The same U enrichment is used throughout a given PWR fuel assembly, but the core usually contains several levels of enrichment arranged to give uniform power distribution. In contrast, BWR fuel rods have

several axial segments with different enrichments and a BWR fuel assembly has several different rods with different enrichments. Thus, there are a variety of UO2 pellets with different U enrichments depending on reactor design; the enrichments are within 5% which is due to the limits of fuel fabrication facilities and fuel shipments.

For current LWR MOX fuels, depleted uranium (0.2—0.3% 235U), which is obtained in the form of tails from the enrichment process, is coupled with plutonium because there are economic incentives to concentrate as much plutonium in as few fuel assemblies as possible as it conserves the expensive fabrication cost of MOX fuel. As the quality of plutonium, from a neutronic aspect, varies with the isotope composition of plutonium, the specification of the plutonium content of LWR MOX fuel is affected by the quality ofplutonium. Total plutonium concentrations of 7.5% are considered to be equiva­lent to U enrichments of 4.0-4.3% for the current usual plutonium that is recycled from spent LWR UO2 fuel.2

To determine plutonium content of FBR MOX fuel, equivalent 239Pu (239Pu/(U + Pu)) is used. The actual plutonium content for a given batch is obtained by a calculation that uses the neutronic equivalent coefficient of each isotope and the isotope composition of plutonium to be used for the batch. 241Am, a daughter product of 241Pu, is considered in the calculation as well. The specification for equiva­lent 239Pu (239Pu/(U + Pu)) is relatively low for a large size core; equivalent 239Pu is 12-15% for the SUPERPHENIX (1200 GWe),28 1 4 -22% forMONJU (280 GWe).

Actinides, rare earths, and transition metals can form mixed oxides with UO2 or (U, Pu)O2. Examples of these elements are the fission products Zr, Ce, Nd, Ba, La, Pr, Sr, Sm, Y, Rb, Te, Pu, Np.12 Their solubil­ity limits determined for binary systems are never reached in the case of irradiated fuel, and these ele­ments can be completely or partially dissolved in the
fuel matrix. When such solid solutions are formed, these atoms act as phonon scattering centers as a result of the differences in bonding potential, ionic radii, or mass between the impurities and the sub­stituted atoms (U or Pu). The total scattering coeffi­cient can be evaluated from the differences in atomic mass and ionic radii13 and from the Griineisen con­stant, which represents the strain generated in the lattice by the difference in ionic radius and is usually treated as an empirical parameter obtained from experimental data.14-17

2.17.2.2.1 Volatiles and fission gases

Insoluble or volatile fission products (Kr, Xe, Cs, Te, I, etc.) are partially dispersed as interstitials and induce static displacements of host lattice atoms U or Pu from their mean lattice sites. In that case, their effect can be interpreted with the same equa­tions as for the dissolved fission products. The fission gas, thermodynamically insoluble in the matrix, is initially injected into the lattice and may precipitate into bubbles. Since collisions with fission fragment recoil cascades tend to re-inject gas into the lattice, for temperatures below about 1100 K, a fraction of the gas is kept in dynamical solution. At higher tempera­tures, most of the gas precipitates into bubbles or pores or can be released from the pellet. The simul­taneous mechanisms of gas diffusion, precipitation, and release can be described by reaction-rate
equations18 to calculate the partitioning of the gas in the different states starting from a number of kinetic (gas creation rate, diffusion coefficient, and resolu­tion rate) and structural (grain size, radii, and con­centrations of the bubbles) parameters. The entire irradiation history of the sample and, when labora­tory annealing is involved, the applied temperature program, have to be considered.

Figure 15 illustrates the temperature dependence of the heat capacity of zirconium hydride. It is clear that the heat capacity of the metal hydride is higher than that of the pure metal, particularly at higher temperatures. This behavior can be explained by the observation that while lattice vibrations are dominated by the acoustic mode at low temperatures, the contribution ofthe optical mode increases steadily as the temperature increases beyond ambient values.

2.11.3.5 Thermal Conductivity of Metal Hydrides23

Figure 16 shows the thermal conductivity of zirco­nium hydride, which is seen to be almost identical to that of the pure metal, and shows no dependence on temperature.

In order to analyze the thermal conductivity results, we expressed thermal conductivity as the sum of a lattice-vibration contribution (1lat) and an electronic contribution (1el). The electronic

contribution was evaluated from the Wiedemann — Franz relation as follows:

1el = LaT

Here, L is the Lorentz constant and a is electrical conductivity. Figure 17 plots the values of each con­tribution to the thermal conductivity of zirconium hydride. Here, the electronic contribution is greater than that of lattice vibrations, and the former increases with temperature, whereas the latter decreases as the temperature rises.

2.11.3.6 Comparison of Thermal Conductivity of Zirconium Hydride with those of the Hydrides of Titanium and Yttrium

Figure 18 shows the thermal conductivity of tita­nium hydride.24 The thermal conductivity of the hydride is approximately equal to that of the pure metal, but in this case, it increases slightly with hydrogen content. Figure 19 shows the thermal con­ductivity of yttrium hydride.25 In this case, the ther­mal conductivity of the hydride is higher than that of

Figure 18 Temperature dependence of the thermal conductivity of titanium hydride.

Temperature, T (K)

the metal, and it decreases with increasing hydrogen content. Additionally, the hydride’s thermal conduc­tivity decreases with decreasing temperature, whereas that of the metal remains more or less con­stant. Figure 20 plots the values of a lattice-vibration contribution and an electronic contribution to the thermal conductivity of titanium hydride. The results for titanium hydride are not much different from
those for zirconium hydride, as shown in Figure 17. However, as shown in Figure 21, the results for the case of yttrium reveal that both the lattice-vibration and electronic contributions to thermal conductivity are greater for yttrium hydride than for the pure metal. This indicates that the thermal conductivity characteristics of yttrium are different from those of zirconium and titanium.

Temperature, T (K)

Implementation of zirconium-based components in a nuclear reactor core, in fuel cladding or advanced composite fuel coatings and matrix, is enabled by its low thermal neutron capture cross-section. Low — activation structural materials are desired, and par­ticularly for ZrC in fuels, diversion of neutrons from fission reactions is to be avoided. The isotopic average cross-section for Zr for 0.0253 eV thermal neutrons (at room temperature) is 0.19 barn (1.9 x 10- 9m2), and for C is 0.0035 barn (3.5 x 10-31 m2).160 Owing to similar chemistry, Zr naturally occurs together with up to 2 wt% Hf unless specially purified for nuclear reactor applications (<100 ppm Hf). The isotopic average cross-section for Hf is 106 barn (1.06 x 10-26 m2), making it a very undesirable impu­rity in Zr for reactor applications.

2.13.6.2.1 Durability and dimensional stability under neutron irradiation

Keilholtz eta/.161 irradiated hot-pressed, slip-cast, and explosion-pressed ZrC at 403-628 K (temperatures corrected by Watson and Keilholtz162) with a fast neutron (>1 MeV) fluence of (0.4-5.4) x 1021 cm-2, including 63-142 thermal cycles from room temper­ature to the irradiation temperature during the experiment, in the Oak Ridge National Laboratory’s Engineering Test Reactor. Damage due to thermal cycling alone was ruled out by out-of-pile tests. Severe fracturing of the hot-pressed and slip-cast samples were noted for fluences above (2.5-3) x 1021cm-2, with the explosion-pressed (containing Co or Ni binder) samples showing minor to severe damage above 1.1 x 1021cm — . Of the 2-3% radiation-induced volumetric swelling measured for all sample forms, 1% was accounted for by lattice parameter expansion, with the authors proposing point defect clusters and gas bubbles as causing the remainder. Helium gas is produced in carbides through fast-neutron reactions with carbon, and the authors considered the possibility of hydrogen pro­duced by thermal neutron reactions with nitrogen impurities. Swelling increased with fluence up to 2 x 1021 cm — , but further fluence resulted in the same or lesser degree of expansion.

Keilholtz et a/.163 expanded this study to irradiation at 1273-1373 Kat afluence of2.4 x 1021 cm-2. Swelling was lower at the higher temperatures, with <1% volume expansion measured. Watson and Keilholtz162 irradiated the same materials at low temperature and fluence (338-373 K, 0.21-0.72 x 1021cm-2), with

1. 7-2.5% volume expansion reported. The irra­diated samples were annealed at 973-1373 K until dimensional change ceased. Volume contracted with increasing temperature up to about 1173 K, with the degree of contraction saturating at higher tempera­ture. Some evidence for reexpansion of slip-cast ZrC at higher temperatures was reported, but there were too few data points to determine this conclusively. The authors proposed that expansion/contraction behavior as a function of fluence was caused by atomic displacements and point defect clusters produced by initial fast neutron cascades, with subsequent cascades at higher fluence returning some displaced atoms to lattice sites. Contraction was also attributed to the annealing of defects dur­ing postirradiation heat treatment. As temperature increases, easily annealed single point defects are consumed, leaving more difficult-to-anneal defect clusters, and further contraction is limited.

These observations are consistent with the find­ings of Andrievskii et a/.,164 who irradiated sintered ZrCo.98 at either 423 or 1373 K with a fast neutron fluence of 1.5 x 1020 cm—2 Lattice parameter expanded with irradiation but to a lesser degree at the higher temperature: 0.47% at 423 K versus 0.13% at 1373 K (volume increase of 1.4% vs. 0.38%). Correspond­ingly, density decreased after irradiation; however, the decrease was more, not less, pronounced at a higher temperature (—1.7% at 423 K vs. —2% at 1373 K). The authors propose that despite a lesser degree of lattice parameter swelling at higher tem­peratures, intergranular porosity increased and accel­erated swelling.

Koval’chenko and Rogovoi165 irradiated ZrC0 98 at 323 K with thermal neutrons to a fluence of 1 x 1019—1.5 x 1020cm— , observing a lattice param­eter expansion of 0.07-0.71% (volume expansion

0. 21-2.15%) that increased with fluence. No change in the porosity or grain size of the samples was detected. Andrievskii et a/.164 attributed their lower lattice swelling to higher sample purity, as the sam­ples of Koval’chenko and Rogovoi165 had low initial lattice parameter and were likely high in O and N impurities.

Andrievskii et a/.166 considered swelling as a func­tion of C/Zr ratio. They irradiated ZrC07-094 at 413 K in a fast neutron of fluence of 1 x 1019cm— . Lattice parameter increased after irradiation for all samples, but superimposed on the expected trend of increasing lattice parameter with increasing C/Zr ratio was a more pronounced increase for samples closer to stoichiometry. Lattice parameter of ZrC073 expanded by 0.04% (0.12% volume expan­sion), while ZrC094 expanded by 0.33% (0.99% volume expansion). The authors proposed that in near-stoichiometric compositions, fast neutron-induced atomic displacements may force C atoms into tetrahe­dral interstitial sites, while in more nonstoichiometric compositions, C atoms may be displaced to already vacant octahedral sites. In this sense, the authors judged irradiation-induced nonstoichiometry in more carbon — deficient ZrCx to be qualitatively similar to unirradi­ated nonstoichiometric ZrCx.

ZrC has also been subjected to high-temperature heat treatment and irradiation as a 20-50 q. m thick coating layer in testing of TRISO fuel having a cen­tral actinide fuel kernel coated in a porous carbon buffer layer, a dense pyrocarbon layer, a ZrC layer, and an outer pyrocarbon layer. Particles have been irradiated loose or embedded in the matrix of a fuel compact. The performance of ZrC in this configuration is inevitably tied to that of the system as a whole, as the neighboring coatings and fuel matrix not only add structural support but also intro­duce the possibility of reactions among ZrC, fission products, gases, graphite, and actinides.

Reynolds eta/.167 fabricated ZrC coatings either in the standard TRISO configuration or directly on top of fissile 235UC2 or fertile (232Th,233U)O2 kernels, the latter designed as a test of ZrC corrosion. These were irradiated at 1473 K with a fast neutron (>0.18 MeV) fluence of 5 x 1021 cm—2, to a burnup of 70% fissions per initial actinide metal atom (%FIMA) for fissile and 8% FIMA for fertile particles, in the Commissar­iat a l’Energie Atomique’s Siloe Test Reactor. Postir­radiation examination revealed that the only ZrC damage was radial cracking in almost all the particles with ZrC directly atop kernels; as this configuration lacked buffer volume to accommodate fission gases, such failures were expected. ZrC in the standard TRISO configuration was crack-free. No diffusion or reactions between actinides/fission products and ZrC was evident in any configuration.

Ogawa et a/.168 fabricated TRISO particles with a 20-30 qm thick ZrC layer and UO2 kernel and compacted these in a graphite-resin matrix at 2073 K. Irradiation by fast neutrons (>0.18 MeV) under various conditions (1173-1873 K, fluence (1-2.2) x 1021 cm—2, burnup of 1.5-4% FIMA, during 81-156 effective full-power days) was carried out in the Japan Materials Test Reactor at the Japan Atomic Energy Research Institute. Following decon­solidation of the fuel compacts to recover loose par­ticles, ceramography showed no ZrC degradation in particles irradiated at the highest burnup, fluence, and temperature for over 135 effective full-power days. A zero particle failure rate was assessed by in-reactor monitoring of fission gas 85Kr release rate during 80 effective days of irradiation at 1173 K, which was an order of magnitude smaller than that expected for a single particle rupture out of 7000 particles in this test.

Minato eta/.169 irradiated similarly prepared com­pacts between 1673-1923 K with a fast neutron (>0.18MeV) fluence of 1.2 x 1021cm—2 to 4.5% FIMA burnup during 100 effective full-power days, finding a through-coating failure rate of 0.01%, that is, failure of less than one out of 2400 particles irradiated.

Some of the particles irradiated by Ogawa eta/.168 were subsequently heat treated at 1173-2273 K. Par­ticles originally irradiated at 1173 K to a fluence of

1.2 x 1021 cm—2 and burnup of 1.5% FIMA during 80 effective days were annealed in flowing He by Minato et a/.170 at 1873 K for a total of 4500 h and by Minato et a/.120,171 at 2073 K for 3000h and at 2273 K for 100 h. In situ 85Kr release monitoring showed none of the 100 particles annealed during each test ruptured. Ceramography and X-ray micro­radiography ofparticles from each test showed that at 1873 K, there was no thermal degradation or corro­sion of ZrC coatings. At 2073 K, the ZrC coating was intact, but there was some surface roughness attrib­uted to thermal degradation and evidence of attack along the grain boundaries. At 2273 K, all but 7 of the 100 particles showed some failed or damaged coating layers, including the ZrC layer, and evidence of reac­tion or interdiffusion between ZrC and U.

Interpreting the results via a thermodynamic analysis of the Zr-C-U-0 system, the authors attri­bute deterioration of ZrC at these temperatures, at least in part, to mechanical failure of the inner pyrocarbon layer combined with oxidation of carbon by the oxygen released during the transmutation of U in U02. Subsequent exposure of ZrC to C0(g) oxidizes ZrC to Zr02 and C and reduces the ZrC coating integrity.

Durability of ZrC is more likely to be limited by irradiation of the system contained within rather than by high-temperature degradation of ZrC alone. Ogawa and Ikawa172 subjected unirradiated TRISO particles having either U02 or (Th, U)02 kernels to annealing in He atmosphere for 1h at 2073 K (as during fuel compact fabrication) followed by 1 h at 2173-2823 K. ZrC coatings on all (Th, U)02 particles were intact after 1 h at 2823 K, but durability of U02 particles was guaranteed only to 2373 K, with swelling noted at 2723 K and U migration out of the ZrC coating at 2773 K. ZrC grain growth and plastic deformation occurred, especially above 2723 K.

Two MOX pellet fabrication processes were devel­oped in Germany, the Optimized CO-Milling (OCOM) process and the AUPuC process.7,62

The OCOM process was developed by Alkem and uses UO2 powder, PuO2 powder, and recycled scrap powder as feed materials. The manufactured MOX pellets are made fully soluble in nitric acid by opti­mizing the co-milling of the three powders. In the OCOM process, two different MOX pellet fabrica­tion routes can be taken as shown in Figure 16.

In the first route (left half of Figure 16), three powders are prepared to achieve specified plutonium concentrations required for the fuel to be used in

FBRs and LWRs. The powders are co-milled to obtain a homogeneous distribution of plutonium, and the milled powder is pressed into green pellets after granulation. The second route (right half of Figure 16) is used to fabricate MOX pellets for LWRs; it effectively introduces the master blend concept into the process for better economy.7 This means that a mixture containing ^30% plutonium is made from UO2 powder and PuO2 powder, and this mixture is then milled using the OCOM milling process. The MOX powder that results from the milling process is no longer free-flowing. By mixing this master blend with the eight — to tenfold amount of free-flowing UO2 powder to obtain the required plu­tonium content for LWR MOX fuel, a feed powder is obtained with sufficient flowability for direct pelle­tizing. An issue requiring special attention for this route is the homogeneity of the plutonium distribu­tion; two powders of very different physical proper­ties have to be mixed together to obtain the desired plutonium content. One powder is the master blend of PuO2 and UO2, which after milling consists of a powder with very fine nonflowing grains and having a high tendency to self-agglomerate, while the second part is the free-flowing UO2 powder prepared by the AUC process with its rather coarse grains.7 The mix­ing of the two powder components and preventing their segregation during further processing steps

require special attention and expertise. The green pellets prepared by the two routes are sintered in a reducing atmosphere after dewaxing. A typical a-autoradiograph of a transverse section of an LWR pellet manufactured by the OCOM process has been reported by Roepennack et a/.62 The density and appearance of sintered pellets are inspected after centerless grinding.

The AUPuC process (Figure 177) was developed as a coprecipitation process based on the AUC pro­cess. The AUPuC process uses plutonium in the form of a nitrate solution. NH3 and CO2 gases are introduced into a mixed solution ofplutonium nitrate and uranyl nitrate with a concentration of about 400 gl-1 of heavy metal at first, and then tetra — ammonium tricarbonate dioxo urinate/plutonate is precipitated by the following reaction.7

(U, Pu)O2(NOb)2 + 6NH3 + 3CO2 + 3H2O! (NH4)4[(U, Pu)O2(CO3)3] +NH4NO3

The precipitated AUPuC is filtered and directly reduced at ~-750 °C in an atmosphere of hydrogen gas. The obtained MOX powder with about 30% plutonium concentration is utilized as the master blend and is the same as in the OCOM process. The homogeneity of plutonium in the master blend is much better in the AUPuC process than in the

OCOM process because solid solutions have already formed during precipitation in the AUPuC process. This coconverted powder is also diluted like the master blend by the free-flowing UO2 prepared by the AUC process and recycled MOX powder so that the final blended MOX powder has the desired plu­tonium concentration. This final blended MOX pow­der flows easily, just as in the OCOM process, and it is pressed into green pellets by a rotary pressing machine without granulation.43 The steps after pel­letizing are the same as those in the OCOM process. A typical a-autoradiograph of a transverse section of a LWR pellet manufactured by the AUPuC process has also been reported by Krellmann.7

On the basis of the above processes, Siemens constructed the MOX fuel fabrication facility in Hanau as a dual purpose (FBR and LWR) facility and started operation in 1972. After reaching an effective capacity of 20-25 tHM per year of LWR fuel in the 1987-1991 period, it was shut down, as a result of a contamination incident in 1991.6 This plant was subsequently decommissioned. On the same site, Siemens constructed a larger plant with an annual capacity of 120 tHM for LWRs.7 However, this plant was abandoned before starting operation
because Siemens never received an operating license from the local government.

The general mechanical behavior properties of austenitic stainless steels at room and at elevated temperatures are described. These provide the back­ground for their behavior in various reactor environ­ments. The mechanical properties of the various grades of the 300 series austenitic stainless steels are fairly similar, particularly at room temperature, so available data for type 316 or 316L steel are used as representative of the group. There is more variation in properties at elevated temperatures, particularly creep-resistance and creep-rupture strength, so important properties differences are noted, particu­larly for steels modified with Ti or Nb which have more high-temperature heat-resistance than type 316 steel. Some effects of processing on mechanical properties are noted, but generally properties are described for material in the SA condition.

Austenitic stainless steels such as types 304, 316, and 316L have yield strength (YS — 0.2% offset) of 260-300 MPa in the SA condition at room tem­perature, with up to 50-70% total elongation.1-7 Typ­ical YS values as a function of temperature for type 316 are shown in Figures 2 and 3. Other austenitic stainless steels developed for improved creep resistance at high temperatures, such as fine-grained 347HFG or the high-temperature, ultrafine precipitate — strengthened (HT-UPS) steels (Table 3), have very similar YS of about 250 MPa in the SA condition (typical thicker section pipes or plates), as shown in Figure 3. Many applications of type 304 and 316 stainless steels require a minimum YS of 200 MPa. However, small amounts of cold plastic strain, 1-5%, typical or straightening or flattening for various prod­uct forms, termed ‘mill-annealed,’ raise the YS to about 400 MPa, because austenitic stainless steels tend to have high strain-hardening rates. Large

amounts of cold work (CW) push the YS higher, with 20-30% CW 316 having YS of 600-700 MPa,8,9 but with very low ductility of only 2-3%. The very

fine grain sizes found in thin-sheet and foil products made from 347 steel also tend to push ambient YS to 275-300 MPa or above.7 The ultimate tensile strength (UTS) of SA 316 steel at room temperature is about 600 MPa, and can be higher (600-700 MPa) for steels such as 347HFG, HT-UPS, or some of the high — nitrogen grades. The UTSof20-30% CW 316orother comparable steels can be 700-800 MPa at room

4,8,9

temperature.

The impact-toughness and crack-growth resis­tance of SA 316 at room temperature and tem­peratures below 500 °C are excellent because of its high ductility and strain-hardening behavior. Charpy impact toughness values for SA 316 and 347 steel are about 150J at 22-400 °C, and tend to stay above 100J even at cryogenic (—196 °C) temperatures. Type 316 stainless steels also have good room — temperature fatigue resistance, exhibiting endurance limits for cyclic stresses below the YS.

At elevated temperatures, the YS of SA 316 declines with increasing temperature, reaching levels of about 150MPa at 600-650 °C (Figure 2), and going lower at 700-800 °C. More heat-resistant steels such as 347HFG or HT-UPS steels may be slightly stronger at 700 °C, and can have YS values of 300­350 MPa in the ‘mill-annealed’ (5% CW) (Figure 3). The UTS of SA 316 remains at about 500 MPa up to 500 °C, and then declines rapidly with increasing temperature until YS and UTS approach similar values (120-180MPa) at about 800 °C (Figure 2). More heat-resistant steel, such as 347HFG and the HT-UPS steels, can retain higher UTS values of 200­300 MPa at 800 °C. Unaged SA 316 generally have 30-60% total tensile elongation at temperatures up to 800 °C; similar steels with 20-30% CW can have 5-10% ductility until they recrystallize at tempera­tures of 800 °C or above.9

1000

10

18000 20000 22000 24 000 26000

Larson-Miller parameter

Figure 4 A plot of creep-rupture stress as a function of Larson-Miller parameter (LM P) for nine heats of SA 316 austenitic stainless steel tubing tested by the National Research Institute for Metals (now NIMS) in Japan. LMP10000 represents data for rupture after 10 000 h. LMP = (T[°Cj + 273) (20 + log tr), where T is creep testing temperature and tr is the creep-rupture life in hours. Reproduced from Data sheets on the elevated temperature properties of 18Cr-12Ni-Mo stainless steels for boiler and heat exchanger tubes (SUS 316 HTB), Creep Data Sheet No. 6A; National Research Institute for Metals: Tokyo, Japan, 1978.

At elevated temperatures, time-dependent defor­mation, or creep, becomes a concern for austenitic steels such as 304 and 316 above 500-550 °C. A Larson-Miller parameter (LMP) plot of creep — rupture strength for SA 316 is shown in Figure 4, and for 347HFG and HT-UPS steels in Figure 5. Long-term creep-rupture behavior is affected by precipitation behavior at elevated temperatures, as is described in the following section. Creep-rupture behavior (time to rupture or time to 1% strain) is far more limiting in design for high temperature integrity than tensile properties. The creep-rupture

Temperature for 100 000 h rupture life (°C)

580 620 660 700 740 780 820

strength of SA 316 in Figure 4 is comparable to creep-rupture strength of 347 steel in Figure 5, and both have less creep strength than 347HFG, a steel containing more Nb and C (Table 3). Types 304 and 316L steels would have less creep strength than 316 steel. By comparison, the triply stabilized (additions of Ti, V, and Nb) HT-UPS steel has outstanding creep — rupture resistance at 700-800 °C, comparable to that of the solid-solution Ni-based alloy 617. A more direct comparison of creep resistance at 700 °C and 170 MPa is shown in Figure 6. For this creep-rupture condi­tion, SA 316 ruptures after about 40 h, whereas the SA HT-UPS steel resists creep and rupture until 18 745 h.4,7 For elevated temperature creep behavior of heat-resistant stainless steels with additions of Ti and Nb, processing conditions are also important, including prior cold-strain and the SA temperature. The creep resistance of SA 304 and 316 steels is not affected significantly by different annealing tem­peratures, and both steels have less creep resistance in the 10-30% CW condition. By contrast, 347HFG and HT-UPS steels benefit dramatically from higher solution annealing temperatures (1050-1100 °C com­pared to 1150-1200 °C) and small amounts of CW, because these enhance the formation and stability of nano-dispersions of MC carbide precipitates, which are responsible for their high-temperature creep

4,7,10,11

resistance.

Figure 6 Direct comparison of creep-resistance of D9 and high-temperature, ultrafine precipitate-strengthened steels. Adapted from Swindeman, R. W.; Maziasz, P. J.; Bolling, E.; King, J. F. Evaluation of Advanced Austenitic Alloys Relative to Alloy Design Criteria for Steam Service: Part 1 — Lean Stainless Steels; Oak Ridge National Laboratory Report (ORNL-6629/P1); Oak Ridge National Laboratory: Oak Ridge, TN, May 1990; Data sheets on the elevated temperature properties of 18Cr-12Ni-Mo stainless steels for boiler and heat exchanger tubes (SUS 316 HTB), Creep Data Sheet No. 6A; National Research Institute for Metals: Tokyo, Japan, 1978; Teranishi, H.; etal. In Second International Conference on Improved Coal Fired Power Plants; Electric Power Research Institute: Palo Alto, CA, 1989; EPRI Publication GS-6422 (paper 33-1); Swindeman, R. W.; Maziasz, P. J. In Creep: Characterization, Damage and Life Assessment; Woodford, D. A., Townley, C. H. A., Ohnami, M., Eds.; ASM International: Materials Park, OH, 1992; pp 33-42.

2.12.6.1 Tensile Stress-Strain Behavior

Figures 1 and 2 summarize the typical stress-strain behavior of 2D CVI SiC/SiC composites. The behav­ior is initially linear under strains below 0.03%. Then,

Source: Aubard, X.; Lamon, J.; Allix, O. J. Am. Ceram. Soc. 1994, 77, 2118-2126.

Property

the nonlinear deformations result essentially from transverse cracking in the matrix (the cracks are per­pendicular to fibers oriented in the loading direction). Saturation of matrix damage is indicated by the end of the curved domain marked by a point of inflection. Then the ultimate portion of the curve reflects the deformation of fibers. Fiber failures may initiate prior to ultimate fracture. Such mechanical behavior is essentially damage-sensitive.

A damage-sensitive stress-strain behavior is obtained when the initial contribution of the matrix to load carrying is significant. The elastic modulus of the matrix (Em) is not negligible when compared to that of the fiber (Ef). Its contribution to the modulus of the composite (Ec) is illustrated by the mixtures law, which provides satisfactory trends for continuous fiber-reinforced composites:

Ec = EmVm + Ef Vf [9]

where Vm is the volume fraction of matrix and Vf is the volume fraction of fibers oriented in the loading direction in a 2D woven composite.

In 2D CVI SiC/SiC composites, Em («410 GPa) > Ef (200-380 GPa), Vm ~ Vf the initial contribution of the matrix to Ec is significant. Then, as it decreases when the matrix cracks, the behavior becomes con­trolled by the tows. The 2D SiC/SiC composites exhibit an elastic damageable behavior (Figure 3). This means that the response of the damaged mate­rial is elastic as indicated by the linear portion of the curves on reloading. Figure 4 shows the dependence of the elastic modulus on damage.

In spite of difficulties existing in the measurement of the heat capacity of LM, it was measured with a good precision for liquid Na at normal atmospheric pressure — the recommendations from different sources differ for <1% in the temperature range from normal melting point up to normal boiling

point at normal atmospheric pressure.7,10,67 Higher uncertainty is observed at higher pressures and tem­peratures and on the saturation line.68 The heat capacity of liquid Pb was satisfactorily measured only at temperatures up to about 1400 K5,2 , 8 and with a precision ~5%. At higher temperatures, the available experimental data often give contradictory results. The heat capacity values for liquid Pb in a large range of temperatures at normal atmospheric pressure were estimated by Gurvich and Veyts69 with theoretical models benchmarked on the existing experimental results. Available data on the heat capacity of Pb-Bi(e) are very limited.70-72 In order to describe the temperature dependence of LM heat capacity, often the following correlation is used:

СДГ, p0) = + bcfT + ccf T2 + dcf T -2 [12]

The recommended coefficients of correlation [12] for liquid Na were taken from the compilation of IAEA,26 for Pb from Gurvich and Veyts,69 and for Pb-Bi(e), they were deduced in Sobolev34 on the basis of a review of the existing data and recommen­dations; the coefficients are given in Table 10. The uncertainty is about ±1% forNa and ±(5-7)% forPb and Pb-Bi(e) at temperatures up to T = 1100-1400 K; the uncertainty increases at higher temperatures where no experimental data were found for Pb and Pb-Be(e) in the literature.

The calculated with correlation [10] isobaric heat capacities of liquid Na, Pb, and Pb-Bi(e) are pre­sented in Figure 9 versus temperature.

The isochoric heat capacity can be estimated using correlations for the isobaric heat capacity (cp),

the isothermal compressibility (br), the density (p), and the isobaric volumetric CTE (a^):

pbr

The molar enthalpy (H) of LM as a function of temperature at the given pressure can be presented as a sum of the LM enthalpy at the melting point H(Tm, p) and the LM enthalpy increment caused by temperature increase AH(T — TM, p), which is expressed through an integral of the isobaric heat capacity over temperature:

H (T, p) = H ( Tm, p) + AH (T — Tm, p)

T

= H (Tm, p)-

2.14.4.1 Equation of State

During the past years, considerable progress has been achieved in the development of empirical, semi­empirical, and mechanistic EOS for fluids. Simple thermal EOS is frequently used in engineering practice, which relates the main TD variables pressure, temperature, and volume (or density): F(p, T, p) = 0, which is equivalent to p = p(T, p) considered in Section 2.14.4.1. Knowledge of the temperature and pressure dependence of one of the thermodynamic potentials (e. g., enthalpy H) allows to construct the caloric EOS: H = H(T, p).

The first term on the right-hand side is described by eqn [5] in Section 2.14.4.1. The effect of pressure can be estimated using the information on the sound velocity, thermal expansion, and heat capacity, with the following thermodynamic relationship:

dp _ / 1 MaTa2(T)

dp T ~ U(T)+ cp (t)

The results of the calculation of the pressure coeffi­cient [16] for liquid Na, Pb, and Pb-Bi(e) show34 that it is rather small: the density correction does not exceed 0.04% per 1 MPa of pressure for Na and 0.01% per 1 MPa for Pb and Pb-Bi(e) in the tem­perature range of the normal operation of these cool­ants in Gen IV reactors. Thus, at normal operation pressures of these reactors (0.1—2.0 MPa), the thermal EOS developed at normal atmospheric pressure can be used for design estimations.

Gadolinium is now the most commonly used burnable poison in commercial reactors. Natural gadolinium consists of the isotopes 152, 154, 155, 156, 157, 158, and 160, with abundances of 0.2%, 2.18%, 14.8%, 20.47%, 15.65%, 24.84%, and 21.86%, respectively.1,2 Of these, 155Gd and 157Gd have extraordinarily high thermal neutron capture cross-sections of 61 000 and 254 000 barns, respectively (Figure 5). This means that gadolinia can effectively suppress the neutron multiplication factor at even a very low concentration.

However, gadolinia is usually concentrated spatially rather than dispersed to take advantage of spatial self­shielding3,4; when concentrated into a small number of fuel rods, for example, thermal neutrons entering the poisoned fuel rod are absorbed near the surface because of the high cross-section. 155Gd and 157Gd atoms near the center of the fuel rod see virtually zero thermal neutron flux, and are thereby shielded from neutron captures. Self-shielding thereby limits the initial multiplication effect of lumped gadolinium and extends the depletion time for 155Gd and 157Gd. Self-shielding has the effect that the initial reaction rate is proportional to the surface area, while the time to deplete the 155Gd and 157Gd is proportional to the ratio of surface area to volume. It allows the nuclear designer flexibility in controlling both the initial absorption effect and the depletion rate independently.

Gadolinium is usually incorporated in fuel assem­blies in the form of gadolinia/urania Gd2O3/UO2 fuel pellets, with properties only slightly different from those of conventional UO2 pellets and a virtu­ally identical manufacturing route. Figures 6 and 7 show typical distributions of Gd2O3/UO2 fuel rods in PWR and BWR fuel assemblies, respectively. Gadolinia rods offer the nuclear designer flexibility in choosing the optimal combination of initial reactiv­ity worth and poison depletion rate. There is a residual absorption penalty that, though less than that for dis­crete burnable poison rods, could in theory be reduced by using gadolinium enriched in 157Gd. Figure 8 shows the radial distribution of 157Gd atoms as a function of time. The self-shielding effect is evident in that the depletion proceeds from the outside in shells, usually likened to peeling an onion. 155Gd behaves similarly, though on a slower timescale because of its smaller cross-section.

Gadolinia is used routinely in the UK’s AGRs, but in a different form to that used in LWRs. AGR fuel elements incorporate discrete absorber cables containing gadolinia Gd2O3 powder in a stainless steel tube. These are located on a support structure within the outer graphite sleeve, with provision for up to three cables each at of the bottom, mid­dle, and top of the element, giving a maximum of nine cables per element. The complete AGR fuel assembly, called a stringer, consists of eight fuel elements stacked on top of one another, and at the interfaces between elements, the absence of fuel causes the thermal neutron flux and thermal power production to peak. This is because the thermal neutron flux is determined by the balance between the source of thermal neutrons slowing

down in the moderator and their removal by (prin­cipally) the nuclear fuel. Where fuel is absent, the balance shifts to produce a higher thermal flux. The gadolinia cables are used to counter this
deleterious axial heterogeneity, helping to reduce flux peaking in the axial gaps between fuel elements.

2.16.3.2

Erbium

Erbium is a less commonly used burnable poison mate­rial, but has been used in some commercial PWRs and is potentially useful for specialized applications. Natural erbium consists of the isotopes 162, 164, 166, 167, 168, and 170 with abundances of 0.14%, 1.61%, 33.6%, 22.95%, 26.8%, and 14.9%, respectively.2 The thermal neutron capture cross-sections are modest however, 167Er having the highest thermal cross­section of 700 barns and the others all less than 20 barns, which makes erbium characteristically slow to deplete in reactor and causes it to have a high residual absorption penalty. It is normally deployed in the form of erbia/urania Er2O3/UO2 fuel pellets in selected fuel rods.

Unlike boron, erbium acts as a resonant absorber, meaning that there are resonance peaks in the absorp­tion cross-section plotted against incident neutron kinetic energy (Figure 9). Erbium is therefore able to mimic the negative fuel temperature feedback mecha­nism due to resonance absorptions in 238U, which could theoretically be helpful in the so-called inert matrix fuel (IMF) designs currently being considered to irra­diate and destroy the minor actinides Np, Am, and Cm. Destruction of the minor actinides is more efficient if the fuel does not contain any 238U, which would gener­ate fresh 239Pu through fertile captures. IMF therefore uses matrix materials such as cerium, zirconium, and
yttria which dilute the nuclear materials, but which contribute little to neutron captures.

A thermodynamic model of the Pu-O system was proposed by Kinoshita et a/.27 and Gueneau et a/.28 The calculated phase diagram by Gueneau et a/.28 reproduces the main features of the phase diagram proposed by Wriedt29 in his critical review (Figure 2).

In the Pu-Pu2O3 region of the phase diagram, the experimental data are rare. The existence of

Figure 1 U-O phase diagram (a) calculated using the model derived by Gueneau et a/.8; (b) calculated from 60 to 75at.% O8; the green points come from the critical review by Baichi et a/.9 and Labroche et a/.10 and the blue points show the results of Manara eta/.11; (c) calculated from O/U = 1.9 to 2.4 after Higgs eta/.12 The references of the experimental data are given in Higgs et a/.12 © Elsevier, reprinted with permission.

a miscibility gap in the liquid state was shown by Martin and Mrazek.30 The monotectic reaction was measured at 2098 K.30 There are no data on the oxy­gen solubility limit in liquid plutonium.

More data are available in the region between Pu2O3 and PuO2. The phase relations are complex below 1400 K. PuO2 _ x starts to lose oxygen above
approximately 900 K. A narrow miscibility gap was found to exist in the fluorite phase below approxi­mately 900 K leading to the simultaneous presence of two fcc phases with different stoichiometries in oxygen. Two intermediate oxide phases were found to exist with the formula PuO161 and PuO152. The PuO1.61 phase exhibits a composition range and is

stable between 600 and 1400 K. The PuO152 com­pound only exists at low temperature (T< ^700 K).

Above ^1400 K, the dioxide PuO2 _ x exhibits a large homogeneity range with a minimum O/Pu ratio equal to approximately 1.6 and is in equilibrium with the sesquioxide Pu2O3. The liquidus tempera­tures between Pu2O3 and PuO2 remain uncertain and would need future determinations.

The melting temperature of PuO2 is still a subject of controversy. The recommended value for the melt­ing of PuO2 was for a long time Tm = 2674 ± 20 K, based on measurements from Riley.31 Recent mea­surements are available that suggest higher values. In 2008, Kato et at:2 measured the melting point of PuO2 at 2843 K that is higher by 200 K than the previous measurements. The authors used the same thermal arrest method as in previously published works but paid more attention to the sample/crucible chemical interaction by using rhenium instead of tung­sten for the container. Very recently, a reassessment of the melting temperature of PuO2 was performed by De Bruycker et at.33 using a novel experimental approach used in Manara et at.11 for UO2. The new value of 3017 ± 28 K exceeds the measurement by Kato et at. by 174 K. The noncontact method and the short duration of the experiments undertaken by De Bruycker et at.33 give confidence to their new value which has been very recently taken into account in the thermodynamic modeling ofthe Pu-O system.42 Both studies agree on the fact that the values measured in the past were underestimated.