Đang tải... (xem toàn văn)
Comprehensive nuclear materials 1 07 radiation damage using ion beams Comprehensive nuclear materials 1 07 radiation damage using ion beams Comprehensive nuclear materials 1 07 radiation damage using ion beams Comprehensive nuclear materials 1 07 radiation damage using ion beams Comprehensive nuclear materials 1 07 radiation damage using ion beams Comprehensive nuclear materials 1 07 radiation damage using ion beams Comprehensive nuclear materials 1 07 radiation damage using ion beams Comprehensive nuclear materials 1 07 radiation damage using ion beams
1.07 Radiation Damage Using Ion Beams G S Was University of Michigan, Ann Arbor, MI, USA R S Averback University of Illinois at Urbana-Champagne, Urbana, IL, USA ß 2012 Elsevier Ltd All rights reserved 1.07.1 1.07.2 1.07.3 1.07.3.1 1.07.3.2 1.07.3.3 1.07.3.4 1.07.4 1.07.4.1 1.07.4.1.1 1.07.4.1.2 1.07.4.2 1.07.4.2.1 1.07.4.2.2 1.07.4.2.3 1.07.4.2.4 1.07.4.2.5 1.07.4.2.6 1.07.4.3 1.07.5 1.07.5.1 1.07.5.2 1.07.5.3 1.07.6 References Introduction Motivation for Using Ion Beams to Study Radiation Damage Review of Aspects of Radiation Damage Relevant to Ion Irradiation Defect Production Primary and Weighted Recoil Spectra Damage Morphology Damage Rate Effects Contributions of Ion Irradiation to an Understanding of Radiation Effects Electron Irradiations Displacement threshold surfaces Point defect properties Ion Irradiations The damage function Freely migrating defects Alloy stability under ion irradiation Mechanical properties Multiple ion beams Swift ions Comparison with Neutrons Advantages and Disadvantages of Irradiations using Various Particle Types Electrons Heavy Ions Light Ions Practical Considerations for Radiation Damage Using Ion Beams Abbreviations AES APT bcc BWR dpa fcc FMD FP IASCC IGSCC LWR MD NRT Auger electron spectroscopy Atom probe tomography Body-centered cubic Boiling water reactor Displacements per atom Face-centered cubic Freely migrating defect Frenkel pair Irradiation assisted stress corrosion cracking Intergranular stress corrosion cracking Light water reactor Molecular dynamics Norgett–Robinson–Torrens NWC PKA RCS RIS SCC STEM/EDS TEM 195 196 197 197 199 200 202 204 204 204 205 206 206 207 207 209 209 209 211 215 216 217 219 219 221 Normal water chemistry Primary knock-on atom Recoil collision sequence Radiation induced segregation Stress corrosion cracking Scanning transmission electron microscopy/energy dispersive spectrometry Transmission electron microscopy 1.07.1 Introduction Radiation effects research has been conducted using a variety of energetic particles: neutrons, electrons, protons, He ions, and heavy ions Energetic ions 195 196 Radiation Damage Using Ion Beams can be used to understand the effects of neutron irradiation on reactor components, and interest in this application of ion irradiation has grown in recent years for several reasons including the avoidance of high residual radioactivity and the decline of neutron sources for materials irradiation The damage state and microstructure resulting from ion irradiation, and thus the degree to which ion irradiation emulates neutron irradiation, depend upon the particle type and the damage rate This chapter will begin with a summary of the motivation for using ion irradiation for radiation damage studies, followed by a brief review of radiation damage relevant to charged particles The contribution of ion irradiation to our understanding of radiation damage will be presented next, followed by an account of the advantages and disadvantages of the various ion types for conducting radiation damage studies, and wrapping up with a consideration of practical issues in ion irradiation experiments 1.07.2 Motivation for Using Ion Beams to Study Radiation Damage In the 1960s and 1970s, heavy ion irradiation was developed for the study of radiation damage processes in materials As ion irradiation can be conducted at a well-defined energy, dose rate, and temperature, it results in very well-controlled experiments that are difficult to match in reactors As such, interest grew in the use of ion irradiation for the purpose of simulating neutron damage in support of the breeder reactor program.1–3 Ion irradiation and simultaneous He injection were also used to simulate the effects of 14 MeV neutron damage in conjunction with the fusion reactor engineering program The application of ion irradiation (defined here as irradiation by any charged particle, including electrons) to the study of neutron irradiation damage caught the interest of the light water reactor community to address issues such as swelling, creep, and irradiation assisted stress corrosion cracking of core structural materials.4–6 Ion irradiation was also being used to understand the irradiated microstructure of reactor pressure vessel steels, Zircaloy fuel cladding, and materials for advanced reactor concepts There is significant incentive to use ion irradiation to study neutron damage as this technique has the potential for yielding answers on basic processes in addition to the potential for enormous savings in time and money Neutron irradiation experiments are not amenable to studies involving a wide range of conditions, which is precisely what is required for investigations of the basic damage processes Simulation by ions allows easy variation of the irradiation parameters such as dose, dose rate, and temperature over a wide range of values One of the prime attractions of ion irradiation is the rapid accumulation of end of life doses in short periods of time Typical neutron irradiation experiments in thermal test reactors may accumulate damage at a rate of 3–5 dpa yearÀ1 In fast reactors, the rates can be higher, on the order of 20 dpa yearÀ1 For low dose components such as structural components in boiling water reactor (BWR) cores that typically have an end-of-life damage of 10 dpa, these rates are acceptable However, even the higher dose rate of a fast reactor would require 4–5 years to reach the peak dose of $80 dpa in the core baffle in a pressurized water reactor (PWR) For advanced, fast reactor concepts in which core components are expected to receive 200 dpa, the time for irradiation in a test reactor becomes impractical In addition to the time spent ‘in-core,’ there is an investment in capsule design and preparation as well as disassembly and allowing for radioactive decay, adding additional years to an irradiation program Analysis of microchemical and microstructural changes by atom probe tomography (APT), Auger electron spectroscopy (AES) or microstructural changes by energy dispersive spectroscopy via scanning transmission electron microscopy (STEM-EDS) and mechanical property or stress corrosion cracking (SCC) evaluation can take several additional years because of the precautions, special facilities, and instrumentation required for handling radioactive samples The result is that a single cycle from irradiation through microanalysis and mechanical property/SCC testing may require over a decade Such a long cycle length does not permit for iteration of irradiation or material conditions that is critical in any experimental research program The long cycle time required for design and irradiation also reduces flexibility in altering irradiation programs as new data become available The requirement of special facilities, special sample handling, and long irradiation time make the cost for neutron irradiation experiments very high In contrast to neutron irradiation, ion (heavy, light, or electrons) irradiation enjoys considerable advantages in both cycle length and cost Ion irradiations of any type rarely require more than several tens of hours to reach damage levels in the 1–100 dpa range Ion irradiation produces little or no residual radioactivity, allowing handling of samples without Radiation Damage Using Ion Beams the need for special precautions These features translate into significantly reduced cycle length and cost The challenge then is to verify the equivalency between neutron and ion irradiation in terms of the changes to the microstructure and properties of the material The key question that needs to be answered is how results from neutron and charged particle irradiation experiments compare? How, for example, is one to compare the results of a component irradiated in-core at 288 C to a fluence of  1021 n cmÀ2 (E > MeV) over a period of one year, with an ion irradiation experiment using MeV protons at 400 C to dpa (displacements per atom) at a dose rate of 105 dpa s1 ($1 day), or MeV Ni2ỵ at 500 C to 10 dpa at a dose rate of  10À3 dpa sÀ1 ($1 h)? The first question to resolve is the measure of radiation effect In the Irradiation assisted stress corrosion cracking (IASCC) problem in LWRs, concern has centered on two effects of irradiation: radiation-induced segregation of major alloying elements or impurities to grain boundaries, which may cause embrittlement or enhance the intergranular stress corrosion cracking (IGSCC) process, and hardening of the matrix that results in localized deformation and embrittlement The appropriate measure of the radiation effect in the former case would then be the alloy concentration at the grain boundary or the amount of impurity segregated to the grain boundary This quantity is measurable by analytical techniques such as AES, APT, or STEM-EDS For the latter case, the measure of the radiation effect would be the nature, size, density, and distribution of dislocation loops, black dots, and the total dislocation network, and how they impact the deformation of the alloy Hence, specific and measurable effects of irradiation can be determined for both neutron and ion irradiation experiments The next concern is determining how ion irradiation translates into the environment describing neutron irradiation That is, what are the irradiation conditions required for ion irradiation to yield the same measure of radiation effect as that for neutron irradiation? This is the key question, for in a postirradiation test program, it is only the final state of the material that determines equivalence, not the path taken Therefore, if ion irradiation experiments could be devised that yielded the same measures of irradiation effects as observed in neutron irradiation experiments, the data obtained in postirradiation experiments will be equivalent In such a case, ion irradiation experiments can provide a direct substitute for neutron irradiation While neutron irradiation will always be required to qualify materials for reactor 197 application, ion irradiation provides a low-cost and rapid means of elucidating mechanisms and screening materials for the most important variables A final challenge is the volume of material that can be irradiated with each type of radiation Neutrons have mean free paths on the order of centimeters in structural materials One MeV electrons penetrate about 500 mm, MeV protons penetrate about 10 mm, and MeV Ni ions have a range of less than mm Thus, the volume of material that can be irradiated with ions from standard laboratory-sized sources (TEMs, accelerators), is limited 1.07.3 Review of Aspects of Radiation Damage Relevant to Ion Irradiation 1.07.3.1 Defect Production The parameter commonly used to correlate the damage produced by different irradiation environments is the total number of displacements per atom (dpa) Kinchin and Pease7 were the first to attempt to determine the number of displacements occurring during irradiation and a modified version of their model known as the Norgett–Robinson–Torrens (NRT) model8 is generally accepted as the international standard for quantifying the number of atomic displacements in irradiated materials.9 According to the NRT model, the number of Frenkel pairs (FPs), nNRT(T ), generated by a primary knock-on atom (PKA) of energy T is given by nNRT T ị ẳ kED T ị 2Ed ½1 where ED(T ) is the damage energy (energy of the PKA less the energy lost to electron excitation), Ed is the displacement energy, that is, the energy needed to displace the struck atom from its lattice position, and k is a factor less than (usually taken as 0.8) Integration of the NRT damage function over recoil spectrum and time gives the atom concentration of displacements known as the NRT displacements per atom (dpa): ẵ2 dpa ẳ fEịvNRT ðT ÞsðE; T ÞdT dE where f(E) is the neutron flux and s(E,T ) is the probability that a particle of energy E will impart a recoil energy T to a struck atom The displacement damage is accepted as a measure of the amount of change to the solid due to irradiation and is a much better measure of an irradiation effect than is the particle fluence As shown in Figure 1, seemingly different effects of 198 Radiation Damage Using Ion Beams 300 LASREF, 40 ЊC RTNS-II, 90 ЊC OWR, 90 ЊC 250 Yield stress change (MPa) Yield stress change (MPa) 300 200 150 100 50 1017 1018 1019 LASREF, 40 ЊC RTNS-II, 90 ЊC OWR, 90 ЊC 250 200 150 100 50 1020 10−3 Neutron fluence, E > 0.1 MeV 10−2 DPA Figure Comparison of yield stress change in 316 stainless steel irradiated in three facilities with very different neutron energy flux spectra While there is little correlation in terms of neutron fluence, the yield stress changes correlate well against displacements per atom (dpa) Reprinted, with permission, from ASTM, copyright ASTM International, 100 Barr Harbor Drive, West Conshohocken, PA 19428 7.5 MeV tantalum 10−15 1012 MeV nickel 1010 Protons ITER be first wall HFIR target FFTF mid-core PWR 1/4-T RPV 108 106 104 −9 10 10−7 10−5 10−1 10−3 Particle energy (MeV) 10 Figure Energy spectrum for neutrons from a variety of reactor types and a monoenergetic proton beam Reproduced from Stoller, R E.; Greenwood, L R J Nucl Mater 1999, 271–272, 57–62 Calculated dpa/(incident particle) (cm2) Neutron flux/lethergy (n cm−2 s−1) proton flux (ions cm−2 s−1) 10−14 1014 10−16 20 MeV carbon 10−17 1.3 MeV hydrogen 10−18 10−19 14 MeV neutrons −20 MeV neutrons 10 irradiation on low temperature yield strength for the same fluence level (Figure 1(a)) and disappear when dpa is used as the measure of damage (Figure 1(b)) A fundamental difference between ion and neutron irradiation effects is the particle energy spectrum that arises because of the difference in the way the particles are produced Ions are produced in accelerators and emerge in monoenergetic beams with very narrow energy widths However, the neutron energy spectrum in a reactor extends over several orders of magnitude in energy, thus presenting a much more complicated source term for radiation damage Figure shows the considerable difference in neutron and ion energy spectra and also between neutron spectra in different reactors and at different locations within the reactor vessel 10−21 Distance into solid (m) 10 12 Figure Displacement–damage effectiveness for various energetic particles in nickel Reproduced from Kulcinski, G L.; Brimhall, J L.; Kissinger, H E In Proceedings of Radiation-Induced Voids in Metals; Corbett, J W., Ianiello, L C., Eds.; USAEC Technical Information Center: Oak Ridge, TN, 1972; p 453, CONF-710601 Another major difference in the characteristics of ions and neutrons is their depth of penetration As shown in Figure 3, ions lose energy quickly because of high electronic energy loss, giving rise to a spatially nonuniform energy deposition profile caused Radiation Damage Using Ion Beams where Rd is the number if displacements per unit volume per unit time, N is the atom number density, and f is the particle flux (neutron or ion) In the case of neutron–nuclear interaction described by the hardsphere model, eqn [3] becomes Rd gE ss ẳ ẵ4 Nf 4Ed where g ẳ 4mM/(m ỵ M)2, M is the target atom mass, m is the neutron mass, E is the neutron energy, and ss is the elastic scattering cross-section For the case of ion– atom interaction described by Rutherford scattering, eqn [3] becomes Rd pZ2 Z2 e4 M1 gE ẳ ln ; ẵ5 NI 4EEd M2 Ed where e is the unit charge, M1 is the mass of the ion, and M2 is the mass of the target atom As shown in Figure 3, for comparable energies, 1.3 MeV protons cause over 100 times more damage per unit of fluence at the sample surface than MeV neutrons, and the factor for 20 MeV C ions is over 1000 Of course, the damage depth is orders of magnitude smaller than that for neutron irradiation 1.07.3.2 Primary and Weighted Recoil Spectra A description of irradiation damage must also consider the distribution of recoils in energy and space The primary recoil spectrum describes the relative number of collisions in which the amount of energy between T and T þ dT is transferred from the primary recoil atom to other target atoms The fraction of recoils between the displacement energy Ed, and T is ð T sðE; T ịdT ẵ6 PE; T ị ẳ N Ed where N is the total number of primary recoils and s(E,T ) is the differential cross-section for a particle of energy E to create a recoil of energy T The recoil fraction is shown in Figure 4, which reveals only a small difference between ions of very different masses Figure shows the difference in the types of damage that are produced by different types of 1.0 0.8 Fraction of recoils by the varying importance of electronic and nuclear energy loss during the slowing down process Their penetration distances range between 0.1 and 100 mm for ion energies that can practically be achieved by laboratory-scale accelerators or implanters By virtue of their electrical neutrality, neutrons can penetrate very large distances and produce spatially flat damage profiles over many millimeters of material Further, the cross-section for ion–atom reaction is much greater than for neutron–nuclear reaction giving rise to a higher damage rate per unit of particle fluence The damage rate in dpa per unit of fluence is proportional to the integral of the energy transfer cross-section and the number of displacements per PKA, nNRT(T): gE Rd ẳ sE; T ịnNRT T ịdT ẵ3 Nf Ed 199 He H Kr Ar 0.6 Ne 0.4 Fraction of recoils with energy above Ed and below T 0.2 MeV ions ® Cu 101 102 103 104 T (eV) Figure Integral primary recoil spectra for MeV particles in copper Curves plotted are the integral fractions of primary recoils between the threshold energy and recoil energy, T from eqn [6] Reproduced from Averback, R S J Nucl Mater 1994, 216, 49 MeV electrons T = 60 eV e = 50−100% 106 E 105 104 MeV protons T = 200 eV e = 25% Ti 103 102 MeV heavy ions T = keV e = 4% Tn Ed Tp Te 101 E MeV neutrons T = 35 keV e = 2% Figure Difference in damage morphology, displacement efficiency, and average recoil energy for MeV particles of different types incident on nickel Reproduced from Was, G S.; Allen, T R Mater Char 1994, 32, 239 Radiation Damage Using Ion Beams particles Light ions such as electrons and protons will produce damage as isolated FPs or in small clusters while heavy ions and neutrons produce damage in large clusters For MeV particle irradiation of copper, half the recoils for protons are produced with energies less than $60 eV while the same number for Kr occurs at about 150 eV Recoils are weighted toward lower energies because of the screened Coulomb potential that controls the interactions of charged particles For an unscreened Coulomb interaction, the probability of creating a recoil of energy T varies as 1/T2 However, neutrons interact as hard spheres and the probability of creating a recoil of energy T is independent of recoil energy In fact, a more important parameter describing the distribution of damage over the energy range is a combination of the fraction of defects of a particular energy and the damage energy This is the weighted average recoil spectrum, W(E,T ), which weights the primary recoil spectrum by the number of defects or the damage energy produced in each recoil: ðT sE; T ịED T ịdT ẵ7 W E; T ị ẳ ED Eị Ed ED Eị ¼ ð T^ sðE; T ÞED ðT ÞdT ½8 Ed ^ is the maximum recoil energy given by where T ^ T ẳ gEi ẳ 4EiM1M2/(M1 ỵ M2)2 Ignoring electron excitations and allowing ED(T ) ¼ T, then the weighted average recoil spectra for Coulomb and hard sphere collisions are WCoul E; T ị ẳ lnT lnEd ^ À lnEd lnT ½9 T À Ed2 Ed2 ẵ10 WHS E; T ị ẳ Equations [9] and [10] are graphed in Figure for MeV particle irradiations of copper The characteristic energy, T1/2 is that recoil energy below which half of the recoils are produced The Coulomb forces extend to infinity and slowly increase as the particle approaches the target; hence the slow increase with energy In a hard sphere interaction, the particles and target not interact until their separation reaches the hard sphere radius at which point the repulsive force goes to infinity A screened Coulomb is most appropriate for heavy ion irradiation Note the large difference in W(E,T ) between the various types of irradiations at E ¼ MeV 1.0 Copper 0.8 Protons Ne 0.6 Kr W (T) 200 0.4 Neutrons 0.2 101 102 103 104 T (eV) 105 106 107 Figure Weighted recoil spectra for MeV particles in copper Curves representing protons and neutrons are calculated using eqns [9] and [10], respectively W(T ) for other particles were calculated using Lindhard cross-sections and include electronic excitation Reproduced from Averback, R S J Nucl Mater 1994, 216, 49 While heavy ions come closer to reproducing the energy distribution of recoils of neutrons than light ions, neither is accurate in the tails of the distribution This does not mean that ions are poor simulations of radiation damage, but it does mean that damage is produced differently and this difference will need to be considered when designing an irradiation program that is intended to produce microchemical and microstructural changes that match those from neutron irradiation There is, of course, more to the description of radiation damage than just the number of dpa There is the issue of the spatial distribution of damage production, which can influence the microchemistry and microstructure, particularly at temperatures where diffusion processes are important for microstructural development In fact, the ‘ballistically’ determined value of dpa calculated using such a displacement model is not the appropriate unit to be used for dose comparisons between particle types The reason is the difference in the primary damage state among different particle types 1.07.3.3 Damage Morphology The actual number of defects that survive the displacement cascade and their spatial distribution in solids will determine the effect on the irradiated microstructure Figure summarizes the effect of Radiation Damage Using Ion Beams 201 Total dpa Particle type and energy Loss to displacement cascades Freely migrating defects Mutual recombination outside of cascade Loss to sinks in matrix Loss at grain boundaries Void swelling loop structure Defect diffusion matrix chemistry Boundary structure and micro chemistry Radiation-induced segregation Figure History of point defects after creation in the displacement cascade damage morphology from the viewpoint of the grain boundary and how the defect flow affects radiationinduced grain boundary segregation Of the total defects produced by the energetic particle, a fraction appears as isolated, or freely migrating defects, and the balance is part of the cascade The fraction of the ‘ballistically’ produced FPs that survive the cascade quench and are available for long-range migration is an extremely important quantity and is called the migration efficiency, e These ‘freely migrating’ or ‘available migrating’ defects10 are the only defects that will affect the amount of grain boundary segregation, which is one measure of radiation effects The migration efficiency can be very small, approaching a few percent at high temperatures The migration efficiency, e, comprises three components: gi,v: the isolated point defect fraction, di,v: clustered fraction including mobile defect clusters such as di-interstitials, and z: fraction initially in isolated or clustered form after the cascade quench that is annihilated during subsequent short-term (>10À11 s) intracascade thermal diffusion They are related as follows: e ẳ di ỵ g i þ z i ¼ d v þ g v þ z v ½11 Figure shows the history of defects born as vacancies and interstitials as described by the NRT model Displacement cascade efficiency (x) Intracascade thermal recombination (z ) Surviving defect fraction (QDF) (x – z ) Isolated point defect fraction (IDF) (g i,v) Clustered point defect fraction (CDF) (d i,v) Mobile clusters Immobile clusters Evaporating defects Available defects (li,v) Figure Interdependence of isolated point defects, mobile defect clusters, and thermally evaporating defect clusters that contribute to the fraction of surviving defects that are ‘available’ for radiation effects Reproduced from Zinkle, S J.; Singh, B N J Nucl Mater 1993, 199, 173 Due to significant recombination in the cascade, only a fraction ($30%) is free to migrate from the displacement zone These defects can recombine outside of the cascade region, be absorbed at sinks in the 202 Radiation Damage Using Ion Beams matrix (voids, loops), or be absorbed at the grain boundaries, providing for the possibility of radiationinduced segregation The fraction of defects that will be annihilated after the cascade quench by recombination events among defect clusters and point defects within the same cascade (intracascade recombination), z, is about 0.07, for a migration efficiency of 0.3 (see below for additional detail).10 The clustered fraction, d includes large, sessile clusters and small defect clusters that may be mobile at a given irradiation temperature and will be different for vacancies and interstitials For a keV cascade, di is about 0.06 and dv is closer to 0.18.10 Some of these defects may be able to ‘evaporate’ or escape the cluster and become ‘available’ defects (Figure 8) This leaves g, the isolated point defect fraction that are available to migrate to sinks, to form clusters, to interact with existing clusters, and to participate in the defect flow to grain boundaries that gives rise to radiation-induced segregation Owing to their potential to so strongly influence the irradiated microstructure, defects in this category, along with defects freed from clusters, make up the freely migrating defect (FMD) fraction Recall that electrons and light ions produce a large fraction of their defects as isolated FPs, thus increasing the likelihood of their remaining as isolated rather than clustered defects Despite the equivalence in energy among the four particle types described in Figure 5, the average energy transferred and the defect production efficiencies vary by more than an order of magnitude This is explained by the differences in the cascade morphology among the different particle types Neutrons and heavy ions produce dense cascades that result in substantial recombination during the cooling or quenching phase However, electrons are just capable of producing a few widely spaced FPs that have a low probability of recombination Protons produce small widely spaced cascades and many isolated FPs due to the Coulomb interaction and therefore, fall between the extremes in displacement efficiency defined by electrons and neutrons The value of g has been estimated to range from 0.01 to 0.10 depending on PKA energy and irradiation temperature, with higher temperatures resulting in the lower values Naundorf12 estimated the freely migrating defect fraction using an analytical treatment based on two factors: (1) energy transfer to atoms is only sufficient to create a single FP, and (2) the FP lies outside a recombination (interaction) Table Efficiency for producing freely migrating defects, g, in nickel by different kinds of irradiations (Ed ¼ 40 eV, riv ¼ 0.7 nm) using Lindhard’s analytical differential collision cross-section Irradiation (%) MeV Hỵ MeV Hỵ MeV Liỵ 1.8 MeV Neỵ 300 keV Niỵ MeV Niỵ 3.5 MeV Krỵ keV Oỵ 24.0 19.2 16.9 8.7 2.3 3.8 3.0 9.8 Source: Naundorf, V J Nucl Mater 1991, 182, 254 radius so that the nearby FPs neither recombine nor cluster The model follows each generation of the collision and calculates the fraction of all defects produced that remain free Results of calculation using the Naundorf model are shown in Table for several ions of varying mass and energy Values of Z range between 24% for proton irradiation to 3% for heavy ion (krypton) irradiation Recent results,13 however, have shown that the low values of FMD efficiency for heavy ion or neutron irradiation cannot be explained by defect annihilation within the parent cascade (intracascade annihilation) In fact, cascade damage generates vacancy and interstitial clusters that act as annihilation sites for FMD, reducing the efficiency of FMD production Thus, the cascade remnants result in an increase in the sink strength for point defects and along with recombination in the original cascade, account for the low FMD efficiency measured by experiment 1.07.3.4 Damage Rate Effects As differences in dose rates can confound direct comparison between neutron and ion irradiations, it is important to assess their impact A simple method for examining the tradeoff between dose and temperature in comparing irradiation effects from different particle types is found in the invariance requirements For a given change in dose rate, we would like to know what change in dose (at the same temperature) is required to cause the same number of defects to be absorbed at sinks Alternatively, for a given change in dose rate, we would like to know what change in temperature (at the same dose) is required to cause the same number of defects to be absorbed at sinks The number of defects per unit volume, NR, that have recombined up to time t, is given by Mansur14 Radiation Damage Using Ion Beams ðt NR ¼ Riv Ci Cv dt ½12 where Riv is the vacancy–interstitial recombination coefficient and Ci and Cv are interstitial and vacancy concentrations, respectively Similarly, the number of defects per unit volume that are lost to sinks of type j, NSj, up to time t, is t NSj ẳ kSj Cj dt ẵ13 where kSj is the strength of sink j and Cj is the sink concentration The ratio of vacancy loss to interstitial loss is RS ẳ NSv NSi ẵ14 where j ¼ v or i The quantity NS is important in describing the microstructural development involving total point defect flux to sinks (e.g., RIS), while RS is the relevant quantity for the growth of defect aggregates such as voids that require partitioning of point defects to allow growth In the steady-state recombination dominant regime, for NS to be invariant at a fixed dose, the following relationship between ‘dose rate (Ki) and temperature (Ti)’ must hold: 2 kT1 K2 Evm ln K1 T2 À T1 ẳ ẵ15 K2 ln kT Evm K1 where Evm is the vacancy migration energy In the steady-state recombination dominant regime, for RS to be invariant at a fixed dose, the following relationship between ‘dose rate and temperature’ must hold: kT12 K2 Evm þ2Evf ln K1 ½16 T2 À T1 ẳ K2 ln EvmkT ỵ2Evf K1 where Evf is the vacancy formation energy In the steadystate recombination dominant regime, for NS to be invariant at a fixed temperature, the following relationship between ‘dose (F) and dose rate must hold: 1=2 F2 K2 ẳ ẵ17 F1 K1 Finally, in the steady-state recombination dominant regime, for NS to be invariant at a fixed dose rate, the following relationship between ‘dose and temperature’ must hold: À2kT12 ln F Evm F1 ẵ18 T2 T1 ẳ F2 ln À kT Evm F1 Figure shows plots of the relationship between the ratio of dose rates and the temperature difference required to maintain the same point defect absorption at sinks (a), and the swelling invariance (b) The invariance requirements can be used to prescribe an ion irradiation temperature–dose rate combination that simulates neutron radiation We take the example of irradiation of stainless steel under typical BWR core irradiation conditions of $4.5  10À8 dpa sÀ1 at 288 C If we were to conduct a proton irradiation with a characteristic dose rate of 7.0  10À6 dpa sÀ1, then using eqn [15] with a vacancy formation energy of 1.9 eV and a vacancy migration 50 700 40 500 Em ν = 0.5 400 300 200 1.0 1.5 100 (a) DTemperature (ЊC) DTemperature (ЊC) 600 203 10 100 Ratio of dose rates Eνm = 0.5 30 1.0 1.5 20 10 1000 (b) 10 100 Ratio of dose rates 1000 Figure Temperature shift from the reference 200 C required at constant dose in order to maintain (a) the same point defect absorption at sinks, and (b) swelling invariance, as a function of dose rate, normalized to initial dose rate Results are shown for three different vacancy migration energies and a vacancy formation energy of 1.5 eV Adapted from Mansur, L K J Nucl Mater 1993, 206, 306–323; Was, G S Radiation Materials Science: Metals and Alloys; Springer: Berlin, 2007 204 Radiation Damage Using Ion Beams energy of 1.3 eV, the experiment will be invariant in NS with the BWR core irradiation (e.g., RIS) at a proton irradiation temperature of 400 C Similarly, using eqn [16], a proton irradiation temperature of 300 C will result in an invariant RS (e.g., swelling or loop growth) For a Ni2ỵ ion irradiation at a dose rate of 10À3 dpa sÀ1, the respective temperatures are 675 C (NS invariant) and 340 C (RS invariant) In other words, the temperature ‘shift’ due to the higher dose rate is dependent on the microstructure feature of interest Also, with increasing difference in dose rate, the DT between neutron and ion irradiation increases substantially The nominal irradiation temperatures selected for proton irradiation, 360 C and for Ni2ỵ irradiation, 500 C represent compromises between the extremes for invariant NS and RS 1.07.4 Contributions of Ion Irradiation to an Understanding of Radiation Effects Ion irradiations have been critical to the development of both our fundamental and applied understanding of radiation effects As discussed in Sections 1.07.2 and 1.07.3, it is the flexibility of such irradiations and our firm understanding of atomic collisions in solids that afford them their utility Principally, ion irradiations have enabled focused studies on the isolated effects of primary recoil spectrum, defect displacement rate, and temperature In addition, they have provided access to the fundamental properties of point defects, defect creation, and defect reactions In this section, we highlight a few key experiments that illustrate the broad range of problems that can be addressed using ion irradiations We concentrate our discussion on past ion irradiations studies that have provided key information required by modelers in their attempts to predict materials behavior in existing and future nuclear reactor environments, and particularly information that is not readily available from neutron irradiations In addition, we include a few comparative studies between ion and neutron irradiations to illustrate, on one hand, Table the good agreement that is possible, while on the other, the extreme caution that is necessary in extrapolating results of ion irradiations to long-term predictions of materials evolution in a nuclear environment 1.07.4.1 Electron Irradiations The unique feature of electron irradiations in comparison to ions and neutrons is that they create defects in very low-energy recoil events As a consequence, nearly all FPs are produced in isolation This has been of foremost importance in developing our understanding of radiation damage, as it made studies of defect creation mechanisms as well as the fundamental properties of FPs possible Recall that the properties of vacancies andvacancy clusters, for example, formation and migration energies, stacking fault energies, etc., could be determined from quenching studies It is not possible, however, to quench in interstitials in metals Very little was therefore known about this intrinsic defect prior to about 1955 when irradiation experiments became widely employed In this section, we highlight some of the key findings derived from these past studies 1.07.4.1.1 Displacement threshold surfaces The creation of a stable FP requires that a lattice atom receives an energy greater than Tm, which is the minimum displacement energy This value has been determined experimentally in many materials by measuring the change in some physical property, such as electrical resistivity or length change, as a function of maximum recoil energy of a target atom Such experiments are practical only for electron irradiations for which recoil energies can be kept low, but with the irradiation particles still penetrating deeply into, or through, the specimen Typical values are shown in Table As a crystal is not homogeneous, the threshold energy depends on the crystallographic direction in which the knock-on atom recoils The anisotropy of the threshold energy surface has been mapped out in various crystals by measuring the production rate of defects as a function of both the electron energy, near threshold, and the orientation of single crystalline Minimum displacement energies in pure metals, semiconductors, and stainless steel (SS) Materials Al Cgraph Cu Fe Ge Mo Ni W Si SS Tm (eV) 16 25 19 17 15 33 23 41 13 18 Source: Lucasson, P In Fundamental Aspects of Radiation Damage in Metals; Robibnson, M T., Young, F W., Jr., Eds.; ERDA Report CONF-751006; 1975; p 42; Andersen, H H Appl Phys 1979, 18, 131 Radiation Damage Using Ion Beams 207 Cu H Experiment Calculation 0.8 He x Li 0.6 CN O 0.4 Ne Cu Kr Ar Fe Ag Bi 1.0 Relative efficiency 1 MeV H 0.8 0.6 MeV He 0.4 MeV Li FF 0.2 10 0.2 FN MD simulation 10 10 10 T, T1/2 (eV) Figure 13 Damage function efficiency factor of Cu (see eqn [20]) showing the decrease in efficiency versus cascade energy The experimental data (solid squares) represent efficiencies for different ion irradiations plotted versus the characteristic cascade energy for the irradiation, T1/2 (see text) The open triangles represent the efficiency versus cascade energy, T, obtained by molecular dynamics (MD) simulation The open circles represent the calculated efficiencies for the different irradiations using the MD efficiency function and eqn [2] Reproduced from Averback, R S.; de la Rubia, T D In Solid State Physics; Ehrenreich, H., Spaepen, F., Eds.; Academic Press: New York, 1998; pp 281–402 materials, however, the damage function remains poorly known 1.07.4.2.2 Freely migrating defects The damage function refers to the number of FPs created within the first several picoseconds of the primary recoil event At longer times, defects migrate from their nascent sites and interact with other defects and microstructural features As noted earlier, many radiation effects, such as radiation-enhanced diffusion, segregation, and void swelling, depend more strongly on the number of defects that escape their nascent cascades and migrate freely in the lattice before annihilating, trapping, or forming defect clusters The same general approach used to determine the damage function has been employed to determine the relative fraction of freely migrating defects, that is, e/nNRT, as illustrated by Figure 14 Here, the relative number of Si atoms segregating to the surface during irradiation, per dpa, is plotted versus a characteristic energy of the recoil spectrum, T1/2 It is seen that the fraction decreases rapidly with increasing recoil energy Similar experiments were performed using radiationenhanced diffusion, as described in Section 1.07.2 While ion irradiation has proved extremely useful in illustrating the spectral effects on freely migrating 102 MeV Ni 3.25 MeV Kr 103 104 105 T1/2 (eV) 106 107 Figure 14 Relative efficiencies for producing freely migrating defects plotted as a function of the characteristic recoil energy, T1/2 Reproduced from Rehn, L E.; Okamoto, P R.; Averback, R S Phys Rev 1984, B30, 3073 defects, extracting quantitative information about freely migrating defects from such experiments is difficult These measurements, unlike the damage function, require very high doses, and several dpa; the buildup of the sink structure must be adequately taken into account It is also difficult to estimate, for example, how many interstitials are required to transport one Si atom to the surface We mention in passing that experiments performed using ordering kinetics in order–disorder alloys have provided a more direct measure of the number of freely migrating defects (vacancies in this case), as these experiments require doses less than %10À7 dpa so that no damage build-up can occur.25 These experiments show similar effects of primary recoil spectrum on the fraction of freely migrating defects, although the fractions of such defects were found to be somewhat higher in these experiments, %5–10% These fractions are in good agreement with radiation-enhanced diffusion experiments using self-ions on Ni, when the effect of sink strength is taken into account.26 1.07.4.2.3 Alloy stability under ion irradiation Irradiation of materials with energetic particles drives them from equilibrium, and in alloys, this becomes manifest in a number of ways One of them concerns nonequilibrium segregation The creation of large supersaturations of point defects leads to persistent defect fluxes to sinks In many cases, these point defect fluxes couple with solutes, resulting in either the enrichment or depletion of solutes at these sinks This effect was first discovered by using in situ electron 208 Radiation Damage Using Ion Beams irradiations in a high voltage electron microscope,27 and it has been systematically investigated subsequently using ion irradiations,28 as the surface sink provides a convenient location to measure composition changes Unlike neutron irradiation, moreover, the damage created by ions is generally inhomogeneous, reaching a peak level at some depth in the sample As a consequence, point defect fluxes emanate from these regions An example of this effect is shown in Figure 15 where a Ni–12.7 at.% Si alloy was irradiated with protons As the alloy is supersaturated with Si prior to irradiation, Ni3Si precipitates Ni plating Peak damage region Ni3Si surface film Bombarded surface Figure 15 Behavior of silicon in a Ni–12.7 Si alloy following irradiation with protons Note the region depleted of Ni3Si precipitates at the peak damage location and just below the surface Courtesy of P R Okamoto form in the sample At the location of peak damage, the concentration of interstitials is the highest, and hence these defects flow outward from this region These interstitials form interstitial–solute complexes with Si, resulting in a Si flux out of this area as well, depleting the region of Si As a consequence, a region depleted of Ni3Si precipitates is observed at the peak damage depth Note too that the surface sink for interstitials leads to enrichment of Si, resulting in a surface layer of Ni3Si The region just below the surface accordingly becomes depleted of Si, leaving a zone depleted of Ni3Si precipitates While irradiation induced segregation can lead to nonequilibrium segregation and precipitation in single phase alloys, irradiation can also lead to dissolution of precipitates in nominally two-phase alloys An interesting example of this behavior concerns Ni–12 at.% Al alloys irradiated with 300 keV Ni ions.29 These alloys were first annealed at high temperatures to develop a two-phase structure of Ni3Al (g0 ) and Ni–10.5 at.% Al (g) The initial precipitate size, depending on the annealing time was 2.5 or 4.6 nm As shown in Figure 16, the precipitates disorder during irradiation at room temperature, owing to atomic mixing in cascades The rate of disordering depends on the size of the precipitates, being slowest for homogeneous Ni3Al sample and fastest in the alloy with the smallest precipitates The authors Ni3AI NiAI (r = 4.6 nm) NiAI (r = 2.5 nm) 0.8 0.6 0.4 0.2 Degree of LRO S/S0 Degree of LRO S/S0 1.0 1.0 Ni3AI NiAI (r = 4.6 nm) 0.5 0.0 0.0 0.0 0.00 0.05 0.10 0.15 0.20 0.25 0.30 (b) (a) Irradiation dose F (dpa) 550 ЊC 450 ЊC 2.0 4.0 Irradiation dose F (dpa) 6.0 0.8 f(r ) dpa 0.4 0.0 0.0 (c) dpa dpa 4.0 8.0 0.0 4.0 8.0 Radius (nm) 0.0 4.0 8.0 Figure 16 (a) Disordering rate Ni3Al precipitates in two-phase Ni–12 at.% Al alloys and homogeneous Ni3Al during 300 keV Ni bombardment at room temperature; (b) same as (a) but irradiation at 550 C; (c) size distribution of Ni3Al precipitates after irradiation to two doses After dpa, a steady state size is obtained Reproduced from Schmitz, G.; Ewert, J C.; Harbsmeier, F.; Uhrmacher, M.; Haider, F Phys Rev B 2001, 63, 224113 Radiation Damage Using Ion Beams suggest that the reason for this dependence on precipitate size is that atomic mixing reduces the concentration of Al in the precipitates, which thereby accelerates the disordering When the same irradiation is performed at higher temperatures, and radiation-enhanced diffusion takes place, the system does not completely disorder, but rather remains partially ordered, owing to a competition between disordering in the displacement cascades and reordering by radiation-enhanced diffusion Noteworthy, however, is the size of the precipitate, as shown in Figure 16(c), where it is observed that the precipitates initially shrink in size, but then reach a steady state radius Therefore, unlike in thermal aging, precipitates in irradiated alloys can reach a stable steady state size that is a function of irradiation intensity and temperature Similar behavior has been observed in two-phase immiscible alloys in which case a steady state size of precipitates is formed.30 This so-called ‘patterning’ phenomenon has been explained on the basis of a competition between disordering by atomic mixing in energetic collision events and reordering during thermally activated diffusion For patterning, however, it is required that the atomic relocation distances during collisional mixing are significantly larger than the nearest neighbor distance An interesting consequence of this requirement in regard to the present discussion of using ion irradiation to simulate neutron damage is that electron and proton irradiations, which not produce energetic cascades or long relocation distances, should not induce compositional patterning, but heavy ions and fast neutron irradiation, which produce cascades, will cause patterning Further details can be found in Enrique31 and Enrique et al.32 1.07.4.2.4 Mechanical properties Measurements of mechanical properties on irradiated materials usually require bulk samples and therefore neutron irradiation Ion beams, however, can be employed for some measurements, such as plastic deformation Typically, these experiments employ high energy protons, E > % MeV, or He ions, E > MeV, as these particles can penetrate through thin foils, such as Fe or steel, that are greater than 15 mm in thickness Moreover, displacement rates %10À5 dpa sÀ1 are obtainable without excessive beam heating.33 Deformation experiments have also been performed using GeV heavy ions, as these penetrate targets several microns in thickness The displacement rates, however, are low as most of the beam energy is lost through electronic excitations Heavy 209 ions with lower energies, E % 1–4 MeV, have also been used in deformation studies; for these, however, specimen must be very thin, %200 nm, and effects of the surface must be taken into account.34,35 1.07.4.2.5 Multiple ion beams One of the difficulties in using ion beams to simulate neutron irradiation damage is the potential for missing certain synergistic behaviors in the damage evolution For example, neutron irradiation leads to transmutation products and the generation of He and fission gases in addition to displacement damage Generation of gas is particularly relevant to 14 MeV neutron irradiation for which large amounts of He and H are produced Ion beams, however, offer the opportunity of using two or even three beams simultaneously and thus to tailor test irradiations to meet expected reactor conditions; see, for example, Serruys et al.36 This is often not possible in existing test reactor facilities, and the building of new test facilities for fusion machines has been formidably expensive The application of multiple ion beams is illustrated in Figure 17 in a study of void swelling in vanadium Here, the synergistic effects of simultaneously implanting 350 keV H and MeV He, while irradiating with 12 MeV Ni ions are shown Without the He beam, swelling is negligible, even with the implantation of H, but with it, the H greatly enhances the swelling H implantation, on the other hand, is seen to reduce the density of cavities 1.07.4.2.6 Swift ions An important contribution to the damage in nuclear fuels derives from fission fragments There are two groups of fission products: one group with atomic number near 42 (Mo) and energy %100 MeV and the other with atomic number near 56 (Ba) and energy %70 MeV The maximum electronic stopping powers of these energetic particles, %18 keV nmÀ1 for the heavier and 22 keV nmÀ1 for the lighter, are far greater than their respective nuclear stopping powers Similar to ion irradiation studies described above, where the primary recoil spectrum can be systematically varied, the masses and energies of ions can be varied to examine effects of electronic stopping power An example is shown in Figure 18 where the electronic stopping power is plotted as a function of energy (per nucleon) for different ion irradiations of UO2 The two boxes in the figure indicate stopping powers associated with the fission fragments and the heavy particle recoils of a emitters One of the questions addressed by such studies Radiation Damage Using Ion Beams Swelling (%) 20 10 20 20 10 Cavity density (1020 m−3) 210 20 15 10 20 15 10 pa )d pm (ap He pa )d pm (ap He 20 10 10 0 0 –1 –1 (a) 20 10 a–1 p d ) m p p H(a (b) 20 10 pa–1 d ) m p p (a H dE/dx (keV nm–1) 70 60 20 1.4 1.2 Heavy FP Light FP 1.0 0.8 10 0.6 238U 208Pb 0.4 50 U Fission 40 197Au 0.2 235 dE/dx (keV nm–1) Energy (MeVamu–1) Figure 17 Cavity volume fraction (a) and cavity density (b) in pure vanadium irradiated with 12 MeV Ni3ỵ ions to 30 dpa at 873 K with and without simultaneous irradiation of He and H Reproduced from Sekimura, N.; Iwai, T.; Arai, Y.; et al J Nucl Mater 2000, 283–287, 224–228 −8 −6 −4 −2 FPs range (μm) 0.0 129Xe 116Sn 30 GANIL HMI GSI TASCC 106Cd 100Mo 127I dE/dxFP 20 70Zn Recoils 10 Zn70Zn Efission 10−5 10−4 10−3 10−2 10−1 10 102 Energy (MeVamu–1) Figure 18 Plot of dE/dx as a function of the energy for a series of ions The circle indicates the conditions for 72 MeV ions of 127I The two large squares show dE/dx representative of fission products and for the heavy recoil atoms of a-decaying actinides The inset shows the energy loss and the remaining energy of typical light and heavy fission products along their range of %7 mm length Reproduced from Matzke, Hj.; Lucuta, P G.; Wiss, T Nucl Instrum Meth B 2000, 166–167, 920 Radiation Damage Using Ion Beams 1.07.4.3 Comparison with Neutrons Proton irradiation has undergone considerable refinement as a radiation damage tool Numerous experiments have been conducted and compared to equivalent neutron irradiation experiments in order to determine whether proton irradiations capture the effects of neutron irradiation on microstructure, microchemistry, and hardening In some cases, benchmarking exercises were conducted on the same native alloy heat as neutron irradiation in order to eliminate heat-to-heat variations that may obscure comparison of the effects of the two types of irradiating particles The following examples cover a number of irradiation effects on several alloys in an effort to demonstrate the capability of proton irradiation to capture the critical effects of neutron irradiation Figures 19–23 show direct comparisons of the same irradiation feature on the same alloy heats (commercial purity (CP) 304 and 316 stainless steels) following either neutron irradiation at 275 C or 24 CP-316 SS Protons at 360 ЊC to 1.0 dpa Neutrons at 275 ЊC to 1.1ϫ1021 n cm–2 (~1.5 dpa) 20 16 Cr Ni 12 Measured Si (wt%) Measured Cr or Ni (wt%) has been the formation of fission fragment tracks Tracks have not yet been observed in the bulk of UO2 due to fission; however, by using ion irradiation, the stopping powers could be increased The dashed line at 29 keV nmÀ1 in Figure 18 represents the threshold stopping power for track formation.37 This value is %30% greater than the maximum for fission fragments, thus helping to explain why fission fragment tracks are not seen in the bulk Such tracks are observed, however, close to the surface They are explained by fission products passing near or parallel to the surface and creating shock waves which interact with the surface.38 These studies have also been useful in gaining important data for understanding fission gas evolution in nuclear fuels For example, 72 MeV iodine ions (see Figure 18), approximate very closely the stopping power of fission fragments Such studies have shown that 72 MeV I irradiations cause Kr atoms preimplanted into UO2 to nucleate into bubbles, and preformed bubbles to undergo resolution A radiation-enhanced diffusion coefficient for the Kr was estimated from these studies to be D % 1.2  10À30 cm5  F_ , where F_ is the fission rate per cubic centimeter, and found independent of temperature below %500 C (see Matzke et al.37 for details) The importance of such studies as these is that the basic processes in complex nuclear fuels can be elucidated by studies that carefully control singly the irradiation conditions and materials parameters in the fuel, such as fission gas concentration, damage, etc 211 Si −12 −8 −4 Distance from grain boundary (nm) 12 Figure 19 Comparison of grain boundary segregation of Cr, Ni, and Si in commercial purity 16 stainless steel following irradiation with either protons or neutrons to similar doses From Was, G S.; Busby, J T.; Allen, T.; et al J Nucl Mater 2002, 300, 198–216 MeV proton irradiation at 360 C to similar doses Figure 19 compares the RIS behavior of Cr, Ni, and Si in a 316 stainless steel alloy following irradiation to approximately dpa Neutron irradiation results are in open symbols and proton irradiation results are in solid symbols This dose range was chosen as an extreme test of proton irradiation to capture the ‘W’-shaped chromium depletion profile caused by irradiation of a microstructure, which contained grain boundaries that were enriched with chromium prior to irradiation Note that the two profiles track each other extremely well, both in magnitude and spatial extent Good agreement is obtained for all three elements Figure 20 shows a comparison of the dislocation microstructure as measured by the dislocation loop size distribution (Figure 20(a)) and the size and number density of dislocation loops (Figure 20(b)) for 304 SS and 316 SS The main features of the loop size distributions are similar for the two irradiations, viz a sharply peaked distribution in the case of 304 SS and a flatter distribution with a tail in the case of 316 SS The agreement in loop size is good for the 304 SS alloy, while loops are smaller for the protonirradiated 316 alloy The loop density is about a factor of less for the proton-irradiated case than the neutron-irradiated case, which is expected as the proton irradiation temperature was optimized to track RIS (higher temperature) rather than the 30 Fraction of loop population (%) Radiation Damage Using Ion Beams Fraction of loop population (%) 212 Protons at 360 ЊC (1.0 dpa) Neutrons at 275 ЊC (0.7 dpa) 20 10 CP 304 SS 0 10 20 15 Loop diameter (nm) (a) 25 30 12 50 Protons at 360 ЊC (1.0 dpa) 40 Neutrons at 275 ЊC (1.1 dpa) 30 20 CP 316 SS 10 0 10 15 20 Loop diameter (nm) 25 30 1024 Loop density (m−3) Loop diameter (nm) 10 Protons at 360 ЊC 304 1023 1022 316 Protons at 360 ЊC Neutrons at 275 ЊC 0 (b) 304 316 Neutrons at 275 ЊC Dose (dpa) 1021 Dose (dpa) Figure 20 Comparison of (a) loop size distributions and (b) loop diameter and loop number density for commercial purity 304 and 316 stainless steels irradiated with neutrons or protons to similar doses From Was, G S.; Busby, J T.; Allen, T.; et al J Nucl Mater 2002, 300, 198–216 1500 1500 1000 500 (a) CP 316 SS Yield strength (MPa) Yield strength (MPa) CP 304 SS Dose (dpa) 1000 500 (b) Dose (dpa) Protons at 360 ЊC (hardness) Neutrons at 275 ЊC (hardness) Neutrons at 275 ЊC (shear punch) Figure 21 Comparison of hardening in commercial purity 304 (a) and 316 (b) stainless steel irradiated with neutrons or protons to similar doses From Was, G S.; Busby, J T.; Allen, T.; et al J Nucl Mater 2002, 300, 198–216 dislocation loop microstructure That the loop sizes and densities are even close is somewhat remarkable considering that loop density is driven by in-cascade clustering, and cascades from proton irradiation are much smaller than those from neutron irradiation The surviving fraction of interstitial loops, however, is greater for proton irradiation, partially compensating the greater loop formation rate under neutron Radiation Damage Using Ion Beams 1.4 Fast neutron fluence (E > MeV) ϫ1025 n m−2 0.5 1.5 2.5 3.5 Neutrons With He Without He 1.2 100 CP 304 SS Protons at 360 ЊC Neutrons at 275 ЊC NWC 213 0.8 s/s0 Measured IG percentage 80 60 0.6 0.4 40 0.2 20 0 Dose (dpa) Figure 22 Comparison of the extent of intergranular stress corrosion cracking in commercial purity 304 stainless steel following similar stress corrosion cracking tests of either neutron- or proton-irradiated samples from the same heat From Was, G S.; Busby, J T.; Allen, T.; et al J Nucl Mater 2002, 300, 198–216 0.14 Ni+ irradiation 675 ЊC 140 dpa 70 60 0.13 0.12 Proton irradiation 400 ЊC 3.0 dpa 50 40 30 0.11 0.10 0.09 Neutron irradiation 510 ЊC 2.6 ϫ 1026 n m−2 E > 0.1 MeV 20 0.08 10 Swelling (%) protons Swelling (%) neutron and Ni ion 80 0.07 20 40 60 80 0.06 100 Bulk nickel concentration (at.%) Figure 23 Effect of bulk nickel concentration on swelling resulting from irradiation with different particles: neutrons, nickel ions, and protons Reproduced from Allen, T R.; Cole, J I.; Gan, J.; Was, G S.; Dropek, R.; Al Kenik, E J Nucl Mater 2005, 341, 90–100 irradiation and resulting in loop densities that are within a factor of 3.39 Figure 21 shows a comparison of irradiation hardening between the two types of irradiation The results 0.5 1.5 Dose (dpa) 2.5 Figure 24 Comparison of relaxation in residual stresses between neutron- and proton-irradiated stainless steel after removing the effect of thermally-induced relaxation From Sencer, B H.; Was, G S.; Yuya, H.; Isobe, Y.; Sagasaka, M.; Garner, F A J Nucl Mater 2005, 336, 314–322 are again similar, with proton irradiation resulting in slightly lower hardness Figure 22 shows the IASCC susceptibility of CP 304 SS as measured by the %IG on the fracture surface following constant load testing (neutron-irradiated samples) and constant extension rate testing (proton-irradiated samples) in BWR normal water chemistry (NWC) Despite the significantly different testing mode, the results are in excellent agreement in that both proton and neutron irradiation result in the onset of IGSCC, at about dpa.40 Figure 23 shows the swelling behavior in austenitic stainless steels as a function of nickel content for proton, Ni ion, and neutron irradiation While these experiments were conducted on different sets of alloys, and under highly disparate irradiation conditions, they all show the same dependence of nickel on swelling In the two commercial purity alloys, no voids were formed in either neutron or protonirradiated samples As a last example of stainless steel alloys, Figure 24 shows the relaxation of residual stress by neutron and proton irradiation Here again, results are from different alloys and different types of tests, but both show the same dependence of stress relaxation on dose The next examples are from reactor pressure vessel steel and Zircaloy Figure 25 shows an experiment on model reactor pressure vessel alloys in which the 214 Radiation Damage Using Ion Beams 500 300 Tin = 300 ЊC (all) −7 Proton: 3–7 ϫ 10 dpa s–1 −10 Neutron: ϫ 10 dpa s–1 −9 Electron: ϫ 10 dpa s–1 280 Vickers hardness (Hv) Change in yield strength (MPa) 400 300 VA, Fe, neutron VA, Fe, proton VA, Fe, electron VD, Fe–0.9Cu–1.0 Mn, neutron VD, Fe–0.9Cu–1.0 Mn, proton VD, Fe–0.9Cu–1.0 Mn, electron VH, Fe–0.9Cu, neutron VH, Fe–0.9Cu, proton 200 100 −100 10−5 260 240 220 200 p - Zircaloy 4, 350 ЊC n - Zircaloy 2, 350–400 ЊC p - Zircaloy 4, 310 ЊC 180 10−4 10−3 Dose (dpa) 10−2 10−1 160 Dose (dpa) Figure 25 Irradiation hardening in model reactor pressure vessel steels following neutron, proton, and electron irradiation at about 300 C From Was, G S.; Hash, M.; Odette, G R Philos Mag 2005, 85(4–7), 703–722 Figure 26 Hardening of Zircaloy-4 irradiated with MeV protons at 310 and 350 C and comparison to neutronirradiated Zircaloy-2 From Zu, X T.; Sun, K.; Atzmon, M.; et al Philos Mag 2005, 85(4–7), 649–659 same model alloy heats were irradiated with neutrons, electrons, or protons at %300 C to doses spanning two orders of magnitude The alloys include a high-purity Fe heat (VA) that hardens very little under irradiation, an Fe–0.9Cu (VH) heat that hardens rapidly initially, followed by a slower hardening rate above 0.1 mpda, and a Fe–0.9Ce–1.0Mn alloy (VD) in which the hardening rate is greatest over the dose range studied Despite the very different compositions and hardening rates, the results of the three types of irradiation agree well Figure 26 shows hardening for Zircaloy-2 and Zircaloy-4 irradiated with either neutrons or protons Although the irradiations were not conducted on the same heats of material, or using similar irradiation parameters, there is good agreement in the magnitude and dose dependence of hardening Proton irradiation also induced amorphization of a Zr(Fe,Cr)2 precipitate after irradiation to dpa at 310 C, similar to that observed in reactor These examples represent a comprehensive collection of comparison data between proton and neutron irradiation and taken together serve as a good example for the capability of charged particles to emulate the effect of neutron irradiation on the alloy microstructure As a final example, to emphasize the care that must be exercised in extrapolating the results of one type of irradiation to make predictions for another, we discuss a comparison of void swelling in Cu due to 2.5 MeV electrons, 3.0 MeV protons, and fission neutrons.41 An attempt was made to keep all irradiation variables constant during the experiments, sample purity, defect production rate, and temperature; only the primary recoil spectrum was varied The results for nucleation rates of voids and void swelling are shown in Figure 27(a) and 27(b), respectively Clearly observed is that void swelling and void nucleation are significantly enhanced for neutron irradiation in comparison to proton or electron irradiation This result is notably in strong contrast to the efficiencies obtained for defect production and radiation-induced segregation (or FMDs) for these three types of irradiation The reduced efficiency of the production of FMDs was attributed to defect annihilation within the cascade core; these results for void swelling, however, indicate that the defect clustering process is also critical to microstructural evolution in irradiated alloys Singh and coworkers41,42 argue that the clustering of interstitials in cascades, and their collapse into dislocation loops, result in interstitial migration by one-dimensional glide of loops, the so-called production bias model.43 As a consequence, interstitials and vacancies become efficiently separated Swelling therefore is more severe for irradiations that produce energetic cascade, for example, neutrons, than for those that not, electrons Proton irradiation is intermediate; that is, small cascades are produced Radiation Damage Using Ion Beams 215 100 Copper 523 K 10−1 1022 523 K Void density (m−3) Swelling (%) Copper 10−2 10−3 10−4 10−5 −4 10 10−2 10−1 Dose (NRT dpa) Fission neutrons 10 MeV protons 20 1019 Fission neutrons MeV protons 2.5 MeV electrons 10−3 1021 2.5 MeV electrons 100 1018 −4 10 10−3 10−2 10−1 Dose (NRT dpa) 100 Figure 27 Void swelling as a function of dose in oxygen-free high conductivity (OFHC)-copper during irradiations with electrons, protons, and fission neutron Reproduced from Singh, B H.; Eldrup, M.; Horsewell, A.; Ehrhart, P.; Dworschak, F Philos Mag A 2000, 80, 2629 1.07.5 Advantages and Disadvantages of Irradiations using Various Particle Types ton = 50 ms 50 toff = 2000 ms 40 K0/K0,avg Each particle type has its advantages and disadvantages for use in the study of radiation effects or for emulating neutron irradiation damage Common disadvantages of charged particle beams are the lack of transmutation reactions and the need to use a rasterscanned beam With the exception of some minor transmutation reactions that can occur with light ion irradiation, charged particles not reproduce the types of transmutation reactions that occur in reactor core materials due to the interaction with neutrons The most important of these is the production of He by transmutation, particularly in alloys that contain elements such as Ni or B But a second consideration is that of a raster-scanned beam in which any volume element of the target is exposed to the beam for only a fraction of the raster-scan cycle For a typical beam scanner and beam parameters, the fraction of time that any particular volume element in the solid is being bombarded is $0.025 Thus, the instantaneous dose rate during the beam-on portion of the cycle is 40 times that of the average, Figure 28 The result is that the defect production rate is very high and defects can anneal out in the remaining 0.975 portion of the cycle before the beam again passes through the volume element As such, the effective defect production 60 30 20 10 K0,avg 0 Time (ms) Figure 28 The effect of a raster-scanned beam on the instantaneous production rate of point defects with the same time averaged rate as a continuous source From Was, G S.; Allen, T R In Radiation Effects in Solids, NATO Science Series II: Mathematics, Physics and Chemistry; Sickafus, K E., Kotomin, E A., Uberuaga, B P., Eds.; Springer: Berlin, 2007; Vol 235, pp 65–98 rate in raster-scanned systems will be less, and must be accounted for One objective of ion irradiation is to emulate the effect of neutrons, and a second is to understand basic physical radiation damage processes, for which 216 Radiation Damage Using Ion Beams neutron irradiation is often less well suited While ion irradiation can be conducted with great control over temperature, dose rate, and total dose, such control is a challenge to reactor irradiations For example, instrumented tubes with active temperature control are expensive to design, build, and operate Even so, frequent power changes can be difficult to handle as the flux–temperature relationship will change and this can result in artifacts in the irradiated microstructure.44 On the other hand, temperatures in cheaper irradiation vehicles that use passive gas gaps and gamma heating (such as ‘rabbit’ tubes) are known with even less certainty While neutron dosimetry is used in some experiments, doses and dose rates are often determined by neutronic models of the core locations and are not verifiable As such, ion irradiations enjoy the advantage of better control and verification of irradiation conditions as compared to neutron irradiation Table provides a list for each of three particle types: electrons, heavy ions, and light ions (protons), and they are discussed in detail in the following sections 1.07.5.1 Electrons Electron irradiation is easily conducted in a highvoltage transmission electron microscope using either Table a hot filament or a field emission gun as an electron source An advantage is that the same instrument used for irradiation damage can be used to image the damage Another advantage is that the high dose rate requires very short irradiation time, but will also require a large temperature shift as explained in the Section 1.07.3 There are several disadvantages to electron irradiation using a TEM First, energies are generally limited to MeV This energy is sufficient to produce an isolated FP in transition metals, but not cascades The high dose rate requires high temperatures that must be closely monitored and controlled, which is difficult to precisely in a typical TEM sample stage Another drawback is that as irradiations are often conducted on thin foils, defects are created in close proximity to the surface and their behavior may be affected by the presence of the surface Perhaps the most serious drawback is the Gaussian shape to the electron beam that can give rise to strong dose rate gradients across the irradiated region Figure 29 shows the composition profile of copper around a grain boundary in Ni–39%Cu following electron irradiation Note that while there is local depletion at the grain boundary (as expected), the region adjacent to the minimum is strongly enriched in copper because of the strong defect flux out of the irradiated Advantages and disadvantages of irradiations with various particle types Advantages Electrons Relatively ‘simple’ source – TEM Uses standard TEM sample High dose rate – short irradiation times Heavy ions High dose rate – short irradiation times High Tavg Cascade production Light ions Accelerated dose rate – moderate irradiation times Modest DT required Good depth of penetration Flat damage profile over tens of microns Disadvantages Energy limited to $1 MeV No cascades Very high beam current (high dpa rate) leading to large temperature shifts relative to neutrons Poor control of sample temperature Strong ‘Gaussian’ shape (nonuniform intensity profile) to beam No transmutation Very limited depth of penetration Strongly peaked damage profile Very high beam current (high dpa rate) leading to large temperature shifts relative to neutrons Potential for composition changes at high dose via implanted ion No transmutation Minor sample activation Smaller, widely separated cascade No transmutation Source: Was, G S.; Allen, T R In Radiation Effects in Solids, NATO Science Series II: Mathematics, Physics and Chemistry; Sickafus, K E., Kotomin, E A., Uberuaga, B P., Eds.; Springer: Berlin, 2007; Vol 235, pp 65–98 Radiation Damage Using Ion Beams 217 Si concentration (at.%) 494 ЊC Cu concentration (at.%) e-beam diameter 400 ЊC D+ e− 6 −4 400 ЊC −6 −4 −2 Distance from grain boundary (μm) Figure 29 Enrichment of copper surrounding a local depletion at the grain boundary The enrichment is caused by the high defect flux away from the irradiated region defined by the horizontal line From Ezawa, T.; Wakai, E Ultramicroscopy 1991, 39, 187 Solute concentration (wt%) 60 50 Iron Chromium Nickel 40 30 −3 −2 −1 Distance from grain boundary (μm) Figure 31 Comparison of (a) deuteron and (b) electron irradiation showing the greater amount of segregation and the narrower profile for the deuteron irradiation From Wakai, E Trans J Nucl Mater 1992, 33(10), 884 zone defined by the horizontal line below the spectrum This outward-directed defect flux causes a reversal in the direction of segregation from that caused by a defect flux to the sink Another often observed artifact in electron irradiation is very broad grain boundary enrichment and depletion profiles Figure 30 shows that the enrichment profile for Ni and the depletion profiles for Fe and Cr in stainless steel have widths on the order of 75–100 nm, which is much greater than the 5–10 nm widths observed following neutron irradiation under similar conditions and model simulations of radiationinduced segregation A similar effect was observed by Wakai45 using electron and Dỵ irradiation of the same alloy in which the segregation profile was much higher and narrower around the grain boundary in the deuteron-irradiated sample as compared to the electron irradiation (Figure 31) 20 1.07.5.2 10 100 200 300 400 Distance (nm) 500 600 Figure 30 Broad grain boundary enrichment and depletion profiles in Fe–20Cr–25Ni–0.75Nb–0.5Si following irradiation with electrons at 420 C to 7.2 dpa From Ashworth, J A.; Norris, D I R.; Jones, I P J Nucl Mater 1992, 189, 289 Heavy Ions Heavy ions enjoy the benefit of high dose rates resulting in the accumulation of high doses in short times Also, because they are typically produced in the energy range of a few MeV, they are very efficient at producing dense cascades, similar to those produced by neutrons The disadvantage is that as with electrons, the high dose rates require large 218 Radiation Damage Using Ion Beams dpa versus depth for various ions incident on nickel Ni Al 8.1 MeV aluminum ions (dpa per 1016 ions cm−2) 1.2 1.0 0.8 0.6 0.4 0.2 0 0 0.5 1.5 2.5 MeV carbon ions (dpa per 1016 ions cm−2) C 12 Al Ni C 14 MeV nickel ions (dpa per 1016 ions cm−2) 15 Depth (μm) Figure 32 Damage profiles for C, Al, and Ni irradiation of a nickel target at energies selected to result in the same penetration depth From Whitley, J B Ph.D Thesis, University of Wisconsin-Madison, Madison, WI, 1978 1.5 250 3.2 1.5 200 Swelling (%) 2.4 Observed 150 1.6 dpa 1.2 0.8 100 50 0.4 0 (a) 0.2 0.4 0.6 0.8 Depth (μm) Displacement rate (10−3 dpa s–1) MeV 2.8 0.5 0 1.2 1.4 1.6 (b) Ni2+ on Ni 0.5 0.2 0.4 0.6 0.8 1.2 1.4 1.6 Depth (m) ỵ Figure 33 (a) Subsurface swelling resulting from MeV Ni ion irradiation of Fe–15Cr–35Ni at 625 C and (b) displacement rate and ion deposition rate calculated for MeV Ni2ỵ on nickel Adapted from Garner, F A J Nucl Mater 1983, 117, 177–197; Lee, E H.; Mansur, L K.; Yoo, M H J Nucl Mater 1979, 85&86, 577–581 temperature shifts so that irradiations must be conducted at temperatures of $500 C in order to create similar effects as neutron irradiation at $300 C Clearly, there is not much margin for studying neutron irradiations at higher reactor temperature as higher ion irradiation temperatures will cause annealing Another drawback is the short penetration depth and the continuously varying dose rate over the penetration depth Figure 32 shows the damage profile for several heavy ions incident on nickel Note that the damage rate varies continuously and peaks sharply at only mm below the surface As a result, regions at a very well-defined depth from the surface must be isolated and sampled in order to avoid dose or dose rate variation effects from sample to sample Small errors (500 nm) made in locating the volume to be characterized can result in a dose that varies by a factor of from the target value A problem that is rather unique to nickel ion irradiation of stainless steel or nickel-base alloys is that in addition to the damage they create, each bombarding Ni ion constitutes an interstitial Figure 33(a) shows Radiation Damage Using Ion Beams that MeV Ni2ỵ irradiation of a Fe15Cr35Ni alloy resulted in high swelling in the immediate subsurface region compared to that near the damage peak As shown in Figure 33(b), the Ni2ỵ ions come to rest at a position just beyond the peak damage range So even though the peak damage rate is about 3 that at the surface, swelling at that location is suppressed by about a factor of compared to that at the surface.46 The reason is that the bombarding Ni2ỵ ions constitute interstitials and the surplus of interstitials near the damage peak results in a reduction of the void growth rate.47,48 In the dose rate–temperature regime where recombination is the dominant point defect loss mechanism, interstitials injected by Ni2ỵ ion bombardment may never recombine as there is no corresponding vacancy production 1.07.5.3 Light Ions In many ways, proton irradiation overcomes the drawbacks of electron and neutron irradiation The penetration depth of protons at a few MeV can exceed 40 mm and the damage profile is relatively flat such that the dose rate varies by less than a factor of over several tens of micrometers Further, the depth of penetration is sufficient to assess such properties as irradiation hardening through microhardness measurements, and stress corrosion cracking through crack initiation tests such as the slow strain rate test 219 Figure 34 shows schematics of 3.2 MeV proton and MeV Ni2ỵ damage profiles in stainless steel Superimposed on the depth scale is a grain structure with a grain size of 10 mm Note that with this grain size, there are numerous grain boundaries and a significant irradiated volume over which the proton damage rate is flat The dose rate for proton irradiations is 2–3 orders of magnitude lower than that for electrons or ions, thus requiring only a modest temperature shift, but as it is still 102–103 times higher than neutron irradiation, modest doses can be achieved in reasonably short irradiation time The disadvantages are that because of the small mass of the proton compared to heavy ions, the recoil energy is smaller and the resulting damage morphology is characterized by smaller, more widely spaced cascades than with ions or neutrons Also, as only a few MeV are required to surmount the Coulomb barrier for light ions, there is also a minor amount of sample activation that increases with proton energy 1.07.6 Practical Considerations for Radiation Damage Using Ion Beams In the process of setting up an ion irradiation experiment, a number of parameters that involve beam 105 Ion 10−15 MeV Ni 10−17 Calculated range (μm) dpa/(ion cm−2) 10−16 1000 2+ 3.2 MeV protons 10−18 10−19 10−20 10 0.1 MeV neutrons 10−21 10−22 H He Ni 10 20 30 Depth (μm) 40 Figure 34 Damage profiles for MeV neutrons, 3.2 MeV protons, and MeV Ni2ỵ ions in stainless steel From Was, G S.; Allen, T R In Radiation Effects in Solids, NATO Science Series II: Mathematics, Physics and Chemistry; Sickafus, K E., Kotomin, E A., Uberuaga, B P., Eds.; Springer: Berlin, 2007; Vol 235, pp 65–98 Calculated by SRIM 2000 Stainless steel (Fe–20Cr–10Ni) 0.001 0.01 0.1 10 100 Energy (MeV) Figure 35 Range of hydrogen, helium, and nickel ions in stainless steel as a function of ion energy From Was, G S.; Allen, T R In Radiation Effects in Solids, NATO Science Series II: Mathematics, Physics and Chemistry; Sickafus, K E., Kotomin, E A., Uberuaga, B P., Eds.; Springer: Berlin, 2007; Vol 235, pp 65–98 Radiation Damage Using Ion Beams Time to reach dpa (h) (a) Energy deposited (W) (b) Beam current (μA) (c) 10−4 10−5 10−6 10−7 600 500 400 300 200 100 400 500 300 400 Residual activity 200 100 100 Maximum current at 360 ЊC Maximum current at 400 ЊC 80 60 40 20 (d) At 360 ЊC At 400 ЊC behavior during proton irradiation vary with energy, dose rate, the time to reach dpa, deposited energy, and the maximum permissible beam current (which will determine the dose rate and total dose), given a temperature limitation of 360 C With increasing energy, the dose rate at the surface decreases because of the drop in the elastic scattering cross-section (Figure 36(a)) Consequently, the time to reach a target dose level, and hence the length of an irradiation, increases rapidly (Figure 36(b)) Energy deposition scales linearly with the beam energy, raising the burden of removing the added heat in order to control the temperature of the irradiated region (Figure 36(c)) The need to remove the heat due to higher energies will limit the beam current at a specific target temperature (Figure 36(d)), and a limit on the beam current (or dose rate) will result in a longer irradiation to achieve the specified dose Figure 37 summarizes how competing features of an irradiation vary with beam energy, creating tradeoffs in the beam parameters For example, while greater depth is generally favored in order to increase the volume of irradiated material, the higher energy required leads to lower dose rates near the surface and higher residual radioactivity For proton irradiation, the optimum energy range, achieved by balancing these factors, lies between and MeV as shown by the shaded region Range (μm) Residual activity (arbitrary units) Dose rate (dpa s−1) characteristics (energy, current/dose) and beamtarget interaction must be considered ASTM E 521 provides standard practice for neutron radiation damage simulation by charged-particle irradiation49 and ASTM E 693 provides standard practice for characterizing neutron exposures in iron and low alloy steels in units of dpa.9 One of the most important considerations is the depth of penetration Figure 35 shows the range versus particle energy for protons, helium ions, and nickel ions in stainless steel as calculated by SRIM.50 The difference in penetration depth between light and heavy ions is over an order of magnitude in this energy range Figure 36 shows how several other parameters describing the target 10 Energy (MeV) 15 400 300 Energy minimum due to depth penetration 350 Energy maximum due to residual activity 300 250 Range 200 200 150 Time to dpa 100 50 20 Figure 36 Behavior of beam-target parameters as a function of beam energy proton irradiation at 360 C; (a) dose rate, (b) time to reach dpa, (c) energy deposition, and (d) beam current limit to maintain a sample temperature of 360 C From Was, G S.; Allen, T R In Radiation Effects in Solids, NATO Science Series II: Mathematics, Physics and Chemistry; Sickafus, K E., Kotomin, E A., Uberuaga, B P., Eds.; Springer: Berlin, 2007; Vol 235, pp 65–98 100 0 10 Energy (MeV) 20 Figure 37 Variation of ion range, residual activity, and time to reach dpa as a function of proton energy Reproduced from Was, G S.; Allen, T R In Radiation Effects in Solids, NATO Science Series II: Mathematics, Physics and Chemistry; Sickafus, K E., Kotomin, E A., Uberuaga, B P., Eds.; Springer: Berlin, 2007; Vol 235, pp 65–98 Time to reach dpa (h) 220 Radiation Damage Using Ion Beams References 25 26 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Garner, F A J Nucl Mater 1983, 117, 177 Mazey, D J J Nucl Mater 1990, 174, 196 Standard Practice for Neutron Irradiation Damage Simulation by Charged Particle Irradiation, Designation E521-89, American Standards for Testing and Materials, Philadelphia, 1989; p D–9 Was, G S.; Andresen, P L JOM 1992, 44(4), Andresen, P L.; Ford, F P.; Murphy, S M.; Perks, J M In Proceedings of the Fourth International Symposium on Environmental Degradation of Materials in Nuclear Power Systems – Water Reactors; National Association of Corrosion Engineers: Houston, TX, 1990; pp 1–83 Andresen, P L In Stress Corrosion Cracking, Materials Performance and Evaluation; Jones, R H., Ed.; ASM International: Meals Park, OH, 1992; p 181 Kinchin, G H.; Pease, R S Prog Phys 1955, 18, Norgett, M J.; Robinson, M T.; Torrens, I M Nucl Eng Des 1974, 33, 50 ASTM E693-01 Standard Practice for Characterizing Neutron Exposures in Iron and Low Alloy Steels in Terms of Displacements Per Atom (DPA), E 706(ID); American Society for Testing and Materials: West Conshohocken, PA, 2007 Zinkle, S J.; Singh, B N JNM 1993, 199, 173 Kulcinski, G L.; Brimhall, J L.; Kissinger, H E In Proceedings of Radiation-Induced Voids in Metals; Corbett, J W., Ianiello, L C., Eds.; USAEC Technical Information Center: Oak Ridge, TN, 1972; p 453, CONF-710601 Naundorf, V J Nucl Mater 1991, 182, 254 Iwase, A.; Rehn, L E.; Baldo, P M.; Funk, L J Nucl Mater 1996, 238, 224–236 Mansur, L K J Nucl Mater 1994, 216, 97 Jung, P.; Chaplin, R L.; Fenzl, H J.; Reichelt, K.; Wombacher, P Phys Rev B 1973, 8, 553 Vajda Rev, P Mod Phys 1977, 49, 481 King, W E.; Merkle, K L.; Meshii, M Phys Rev B 1981, 23, 6319 Gibson, J B.; Goland, A N.; Milgram, M.; Vineyard, G H Phys Rev 1960, 120, 1229 Lucasson, P In Fundamental Aspects of Radiation Damage in Metals; Robibnson, M T., Young, F W., Jr., Eds.; ERDA Report CONF-751006; 1975, p 42 Corbett, J W.; Smith, R B.; Walker, R M Phys Rev 1959, 114, 1452 Burger, G.; Isebeck, K.; Volkl, J.; Schilling, W.; Wenzl, H Zeitschrift Angew Phys 1967, 22, 452 Garr, K R.; Sosin, A Phys Rev 1969, 162, 669 Ehrhart, P In Landolt –Bornstein New Series, Group III; Ullmaier, H., Ed.; Springer: Berlin, 1991; Vol 25, p 115 See e.g., Bacon, D In Computer Simulations in Materials; Kirchner, H O., et al Eds.; Kluwer: The Netherlands, 1996; p 189 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 221 Wei, L C.; Lang, E.; Flynn, C P.; Averback, R S Appl Phys Lett 1999, 75, 805 Fielitz, P.; Macht, M P.; Naundorf, V.; Wollenberger, H J Nucl Mater 1997, 251, 123 Okamoto, P R.; Harkness, S D.; Laidler, J J ANS Trans 1973, 16, 70 Okamoto, P R.; Wiedersich, H J Nucl Mater 1974, 53, 336 Schmitz, G.; Ewert, J C.; Harbsmeier, F.; Uhrmacher, M.; Haider, F Phys Rev B 2001, 63, 224113 Krasnochtchekov, P.; Averback, R S.; Bellon, P Phys Rev B 2005, 72(17), 174102 Enrique, R A.; Bellon, P Phys Rev Lett 2000, 84, 2885 Enrique, R A.; Nordlund, K.; Averback, R S.; Bellon, P J Appl Phys 2003, 93, 2917 See e.g., Jung, P.; Schwarz, A.; Sahu, H K Nucl Instrum Meth A 1985, 234, 331 Mayr, S G.; Averback, R S Phys Rev B 2003, 68, 214105 Brongersma, M L.; Snoeks, E.; van Dillen, T.; Dillen, A J Appl Phys 2000, 88, 59 Serruys, Y.; Trocellier, P.; Miro, S.; et al J Nucl Mater 2009, 386–388, 967 Matzke, Hj.; Lucuta, P G.; Wiss, T Nucl Instrum Meth B 2000, 166–167, 920 Ronchi, C J Appl Phys 1973, 44, 3573 Gan, J.; Was, G S.; Stoller, R E J Nucl Mater 2001, 299, 53–67 Onchi, T.; Dohi, K.; Soneda, N.; Navas, M.; Castano, M L In Proceedings of the 11th International Conference on Environmental Degradation of Materials in Nuclear Power Systems – Water Reactors; American Nuclear Society: La Grange Park, IL, 2003; p 1111 Singh, B H.; Eldrup, M.; Horsewell, A.; Ehrhart, P.; Dworschak, F Philos Mag A 2000, 80, 2629 Golubov, S I.; Singh, B N.; Trinkaus, H Philos Mag A 2001, 81, 2533 Singh, B N.; Foreman, A J E Philos Mag A 1992, 66, 975 Garner, F A.; Sekimura, N.; Grossbeck, M L.; et al J Nucl Mater 1993, 205, 206–218 Wakai, E Trans J Nucl Mater 1992, 33(10), 884 Garner, F A J Nucl Mater 1983, 117, 177–197 Lee, E H.; Mansur, L K.; Yoo, M H J Nucl Mater 1979, 85&86, 577–581 Brailsford, A D.; Mansur, L K J Nucl Mater 1977, 71, 110–116 ASTM E521-96 Standard Practice for Neutron Radiation Damage Simulation by Charged-Particle Irradiation; American Society for Testing and Materials: West Conshohocken, PA, 2009 Ziegler, J F.; Biersack, J P.; Littmark, U The Stopping and Range of Ions in Matter; Pergamon: New York, 1996 ... conducting radiation damage studies, and wrapping up with a consideration of practical issues in ion irradiation experiments 1.07. 2 Motivation for Using Ion Beams to Study Radiation Damage In the... neutron irradiation That is, what are the irradiation conditions required for ion irradiation to yield the same measure of radiation effect as that for neutron irradiation? This is the key question,... type and the damage rate This chapter will begin with a summary of the motivation for using ion irradiation for radiation damage studies, followed by a brief review of radiation damage relevant