The fiber-matrix interfacial domain is a critical part of composites because load transfers from the matrix

to the fiber and vice versa occur through the interface. Most authors support the concept of weak interfaces to increase fracture toughness. They assign toughening to crack-bridging and fiber pullout. Weak interfaces are detrimental to the composite strength. A high strength requires that the matrix carry a part of the load. This is obtained with strong interfaces, which implies that the deflection cracks at interfaces are short and/or that significant sliding friction takes place. These latter requirements, to be met for strong composites, are therefore incompatible with the former ones for tough composites, if toughening is based solely upon crack-bridging and fiber pullout.

Fiber-matrix interfaces exert a profound influ­ence on the mechanical behavior and lifetime of composites. Efforts have been directed toward opti­mization of interface properties. Fiber-matrix inter­faces in CVI SiC/SiC composites consist of a thin coating layer (<1-pm thick) of one or several materi­als deposited on the fiber (interphase). CVI SiC/SiC composites with rather strong interfaces have been obtained using fibers that have been treated in order to increase the fiber/coating bond.35,42 The concept of strong interfaces has been established on CVI SiC/SiC composites with PyC and multilayered (PyC/SiC)n fiber coatings. Less interesting results have been achieved with BN interphases.43 Table 6 gives the various values of the interfacial shear stres­ses measured using various methods on CVI SiC/SiC composites with PyC-based fiber coatings: the inter­facial shear stresses range between 10 and 20 MPa for the weak interfaces, whereas they are larger than 100-300 MPa for the strong interfaces.43-47

In the presence of a weak bond between the fibers and the matrix or coating, single, long interface cracks are created during matrix cracking (adhesive failure type, Figure 10). The associated interface shear stresses are low, and load transfers through the interface crack are poor. The matrix is subjected to low stresses and the volume of matrix that may experience further cracking is reduced by the pres­ence of the long interface cracks. The matrix crack density is small. The crack spacing at saturation as well as the pull-out length tends to be long (>100 pm). Toughening results essentially from slid­ing friction along the cracked interfaces. However, as a result of matrix unloading due to long interface cracks, the fibers carry most of the load, which reduces the composite strength. The corresponding tensile stress-strain curve exhibits a narrow curved domain limited by a stress at matrix saturation which is distinctive of the ultimate strength (Figure 1).

Source: Rebillat, F.; Lamon, J.; Guette, A. Acta Mater. 2000, 48, 4609-4618; Lamon, J.; Rebillat, F.; Evans, A. G. J. Am. Ceram. Soc. 1995, 78, 401-405; Lissart, N.; Lamon, J. Acta Mater. 1997, 45, 1025; Rebillat, F.; Lamon, J.; Naslain, R.; Lara-Curzio, E.; Ferber, M. K.; Besmann, T. J. Am. Ceram. Soc. 1998, 81, 965; Rebillat, F.; Lamon, J.; Naslain, R.; Lara-Curzio, E.; Ferber, M. K.; Besmann, T. J. Am. Ceram. Soc. 1998, 81, 2315-2326.

In the presence of stronger fiber/coating bonds, the matrix cracks are deflected within the coating (cohesive failure type, Figure 10) into short and branched multiple cracks. Short interphase cracks as well as improved load transfers allow further cracking of the matrix via a scale effect, leading to a higher density of matrix cracks (which are slightly opened). Sliding friction within the coating as well as multiple cracking of the matrix increases energy absorption, leading to toughening. Short interphase cracks and improved load transfers reduce the load carried by the fibers, leading to strengthening. The associated tensile stress-strain curve exhibits a wide, curved domain and the stress at matrix cracking saturation is close to the composite strength (Figure 1).

The interphase is ineffective when fiber surface is too rough, although deflection of matrix cracks occurs. Because of strong fiber-matrix interactions in the interface cracks, premature fracture of com­posite occurs under small strains close to the strain at proportional limit. This phenomenon is observed on CVI SiC/SiC reinforced with Tyranno-SA3 fibers.38

The experimental determination of the thermal con­ductivity of LM is very difficult because of the pro­blems related to convection and to wetting, therefore large discrepancies exist between different sets of data. The high thermal conductivity of LM is mainly due to free electrons. A simple theoretical relation exists for pure metals between electrical and thermal conductivities, known as the Wiedemann-Franz — Lorenz (WFL) law:

le = L0TI r [21]

where 1e is the electronic thermal conductivity, r is the electrical resistivity, and L0 = 2.45 x 10-8W O K-2 is the Lorenz number.

With reasonable uncertainties, this law has been confirmed for many LM, taking into account the fact that the contribution of phonons to the thermal conductivity of the metals of interest is small. There­fore, the approximate prediction of the thermal

Figure 13 Electric resistivity of liquid Na, Pb-Bi(e), and Pb at normal atmospheric pressure.

conductivity of LM and several alloys is possible by combining WFL law and the existing, reliable values of the electrical resistivity.

Valuable recommendations for the thermal conductivity of Na, Pb, and Pb-Bi(e) based on the available at this time experimental data were pub­lished by Touloukian et a/.86 in 1970 and for Na by Cook and Fritsch87 in 1985. Later, Mills et a/.88 took the first publication as the starting point and reestimated recommendations for the thermal con­ductivity of many LM. Fink and Leibowitz22 exam­ined the recommendations from various assessments for the thermal conductivity of liquid Na and con­cluded that significant differences (up to ±15%) exist over the range of experimental data (371­1500 K). Available data on the thermal conductivity of liquid Pb and Pb-Bi(e) were also analyzed by Sobolev et a/.23,24 in the temperature range from TM,0 to 1300 K. It was found that all data on the Pb thermal conductivity were in good agreement close to the melting temperature; however, they differed in the temperature dependence and some of them were in serious contradiction with WFL law. These anomalies were explained by the effects of impurities, oxidation and by not relevant experi­mental conditions and techniques. In an effort to find a physically reasonable compromise between the available data and taking into account the WFL law, the linear correlation was recommended for the thermal conductivity of a pure liquid, which allows to describe the most reliable data with the maximum difference of ±15% in the temperature range of TM0-1300K. At present, few experimental
data are available on the thermal conductivity of liquid Pb-Bi(e). A nonnegligible difference exists between different recommendations at lower tem­peratures. The parabolic function can describe the temperature dependence of the Pb-Bi(e) ther­mal conductivity up to 1100 K with an uncertainty of 10-15%. The WFL law can be used for an estimate of the Pb-Bi(e) thermal conductivity with the same precision. In the report,34 the following correlation was used to describe the temperature dependence of the thermal conductivities of liquid Na, Pb, and Pb-Bi(e) at normal atmospheric pressure:

1(T;p0) = 1M,0 + Al,0(t- tm,0)±b2,q(t- TM,0)2 [22]

The parameters of this correlation are presented in Table 13. In Figure 14, the recommended values of the thermal conductivity of liquid Na, Pb, and Pb-Bi(e) are presented as a function of temperature.

In nonstationary thermal calculations, the thermal diffusivity is often used, which is defined as follows:

1(T, p)Ma
p(T, p)Cp (T, p)

Temperature (K)

Figure 14 Thermal conductivity of liquid Na, Pb-Bi(e), and Pb at normal atmospheric pressure.

The thermal diffusivities of the considered LM cal­culated at normal atmospheric pressure with the recommended correlations presented earlier are pre­sented in Figure 15.

2.14.6 Conclusions

For liquid Na, Pb, and Pb-Bi(e), the experimental data and correlations for the prediction of their ther­mophysical parameters of interest are available in the temperature region of the normal operation of nuclear installations. In spite of the fact that most of the properties were mainly measured at atmospheric
pressure and some of them have not yet been deter­mined with the needed accuracy, the proposed recom­mended correlations can be used for the predesign calculations of Gen IV nuclear installations with these coolants.

The simplified EOS can be applied for the pre­diction of the effect of pressure far away from the critical point in the pressure and temperature range typical for normal and abnormal operation of new generation power nuclear reactors with LM cool­ants. However, for the prediction of the properties of the Pb and Pb-Bi(e) coolants at higher tem­peratures and pressures, which can be potentially reached under accidental conditions, the existing

EOS can be used with utmost care. In order to improve the precision of EOS, the critical para­meters of Pb and Pb-Bi(e) should be determined with lower uncertainty.

Acknowledgments

This work was supported by funds of the SCKCEN project MYRRHA and by the EURATOM FP6 pro­jects ELSY and IP EUROTRANS.

For integral burnable poisons (gadolinia, erbia, and dysprosia), the poison material is intimately mixed with the UO2 fuel, and it is important that the mate­rials properties of the fuel/poison matrix are not too far removed from those of pure UO2. Intermixing UO2 with another ceramic oxide usually has the effect of decreasing the thermal conductivity. For a given fuel rating, this leads to somewhat elevated fuel pellet center temperatures, with consequent implica­tions for fuel melting, fission gas release, and other fuel behavior parameters.

For this reason, the fuel properties of urania/ gadolinia and urania/erbia fuel have been investi­gated very carefully.5-9 The main parameters of interest are the thermal expansion coefficient, heat capacity, fuel melting point, and thermal conductiv­ity, which have been extensively measured to ensure that the thermal performance of the fuel/poison matrices remains acceptable. In this respect, the per­formance of urania/gadolinia and urania/erbia as fuels is very similar, which might be expected, since
gadolinium and erbium are closely related rare earth elements and form oxides with the same structure. Other properties of the fuel that may be affected by the gadolinia or erbia phase include the UO2 grain size (which decreases with gadolinia or erbia fraction) and the fuel diffusivity (which affects fission gas release). However, this is a small effect that does not have a significant impact on fuel behavior.

The thermal expansion coefficients of gadolinia and erbia are both compatible with that of UO2 and there are no significant implications for fuel behavior. The concentrations of gadolinia used today range up to a maximum of about 8.0 wt%. At these concentra­tions, the melting point is decreased by just a few tens of degrees, which is relatively insignificant compared with the ^2600° C melting point of UO2. Erbia has a similar effect, but because the design concentrations of typically 2-3 wt% are lower, the overall impact is a reduction of the order of 10° C.

Similarly, the thermal properties of UO2 are affected when gadolinia or erbia is intermixed. Figures 12-14 show the variation in linear expansion coefficient, heat capacity, and thermal conductivity in urania/gadolinia as a function of temperature and gadolinia content. These data are recommendations made by IAEA5 and are intended to be used here only for illustration. For details of the experimental data underlying these recommendations, the reader is referred to IAEA-TECDOC-1496 or the original sources cited therein.

Recommended materials properties data are not as readily available for urania/erbia fuel, but Figure 15 illustrates one evaluation of the thermal conductivity that has been published in the open literature (see Kim et a/.8). This illustrates that the thermal properties of urania/erbia are similar to those of urania/gadolinia, weight for weight. However, since lower concentrations of erbia are required for practi­cal applications (because of the slower depletion of

erbia compared with gadolinia), the depression of the thermal conductivity is less significant.

Much of the data for gadolinia and erbia fuels used by industry are regarded as being proprietary information and are therefore not made available in open publications.

While the absorbing nuclides are still present, the change in thermal properties caused by the poi­son material is not a concern, because the fission

power produced in the fuel rods containing the poi­son material is depressed to the point where these rods are far from being limiting. However, a problem may occur when the poison material is fully depleted because the poisoned fuel rods will then increase in power and possibly become limiting. Indeed, because the poison material initially holds down the fission power in the poisoned rods, the fissile material is initially depleted more slowly than in the rest of the assembly and this can cause the poisoned rods to become the highest power rods in the entire assembly. This is undesirable, since the thermal con­ductivity is depressed and the fuel center tempera­ture elevated. Furthermore, the materials properties of two-phase ceramics such as urania/gadolinia or urania/erbia may not be known with the same degree of precision as for the urania phase on its own, and it may be necessary to apply larger uncertainties in the fuel behavior assessments that feed into the reactor safety case.

The remedy is simple and involves reducing the 235U enrichment in the poisoned rods relative to the remaining rods in the assembly. When the poison material is fully depleted, the power in the poison rods is reduced because of the reduction in fissile content. Since the two rod types are invariably fabri­cated in different facilities, this approach does not cause any difficulties in the fabrication logistics. There is a slight additional enrichment cost for the entire assembly, but this is not very significant. Fuel
vendors have been able to demonstrate that this approach ensures that the poisoned rods are never the limiting ones and that the materials properties uncertainties for the two-phase poison fuels do not affect the safety case.

2.16.2 Effect of Burnable Poisons on Fuel and Core Operating Parameters

Burnable poisons affect the operating characteristics of the core by reducing the excess reactivity control requirements, reducing power peaking in fresh fuel assemblies, and by modifying the reactivity feedback coefficients. BWRs have the most stringent require­ments for reactivity control, since in the absence of burnable poison, an excessive amount of control rod insertion would be required, especially if the reactor is operating with long fuel cycles (18 months or more). Control rod insertion in power operation is undesirable as it distorts the radial and axial neutron flux distributions, increasing the core power peaking factor (the ratio of peak power to average power in the core). Burnable poisons allow a much more uniform flux distribution and a lower peaking factor. A further deleterious effect of control rod insertion is that fuel rods near the control rods operate at reduced powers and can be subject to a rapid power ramp when the control rods are removed. This can lead to fuel failures, which burnable poisons help to avoid.

PWRs have a smaller reactivity control require­ment than BWRs because of the use of boron dis­solved in the coolant. PWRs typically operate with 1000-1500 ppm of boric acid in the coolant at the start of a fuel cycle, ramping gradually to zero by the end of the cycle. This can control as much as 15 000pcm of excess reactivity. However, even this is insufficient for long fuel cycles, and more boric acid cannot be added indefinitely due to the need to maintain a negative moderator temperature coefficient and also for other reasons such as the need to carefully control the acidity of the coolant.

An increase in water temperature in a PWR nor­mally reduces reactivity because the water is also the moderator and the fuel assembly design is such that reducing moderation reduces the density of thermal neutrons available to propagate the chain reaction. The presence of boron has the opposite effect, how­ever, because when the temperature of the water increases, the density decreases, and with it the density of 10B atoms decreases. At a high-enough concentra­tion of boric acid (usually 1500 ppm), the effect of changing absorption outweighs that of moderation and the moderator temperature coefficient becomes positive. This sets an upper limit to the reactivity hold-down that is achievable with soluble boron and burnable poisons are now routinely used to supple­ment soluble boron.

The presence ofburnable poisons in a fuel assembly needs to be accounted for in the thermal-hydraulic and fuel thermomechanical performance design assess­ments. For discrete burnable poisons, it is important to ensure that there is sufficient cooling to remove the heat production that accompanies neutron captures in the poison material. As noted in Section 37.3, the fuel thermal conductivity is the material property that is the most affected and has to be carefully taken into account in any thermomechanical simulations of the individual fuel rods. It is dependent on the total con­centration of gadolinia or erbia and has the same effect irrespective ofwhether the neutron-absorbing isotopes are still present or have been burned up.

Some additional physical phenomena are relevant in the first phase of irradiation. One important phys­ical effect results from the strong resonance absorp­tion of neutrons within a fuel rod. Resonance absorption effects distort the radial power profile across the fuel pellets and lead to a different radial temperature gradient at low burnups. Another effect is that the low fuel temperatures lead to reduced in­pile densification and delayed cracking of the fuel at beginning-of-life.

As these issues are very difficult to measure experimentally, thermomechanical simulations usu­ally rely on radial power profiles that are precalcu­lated using neutron transport codes. Densification effects are difficult to model and usually neglected in the thermomechanical models, or allowed for by applying a reduced swelling rate. Existing fuel relocation models may need to be refined in order to simulate delayed cracking. The overall effect of these physical mechanisms, however, dis­appears after the burnable poison is consumed (which typically occurs before the end of the first cycle of irradiation cf. Figure 1). For example, the time of closure of the fuel-to-cladding gap is hardly affected at all. Moreover, fission gas release in the later phases of irradiation is similar to that of nonpoisoned fuel and is consistent with experi­ments where the fission gas diffusion coefficient in gadolinia fuels was judged to be independent of the Gd2O3 content. Also, no differences have been found between the temperature dependence of the fission gas diffusion coefficient in gadolinia fuels and nonpoisoned UO2 fuels.

Synthetic graphite is a truly remarkable material whose unique properties have their origins in the material’s complex microstructure. The bond anisot­ropy of the graphite single crystal (in-plane strong covalent bonds and weak interplanar van der Waals bonds) combined with the many possible structural variations, such as the filler-coke type, filler size and shape distribution, forming method, and the distribu­tion of porosity from the nanometer to the millimeter scale, which together constitute the material’s ‘texture,’ make synthetic graphite a uniquely tailorable material.

The breadth of synthetic graphite properties is controlled by the diverse, yet tailorable, textures of synthetic graphite. The physical and mechanical properties reflect both the single crystal bond anisot­ropy and the distribution of porosity within the mate­rial. This porosity plays a pivotal role in controlling thermal expansivity and the temperature dependency of strength in polygranular synthetic graphite. Elec­trical conduction is by electron transport, whereas graphite is a phonon conductor of heat. This complex combination of microstructural features bestows many useful properties such as an increasing strength with temperature and the excellent thermal shock resistance and also some undesirable attributes such as a reduction in thermal conductivity with increasing temperature. The chemical inertness and general unreactive nature of synthetic graphite allow applica­tions in hostile chemical environments and at ele­vated temperatures, although its reactivity with oxygen at temperature above ^300 °C is perhaps graphite’s chief limitation.

Despite many years of research on the behavior of graphite, the details of the interactions between the graphite crystallites and porosity (pores/cracks within the filler coke or the binder and those asso­ciated with the coke/binder interface) have yet to be fully elucidated at all length scales. There is more research to be done.

Acknowledgments

This work is sponsored by the U. S. Department of Energy, Office of Nuclear Energy Science and Tech­nology under Contract No. DE-AC05-00OR22725 with Oak Ridge National Laboratories managed by UT-Battelle, LLC.

This manuscript has been authored by UT-Battelle, LLC, under Contract No. DE-AC05- 00OR22725 with the U. S. Department of Energy. The US government retains and the publisher, by accepting the article for publication, acknowledges that the US government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for US government purposes.

Thermal expansion has been investigated via low — and high-temperature X-ray diffraction,60-67 neutron diffraction,68 and dilatometry.32,54,57,69-74 Elongation (AL/L298) and linear coefficient of ther­mal expansion (CTE) are plotted as a function of temperature with respect to 298 K in Figures 18 and 19, respectively. Elongation results are gener­ally consistent between lattice parameter and dila — tometric methods, diverging at high temperatures. Scatter is magnified on the CTE versus T curve, which is akin to the second derivative of length versus T experimental data. Elongation is fairly linear, permitting authors to report a mean CTE over various temperature ranges; slope increases slightly with temperature, consistent with an observed rising CTE with temperature. Increase in CTE is more pronounced at temperatures up to 500 K with a more modest increase at higher tem­perature, although more lower-temperature values are needed to fully understand this behavior. At subambient temperatures, elongation (or contrac­tion, as the reference temperature is 298 K) is non­linear with temperature.

CTE values with respect to 298 K lie in the range (5-7) x 10~6K~ but the degree of scatter

-0.005

Figure 18 Elongation with respect to 298 K of ZrCx as a function of temperature.

precludes a more precise recommended value. Thermal expansion coefficient at 1273 K as a func­tion of C/Zr ratio is plotted in Figure 20, where a trend of increasing CTE with deviation from
stoichiometry can be seen. This composition depen­dence of CTE confirms the general picture of decreasing bond strength as C atoms are removed from the lattice.5

2.13.4.2 Diffusion

The results of diffusion studies are summarized in Table 1. The temperature dependence of diffusion
coefficient conforms to an Arrhenius relationship, according to

D(T) = D0e~Q/RT [10]

aZotov and Tsedilkin,75 14C tracer diffusion. bAgarwala and Paul,76 14C tracer diffusion on Zr rod, vacuum. cPavlinov and Bykov,77 ZrI4/14C-ZrI4 diffusion couple, vacuum. dAndrievskii et a/.,78 14C tracer diffusion on ZrI4, vacuum.

eUshakov et a/. ,79 rate of ZrC layer growth on alternating ZrI4 and graphite pellets stacked in Mo crucible, vacuum. fAdelsberg et a/. ,23 rate of ZrC layer growth on Zr bar melted in graphite crucible, vacuum.

9Andrievskii et a/. ,80 14C tracer diffusion on hot-pressed ZrC0 96, He atmosphere.

hSarian and Criscione,81 14C tracer diffusion on single crystal and arc-melted ZrC0 965, vacuum.

‘Andrievskii et a/. ,82 14C tracer diffusion on hot-pressed ZrC0 85, Ar atmosphere.

‘Andrievskii et a/. ,83 14C tracer diffusion on hot-pressed ZrC0 97 (Zr self-diffusion composition-independent from ZrC0 84-0 .97).

where Tis absolute temperature, R is the gas constant, Qis the activation energy for diffusion (kJ mol-1), and D0 is a preexponential factor having the same units as D, the diffusion coefficient, (cm2 s — ).

Diffusion of carbon in a-Zr (hcp) and p-Zr (bcc) has been investigated through diffusion of 14C tracer deposited onto Zr75-79 and by the rate of ZrC layer growth on Zr in contact with graphite.23,79

Self-diffusion of C in ZrCx has been determined by tracer diffusion.80-83 The study by Andrievskii et a/.83 provides the only reported value for self-diffusion of Zr in ZrC, which was found to be independent of C/Zr ratio. Activation energy for C self-diffusion in ZrCx increased with decreasing C/Zr ratio, while diffusion coefficient at a given temperature increased with increasing C/Zr ratio. However, O (0.16-0.19 wt%) and N (0.27-0.55 wt%) impurity content was substan­tial and varied for different samples. No further studies of C self-diffusion in ZrCx as a function of C/Zr ratio are available to clarify differences between C self­diffusion in pure ZrCx versus oxycarbonitride phases.

Carbon and zirconium self-diffusion in ZrC is slower than the inter-diffusion of C in Zr, with cor­respondingly higher preexponential factors and acti­vation energies. Pavlinov and Bykov77 remarked that the activation energy for C diffusion in Zr was close to that of Zr self-diffusion in Zr. As for self-diffusion,

Zr diffuses much slower than C, which may be under­stood in terms of the interstitial nature of C in ZrC: the smaller C atom is able to diffuse via either ther­mal metal vacancies or interstitial sites, the latter dwarfing the former in most cases.

Matzke84 proposed three potential mechanisms for C self-diffusion in ZrC. First, a C atom may jump along (110) directions to its nearest neighbor vacant C octahedral interstitial site, which, according to the author, requires a large lattice strain and the movement of two Zr atoms. Second, a C atom may jump along (111 ) directions to its nearest neighbor vacant C octahedral interstitial site via an unoccu­pied tetrahedral interstice, requiring lower strain energy. Third, a C atom may jump to a vacant octa­hedral site via a thermal metal vacancy. The author proposes that this divacancy mechanism requires the lowest energy, close to the activation energy for gen­eration of a metal vacancy.

The operative diffusion mechanism depends on the C/Zr ratio. Upadhyaya5 suggested that carbon diffu­sion in near-stoichiometric compositions occurs via thermal metal vacancies, while jumps via tetrahedral interstices are favored at higher carbon vacancy con­centration. No adequate explanations are available for the composition dependence of activation energy of C in ZrC, or the composition independence of that of Zr. Other properties (formation enthalpy, hard­ness) indicate a decrease in bond strength as the C/Zr ratio decreases, which would suggest that dif­fusion would be enhanced as well. This stands in opposition to measured activation energies for the diffusion of C in ZrC0.84-o.97, which increased with deviation from stoichiometry.83 As for Zr diffusion, Upadyaya5 suggested that two effects in operation when the C/Zr ratio decreases, a decrease in the energy required to form thermal metal vacancies, and an increase in the energy required for metal vacancy motion due to the decreased interatomic distance, cancel each other out.

Further discussion of diffusion mechanisms in the context of mechanical creep are considered in Section 2.13.5.6.

The prepared UO2 powder is pressed into green pel­lets in reciprocal or rotary presses at 150-500 MPa. The density of green pellets reaches 50-60% TD. Pellets are normally fabricated with dished ends and/or chamfered edges. The dishes compensate for radial variation in thermal expansion in-reactor, and the chamfers reduce the pellet-cladding mechanical interaction (PCMI). In VVERs and some fast reactors, pellets are made with a central hole to reduce fuel centerline temperatures. The pressing actions of the dies and the punches are carefully controlled to obtain a homogeneous local density distribution in the green pellet and to prevent defects in the green pellet. Two typical LWR UO2 pellets are shown in Figure 11.

2.15.4.2.2 Dewaxing and sintering

The volatile additives such as binders, lubricants and pore formers (if used) are removed from the green pellets by heating at 600-800 °C in a furnace for several hours. The additives will decompose into harmless gases at low temperature. This dewaxing process is generally done as the first step of the sintering process. The green pellets are then sintered in a reduction atmosphere at 1600-1800 °C for times that are based on control samples from previous batches, but are typically 3-10 h. U3O8 powder, mixed with the

(a) (b)

original UO2 powder, can also be used to control the final product density.39

The properties of UO2 fuel pellets such as thermal conductivity, gas bubble mobility, and creep rate influence fuel performance in-reactor. These proper­ties are affected by the grain size and the porosity distribution of the pellets. Early LWR fuel pellets had a small grain size (2-3 pm), but the requirement for greater fission gas retention by large grain fuel has led to the current use of 10-20 pm grain size material. As higher burn-ups become required, greater fission gas retention in the fuel pellets may be expected in the future. The grain size of UO2 pellets can be increased by controlling the sintering conditions or by using sintering additives such as Al2O3, SiO2, TiO2, Nb2O5, or Cr2O3.40-42

2.15.4.2.3 Finishing and inspecting

As-sintered pellets have an hour-glass shape because of the internal density distribution generated during pressing, and the diameter of the pellet must be accu­rate at 10 pm. Also, from the viewpoint of gap conduc­tance, the pellet surface must be smooth. Therefore, pellets are ground by a centerless grinding machine.

After grinding, pellets are inspected to check their diameter, length, density, and appearance; inspec­tions are almost completely automated except for appearance. Analyses for their uranium enrichment, impurities, and microstructures are also done.

The fuel thermal conductivity changes during irradi­ation as a result of fission and high operating tem­peratures; the chemical composition, lattice structure, and microstructure evolve in a complex and correlated manner. The fuel microstructure and state result from the irradiation history (transients generate cracking, shutdown periods result in autoirradiation at low tem­peratures, etc.). A complete and three-dimensional knowledge of the fuel characteristics is required for the prediction of the thermal conductivity. The num­ber of parameters is large and it is difficult to isolate and model their effects individually. Furthermore, many parameters act in a coupled manner: that is, the impact of the individual parameters is not the sum of the individual effects. Therefore, no purely theoretical model is available and semiempirical correlations are built from the interpretation of experimental results by selecting the most influential parameters, the effect of the others being implicitly included when the models are adjusted to measurement results.

Two categories of parameters can be distin­guished: first, the parameters that depend on burnup but not on irradiation conditions. The burnup is a global parameter that integrates all the effects which are proportional or related to it only, for instance, the concentration of soluble fission products or precipi­tates. Second, the parameters are those that depend on burnup and irradiation temperature history. This is the case for radiation damage, for the state of fission products that are present as isolated atoms and can precipitate, or for the distribution of volatile fission products between the states dynamically dissolved, precipitated in bubbles or pores, or released.

The proposal of a model implies a reduction in the number of parameters remaining, for instance, only the burnup or a second parameter summarizing the effect of the irradiation history, such as the irradiation temperature1 or the lattice parameter,32 assuming that these parameters describe, with sufficient preci­sion, the state of the fuel.

The general expression of the heat conduction used for irradiated fuels is similar to the one adopted for the fresh fuel (eqn [4]). It includes the lattice conduction mechanism by phonons, empirically represented by 1/(A + BT) and largely dominant up to temperatures of about 1600 K, and the high — temperature contribution attributed to the electron vacancy pair mobility, usually represented by adding an expression of the form CeDT This last contribution

cannot be accurately quantified because of the lack of measurements at high temperatures.

1

A + BT

The quantity 1/A + BT applies only to perturbations at the atomic scale, that is, the effects of soluble fission products, and to point defects (radiation point defects, nonstoichiometry, dynamically dis­solved atoms and fission gases). It is not rigorous for precipitates and porosity, as the effect of these para­meters is macroscopic and described by composite materials formulae derived from the solution of the Fourier law. In practice, this formalism is often applied, including the effect of all the parameters. Fuel variants, such as (U, Gd)O2, UO2 doped with Cr, or MOX, are modeled on the basis of UO2, with supplementary parameters describing the effect of the additive.

Nickel maintains its passivating oxide film in fast­flowing seawater, and its corrosion rate is <0.125 mm year-1. However, it becomes corroded under deposits in static seawater due to breaking down of the passive film by organic deposits.59

Nickel-copper alloys also show excellent corro­sion resistance in flowing sea water, with corrosion rates under 0.02 mm year-1. However, they also can be corroded under deposits in static seawater by the same mechanism as for nickel. Both nickel and nickel-copper alloys show higher resistance to cavi­tation and erosion corrosion in seawater than copper — nickel alloys.

Nickel-chromium-iron alloys have even more outstanding corrosion resistance and can be used in water polluted with substances such as carbon dioxide, iron compounds, chloride, and dissolved oxygen. They also exhibit excellent corrosion resis­tance in fast-flowing seawater but are subject to pitting and crevice corrosion in slow-flowing seawater.

Nickel-chromium-molybdenum alloys have excel­lent SCC resistance in sea water and chloride solutions

due to their high nickel content. Table 13 shows SCC initiation times in a boiling magnesium chloride solu — tion,31,34,37 whereas 304 and 316 stainless steels formed cracks within just 1-2 h, and Alloy 825 formed cracks in 46 h. However, SCC was not detected in Alloys 625, C-276, and C-22, even after testing for 1000 h.

SCC was not detected in Alloy G, which also shows excellent resistance to SCC in a boiling magnesium chloride solution. The SCC resistance of Alloy 825 is superior to that of 304 or 316 stainless steels, but inferior to that of Alloy G as shown in Table 13 .

The addition of molybdenum improves the resis­tance of nickel-based alloys to pitting and crevice corrosion. Nickel-chromium-molybdenum alloys have excellent pitting resistance. In addition, they have higher pitting and crevice corrosion initiation temperatures, as shown in Table 14. They also show much better resistance compared to 316 stainless steel in strong oxidizing environments including

— 33,34,37,38

24 300 ppm Cl.

Crevice corrosion resistance is usually evaluated by measuring the crevice repassivation potential. Figure 22 shows the temperature dependence of the crevice repassivation potential for nickel — chromium-molybdenum alloys in a 20% NaCl solution.59 Alloy C-276 shows a higher crevice repassivation potential and a higher crevice corrosion resistance than Alloy 625.

By contrast, the pitting and crevice corrosion resistance of Alloy G are inferior to those of Alloy C-276 and superior to those of 316 stainless steel and Alloy 825, as shown in Table 14.

The shear modulus at room temperature of191 GPa for CVD SiC has been determined by the four-point bend­ing technique. This value was also derived from the elastic modulus and Poisson’s ratio (n), using the con­ventional formula for isotropic solids: G = E/2(1 + n). The temperature dependence ofshear modulus can be estimated from E by applying this formula.

2.12.2.1.3 Hardness23

There appears to be no significant difference between Vicker’s and Knoop hardness: H~ 20.7-24.5 GPa has been reported for CVD p-SiC. By contrast, slightly higher values were obtained by nanoindentation. Nanoindentation is known to yield local values which depend on microstructural features. The afore­mentioned exponential function ofporosity for elastic modulus can be extended to the hardness evaluation:

Hv = 27.7exp(-5.4Vp) [3]

where HV is the Vicker hardness.

Currently, there is no high-temperature data reported for high-purity CVD SiC.

At pressures below 6 GPa, the melting temperatures of Na, Pb, and Pb-Bi(e) increase monotonically with decreasing rate with pressure. The melting tempera­ture of Na increases from 371 K at an atmospheric pressure up to 507-522 K when pressure increases up to 3 GPa37-39; the melting temperature of Pb increases from 600.6 to 795-815 K at the same pressure increase.38,40 For Pb, the rate of the melting tempera­ture increase of 0.0792 KMPa-1 in the pressure range of 15-200 MPa, 0.0671 K per 1 MPa in the range of 0.8-1.2 GPa, and an increase of 5.4 K for the pressure increase from 2 to 3 GPa, were cited in Hofmann.2

The eutectic point of Pb-Bi(e) is shifted to lower Pb contents and higher melting temperature with pres­sure. The eutectic temperature increases from 398 K at normal atmospheric pressure to ^422 K at pressure 0.75 GPa and to ~-481 K at 1.8 GPa41

In the pressure range of 0.1 MPa-3 GPa, the para­bolic function can be used for the description of the pressure dependence of the melting temperatures of Na, Pb, and Pb-Bi(e), (Table 3):

Tm(p) = tm, o + bTM (p — po) + cTm (p — po)2 I1]

The melting temperatures of Na and Pb as functions of pressure up to p = 6 GPa and up to 1.8 GPa for Pb-Bi(e), are presented in Figure 2. At higher pres­sures, a more complicated behavior of the melting temperatures of the considered metals in the function

of pressure is observed.39,42