The fission products that form a solid solution with UO2 and the point defects influence the thermal

conductivity at the atomic scale. Their effect on the thermal conductivity is interpreted in terms of pho­non scattering and is described by the formula l = 1/ (A + BT). The constant A can be expressed as the sum of the thermal resistance due to phonon scatter­ing by substitutional atoms or point defects (impuri­ties, interstitial atoms, vacancies) using the expression obtained by Ambegaoker.10 The main parameters are the Debye temperature, the mean phonon velocity, and the phonon diffusion cross section of the defects. Extended defects such as grain boundaries scatter phonons by limiting their mean free path. The product BT corresponds to the intrinsic lattice thermal resis­tivity caused by phonon-phonon scattering. The value of B can be evaluated from a simplified model by Leibfried and Schlomann,11 but the information avail­able on the physical and thermodynamic data of UO2 is not sufficiently accurate. Therefore, B is usually obtained empirically from the measured thermal resistivity slopes.

Figure 14 shows the temperature dependence of the electrical conductivity of zirconium hydride. In line with the behavior of most metals, electrical conductivity decreases with increasing temperature for zirconium hydride. The hydride has a lower elec­trical conductivity than the pure metals.

.

ZrC is a material of interest for next-generation nuclear fuel applications — for example, as a replace­ment or supplement for the SiC diffusion barrier coating in Tri-structural isotropic coated fuel particle (TRISO) coated fuel particles in high-temperature gas-cooled reactors. There are two main incentives to develop ZrC for this application. First, higher fuel operating temperatures, and thus higher efficiency of next-generation reactors, would be enabled by the higher degradation temperatures ZrC offers over SiC. There is evidence that fission product diffusion will be slower in ZrC and that ZrC is more resistant to fission product attack.158 Second, its sensitivity to oxidation recommends ZrC as an effective oxygen getter, inhibiting the so-called ‘amoeba effect’ insidi­ous in SiC-based TRISO, which involves a thermal gradient-induced diffusion of carbon and effective migration of UO2 fuel out of its protective coating layers, in part, due to an excessive oxygen potential (see, for instance, Bullock and Kaae).159

In France, the Complexe de Fabrication de Cadar — ache (CFCa) started operation in 1962, on a pilot scale, for developing FBR fuel. The Cobroyage

(co-milling) Cadarache (COCA) process was devel­oped there in the 1970s to fabricate MOX pellets for FBRs using two fuel fabrication lines.

Figure 14 shows the flow sheet for the COCA process. It utilizes an optimized ball mill as a blender and involves the forced extraction of the lubricated micronized powder through a sieve. This results in free-flowing granules which are suit­able for feeding at the pelletizing step.49 In the COCA process, the lubricant and the porogen, which is a pore former to control pellet density, are added to the force-sieved powder.51 One of the two FBR fuel fabrication lines in CFCa was switched to a LWR fuel fabrication line which intro­duced the LWR fuel fabrication technology devel­oped by BN. This LWR fuel fabrication line started producing PWR fuel in 1990.6 MOX fabrication at CFCa was stopped in 2005 because of seismic safety issues and the facility is now undergoing preparative work for its decommissioning.

In 1985, the construction of the MELOX plant at Marcoule was started; it had an annual production capability of 100 tons of heavy metal (tHM) for PWR fuel which was decided on the basis of operational experiences with the MIMAS process obtained at CFCa and it started MOX fuel production in 1995. Gradually, its licensed annual production capability was expanded and it reached 195 tHM as of April 2007; MOX fuel fabrication for BWRs was also cov­ered during this expansion. The process adopted in the MELOX plant is called the advanced MIMAS process and its flow sheet is shown in Figure 15. The accumulated MOX fuel production at the MELOX plant reached 1426 tHM at the end of 2008. The features of this process are given below.

In order to utilize up to 50% of dry recycled scrap powder in the master blend powder and to achieve excellent homogeneity and uniformity of PuO2 as well, a new ball mill was developed for the first blend­ing step.6 This mill uses three-dimensional movement and U—Ti alloy balls. For the second blending, a high capacity (640 kg) blender consisting of a conical screw mixer with a double envelope cooling system was adopted.6,49 In order to achieve MOX fuel production on a large scale, complete automation was implemen­ted in the production line. Similar to the original MIMAS process invented in BN, three kinds of feed powders, PuO2 powder, UO2 powder, and dry recycled scrap powder, are ball milled to obtain the master blend powder with about 30% plutonium

concentration. The force-sieved master blend powder is diluted with the free-flowing UO2 powder, pre­pared by the ADU process or the AUC process and additional dry recycled scrap powder using the high capacity conical screw mixer. This free-flowing diluted power is pelletized into green pellets using a pressing machine with multiple punches and a reci­procating mechanism. Approximately 10-14 green pellets can be pressed simultaneously. The green pel­lets are sintered in a continuous-type sintering fur­nace consisting of a dewaxing part and a sintering part. After dry centerless grinding of sintered pellets, the exterior of all pellets are inspected.

A mapping image of plutonium, acquired by X-ray microanalysis of a transverse section of a MOX pellet prepared by the advanced MIMAS process, was reported by Oudinet et al5 In the MIMAS process, a two-step blending method is utilized to obtain the desired plutonium content in the pellets, as described above. This results in the presence of two or three phases in the transverse section of a sintered pellet. The MOX pellets prepared with UO2 powder from the ADU process show three phases, plutonium rich clusters, a coating phase and a UO2 phase on their transverse sections while those prepared with UO2 powder from the AUC process show two phases, plutonium rich clusters and a UO2 phase.58,59 The MOX pellets manufactured by the short binderless route (SBR) and Japan Atomic Energy Agency (JAEA) processes in which a one-step blending method is adopted to obtain the desired plutonium concentration of pellets show a single homogeneous phase on their transverse sections, and are different from pellets fabricated by the MIMAS process.51,60 The MOX pellets currently manufactured in the MELOX plant are reported to have a mean grain size of 5.8 pm.61

Physical properties of 300 series stainless steels tend to be fairly similar, and the typical physical prop­erties of 316L stainless steel are given in Tables 1 and 2.1- The 316L stainless steel has a density at room temperature of 8000 kg m-3 and a melting temperature of slightly above 1400 °C (Table 1). The elastic (Young’s) modulus at room tempera­ture is 190-200 GPa, which is typical of a range of engineering alloys, including ferritic steels and solid-solution Ni-based superalloys. At 100 °C, the coefficient of thermal expansion of 316L is about 16 x 10-6cm cm-1 °C-1 (Table 2), and values of that property may vary by up to 3-4% for types 316 and 347 steels. The 300 series stainless steels

have much more thermal expansion than martensi — tic/ferritic steels or Ni-based superalloys, with the thermal expansion of 316L at 100 °C being about
50% higher than that of type 410 ferritic steel.3 The thermal conductivity of 316L stainless steel at 100 °C is 16.3 W mK~ , which is to the higher end of the range for such alloys, with type 316 or 347 steel having 15-30% lower thermal conductivity. Thermal con­ductivity of 300 series stainless steels is lower than that of ferritic steels or Ni-based superalloys. If the 300 series stainless steel is fully (100%) austenitic, such as 316 or 347, then it has no ferromagnetic behavior, but if it contains ferromagnetic phases (like delta-ferrite or martensite), then such steels have some degree of ferromagnetic behavior. Adding nitrogen to 316L produces fully stable austenitic phase structures.

The matrix of NITE-SiC/SiC comprises polycrys­talline SiC and a small amount of isolated oxides. The microstructure is highly crystalline and highly dense. Table 5 lists the typical available pro­perties of NITE-SiC/SiC.7 Thermal conductivity (~30Wm-1K-1) is quite high when compared to CVI SiC/SiC (below 15Wm-1K-1) reinforced with either Nicalon (Table 1) or Hi-Nicalon fibers.37 The high proportional stress limit is claimed to be an inter­esting feature.7 However, it is worth pointing out that it reflects a high load-carrying capacity. By contrast,

the low strain-to-failure indicates a limited damage tolerance. The strain-to-failure does not increase after aging at high temperatures up to 1500 °C. This trend is consistent with the strong fiber-matrix interactions induced by the surface roughness of Tyranno-SA3 fibers.38 A comprehensive database on properties of NITE-SiC/SiC is not available. NITE-SiC/SiC has been reported to retain ultimate strength and a propor­tional stress limit after exposure at temperatures up to 1300 °С6

The surface tension is a measure of the cohesive energy of atoms and correlates with the latent heat of evaporation. The surface tension of normal liquids should decrease linearly with temperature and becomes zero at critical temperature, where the dif­ference between liquid and gas phases disappears. In accordance with Eotvcis’ law (cited in Iida and Guthrie27), it can be presented as follows:

s(T) = kaV-2=3(Tc — T) [10]

where Va is the molar volume and ks is a constant, which is about the same for normal LM.

Considering liquid Na, Pb, and Pb-Bi(e) as nor­mal liquids, a linear correlation can be recommended for the description of the temperature dependence of their surface tension:

s(T; p0) = sM,0 — Aff,0 (T — TM,0) [11]

The experimental data on the surface tension of sodium were reviewed by Golden and Tokar,3 Allen,65 Fink, and Leibowitz.22 In 1993, Keene66 reviewed many data on the surface tension of pure metals (including Na and Pb) at normal atmospheric pressure and concluded that the linear temperature dependence is valid for most LM in the tempera­ture range from normal melting to normal boiling
point. The available recommendations on the surface tension of Pb and Pb-Bi(e) were summarized by Sobolev and Benamati.24 The surface tension of liq­uid Na, Pb, and Pb-Bi(e) is well measured at normal atmospheric pressure from temperatures close to their melting points up to 1100-1300 K. In this tem­perature range, a variation of ±(3-6)% exists between values given by different sources. At higher temperatures, the scatter of the experimental results increases significantly. The coefficients of correlation [11] for these LM, recommended in the report34 and adopted in this work, are given in Table 9, and the calculated surface tension of liquid Na, Pb, and Pb-Bi(e) at normal atmospheric pressure is pre­sented in Figure 8 as a function of temperature.

There are three burnable poison materials in common use in current fuel assembly designs, and they are boron, gadolinium, and erbium. There is also an advanced fuel design for CANDU reactors (called the CANFLEX bundle) that uses dysprosium burnable poison, but it has yet to be used on a commercial scale. They all have one or more isotopes with a large neutron capture cross-section that, following a neutron capture, are transformed into isotopes with small cross-sections.

2.16.3.1 Boron

Natural boron consists of the two isotopes 10B and 11B at 19.9% and 80.1% natural abundance,

respectively.1,2 10B has a thermal neutron capture cross-section (meaning the neutron absorption cross­section for a neutron moving with 0.0256 eV kinetic energy) of 3837 barns2 (where a barn is a convenient unit of area 10—28m2). Following a neutron capture, it is transmuted to 7Li and 4He, both ofwhich have very low neutron absorption cross-sections. For some appli­cations, for example, where it is difficult to incorporate

1.0E + 06 1.0E + 05

1.0E + 04

c

ГО Q

■I 1.0E + 03

о

Ф от от

2 1.0E + 02

о ф =5

g 1.0E + 01

с о

Z 1.0E + 00 1.0E — 01 1.0E — 02

sufficient quantity of 10B as natural boron, isotopically enriched 10B is available commercially. The neutron capture cross-section of 10B decreases smoothly with increasing neutron energy (Figure 2), so that slow moving (thermal) neutrons are the most likely to be absorbed. (To be strictly accurate, the cross-section shown in Figure 2 is the cross-section for neutron capture, followed by transmutation to 7Li and 4He; the true neutron capture cross-section of 10B is actually very small and is insignificant relative to the 10B! 7Li + 4He reaction.)

Early applications of boron burnable poisons in PWRs used natural boron in borosilicate glass rods that fitted into the control rod guide tubes of assem­blies not positioned under a control rod location, as illustrated in Figure 3. Such a design is called a dis­crete burnable poison rod. It has the advantage that the burnable poison material does not need to be incorporated in the fuel, and can therefore be manu­factured separately. Also, the precise number ofpoison rods can be fine-tuned before the fuel assembly is loaded in the core. Such discrete poison rods are now seldom used because the stainless steel outer clad and other structural components continue to absorb neu­trons after all the 10B is depleted; this represents a parasitic absorption penalty that costs the utility because a higher initial enrichment of 235U is needed to compensate. This effect is made worse because the
poison rods also displace water, reducing moderation in the fuel assembly and further decreasing the mul­tiplication factor. Another disadvantage is that dis­crete poison rods constitute an additional source of intermediate level waste that adds to waste manage­ment costs.

An alternative to discrete boron burnable poison rods is to incorporate a boron compound with the fuel rods themselves. The so-called integral fuel burnable absorber (IFBA) is used in many commer­cial PWRs in the United States. It consists of a thin coating of zirconium diboride (ZrB2), which is applied to the surface of some of the UO2 fuel pellets in the fuel assembly. Since zirconium has a very low capture cross-section and there is no structural mate­rial, IFBA has practically zero residual absorption penalty. A disadvantage is that the application of the coating adds an extra process in fuel manufacture and since it is hygroscopic, manufacturing needs to take place under a dry atmosphere in glove boxes. Figure 4 illustrates a typical distribution of IFBA fuel rods in a PWR assembly.

Two arbitrarily defined types of microstructure were identified in the binder phase: (1) domains, which were regions of common basal plane align­ment extending over linear dimensions >100 pm and (2) mosaics, which were regions of small ran­domly oriented pseudocrystallites with linear dimen­sions of common basal plane orientation of less than about 10 pm. Cleavage of domains occurred at stres­ses well below the fracture stress, and such regions acted as sites for crack initiation, particularly when in the vicinity of pores. Fracture of mosaic regions was usually observed only at stresses close to the fracture stress. At lower stresses, propagating cracks that encountered such regions were arrested or deflected.

2.13.3.1 Zr-C Phase Diagram

The most recent critical assessment of the Zr-C system was carried out by Fernandez-Guillermet14 and is depicted in Figure 3. The phase diagram shows the formation of a monocarbide phase which exists between 37.5 and 49.5 at.% C (ZrC06-098 with extent of phase field temperature-dependent), melts congruently at 3700K and 46at.% C (ZrC0 85), and forms a eutectic with carbon at 3200 K at 67.6 at.% C. Solid solubility of C in Zr has not been established conclusively but is estimated to be between 1 and 3 at.% C by Sara15, Rudy,16 and Kubaschewski-von Goldbeck.17 The Zr + ZrC eutec­tic is close to the melting temperature of bcc Zr, 2127 K, contributing to the assessment of low carbon solubility. Solubility of Zr in C is taken as nil.

Figure 4 shows the results of experimental phase diagram studies superimposed on the assessed dia­gram. Phase boundaries of the ZrC phase were estab­lished via ceramography by Farr,18 Sara and Doloff,19 Sara et al.,20 Sara,15 and Rudy et al.,21 while Storms and Griffin13 used C and Zr activity values deter­mined during a Knudsen effusion study. Rudy et al. prepared mixtures of Zr, ZrH2, or graphite with ZrC and determined ZrCx solidus temperatures and ZrC-C eutectic temperature via differential thermal analysis (DTA), ceramography, or melting in a Pirani furnace. As described by Rudy and Progulski,22 the Pirani technique subjects a bar specimen with a central blackbody hole to resistance heating; melting is determined by the temperature at which liquid forms in the blackbody hole. The technique is noted to be most precise for isothermal transformations (i. e., congruent melting or eutectic), as the sample often collapses or the blackbody hole closes before the liquidus is reached. Sara15 prepared zirconium car­bides having various C/Zr ratios from mixtures of ZrH2 and graphite to determine melting tempera­tures and the congruent melting temperature and composition. Adelsberg etal.23 performed ceramogra — phy on C-Zr diffusion couples to contribute data points to the low-carbon liquidus line; ZrC-C eutec­tic temperature was also determined by ceramogra — phy. Zotov and Kotel’nikov24 placed ZrCx bars with a radial hole under axial loading and resistance heating; fracture of the sample at the temperature at which the hole melted determined ZrCx solidus. For the ZrC0.88 sample, at least, their value is

C/Zr ratio

0 0.2 0.4 0.6 0.8 1 1.4 2

Figure 3 Zr-C phase diagram, as assessed by Fernandez-Guillermet.14

4000

3500

anomalously high. Heating the sample in an effusion cell, Bhatt et a/.25 determined Zr-ZrC eutectic tem­perature by an optical pyrometric ‘spot technique.’

2.13.3.2 Enthalpy of Formation

Other properties on which the current phase diagram is based include enthalpy of formation, enthalpy increment or heat content, specific heat capacity (Cp), and activity of C and Zr in ZrC. Standard enthalpy of formation, AHf, of ZrCx as a function of the C/Zr ratio is plotted in Figure 5. A quadratic fit to the reviewed data is provided by

AHf° = 2.03 x 105×2 — 5.04 x 105x — 9.92 x 104 [2]

where x is the C/Zr ratio and A Hf is in units of joules per mole. Within the compositional range, AHf is most negative at the stoichiometric composi­tion and the recommended value is -197 kJ mol-1.26 Toth3 attributes this to decreasing ZrCx bond strength with removal of C from the lattice.

2.13.3.3 Enthalpy and Heat Capacity

Enthalpy increment of ZrCx with respect to 298 K (HT — H298) is plotted as a function of tempera­ture in Figure 6 and as a function of C/Zr ratio at 1600 K in Figure 7. Storms and Griffin report the following equation to fit the experimental values of

Mezaki et a/.,27 Levinson,28 Kantor and Fomichev,29 and Turchanin and Fesenko30:

HT-H298 = -2.14 x 104 + 56.86T-5.46×10-3T2 1.456 x 106

T

where H is in units of joules per mole and T is absolute temperature, valid from 298 to 3200 K. From their low-temperature heat capacity measure­ments on ZrC0 96, Westrum and Feick31 determined a value of H298 — H0 of 5.9 kJ mol-1 and an entropy, S298 — S0 of 33.3Jmol-1.

Heat capacity of ZrCx is plotted as a function of temperature in Figure 8 and as a function of C/Zr ratio at 298 K in Figure 9. Heat capacity is equal to the first derivative of enthalpy with temperature, and the function recommended by Storms and Griffin13 is

Cp = 56.86 — 0.0109T + 5.586 x 10-6T2

1.456 x 106 [4]

T2

where Cp is in units of joules per mole per kelvin.

Low-temperature heat capacity of ZrC0.96 was measured by Westrum and Feick31 by adiabatic calo­rimetry between 5 and 350 K. No data are available for more carbon-deficient compositions, limiting efforts to quantify the entropy of mixing introduced by carbon vacancies. High-temperature drop calorimetry

Temperature (K)
Figure 6	Enthalpy of ZrCx as a function of temperature.
T
66 x 103
1600K ♦ Neel et a/.32 ■» Levinson28 A Kantor and Fomichev29 Bolgar et a/33 ♦ Turchanin and Fesenko30 ♦ Storms and Griffin13
♦ A
64 x 103
62 x 103
60 x 103
58 x 103
56 x 103
54 x 103
………..
_l_d
0.6	0.7	0.8 C/Zr ratio

Temperature (K) Figure 8 Heat capacity of ZrCx as a function of temperature.
I………….	……….. I…………….
40
Ж Westrum and Feick31 X Bolgar et al.33 IX Kantor and Fomichev29 Storms and Griffin13 a Storms and Wagner35
39
~o E 72, ЪА
38	, Art
37
га ‘о
36
Ай
35
34
Ай
33 0.6
C/Zr ratio

measurements were made on ZrCo.92-1 by Neel eta/.,32 Mezaki et a/.,27 Levinson,28 Bolgar et a/.,33 Kantor and Fomichev,29 and Turchanin and Fesenko.30 Petrova and Chekhovskoi34 determined heat capacity, using a pulsed electric current method to measure thermal diffusivity. Storms and Wagner35 used the laser flash method to measure thermal diffusivity for ZrC0.64-1 at 300 K and estimated Cp for these compositions, using a known value for ZrC09631 and by assuming a curve parallel to that established for NbCx as a function of C/Nb ratio.36 Heat capacity increases sharply between 0 and 500 K, saturates, then begins to increase more rapidly near the melting point. Both room — temperature heat capacity and high-temperature enthalpy increase with C/Zr ratio in the homogeneity range. Room-temperature heat capacity of ZrC096 is 38Jmol-1K-1.31,35