1.03.5.1 Dislocation Loop Formation

A common feature in many irradiated metals and nonmetals at temperatures between recovery Stage III and Stage V is dislocation loop formation (either perfect or faulted), with typical loop diameters rang­ing from ^2 to ^100 nm. Both vacancy (intrinsic) and interstitial (extrinsic) loops are frequently observed in irradiated materials. The dislocation loop shape is frequently circular (in order to minimize dislocation line length), but rhombus, square, hexagonal, or other shapes have been observed in some materials due to elastic energy considerations.21Figure 31 shows an example of circular faulted interstitial-type disloca­tion loop formation in MgAl2O4 due to ion irradia­tion at 650 °C. The parallel fringes visible in the loop

Figure 31 Faulted interstitial-type dislocation loop formation in MgAl2O4 irradiated with 2 MeV Al+ ions at 650°C to 14 dpa. The image was taken with a beam direction near [101] using weak beam dark field (g, 6g), g = 202 diffraction imaging conditions (data from

S. J. Zinkle, unpublished research).

500 nm

Figure 32 Defect cluster patterning into aligned {001} walls in single crystal copper irradiated with protons at 100 °C to 2 dpa. Reproduced from Jager, W.;

Trinkaus, H. J. Nucl. Mater. 1993, 205, 394-410.

interiors are a signature of the stacking fault and are visible in TEM by selecting the appropriate diffrac­tion imaging conditions. Faulted loop formation is energetically unfavorable in most bcc materials due to their high stacking fault energies, although there is some evidence for formation of small faulted loops in some cases.224 Experimental studies using energetic ion beams at cryogenic temperatures (where long range point defect migration does not occur) have obtained convincing evidence for direct formation of visible defect clusters directly within displacement cascades above a threshold energy value.294 Dislocation loop formation is usually ran­domly distributed on the relevant habit planes, with no pronounced spatial correlation. In some cases where mechanical or radiation-induced stresses are present, significant anisotropy occurs regarding the habit planes for loop formation.295,296 Within a limited temperature and damage rate regime, the dislocation loop microstructure in some materials also exhibits a tendency to self-organize into aligned walls.297-299 Figure 32 shows an example of well-developed defect cluster patterning in pure copper following proton irradiation to 2 dpa.298 The defect clusters within the walls consist of SFTs and small dislocation loops.

In this section, we discuss briefly some important radiation effects in a few ceramics that are used in nuclear reactor applications. We will consider three representative ceramic materials: (1) urania (UO2); (2) silicon carbide (SiC); and (3) graphite (C). Unfor­tunately, we cannot provide a thorough review of the radiation damage studies that have been performed on many hundreds of other nonmetallic solids.

1.05.3.1 Radiation Effects in Uranium Dioxide

UO2 is an important nuclear material because it is the fuel form of choice for conventional light water reac­tors. Unfortunately, our knowledge of pure radiation effects in UO2 is somewhat limited. This is because 235U undergoes fission in a thermal neutron radiation environment, and consequently, the radiation response of UO2 is dictated by chemical evolutionary effects rather than by conventional, point defect condensation effects. Swelling in UO2 during service as a nuclear fuel can be significant; several percent for some percent burnup of heavy metal.29 This swelling is primarily due to the accumulation of gaseous fission products as well as to some degree, solid fission pro­ducts. It is not believed that UO2 is susceptible to void swelling (described in previous sections).

Under ballistic radiation damage conditions, UO2 exhibits polygonization, that is, a grain subdivision process in which UO2 grains initially ~10 pm diame­ter subdivide into 104 to 105 new small grains of ^0.2 pm size.30 These authors demonstrated that polygonization is initiated at a critical ballistic dam­age dose, apparently independent of temperature. In particular, irradiation of single crystal UO2 with 300 keV Xe ions at 77 K, 300 K, and 773 K, to a fluence of 4 x 102°Xem~2 or higher, produces the polygonization transformation.30 However, these authors concluded that this transformation cannot be due to radiation damage alone but is probably also related to the implanted impurity atoms (Xe), which reach a concentration of 5-7% at the critical fluence described above. Despite the polygonization transformation in UO2, no amorphization transfor­mation, induced by ballistic damage conditions, has ever been observed.

Under SHI (electronic stopping) irradiation dam­age conditions, once again amorphization was not observed (even with overlapped ion tracks), and the SHI-induced swelling is negligible.3 These experi­ments included numerous ion species (Zn, Mo, Cd, Sn, Xe, I, Pb, Au, and U) and energies ranging from 72MeV to 2.7 GeV. Latent tracks were visible by TEM for electronic stopping powers greater than 29 keV nm~ , but all tracks were crystalline. Lattice parameter expansion and polygonization were also observed.

1.01.7.1 Introduction

Global thermodynamic equilibrium of a crystalline solid is nearly impossible to realize. Such a system would have to be a single crystal free of any defects except for a small concentration of vacancies. This concentration depends on the temperature. If the temperature is changed, these vacancies could not spontaneously appear and disappear within the per­fect crystal lattice. The thermal fluctuations are too low in energy to nucleate a Frenkel pair, that is, a vacancy and a self-interstitial. However, at surfaces of this perfect solid, vacancies can form without the creation of a self-interstitial. Of course, surfaces are in reality extended defects just as grain boundaries are in real crystals. The latter contain also dislocations, which are lattice imperfections formed during the solidification of the crystal from its melt, and when thermal stresses are relaxed by plastic deformation.

The conclusion one reaches is that the extended crystal defects, namely grain boundaries, dislocation cores, incoherent interfaces, and surfaces, are the places where vacancies are produced by thermal fluctuations and where they also disappear. It is at these places, called sinks (or sources), where a local equilibrium concentration of vacancies is established and maintained. The vacancy concentration in the remaining, perfect part of the crystal, adjusts by dif­fusion to the local equilibrium concentrations at the sinks. However, these local equilibrium concentra­tions are not necessarily all equal. In fact, they can differ depending on the type of sink, the local state of stress, and the local composition in the case of alloys.

Here, we shall derive local equilibrium vacancy concentrations for some of the important types of sinks that are typically found in irradiated metals and alloys. The procedure we will employ is the same for all sink types, namely we will consider the reaction of species indicated by square brackets

N [V] + [S] $ (n* + 1)[V] + [S’]

in which a sink of type [S] surrounded by Nv vacan­cies [ V] will emit one more vacancy and change to a different sink [S’]. The two sinks [S] and [S0] do not differ from each other in type, but may differ in their internal energies. The change in Gibbs free energy, AG(T), for this reaction will be equal to zero when local thermodynamic equilibrium exists around the sink. The following specific example will clarify the meaning of the procedure. The outcome of this procedure is a thermal vacancy concentration that is in local thermodynamic equilibrium with the particu­lar sink, and this concentration defines a boundary condition for the diffusion of vacancy into or out of the sink or source, respectively. Henceforth, sink and source are considered synonymous.

1.03.3.1 Irradiation Dose

As discussed in Chapter 1.01, Fundamental Proper­ties of Defects in Metals; Chapter 1.02, Fundamental Point Defect Properties in Ceramics; and Chapter

1.11, Primary Radiation Damage Formation, the

international standardized displacement per atom (dpa) unit for radiation damage34 is a useful parame­ter for comparing displacement damage levels in a variety of irradiation environments. The calculated damage level is directly proportional to the pro­duct of the fluence and the average kinetic energy transferred to the host lattice atoms (damage energy). The effective damage cross-sections for 1 MeV particles incident on copper range from ^30 barns (1 barn = 1 x 10-24 cm2) for electrons35 to ^600 barns for neutrons36 and ~2 x 109 barns for Cu ions.37

The dpa unit is remarkably effective in correlating the initial damage production levels over a wide range of materials and irradiating particles and is the singular most important parameter for quantifying radiation effects in materials. Numerous aspects of microstruc­tural evolution are qualitatively equivalent on a dpa basis for materials irradiated in widely different irradiation environments. However, the dpa unit does not accurately capture some of the complex differences in primary damage production for ener­getic displacement cascade conditions compared to isolated Frenkel pair production.38 For example, defect production at cryogenic temperatures (where long-range defect migration and annihilation does not occur) for neutron and heavy ion-irradiated materials is about 20-30% of the calculated dpa value due to athermal in-cascade recombination processes.38,39 In addition, the accumulated damage, as evident in the form of point defect clusters or other microstructural features, typically exhibits a complex nonlinear rela­tionship with irradiation dose that depends on irradi­ation temperature and several other factors. The impact of other experimental variables on the dose- dependent damage accumulation behavior is dis­cussed in Sections 1.03.3.2—1.03.3.9.

Tensile ductility is a more vulnerable parameter than strength to radiation effects since it tends to be very high in unirradiated austenitic stainless steels and is often reduced to quite low levels by irradiation. It is also of more concern since strengthening, although not reliable due to its slow initiation, is usually a beneficial change. In contrast, embrittlement is always detrimental. Like strength, ductility exhibits saturation with increasing fluence, although the behavior is significantly more complex than that of strength. The general trends in type 316 stainless steel are shown in Figure 7 for material irradiated in the EBR-II. These data are for the same specimens for which the yield strength was shown in Figure 2.9 Fast reactor data are used here to avoid the compli­cation of helium effects. Once stabilization of the dislocation microstructure is achieved, a smooth curve approaching an apparent saturation is observed.

More information can be gleaned from ductility data if they are viewed in terms of irradiation and test temperature. Figure 822 shows total tensile elon­gation for a series of irradiated austenitic alloys at a displacement level of 30 dpa in both annealed and cold-worked conditions. The room temperature ductility exceeds 10%, but it decreases rapidly with increasing temperature up to approximately 300 °C and then exhibits the expected increase with tem­perature observed for unirradiated alloys. Beyond 500 °C, ductility again decreases with an onset of intergranular embrittlement resulting from helium introduced through transmutations in the thermal flux of the HFIR.

Energy (MeV) Figure 6 Cross-section for (n, a) reactions as a function of neutron energy.

Uniform elongation, the elongation at the onset of plastic instability, or necking, appears to be most sensi­tive to the effects of irradiation and, in general, is less dependent on specimen geometry than other para­meters such as total tensile elongation. The low values of uniform elongation are often cause for great con­cern, which is usually justified. However, it should be borne in mind that if stresses remain below the yield
stress of a metal, elongation becomes a secondary con­cern. As long as limited plastic deformation relieves the stress that produced it, a structure remains intact.

The high level of irradiation strengthening observed at temperatures below 300 °C, which is due to black dot defect clusters and small loops, also results in low ductility throughout this tempera­ture range. Small helium bubbles and helium-defect

Figure 9 Uniform elongation as a function of irradiation and test temperature at a displacement level of 10dpa.

The trend curves are for type 316 stainless steel and PCA. Reproduced from Grossbeck, M. L.; Ehrlich, K.; Wassilew, C. J. Nucl. Mater. 1990, 174, 264.

clusters also contribute to hardening and reduction in ductility, but this form of helium embrittlement is not related to the severe intergranular embrit­tlement that is observed above 500 °C. Both these effects are apparent in Figure 9 where uniform elongation for an extensive set of austenitic alloys irradiated in thermal and fast spectrum reactors is shown.1 The specimens irradiated in the fast spec­trum (<5 appm He) exhibit consistently higher duc­tility than the mixed-spectrum reactor specimens (500-1000 appm He) even at this low displacement level, especially above 600 °C, where helium embrit­tlement is certain to control.

A similar pattern is exhibited at 30 dpa where a very limited uniform elongation characteristic of lower temperatures is apparent. After a restoration of ductility above 400 ° C, ductility again decreases above 500 °C due to the onset of intergranular helium embrittlement. Differences in alloy behavior, especially in the case of titanium-modified alloys somewhat clouds the understanding of helium
embrittlement observed in Figure 10.11 However, at 50 dpa, where helium levels exceed 4000 appm, the trend becomes clear with the fast reactor specimens showing uniform elongations several times larger than those observed in mixed-spectrum reactors (Figure 11).11 What is less expected is the recovery of ductility at 50 °C at 50 dpa compared to the results at 30 dpa. This irradiation annealing effect has also been observed at 230 °C by Ehrlich, where strength of the alloy 1.4988 decreased continuously from 10 to 30 dpa.20 Results from an experiment in the Oak Ridge Research Reactor (ORR), where the spectrum was tailored to produce a ratio of He per dpa characteristic of a fusion reactor, show similar low levels of uniform elongation for cold-worked alloys at low temperatures, but high uniform elonga­tions were observed in annealed type 316 stainless steel at 60 °C. This high ductility was drastically reduced between 200 and 330°C before the micro­structure characteristic ofhigher temperatures became

effective.21

20

700

Figure 10 Uniform elongation of austenitic stainless steels irradiated in fast and thermal reactors to a displacement level of 30dpa. Severe helium embrittlement is shown at 600°C. Reproduced from Grossbeck, M. L.; Ehrlich, K.; Wassilew, C.

J. Nuct. Mater. 1990, 174, 264.

1.06.3.1 Background

Clearly, it is not possible to cite, let alone describe in detail, the extensive literature on He effects in irradiated alloys. This literature encompasses both mechanical properties, especially HTHE, and the effects of He on microstructural evolutions, particu­larly void swelling. There is also a more limited literature on fundamental processes and properties related to He in solids, like desorption measurements and He solution, binding, and diffusion activation energies. Much of previous work pertains to fcc (face-centered cubic) AuSS, which is one of interest for fast reactor cladding applications. However, stan­dard AuSS, like AISI 316 («Fe-0.17Cr-0.12Ni-bal Mo, Si, Mn, …) are highly prone to both HTHE and void swelling. Thus, advanced AuSS and bcc FMS have supplanted conventional AuSS as the leading candidates for nuclear applications. Never­theless, conventional AuSS alloys nicely illustrate the damaging effects of He (see Section 1.06.3.2 and following), which are both subtle and signifi­cantly mitigated in advanced steels. Swelling and HTHE resistance are largely due to microstructural designs that manage He.

Particular emphasis in this section is placed on the critical bubble model (CBM) concept of the transition of stable He bubbles to unstably growing voids, both under irradiation-driven displacement damage, and stress-driven growth of grain boundary creep cavities. We believe this focus is appropriate, since it seems that many current modeling efforts have lost connection with the basic thermody­namic-kinetic foundation for understanding He effects provided by the CBM concept and the large body of earlier related research.

The organization of this section is as follows. Section 1.06.3.2 outlines the historical motivation for concern about He effects in structural alloys, including examples of HTHE and void swelling. Section 1.06.3.3 describes the mechanisms of swelling and its relation to He and He bubbles, especially in AuSS. Section 1.06.3.4 presents a quantitative CBM for void nucleation and a simple rate theory (RT) model of swelling. Section 1.06.3.5 summarizes the implications of the experimental observations and models, and the development of irradiation-resistant alloys. Sections 1.06.3.6 and 1.06.3.7 discuss the application of the CBM to HTHE and corresponding experimental observations, respectively.

Several past decades of intense research have resulted in a good understanding of the fundamental proper­ties of vacancies and self-interstitials in pure metals. We have reviewed this understanding from the following point of view: how do these fundamental properties affect radiation damage at elevated tem­peratures that exist in nuclear reactors. The key parameters that emerge from this perspective are the displacement energy of Frenkel pairs, the forma­tion and migration energies of vacancies and self­interstitials, and their relaxation volumes and elastic polarizabilities. While the physical basis for these key parameters is understood, obtaining precise values for them by experimental and theoretical means remains a formidable challenge. In particular, this is true for the type of alloys that are used for compo­nents in the core of nuclear reactors. In general, these are complex alloys. For example, the austenitic stain­less steels are composed of major alloy constituents, namely iron, nickel, and chromium, and many minor alloy elements such as molybdenum, titanium, man­ganese, carbon, and silicon. Therefore, many different types of vacancies and self-interstitials can exist in these alloys with potentially different properties. It is unlikely that all these different properties can actu­ally be measured. Rather, only effective average prop­erties, such as the self-diffusion coefficient, can be determined experimentally, and theoretical models must be employed to relate effective properties to the individual properties of the different vacancies.

At the present time, electronic structure method still require further development before effective properties of defects in complex alloys can be calcu­lated. In fact, only recently has it become possible to calculate, for example, accurate values for the forma­tion energies of mono — and divacancies in pure metals. Two advances have been responsible for the progress.

First, density functional theory requires different implementations when applied to bulk and to surface properties of metals. The uniform electron gas that serves as a starting point for the electron density functional in the bulk interior of solids is not suitable to formulate the corresponding functional for the ‘electron edge gas.’ As shown by Kohn and Mattsson,61,62 functionals must be developed that join the edge and the interior bulk regions, and Armiento and Mattsson63,64 have proposed and tested func­tionals for these two regions and how to join them. When applied to vacancies in metals,65,66 formation energies are predicted that are in much better agree­ment with experimental results. But there are also differences. For example, Carling et a/65 obtain a repulsive (positive) binding energy for divacancies in Al. However, this result may be due to the limited number of atoms employed in the calculations and the periodic boundary conditions.

This brings us to the second advance that has recently been made, namely the implementation of an orbital-free electron density functional theory based on finite-element methods.67 With this approach, much larger systems containing effectively millions of atoms can be treated; these systems are truly finite, and realistic boundary conditions can be applied to them.

Figures 28 and 29 reproduced from Gavini eta/.67 reveal a surprisingly large effect of the system size, that is, the effective number of atoms in a finite crystal into which one or two vacancies have been introduced. As demonstrated by these results, in order to obtain defect properties that are indepen­dent of the size of a finite system requires thousands of atoms as well as their full relaxation. In other words, electronic structure calculations need to be combined with continuum elasticity descriptions to predict radiation effects and to develop better alloys for nuclear power generation.

The damage accumulation is independent of dose rate at very low temperatures, where point defect migration does not occur. However, at elevated temperatures (above recovery Stage I) the damage rate can have a significant influence on the damage accumulation. Simple elevated temperature kinetic models for defect accumulation72,142-144 predict a transition from linear to square root dependence on the irradiation fluence when the radiation-induced defect cluster density becomes comparable to the density of preexisting point defect sinks such as line dislocations, precipitates, and grain boundaries. Similar square root flux depen­dence is predicted from more comprehensive kinetic rate theory models6,70,71,145 for irradiation tempera­tures between recovery Stage II and IV. Electron microscopy analyses of electron5 and neutron146 irra­diation experiments performed above recovery Stage I have reported defect cluster densities that exhibit square root dependence on irradiation flux or fluence.

Figure 18 summarizes the square root dose rate dependence for dislocation loop densities at inter­mediate temperatures in several electron-irradiated pure metals.5

Similarly, the predicted critical dose to achieve amorphization is independent of dose rate below

recovery Stage I and depends on the inverse square root of dose rate for temperatures above recovery Stage I.147 Experimental studies have confirmed that the threshold dose to achieve amorphization in ion-irradiated SiC is nearly independent of dose rate below ~-350 K (corresponding to recovery Stage I) and approaches an inverse square root flux dependence for irradiation temperatures above 380 K, as shown in Figure 19.148

In the void swelling149-151 and high temperature helium embrittlement119,152,153 regimes, damage rate effects are very important considerations due to the competition between defect production and ther­mal annealing processes. Experimental studies using ion irradiation (^10-3 dpas-1) and neutron irradia­tion (^10-6 dpa s-1) damage rates have observed that the peak void swelling regime is typically shifted to higher temperatures by about 100-150 °C for the high-dose rate irradiations compared to test reactor neutron irradiation conditions.114,154-158 Similarly, the minimum and maximum temperature for measureable void swelling increase with increasing dose rate. For example, recent low dose rate neutron irradiation studies111-113 performed near 10-9-10-8dpas-1 have observed void swelling in austenitic stainless steel at temperatures as low as 280-300 °C, which is signifi­cantly lower than the ^400 ° C lower limit for void swelling observed during fission reactor irradiations near 10-6dpas-1 (cf. Figure 12).

Next, we must consider the lattice registry of the layer blocks inserted into alumina and spinel to form interstitial dislocation loops along 3. Registry refers to the relative translational displacements between successive layers in a stack. In alumina, O anion layers are fully dense triangular atom nets, stacked in an hcp, BCBCBC… geometry. B and C represent two distinct layer registries (displaced lat­erally with respect to one another). All the Al cation layers occur within the same registry, labeled a in Table 1 (a is displaced laterally relative to B and C). These Al layers are 2/3 dense, relative to the fully dense O layers, forming honeycomb atomic patterns. The successive Al layers are differentiated by where the cation ‘vacancies’ occur within each a layer. There are three possibilities that occur sequentially, hence the subscripted labels in Table 1 (a1, a2, a3).11 Thus, the registry of cation/anion stacking in alumina follows the sequence: a1 B a2 C a3 B a1 C a2 B a3 C.

When extra pairs of Al and O layers are inserted into the stacking sequence, a1 Ba2 C a3 Ba1 C a2 B a3 C, a mistake in the stacking sequence is introduced. In other words, the dislocation loop formed by the block insertion is faulted (contains a stacking fault). Let us see how this works by inserting a 1/3 [0001] four-layer block, Al2-O3-Al2-O3, into the stacking sequence described above. We obtain:

a1 B a2 C a3 B a1 C a2 B a3 C a1 B a2 C a3 B

a1 C a2 B a3 C (before) a1 B a2 C a3 B a1 C a2 B a3 C a1 B a2 C a1 B

a2 C a3 B a1 C a2 B a3 C (after)

a1 a2 a3 a1 a2 a3 a1 a2 a1 a2 a3 a1 a2 a3

(after, showing only cations and showing stacking fault position) [2]

Notice in eqn [2] that after block insertion, the anion sublattice is not faulted (BCBC… layer stacking is preserved), whereas the cation sublattice is faulted, specifically at the position of the red vertical line in the last sequence. Kronberg13 refers to this as an unsymmetrical electrostatic fault. This fault is seen to be intrinsic and only in the cation sublattice; the anion sublattice is undisturbed. In summary, the dis­location loop formed by 1/3 [0001] block insertion in alumina is an intrinsic, cation-faulted, interstitial Frank loop. This is also a sessile loop.

Comparison of the STIP data (high helium) with neutron-irradiation (lower He) data for FMS leads to the following conclusions:

• Up to about 500 appm, excess irradiation hardening and ductility loss in FMS due to He are modest.

• At higher damage levels, due to contributions from bubbles, hardening continues to increase with dpa and He in SPNI but saturates in neutron irradiations.

• At high He levels, bubbles contribute to hardening even more significantly at higher irradiation temperatures.

• Reductions in the uniform and total elongation strains are also similar in neutron and SPN irradiations up to 500 appm, but elastic fracture and increasing brittle IG fracture occur even in tensile tests at higher He levels.

• The effect of He on fast fracture and DBTT shifts is also modest below «500 appm, but at higher
levels it increases rapidly due to both extra hard­ening and reduction in the critical stress for IG fracture that fall below that for cleavage.

• Synergistic hardening and nonhardening embrit­tlement lead to enormous DBTT shifts and an increase in the maximum temperature for signifi­cant DBBT shifts up to irradiation temperatures that may be well in excess of 400 °C.

The effects of He on tensile and fracture properties are less apparent in AuSS. Unpublished results from SPNI also show that He is trapped in small bubbles in NFA in a way that appears to protect GBs from IG embrittlement for the same irradiation conditions that result in severe synergistic He-hardening DBTT shifts.