T. D. Burchell

4.10.1 Introduction

There are many graphite-moderated, power — producing, fission reactors operating worldwide today.1 The majority are in the United Kingdom (gas-cooled) and the countries of the former Soviet Union (water — cooled). In a nuclear fission reactor, the energy is derived when the fuel (a heavy element such as 92U235) fissions or ‘splits’ apart according to the following reaction:

235 1 236

92U +0 n ^92 U! Fi + F2 + n

+g — energy

An impinging neutron usually initiates the fission reac­tion, and the reaction yields an average of 2.5 neutrons per fission. The fission fragments (F1 and F2 in eqn [I]) and the neutron possess kinetic energy, which can be degraded to heat and harnessed to drive a turbine — generator to produce electricity. The role of graphite in the fission reactor (in addition to providing mechani­cal support to the fuel) is to facilitate the nuclear chain reaction by moderation of the high-energy fission neu­tron. The fission fragments (eqn [I]) lose their kinetic energy as thermal energy to the uranium fuel mass in which fission occurred by successive collisions with the fuel atoms. The fission neutrons (n in eqn [I]) give up
their energy within the moderator via the process of elastic collision. The g-energy given up in the fission reaction (eqn [I]) is absorbed in the bulk of the reactor outside the fuel, that is, moderator, pressure vessel, and shielding. The longer a fission neutron dwells in the vicinity of a fuel atom during the fission process, the greater is its probability of being captured and thereby causing that fuel nucleus to undergo fission. Hence, it is desirable to slow the energetic fission neu­tron (E ~ 2 MeV), referred to as a fast neutron, to lower thermal energies (^0.025 eV at room temperature), which corresponds to a velocity of 2.2 x 1015 cms-1.

The process of thermalization or slowing down of the fission fast neutron is called ‘moderation,’ and the material in a thermal reactor (i. e., a reactor in which fission is caused by neutrons with thermal energies) that is responsible for slowing down the fast fission neutrons is referred to as the moderator. Good nuclear moderators should possess the following attributes:

• do not react with neutrons (because if they are captured in the moderator the fission reaction cannot be sustained);

• should efficiently thermalize (slowdown) neutrons with few (elastic) collisions in the moderator;

• should be inexpensive;

• compatible with other materials in the reactor core;

• meet the core structural requirements; and ideally

• do not undergo any damaging chemical or physi­cal changes when bombarded with neutrons.

In the fast neutron thermalization process, the maxi­mum energy lost per collision occurs when the target nucleus has unit mass, and tends to zero for heavy
target elements. Low atomic number (Z) is thus a prime requirement of a good moderator. The density (number of atoms per unit volume) of the moderator and the likelihood of a scattering collision taking place must also be accounted for. Frequently used ‘Figures of merit’ for assessing moderators are the ‘slowing down power’ and the ‘moderating ratio.’ Figure 1 shows these Figures of merit for several candidate moderator materials. The slowing down power accounts for the mean energy loss per collision, the number of atoms per unit volume, and the scatter­ing cross-section of the moderator. The tendency for a material to capture neutrons (the neutron capture cross-section) must also be considered. Thus, the sec­ond figure of merit, the moderation ratio, is the ratio of the slowing down power to the neutron absorption (capture) cross-section. Ideally the slowing down power is large, the neutron capture cross-section is small, and hence the moderating ratio is also large.

Practically, the choices of moderating materials are limited to the few elements with atomic number <16. Gasses are of little use as moderators because of their low density, but can be combined in chemical compounds such as water (H2O) and heavy water (D2O). The available materials/compounds reduce to the four shown in Figure 1 (beryllium, carbon (graphite), water, and heavy water). Water is rela­tively unaffected by neutron irradiation, is easily contained, and inexpensive. However, the moderating ratio is reduced by the neutron absorption of hydro­gen, requiring the use of enriched (in 235U) fuels to maintain the neutron economy. Heavy water is a good moderator because 1H2 and 8O16 do not absorb neu­trons, the slowing down power is large, and the mod­erating ratio is therefore very large. Unfortunately,

the cost of separating the heavy hydrogen isotope is large. Beryllium and beryllium oxide are good mod­erators but are expensive, difficult to machine, and suffer toxicity problems. Finally, graphite (carbon) is an acceptable moderator. It offers a compromise between nuclear properties, utility as a core structural material, and cost. It also has the advantage of being able to operate at very high temperatures (in the absence of oxygen). Unfortunately, the properties of graphite are markedly altered by neutron irradiation and this has to be considered in the design of graphite reactor cores.

Atomic displacements due to fast neutron irradiation modify the ‘crystallite’ dimensions and most of their material properties. Neutron energies of around 60 eV are required to permanently displace carbon atoms from the lattice. However, most damage in graphite is due to fast neutron energies >0.1 MeV; a typical thermal reactor has neutron energies of up to 10 MeV, with an average of 2 MeV. High-energy neutrons knock an atom out of the lattice, leading to a cascade of secondary knock-ons. This process knocks atoms into interstitial positions between the basal planes, leaving vacant positions within the lat­tice. Many of the interstitial atoms will immediately find and fill these vacancies. However, others may form semistable Frenkel pairs or other small clusters or ‘semistable’ clusters. With increasing fast neutron damage, the stability, size, and number of these clus­ters will change depending on the irradiation tem­perature. The higher the irradiation temperature, the larger are the interstitial clusters or ‘loops.’ This process leads to considerable expansion in the graph­ite crystal ‘c’ axis. Conversely, vacancy loops also form and grow in size with increased irradiation temperature. It has been postulated that this process will cause the lattice to collapse leading to the ‘a’ axis shrinkage observed on irradiating graphite crystal structures. This process is illustrated in Figure 15.

Thrower32 carried out an extensive review of transmission electron microscopic (TEM) studies of defects in graphite, particularly those produced by fast neutron irradiation. He demonstrated that interstitial loops and vacancy loops could be distin­guished by tilting the specimen. He was able to observe vacancy loops in graphite irradiated only at and above 650 °C, whereas interstitial loops and defects were observed at all temperatures of interest to reactor graphite. It is proposed that the dimen­sional change in bulk polycrystalline graphite may be understood by eqn [29]33:

Ac

ffi +

c where Lc is the crystal dimension perpendicular to the basal plane, ‘c’ is the atomic lattice parameter, and r0 and r1 are the mean defect radius and mean half separation of defects in the basal plane, respectively. However, it was noted that this does not completely explain the expansion. In order to explain basal plane contraction it is necessary to postulate that vacancy lines cause the collapse of the basal planes.34-36

More recent atomistic calculations due to Telling and Heggie37 have sought to explain the process by the ‘buckling’ of basal planes until they twist round upon themselves. This latter explanation is more satisfying as it accounts for the atomistic bonding around the edges of the interstitial loops and vacan­cies. However, more HRTEM (high-resolution trans­mission electron microscopy) observations and other techniques are required to validate these theories.

Whichever mechanism is correct, empirical observations made on HOPG, and some natural crystal flakes,35 show that graphite crystal structures expand in V axis and shrink in the ‘a’ axis, the degree of deformation being a function of fast neu­tron fluence and irradiation temperature. Crystal dimensional change is discussed in more detail later in this section.

In the blanket, the tritium inventory is not considered to be the issue once liquid Li is used as the breeding and cooling materials owing to the high hydrogen solubility of Li. The behavior of hydrogen and its isotopes in vanadium alloys is a concern for tritium retention in the first wall. Deuterium retention of V-4Cr-4Ti was investigated by deuterium ion implantation followed by thermal desorption, in comparison with other candidate first wall materials. The study showed that the retained amount at 380 K was one and two orders of magnitude larger than graphite and tungsten, respectively. For the irra­diation at 773 K, the retained amount was almost the same as that of graphite and one order larger than tungsten.42 Surface composition was also known to influence the hydrogen transport. For example, the rate of absorption was highly influenced by prior heat treatment, inducing Ti surface segregation.43

Recent progress in detecting tritium by means of imaging plate (IP) enhanced the understanding of the tritium behavior in vanadium alloys. Figure 20 com­pares IP images of cold rolled V-4Cr-4Ti and pure V after tritium charging. Tritium is preferentially absorbed in Ti-rich precipitates that have a band structure to the rolling direction.44

Figure 20 Distribution of tritium measured by imaging plates for cold-rolled V-4Cr-4Ti and pure vanadium. The tritium was charged by gas absorption. After Homma, H.; Hatano, Y.; Daifuku, H.; et al. J. Nucl. Mater. 2007, 367-370, 887-891.

For most, but not all fission-derived spectra, stainless steels are relatively immune to transmutation, espe­cially when compared to other elements such as aluminum, copper, silver, gold, vanadium, tungsten, and rhenium,5,21,24-27 each of which can rapidly become two or three component alloys via transmu­tation arising from thermal or epithermal neutrons. Whereas the properties of these metals are particu­larly sensitive to formation of solid transmutation products, stainless steels in general do not change their composition by significant amounts compared to preexisting levels of impurities, but significant amounts of helium and hydrogen can be produced in fission-derived spectra, however.

In stainless steels the primary transmutant changes that arise in various fission and fusion reactor spectra involve the loss of manganese to form iron, loss of chromium to form vanadium, conversion of boron to lithium and helium, and formation of helium and hydrogen gas.4,28 While each of these changes in solid or gaseous elements are produced at relatively small concentrations, they can impact the evolution of alloy properties and behavior.

For instance, vanadium is not a starting compo­nent of most 300 series stainless steels, but when included it participates in the formation of carbide
precipitates that change the distribution and chemi­cal activity of carbon in the alloy matrix. Carbon plays a number of important roles in the evolution of microstructure1 and especially in grain boundary composition. The latter consideration is very impor­tant in determining the grain boundary cracking behavior, designated irradiation-assisted stress corro­sion cracking (IASCC), especially with respect to the

29

sensitization process.

The strong loss of manganese in highly therma — lized neutron spectra has been suggested to degrade the stability of insoluble MnS precipitates that tie up S, Cl, and F, all of which are elements implicated in grain boundary cracking.30 Late-term radiation — induced release of these impurities to grain bound­aries may participate in cracking, but this possibility has not yet been conclusively demonstrated.

In some high-manganese alloys such as XM-19 manganese serves to enhance the solubility of nitrogen which serves as a very efficient matrix strengthener. In highly thermalized spectra the loss ofmanganese via transmutation has been proposed to possibly lead to a decrease in the strength of the alloy and perhaps to induce a release of nitrogen from solution to form bubbles.31

The overwhelming majority of published trans­mutation studies for stainless steels and high-nickel alloys steels have addressed the effects of He/dpa ratio on mechanical properties and dimensional instabilities. Much less attention has been paid to the effect of H/dpa ratio based on the long-standing perception that hydrogen is very mobile in metals and therefore is not easily retained in steels at reactor-relevant temperatures. As presented later, this perception is now known to be incorrect, espe­cially for water-cooled reactors.

The focus of most published studies concerned the much higher helium generation rates anticipated in fusion spectra (~3—10 appm He/dpa) compared to the lower rates found in fast reactors (~0.1—0.3 appm He/dpa).32 It was later realized that in some highly thermalized test reactors, such as HFIR, very large generation rates could be reached (~100 appm He/dpa), and even in pressurized water reactors the rate could be very high (^15 appm He/dpa).3 In heavy water reactors the rate can be much larger, especially in out-of-core regions.34,35

While some helium arises from (n, a) reactions with thermal and epithermal neutrons interacting with the small amounts of boron found in most stainless steels, the major contribution comes initially from high-energy threshold-type (n, a) reactions with the major alloy components. This type of reac­tion occurs only above high neutron threshold ener­gies (>6MeV). Figure 8 shows that nickel is the major contributor to helium production by (n, a) reactions,36 and thus the helium generation rate scales almost directly with nickel content for a large number of commercial steels.

A similar behavior occurs for production of hydrogen by transmutation via high-energy neutrons, where nickel is also the major source of hydrogen compared to other elements in the steel.4,7 In this case, the threshold energy is around 1 MeV with 58Ni being the major contributor.

This generality concerning nickel as the major source of He and H is preserved in more energetic fusion-derived spectra, although the He/dpa and H/dpa generation rates in fusion spectra are much larger than those of fast reactor spectra. When moving to very energetic spallation-derived neutron and proton spectra, however, the observation that nickel accounts for most of the helium and hydrogen is no longer correct. Iron, nickel, chromium, cobalt, and copper produce essentially the same amounts of helium and hydrogen for energies above ^100 MeV as shown in Figure 9.6

Another very important helium-generation pro­cess also involves nickel. Helium is produced via the two-step 58Ni(n, g)59Ni(n, a)56Fe reaction sequence.37,38 This sequence operates very strongly in mixed-spectrum reactors. 59Ni is not a naturally occurring isotope and is produced from 58Ni. Thus, this helium contribution involves a delay relative to

250 both steps of the sequence involve cross-sections that increase with decreasing energy and the second step exhibits a resonance at 203 eV, the generation rate per dpa in fast reactors increases near the core boundaries and out-of-core areas.

It is in thermalized neutron spectra characteristic of light and heavy water-cooled reactors, however, where the 59Ni(n, a) reaction can produce He/dpa generation rates that are significantly larger than those characteristic of fusion-derived spectra.

Nickel has five naturally occurring stable isotopes with 58Ni comprising 67.8% natural abundance, 60Ni comprising 26.2%, and ~6.1% total of61Ni, 62Ni, and 64Ni. There is no natural 59Ni or 63Ni at the beginning of radiation. During irradiation in a highly therma — lized neutron spectrum, all nickel isotopes are strongly transmuted, primarily to the next higher isotopic number of nickel. 59Ni has a half-life of 76 000 years and is progressively transmuted to 60Ni while 58Ni is continuously reduced in concentration. Therefore, the 59Ni concentration rises to a peak at a thermal neutron fluence of 4 x 1022 n cm-2 where the 59/58 ratio peaks at ^0.04 and then declines, as shown in Figure 10.

This transmutation sequence in nickel is an exam­ple of the isotopic shift category of transmutation defined earlier. For other elements used to make stain­less steels, there are no consequences to such a shift since the total amount of the element is unchanged

6.1%

total

and isotope shifts induce no significant consequences. However, in the case of nickel there is an intimate linkage between the displacement and transmutation processes that arises from the isotope shift.

The recoil of the 59Ni upon emission of the gamma ray produces only about five displacements per event, and usually is not a significant addition to the displacement dose. However, the isotope 59Ni undergoes three strong reactions with thermal and resonance (~0.2 keV) neutrons, two of which are exceptionally exothermic and can significantly add to the dpa level. These reactions, in order of highest-to-lowest thermal cross-section, are (n, g) to produce 60Ni, followed by (n, a) and (n, p) to produce helium and hydrogen, respectively.

Even at relatively low thermal-to-fast neutron ratios, the reaction sequence can produce significant amounts of helium. For example, He/dpa ratios in the order of ^3-8 appm dpa-1 can be experienced along the length of a 316 stainless baffle bolt in the baffle-former assembly of a pressurized water

reactor4’33’39 while comparable rates in fast reactors are in the order of 0.1—0.2 appm dpa-1. In therma — lized spectra the latter two reactions can quickly overwhelm the gas production produced by nickel at high neutron energies.

As mentioned previously, the thermal neutron reactions of 59Ni are quite exothermic in nature and release large amounts of energy’ thereby causing increases in the rate of atomic displacements’ and con­comitant increases in nuclear heating rates. Nuclear heating by elastic collisions with high-energy neu­trons is usually too small to be of much significance.

The 59Ni(n, a) reaction releases 5.1 MeV, produc­ing a 4.8 MeV alpha particle which loses most of its energy by electronic losses, depositing significant thermal energy but producing only ^62 atomic dis­placements per each event. However, the recoiling 56Fe carries 340 keV, which is very large compared to most primary knock-on energies, and produces an astounding 1701 displacements per event.

The thermal (n, p) reaction of 59Ni produces about one proton per six helium atoms, reflecting the difference in thermal neutron cross-sections of 2.0 and 12.3 barns, and is somewhat less energetic (1.85 MeV), producing a total of ^222 displacements per event.7,40 In addition, approximately five dis­placed atoms are created by each emission-induced recoil of60Ni. This reaction occurs at six times higher
rate compared to the 59Ni(n, a) reaction, resulting from a thermal neutron cross-section of 77.7 barns. In effect, the dpa rate increases during irradiation due to the three 59Ni reactions even though the neutron flux-spectrum may not change.

The major point here is that use of standardized computer codes to calculate dpa does not track shifts in isotopic distribution and therefore will underpredict the dpa level when 59Ni production is an important consideration.

A strong example of this time-dependent increase in dpa rate in highly thermalized light water spectra is shown for pure nickel in Figure 11 for a thermal — to-fast ratio of 2.0. Note that the calculated increase in this figure addresses only the 59Ni(n, a) reaction. Additional increases occur as a result of the 59Ni(n, p) and 59Ni(n, g) reactions, resulting in almost doubling of dpa by the three 59Ni reactions before a calculated dose of ^40 dpa is attained.

Recently, however, an even stronger example of the linkage of the 59Ni transmutation effect and the displacement process has been observed.34,35 In-core thermal-to-fast ratios in heavy water-moderated reactors such as CANDUs are in the order of ~10, but far from the core the ratio can be near ^1000. Compression-loaded springs constructed of high — nickel alloy X-750 were examined after 18.5 years of operation far from the core and were found to be
completely relaxed. Calculating the 59Ni contribu­tion, it was deduced that full relaxation occurred in ^3-4 years rather than the 650-700 years one would predict based on dpa calculated without taking into account the 59Ni contribution.

Therefore, in this case 59Ni contributed ^95% of the dpa. Additionally, 1100 appm of helium was cal­culated to have been produced at the mid-section of the spring in ^3 years, with ^20 000 appm helium having been produced when the spring was examined after 18.5 years of exposure.

There is another consequence of the 59Ni sequence that causes the temperature to increase during irradia­tion. At the peak 59Ni level reached at 4 x 1022 n cm-2, the nuclear heating rates from the energetic (n, a) and (n, p) reactions are 0.377 and 0.023 Wg-1 of nickel, significantly larger than the neutron heating level of -0.03 Wg-1 of natural nickel. Thus, an increase in nuclear heating of —0.4 W g — of nickel must be added to the gamma heating rate at the peak 59Ni level. Fractions of the peak heating rates that are pro­portional to the current 59Ni level should be added at nonpeak conditions. Depending on the nickel level of the steel and the level of gamma heating, which is the primary cause of temperature increases in the interior of thick plates, this additional heating contribution may or may not be significant.

Gamma heating is also a strong function of the thermal-to-fast (T/F) neutron ratio and the neutron flux, being —54 W g-1 in the center of the HFIR test reactor where the T/F ratio is —2.0. In pressurized water reactors at the austenitic near-core internals, however, the T/F ratios are lower by a factor of 2-10, depending on location, and the gamma heating rates in the baffle-former assembly are — 1-3 W g-1. In this case, an additional 0.4 Wg-1 of nuclear heating can be a significant but time-dependent addition to total heating, especially for high-nickel alloys.

It should be noted that thermal neutron populations can vary during an irradiation campaign with conse­quences not only on 59Ni production but also on gamma heating levels. In PWRs boric acid is added to the water as a burnable poison at the beginning of each cycle. As the 10B burns out the thermal neutron population increases, leading to an increase in gamma heating and transmutation.3,4 Over successive cycles there is a saw­tooth variation of gamma heating rate in the baffle — former assembly and therefore in A T, with the latter reaching values as large as ±20 °C in the worst case.

Additionally, another concern may arise in that small radiation-induced nickel-rich phases such as g0, Ni-phosphides, and G-phase may become less stable. This concern arises due to cascade-induced dissolution as the 56Fe from the 59Ni(n, a) reaction recoils within the precipitates, thereby altering the phase evolution in thermalized neutron spectra com­pared to nonthermalized spectra typical of fast reac­tors. These precipitates are known to form as a direct result of irradiation and contribute to hardening, swelling, and irradiation creep processes.1 The size of these precipitates at PWR-relevant temperatures (290-400 °C) is often comparable to or smaller than the —80nm range of the recoiling 56Fe atom.

Finally, another significant source of helium can arise from the implantation of energetic helium resulting from collisions with neutrons into the sur­face layers of helium gas-pressurized or gas-cooled components, often involving hundreds and often thousands of appm of injected helium. In gas-cooled reactors helium injection has been investigated as a possible degradation mechanism of alloy surfaces.41

In fast reactor fuel cladding helium was found to be injected into the inner surface, coming from two major sources, ternary fission events (two heavy fis­sion fragments plus an alpha particle) in the fuel and from helium recoiling from the pins’ helium cover gas as a result of collisions with neutrons.42

The injection rates from these two sources of injected helium are slowly reduced during irradia­tion, however, as heavy fission gases build up in the space between the fuel pellet and the cladding. These gases slow down the energetic helium atoms, reducing their energy sufficiently to prevent most of them from reaching the cladding. Helium injection at high levels was also found on the inner surface of helium-pressurized creep tubes.42 Although helium injection tends to saturate in fuel pin cladding with increasing dose, it does not saturate in pressurized tubes due to the lack of increasing fission gases to reduce the range of helium knock-ons in the gas phase.

Some studies have cited this early source of helium as contributing to the embrittlement of fuel pin clad­ding and its poor performance during transient heating tests,43 although more recent studies have linked the major mechanism to delayed grain boundary attack by the fission products cesium and tellurium.44,45

Point defects created by atomic displacements are lost either through mutual recombination or by migration to sinks. Void swelling requires a mobile population of excess vacancies and can only occur over a limited temperature range, typically 350—

700 °C in neutron-irradiated steels and nickel-based alloys. Rapid diffusion at higher temperatures reduces the concentration of radiation-induced vacancies to near thermal equilibrium levels. Recombination dom­inates at lower temperatures, where reduced vacancy mobility prevents the formation of voids as the neces­sary counter-migration of matrix atoms cannot occur. In the swelling regime, an increased bias for intersti­tials over vacancies at dislocation sinks gives rise to the surplus vacancies which agglomerate to form voids.

The flux of point defects to sinks, including void surfaces, dislocations, and grain boundaries, results in the segregation of particular solute atoms at the sinks and the depletion of others. In austenitic steels and nickel-based alloys, it is generally found that nickel segregates at the point defect sinks. This is generally attributed to the inverse Kirkendall effect described by Marwick,29 whereby faster diffusing solutes such as Cr move in the opposite direction to the vacancy flux and are depleted at the sink, and slower diffusing solutes such as Ni are enriched. One of the earliest observations of nickel segregation at void surfaces due to the inverse Kirkendall effect was made by Marwick et al.30 in an alloy with a composition cor­responding to that of the matrix phase in Nimonic PE16. (For more detailed discussions on radiation — induced segregation effects, see the reviews of Wiedersich and Lam,31 and Rehn and Okamoto.32)

Venker and Ehrlich33 recognized that differences in the partial diffusion coefficients of alloy constitu­ents might account for the effects of composition on swelling. Any effect of this kind would generally be expected to be more significant the larger are the differences between the partial diffusion coefficients of the alloy components. Garner and Wolfer34 exam­ined Venker and Ehrlich’s conjecture and concluded that the addition of even small amounts of a fast — diffusing solute such as silicon to austenitic alloys would greatly increase the effective vacancy diffusion
coefficient (i. e., would enhance the diffusion rate for all matrix elements). The overall effect is analogous to an increase in temperature — resulting in an effective decrease in the vacancy supersaturation and hence a reduction in the void nucleation rate. This mecha­nism is generally accepted as the explanation for the beneficial effect of silicon in reducing swelling in austenitic steels and nickel-based alloys. Although this relies on the diffusion of silicon via vacancy ex­change, silicon is also generally observed to segregate to point defect sinks and since it is an undersized solute, this is believed to occur by the migration of interstitial-solute complexes. There is, however, no reason to suppose that both diffusion mechanisms cannot operate simultaneously.

Garner and Wolfer34 originally considered that since nickel diffuses relatively slowly in austenitic alloys, an increase in nickel content would have the opposite effect to silicon. However, a later assessment made by Esmailzadeh and Kumar,35 based on diffu­sion data reported by Rothman eta/.,36 indicated that the void nucleation rate in Fe-15Cr-Ni alloys would decrease with an increase in nickel content from 20 to 45%. This result is obtained because, although nickel remains the slowest diffusing species, the effective vacancy diffusion coefficient of the system is calcu­lated to increase at the higher nickel content. Esmail — zadeh and Kumar’s calculations also confirmed the beneficial effect of silicon, with the addition of 1% Si predicted to be as effective in suppressing void nucleation as increasing the nickel content from 20 to 45%. Effects at nickel contents above 45% could not be examined due to a lack of appro­priate diffusion data.

As well as affecting the nucleation of voids, differ­ences in the diffusion rates of the various solutes might also be expected to influence void growth. Simplistically, this can be thought of as being partly due to the segregation of slower diffusing solutes reducing the rate of vacancy migration in the vicinity of the voids. However, a further consequence of such nonequilibrium solute segregation was identified by Marwick,2 who realized that it would give rise to an additional vacancy flux which would oppose the radiation-induced flux to the sink. As discussed by Marwick, this additional flux (the Kirkendall flux) may itself be an important factor in limiting void growth, since it will reduce the probability ofvacancy annihilation at sinks and increase the likelihood of point defect recombination.

The effect of nickel content on void swelling was considered further in a model developed by Wolfer and coworkers.37,38 The model examined the compo­sitional dependence of the void bias and focused on the effects of nickel segregation at void surfaces. Wolfer’s model indicated that the compositional gra­dients produced by radiation-induced segregation give rise to additional drift forces which affect the point defect fluxes and thereby modify the bias terms. These additional drift forces arise from the effects of composition on point defect formation and migration energies, on the lattice parameter and the elastic mod­uli, and from the Kirkendall flux. Wolfer’s calculations for binary Fe-Ni alloys indicated that the effect of the Kirkendall flux is small for interstitials but significant for vacancies. Nevertheless, it was considered that the overall effect of compositional gradients on the bias terms is likely to be greater for interstitials than for vacancies due to other factors, particularly the effect of variations in the elastic moduli. As noted by Garner and Wolfer,39 an increase in the shear modulus in the segregated regions around voids would reduce the bias for interstitials and therefore help to stabilize voids. It is difficult to predict the significance of this effect in complex alloys, however, since depletion of Cr in the segregated region will tend to reduce the shear modu­lus, whereas enrichment of Ni in high-Ni alloys will tend to increase it.38 A more significant result of the model with regard to the effect of nickel on swelling is that there is a reversal in the sign of the Kirkendall force for vacancies in Fe-Ni alloys at ^35% Ni. Below this level, vacancies are predicted to be attracted into regions of higher Ni concentration, but above it, the opposite occurs. Wolfer et a/. considered that this effect may account for the dependence of swelling on Ni content in austenitic alloys containing less than 35% Ni.

A generalized description of the swelling behavior of austenitic alloys, which was consistent with the model developed by Wolfer et a/., was put forward by Garner40 (see also Chapter 4.02, Radiation Damage in Austenitic Steels). Garner’s ideas were largely based on the results of the EBR-II irradiation experiments and the earlier ion bombardment work of Johnston et a/., both of which showed a strong dependence of swelling on nickel content. It was considered that swelling was characterized by a tran­sient period followed by a regime in which the swelling rate became constant. In neutron-irradiated alloys, the swelling rate in the posttransient regime was generally found to be ~ 1% per dpa. In swelling — resistant alloys, however, it was argued that such high swelling rates might not be observed owing to ex­tended transient periods. The duration of the transient regime was shown to be dependent on alloy composition and could extend for many tens of dpa in low-swelling materials. The duration of the transient regime was implicitly linked to the completion of void nucleation but, at the time these ideas were put forward, relatively few measurements of void concentrations were available, as swelling data were mainly derived from dimensional or density changes.

Factors that were proposed to account for the influence of nickel on the void nucleation rate in­cluded the effect on vacancy diffusivity described by Esmailzadeh and Kumar35; a possible correlation with the development of fine scale compositional fluctua­tions by a spinodal-like decomposition process (observed by Dodd et a/.41 in ion-irradiated ternary Fe-Cr-Ni alloys); and an effect of nickel on the minimum critical radius for the formation of stable voids.42 Voids are unstable below a critical size, and will generally shrink unless stabilized by gas atoms; the minimum stable void radius is dependent on a number of factors, including temperature and defect bias, and Coghlan and Garner suggested that the compositional dependence of the vacancy diffusivity would also affect this critical size. In other words, it was considered that the transition from gas bubble to void would require a larger bubble size in high — nickel alloys, particularly at relatively high tempera­tures in the swelling regime where void nucleation becomes increasingly difficult. Hoyt and Garner43 subsequently argued that the minimum critical void radius concept might account for the minimum in swelling found at the intermediate nickel contents, provided that a compositional-dependent bias factor for dislocations was also incorporated into the model. The compositional dependence of the bias factor arises from solute segregation, which reduces the strain energy of dislocations and decreases the ratio of the bias for interstitials compared to vacancies.

It is of interest that early evidence for the opera­tion of the bubble to void transition was obtained by Mazey and Nelson,44 who implanted Nimonic PE16 (STA condition) and a PE16 matrix alloy (ST condi­tion) with 1000 appm He to produce a high density of gas bubbles before subsequent irradiation with

46.5 MeV Ni6+ ions. The PE16 matrix alloy used in this particular experiment was a low Si variant (<0.02 wt%) which was known to exhibit relatively high swelling. The mean bubble size following helium implantation at 625 ° C was higher by a factor of about two in the matrix alloy (~11 nm diameter) than in the commercial PE16 alloy (~5 nm diameter). Examination of the alloys following subsequent irradiation also at 625 °C revealed high swelling (12% at 60 dpa) with a uniform distribution of large voids but no remaining helium bubbles in the matrix alloy, and low swelling (~1% at 60 dpa) with a bimodal distribution of bubbles plus voids in the standard PE16 alloy (see Figure 5). These results were interpreted as providing evidence for the con­cept of a critical stable void size, with only a small fraction of bubbles in the commercial PE16 alloy, but all of the bubbles in the matrix alloy, being sufficiently large to grow as voids. Although not specifically discussed by Mazey and Nelson, the compositional differences between the two alloys suggest that the presence of Si and/or the g forming solutes Al plus Ti may help to reduce void nucleation in PE16.

The belief advanced by Garner,40 that sluggish void nucleation generally accounted for low swelling in nickel-based alloys, persisted for some time. However, data reported by Muroga et a/45,46 largely overturned this view. Muroga et a/. carried out microstructural examinations of a series of EBR-II-irradiated Fe-15Cr-Ni ternary alloys with Ni contents ranging from 15 to 75 wt%, and of archived samples of similar alloys from the heavy-ion bombardment experiments of Johnston eta/.12 Examination of alloys irradiated in EBR-II at 510 ° C showed that the saturation void con­centration was dependent on nickel content and was minimized at 35—45 % Ni, but revealed that there was no increase in void numbers in any of the materials above a fluence of 2.6 x 1026nm~2 (E>0.1 MeV) (see Figure 6). Alloys containing 19% and 30% Ni exhib­ited high swelling rates at higher fluences, but swelling remained low in higher nickel alloys. Similar effects were found in the ion-bombarded samples, where, for example, it was shown that there was no significant change in the void concentration in Fe—15Cr—45Ni at doses above 50 dpa in irradiations at 675 °C, yet a marked increase in swelling rate occurred above 120 dpa. Thus, contrary to earlier ideas, these investi­gations clearly demonstrated that the onset of a high swelling rate was not related to the cessation of void nucleation. It follows that the transition to a high rate of swelling must be due to an increase in the growth rate of existing voids.

Muroga et a/.45,46 observed that the total disloca­tion density in the irradiated Fe—15Cr—Ni alloys was only weakly dependent on nickel content. This sug­gested that at the intermediate nickel levels, where the void concentration was low, dislocations were weak sinks (for both vacancies and interstitials) relative to voids. In addition, it was observed that

dislocation loops persisted to higher doses at the intermediate nickel contents, indicating a lower growth rate for the loops — again implying an effect of nickel on dislocation sink strength. Based on these observations, Muroga et al. suggested that a reduced dislocation bias for interstitials at the intermedi­ate nickel contents might explain the influence of nickel on the early stages of void development. An additional factor was required to account for the eventual transition to a high swelling rate. Microche­mical data presented by Muroga et al46 suggested that this transition was related to the depletion of nickel in the matrix owing to its enrichment at void surfaces.

A complete description which incorporates all of the composition-dependent factors which affect the nucleation and growth of voids is lacking. However, there is a general consensus that the major influence of alloy composition arises through its effects on the effective vacancy diffusivity and on segregation aris­ing from the inverse Kirkendall effect. A correlation between the magnitude of void swelling and radia­tion-induced segregation was shown for Fe-Cr-Ni
ternary alloys by Allen et a/.48 The compositional dependence of radiation-induced segregation was determined using a model based on the earlier work of Marwick,2 which incorporates both the vacancy flux to the voids and the back-diffusion of vacancies due to the solute gradients set up by the inverse Kirkendall effect. Vacancy diffusivities for various alloy compositions were determined by the measure­ments of grain boundary segregation in proton- irradiated samples. Swelling data for ion and neutron-irradiated alloys were then compared with the expected swelling propensity defined by the ratio ofthe forward to back diffusion terms calculated at the appropriate irradiation temperature. The materials for which vacancy diffusivity data were determined included Fe-based alloys containing 16-24% Cr and 9-24% Ni, and Ni-based alloys containing 18% Cr and either zero or 9% Fe. This work did not specifi­cally examine 40-50% Ni alloys corresponding to the highest swelling resistance, though the results indi­cated that swelling generally decreased with increas­ing levels of nickel enrichment and chromium depletion at void surfaces.

The overall mechanical property data for irradiated Ta and Ta-base alloys are very limited, with most studies involving irradiation at temperatures <1073 K. In general, the behavior of Ta and its alloys is similar to that of other bcc materials in that radiation harden­ing is observed with significant reductions in elonga­tion at temperatures <0.3 Tm (Tm = 3290 K, pure Ta). As is discussed in this section, the addition of solute strengthening elements creates an increased sensitivity to radiation hardening of the material. In addition to the lack of high-temperature irradiation behavior, impact and fracture toughness data for irradiated Ta and Ta alloys are also limited.

As with all refractory metals, the mechanical be­havior of pure Ta is highly dependent on the impu­rity levels in the material. This may explain the observed differences between the work of Brown et a/.54 and Chen et a/.,55 of 800 MeV proton irradia­tions up to 11 dpa at temperatures <673 K (Figure 7). While chemical analysis quantifying the purity of Ta was not reported in the former, irradiation to 0.26 dpa resulted in a yield strength increase from 350 to 525 MPa over the unirradiated value with a corresponding drop in ductility below 2%. Flow insta­bility following yield was characteristic of samples irradiated to 0.26 and 2.9 dpa.54 Tensile properties of high-purity Ta irradiated to 0.6-11 dpa tested at room temperature and 523 K showed similar increases in tensile strength, while the uniform elongation re­mained near 8% following irradiation to 0.6 dpa or

higher.55

The tensile properties of neutron-irradiated Ta were reported by Claudson and Pessl,30 Wiffen,19
and more recently by Byun and Maloy.56 In the first, irradiation to 0.13 dpa (where irradiation to 0.76 x 1022ncm~2, E > 0.1 MeV is ~1.0 dpa in pure Ta57) at 673 K resulted in increased yield strength, though no significant loss in ductility occurred over the unirradiated control. However, work softening following the yield drop was observed.

Irradiation to higher displacement doses in pure Ta by Wiffen19 showed the potential lower operating temperature limitation of Ta. Following irradiation to 1.97 dpa at 663 K, yield and ultimate tensile strengths increased to near 600 MPa with a corresponding drop in ductility to <0.3% uniform but with total elonga­tion near 10%. The observed plastic instability, at­tributed to the lack of uniform elongation following yielding, resulted from dislocation channeling. Some recovery of ductility is observed following irradia­tion to 913 K, which correlates with temperatures approximating the maximum swelling temperature (Figure 6) and a change in the dominating microstruc­tural features influencing deformation behavior in the metal. The tensile data are presented in Figure 8, along with the irradiated properties of T-111, which are discussed later.

The recent work of Byun and Maloy56 investi­gated tensile behavior as a function of fluence for pure Ta, Ta-1W, and Ta-10W, establishing deforma­tion mode maps for pure Ta and Ta-1W that outline the conditions in which brittle failure and uniform and unstable plastic deformation occur. Following fast-reactor exposures at temperatures <373 K, a progressive hardening and gradual loss in ductility are observed in the tensile properties of pure Ta, leading to a near doubling of the yield stress by 0.14 dpa over the unirradiated value (Figure 9(a)).

An early onset of necking or plastic instability was observed in Ta at doses above 0.0004 dpa. The lower elongation strains in the pure Ta compared with the work by Chen et al.55 is believed to be due to the higher oxygen content in the material.56

The introduction of 1 wt% W resulted in a near — 30% increase in unirradiated strength over pure Ta (Figure 9(b)). The Ta—1W alloy showed greater sen­sitivity to radiation hardening than the pure metal. The tensile properties as a function of dose were similar to those of the pure Ta. However, above 0.004 dpa, plastic instability becomes more predomi­nant in the Ta—1W alloy and occurs immediately following yielding. For Ta—1W irradiated from 0.7 to 7.5 dpa in a mixed proton and neutron irradiation from the same study, hardening was saturated with little change in ductility (insert shown in Figure 9(b)).

Macroscopic deformation mode maps produced for Ta and Ta—1W by Byun and Maloy56 are a graphi­cal way of predicting the performance of a material in an irradiation environment. The deformation mode map for pure Ta is shown in Figure 10(a), while that
of Ta—1W is shown in Figure 10(b). The yield and plastic instability stress were directly obtained from tensile data, while the fracture stress was calculated through a linear strain hardening model for necking deformation, assuming that during instable deforma­tion, the strain hardening rate remains unchanged and is approximately the plastic instability stress. The frac­ture and plastic instability stresses are independent of dose, with a ratio between the stresses of ^2 for the materials studied. The fracture strength decreases with dose if the material becomes embrittled, for example, through interstitial segregation or secondary phase precipitation at grain boundaries, though this was not observed in their work. The yield strength is highly dose dependent, though the yield stress was signifi­cantly lower than the fracture strength in Ta—1W, suggesting that the material may show limited ductil­ity to even higher displacement doses. The effect of increasing test temperature for each material further increases the boundaries for uniform deformation behavior. This increase was found to be greater in pure Ta.

The room temperature unirradiated tensile strength of Ta-10W is nearly double the value of the Ta—1W and triple that of pure Ta in the material investigated by Byun and Maloy,56 and also shows an increased sensitivity in radiation hardening over the pure metal (Figure 9(c)). This sensitivity is also clearly apparent at higher irradiation temperatures near 673 K, as shown in the comparison of tensile curves that were compiled by Ullmaier and Carsughi58 of earlier work (Figure 11). Near room temperature irradiation of Ta-10W to the mixed proton and spallation neutron exposure by Byun and Maloy56 to doses between 2 and 25.2 dpa showed prompt necking following yielding. Total elongation values of <3% were observed for doses between 2 and 7.5 dpa, with near-zero ductility observed at 25.2 dpa. Fast neutron irradiation studies of Ta-10W by Gorynin et a/.59 observed brittle failure after 0.13 dpa in materials irradiated and tested near 600 K. Less than 5% total elongation was measured following 1.97 dpa irradiation at 700 K, despite a near

doubling of the yield stress over the unirradiated mate­rial. Limited ductility was also observed following 2.63 dpa exposure in materials irradiated and tested at 1073 K, with a yield strength increase from 240 to 315 MPa over the unirradiated control. While low- temperature embrittlement following exposure to 0.13 dpa was reported in the neutron-irradiated mate — rials59 and limited ductility following mixed proton and neutron exposure,56 the interstitial concentra­tions on the behavior of these materials may be more influential than the irradiation spectrum.

Similar to Ta and Ta—10W, very limited data exist on the irradiated properties of T-111. The most referenced base-line study is that by Wiffen,1 shown as in Figure 8. Large increases in yield and ultimate tensile strengths are observed following irra­diations to 1.9 x 1022ncm~2 (E> 0.1 MeV), 2.5 dpa, at 688 and 913 K. The increase in radiation hardening is substantially greater than that observed in pure Ta irradiated under similar conditions. Yield and

Figure 10 Deformation mode map of (a) pure Ta and (b) Ta-1W for room temperature irradiations, illustrating fracture, plastic instability, uniform plasticity, and elastic regions as a function of stress and displacement dose. The increases in the uniform plasticity region for temperatures of 523 K are superimposed. Reproduced from Byun, T. S.; Maloy, S. A. J. Nucl. Mater. 2008, 377, 72-79.

ultimate tensile strengths of around 1250 MPa are reported for irradiation at 688 K, with uniform and total elongation of <0.3% and 4.5%, respectively. Irradiation at 913 K improves uniform and total elon­gation values only slightly to ^2.5% and 8%. These values represent more than a 50% reduction in ductil­ity over the unirradiated values. No known irradiated property data for T-111 exist for temperatures above
913 K. As tensile strengths ofboth Ta-10W and T-111 exceed 1000 MPa at temperatures below 1000 K19,56,59 and are well above the stresses that produce brittle behavior in vanadium alloys for which more data are available, it is likely that these Ta alloys are embrittled under these conditions.3 Further expansion of the irradiated materials database including fracture tough­ness data for Ta and Ta alloys irradiated near and above 1000 K is much needed to ascertain the upper temperature limitations. However, based on this pre­liminary data, temperatures below1000 K may need to be avoided for Ta and Ta-base alloys.

Low-fluence irradiations to 1.2 x 1015ncm~2 at room temperature and 623 K have been performed to evaluate the performance of T-111 and Ta-10W for use in radioisotope power applications.60 These low-dose irradiations produced little change in the tensile properties of the two alloys. Some variations in the total elongation were observed in T-111, which may be related to the distribution and make-up ofthe Hf-rich compounds in the material as well as the effects of radiation. Thermal stability of T-111 can be an issue, as a brittle behavior following 1100 h aging at 1398 K has been reported,41 due to precipi­tation of Hf-rich compounds along grain boundaries. It is not known how the combination of long-term thermal aging under irradiation affects the structure- property relationships or how the detrimental pre­cipitation of the interstitial elements with Hf can be controlled.

Figure 3457 shows the effects of Cr and Al content on the weight gain of ODS ferritic steels after exposure to SCPW at 500 °C with 8 ppm of dissolved oxygen. Increasing the Cr content from 14 to 17 wt % does not affect corrosion resistance if ODS ferritic steels contain 4wt % Al. For 16wt% Cr, the addition of A1 increases corrosion resistance in 16Cr-ODS steels. As shown in Figure 35,43 tested at SCPW (510°C, 25 MPa) for 600 h, the addition of 4wt% Al did not significantly influence corrosion resistance in 19Cr — ODS steel, though a rather dense chromia film was observed on the specimen surface. The 16wt% Cr is not large enough to form homogeneous and stable chromia on the entire surface of the specimen, whereas a very thin alumina film covers the entire surface of the specimen with the Al addition of 2 wt%. Thus, the addition of Al effectively improves corrosion resis­tance in 16Cr-ODS steel. As shown in a comparison with 9Cr-ODS steel in Figure 35, its weight gain is much larger than 16Cr-ODS steel, indicating that 9Cr-ODS steel is not adequate for application to SCWR. The suppression of SCPW corrosion by the addition of Al to 16Cr-ODS steel is due to the for­mation of a very thin alumina film on the surface.

4.11.1 Introduction

This chapter aims to address that need by explaining the influence of microstructure on the properties of nuclear graphite and how irradiation-induced changes to that microstructure influence the behavior of graph­ite components in reactor. Nuclear graphite is manu­factured from coke, usually a by-product of the oil or coal industry. (Some cokes are a by-product of refining naturally occurring pitch such as Gilsonite.9) Thus, nuclear graphite is a porous, polycrystalline, artificially produced material, the properties of which are de­pendent on the selection of raw materials and man­ufacturing route. In this chapter, the properties of the graphite crystal structures that make up the bulk poly­crystalline graphite product are first described and then the various methods ofmanufacture and resultant properties of the many grades of artificial nuclear graphite are discussed. This is followed by a description of the irradiation damage to the crystal structure, and hence the polycrystalline structure, and the implica­tion of graphite behavior. The influence of radiolytic oxidation on component behavior is also discussed as this is of interest to operators or designers of graphite­moderated, carbon dioxide-cooled reactors, many of which are still operating.

Nuclear graphite has, and still continues, to act as a major component in many reactor systems. In prac­tice, nuclear graphite not only acts as a moderator but also provides major structural support which, in many cases, is expected to last the life of the reactor. The main texts on the topic were written in the 1960s and 1970s by Delle et al.l Nightingale,2 Reynolds,3 Simmons,4 in German, and Pacault5 Tome I and II, in French with more recent reviews on works by Kelly6,7 and Burchell. This text is mainly on the basis of the UK graphite reactor research and operating experi­ence, but it draws on international research where necessary.

During reactor operation, fast neutron irradiation, and in the case of carbon dioxide-cooled systems radiolytic oxidation, significantly changes the graph­ite component’s dimensions and properties. These changes lead to the generation of significant graphite component shrinkage and thermal stresses. Fortu­nately, graphite also exhibits ‘irradiation creep’ which acts to relieve these stresses ensuring, with the aid of good design practice, the structural integ­rity of the reactor graphite core for many years. In order to achieve the optimum core design, it is important that the engineer has a fundamental under­standing of the influence of irradiation on graphite dimensional stability and material property changes.

The unirradiated stress-strain behavior of graphite is nonlinear and exhibits hysteresis and permanent set. It is different in tension to compression (Figure 45) and graphite is also much stronger in compression than in tension.

Similar curves can be found for Gilsocarbon.74 On irradiation, in an inert atmosphere, there is a rapid and significant increase in modulus attributed to pinning of dislocations in the basal plane. Also, the stress-strain behavior becomes almost linear (Figure 46). This increase soon saturates, but there is a secondary increase attributed to structure tight­ening (or closure of porosity due to high crystal strain). Finally, at very high fluence, there is a rapid fall in modulus due to the degeneration of the graphite microstructure. Brown75 also showed that the Vickers hardness of isotropic graphite was con­siderably increased by irradiation. Young’s modulus is significantly reduced by radiolytic oxidation.

Graphite Young’s modulus increases with increas­ing temperature (Figure 47), which is attributed to the tightening of the structure, presumably because of the closure of microcracks; Maruyama et a/.76 tested samples in vacuum to avoid thermal oxidation.

 

Kq(30) K0(30) Ki(30) Kirr(30, 30)

 

f [45]

 

Substituting in the previous equation then gives

 

1 Klrr(T)

 

[46]

 

Thus, the irradiated thermal conductivity can be pre­dicted at any temperature for graphite irradiated in an inert atmosphere. The effect of weight loss and high fast neutron fluence is dealt with by a version of the ‘product’ rule leading to

 

1 Krr(T )

 

[47]

 

where Sk is the high dose reduction in thermal con­ductivity and [K0/K]ox is the reduction in thermal conductivity due to radiolytic oxidation.

 

Figure 45 Stress-strain curves of unirradiated pile grade A graphite. (a) Tension and (b) Compression. Modified from Losty, H.; Orchard, J. In Fifth Conference on Carbon; Pergamon, 1962; pp 519-532.

However, note the significant difference in strength at room temperature between samples tested in air and in vacuum. Several other authors have reported similar findings, attributing the difference to adsorbed moisture.77 The increase in strength with temperature is significant above 600 °C, making it of interest only for HTR reactor components. Also of interest in Figure 47 is the correlation between modulus and strength.

Design errors that can lead to subsequent deteriora­tion of concrete structures can be placed into two categories: inadequate structural design and lack of attention to details.57 Inadequate structural design occurs when the structure is exposed to a load greater than it is capable of carrying or if it sustains greater strain than its strain capacity. Inadequate considera­tions of temperature change or concrete creep and accidental impact can also result in damage. Typical symptoms of inadequate design include spalling and cracking of concrete. Poor detailing of a structure may result in localized concentration of stresses that result in cracking, which in turn can permit water or chemicals to access the concrete or ponding of water to produce saturated concrete. Poor detailing does not generally lead directly to concrete failure but can contribute to the action of one of the other specific causes of concrete failure.57 Examples of inadequate structural design include insufficient concrete cover over steel reinforcement, improper sizing and place­ment of steel reinforcement, inadequate section geometry, inadequate provision for drainage, abrupt changes in section, material incompatibility, and inadequate provision for deflection.

Poor construction practices and negligence can result from not following specified procedures or from carelessness. Poor construction practices do not lead directly to failure or deterioration of concrete but can cause defects that lead to concrete cracking. Examples of concrete cracks that can result from poor construction practices include plastic shrinkage, plastic settlement, early thermal contraction, crazing, and long-term drying shrinkage. The resulting con­crete cracking then can enhance the adverse impacts of mechanisms (such as described in the next section) and lead to concrete degradation. Poor construction prac­tices and negligence are best addressed through ade­quate quality assurance/quality control in conjunction with an aggressive inspection program. Examples of poor construction practice include adding additional water to concrete to facilitate placement or finishing, improper mixing and curing, improper consolidation, and improper location of steel reinforcement.

Lack of knowledge about the importance of care­ful selection and specification of materials and use of admixtures can also result in durability issues. This can include improper cement contents, use of poor quality or contaminated aggregates, incorporation of additives that can produce corrosion such as calcium chloride accelerators, and incorrect water-cement ratios.

Improper or inadequate maintenance also can con­tribute to the deterioration of concrete structures. Examples ofinadequate maintenance include moisture exposure and penetration caused by unrepaired cracks, improper application of coatings, damaged waterstops, and failure to clean drains and drain pathways.