Nuclear Materials Under Irradiation E-Book
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- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
At every stage of the fuel cycle, the materials used are at the heart of nuclear energy safety issues. These materials, which range from steel to polymers, including ceramics, glass, concrete and graphite, are submitted to extreme stresses combining mechanical, thermal and irradiation constraints.
The objective of this book is to provide a basis for the research of nuclear materials subjected to irradiation, with the desire to contextualize them in the industrial environment. Therefore, most of the chapters are co-authored and contain a mix of basic and applied research. The reader will find chapters on nuclear reactor materials (structural materials, neutron absorbers, moderators and nuclear fuel) and on materials in waste management (glass, concrete and organic materials). These material chapters are complemented by more general information on defects and their creation, radiolysis and irradiation and characterization tools.
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Table of Contents
Cover
Title Page
Copyright Page
Preface
1 Irradiation Defects
1.1. Introduction
1.2. Some basic data
1.3. Defect creation mechanisms
1.4. Kinetics of defect evolution
1.5. Open-ended problems
1.6. Acknowledgements
1.7. References
2 Metal Alloys
2.1. Introduction
2.2. Fuel cladding
2.3. Internal structures in austenitic steel
2.4. The vessel
2.5. Perspectives
2.6. References
3 Ceramics within PWRs
3.1. Introduction
3.2. Development and typical properties of UO
2
and B
4
C ceramics
3.3. Aging of ceramics under irradiation
3.4. Future challenges
3.5. References
4 Nuclear Graphite
4.1. What is nuclear graphite?
4.2. Why use graphite in nuclear reactors?
4.3. Evolution of nuclear graphite in reactors
4.4. Conclusion
4.5. Acknowledgements
4.6. References
5 Nuclear Glasses
5.1. Glass of nuclear interest: their role and their aging conditions under irradiation
5.2. How are the effects of long-term irradiation studied at the laboratory scale?
5.3. Closed system: evolution of glass subjected to its self-irradiation and to the accumulation of helium
5.4. Open system: alteration of glass by water under irradiation
5.5. Summary and prospects
5.6. Acknowledgements
5.7. References
6 Radiolysis of Porous Materials and Radiolysis at Interfaces
6.1. Introduction
6.2. General information on radiolysis
6.3. Main porous materials of interest
6.4. Dosimetry in heterogeneous media
6.5. Production of dihydrogen by radiolysis of water in a confined medium
6.6. Understanding transient phenomena
6.7. Conclusion: what about the effects of radiolytic species on materials?
6.8. References
7 Concrete and Cement Materials under Irradiation
7.1. Introduction
7.2. Radiation shielding concrete
7.3. Waste conditioning matrices
7.4. Conclusion
7.5. References
8 Organic Materials
8.1. Introduction
8.2. Technological context
8.3. Radiation exposure
8.4. Irradiated polymers: phenomenology
8.5. Radiolysis in anoxic polymers: fundamental effects
8.6. The radio-oxidation of polymers
8.7. Conclusion and perspectives
8.8. References
9 Irradiation Tools
9.1. Why experiment with accelerators?
9.2. Irradiation conditions in nuclear energy
9.3. Tools for simulation
9.4. Some major irradiation research centers
9.5. Conclusion
9.6. References
10 Characterization of Irradiation Damage
10.1. Introduction
10.2. Characterization of point defects
10.3. Characterization of the global disorder and elastic strain
10.4. Imaging of extended defects and cavities
10.5. Elemental analysis
10.6. In situ microstructural characterization of materials subjected to irradiation
10.7. Conclusion and perspectives
10.8. References
List of Authors
Index
End User License Agreement
List of Tables
Chapter 1
Table 1.1. Total elastic cross-section, mean free path between two collisions ...
Table 1.2. Some examples of displacement threshold energy in eV, for metals (L...
Table 1.3. Radiolytic yield G for some defects
Chapter 2
Table 2.1. Main components of generation II and III nuclear reactors subjected...
Chapter 3
Table 3.1. Inventory and concentration of fission products and plutonium in ir...
Chapter 4
Table 4.1. Major users of nuclear graphite in the world (extracted from IAEA (...
Table 4.2. Carbon displacement threshold in a graphitized material for an inci...
Table 4.3. Comparison between the values of the mesh parameters (a and c) (Gos...
Table 4.4. Summary of recent theoretical data on the formation and migration o...
Chapter 5
Table 5.1. Nature of the decay/radiation affecting the glass and the associate...
Table 5.2. Schematic view of the main parameters considered in a decoupled way...
Chapter 7
Table 7.1. Primary yields (molecules/100 eV) used to simulate α
radiolysis (LE
...
Chapter 9
Table 9.1. Particles that can damage materials in the nuclear power industry
Table 9.2. List of major reactors that allow testing of materials under irradi...
Table 9.3. Non-exhaustive list of centers of research on irradiated materials
List of Illustrations
Chapter 1
Figure 1.1. Neutron spectrum of a PWR reactor (IAEA/CRP DPA data, 2019). The d...
Figure 1.2. Stopping power of iron for different ions. The nuclear stopping po...
Figure 1.3. Range in iron of a proton beam for four energies. The bell-shaped ...
Figure 1.4. Evolution of the energy distribution of a neutron beam with an ini...
Figure 1.5. Some examples of defects: a) Frenkel pair: vacancy and interstitia...
Figure 1.6. A displacement cascade created by a 10 keV primary in iron from a ...
Figure 1.7. Damage efficiency (ratio of measured to calculated number of Frenk...
Figure 1.8. On the left is the evolution of the amorphized volume fraction as ...
Figure 1.9. Structure of a self-trapping exciton (left) and the F–H pair (righ...
Figure 1.10. Evolution of the trans-vinylene concentration as a function of th...
Figure 1.11. (a) Distribution of ionizations around the trajectory of a 160 Me...
Figure 1.12. Evolution of the damage efficiency in iron (ratio of the experime...
Figure 1.13. TEM images of silicon cavities and precipitates in aluminum irrad...
Figure 1.14. Kinetics of lead precipitate formation induced by electron irradi...
Figure 1.15. The microstructures that can appear under irradiation in an immis...
Chapter 2
Figure 2.1. Main metallic alloys used in pressurized water reactors (EDF figur...
Figure 2.2. Illustration of the fuel assembly (EDF figure).
Figure 2.3. Neutron irradiation growth at 320°C (BOR60 reactor) of different r...
Figure 2.4. Effect of temperature on the creep of hardened zircaloy-2, compari...
Figure 2.5. Effect of a power ramp on the fuel pellet diameter and its stress ...
Figure 2.6. Growth versus fluence of zirconium single crystals (figure adapted...
Figure 2.7. On the left is a diagram of a pressurized water reactor and on the...
Figure 2.8. Temperature and flux dependence (expressed here in dpa/s) of the i...
Figure 2.9. Concentration profiles plotted across a grain boundary in a sample...
Figure 2.10. Evolution of the Cr concentration at the grain boundaries as a fu...
Figure 2.11. The main processes that may be involved in irradiation-induced st...
Figure 2.12. Example of a crack at the head-to-shank connection of a bolt of a...
Figure 2.13. Tenacity of pressurized water reactor vessel steel as a function ...
Figure 2.14. The effect of irradiation on the resilience and the increase of t...
Figure 2.15. Cu-, Ni-, Mn-, Si-, P-rich solute clusters in a French steel 16MN...
Figure 2.16. Cross-section of a simplified Cu–Mn–Ni ternary phase diagram show...
Figure 2.17. Three-dimensional reconstruction of a 3° low angle grain boundary...
Figure 2.18. From Nishiyama et al. (2008): (a) level of phosphorus segregation...
Chapter 3
Figure 3.1. From left to right: fuel assembly with control rod; diagram of a f...
Figure 3.2. Crystallographic structure of boron carbide in its form (B11Cp)CBC...
Figure 3.3. Evolution of the thermal conductivity of boron carbide (Tf1=2,720 ...
Figure 3.4. Illustration of the volatility of fission products released (onlin...
Figure 3.5. Transmission electron microscopy (TEM) image recorded on a UO2 cry...
Figure 3.6. Partial pressure and speciation of major gases (excluding He and X...
Figure 3.7. Microstructure evolution of UO2 irradiated with 265 keV La ions at...
Figure 3.8. Scanning electron microscopy observations of the polygonization ph...
Figure 3.9. Porous structure at the periphery of an irradiated UO2 fuel with a...
Figure 3.10. Displacement cross-sections in boron carbide as a function of neu...
Figure 3.11. Experimental Raman spectrum of B4C compared to a theoretical spec...
Figure 3.12. Raman spectra performed after different irradiation conditions (6...
Figure 3.13. Comparison of microstructures of non-doped and chromium oxide-dop...
Chapter 4
Figure 4.1. Nuclear graphite structure – comparison with a single crystal stru...
Figure 4.2. (a) Optical microscopy (reflection mode) of a non-irradiated graph...
Figure 4.3. Schematic cross-section of a UNGG reactor of the “integrated vesse...
Figure 4.4. Irradiation-induced structural defects in graphite as a function o...
Figure 4.5. Bi-vacancies between two planes. On the left, the slightly more en...
Figure 4.6. Evolution of the differential enthalpy of an irradiated graphite (...
Figure 4.7. TEM images of graphite irradiated with 13C ions at 15°C (a, photo ...
Chapter 5
Figure 5.1. Main chemical elements contained in a typical nuclear glass. Facto...
Figure 5.2. (a) Principle of fission products (FP) incorporation in the glass ...
Figure 5.3. Dose (top) and dose rate (bottom) evolutions of a typical R7T7 gla...
Figure 5.4. Evolution of the glass package under disposal conditions as a func...
Figure 5.5. Schematic view of the model making it possible to explain the impa...
Figure 5.6. Phenomenology of glass alteration over time (in liquid water). The...
Figure 5.7. Schematic view of the alteration profile at the glass/water interf...
Figure 5.8. Evolution of the initial alteration rate of R7T7 glass (R0), measu...
Figure 5.9. TEM images of leached 239Pu-doped glass grains. Phyllosilicates ar...
Figure 5.10. (a) Raman spectra of simplified composition glass irradiated with...
Chapter 6
Figure 6.1. Time/distance equivalence diagram for the different steps of the ...
Figure 6.2. Main porous materials of interest
Figure 6.3. Radiolytic yields of dihydrogen production as a function of the fr...
Figure 6.4. Comparison of the radiolytic yields obtained for borosilicate glas...
Figure 6.5. Benzoate hydroxylation mechanisms. The value of the rate constant ...
Figure 6.6. Evolution of hydroxyl radical production relative to free water in...
Figure 6.7. Evolution of the hydrated electron concentration in different syst...
Figure 6.8. Injection of electrons from the solid matrix to the confined liqui...
Chapter 7
Figure 7.1. Relative compressive strength of different concretes as a function...
Figure 7.2. Pore size distribution (mercury porosimetry) in a Portland cement ...
Figure 7.3. Density variation of alpha quartz and silica glass under neutron i...
Figure 7.4. Two empirical radiation-induced volumetric expansion (RIVE) models...
Figure 7.5. Radiolytic H2 production by cement pastes (pure Ca3SiO5) in a clos...
Figure 7.6. Radiolytic H2 recycle rate (R) for CEM I and CEM III cement pastes...
Figure 7.7. Radiolytic H2 degassing rate for a cemented waste package as a fun...
Chapter 8
Figure 8.1. Different classes of polymers used in the nuclear industry. Taken ...
Figure 8.2. Electronic stopping power as a function of the incident ion path i...
Figure 8.3. Irradiation resistance of different thermoplastic polymers. Green:...
Figure 8.4. Dose evolution of the different groups produced in polyethylene, b...
Figure 8.5. Basic diagram of the radio-oxidation of a polymer. A model hydroca...
Figure 8.6. Dioxygen consumption radiochemical yield G(–O2) as a function of o...
Figure 8.7. Spatial distribution of POO
•
macroradicals, in a stationary...
Chapter 9
Figure 9.1. Fraction of the displacements W(T) created by primaries of energy ...
Figure 9.2. The blue arrows symbolize the path of the alphas, and the red arro...
Figure 9.3. Energy distribution of Compton electrons emitted by the 661 keV ga...
Figure 9.4. C19 shielded cells of the “High Activity Waste” unit of the ATALAN...
Figure 9.5. Representation of the particles encountered in nuclear energy usin...
Figure 9.6. 400 keV Bi ion irradiation/implantation in a glass with a flux of ...
Figure 9.7. On the left is the operating principle of a Cockroft–Walton machin...
Figure 9.8. Distribution by country of electrostatic accelerators according to...
Figure 9.9. The left side of the photo shows an irradiation chamber installed ...
Chapter 10
Figure 10.1. Schematic diagram of the two main positron annihilation spectrosc...
Figure 10.2. Raman spectra of UO2, non-irradiated (bottom) and irradiated (top...
Figure 10.3. Raman spectra of 6H-SiC, irradiated with 20 MeV Au ions at a flue...
Figure 10.4. “Line” images of Raman spectra of 6H-SiC, irradiated with 20 MeV ...
Figure 10.5. (a) RBS spectra obtained with He ions of 1.6 MeV, recorded in ran...
Figure 10.6. X-ray scattered intensity distribution along the direction normal...
Figure 10.7. Conventional TEM images of austenitic stainless steel, irradiated...
Figure 10.8. Cr and Mn/Ni/Si-enriched precipitates, induced in HT9 ferritic-ma...
Figure 10.9. Comparison of the irradiation of two interfaces UO2/argon and UO2...
Guide
Cover Page
Table of Contents
Title Page
Copyright Page
Preface
Begin Reading
List of Authors
Index
WILEY END USER LICENSE AGREEMENT
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SCIENCES
Energy, Field Directors – Alain Dollet, Pascal Brault
Nuclear Energy, Subject Head – Sylvain David
Nuclear Materials under Irradiation
Coordinated by
Serge BouffardNathalie Moncoffre
First published 2023 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.
Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address:
ISTE Ltd27-37 St George’s RoadLondon SW19 4EUUK
www.iste.co.uk
John Wiley & Sons, Inc.111 River StreetHoboken, NJ 07030USA
www.wiley.com
© ISTE Ltd 2023The rights of Serge Bouffard and Nathalie Moncoffre to be identified as the authors of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988.
Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s), contributor(s) or editor(s) and do not necessarily reflect the views of ISTE Group.
Library of Congress Control Number: 2023938464
British Library Cataloguing-in-Publication DataA CIP record for this book is available from the British LibraryISBN 978-1-78945-148-1
ERC code:PE2 Fundamental Constituents of Matter PE2_3 Nuclear physicsPE4 Physical and Analytical Chemical Sciences PE4_14 Radiation and Nuclear chemistry
Preface
Serge BOUFFARD1and Nathalie MONCOFFRE2
1 CIMAP, CEA – CNRS – ENSICAEN, Université Caen Normandie, France
2 Institut de Physique des 2 Infinis de Lyon, Université Claude Bernard Lyon 1, CNRS/IN2P3, Villeurbanne, France
The nuclear power industry is based on the major discoveries of the early 20th century: the discovery of natural and then artificial radioactivity, the neutron and lastly the fission of uranium. America’s mobilization for the atomic weapon during World War II allowed the first nuclear reactor to be built very quickly. Thus, between 1942 and the end of the war, the Chicago pile 1 was followed by seven others. Their goal was to produce the plutonium that was necessary for the atomic bomb. Even though material considerations were not the focus of attention for these graphite-gas reactors of modular design, the effects of irradiation on materials were beginning to be known. Consequently, as early as 1942, Eugene Paul Wigner warned of the defects created in graphite and the energy stored in it.
However, it was with the first nuclear power reactors that research on irradiation damage really took off. Although the basic phenomena are now relatively well known, their complexity in industrial materials means that research is still active. Moreover, the increase in the life span of reactors requires a better understanding of the aging mechanisms of materials. Even though it is only slightly discussed in this book, the future 4th generation reactors, especially fusion reactors, will impose much harder irradiation and operating temperature constraints, and therefore specific research. All this research takes full advantage of the advanced techniques of material studies, which are increasingly efficient, making it possible to finely probe the material, giving access to a more accurate vision of the structure of materials and their defects.
The objective of this book is to provide the basis for research on nuclear materials subjected to irradiation, with a view to contextualizing them in the industrial environment. The reader will find chapters on nuclear reactor materials (vessel and internal steels, fuel cladding alloys, neutron absorbers and, of course, nuclear fuel). A chapter is devoted to graphite, which played an important role in the first generation of reactors. The management of nuclear waste and the safety of long-term storage and disposal are essential points, so it is important that there is a chapter on storage glasses. Two types of materials are found both on the reactor side and in the management of waste: concrete and organic materials. These material chapters are completed by four others on the basic notions of defects, radiolysis, and irradiation and characterization tools.
We thank the CNRS – IN2P3, and in particular Sylvain David, for offering to coordinate this book, which only exists thanks to the work of all the co-authors and their expertise recognized in the academic or industrial world. We would also like to thank Emmanuel Balanzat, Nicolas Bérerd, Pascal Bouniol, Christine Delafoy, Christophe Domain, Muriel Ferry, Frederico Garrido, Aurélie Gentils, Stéphanie Jublot-Leclerc, Sophie Le Caër, Philippe Pareige, Laurent Petit, Yves Pipon, Jean-Philippe Renault, David Siméone, Patrick Simon and Magaly Tribet for accepting this additional work.
1Irradiation Defects
Serge BOUFFARD1and David SIMÉONE2
1 CIMAP, CEA – CNRS – ENSICAEN, Université Caen Normandie, France
2 CEA/Paris-Saclay, Service de Recherches Métallurgiques Appliquées, Gif-sur-Yvette, France
1.1. Introduction
The creation of defects is at the origin of the history of irradiation aging of nuclear materials. Subjected to bombardment by charged particles (electrons, ions) or neutral particles (photons, neutrons), the atoms of solids can be displaced from their equilibrium sites. The concentrations of displaced atoms and vacancies created depend, of course, on the nature of the particles, their energy, the flux and the fluence. These concentrations are, in all cases, much higher than those existing at the thermodynamic equilibrium. This is why the behavior of solids under irradiation escapes the thermodynamic description, which is nevertheless widely used by engineers to describe the microstructure (phase morphology, etc.) and properties (elastic constants, etc.) of materials. After this phase of defect production, a series of steps will follow during which the defects will migrate, and interact with each other and with impurities and native defects (dislocations, cavities, macles, grain boundaries, etc.). These different steps are, in essence, material-dependent and much more complicated to describe in a general way. Indeed, the recombination kinetics of defects created under irradiation depend on the nature of the interatomic bonds, the crystal structure, the cohesion energy, etc. The study of the microstructure induced by irradiation is therefore part of the thermodynamics of so-called forced systems, developed by the Prigogine school in the 1980s (Walgraef 1996). The continuous injection of defects acts as an external “force”, preventing the material from relaxing towards its thermodynamic equilibrium. The microstructure induced by the irradiation depends on the conditions of this irradiation (the particle, its energy, the rate of production of the defects, the temperature, etc.) and on the initial state of the material (purity, density of dislocation and clusters, grain size, etc.). The new microstructure that is thus produced under irradiation will modify the properties of use, typically by degrading them. Outside the nuclear sphere, there are many cases in which the impact of irradiation can be positive. Some examples are given at the end of section 1.2.3.
This chapter is not intended to be a detailed course on the mechanisms of defect creation, nor on the different kinetics occurring in materials under irradiation, but it will give readers the elements to understand the following chapters on different materials.
1.2. Some basic data
Neutrons or any other fast particle lose their kinetic energy in matter during elastic or inelastic collisions. Elastic collisions imply the conservation of kinetic energy and the momentum of the projectile–target set. Collisions are said to be inelastic (conservation of the momentum, but not of the kinetic energy) when there is a change in the internal energy of the projectile and/or the target. The excited particle de-excites through the emission of X photons if the electronic system has been excited or gamma photons if it is the nucleus, or by a profound rearrangement of the nucleus with the emission of ions of high kinetic energy (recoil nucleus, alpha) or radiation β. All these conditions of irradiation are found in the nuclear power industry. This chapter gives a brief overview of the different elementary mechanisms of defect production induced by elastic and inelastic collisions. For more details on these mechanisms, as well as on the transport of particles in materials, see, for example, Agullo-Lopez et al. (1988), Balanzat and Bouffard (1993), Was (2017) and Ortiz et al. (2020).
1.2.1. Radiative environments and nuclear materials
In the nuclear industry, materials undergo irradiation from four major sources of irradiation: 1) the reactor core, which imposes the most severe conditions, 2) fuel extracted from the core that has reached its maximum burnup rate, 3) recycled fuel containing plutonium and uranium from reprocessing (MOX) and 4) nuclear waste packages, mainly those of high activity. These sources emit practically all types of particles: fast neutrons (1–2 MeV), fast heavy ions (fission fragments), low-energy heavy ions (recoil of the nucleus when an alpha is emitted), light ions (alphas of a few MeV), and, of course, gammas and betas that are emitted by actinides and fission products.
The reactor core: in operation, the core of a 1,300 MWe reactor has a nominal thermal power of 3,817 MWth, of which 6.5% comes from the decay of fission products. Each fission of 235U releases an average of 202.8 MeV. The core of a 1,300 MWe reactor is thus the site of 1.1 1020 fissions per second, generating the emission of 2.8 1020 neutrons/second. The energy spectrum of the neutrons depends on their production rate, their capture cross-sections and their thermalization rate. The shape of the spectrum is schematically represented in Figure 1.1. Fast neutrons whose kinetic energy is greater than 0.1 MeV are responsible for the creation of defects. The flux of these neutrons is in the range of 1018 m-2.s-1.
Figure 1.1.Neutron spectrum of a PWR reactor (IAEA/CRP DPA data, 2019). The damage of materials is due to the fast part of this spectrum.
Neutrons are the cause of damage to all the materials in the reactor vessel (internal structures, fuel, cladding, control rods, etc.) and to the vessel itself, but they are not the only particles. They are accompanied by a large flux of gammas, whose main action is to participate in the heating and, indirectly, to produce some defects by the emission of high energy electrons by Compton scattering. Within the fuel, the fission fragments are an important source of irradiation by fast heavy ions (a light fragment A = ∼95, ∼98 MeV and a heavy fragment A = ∼138, ∼68 MeV). They are also, with the alphas, the source of gas bubble creation at the origin of fuel swelling.
Spent fuel: when a 1,300 MWe PWR reactor is shut down, the residual power as a result of the activity of the fission fragments is equal to 265 MW, or about 7% of the thermal power of the reactor (23 MW after one day and 1.5 MW after one year). After one year of cooling, a fuel assembly1 has a power of about 8 kW. After four years of cooling, an assembly of UOX enriched to 3.5% in 235U and having reached a burn-up rate2 of 33 GWjt-1 has an activity of 24,000 TBq, of which 32% comes from actinides, 67% from fission fragments and less than 1% from the activation of metallic elements (Guillaumont 2004). This significant flux of particles requires radiation protection and transport precautions, the legal limit being fixed at 5.3 kW per container, but this radiative environment does not really pose an irradiation problem for the materials.
MOX fuel: the process of recycling spent fuel leads to the fabrication of mixed UO2–PuO2 fuel. Given that the majority of 239Pu has a lifetime of 24,110 years, much shorter than that of 235U (7.04 108 years), the plutonium oxide grains are relatively intense sources of alpha irradiation: 2.3 109 α/gPu/s. However, with an isotropic emission, a non-negligible part of the alpha energy is deposited in the PuO2 grains. Nevertheless, this activity must be taken into account in the MOX manufacturing process: aging of the transfer tubes of the oxide powder and of the various organic additives added, before the sintering operation.
Waste packages: the different categories of nuclear waste do not present the same problems of irradiation. Indeed, the vast majority of waste is low and intermediate-level short-lived waste (LILW-SL) and very low-level waste (VLLW), which do not present any problem of aging of materials under irradiation. In contrast, high-level waste (HLW) integrated into a glassy matrix is subjected to intense irradiation with a dose rate of 20 kGy/hour at one year and a cumulative dose of 10–20 GGy at 10,000 years (see Chapter 5 of this book). Intermediate-level long-lived waste (ILW-LL) may contain organic materials. For these materials, the focus is on the emission of dihydrogen and molecules that can corrode the container under irradiation (see Chapter 8 of this book).
1.2.2. Some notions about the transport of particles in matter
1.2.2.1. Ion transport
Even though the vast majority of researchers use the SRIM software (Stopping and Range of Ions in Matter) to calculate the ion range, stopping powers and number of displacements (Ziegler and Biersack 1985), it is worthwhile to recall some data on ion transport in matter. First of all, let us give some reminders about SRIM. The values for the nuclear stopping power come from an analytical model based on the Firsov potential (see equation [1.1]) (Wilson et al. 1977)
with ;
Z1, m1 are the atomic number and mass of the projectile (Z2, m2 for the target).
Figure 1.2.Stopping power of iron for different ions. The nuclear stopping powers are shown using dashed lines, and the electronic stopping powers are shown using solid lines, according to the SRIM software. The electronic stopping powers of argon are shown using light green lines, according to the formulas of Lindhard and Bethe.
As for the electronic stopping power, it comes from adjustments on the experimental data, energy domain and atomic number class3. Indeed, there is no theory or model to calculate the electronic stopping power in the whole energy range. We find a perturbative calculation by Bethe (1930), which only applies in the high energy range4, as shown in Figure 1.2. It can be extended to low energies by considering that the charge of the ion decreases with its energy, Z1 is replaced by a , an effective charge
with me being the mass of the electron, v1 being the speed of the projectile, N being the number of target atoms per unit volume, and I being the mean ionization energy (I ≈10Z2).
The electronic stopping power is, at low energy, proportional to the speed of the ion. There are several models based on different interaction potentials (Firsov 1959; Lindhard and Scharff 1961). The loss of energy by electronic excitation dominates at high energy, but it will not necessarily be the dominant mechanism for the creation of defects. Indeed, the yield of this process can be zero.
For all these calculations, the ions are assumed to be at their equilibrium charge, but near the surface, this is not always verified. This is particularly the case for experiments with multi-charged slow ions. Indeed, when a highly charged slow ion (e.g. Ar18+) approaches a surface, it locally captures a large number of electrons, thus changing the stability of the material (Haranger et al. 2006; Aumayr et al. 2011).
With knowledge of the stopping powers, it is possible to calculate the ranges:
This calculation gives the mean length of the trajectories of the ions (R). However, it is the depth of penetration of the ions, known as the projected range (Rp), that is the quantity of interest for the irradiations. Figure 1.3 shows the difference between R and Rp. The projected range and the range distribution can be calculated analytically in the case where the electronic excitations are negligible (Winterbon et al. 1970); otherwise, it can be calculated more generally using Monte Carlo-type simulations.
The mechanisms of energy transfer are described in great detail and clarity in Peter Sigmund’s books (Sigmund 2006, 2014).
Figure 1.3.Range in iron of a proton beam for four energies. The bell-shaped curves represent the statistics of the ranges projected on the direction of incidence (Rp), and the vertical green lines represent the ranges along the trajectories (R).
1.2.2.2. Electron transport
The main differences for the transport of electrons come from their speed and mass. Indeed, from a few hundred keV, they must be considered as relativistic and be treated as such: relativistic formulas, introduction of the Bremsstrahlung effect and Cherenkov emission. As a result of their low mass, they will undergo much larger angular deflections during elastic collisions, with a high probability of being backscattered. The difference between R and Rp is maximal.
1.2.2.3. Neutron transport
During inelastic collisions, part of the kinetic energy of the neutrons is converted into excitation of the nucleus, which will de-excite by emitting a gamma or another particle. The neutrons can also be captured to give a heavier isotope, usually following the reaction AX (n,γ) A+1X. From the irradiation perspective, these capture processes are the source terms for the introduction of impurities and gases. However, the main interaction of neutrons with the target atoms remains the elastic collisions. To a first approximation, the interaction potential can be approximated by a hard sphere potential, thus with an equiprobability of transferring energy between 0 and Tmax, undergoing an angular deflection between 0 and 180°. Figure 1.4 shows the evolution of the energy of a neutron beam with an initial energy of 1 MeV as a function of the number of collisions with carbon atoms, calculated with a hard sphere potential. In a reactor core, neutrons are found at all stages of thermalization. Additionally, a particularity of neutron irradiation is that materials are always irradiated by a spectrum of neutrons, as shown in Figure 1.1.
Figure 1.4.Evolution of the energy distribution of a neutron beam with an initial energy of 1 MeV as a function of the number of collisions (from 1 to 15) in graphite. The average energy (vertical lines) decreases as E((m-1)/(m+1))n.
1.2.2.4. Available software
There are a large number of codes to describe the transport of charged particles in matter. These codes are all based on the solution of the linear Boltzmann equation. This equation is either solved numerically (DART code) or via Monte Carlo-type simulations. Although the most widely distributed code in the community is SRIM, there are generally a few codes developed to simulate particle physics experiments and for radiation protection purposes.
– PENELOPE (Penetration and ENErgy LOss of Positrons and Electrons) is a Monte Carlo code for the simulation of electron and photon transport in materials in the energy range of 50 eV to 1 GeV. The code is based on data from first principles calculations, semi-empirical models and databases. PENELOPE tracks particles in complex geometries limited by quadratic surfaces (Baro et al. 1995). PENELOPE is distributed by the OECD-Nuclear Energy Agency at http://www.oecd-nea.org/lists/penelope.html.
– MCNP (Monte Carlo N-Particle transport) can be used for the transport of neutrons (<20 MeV), ions, photons and electrons from 1 keV to 1 GeV in a three-dimensional geometry (Forster and Godfrey 1985). MCNP is distributed by the Los Alamos National Laboratory at https://mcnp.lanl.gov/.
– DART makes it possible to estimate the rate of production of vacancies, interstitials and anti-site defects produced by a beam of neutrons, ions and electrons in the material. The main interest of this code is to use different libraries of neutron-isotope cross-sections, in order to calculate the damage production rates induced by all nuclear reactions for a given material (Lunéville et al. 2006). DART is distributed by the OECD-Nuclear Energy Agency at http://www.oecd-nea.org/tools/abstract/detail/nea-1885.
– GEANT4 is a collaborative software that simulates the transport of particles in matter (Geant4 collaboration 2003). Initially dedicated to high-energy physics, it has been extended to low-energy physics, in particular for applications in particle therapy. The software is a bit too heavy to use for simple calculations of the path and dose distribution. GEANT4 is distributed by CERN at https://geant4.web.cern.ch/.
1.2.3. The zoology of irradiation defects
Obtaining a defect-free material is practically impossible, regardless of the method of production. There are several reasons for deviations from a perfect crystallographic structure, such as the presence of impurities, inhomogeneities and temperature fluctuations in the growth furnaces, thermal cycles or mechanical stresses applied to the material, and irradiation by cosmic and telluric radiation. Figure 1.5 gives some examples of defects. Defects can be classified according to their dimensionality: point defects or dimension 0 such as the vacancy, the interstitial or a foreign atom, dimension 1 involving dislocations, dimension 2 such as macles, stacking faults, grain boundaries, etc., dimension 3 such as pores, bubbles and precipitates, etc. Most of these defects exist at thermodynamic equilibrium in solids. It is, for example, possible to estimate the concentration of vacancies as a function of temperature and at constant pressure in a metal using the following formula: . The latter is obtained by minimizing the Gibbs energy (k being the Boltzmann constant, Sf and Hf being the entropy and entropy of formation, respectively). Thus, in a metal like gold at a temperature equal to nine-tenths of the melting temperature, the equilibrium concentration of vacancies is equal to 10-5. The mechanical stress of a material can also cause defects such as dislocations. However, under irradiation, a wider range of topological defects is generated for those existing at thermodynamic equilibrium, in atomic fractions of higher orders of magnitude.
Figure 1.5.Some examples of defects: a) Frenkel pair: vacancy and interstitial on the same sublattice, b) Schottky defect: an anionic vacancy associated with a cationic vacancy, c) an anti-site defect and an impurity in substitution, d) dislocation vacancy loop and e) macle.
Moreover, in metallic materials, the defects formed are electrically neutral and the concentrations of vacancies and interstitials can therefore be different. On the other hand, in semi-conductors and insulators, electrical neutrality must be ensured locally, so that the formation of a single vacancy will be accompanied by a local redistribution of electrical charges. Depending on its environment, this vacancy may have a different charge, which is likely to modify its properties.
If the term “defect” with a negative connotation is used, it is in reference to a perfect crystalline order that is repeating itself in all directions to infinity (at least to the limits of the crystal). In reality, disorder governs many properties and improves a number of them:
– Electrical properties: the entire operation of microelectronics is based on the doping of silicon. The introduction of very small quantities of electron donor elements (P, As, Sb, etc.) or receivers (B, Ga, In, etc.) radically changes the electrical conductivity, as well as the transport mechanism, by electrons or by holes.
– Optical properties: alumina α-Al2O3 , which is transparent when pure and monocrystalline, becomes a precious stone with the addition of impurities. It becomes a red ruby with about 1% of chromium, and a blue sapphire for titanium and iron. An equally important occurrence is the rare earth doping of crystals (YAG, LiYF4, Y2O3, CaF2, etc.) to obtain laser sources and optical amplifiers.
– Mechanical properties: the dislocation sliding is at the origin of the plasticity of metals, but their trapping by other defects induces hardening and embrittlement.
– Superconducting properties: the pinning of vortices by fast ion traces in type II superconductors makes it possible to increase the critical current.
– Magnetic properties: in ferromagnetic materials, the Bloch walls can be trapped by defects, thus increasing the coercive field.
Defects therefore play an important role in the properties of materials. Irradiations create a non-equilibrium situation by increasing the defect concentration, which accelerates the evolution of material properties.
1.3. Defect creation mechanisms
The creation of defects by irradiation is the result of the interaction of particles with the material. We can distinguish three types of particles that will interact with the constituents of the material: photons, neutrons and charged particles. Photons, UV, X-rays and γ are scattered or absorbed by the electronic system of the target, creating electron–hole pairs, which, in certain materials, can be the source of a radiation chemistry. Neutrons will only interact with the nucleus of the atoms of the material. Depending on their energy and the nature of the nucleus, the collision can be elastic (transfer of kinetic energy to the nucleus) or inelastic (with internal excitation of the nucleus, or even a nuclear reaction). In both cases, defects will be created. As for the charged particles, the ions and electrons, they interact with the ions and electrons of the target. The slowing down of the ions is thus composed of a succession of inelastic collisions of low energy transfer and elastic collisions with the nuclei, shielded by a certain number of electrons. In general, we can consider that the ions undergo a continuous slowing down by electronic excitation between two elastic collisions, which will induce an angular deviation. The two types of energy loss are therefore considered as independent. In reality, a collision with a nucleus can only disrupt the electron cloud. In the case of electrons, the situation is identical, except that their angular deviation will be much more significant as a result of their small mass.
The different processes we have just mentioned are characterized by their interaction probability and their total and differential sections in angles or energy.
Table 1.1.Total elastic cross-section, mean free path between two collisions and mean energy transferred to a target atom for three 1 MeV particles in aluminum
Neutrons
Protons
Electrons
Total elastic cross-section
∼10
-28
m
2
∼10
-22
m
2
∼10
-24
m
2
Mean free path between two collisions
16 cm
160 nm
1.6 μm
Mean energy transferred
68 keV
220 eV
40 eV
The total cross-sections in Table 1.1 give an indication of the mean distance between two elastic collisions. During one of these collisions, a target nucleus may receive enough energy to be displaced from its equilibrium position, creating a vacancy, before stabilizing in an interstitial position, in a normally unoccupied site. The vacancy-interstitial pair is called the Frenkel pair. If the atom is ejected with enough energy, it becomes a projectile that can create a succession of collisions leading to a localized energy deposit in a volume of a few tens of nanometers. These energy deposits, which occur randomly within the material, are called collision cascades. The electronic excitations produced during this localized energy deposition are transformed into heat in metallic materials, but can also lead to the formation of charged defects in insulators and semi-conductors.
Once the defects are created, they evolve according to complex processes that are similar to the thermally produced defects. Indeed, many of the defects formed are mechanically or chemically unstable and evolve spontaneously towards more stable configurations, which can lead to phase transitions and drastic changes in the properties of the materials. The strongly non-homogeneous nature of the energy deposit reflects the essence of difficulty in modeling and simulating (e.g. via a heat flux, a pressure wave or doping) the mechanisms of creation of defects induced by the irradiation and, a fortiori, the long-term evolution of materials and their properties under irradiation.
1.3.1. Creation of defects by elastic collisions
The creation of defects by elastic collision is a universal process that exists regardless of the structure and properties of the material. On the other hand, it is not always the dominant process of defect creation. For a defect to be created during an elastic collision, there must be a sufficient amount of energy transferred in order to extract the atom from its site and send it out of the spontaneous recombination volume, thus forming a Frenkel pair. This reflects the existence of a minimal energy that the target atom must receive for a defect to be created, the threshold energy of displacement. In reality, this threshold energy depends on the emission direction, so there is a displacement threshold distribution. The mapping of the displacement threshold energy has only been measured for a few metals, such as copper (King et al. 1981), but we will see that an average value is largely sufficient. Table 1.2 presents some values of displacement threshold energy.
Table 1.2.Some examples of displacement threshold energy in eV, for metals (Lucasson and Walker 1962), UO2 (Soullard 1985) and SiC (Lefèvre et al. 2009)
Cu
Ni
Fe
Ag
Ti
Al
Mo
UO
2
SiC
22
24
24
28
29
32
37
40 (U)20 (O)
25 (Si)
We consider that, for a transmitted energy T, the number of displacements is equal to n(T) = 0 si T < Ts and n(T) = 1 si T ≥ Ts, with Ts being the threshold displacement energy. If the transmitted energy is large in front of Ts, the ejected atom, known as PKA for primary knock-on atom, in turn becomes a projectile (see Figure 1.6). The number of displacements n(T) thus increases with the transferred energy, n(T) = T/2Ts if we consider that all energy is converted into displacement (Kinchin and Pease 1955) or, more realistically, if we consider that when T ≥ 2,5 Ts, a fraction of the PKA’s energy is lost through electronic excitation: , where is the damage energy, in other words, the energy of the primary minus the energy lost through electronic excitation by the primary (Norgett et al. 1975).
The number of displacements per atom produced by a particle flux5 φ(t) of energy E is given by:
where represents the probability of creating an energy primary T. This probability depends on the interaction potential between the two particles (hard sphere, Coulombian, shielded sphere, etc.).
Figure 1.6.A displacement cascade created by a 10 keV primary in iron from a SRIM simulation (Ziegler and Biersack 1985). The symbols indicate the location of a vacancy creation, and the solid symbols mark the path of the primary ion.
It is important to keep in mind that the number of dpa (displacements per atom) and the number of defects are two different quantities. The dpa number represents the number of atoms that have been ejected from their site. As an atom can be displaced several times, the dpa number can be greater than 1. For example, the internal structures of reactor vessels nominally undergo damage in the range of 60 dpa in 60 years and, obviously, the number of defects cannot be greater than the number of sites, with the number even being much lower as a result of the recombinations between defects (with a recombination volume of 1.5 nm radius, the maximum concentration is about 4 10-3). Furthermore, the number of defects is difficult to calculate because it depends on many parameters: the particle through the size of the collision cascades, the fluence reached, the temperature, the material through its structure, the migration energy of the defects and the presence of traps for the defects (surface, grain boundaries, dislocations, etc.).
Figure 1.7.Damage efficiency (ratio of measured to calculated number of Frenkel pairs) as a function of the number of displacements created by an ion in copper (solid dots) and silver (white dots), from Averback et al. (1978).
On pure metals, some experiments at low temperature and low dose have shown that the fraction of non-recombined Frenkel pairs in the collision cascade decreases when the number of dpa increases6 (see Figure 1.7). This possibility, in the case of metals and metal alloys, to relate the number of non-recombined Frenkel pairs to the number of displacements, regardless of the fact that this relationship is neither universal nor simple, is the reason why dpa has become the reference for quantifying elastic collision damage, despite its obvious limitations. The dpa is only an estimate of the quantity of atoms set in motion in a material during an irradiation. It does not make it possible to calculate the number of defects present over the long term (a few picoseconds) in the irradiated material. Through its simplicity of calculation and its universal nature, it is an estimate characterizing the damage produced under different conditions (irradiations in reactor and with ion beams, for example). This is also the reason why the exact value of the energy displacement threshold does not matter; the fact that the community agrees on a standard value is sufficient. Even so, there are proposals to improve the representativeness of dpa (Nordlund et al. 2018).
The existence of a recombination volume imposes a limit on the concentration of point defects, and the probability of creating a vacancy or interstitial outside a recombination volume decreases as the defect concentration increases. In addition, thermal or athermal diffusion of defects increases their probability of encountering a trap in the form of a point or extended defect (Sizmann 1978).
1.3.2. Amorphization
Under irradiation, many crystalline materials of nuclear interest amorphize. This amorphization induces deep modifications of their intrinsic properties such as self-diffusion coefficients, their mechanical properties (elastic constants, etc.). The amorphization of a material has a well-defined meaning in solid state physics and is, strictly speaking, translated by the disappearance of long-range order, in other words, Bragg peaks in diffraction and the disappearance of scattering peaks in infra-red and Raman spectroscopy. It should be noted that geologists use the term metamict to designate amorphized minerals (Ewing 1994).
Amorphization under irradiation has been observed in practically all classes of materials, except pure metals and some ceramics with a mean fluorine-like structure such as UO2 and MgO. In the case of electron irradiations that only produce point defects, amorphization is usually associated with the accumulation of local deformations induced by point defects. It is, for example, the case for quartz irradiated by electrons (Pascucci et al. 1983). On the other hand, during irradiations by ions, the damage has a heterogeneous aspect due to the presence of collision cascades. In a very qualitative way, it is possible to describe this heterogeneous amorphization via an empirical approach developed by Gibbons (1972). The amorphized volume fraction is related to the fluence through a formulation called k-impact. The material becomes amorphous in zones where k impacts overlap (see Figure 1.8):
In order to explain the existence of a critical amorphization temperature that has been observed experimentally in pyrochlores, more elaborate empirical models involving annealing of amorphous zones during the development of collision cascades have been proposed (Weber 2000).
However, all these models are phenomenological and cannot predict the amorphization of a material under irradiation. At best, they are used to classify materials by characterizing them via an “effective amorphization cross-section” derived from experiments.
The basic mechanisms of amorphization remain largely uncomprehended, partly because of the difficulty in quantifying the amorphous nature of a material. The development of total scattering diffraction measurements should allow a better quantification of the amorphous state (Meldrum et al. 1998; Egami and Billinge 2012). On the theoretical side, a few attempts were made to relate the amorphization of materials to the connectedness of polyhedra in ceramics. This geometrical approach aims to explain the difficulty in amorphizing simple crystalline structures such as fluorines (Hobbs 1995). The main challenge in understanding irradiation-induced amorphization is essentially due to the difficulty of explaining the formation of an amorphous state, which is a major issue in materials physics.
Figure 1.8.On the left is the evolution of the amorphized volume fraction as a function of fluence for direct impact (k = 1 in the Gibbons formula) and double impact (k = 2) kinetics from the Gibbons formula, and on the right, the evolution of the amorphization dose as a function of temperature.
1.3.3. Creation of defects by electronic excitation
The observation of the effects of electronic excitations on the color of certain materials was reported long before the origin was described. For example, in the 18th century, Schulze (1727) showed that the change in color of chalk that was soaked with a solution of silver in nitric acid, and exposed to sunlight, was due to the presence of silver. This is the basis of the photographic process. In the following century, Goldstein (1894) studied the origin of the coloring of sodium chloride subjected to cathode radiation. Establishing a link between phosphorescence and coloration, he introduced the hypothesis of atomic displacement. However, it was not until the 1930s that electronic excitations were associated with the creation of defects.
The structural modifications induced by electronic excitation result from more complex processes than those described for elastic collisions. In particular, their efficiency is very material-dependent, zero for metals, and maximal for organic matter. For an atomic displacement to occur, the energy absorbed by the electronic system must be transferred with high efficiency to the atomic lattice by a material-dependent mechanism. This mechanism is only described in detail in alkali halides. Therefore, it seemed interesting to devote a section to the creation of defects by electronic excitation in these materials, even if they are not found in nuclear materials.
Whatever the incident particle, the story begins with the creation of an electron–hole pair. In these materials, electrons and holes are strongly coupled to the lattice, resulting in strong atomic relaxation in their presence. In alkali halides, this relaxation of the atomic lattice, which is not very mobile, leads to a self-trapping of the hole on a pair of anions . This configuration, known as the VK center, can trap an electron to form a metastable species: a self-trapped exciton (STE). The de-excitation of the STE can be achieved in three ways: luminescences7 π and σ or the creation of a F + H pair (see Figure 1.9), in other words, a Frenkel pair composed of an anionic vacancy that has trapped an electron (F center) and of a hole trapped on an anionic interstitial (H center). The yield of defect creation thus depends on the relative weight of these pathways. In some class I alkali halides, there is an anti-correlation in temperature between luminescence π and the creation of the F center. Luminescence dominates at low temperature and F-center creation at ordinary temperature. The F–H pair would result from a thermally activated conversion of the self-trapped exciton, following a potential surface of lower excitation. The yield will also depend on the distance at which the two elements of the pair are created. The transport of the interstitial away from its vacancy is achieved by a sequence of replacement collisions along the <110> row of halogen ions. The efficiency of these collision sequences depends on geometric considerations: the diameter of the halogen atom D and the distance S between two halogens in the <110> direction. When S and D are very different, many close pairs are created; they will disappear during correlated recombinations in a few tens to hundreds of picoseconds. At 4 K, the energy to create an F center varies according to the ionic crystal from 103 to 107 eV, with a maximum efficiency for S/D between 0.5 and 1.5, in other words, approximately 1 (Townsend 1973). Noriaki Itoh has published many articles on this mechanism; the reference (Itoh and Tanimura 1990) is a good introduction.
Figure 1.9.Structure of a self-trapping exciton (left) and the F–H pair (right) in an alkali halide. Themolecule can be shared on both halogen sites (on-center) or be localized on one site (off-center). In the latter case, the exciton prefigures the F–H pair.
This example shows that both experimental and theoretical approaches have allowed us to understand the mechanisms of defect creation in these ionic crystals, but do not allow us to calculate a quantity comparable to the dpa of elastic collisions. The defect creation yield must therefore be determined experimentally. In order to consider defect creation by electronic excitation, it is necessary but not sufficient that four conditions are met:
the excitation must be localized on a limited number of sites;
its energy must be of the order of the threshold energy of displacement in the direction of displacement;
its life time must be of the order of the characteristic times of atomic vibrations;
there must be a non-radiative de-excitation pathway.
Metals do not meet the first three conditions, so they are considered insensitive to electronic excitations. For semi-conductors and insulators, electrons ejected to a high level of the conduction band relax to the bottom of the band. The energy available for the creation of a defect is then of the order of magnitude of the width of the band gap. Electronic excitations can therefore only create defects in large gap insulators.
The defect concentration depends on the amount of energy absorbed by the material per unit mass, in the form of electronic excitation and ionization. The coefficient that links the two quantities is called radiolytic yield. In the international system, it is expressed in moles per joule (mol/J). The legal unit of absorbed energy (dose) is the Gray [Gy], which is equal to 1 J/kg8.
Table 1.3.Radiolytic yield G for some defects
Materials
Silica 77K E’ center
KBr 4K F center
Polystyrene cross-linking
Polyethylene creation H2
G 10
-7
mol/J
∼0.001
0.02
0.02
3.3
Therefore, when this yield has been measured, the structural change can be expressed in defect concentration, unlike the calculation of the number of displacements produced by elastic collision, which does not allow us to calculate the number of stabilized defects. The defect concentration is related to the particle fluence by the following relation:
However, it is important to remember that only those species for which the signal was used to determine the efficiency are counted. Here, we speak of creation yield of F center, of cross-linking, etc. A defect which does not have an optical or magnetic signature could therefore not be taken into account. Given that only insulators are sensitive to electronic excitations, optical methods (infrared or UV–visible spectroscopies, etc.) are the preferred tools to follow the evolution of these materials under irradiation. In this case, it is necessary to know the molar absorption coefficients in order to access the absolute values of concentrations.
Moreover, as shown in Figure 1.10, the evolution of the defect concentration shows saturation at high doses. The yield therefore evolves continuously with the dose. The tabulated yields are generally the initial yields, at zero dose. There are also temporal variations of the yield. Indeed, time-resolved optical absorption experiments make it possible to measure the temporal evolution of the yield of transient species. In the case of radiolysis of water, 20 ps after excitation, the radiolytic yield of the solvated electron is equal to 4.2 10-7 mol/J., and after 200 ns, it is only 2.8 10-7 mol/J. In the long term, the solvated electrons all recombine and the yield tends to zero.
Figure 1.10.Evolution of the trans-vinylene concentration as a function of the irradiation dose for polyethylene irradiated with 1 MeV electrons. The radiolytic yield is the derivative of the evolution of the defect concentration. The curves correspond to 1st-order kinetics. The experimental points are taken from Ventura et al. (2016).
The density of electronic excitations is also a quantity that modifies the yields, as well as the mechanisms of the creation of defects, by electronic excitation.
1.3.3.1. Specificities of high electron excitation densities
These high electronic excitation densities are created in the wake of fast ions. In nuclear energy, fission fragments fall into this category, as well as alphas for the most sensitive materials. Although fission fragments were discovered in 1930, their effects on matter were not really studied until the late 1950s. Through different approaches, chemical attack (Young 1958) or electron microscopy in mica (Silk and Barnes 1959) and in UO2 (Noggle and Stiegler 1960), these studies showed that the defects were rod-shaped objects, which they called tracks. Among all these works, those of Fleischer et al. (1965b) and Price and Walker (1962) played a significant role in the understanding and, in particular, the use of tracks. From their first publications, they proposed to use them in geological dating, or as particle detectors or filters for biological applications.
Figure 1.11.(a) Distribution of ionizations around the trajectory of a 160 MeV Kr ion in UO2 and (b) distribution of the dose as a function of the distance to the ion trajectory. For the Monte Carlo simulation, see Gervais and Bouffard (1994).
What do we know now about these heavy ion tracks? First of all, they are the result of very high stopping powers by electronic excitation of swift heavy ions9. Monte Carlo simulations of the transport of these ions and of the electron cascades make it possible to realize the impressive ionization density around the ion trajectory (see Figure 1.11). Within a radius of 1 nm around the trajectory of a 160 MeV krypton ion, 30% of the electrons are ejected. After the passage of the ion over a radius of 1 to 2 nm, all the atoms of the material are ionized, or even multi-ionized. As the electrons have been ejected with very little kinetic energy on average, many of them will be available for recombination after thermalization. Expressed in terms of energy deposited at the track core, the dose exceeds a hundred MGray.
