675 %
Sample width [µm]
Best step fitting with flattened average height profile − 15CRA−3_s6_8
20 40 60 80 100 120
−20
−15
−10
−5
0
5
10
15
20
25
30
Height[nm]
Figure 3.11: Post-processing height profile with 1σ-intervals.

An additional feature included in this program is a routine characterising the roughness
of the imaged region: it is done by comparing the height of each point with its 25 nearest
neighbours, according to a five by five square pattern. The comparison of the values is
done by taking the square root of the sum of the squared differences between the elevation
of the considered point and that of its nth
, n ∈ [1 25], neighbours:
R =


5
i=1=3
5
j=1=3
(xi,j − x3,3)2

 (3.3)
The R values map is then normalised with its average value ¯R. The end result is a
map like the one displayed on Fig.3.12, where values usually go from zero to two. These
are to be understood as follows: the farthest the roughness is from unity, the more the
surface shows grains or crevasses, i.e. the rougher it is.
Figure 3.12: Roughness map of a region of a 15CRA-3 sample irradiated at 500◦C.

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