Thus far, we have considered both structural and electronic defects. In addition, we have derived the relationship between oxygen vacancies and the oxy­gen partial pressure, Po2 , which gives rise to nonstoi­chiometry. It should therefore not come as any surprise that we now consider the equilibrium between isolated structural defects, electronic de­fects, and Po2. Of course, we have also considered the equilibrium that exists between isolated struc­tural defects and defect clusters, but defect clusters will not be considered in the present context. Nevertheless, defect clustering does play an impor­tant role in the equilibrium between electronic and structural defects and cannot, in a research context, be ignored.

In solving defect equilibria in previous sections, we have generally ignored the role that minority defects might have. For example, when considering Schottky disorder in MgO, which we know from experiments is the dominant defect formation pro­cess, the effect that oxygen interstitials might have was not taken into account.2 This is certainly reason­able within the context of determining the oxygen vacancy concentration of MgO. The oxygen vacancy concentration is the important parameter to know when predictions of the oxygen diffusivity in MgO are required. However, minority defects may well play an important role in other physical processes. For example, the electrical conductivity or resistivity will depend on the hole or electron concentration; these may be minority defects compared to oxygen vacancies, but understanding them is nevertheless crucial. Thus, we must be concerned with four different defect processes2 simultaneously:

1. The dominant intrinsic structural disorder process (e. g., Schottky or Frenkel).

2. The intrinsic electronic disorder reaction.

3. The REDOX reaction.

4. Dopant and impurity effects.

Again we begin by considering MgO.6 If we ignore impurity effects, the three reactions are2

MgMg+og ! v(Mg+VO*+MgO Ks = [vmJ [vo*]

Null! e’ + h* Kele = [e’] [h*]

Og! І02 + VO* + 2e’ Kredox = pO=2 [e’]2 [vo*]

These equations contain six unknown quantities: four are defect concentrations, the other two vari­ables are the Po2 and the temperature, which are experimental variables and are thus given. Of course, we must know the enthalpies of the defect reactions. Nevertheless, to solve these equations simultaneously, we need a further relationship. This is provided by the electroneutrality condition, which, for MgO states that2

2[vm J +[e’]= 2[VO*] + [h*]

To make the problem more tractable, we now intro­duce the Brouwer approximations, which simplify the form of the electroneutrality condition. These effectively concern the availability of defects via the partial pressure of oxygen. For example, if the Po2 is very low, the REDOX reaction equilibrium will require that the [VO*] and [e’] concentrations are relatively high so that these are the dominant positive and negative defect concentrations. Therefore, for low Po2,2

[e’] = 2 [VO*]

Conversely at high Po2, both oxygen vacancies and their charge-compensating electrons must have rela­tively low concentrations and therefore, the electro­neutrality condition becomes dominated by the [VmJ and [h*] defects so that2

[h*]= [VMg]

Between these two regimes, the Brouwer approxima­tion depends on whether structural or electronic defects dominate. In the case of MgO, we know that Schottky disorder dominates over electronic disorder (as it is a good insulator) and therefore, at intermedi­ate values of Po2, the appropriate electroneutrality condition is

[VO*] = [VMg]

If the electronic disorder was dominant, this last reaction would be replaced by

[e’] = [h*]

We are now in a position to be able to construct a Brouwer diagram, which is usually in the form of ln (defect concentration) versus lnPO2 for various defect components at a constant temperature. In the case of MgO, as indicated above, the diagram will clearly

Neutrality condition

2[V0] = [e’j [V0′] = [V M] [H]=2[VM]

have three regimes corresponding to the three Brouwer conditions (refer to Figure 18 and Chiang

et at2).

Several different cavity geometries are created in irradiated materials. For helium-filled bubbles, the cavity shape is typically spherical. For voids, faceted cavities with faces corresponding to low-index crys­tallographic planes are often created, e. g. truncated {111} octahedra or {001} cubes in fcc materials, truncated {110} dodecahedra or {001} cubes in bcc materials, and more complex shapes in HCP materials,21,22,340-342 although nearly spherical shapes are also sometimes observed for voids. When helium is generated during irradiation (due to neutron — induced transmutation reactions, etc.), a bimodal cav­ity distribution is usually observed with the small cavities corresponding to helium-filled bubbles and the large cavities corresponding to underpressurized voids. The critical radius transition between bubbles and voids is determined by a balance between disloca­tion bias-induced vacancy influx and pressure-modified thermal emission of vacancies.120,151,208,274,343 Figure 38
shows an example of large faceted voids and small helium-filled spherical bubbles in a neutron — irradiated copper-boron alloy.107 The visible cavity density usually increases rapidly at low doses, and approaches a constant value for damage levels above ~ 1—50 dpa. The void size tends to increase continu­ously with increasing dose.

Well-developed periodic void lattices have been observed in several irradiated materials.297,344,345 Void lattice formation has most frequently been observed in bcc materials, but periodically aligned void struc­tures have also been observed in HCP272,346,347 and fcc303,348-351 materials. Aligned voids have been observed in both metals and ceramic insulators. The aligned cavities in HCP materials are usually mani­fested as one — or two-dimensional arrays perpendicu­lar or parallel to the basal plane, respectively.297,346 The void lattices in bcc and fcc materials adopts the same three-dimensional crystallographic symmetry as the host lattice.297 The swelling levels in bcc metals with well-developed void lattices are typically a few percent, which has led to hypotheses that void lattice formation may coincide with a cessation in steady — state swelling.117,352 The saturation in void swelling is associated with achieving a constant average void size. Figure 39 shows an example of a well-developed bcc void lattice in ion-irradiated Nb—1Zr.353 In the study by Loomis et al. it was reported that void lattice formation did not occur unless a threshold level of oxygen was present (60—2700 appm oxygen, depending on the irradiated material).

1.03.5 Summary

Radiation-induced microstructural modifications can create large changes in the physical and mechanical properties of materials, as detailed in accompanying chapters in this book. The two most important extrin­sic variables that influence microstructural evolution under irradiation are the radiation damage level and temperature. Many similarities are observed for diverse materials and irradiation spectra if the com­parisons are performed at comparable damage levels and defect mobility regimes (defect recovery stages). The PKA energy often exerts a significant influence on the microstructural evolution, in particular by inducing direct cascade amorphization or creation of defect clusters within displacement cascades when the PKA energy exceeds a threshold energy value. Numerous other parameters such as dose rate, crystal structure, and atomic weight typically exert less pronounced influence on microstructural evolu­tion, although very large qualitative and quantitative effects can be observed under some circumstances.

Acknowledgments

Much of the author’s work discussed in this chapter was sponsored by the U. S. Department of Energy, Office of Fusion

The effects of high He levels on microstructure and mechanical properties have been extensively studied in mixed fast-thermal spectrum fission reactor irradia­tions of alloys naturally containing, or doped with, Ni and B. In these cases, high He levels are produced by thermal neutron nth, a reactions, either by (a) the two-step reaction with 58Ni(nth, g) («68% of elemental Ni with a nth, g cross-section of «0.7 barns) and 59Ni
(nth, a) (bred from 58Ni with a n, a cross-section of «10 barns) cited in Section 1.06.1; (b) or by the 10B + nth! 7Li + a reaction («20% of elemental B with a cross-section of «4010 barns) (1 barn = 10-24 cm2). Significant quantities of He can also be generated by epithermal-fast spectrum neutron reac­tions with B as well as prebred 59Ni.29

Figure 4(a) shows calculated and measured He production in natural Ni in the HFIR target capsule position.30 Figure 4(b) shows the corresponding He/dpa ratio for a Fe alloy doped with 2% natural Ni. Two Ni doping characteristics are evident: (a) there is a transient phase in He production regime prior to a He/dpa peak at about «20dpa in HFIR; (b) if the alloy contains more than a few percent Ni, like in AuSS, the He/dpa is much higher than that for fast fission and higher than that for fusion spectra but is comparable to, or slightly less than, the He/dpa for SPNI.

Modifying the amounts of 58Ni and 60Ni (isotope tailoring) can control and target He/dpa ratios (e. g., to fusion). , , An approximately constant He generation rate can be obtained by using irra­diated Ni pre-enriched in 59Ni.29,31 Various amounts of 58Ni, 59Ni, and 60Ni can also be used to control the He/dpa ratio in fast spectrum reactors, like the Fast Flux Test Facility (FFTF), as well as in mixed spec­trum reactors, like HFIR.29,31,32

Boron is not normally added to steels used for nuclear applications, but it has been used in a number of doping studies.33,34 A major advantage of B doping is that significant amounts of He are produced by the 10B, but not the 11B, isotope. Thus, the effect of doping with 10B versus 11B can be used to isolate this effect of

He, in a B-containing alloy. However, the issues asso­ciated with B doping are even more problematic than those for Ni. In mixed spectrum reactors, all the 10B is quickly converted to He and Li by the thermal neutrons. In this case, the He is initially introduced at much too high a rate per dpa but then saturates at the 10B content. The other major limitations are that B is virtually insoluble in steels and primarily resides in Fe and alloy boride phases.35 Boron also segregates to GBs. Thus, He from B reactions is not homo­geneously distributed. Recently, nitrogen additions to FMS steels to form fine-scale BN phases have been used to increase the homogeneity of B and He distributions.36

Varying the He/dpa ratio in Ni — and B-containing alloys can also be achieved by attenuating thermal neutron fluxes (spectral tailoring) in mixed spectrum reactors as well as selecting appropriate fast reactor irradiation positions.31,37,38 Spectral tailoring, either by attenuating thermal neutrons or irradiating in epithermal-fast reactor spectra, is especially helpful in B doping. , ,

However, doping alloys that do not normally con­tain Ni or B can affect both their properties and microstructures, including their response to He and displacement damage. For example, transformation kinetics during heat treatments (hardenability) and the baseline properties of FMS are strongly affected by both Ni and B. Ni also has a strong effect on refining irradiation-induced microstructures and enhancing irradiation hardening.20, 1 As noted previously, to some extent these confounding factors can be evalu­ated by comparing the effects of various amounts of 10B/11B45 and 58Ni/60Ni. However, doped alloys are inherently ‘different’ from those of direct interest. Note that excess dpa due to n, a reaction recoils must be accounted for,46 and in the case of B doping the Li reaction product may play some role as well.

The free energy of a void or bubble, according to eqn [127], depends now on three surface parameters instead of just one as in eqn [105]: it depends on the surface energy g0 of a planar surface, on the residual surface strain e for such a planar surface, and on the
biaxial surface stretch modulus 2(ms + Is). As men­tioned above, the latter has the dimension of N m— , and we may then relate it to the corresponding bulk modulus 2mM/(1—2vM) by multiplying the latter with a surface layer thickness parameter h. The surface energy g0 has been determined both experimentally and from ab initio calculations and can be considered as known. The surface layer has been determined by Hamilton and Wolfer10 from atomistic simulations on Cu thin films to be one monolayer thick; hence d — b. A value for the residual surface strain parameter e* has been chosen in Section 1.01.3.1 such that it reproduces the relaxation volume of a vacancy according to eqn [11].

What if one selects the same value for voids con­taining n vacancies? The relative relaxation volume, that is, the ratio НП^/(пО) — 3e(R(n)), can now be computed with eqn [123] and the results are shown in Figure 23 by the solid curve. As it must, for n — 1 it reproduces the vacancy relaxation volume of—0.25 O. In addition, it also agrees with the overall trend of the atomistic results of Shimomura.48 Of course, the atomistic results for small vacancy cluster vary in a discontinuous manner with the cluster size. The sur­face stress model gives not only a reasonable approx­imation to these atomistic results, but also a valid extrapolation to relaxation volumes of large voids.

The chemical potential of vacancies for voids can now be computed with eqn [127] as Fc(R(n + 1)) — Fc(R(n)). Figure 24 shows the results for Ni as the solid curve. The vacancy chemical potentials for

voids are significantly lower than the capillary approximation predicts with a fixed surface energy (dashed curve). The chemical potentials from atom­istic simulations of voids in Ni have been obtained by Adams and Wolfer49 using the Ni-EAM potential of Foiles et a/.50 These results converge to those pre­dicted with the surface stress model.

The typical microstructural features that appear dur­ing irradiation at temperatures above recovery Stage V include dislocation loops (vacancy and interstitial type), network dislocations, and cavities. SFTs are thermally unstable in this temperature regime and therefore only SFTs created in the latter stages of the irradiation exposure are visible during postirradiation examination.94 A variety of precipitates may also be nucleated in irradiated alloys.11,103-106 Defect cluster accumulation in this temperature regime exhibits

several different trends. The visible SIA clusters evolve from a low density of small loops to a saturation density of larger loops after damage levels of ~1-10dpa. Upon continued irradiation, a moderate density of network dislocations is created due to loop unfault­ing and coalescence. The dislocation loop and net­work dislocation density monotonically decrease with increasing temperature above recovery Stage V,20,107 whereas the density of precipitates (if present) can either increase or decrease with increasing temperature.

The major microstructural difference from lower temperature irradiations in most materials is the emer­gence of significant levels of cavity swelling. After an initial transient regime associated with cavity nucle — ation, a prolonged linear accumulation of vacancies into voids is typically observed.10 ,109 The cavity den­sity monotonically decreases with increasing tempera­ture in this temperature regime. figure 12

summarizes the densities of voids and helium bubbles (associated with n, a transmutations) in austenitic stain­less steel as a function of fission reactor irradiation temperature for damage rates near 1 x 10~6dpas~12° The bubble and void densities exhibit similar tem­perature dependences in fission reactor-irradiated austenitic stainless steel, with the bubble density ap­proximately one order of magnitude higher than the void density between 400 and 650 °C. For neutron-
irradiated copper and Cu-B alloys, the bubble den­sity is similarly observed to be about one order of magnitude larger than the void density for tem­peratures between 200 and 400 °C.107,110 At higher temperatures, the void density in copper decreases rapidly and becomes several orders of magnitude smal­ler than the bubble density. The results from several studies suggest that the lower temperature limits for formation of visible voids111-113 and helium bubbles53 can each be reduced by 100 °C or more when the damage rate is decreased to 10~9-10~8 dpas-1, due to enhanced thermal annealing of sessile vacancy clusters during the time to achieve a given dose. Dose rate effects are discussed further in Section

1. 03.3.7.

The void swelling regime for fcc materials typically extends from 0.35 to 0.6 TM, where TM is the melting temperature, with maximum swelling occurring near 0.4-0.45 TM for typical fission reactor neutron damage rates of 10~6dpas~192,114 Figure 13 summarizes the temperature-dependent void swell­ing for neutron-irradiated copper.110 The results for a neutron-irradiated Cu-B alloy, where ^100 atomic parts per million (appm) He was produced during the 1 dpa irradiation due to thermal neutron trans­mutation reactions with the B solute, are also shown in this figure.107 For both materials the onset

0.7 0.6 0.5

g

0.4

c

03

-C

О

°.з

c

Ф

Q

0.2 0.1 0

150 200 250 300 350 400 450 500 550

Irradiation temperature (°C)

Figure 13 Temperature-dependent void swelling behavior in neutron-irradiated copper and Cu-B alloy after fission neutron irradiation to a dose near 1.1 dpa. Adapted from Zinkle, S. J.; Farrell, K.; Kanazawa, H. J. Nucl. Mater. 1991, 179-181, 994-997; Zinkle, S. J.; Farrell, K. J. Nucl. Mater. 1989, 168, 262-267.

of swelling occurs at temperatures near 180 °C, which corresponds to recovery Stage V in Cu for the 2 x 10~7dpa s-1 damage rates in this experiment.

The swelling in Cu was negligible for temperatures above ^500 °C, and maximum swelling was observed near 300 °C. The lower temperature limit for swelling in fcc materials is typically controlled by the high point defect sink strength of sessile defect clusters below recovery Stage V. The upper temperature limit is controlled by thermal stability of voids and a reduction in the vacancy supersaturation relative to the equilibrium vacancy concentration.

As noted by Singh and Evans,92 the temperature dependence of the void swelling behavior of bcc and fcc metals can be significantly different. In par­ticular, due to the lower amount of in-cascade forma­tion of large sessile vacancy clusters in medium-mass bcc metals compared to fcc metals, the recovery Stage V is much less pronounced in bcc metals. The presence of a high concentration of mobile vacancies at temperatures below recovery Stage V (and a concomi­tant reduction in the density of sessile vacancy-type defect cluster sinks) allows void swelling to occur in bcc metals for temperatures above recovery Stage III (onset of long-range vacancy migration). Figure 14 compares the temperature dependence of the void swelling behavior of Ni (fcc) and Fe (bcc) after high dose neutron irradiation.11 Whereas the peak

occur near 0.3-0.35 TM,116,117 which is much lower than the 0.4-0.45 TM peak swelling temperature ob­served for fcc metals.

K. E. Sickafus

University of Tennessee, Knoxville, TN, USA © 2012 Elsevier Ltd. All rights reserved.

1.05.1. Introduction 123

1.05.2. Radiation Effects in Ceramics: A Case Study — a-Alumina Versus Spinel 124

1.05.2.1 Introduction to Radiation Damage in Alumina and Spinel 124

1.05.2.2 Point Defect Evolution and Vacancy Supersaturation 125

1.05.2.3 Dislocation Loop Formation in Spinel and Alumina 127

1.05.2.3.1 Introduction to atomic layer stacking 127

1.05.2.3.2 Charge on interstitial dislocations 127

1.05.2.3.3 Lattice registry and stacking faults I: (0001) Al2O3 129

1.05.2.3.4 Lattice registry and stacking faults II: {111} MgAl2O4 129

1.05.2.3.5 Lattice registry and stacking faults III: {1010} Al2O3 130

1.05.2.3.6 Lattice registry and stacking faults IV: {110} MgAl2O4 130

1.05.2.3.7 Unfaulting of faulted Frank loops I: (0001) Al2O3 131

1.05.2.3.8 Unfaulting of faulted Frank loops II: {111} MgAl2O4 132

1.05.2.3.9 Unfaulting of faulted Frank loops III: {1010} Al2O3 132

1.05.2.3.10 Unfaulting of faulted Frank loops IV: {110} MgAl2O4 133

1.05.2.3.11 Unfaulting of faulted Frank loops V: experimental observations 133

1.05.2.4 Amorphization in Spinel and Alumina 134

1.05.3. Radiation Effects in Other Ceramics for Nuclear Applications 136

1.05.3.1 Radiation Effects in Uranium Dioxide 136

1.05.3.2 Radiation Effects in Silicon Carbide 136

1.05.3.3 Radiation Effects in Graphite 137

1.05.3.4 Radiation Effects in Other Ceramics 138

1.05.4. Summary 138

References 139

Abbreviations

dpa Displacements per atom BF Bright-field

TEM Transmission electron microscopy

i Interstitial

v Vacancy

ccp Cubic close-packed

hcp Hexagonal close-packed

SHI Swift heavy ion

PKA Primary knock-on atom

CVD Chemical vapor deposition

1.05.1. Introduction

Ceramic materials are generally characterized by high melting temperatures and high hardness values. Ceramics are typically much less malleable than metals and not as electrically or thermally conduc­tive. Nevertheless, ceramics are important materials in fission reactors, namely, as constituents in nuclear fuels, and are widely regarded as candidate materials for fusion reactor applications, particularly as electri­cal insulators in plasma diagnostic systems. These applications call for highly robust ceramics, materials that can withstand high radiation doses, often under very high-temperature conditions. Not many cera­mics satisfy these requirements. One of the purposes of this chapter is to examine the fundamental mechanisms that lead to the relative radiation toler­ance of a select few ceramic compounds, versus the susceptibility to radiation damage exhibited by most other ceramics.

Ceramics are, by definition, crystalline solids. The atomic structures of ceramics are often highly complex compared with those of metals. As a conse­quence, we lack a detailed understanding of atomic processes in ceramics exposed to radiation. Never­theless, progress has been made in recent decades in understanding some of the differences between radi­ation damage evolution in certain ceramic com­pounds. In this chapter, we examine the radiation damage response of a select few ceramic compounds that have potential for engineering applications in nuclear reactors. We begin by comparing and contrasting the radiation damage response of two particular (model) ceramics: a-alumina (Al2O3, also known as corundum in polycrystalline form, or ruby or sapphire in single crystal form) and magnesio- aluminate spinel (MgAl2O4). Under neutron irradia­tion, alumina is highly susceptible to deleterious microstructural evolution, which ultimately leads to catastrophic swelling of the material. On the other hand, spinel is very resistant to the microscopic phenomena (particularly nucleation and growth of voids) that lead to swelling under neutron irradiation. We consider the atomic and microstructural mechan­isms identified that help to explain the marked dif­ference in the radiation damage response of these two important ceramic materials. The fundamental prop­erties of point defects and radiation-induced defects are discussed in Chapter 1.02, Fundamental Point Defect Properties in Ceramics, and the effects of radiation on the electrical properties of ceramics are presented in Chapter 4.22, Radiation Effects on the Physical Properties of Dielectric Insulators for Fusion Reactors.

It is important to be cognizant of the irradia­tion conditions used to produce a particular radiation damage response. Microstructural evolution can vary dramatically in a single compound, depending on the following irradiation parameters: (1) irradiation source-irradiation species and energies — these give rise to the so-called ‘spectrum effects,’ (2) irradia­tion temperature, (3) irradiation particle flux, and (4) irradiation elapsed time and particle fluence. Throughout this chapter, we pay particular attention to the variations in radiation damage effects due to differences in irradiation parameters. A single ceramic material can exhibit radiation tolerance under one set of irradiation conditions, while alter­natively exhibiting damage susceptibility under another set of conditions. A good example of this is MgAl2O4 spinel. Spinel is highly radiation tolerant in a neutron irradiation environment but very suscepti­ble to radiation-induced swelling when exposed to swift heavy ion (SHI) irradiation.

Finally, it is important to note that radiation tolerance refers to two distinctly different criteria: (1) resistance to a crystal-to-amorphous phase trans­formation; and (2) resistance to dislocation and void nucleation and growth. Both of these phenomena lead (usually) to macroscopic swelling of the material, but the causes of the swelling are completely different. The irradiation damage conditions that produce these two materials’ responses are also typically very differ­ent. We examine these two radiation tolerance criteria through the course of this chapter.

The results of experimental studies on He embrittle­ment ofAuSS are broadly consistent with the concepts described here. However, the literature for neutron irradiations is much more limited than in the case of microstructural evolution and matrix swelling, especially for the most pertinent data from reliable in­reactor creep rupture tests. Indeed, there is little quan­titative characterization of grain boundary cavity and other microstructures for neutron-irradiated alloys. The most consistent trend for neutron irradiations is that high-temperature postirradiation tensile tests show significant to severe reductions in tensile ductility and creep rupture times and IG rupture along GBs.11

As noted above, there is a much more significant body of work for well-characterized high-energy He ion implantation studies. Helium can be preimplanted at various temperatures and further subjected to vari­ous postimplantation annealing treatments, prior to tensile or creep testing, or simultaneously with creep testing. The different modes of He implantation result in very different creep rupture behavior.90 Helium implantation during high temperature in-beam creep is perhaps the most relevant, controlled, and systematic approach to studying HTHE. A series of implantation studies carried out at the Research Center Julich in Germany, coupled with the models described above, are the most comprehensive and insightful examples of this research.90’91’99’100’192’199-201 Figure 22(a) shows the mean trend lines for tr versus applied stress for SA 316SS at 1023 K for in-beam creep’ at an implantation rate of 100 appm He/h’ compared with unimplanted controls.90 Clearly’ HTHE leads to a very large reduction in the tr especially at lower stress. The stress power is rк4 for the in-beam creep condition’ compared with к 9 for the unimplanted control. Figure 22(b) shows a corresponding plot for a Ti-modified AuSS (DIN 1.4970) in-beam creep tested at 1073 K.90 HTHE is observed’ but the magni­tude of the reduction in tr is less in this case. The stress power in-beam creep condition is rк 2.85 compared with 5.7 for the control. As expected’ HTHE also reduces er; in the case of Ti-modified steel’ er decreases from к 10% to 1%90 and for the annealed 316SS from more than 30% to 1% or less.99 Similar

comparisons for a test of these two alloys at 873 K also show severe reductions in tr and er in 316SS, whereas there is a much smaller effect in the Ti-modified AuSS.192 This work also showed that the Ti-modified alloy is much stronger in CW condi­tion and suffers only moderate HTHE.

Helium implantation of unstressed specimens at 1023 K to levels between 10 and 1000 appm was used to evaluate the critical bubble size resulting in rapid rupture in subsequent creep tests at the same tem — perature.9 A rapid drop-off in tr and er occurred between 300 and 1000 appm at a stress of 90 MPa. This He concentration correlated with an average grain boundary bubble size of ~13-17nm, which provides a reasonable estimate of the corresponding critical bubble size for these conditions.

However, it must be emphasized that in-beam creep tests do not ‘simulate’ neutron-irradiation con­ditions since the He implantation rates are highly accelerated and yield very high He/dpa ratios. Further, the duration of these tests is limited by schedules of the ion accelerators. The in-beam creep data show that the tr and er decrease with decreasing implantation rates scaling as « G^3 (Schroeder et at91 and see previous discussion). This may be due to the effect of GHe on the number density of matrix bubbles that help shield GBs from He accumulation, as suggested by in eqn [16]. Indeed, matrix bubble densities, Nb, in 316SS increase with the concentration of He preimplanted at 1023 K, scaling as « XH{2 at greater than 100 appm He.

The corresponding number of grain boundary bubbles, Ngb, is insensitive to XHe. 9 Of course, the scaling applies only to high implantation rates that result in significant He concentrations at all GHe. A more relevant scaling law would be based on the He required for creep rupture (XHer), which also scales with tr, as

XHer / tr / GHe [17]

The in-beam creep tests suggest that q« 1/3. Thus, for example, if tr = 10 h at XHe = 1000 appm (see above), for in-beam creep tests, this scaling predicts tr« 2700 h at XHe « 60 appm for He generated at fusion reactor rates of 200 appm year- . Note that this is not a reliable absolute estimate of the creep rupture time since the in-beam irradiation experi­ments involved very thin specimens (0.1 mm).

Figure 23 shows tr versus stress for in-reactor creep tests at 993 K under neutron irradiation. The corresponding ‘control’ curve at 993 K is based on a logarithmic interpolation between curves for

specimens preimplanted with up to 80 appm He at ambient temperature and tested at 973 and 1073 K. Note that data at 1073 K suggest that at such low — temperature preimplantation has little effect on tr. Severe HTHE is again observed in this case at stresses below about 200 MPa for in-reactor creep conditions.

The key results of these studies can be summar­ized as follows:

• High implantation rates of the order 100 appm h-1 result in the formation of a high number density of bubbles in the matrix and on GBs up to and in excess of 1015 m-2.

• Matrix and grain boundary bubbles form both as isolated cavities as well as in association with other features such as second-phase particles, disloca­tions and grain edges, and triple points.

• Essentially all the implanted He precipitates in bubbles.

• Matrix bubbles influence the amount of He flow­ing to GBs.

• The grain boundary bubbles grow stably with the addition of He, until some reach the critical size where they convert to stress-driven growing creep cavities.

• Postimplantation tests at 90 MPa and 750 °C for a wide range of He contents suggest a critical size of 13-17 nm.

• Creep cavity growth and coalescence kinetics are rapid, and tr is dominated by the time needed to establish a population of bubbles and grow (gas driven) them to the critical size.

• The creep rupture time is generally lower for implantation coincident with creep, compared to preimplantation followed by creep testing.

• The stress power r relating rupture time and the applied stress (tr / a^r) is decreased for in-beam and in-reactor creep tests, with r« 2-4 when com­pared with postimplantation and unimplanted values of r« 6-9.

• The tr and XHer decrease with decreasing He gen­eration rates with a scaling law « GH^.

• However, significant He is required to cause HTHE in all cases.

• Alloys with fine-scale matrix and grain boundary precipitates (e. g., TiC) that trap He in a larger number of smaller bubbles mitigate HTHE.

• The CBM also rationalizes the degradation of high-temperature fatigue properties at high He levels.91,99,204

The implantation studies show that HTHE is most severe in conventional AuSS, like 316SS, that contain only coarse carbides. Fine-scale TiC (and phosphide) phases that trap He in a high density of fine- scale matrix bubbles n90,192,203-205 provide greatly enhanced HTHE resistance. Key issues are optimiz­ing the ability of the precipitates to trap He in small bubbles and ensuring their thermal and irradiation stability needed for long-term service. Note that a fine-scale matrix also increases the strength of AuSS alloys, thus enhancing creep constraint reductions of cavity growth rates; and fine grain boundary phases can also impart further resistance to grain boundary cavitation. Indeed, Maziasz and coworkers extended these concepts to developing a new series of AuSS alloys with remarkable unirradiated creep strength (in terms ofboth creep rates and rupture times) based on precise control of microalloyed fine-scale matrix and grain boundary phases.206

A number ofstudies have also shown that the FMS are very resistant to HTHE as well as void swelling.12,13,192,201,207 The most obvious explanation is that the sink densities and numerous trapping sites for He keep bubbles finely distributed and protect prior austenite GBs from He accumulation.176 Lath boundaries may be especially effective if, due to their special nature, they are effective in trapping He in small bubbles, but at the same time, resistant to cavity growth by vacancy accumulation. However, it has been suggested that the bubble microstructures are not that dissimilar in AuSS and FMS and that at least part of the difference in the HTHE sensitivity is that the FMS are inherently weaker at the same tempera­tures and that the corresponding lower grain bound-

12,199

ary stresses increase m.

Several fundamental attributes and properties of crystal defects in metals play a crucial role in radiation effects and lead to continuous macroscopic changes of metals with radiation exposure. These attributes and properties will be the focus of this chapter. However, there are other fundamental properties of defects that are useful for diagnostic purposes to quantify their concentrations, characteristics, and interactions with each other. For example, crystal defects contribute to the electrical resistivity of metals, but electrical resis­tivity and its changes are of little interest in the design and operation of conventional nuclear reactors. What determines the selection of relevant properties can best be explained by following the fate of the two most important crystal defects created during the primary event of radiation damage, namely vacancies and self-interstitials.

The primary event begins with an energetic parti­cle, a neutron, a high-energy photon, or an energetic ion, colliding with a nucleus of a metal atom. When sufficient kinetic energy is transferred to this nucleus or metal atom, it is displaced from its crystal lattice site, leaving behind a vacant site or a vacancy. The recoiling metal atom may have acquired sufficient energy to displace other metal atoms, and they in turn can repeat such events, leading to a collision cascade. Every displaced metal atom leaves behind a vacancy, and every displaced atom will eventually dis­sipate its kinetic energy and come to rest within the crystal lattice as a self-interstitial defect. It is immedi­ately obvious that the number of self-interstitials is exactly equal to the number of vacancies produced, and they form Frenkel pairs. The number of Frenkel pairs created is also referred to as the number of displacements, and their accumulated density is expressed as the number of displacements per atom (dpa). When this number becomes one, then on aver­age, each atom has been displaced once.

At the elevated temperatures that exist in nuclear reactors, vacancies and self-interstitials diffuse through the crystal. As a result, they will encounter each other, either annihilating each other or forming vacancy and interstitial clusters. These events occur already in their nascent collision cascade, but if defects escape their collision cascade, they may encounter the defects created in other cascades. In addition, migrat­ing vacancy defects and interstitial defects may also be captured at other extended defects, such as disloca­tions, cavities, grain boundaries and interface bound­aries of precipitates and nonmetallic inclusions, such as oxide and carbide particles. The capture events at these defect sinks may be permanent, and the migrat­ing defects are incorporated into the extended defects, or they may also be released again.

However, regardless of the complex fate of each individual defect, one would expect that eventually the numbers of interstitials and vacancies that arrive at each sink would become equal, as they are pro­duced in equal numbers as Frenkel pairs. Therefore, apart from statistical fluctuations of the sizes and positions of the extended defects, or the sinks, the microstructure of sinks should approach a steady state, and continuous irradiation should change the properties of metals no further.

It came as a big surprise when radiation-induced void swelling was discovered with no indication of a saturation. In the meantime, it has become clear that the microstructure evolution of extended defects and the associated changes in macroscopic properties of metals in general is a continuing process with dis­placement damage.

The fundamental reason is that the migration of defects, in particular that of self-interstitials and their clusters, is not entirely a random walk but is in subtle ways guided by the internal stress fields of extended defects, leading to a partial segregation of self-interstitials and vacancies to different types ofsinks.

Guided then by this fate of radiation-produced atomic defects in metals, the following topics are presented in this chapter:

1. The displacement energy required to create a Frenkel pair.

2. The energy stored within a Frenkel pair that con­sists of the formation enthalpies of the self­interstitial and the vacancy.

3. The dimensional changes that a solid suffers when self-interstitial and vacancy defects are created,
and how these changes manifest themselves either externally or internally as changes in lattice parameter. These changes then define the forma­tion and relaxation volumes of these defects and their dipole tensors.

4. The regions occupied by the atomic defects within the crystal lattice possess a distorted, if not totally different, arrangement of atoms. As a result, these regions are endowed with different elastic proper­ties, thereby changing the overall elastic constants of the defect-containing solid. This leads to the concept of elastic polarizability parameters for the atomic defects.

5. Both the dipole tensors and elastic polarizabilities determine the strengths of interactions with both internal and external stress fields as well as their mutual interactions.

6. When the stress fields vary, the gradients of the interactions impose drift forces on the diffusion migration of the atomic defects that influences their reaction rates with each other and with the sinks.

7. At these sinks, vacancies can also be generated by thermal fluctuations and be released via diffusion to the crystal lattice. Each sink therefore possesses a vacancy chemical potential, and this potential determines both the nucleation of vacancy defect clusters and their subsequent growth to become another defect sink and part of the changing microstructure of extended defects.

The last two topics, 6 and 7, as well as topic 1, will be

further elaborated in other chapters.

where mc2 is the rest energy of an electron and Л — 4 mM/(m + M) . The approximation on the right is adequate because the electron mass, m, is much smaller than the mass, M, of the recoiling atom.

Changing the direction of the electron beam in relation to the orientation of single crystal film speci­mens, one finds that the threshold energy varies significantly. However, for polycrystalline samples, values averaged over all orientations are obtained, and these values are shown in Figure 1 for different metals as a function of their melting temperatures.1

First, we notice a trend that Td increases with the melting temperature, reflecting the fact that larger energies of cohesion or of bond strengths between atoms also lead to higher melting temperatures.

We also display values of the formation energy of a Frenkel pair. Each value is the sum of the corresponding formation energies of a self-interstitial and a vacancy for a given metal. These energies are presented and further discussed below. The important point to be made here is that the displacement energy required to create a Frenkel pair is invariably larger than its formation energy. Clearly, an energy barrier exists for the recoil process, indicating that atoms adjacent to the one that is being displaced also receive some additional kinetic energy that is, however, below the displacement energy Td and is subsequently dissipated as heat.

The displacement energies listed in Table 1 and shown in Figure 1 are averaged not only over crystal orientation but also over temperature for those metals

50

where the displacement energy has been measured as a function of irradiation temperature. For some mate­rials, such as Cu, a significant decrease of the dis­placement energy with temperature has been found. However, a definitive explanation is still lacking. Close to the minimum electron energy for Frenkel pair production, the separation distance between the self-interstitial and its vacancy is small. Therefore, their mutual interaction will lead to their recombina­tion. With increasing irradiation temperature, however, the self-interstitial may escape, and this would mani­fest itself as an apparent reduction in the displacement energy with increasing temperature. On the other hand, Jung2 has argued that the energy barrier involved in the creation of Frenkel pairs is directly dependent on the temperature in the following way. This energy barrier increases with the stiffness of the repulsive part of the interatomic potential; a measure for this stiffness is the bulk modulus. Indeed, as Figure 2 demonstrates, the displacement energy increases with the bulk mod­ulus. Since the bulk modulus decreases with tempera­ture, so will the displacement energy.

The correlation of the displacement energy with the bulk modulus appears to be a somewhat better

empirical relationship than the correlation with the melt temperature. However, one should not read too much into this, as the bulk modulus B, atomic

volume O, and melt temperature of elemental metals approximately satisfy the rule

BO « 100kBTm

discovered by Leibfried3 and shown in Figure 3.

A. Chroneos

University of Cambridge, Cambridge, UK

M. J. D. Rushton and R. W. Grimes

Imperial College of Science, London, UK

© 2012 Elsevier Ltd. All rights reserved.

of greater spatial extent, such as dislocations and grain boundaries, in greater detail; here, however, we begin by comparing them with point defects.

Thermal and electrical conductivity degradation can occur over a wide range of irradiation temperatures. For pure metals, there are two primary contributions: electron scattering from point defects (and associated defect clusters) and nuclear transmutation solute atoms. The conductivity degradation associated with radiation defects usually amounts to less than ~1% change except in the case of high void swelling conditions.233-236 Conversely, the conductivity deg­radation associated with neutron-induced transmuta­tion products tends to monotonically increase with increasing dose and typically becomes larger than the radiation defect contribution for doses above ~1 dpa. Thermal conductivity degradation much greater than 10% can occur in high-conductivity metals and ceramics.235,237 The conductivity degradation in irradiated alloys can be complex due to short — range ordering and precipitation phenomena,238 with the possibility for either increased or decreased conductivity compared to the unirradiated condition. For nonmetallic irradiated materials, the electrical conductivity during irradiation typically experi­ences a transient increase due to excitation of valence electrons into the valence band by ionizing radiation.239-243 The thermal conductivity of irra­diated nonmetals is typically degraded by displace­ment damage due to phonon scattering by point

defects and defect clusters.237,243-246