Category Archives: Comprehensive nuclear materials

Electronic Structure22

Figure 12 shows the density of states (DOS) of zirco­nium hydride, determined by DV-Xa molecular orbital (MO) calculations. Here, 0 eV corresponds to the Fermi energy. The new band resulting
from the hydrogen is generated immediately below the d-band of the hydride cluster, in the region of ^5-7 eV. Figure 13 shows the bond order of zirconium hydride. With increasing hydrogen con­tent, there is a marked decrease in the bond order of Zr-Zr metallic bonds, whereas the bond order of Zr-H covalent bonds does not change. This reduction in bond order is likely due to a decrease in the electric charge of the matrix of Zr bonds.

image357

-10 -5 0

Electron energy, E (eV)

Figure 12 Hydrogen content dependence ofthe DOS of zirconium hydride.

image207

Since bond order can be thought to be related to the spring constant of interatomic bonds, these results can be understood to mean that the effective spring constant of zirconium hydride, as a whole, decreases with increasing hydrogen content. This hypothesis offers a good explanation for the hydrogen content dependence of the various properties of zirconium hydride.

Oxidation kinetics

The kinetics of oxidation of ZrC is related to the nature of the oxidation products and microstructure of the oxide scale formed. In general, oxidation accompanied by the formation of a protective scale is associated with low temperatures. The oxide scale is reported to be protective and its growth to be para­bolic with time, that is, controlled by diffusion of oxygen through the cubic ZrO2 scale.134,137,140,143,152

The cubic ZrO2 structure is hypothesized to facilitate adherence of the scale to the cubic ZrC, as evidenced by high-resolution TEM of oxidized single-crystal ZrC with adherent cubic ZrO2 crystallites face having parallel lattice fringes.144

At high temperatures (and high Po2 usually), oxi­dation is reported to be linear with time, controlled by the reaction at the oxide-carbide inter — face.134,147,152 This process is facilitated by porosity in the oxide, rupture due to CO/CO2 gas pressure, or cracking/delamination due to thermal expansion

mismatch between the oxide and carbide,136,140,144,153

and interruptions in the scale allow oxygen easy access to the ZrC surface. Preferential attack of ZrC along the grain boundaries by ZrO2, leading to inter­granular embrittlement, strengthens the case against protective oxidation of ZrC.154,155

In the case of a two-layer scale on single-crystal ZrC097, the inner carbon-rich scale grew paraboli­cally, leveling out at a critical thickness (2-4 pm), above which the outer carbon-poor scale grew line­arly with time.144,146 The inner scale was crack-free, dense, and adherent, while the outer scale was char­acterized by cracks and porosity. The authors proposed that scale cracking continually exposed fresh surfaces to oxygen, leading to an overall linear oxidation rate.

Oxidation behavior also depends on the pressures of volatile ZrOx species, implicated in active oxida­tion. According to thermodynamic calculations by Maitre and Lefort156 and Minato and Fukuda157 of equilibrium pressures in the Zr-C-O and Zr-C-O — He systems, the maximum pressure of ZrO(g) at 1600 K was predicted to be less than 10~9 Pa, indicat­ing negligible active oxidation.

2.13.6.1.2 Oxidation by water vapor

One study of oxidation by water vapor is reported.134 At 723-843 K, with PO2 > 0.5 kPa (i. e., sufficient for surface saturation with adsorbed oxygen) and Ph2o 21-42 kPa, water vapor did not appreciably oxidize ZrC but did accelerate the oxidation rate in the presence of O2(g).

2.13.6.1.3 Summary and outlook

Clearly, oxidation resistance of monolithic ZrC is compromised at temperatures above about 700 K, and its use at higher temperatures is restricted to inert or reducing atmospheres. To enable the predic­tion of structural component performance under acci­dental oxidizing conditions, it is important to understand the effects of oxidation on mechanical properties. For instance, strength and toughness deg­radation must be characterized for ZrC partially oxi­dized to ZrO2 and ZrC^Oj,, and failure mechanisms must be identified, such as grain boundary attack or scale rupture. Oxidation to ZrO2 will also lower ther­mal conductivity, which is relevant to applications where the high thermal conductivity of ZrC is exploited, but heat transport in ZrC^O,, must also be established.

Belgium

In Belgium, the micronized master blend (MIMAS) process was developed by Belgonucleaire (BN) in the early 1980s based on the experiences acquired in the reference fabrication process developed earlier and commercially used in the 1970s at BN’s Dessel plant.2 The reference process consisted of a single blending of PuO2 powder with free-flowing UO2 powder and this blending resulted in a blend with adequate flow — ability to feed the pelletizing press.6 As MOX pellets fabricated by the reference process could not satisfy the preprocessor’s new requirement, which was that MOX pellets had to be soluble in a nitric acid solu­tion, BN had to improve the solubility of MOX pel­lets in the nitric acid solution. In order to improve their solubility, the MIMAS process was introduced in the Dessel plant. Figure 13 shows the flow sheet for the MIMAS process.

Подпись:
In the MIMAS process, suitable amounts of PuO2 powder, UO2 powder, and dry recycled scrap powder are prepared to get a 60 kg MOX master blend pow­der with 30% plutonium concentration. The master blend powder is ball milled to obtain a homogeneous distribution of plutonium. In the second blending, force-sieved (i. e., micronized) master blend powder is diluted with the free-flowing UO2 powder and

additional dry recycled scrap to form 80 kg of the final blended MOX powder with the desired pluto­nium concentration.6 In this step, it is very important to obtain uniform distribution of master blend in free-flowing UO2 powder. This final blended MOX powder is pelletized into green pellets using a pressing machine with multiple punches and a reciprocating mechanism. Approximately 10-12 green pellets can be pressed simultaneously. These green pellets are sintered at about 1700 °C under a reduced atmosphere of Ar + H2 mixed gas, after dewaxing. Not only does the intimate contact between the comicronized UO2 and PuO2 powders provide adequate interdiffusion during sintering and therefore enhanced solubility, but also the larger contact area between the more abundant fine powder and the free-flowing UO2 pow­der results in a more heterogeneous MOX structure than in the earlier reference process. This is apparent in measurements such as the a-autoradiograph of a transverse section of a MOX pellet prepared by the MIMAS process, given by Lippens et al5

During the 1990s, the Dessel plant accounted for over 60% of the world’s production of MOX fuel.49 However, MOX fuel fabrication was terminated in 2006. Now, this plant is undergoing preparative work for its decommissioning.

Properties of Unirradiated Alloys

2.09.2.1 General and Fabrication Behavior

Without the effects of irradiation, austenitic stainless steels are fairly stable solid-solution alloys that generally remain in the metallurgical condition in which they were processed at room temperature to about 550 °C. The typical austenitic stainless steel, such as type 304, 316, 316L, or 347 stainless steel, in the SA condition (1000-1050 °C), will have a wrought, recrystallized grain structure of uniform, equiaxed grains that are 50-100 pm in diameter, particularly in products such as extruded bar or flat-rolled plates (6-25 mm thick).1-3 Ideally, such products should be free of plastic strain effects and have dislocation-free grains, but for real applications, products may be straightened or bent slightly (1-5% cold strain), and thus have some dislocation substruc­ture within the grains. Stainless steel products with heavier wall thicknesses (>50 mm) would be forgings and castings, which would have coarser grain sizes, but probably not have additional deformation. Spe­cial stainless steel products would include thin foils, sheets, or wires (0.08-0.5 mm thick), which would have much finer grain-sizes (1-10 pm diameter) due to special processing (very short annealing times) and special considerations (5-10 grains across the foil/ sheet thickness).3 Typical fast-breeder reactor (FBR) cladding for fuel elements can be thin-walled tubes of austenitic stainless steel, with about 0.25 mm wall thickness, so they fall into this latter special pro­ducts category. Although austenitic stainless steels are highly weldable, welding changes their structure and properties in the fusion (welded and resolidified) and adjacent heat-affected zones relative to the wrought base metal, so they may behave quite dif­ferently than the base metal, which is what was described above. The detailed behavior of welds under irradiation is beyond the scope of this chapter, so the remainder of this chapter focuses on typical wrought metal behavior.

Another important aspect of austenitic stainless steel that defines it is the stability of the parent austenite phase. The addition of nickel and elements that behave like nickel including carbon and nitrogen to the alloy causes it to have the austenite parent phase and its beneficial properties, which is also the same fcc crystal structure found in nickel-based alloys. Otherwise, the steel alloy would have the natural crystal structure of iron and chromium, which is body-centered cubic (bcc) ferrite, as the parent phase, and alloying elements that make the alloy behavior like this include molybdenum, nio­bium, titanium, vanadium, and silicon. A stable aus­tenitic alloy will be 100% austenite, with no 8-ferrite formed at high temperature and no thermal or strain — induced martensite, whereas an unstable austenitic alloy may have all of these. A useful way of expressing these different phase formation tendencies at room temperature in terms of the alloy behaving more like Cr (bcc ferritic) or Ni (fcc austenitic) is a Schaeffler diagram, as shown in Figure 1. The fcc austenite phase is nonmagnetic and maintains good strength and ductility even at cryogenic temperatures, with no embrittling effects of martensite formation. The bcc phase by comparison is ferromagnetic, has a little less

image303

Figure 1 Schaeffler diagram showing regions of stable austenite, martensite, and delta-ferrite in austenitic stainless steels at room temperature as a function of steel alloys compositional effects acting as the equivalent of Cr or Ni. Reproduced from Lula, R. A., Ed. Stainless Steel; ASM International: Materials Park, OH, 1986.

ductility (less active slip systems), and has a ductile- to-brittle transition temperature (DBTT), below which the steel has low ductility and impact resis­tance, with a brittle fracture mode. Maintaining suf­ficient carbon and adding nitrogen are two ways of imparting good, stable austenite phase behavior to the common grades of austenitic stainless steels, like 304LN or 316LN.

The NITE Process

Reaction sintering (RS), liquid phase sintering (LPS), PIP, melt infiltration (MI), and their hybrid processes are alternative options. PIP requires development of a near-stoichiometric polymer precursor. The other methods have issues in phase and uniformity control.

The NITE process is based on LPS,5,7,30 which has been improved owing to the progress in reinfor­cing fibers and availability of fine nano-SiC powders. A slurry of p-SiC nanopowders and additives is infil­trated into SiC fabrics and dried for making prepreg sheets. After the layup of the sheets, hot pressing is applied to make NITE-SiC/SiC. Small amounts of sintering aids (Al2O3, Y2O3, SiO2), high temperatures (1750-1800 °C), and pressures ranging from 15 to 20 MPa are required for matrix densification. The NITE process was claimed to present great advan­tages such as flexibility in the shape and size of the components.7 The successful development of NITE is due to appropriate fiber protection and the emer­gence of advanced SiC fibers such as Tyranno-SA3.

2.12.2 Properties of CVI SiC/SiC

Подпись: Table 1 Mechanical and thermophysical properties of 2D SiC/SiC composites reinforced with 0/90 balanced Nicalon™ fabrics Property Temperature 23 °C 1000°C 1400°C Fiber content (%) 40 40 40 Specific gravity 2.5 2.5 2.5 Porosity (%) 10 10 10 Tensile strength (MPa) 200 200 150 Strain-to-failure (%) 0.3 0.4 0.5 Young’s modulus (GPa) 230 200 170 Poisson’s ratio n12 0.5 n13 0.18 Flexural strength (MPa) 300 400 280 In-plane compressive strength (MPa) 580 480 300 Thru-the-thickness compressive strength (MPa) 420 380 250 Interlaminar shear strength (MPa) 40 35 25 In-plane thermal diffusivity (10-5m2s-1) 12 5 5 Thru-the-thickness thermal diffusivity (10-5m2s-1) 6 2 2 In-plane coefficient of thermal expansion (10-6 K-1) 3 3 Thru-the-thickness coefficient of thermal expansion (10-6 K-1) 1.7 3.4 Fracture toughness (MPa/m) 30 30 30 Specific heat (J kg-1 K-1) 620 1200 Total emissivity 0.8 0.8 0.8 In-plane thermal conductivity (Wm-1 K-1) 19.0 15.2 Thru-the-thickness thermal conductivity (Wm-1 K-1) 9.5 5.7
Подпись: Source: Choury, J. J. Thermostructural composite materials in aeronautics and space applications. In Proceedings of GIFAS Aeronautical and Space Conference, Bangalore, Delhi, India, Feb 1989; pp 1-18; Lacombe, A.; Rouges, J. M. In AIAA'90, Space Program and Technologies Conference'90, Huntsville, AL, Sept 1990; The American Institute of Aeronautics and Astronautics: Washington, DC, 1990; AIAA-90-3837.

Table 1 is a complete list of the mechanical and thermophysical properties of first generation 2D CVI SiC/SiC composites reinforced with SiC Nica — lon fibers of first generation.2, 1 An average strain-to — failure of 0.3% and a tensile strength of 200 MPa have been reported. Higher strengths and strains — to-failure appear in Tables 2 and 3, which give the available properties measured on other generations of SiC/SiC composites reinforced with advanced Hi-Nicalon or Hi-Nicalon type S fibers.3,32,33 The behavior of stronger Nicalon-reinforced SiC/SiC is discussed in a subsequent section. It can be noted that the strain-to-failure can reach 1%, and the ten­sile strength can exceed 300 MPa. As discussed in a subsequent section, a high strain-to-failure can be obtained when the performances of the reinforcing tows and the load transfers during loading have not been impaired as a result of the processing condi­tions. Ideally, the strain-to-failure should coincide with that of reinforcing tows, that is, about 0.8%.

Table 2 Mechanical properties of a CVI SiC/Si-B-C composite with a self healing matrix and a multilayer rein­forcement of Hi-Nicalon™ fibers, and 2D CVI-enhanced SiC/SiC composite reinforced with 0/90 five harness satin fabrics of Hi-Nicalon™ fibers

Property

Temperature

Room

temperature

1200°C

CVI SiC/Si-B-C

Fiber type

Hi-Nicalon™

Hi-Nicalon™

fibers

fibers

Reinforcement

Plain weave

Plain weave

Density

2.3

Porosity (%)

13

Tensile strength

315

(MPa)

Strain-to-

0.5

failure (%)

Young’s modulus

220

(GPa)

Interlaminar shear

Strength (MPa)

31

23

Flexural strength

699

620

(MPa)

2D CVI-enhanced SiC/SiC composite

Fiber type

Hi-Nicalon™

Hi-Nicalon™

Fiber content (%)

35

35

Reinforcement

0/90 five harness

0/90 five

satin

harness satin

Density

2.2

2.2

Porosity (%)

10

10

Tensile strength

324

259

(MPa)

Strain-to-failure

0.74

0.50

(%)

Young’s modulus

207

212

(GPa)

Source: Bouillon, E.; Habarou, G.; Spriet, P.; et al. Characterization and nozzle test experience of a self sealing ceramic matrix composite for gas turbine applications. In Proceedings ofIGTI/ASME TURBO EXPO Land, Sea and Air 2002, Amsterdam, The Netherlands, June 3-6, 2002; Power Systems Composites Datasheet.

The strain-to-failure is an interesting characteristic for CMCs for several reasons. First of all, it is not sensitive to scale effects, so that it may be regarded as an intrinsic property and so various CMCs can be compared easily. Then, it reflects the degree of damage tolerance, whereas the strength reflects the load-carrying capacity. These characteristics need to be differentiated, as most components are usually subjected to strain-controlled loading conditions.

A fracture toughness of 30MPaVm was measured using conventional techniques designed for mono­lithic materials. It can be regarded as a high value when compared to monolithic SiC. However, it is

Table 3 Room-temperature properties of 2D melt infil­trated CVI SiC/SiC and 2D CVI SiC/SiC composites rein­forced with Hi-Nicalon type S fibers

2D melt infiltrated CVI SiC/SiC

Fiber type

Hi-Nicalon type S™

Fiber content (%)

35

Density

2.2

Tensile strength (MPa)

341-412

Strain-to-failure (%)

0.60

Young’s modulus (GPa)

232-262

2D CVI SiC/SiC

Fiber type

Hi-Nicalon type S™

Fiber content (%)

35

Density

2.25

Tensile strength (MPa)

305

Strain-to-failure (%)

0.60

Young’s modulus (GPa)

214

45° off-axis tensile strength (MPa)

167

45° off-axis strain-to-failure (%)

0.66

Source: Morscher, G.; Pujar, V. Int. J. Appl. Ceram. Technol. 2009, 6, 151-163.

worth pointing out that it represents the fracture toughness of an equivalent homogeneous material. As discussed in a subsequent section, critical stress intensity factor (KIC) is not an intrinsic property, and it is not an appropriate concept for long fiber- reinforced composites. Furthermore, besides the resistance to crack propagation, damage tolerance is an important property for CMCs. It cannot be char­acterized by fracture toughness. This situation is new when compared to homogeneous materials. Anyway, the fracture toughness KIc may be regarded as an index to compare materials. It cannot be used for design purposes for the aforementioned reasons.

Table 1 shows that CVI SiC/SiC retains its prop­erties at high temperatures. These properties can be enhanced by using advanced fibers. Durability will be addressed in a subsequent section.

Properties vary according to factors, including preform architecture, fiber type, matrix properties, fiber-matrix bond strength, loading conditions, etc. For instance, high tensile strengths (up to 400 MPa) were obtained with Hi-Nicalon™ SiC fibers,34 or with Nicalon fibers and rather strong interfaces.35 Further details on microstructure versus properties are discussed in subsequent sections. The mechanical behavior of 2D CVI SiC/SiC composites exhibits features that are related to composite microstructure. Thus, it deserves special attention because it differs significantly from that of the more conventional homogeneous materials. A clear understanding will be beneficial to a sound use of CVI SiC/SiC.

Tables 3 and 4 show that the ultimate strength and Young’s modulus tend to decrease under off-axis tensile conditions.36 It is worth pointing out that the strain-to-failure is an invariant. It is interesting to note that in 2D CVI SiC/SiC, the directions of the princi­pal stresses coincide with those of the fiber tows.

Sound Velocity and Compressibility2

The velocity of the propagation of sound («) in Na, Pb, and Pb-Bi(e) was mainly measured at normal atmospheric pressure and at temperatures below 1773 K for Na, <1423 K for Pb, and <1073 K for Pb-Bi(e).7,33,34,60-64 It decreases with temperature due to decreasing interatomic interactions. In the temperature range limited by the normal melting and boiling temperatures, the temperature depen­dence of the sound velocity in Na, Pb, and LBE is almost linear and can be presented as follows:

u(T; P0) = »M,0 — A*,0 (T — TM,0) [7]

The recommended values of the sound velocity at the normal melting temperature «M0 and the coefficients Au,0 of eqn [7] for liquid Na, Pb, and Pb-Bi(e) are given in Table 8 and their sound velo­cities as a function of temperature are presented in Figure 6.

Experimental results at higher temperatures were found only in a few publications. For Na, the mea­surements of the sound velocity were performed in the temperature range from Tm,0 up to 1773 K, and a parabolic function was proposed in Fink and Leibowitz7 to take into account its deviation from the linear temperature dependence. In Mustafin and Shaikhiev,63 it was shown that the sound velocity in the liquid Pb can also deviate from the linear tem­perature dependence at high temperatures.

image412

image397

Figure 4 Density of liquid Na, Pb-Bi(e), and Pb at normal atmospheric pressure.

 

image398

Figure 5 Isobaric volumetric coefficient of the thermal expansion of liquid Na, Pb-Bi(e), and Pb at normal atmospheric pressure.

 

Temperature (K)

Подпись:Подпись:Подпись: bs +

The adiabatic (isentropic) compressibility bs can be deduced from the results of the measurements of the sound velocity and density:

= 4@r) = — L2 M

P dp S — L2

The adiabatic compressibility of the liquid Na, Pb, and Pb-Bi(e), at normal atmospheric pressure, calcu­lated with formula [8] and correlations [4] and [7], and using the parameters given in Tables 7 and 8, are presented in Figure 7 as a function of temperature.

The isothermal compressibility can be expressed through the adiabatic compressibility (bs), the iso­baric molar heat capacity (Cp, see Section 2.14.4.4), the density (-), and the isobaric volumetric CTE (ap, see Section 2.14.4.1): мат

-Cp where Ma is the molar mass.

image399

Figure 6 Ultrasound velocity in liquid Na, Pb-Bi(e), and Pb at normal atmospheric pressure.

 

image400

Figure 7 Adiabatic compressibility of liquid Na, Pb-Bi(e), and Pb at normal atmospheric pressure.

 

Control of Neutron Multiplication Factor in Nuclear Reactors

A nuclear reactor operating at a steady power has a neutron multiplication factor of precisely 1.0. In this state, each fission event yields on average one further fission reaction to maintain the chain reaction. If the multiplication factor is <1.0, the nuclear chain reac­tion will die away quickly, while if >1.0, the chain reaction will build up exponentially. A definition of the neutron multiplication factor, usually denoted k, is:

k =(No. of neutrons born in generation j)/

(No. of neutrons born in generation j — 1)

In a reactor operating in the steady state, it is possible to maintain k extraordinarily close to 1 using the inherent negative feedback effects, so that the power output precisely matches the amount of thermal energy extracted from the reactor; thermal power production from the reactor in excess of that removed by the turbine generator raises the temperature of the reactor, and temperature feedback effects reduce the multiplication factor to establish a new balance between reactor output and thermal load.

Some reactors are operated on-load, meaning that fuel can be inserted during full power operation. In such a reactor, it is theoretically possible to start the reactor with just sufficient fissile material (such as 235U) so that k just marginally exceeds 1.0 at full power. As the fissile material is depleted (burns up), fresh fuel is added to compensate and a corresponding quantity of spent fuel is discharged.

However, on-load refueling is not practical in all reactors; many are designed such that access to the fuel is possible only with the reactor shut down and such reactors operate with batch refueling. This means that the reactor is shut down periodically (typically every 12-24 months) and a fraction of the fuel replaced (with an equivalent amount of the highest burnup fuel discharged). In between refueling shutdowns, the reactor operates with no change in the fissile inventory, except for those changes due to fuel depletion and the buildup of fission products and transuranic elements through neutron captures. The next refueling occurs when the fissile content is depleted to the point where, with all control absor­bers removed from the core, the reactor is just capa­ble of maintaining k = 1.0 at full power.

It is useful to note the concept of reactivity at this point, which is a dimensionless quantity usually measured in units of per cent mill or 10—5. It is defined by

p = 105[(k — 1)/k]pcm

A reactor that is just critical has a reactivity of zero and is in steady-state operation. Positive reactivity corre­sponds to a reactor where the neutron flux and power output are increasing with time, while conversely, negative reactivity corresponds with decreasing flux and power. Control rod insertion is said to cause a decrease in reactivity, while their withdrawal is said to increase reactivity.

The upper curve in Figure 1 illustrates the variation of k with irradiation for a typical PWR fuel assembly with an initial 235U enrichment of 4.45 wt% and no burnable poison. At low irradiation, k is around 1.3, while by the time the fuel has reached its discharge burnup of ^55 Gigawatt-days per tonne (1 Gigawatt-days is a convenient unit of thermal energy output for nuclear fuel equivalent to 8.64 x 1013J ton— ; the mass refers to 1 ton of initial heavy metal and the unit is usually abbreviated GWd/tHM), k for the assembly is lower than 1.0. Thus, by the time the fuel is ready for discharge, it is incapable of sustaining a chain reaction by itself. However, the core always contains a mix of fresh fuel in its first cycle of irradiation along with highly irradiated fuel and the fresh fuel effectively donates excess neutrons to the high irradiation fuel such that for the core as a whole, k = 1.0.

Batch refueling causes a problem, however, because if the core is capable of attaining k = 1.0 at the end of the cycle, then by implication, the uncontrolled k must exceed 1.0 at earlier times. In principle of course, control rods can be inserted to control the excess multiplication factor, but in practice, there are limita­tions: First, the control rods have a limited effectiveness and more might be required than is practical within the engineering constraints. Second, inserting control rods distorts the spatial distribution of neutron flux and power within the core, causing localized power peaking that might easily exceed the acceptable performance limits of the fuel. Some means is therefore needed to supplement the control rods.

To an extent, PWRs are able to achieve this with boron as boric acid dissolved in the coolant. This soluble absorber approach has its limitations as well, as will be seen later, and soluble absorber is not an option for most other reactor types. Burnable poisons are used to fill this reactivity control gap. The lower curve in Figure 1 illustrates how a burnable poison (in this case, 24 fuel rods per assembly consisting of 6 wt% Gd2O3 in UO2 with a 235U enrichment of

Подпись: Figure 1 Variation of multiplication factor in a pressurized water reactor with fuel irradiation in GWd/tHM: 4.45 wt% enriched pressurized water reactor assembly with no burnable poison and with 24 poisoned fuel rods containing 6 wt% Gd2O3.

4.45 wt%) might be used to control the excess reac­tivity of fresh fuel by holding down the multiplication factor in low burnup fuel assemblies. Consider, for example, a 3-batch fueling scheme in which the core is made up of equal quantities of fuel assemblies in their first, second, and third irradiation cycles. At the start of the fuel cycle, the first cycle assemblies will have zero burnup, corresponding to points A and A0 unpoisoned and poisoned, respectively. Similarly, the second and third cycle assemblies will correspond to points B and C. The multiplication factor of the unpoisoned core will be k1 = [k(A) + k(B) + k(C)]/3 at the start of the cycle. At the end of the cycle, the three assembly types will have burned up to points B, C, and D and k will be k2 = [k(B) + k(C) + k(D)]/ 3 = 1.0. The difference in reactivity between the start and end of the cycle is k1 — k2 = [k(A) — k(D)]/3. For the poisoned assembly, the corresponding differ­ence is

k0— k2 = [k(A0) — k(D)]/3.

Since k(A0) < k(A), the change in multiplication factor during the cycle is considerably reduced. Ide­ally, the burnable poison material is depleted during the fuel cycle such that there is none left at the end of the first irradiation cycle indicated; any residual poison material left at the end of the cycle means that the cycle will end prematurely or will require an increased initial 235U loading if the cycle length is to be preserved, both of which equate to an economic
penalty. The small gap between the poisoned and unpoisoned curves in Figure 1 represents just such a residual poison penalty.

Porosity

Two important roles of porosity in the fracture pro­cess were identified. First, the interaction between the applied stress field and the pores caused loca­lized stress intensification, promoting crack initiation from favorably oriented pores at low applied stresses. Second, propagating cracks could be drawn toward pores in their vicinity, presumably under the influ­ence of the stress field around the pore. In some instances, such pore/crack encounters served to accelerate crack growth; however, occasionally, a crack was arrested by a pore and did not break free

image345

Figure 23 An optical photomicrograph of the microstructure of grade H-451 graphite revealing the presence of pores [P], coke filler particles [F], and cracks [C] that have propagated through the pores presumably under the influence of their stress fields.

until higher applied stresses were attained. Pores of many shapes and sizes were observed in the graphite microstructure, but larger, more slit-shaped pores were more damaging to the graphite.

Crystallographic Properties and Chemical Bonding

In the Zr-C system, the monocarbide is the only intermetallic phase reported, crystallizing in the face-centered cubic NaCl structure (Fm3m, space group 225) (Figure 1). Zr atoms form a close-packed lattice, and the smaller C atoms (rc = 0.48rZr) fill the octahedral interstices.3

The ZrCx phase exists over a wide compositional range and, as further discussed in Section 2.13.3.1, is stable with up to 50% vacancies on the carbon sublattice. Low-temperature ordered phases have been experimentally reported for the Ti-C, V-C, and Nb-C systems, but so far have been suggested only via thermodynamic calculations for the Zr-C system.6 Metallic vacancies comprise at most a few atomic percent.3

The effect of carbon vacancies on unit cell geom­etry has been investigated extensively (Figure 2),

with the relationship between room temperature lat­tice parameter and C/Zr ratio difficult to establish conclusively. Scatter in literature values is a common theme in the study of transition metal carbides because of the difficulty of preparing pure specimens and adequately characterizing them. Oxygen and nitrogen readily substitute for carbon in the lattice, and their presence is correlated with reduced lattice parameter. On the basis of literature values for a range of impurity contents, Mitrokhin et alJ established a quantitative relationship between the lattice parame­ter of such oxycarbonitrides and carbon, as well as the oxygen-nitrogen impurity content:

azrcx (on) = 4.5621 — 0.2080x V 0.3418x

— 0.80y(1 — x) I1]

where x is the C/Zr atomic ratio (0.62 < x < 1) andy is the (O + N)/Zr atomic ratio (y < 0.3).

In general, lattice parameter increases with C/Zr ratio, with evidence for an increase and a decrease as C content increases above approximately ZrC0.8 toward ZrCi.0. Ramqvist8 qualitatively explained the peak in lattice parameter versus C/Zr ratio as being due to competing influences on lattice size: expansion with increasing carbon content due to the increased space required to accommodate interstitials, and con­traction due to the increased bond strength.

The nature of chemical bonding in ZrCx is not fully understood, and electronic structure investiga­tions have sought to establish the relative influences of covalent, metallic, and ionic contributions. Carbon s — and p-orbitals and zirconium d-orbitals participate in bonding and contribute to strong metal-nonmetal bonding and octahedral coordination.9 Other authors10 emphasize the interstitial nature of carbon in the ZrC structure and the donation of electrons from carbon to metal, strengthening Zr-Zr bonds. Lye and Logothetis11 proposed that some charge transfer from carbon to metal occurs and that carbon stabilizes the carbide structure by contributing bonding states. Hollox12 and Storms and Griffin13 suggest that, depending on the carbide, lattice sta­bility decreases with increasing carbon content if antibonding states become filled; this is consistent with observed hardness and melting temperature measurements for ZrCx. The electronic structure of ZrC must be placed in context with the properties of Groups IV, V, and VI transition metal carbides, and the interested reader is referred to the compar­ative reviews seen earlier.

Fuel rods for CANDU reactors and AGRs

CANDU reactors and AGRs generally have fuel rod design specifications similar to those of LWRs. The CANDU reactors use natural uranium oxide or slightly enriched uranium oxide contained within a thin Zircaloy clad, and design burn-up is lower than that of LWRs. In AGR fuel rods, uranium dioxide pellets, enriched to about 3%, are encased in a stainless steel clad. Fuel bundles of both the reactors have circular, cylindrical shapes to fit in the pressure tube ofCANDU reactors or in the graphite sleeve ofAGRs. The fuel rod diameter differs according to the number of fuel rods per bundle. Typical CANDU fuel rod design specifica­tions for a 28-rod bundle are presented in Table 2.3 The overall fuel rod lengths of both the reactor types are much shorter than those of LWRs in order to fit their fuel assembly design which enables on-load refueling.

2.15.3.1.3 Fuel rods for FBRs

FBR fuel rods contain MOX pellets having high plutonium content, with the exception of Russian FBRs, BN-350, and BN-600 in which high enrich­ment UO2 fuel pellets have been mostly used. Fuel pellets of less than 8 mm diameter are encased in a stainless steel cladding; they operate at a high linear heat rate with centerline temperatures of around 2000 °C or higher. Under these conditions, fission gas release is typically high (>80%) and a very large plenum is included to limit gas pressure. The gas plenum is located at the bottom of the rod in some fuel designs, aimed at minimizing plenum length, thanks to the lower gas temperature at the bottom of the rod. Upper and lower sections of the depleted UO2 pellets are included for breeding. Pellet-smeared density is set not to exceed a crite­rion that is formulated as a function of burn-up to avoid fuel-cladding mechanical interaction at high burn-up; high-density annular pellets or low- density solid pellets are used; the former lower the fuel centerline temperature allowing a higher linear heat rate.3