Despite being a metal, uranium has chemical bonding characteristics of metalloids like arsenic, antimony, or bismuth.

Up to 666 °C, uranium assumes an orthorhombic crystal structure (a-U), with 4 atoms per unit cell: density — 19.04 gcm~3 and lattice constants (a = 2.8541 ± 0.003A, b = 5.8692 ± 0.0015 A, and c = 4.9563 ± 0.0004A) (at 25 °C). The struc­ture is somewhat unique in that it can be thought of as stacks of “corrugated” sheets with atoms parallel to a-c plane with ~2.8 A distance between atoms in the sheets and ~3.3 A distance between the sheets. It can also be described as a dis­torted HCP crystal structure!

In the temperature range of 666-771 °C, uranium has a complex tetragonal crys­tal structure (30 atoms in a unit cell) and is called b-U. Density of b-U is 18.11 g cm~3, and lattice constants a = 10.759 ± 0.001 A and c = 5.656 ± 0.001 A (at 720 ° C).

In the temperature range of 771-1130 ° C, uranium assumes a simple body-cen­tered cubic crystal structure (y-U), that is, with 2 atoms per unit cell. Density is

18.6 g cm~3, and lattice constant a = 3.524 ± 0.002 A (at 805 °C).

Because of the anisotropic nature of the crystal structure of alpha-uranium, thermal expansion coefficients are anomalous along the crystallographic directions deter­mined by lattice parameter measurements and shown in Figure 7.1. That is, the lin­ear thermal expansion coefficient (both linear and volume) increases in the direction of [100] and [001], and decreases along [010] with increasing temperature. However, the volumetric thermal expansion coefficient (i. e., the overall thermal expansion effect due to combination of linear expansion and contraction) does increase with increas­ing temperature. The dilatometry has also been used to measure thermal expansion coefficients and they have shown comparable trend. As noted before, uranium shows allotropic transformation and thus shows increased volumetric thermal expansion coefficients, as the phase transformation occurs as a function of temperature.

Thermal conductivity is a important property with respect to heat removal from the fuel through cladding (by conduction) to the coolant (by convection) in a nuclear reactor. The linear power rating of a reactor fuel element is generally lim­ited by the thermal conductivity of the fuel to avoid center melt. Figure 7.2 shows thermal conductivity of a well-annealed high purity polycrystalline uranium as a

200 400 600

TEMPERATURE (°С)

Figure 7.1 Thermal expansion coefficient of a-U is anisotropic as a function of temperature [2].

function of temperature. Interestingly, the thermal conductivity of uranium keeps on rising as the temperature increases, thus offering the advantage of having better heat conduction at elevated temperatures! However, depending on various factors, thermal conductivity may vary and fall in a data-band.

Heat capacity of uranium in the range of 20-669 °C (293-942 K) is calculated by expression given by Rahn et al. [4]:

Cp [J kg-1 K-1] = 104.82 + (5.3686 x 10-3)T + (10.1823 x 10-5)T2, (7.8)

where T is in K.

The average Cp in the temperature regime of 669-776 °C (beta-phase regime) is

176.4 J kg-1 K-1, whereas the average Cp is 156.8 J kg-1 K-1 in the temperature regime of 776-1132 °C (gamma-phase regime).

An additional hardening effect occurs upon annealing of BCC metals after irradiation. This phenomenon is known as RAH. Note that hardening starts at 120 °C and increases to a maximum at 180 °C before decreasing. A second

hardening peak appears at 300 °C before the yield strength drops due to recovery effect. The first peak is due to migration of oxygen to defect clusters and the second peak is due to the migration of carbon (Figure 6.29). Formation of respective inter­stitial impurity and defect cluster complexes at the corresponding temperature leads to enhanced obstruction from the dislocation movement and manifests in the form of additional hardening peaks. This phenomenon has also been observed in molybdenum, vanadium, iron alloys where the interstitial impurities like car­bon, nitrogen and oxygen are responsible. Irradiated FCC metals/alloys generally do not show this kind of effect upon annealing.

6.2.1.1 Channeling: Plastic Instability

In some highly irradiated metals, the onset of necking coincides with yielding with no uniform deformation. This kind of behavior has been shown in Figure 6.23a in the stress-strain curve of A533B irradiated to 0.89 dpa as well as in Figure 6.24 for

mild steel at the highest fluence. This unusual macroscopic behavior is due to the microscopic phenomenon of dislocation channeling. However, this effect has noth­ing to do with the PKA channeling that occurs due to the crystallinity of materials — so avoid getting confused between the two terms. In dislocation channeling, an avalanche of dislocations can be released to move on particular slip planes along planar channels that have been cleared of obstacles. As dislocations see these paths as the path of least resistance, the dislocations generated move through these chan­nels. Thus, the strain remains highly localized. In this way, eventually stress con­centration sites are created where these dislocation channels intersect the grain boundaries. Figure 6.30 shows microstructural evidence of dislocation channels in a 316-type stainless steel irradiated to 0.78 dpa at 80 °C.

6.2.2

Plutonium is considered a weak material compared to most other structural metals. Also, because of its low melting temperature, even room temperature may show up effects of high homologous temperatures. The mechanical properties are very sen­sitive to impurities, temperature, crystal defects, anisotropy, and phase transforma­tion. Thus, high-temperature application of pure plutonium is not possible. The properties vary with the allotropes. The elastic constants for alpha-plutonium are Young’s modulus: ~82.7-97GPa, shear modulus: ~37.2-43.4GPa, and Poisson’s ratio (0.15). Figure 7.13a shows a comparison of stress-strain curves of alpha-

plutonium and Pu-1.1 at% Ga (delta-phase) alloy. Tensile yield strength and tensile strength vary between ~310 and ~380MPa. Compressive yield strengths are approximately in the range of 345-517 MPa. Elongation to failure and reduction in area are less than 1% at room temperature. The mechanical strength of poly­crystalline plutonium (both a — and b-phases) is quite sensitive to temperature, as illustrated in Figure 7.13b. The upper range shows the trend in ultimate tensile strength and the lower boundary shows the trend in yield strength. There is a con­siderable scatter in the data available for alpha-plutonium, and thus the data are shown in the form of a band. The delta phase has very low strength. Also, the strength of epsilon phase (BCC lattice structure) is very low as the diffusivity is fast through the BCC crystal lattice (more open structure).

Merz and Nelson [9] demonstrated that the tensile behavior of polycrystalline alpha-plutonium is much more sensitive to strain rate at the proximity of ambient temperature than the first thought. This finding is illustrated in Figure 7.14a. Fine­grained (grain size of 1-3 pm) extruded alpha-plutonium at room temperature and with a strain rate of 7 x 10-4s-1 shows good ductility (see Figure 7.14b). This pro­vided the first evidence that deformation mechanisms that can operate at the higher end of the alpha-phase temperature range and into the beta-phase range (i. e., at lower homologous temperatures) could be grain boundary sliding in addi­tion to dislocation glide. For example, grain boundary sliding was shown to play an important role in the deformation of fine-grained alpha phase. At 108 ° C, it exhib­ited superplastic elongation of ~218%, as shown in Figure 7.14c.

Point defects do not tend to change the thermal expansion coefficient, which have been confirmed experimentally.

6.4

Radiation Effects on Corrosion Properties

The chemical environment found in the nuclear reactors is quite harsh as many of the electrochemically active metals/alloys constitute the materials used in nuclear reactors. Furthermore, existence of crevices allowing chemicals to collect can lead to crevice corrosion. Sometimes “crud” formation also causes problems; the word “Crud” stands for Chalk River Unidentified Deposit. “Crud” is the corrosion prod­uct that is created in the steam generator, piping, and reactor pressure vessel walls, get transported via the core thus acquiring induced radioactivity, and get deposited in various locations of the reactor primary system. These result in problem with heat transfer and exacerbation of corrosion issues. Stobbs and Swallow [36] explained the effect of radiation in terms of metal, protective layer, and environ­ment (corrodent).

6.4.1

Metal/Alloy

Radiation damage by generation of Frenkel defects, spikes, or transmutation can affect corrosion to some degree. Possible mechanisms are as follows:

a) Increased chemical activity: This effect becomes less important at higher temperatures.

b) Irradiation-induced dimensional changes: These may lead to enhanced corro­sion by cracking the surface film so that the surface underneath becomes exposed to the corrodent. Thermal cycling is more important than density changes.

c) Radiation-induced losses: Such losses in ductility accompanied by stressing may result in stress corrosion. This has been observed in control rod alloys of boron in steel, titanium, or zirconium.

d) Radiation-induced phase changes: Such changes (e. g., precipitation) may affect the corrosion behavior.

6.4.2

Protective Layer

Lattice defects introduced into the protective oxide layer may affect the corrosion rate in the metallic substrate.

a) Diffusion of anions or cations through the oxide layer — irradiation would increase the number of defects.

b) Activity changes in the oxide layers are a potential source of enhanced corrosion.

c) Phase changes are a possible source of accelerated corrosion. If irradiation influ­ences the transformation in a system such as ZrO2 (monoclinic to tetragonal), an increase in rate may occur.

6.4.3

There are three uranium carbide compounds (UC, U2C3, and U2C) with the great­est interest in UC. UC is often considered the ideal nuclear fuel compared to the metallic uranium and UO2 fuels. UC does not undergo phase change until its melt­ing point (2350 ° C) and has a high uranium density and also a higher thermal con­ductivity than UO2. UC also shows good thermal and irradiation stability (fission gas release and swelling are moderate and little cracking is observed). The higher

uranium atom density and higher thermal conductivity can result into the following:

i) Larger size of fuel elements desired for an economic fuel fabrication.

ii) Higher power density or specific power attainable.

iii) Smaller primary components such as pressure vessel, piping system, and so on.

7.3.3

Pure uranium is a moderately ductile material. However, the mechanical properties depend on crystallographic texture (i. e., preferred orientation of grains) and, thus are in alpha-uranium. The texture is affected by the fabrication history and heat treatment. Grain size and shape are also important parameters affecting the mechanical properties. The tensile properties are sensitive to impurities like carbon or fission products or alloying elements. A typical stress-strain curve of uranium is shown in Figure 7.3. The strength decreases precipitously with increasing tempera­ture, as shown in Table 7.2.

The plastic deformation of uranium generally involves the following mecha­nisms: (i) slip in the {010}(100) system, (ii) {130} twinning, (iii) {172} twinning, and (iv) kinking, cross-slip, {176} twinning, and {011} slip under special condi­tions. Overall, twinning appears to be the major deformation mode at room tem­perature. However, the contribution of slip to plastic deformation increases as the temperature is increased, and above ~450 °C, slip becomes the predominant plas­tic deformation mechanism.

As discussed in earlier chapters, ductility (or toughness) is an important prop­erty of any structural material or any other types of materials in load-bearing nuclear reactor components. Radiation hardening generally leads to radiation embrittlement and occurs in a wide range of materials. However, radiation embrittlement in BCC metals/alloys (such as ferritic and ferritic-martensitic steels) that exhibit ductile-brittle transition temperature (DBTT) refers to an increased DBTT along with decreased upper shelf energy and decreased slope

in the ductile-brittle transition region, as shown in Figure 6.31a. Yield strength decreases with temperature, but fracture stress is roughly temperature indepen­dent. Irradiation causes an increase in the yield stress shifting the point at which fracture stress and flow stress curves intersect at higher temperature, thus raising the DBTT. Figure 6.31b is known as Davidenkov’s Diagram. It is to be noted that in BCC metals the yield stress increases rapidly as temperature decreases, while in FCC and HCP metals the decrease is not that rapid, which results in DBTT occurring at very low temperatures and thus ofless significance (Section 5.1). The effect of irradiation on the use is believed to be due to a reduction in strain hardening and increase in flow localization, leading to lower ductility (also dislocation channeling has an effect).

Earlier we have underscored the importance of having a decreased DBTT for structural applications. This is also applicable for reactor pressure vessel (RPV) steels, and this section is devoted to understanding the origin and implications of radiation embrittlement in RPV steels. Reactor pressure vessel is an integral part of a nuclear power reactor and it is considered a life-limiting reactor com­ponent, which means that the RPV is highly unlikely and extremely difficult (cost-prohibitive) to replace during the operational life of the reactor. Hence, the same RPV stays in place for the entire operational life of the reactor. Currently, many utilities are applying for relicensing their reactors for another 20-30 years as their original design life comes to an end. RPV surveillance pro­gram has facilitated the understanding of radiation embrittlement in RPV steels; however, understanding the behavior over very long period is still evolv­ing. The relicensing of the commercial power reactors beyond their original design lives makes the understanding of radiation embrittlement in RPV steels even more important. Understanding the role of late blooming phases in the

radiation embrittlement of reactor pressure vessel steels will need more sus­tained studies in the wake of LWR sustainability efforts.

Generally, low-alloy ferritic steels (A508 and A533B grades) are used in the RPVs of the light water reactors. The RPV steel in a PWR would have to withstand irradiation temperature of 240-290 ° C and fast neutron fluence of <2 x 1024 nm~2 over a time period of decades, leading to substantial changes in microstructure: (i) formation of radiation defects, (ii) phase transformations accompanied by the generation of various precipitate populations, (iii) formation of impurity-vacancy clusters (like copper-vacancy ones), (iv) intergranular segregation of phosphorus and other impurities, and (v) segregation of phosphorus to interfaces between sec­ondary phases and matrix (i. e., intragranular segregation). These are the likely rea­sons for radiation embrittlement as observed in the RPV steels.

As noted before, plutonium is a highly concentrated fissile material. Thus, it must be diluted before it can be used. Furthermore, its physical, chemical, and mechani­cal properties do not allow it to be used in unalloyed metallic form. Plutonium has a stronger tendency to form intermetallic compounds than uranium. However, they have similar behavior of alloy formation. There are a few elements that can form alloy with plutonium. A plutonium alloy with intended application must have the following characteristics: (i) plutonium required for criticality is kept to a minimum,

(ii) should have good fabricability features, (iii) good thermal and irradiation stabil­ity, (iv) high corrosion resistance, and (v) available alloying elements.

Alloying elements like Al, Ga, Mo, Th, and Zr can stabilize the delta phase, even though it could make it metastable much like the stabilization of gamma-uranium. Gschneider et al. [10] reported that the negative thermal expansion coefficient of delta-plutonium becomes less negative and eventually becomes positive with increased concentrations of alloying additions of Al, Zn, Zr, In, and Ce because of increased electron concentration.

One of the well-known alloys is Pu-3.5 at% Ga alloy. This alloy was developed dur­ing the days of the Manhattan project and was used as a fuel in the erstwhile Los Ala­mos fast reactor. In this alloy, delta phase is stabilized in a wider temperature range. It improves the corrosion resistance of plutonium by several times; for example, the weight loss was only 0.1 mg cm~2 during the test of exposure of27 000 h in moist air.

There has been a deep interest in developing metallic alloy fuels involving fissile — fertile combinations for a breeder reactor like LMFBR as the metallic fuels have the inherent advantages of high fissile atom density leading to higher breeding ratio along with shorter doubling time compared to ceramic fuels. The phase diagram of U-Pu is shown in Figure 7.15. Pu-U is a complex system with complicated phase relations. Plutonium content more than the solubility limit in gamma-uranium leads to an extremely brittle phase. This makes casting of this alloy very difficult and also results in alloys that are quite susceptible to thermal cycling and radiation damage. However, addition of molybdenum has some beneficial effects in that it suppresses the creation of the embrittlement phase. There are many different com­positions that have been studied. A single-phase alloy with better corrosion resist­ance has been found to be U-21Pu-16Mo (in atom%). Other ternary alloy systems like U-Pu-Th, U-Pu-Al, U-Pu-Fe, and so on have also been studied.

7.2.3

Various reactions can occur in the coolant exposed to irradiation. Short-lived radi­cals may form and secondary ionization produced; impurities generated, and sec­ondary ionization occurred.

a) In gases, the effect is quite limited. Apparently, carbon dioxide can decompose to form oxygen in the reactor with increased attack on zirconium, Inconel, and 446, 310, and 316-type stainless steels.

b) Radiolysis of water can pose problem — such as radiolysis of water producing hydrogen may lead to hydriding of zirconium alloy cladding.

c) Liquid metals are generally stable under irradiation.

d) Fused salts are usually unaffected by irradiation.

In uranium-nitrogen system, ceramic compounds such as UN, U2N3, and UN3, with uranium mononitride (UN), are the most stable and the only compound with properties of a nuclear reactor fuel. UN has a NaCl-type (interpenetrating FCC) crystal structure. UN has a theoretical density of 14.32 gcm~3 under normal condi­tions. UN maintains its stoichiometry up to high temperatures, and becomes nonstoichiometric at >1500 °C. Melting temperature of UN is about 2650 °C. UN does not melt congruently and begins to dissociate into free uranium and gaseous nitrogen at a temperature that is a function of the system nitrogen overpressure, which can be analytically described by Eq. (7.14), where Tm represents the melting

temperature in K and PN2 represents the nitrogen partial pressure in the unit of atm (1atm ffi 101.3 kPa) Ref. [18].

Tm = 3035 (Pn2 )°’°2832. (7.14)

The thermal conductivity and specific heat of UN have already been shown in Figures 7.20 and 7.21.

Here we summarize various features of different uranium ceramic fuels in a tabular form (Table 7.5).

7.3.4