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 Comprehensive nuclear materials 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.

1.07.4 Contributions of Ion Irradiation to an Understanding of Radiation Effects 204

1.07.5 Advantages and Disadvantages of Irradiations using Various Particle Types 215

AES Auger electron spectroscopy

APT Atom probe tomography

bcc Body-centered cubic

BWR Boiling water reactor

dpa Displacements per atom

microscopy/energy dispersive spectrometry

TEM Transmission electron microscopy

Radiation effects research has been conducted using

a variety of energetic particles: neutrons, electrons,protons, He ions, and heavy ions Energetic ions

195

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

radia-tion damage relevant to charged particles The

contri-bution 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

prac-tical issues in ion irradiation experiments

Beams to Study Radiation Damage

In the 1960s and 1970s, heavy ion irradiation was

developed for the study of radiation damage

pro-cesses in materials As ion irradiation can be

conducted at a well-defined energy, dose rate, and

temperature, it results in very well-controlled

experi-ments 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.1–3Ion 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

irradi-ation 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 forinvestigations of the basic damage processes Simula-tion by ions allows easy variation of the irradiationparameters such as dose, dose rate, and temperatureover a wide range of values

One of the prime attractions of ion irradiation isthe rapid accumulation of end of life doses in shortperiods of time Typical neutron irradiation experi-ments in thermal test reactors may accumulate dam-age at a rate of 3–5 dpa year
1 In fast reactors, therates can be higher, on the order of 20 dpa year
1 Forlow dose components such as structural components

in boiling water reactor (BWR) cores that typicallyhave an end-of-life damage of 10 dpa, these rates areacceptable However, even the higher dose rate of afast reactor would require 4–5 years to reach the peakdose of 80 dpa in the core baffle in a pressurizedwater reactor (PWR) For advanced, fast reactor con-cepts in which core components are expected toreceive 200 dpa, the time for irradiation in a testreactor becomes impractical

In addition to the time spent ‘in-core,’ there is aninvestment in capsule design and preparation as well

as disassembly and allowing for radioactive decay, ing additional years to an irradiation program Analysis

add-of microchemical and microstructural changes byatom probe tomography (APT), Auger electron spec-troscopy (AES) or microstructural changes by energydispersive spectroscopy via scanning transmissionelectron microscopy (STEM-EDS) and mechanicalproperty or stress corrosion cracking (SCC) evalua-tion can take several additional years because of theprecautions, special facilities, and instrumentationrequired for handling radioactive samples The result

is that a single cycle from irradiation through analysis and mechanical property/SCC testing mayrequire over a decade Such a long cycle length doesnot permit for iteration of irradiation or materialconditions that is critical in any experimental researchprogram The long cycle time required for design andirradiation also reduces flexibility in altering irradia-tion programs as new data become available Therequirement of special facilities, special samplehandling, and long irradiation time make the costfor neutron irradiation experiments very high

micro-In contrast to neutron irradiation, ion (heavy,light, or electrons) irradiation enjoys considerableadvantages in both cycle length and cost Ion irradia-tions of any type rarely require more than severaltens of hours to reach damage levels in the 1–100 dparange Ion irradiation produces little or no residualradioactivity, allowing handling of samples without

the need for special precautions These features

translate into significantly reduced cycle length and

cost The challenge then is to verify the equivalency

between neutron and ion irradiation in terms of

the changes to the microstructure and properties

of the material The key question that needs to be

answered is how do results from neutron and charged

particle irradiation experiments compare? How, for

example, is one to compare the results of a component

irradiated in-core at 288C to a fluence of 1 1021

n

cm
2(E> 1 MeV) over a period of oneyear, with an ion

irradiation experiment using 3 MeV protons at 400C

to 1 dpa (displacements per atom) at a dose rate of

10
5dpa s
1 (1 day), or 5 MeV Ni2 þ at 500C to

10 dpa at a dose rate of 5 10
3dpa s
1(1 h)?

The first question to resolve is the measure of

radia-tion effect In the Irradiaradia-tion assisted stress corrosion

cracking (IASCC) problem in LWRs, concern has

cen-tered 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

mea-surable effects of irradiation can be determined for

both neutron and ion irradiation experiments

The next concern is determining how ion

irradia-tion translates into the environment describing

neu-tron 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

postirra-diation 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

application, ion irradiation provides a low-cost andrapid means of elucidating mechanisms and screeningmaterials for the most important variables

A final challenge is the volume of material that can

be irradiated with each type of radiation Neutronshave mean free paths on the order of centimeters

in structural materials One MeV electrons penetrateabout 500 mm, 1 MeV protons penetrate about 10 mm,and 1 MeV Ni ions have a range of less than 1 mm.Thus, the volume of material that can be irradiatedwith ions from standard laboratory-sized sources(TEMs, accelerators), is limited

Damage Relevant to Ion Irradiation

1.07.3.1 Defect ProductionThe parameter commonly used to correlate the dam-age produced by different irradiation environments isthe total number of displacements per atom (dpa).Kinchin and Pease7were the first to attempt to deter-mine the number of displacements occurring duringirradiation and a modified version of their modelknown as the Norgett–Robinson–Torrens (NRT)model8 is generally accepted as the internationalstandard for quantifying the number of atomic dis-placements in irradiated materials.9According to theNRT model, the number of Frenkel pairs (FPs),

nNRT(T ), generated by a primary knock-on atom(PKA) of energy T is given by

nNRTðTÞ ¼kEDðTÞ

where ED(T ) is the damage energy (energy of thePKA less the energy lost to electron excitation), Edisthe displacement energy, that is, the energy needed todisplace the struck atom from its lattice position, and k

is a factor less than 1 (usually taken as 0.8) Integration

of the NRT damage function over recoil spectrum andtime gives the atom concentration of displacementsknown as the NRT displacements per atom (dpa):dpa¼

ððfðEÞvNRTðTÞsðE; TÞdT dE ½2where f(E) is the neutron flux and s(E,T ) is the proba-bility that a particle of energy E will impart a recoilenergy T to a struck atom The displacement damage isaccepted as a measure of the amount of change to thesolid 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

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

neu-tron irradiation effects is the particle energy spectrum

that arises because of the difference in the way the

particles are produced Ions are produced in

accel-erators 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 2shows 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

Another major difference in the characteristics ofions and neutrons is their depth of penetration Asshown inFigure 3, ions lose energy quickly because

of high electronic energy loss, giving rise to a tially nonuniform energy deposition profile caused

spa-300

RTNS-II, 90 ⬚C OWR, 90⬚C

Figure 2 Energy spectrum for neutrons from a variety

of reactor types and a monoenergetic proton beam.

Reproduced from Stoller, R E.; Greenwood, L R.

Distance into solid ( m)

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

dam-age 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

propor-tional to the integral of the energy transfer cross-section

and the number of displacements per PKA, nNRT(T):

where Rdis the number if displacements per unit

vol-ume 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

hard-sphere model,eqn [3]becomes

, M is the target atom mass, m

is the neutron mass, E is the neutron energy, and ssis

the elastic scattering cross-section For the case of ion–

atom interaction described by Rutherford scattering,

where e is the unit charge, M1is the mass of the ion, and

M2is the mass of the target atom As shown inFigure 3,

for comparable energies, 1.3 MeV protons cause over

100 times more damage per unit of fluence at the

sample surface than 1 MeV neutrons, and the factor

for 20 MeV C ions is over 1000 Of course, the damage

depth is orders of magnitude smaller than that for

neutron irradiation

1.07.3.2 Primary and Weighted

Recoil Spectra

A description of irradiation damage must also

con-sider 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 Tþ dT is transferred from the primary

recoil atom to other target atoms The fraction ofrecoils between the displacement energy Ed, and T is

of energy E to create a recoil of energy T The recoilfraction is shown in Figure 4, which reveals only asmall difference between ions of very different masses

of damage that are produced by different types of1.0

He

Kr Ar Ne Fraction of recoils with energy above

particles Light ions such as electrons and protons

will produce damage as isolated FPs or in small

clusters while heavy ions and neutrons produce

dam-age in large clusters For 1 MeV particle irradiation of

copper, half the recoils for protons are produced with

energies less than 60 eV while the same number

for Kr occurs at about 150 eV Recoils are weighted

toward lower energies because of the screened

Coulomb potential that controls the interactions of

charged particles For an unscreened Coulomb

inter-action, 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:

excitations and allowing ED(T )¼ T, then the

weighted average recoil spectra for Coulomb and

hard sphere collisions are

WCoulðE; TÞ ¼lnT
lnEd

ln ^T
lnEd

½9

WHSðE; TÞ ¼T2
E2

1 MeV particle irradiations of copper The

character-istic energy, T1/2is that recoil energy below which

half of the recoils are produced The Coulomb

forces extend to infinity and slowly increase as the

particle approaches the target; hence the slow

increase with energy In a hard sphere interaction,

the particles and target do not interact until their

separation reaches the hard sphere radius at which

point the repulsive force goes to infinity A screened

Coulomb is most appropriate for heavy ion

irradia-tion Note the large difference in W(E,T ) between

the various types of irradiations at E¼ 1 MeV

While heavy ions come closer to reproducing theenergy distribution of recoils of neutrons than dolight ions, neither is accurate in the tails of the distri-bution This does not mean that ions are poor simu-lations of radiation damage, but it does mean thatdamage is produced differently and this differencewill need to be considered when designing an irradi-ation program that is intended to produce microche-mical and microstructural changes that match thosefrom neutron irradiation

There is, of course, more to the description ofradiation damage than just the number of dpa.There is the issue of the spatial distribution of damageproduction, which can influence the microchemistryand microstructure, particularly at temperatureswhere diffusion processes are important for micro-structural development In fact, the ‘ballistically’determined value of dpa calculated using such adisplacement model is not the appropriate unit to

be used for dose comparisons between particletypes The reason is the difference in the primarydamage state among different particle types

1.07.3.3 Damage MorphologyThe actual number of defects that survive the dis-placement cascade and their spatial distribution

in solids will determine the effect on the irradiatedmicrostructure Figure 7 summarizes the effect of

1.0

0.8 Copper

damage morphology from the viewpoint of the grain

boundary and how the defect flow affects

radiation-induced 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

‘avail-able migrating’ defects10are the only defects that will

affect the amount of grain boundary segregation,

which is one measure of radiation effects The

migra-tion efficiency can be very small, approaching a few

percent at high temperatures The migration

effi-ciency, 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 (>10
11s) intracascade

thermal diffusion

They are related as follows:

e¼ diþ giþ zi¼ dvþ gvþ zv ½11

vacan-cies and interstitials as described by the NRT model

Due to significant recombination in the cascade,only a fraction (30%) is free to migrate from thedisplacement zone These defects can recombine out-side of the cascade region, be absorbed at sinks in the

Total dpa

Loss to displacement cascades

Mutual recombination outside of cascade

Loss to sinks

in matrix

Loss at grain boundaries

Boundary structure and micro chemistry

Radiation-induced segregation

Void swelling loop structure Defect diffusion

matrix chemistry

Particle type and energy

Freely migrating defects

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

Displacement cascade efficiency

Isolated point defect

Clustered point defect

Mobile clusters

Evaporating defects

Immobile clusters

Available

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

matrix (voids, loops), or be absorbed at the grain

boundaries, providing for the possibility of

radiation-induced 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).10The clustered fraction,

d includes large, sessile clusters and small defect

clusters that may be mobile at a given irradiation

temperature and will be different for vacancies and

interstitials For a 5 keV cascade, diis about 0.06 and

dvis 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

clus-ters, to interact with existing clusclus-ters, and to

partic-ipate in the defect flow to grain boundaries that

gives rise to radiation-induced segregation Owing

to their potential to so strongly influence the

irra-diated 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

likeli-hood of their remaining as isolated rather than

clus-tered defects Despite the equivalence in energy

among the four particle types described inFigure 5,

the average energy transferred and the defect

pro-duction efficiencies vary by more than an order of

magnitude This is explained by the differences in

the cascade morphology among the different

parti-cle 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

recombi-nation Protons produce small widely spaced

cas-cades 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

irradia-tion temperature, with higher temperatures resulting

in the lower values Naundorf12estimated the freely

migrating defect fraction using an analytical

treat-ment 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)

radius so that the nearby FPs neither recombine norcluster The model follows each generation of thecollision and calculates the fraction of all defectsproduced that remain free Results of calculationusing the Naundorf model are shown inTable 1forseveral ions of varying mass and energy Values of Zrange between 24% for proton irradiation to 3% forheavy ion (krypton) irradiation Recent results,13however, have shown that the low values of FMDefficiency for heavy ion or neutron irradiation cannot

be explained by defect annihilation within the parentcascade (intracascade annihilation) In fact, cascadedamage generates vacancy and interstitial clustersthat act as annihilation sites for FMD, reducing theefficiency of FMD production Thus, the cascaderemnants result in an increase in the sink strengthfor point defects and along with recombination in theoriginal cascade, account for the low FMD efficiencymeasured by experiment

1.07.3.4 Damage Rate Effects

As differences in dose rates can confound directcomparison between neutron and ion irradiations, it

is important to assess their impact A simple methodfor examining the tradeoff between dose and temper-ature in comparing irradiation effects from differentparticle types is found in the invariance requirements.For a given change in dose rate, we would like to knowwhat change in dose (at the same temperature) isrequired to cause the same number of defects to beabsorbed at sinks Alternatively, for a given change

in dose rate, we would like to know what change intemperature (at the same dose) is required to causethe same number of defects to be absorbed atsinks The number of defects per unit volume, NR,that have recombined up to time t, is given by Mansur14

Table 1 Efficiency for producing freely migrating defects, g, in nickel by different kinds of irradiations (E d ¼ 40

eV, r iv ¼ 0.7 nm) using Lindhard’s analytical differential collision cross-section

NR¼ Riv

ðt 0

CiCvdt 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

NSj ¼

ðt 0

kSjCj dt ½13

where kSj is the strength of sink j and Cj is the sink

concentration The ratio of vacancy loss to interstitial

loss is

RS¼NSv

where j¼ v or i The quantity NS is important in

describing the microstructural development involving

total point defect flux to sinks (e.g., RIS), while RSis 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 NSto be invariant at a fixed dose, the

follow-ing relationship between ‘dose rate (Ki) and temperature

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 relationshipbetween ‘dose rate and temperature’ must hold:

ratio of dose rates and the temperature differencerequired to maintain the same point defect absorption

at sinks (a), and the swelling invariance (b)

The invariance requirements can be used toprescribe an ion irradiation temperature–dose ratecombination that simulates neutron radiation Wetake the example of irradiation of stainless steelunder typical BWR core irradiation conditions of

4.5  10
8dpa s
1at 288C If we were to conduct

a proton irradiation with a characteristic dose rate of7.0 10
6dpa s
1, then usingeqn [15]with a vacancyformation energy of 1.9 eV and a vacancy migration

100 1.0

10 Ratio of dose rates

Figure 9 Temperature shift from the reference 200C 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.

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 400C Similarly,

usingeqn [16], a proton irradiation temperature of

300C will result in an invariant RS (e.g., swelling

or loop growth) For a Ni2þion irradiation at a dose

rate of 10
3dpa s
1, the respective temperatures are

675C (NS invariant) and 340C (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

tem-peratures selected for proton irradiation, 360C and

for Ni2þirradiation, 500C represent compromises

between the extremes for invariant NSand RS

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 inSections 1.07.2

and1.07.3, it is the flexibility of such irradiations and

our firm understanding of atomic collisions in solids

that afford them their utility Principally, ion

irradia-tions have enabled focused studies on the isolated

effects of primary recoil spectrum, defect

displace-ment 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,

the good agreement that is possible, while on the other,the extreme caution that is necessary in extrapolatingresults 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 son to ions and neutrons is that they create defects invery low-energy recoil events As a consequence, nearlyall FPs are produced in isolation This has been offoremost importance in developing our understanding

compari-of radiation damage, as it made studies compari-of defect tion mechanisms as well as the fundamental properties

crea-of FPs possible Recall that the properties crea-of vacanciesand vacancy clusters, for example, formation and migra-tion energies, stacking fault energies, etc., could bedetermined from quenching studies It is not possible,however, to quench in interstitials in metals Very littlewas therefore known about this intrinsic defect prior

to about 1955 when irradiation experiments becamewidely employed In this section, we highlight some ofthe key findings derived from these past studies.1.07.4.1.1 Displacement threshold surfacesThe creation of a stable FP requires that a latticeatom receives an energy greater than Tm, which isthe minimum displacement energy This value hasbeen determined experimentally in many materials

by measuring the change in some physical property,such as electrical resistivity or length change, as afunction of maximum recoil energy of a target atom.Such experiments are practical only for electronirradiations for which recoil energies can be keptlow, but with the irradiation particles still penetratingdeeply into, or through, the specimen Typical valuesare shown inTable 2

As a crystal is not homogeneous, the thresholdenergy depends on the crystallographic direction inwhich the knock-on atom recoils The anisotropy ofthe threshold energy surface has been mapped out invarious crystals by measuring the production rate ofdefects as a function of both the electron energy, nearthreshold, and the orientation of single crystalline

Table 2 Minimum displacement energies in pure metals, semiconductors, and stainless steel (SS)

Source: Lucasson, P In Fundamental Aspects of Radiation Damage in Metals; Robibnson, M T., Young, F W., Jr., Eds.; ERDA Report

specimens with respect to the electron beam

direc-tion.15,16 The total cross-section for FP production

rate is given by the expression

sdðY1; F1; E1Þ ¼

ð2p

0

ðp=2

0

dsðy2; E1Þ

dy2

df22pnðY2; F2; TÞdy2

½19

where the subscripts 1 and 2 refer to incoming

elec-tron and recoiling ion, respectively, and Y1, F1, Y2,

F2are the polar and azimuthal angles of the electron

beam relative to the crystal axis; y2, f2, are these

same angles relative to the beam direction; n is the

anisotropic damage function Near threshold, n¼ 1

for T> Tm, and 0 for T< Tm By measuring the

production rate for many sample orientations and

energies, the damage function can be obtained using

in the deconvolution The results are illustrated

minimum threshold energy is located in the vicinity

of close-packed directions This is also true for bcc

metals The anisotropy reflects the basic mechanism

of defect production, viz., replacement collision

sequences (RCSs), which had been identified by

molecular dynamics simulations as early as 1960.18

The primary knock-on atom in an RCS recoils inthe direction of its nearest neighbor, h110i in fcccrystals, and replaces it, with the neighbor recoilingalso in theh110i and replacing its neighbor Avacancy

is left at the primary recoil site, and an interstitial iscreated at the end of the sequence Replacementsequences are the most efficient way to separatethe interstitial far enough from its vacancy, 2–3interatomic spacings, for the FP to be stable Whilethe lengths of these sequences are still debated, it isclear that the mechanism results in both defect pro-duction and atomic mixing For neutron irradiations,higher energy recoils are numerous, and the averagedisplacement energy, Ed, becomes more relevant forcalculations of defect production (seeeqn [1]) Thisvalue, which can be obtained by averaging over thethreshold displacement energy surface, is usually dif-ficult to determine experimentally A rough estimate,however, can be obtained from, Td  1.4Tm in fccmetals and 1.6Tmin bcc metals.19

1.07.4.1.2 Point defect properties

As FPs are produced in isolation during electronirradiation, the properties of single point defectsand their interactions with impurities and sinkscan be systematically investigated An example isshown in Figure 11(a), where the results of low-temperature isochronal annealing of Cu are shownfollowing 1.4 MeV electron irradiation at 6 K.20Recovery is observed to occur in ‘stages.’ These stud-ies have revealed that interstitial atoms becomemobile at very low temperatures, always below

100 K, in so-called Stage I, while vacancies becomemobile at higher temperatures, Stage III The varioussubstages IA–IEseen inFigure 11(a)arise from theinteraction between interstitial–vacancy pairs, whichare produced in close proximity Stage IE refers tothe free migration of interstitials in the lattice, awayfrom its own vacancy, and annihilation at distantvacancies; these interstitials are freely migrating asdiscussed earlier For comparison, Stage I annealing

of Cu following neutron irradiation is shown in

are suppressed during neutron irradiation, ing the dramatic difference in the defect productionprocess for these types of irradiation Similarly,annealing studies on electron-irradiated Al dopedwith Mg or Ga impurities are shown inFigure 12.22For these, it is observed that Stage I recovery issuppressed as interstitials trap at impurities and donot recombine The recovery at higher temperature,

illustrat-in Stage II, reveals distillustrat-inct subannealillustrat-ing stages

56 150

253 215 47

55 406 43 43 208 22

31 43 103

24 4

4

2 [110]

[100]

[111]

22

26 0 11

25

24

20 21 23 9 12

26 30 10 11

27

6

45 28

3

4 4 20 21 23 29

29

25 25 23

3

3 3

Figure 10 Displacement energy threshold surface for Cu.

The general anisotropy is typical of all fcc metals, although

specific values vary bcc metals show similar behavior of

minima along close-packed directions Reproduced from

King, W E.; Merkle, K L.; Meshii, M Phys Rev B 1981,

23, 6319.

These annealing stages are generally attributed to

either the interstitial dissociating from the impurity,

or the interstitial–impurity complex migrating to a

vacancy or a defect sink Migrating interstitial–solute

complexes lead to segregation A compilation of the

properties of point defects for many metals, and their

interactions with impurities can be found in Ehrhart.23

This information has played a crucial role in

develop-ing an understanddevelop-ing of radiation damage in more

complex engineering alloys and under more complex

irradiation conditions

1.07.4.2 Ion Irradiations

Ion irradiations are the most flexible method for

irradiating materials As discussed inSection 1.07.2,

the primary recoil spectrum can be shifted from near

threshold energies using low energy protons, to tens

of keV using MeV self-ions In addition, defect duction rates can be varied over many orders ofmagnitude, reaching values over0.1 dpa s
1 More-over, by using more than one ion beam, the primaryrecoil spectrum can be tailored to closely match thatproduced by an arbitrary fission neutron spectrum.1.07.4.2.1 The damage function

pro-Calculations of defect production, eqn [2], requireknowledge of the damage function, n(T ) While it isnot possible to measure this function directly, as noirradiation creates monoenergetic recoils except nearthe surface, it can be obtained by measuring defectproduction for a wide range of ion irradiations andsubsequently deconvoluting eqn [3] Low-energylight ions, for example, weight the recoil spectrumnear the threshold energy,25–100 eV, while moreenergetic heavy ions weight it at high energies.Results are shown for Cu inFigure 13 Here, electri-cal resistivity measurements are employed to monitorthe absolute number of FPs produced per unit dose

of irradiation Included in this figure are the damageefficiency function, x(T1/2), deduced from the experi-ments and x(T ) calculated using molecular dynamicscomputer simulation The damage efficiency function

is defined as

nðTÞ ¼ xðTÞnNRTðTÞ; ½20where nNRT(T ) is the NRT damage function defined

and simulations illustrates that the damage function

in Cu is now well understood This is now true formany other pure metals as well.24In alloys and ceramic

2.5 2.7 3.3 Dr°[nW cm]

Figure 12 Recovery of electrical resistivity in Al,

Al–0.06 at.% Ga, and Al–0.085 at.% Ga following 1 MeV

electron irradiation Reproduced from Garr, K R.; Sosin,

30

40 40

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 byFigure 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

Simi-lar experiments were performed using

radiation-enhanced diffusion, as described inSection 1.07.2

While ion irradiation has proved extremely useful

in illustrating the spectral effects on freely migrating

defects, extracting quantitative information aboutfreely migrating defects from such experiments isdifficult These measurements, unlike the damagefunction, require very high doses, and several dpa;the buildup of the sink structure must be adequatelytaken into account It is also difficult to estimate,for example, how many interstitials are required totransport one Si atom to the surface We mention inpassing that experiments performed using orderingkinetics in order–disorder alloys have provided amore direct measure of the number of freely migrat-ing defects (vacancies in this case), as these experi-ments require doses less than10
7dpa so that nodamage build-up can occur.25 These experimentsshow similar effects of primary recoil spectrum onthe fraction of freely migrating defects, although thefractions of such defects were found to be somewhathigher in these experiments, 5–10% These frac-tions are in good agreement with radiation-enhanceddiffusion experiments using self-ions on Ni, when theeffect of sink strength is taken into account.26

1.07.4.2.3 Alloy stability under ion irradiationIrradiation of materials with energetic particles drivesthem from equilibrium, and in alloys, this becomesmanifest in a number of ways One of them concernsnonequilibrium segregation The creation of largesupersaturations of point defects leads to persistentdefect fluxes to sinks In many cases, these point defectfluxes couple with solutes, resulting in either theenrichment or depletion of solutes at these sinks.This effect was first discovered by using in situ electron

1.0 0.8 0.6

2 MeV He

1 MeV H

2 MeV Li

3 MeV Ni 3.25 MeV Kr

Okamoto, P R.; Averback, R S Phys Rev 1984, B30, 3073.

He Li C NO Ne

Ar Fe Cu

Cu Experiment Calculation

Kr AgBi FF FN

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,

T 1/2 (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.