Uranium (atomic number 92) takes up about 4 ppm (parts per million) of the earth crust. Uranium is more abundant than the common elements such as silver, mercury, cadmium, and so on. The amount of economically recoverable uranium in the world has been estimated to be about 5.5 million tons (2007 estimate). Uranium mined from the earth crust is known as “natural ura­nium” that contains two main isotopes U235 (0.71%) and U238 (99.28%) along with a very minor presence (0.006%) of U234. Uranium in general is found in

a variety of minerals, such as pitchblende (U3O8), Uraninite (UO2) followed by carnotite (K2O ■ 2UO3 ■ V2O5 ■ nH2O). High-grade uranium ores are mined in Kazakhstan, Canada, Australia, Namibia, South Africa, Niger, the Rocky Moun­tain region of the United States, and many other nations. Kazakhstan leads the world production of uranium (27%) followed by Canada (20%) and Australia (20%), as per 2010 estimate. However, it can be noted that a sizable portion of uranium is also produced by reprocessing spent nuclear reactor fuels. Note that existing laws presently forbid reprocessing of spent nuclear fuels in the United States. So, almost all commercial uranium fuels in the United States need to be made following extraction from the ores. On the other hand, France uses reprocessing of spent nuclear fuels as one of the major methods for meeting its fuel needs.

7.2.1.1 Extraction of Uranium

Over several decades, many uranium extraction methods have been pursued. Here, only some of the very common extraction techniques are discussed. Almost all ura­nium minerals are present in the ore with a variety of gangue (impurity) materials. Hence, it is essential to separate the gangue minerals from the mineral with a metallic value. The metal extraction process thus contains mineral beneficiation or ore dressing techniques as the first steps that increase the metal value of the ore by removing the gangue materials. The uranium extraction is generally achieved by using chemical methods, as entirely physical beneficiation methods are not effec­tive enough to liberate ore minerals of value. For recovery of the most metal con­tent, it becomes necessary to pursue leaching and precipitation reactions. One of the most common processes is to leach finely ground uranium ores by dilute acids. Sulfuric acid (H2SO4), nitric acid (HNO3), and hydrochloric acid (HCl) can be used for leaching. However, the latter two acids adversely affect the process economics. Also, they present corrosion problems for the process equipment. However, if the solvent extraction process is to be used after leaching, nitric acid must be used. Under certain conditions, sodium carbonate (Na2CO3) is also used as suitable leaching agent.

Leaching is nothing but a dissolution reaction in which uranium forms a soluble compound that remains dissolved in the solution. It is known that uranium can go into solution only when it is in a hexavalent state. This is a common requirement for both acid and alkali leaching. Thus, if uranium is present in the tetravalent state, it needs to be oxidized to the higher oxidation state. This is obtained by the presence of trivalent iron or pentavalent vanadium, which happens to coexist with uranium in most uranium ores. The reactions for acid and alkali leaching are given below:

2U3O8 + 6H2SO4 + (O2) = 6UO2SO4 + 6H2O (7.3)

2U3O8 + 18Na2CO3 + 6H2O + (O2) = 6Na4UO2(CO3)3 + 12NaOH (7.4)

Acid leaching generally leads to greater recovery of uranium than carbonate leaching. However, there are some limitations of acid leaching. This cannot be used for ores that contain magnesium and/or calcium carbonates as these

compounds tend to react with acid leachants wasting an excessive amount of acid. Furthermore, because of corrosion problems, the equipment and procedure used in acid leaching are far more expensive. Conversely, corrosion problems are not so severe (thus reducing the process costs) in alkali leaching. It also allows reagent recovery. However, alkali leaching is not suitable for leaching ores with contents of high gypsum or sulfide or refractory constituent.

After leaching, uranium is to be recovered from the leach solution. This can be done by following one of the methods — chemical precipitation, ion exchange, and solvent extraction. Here, we discuss the ion exchange method. This method is used for recovering uranium after acid leaching by sulfuric acid. The method is based on the principle that uranyl sulfate ions can be selectively removed by allowing them to be adsorbed by an ion exchange resin, and subsequently the adsorbed ions could be separated from the loaded resin with a solution concentrated with nitrate or chlo­ride ions. It can be noted that the ion exchange process is also applicable to alkali leaching process. From the processes discussed above, eventually a yellow powder containing 80-85% of UO2 can be obtained. Nitric acid is used as a dissolving agent for this powder subsequent filtration. This reaction produces uranyl nitrate that is extracted with the help of ether. Then water is used to wash the filtrate to produce an aqueous solution from which pure ammonium diuranate [(NH4)2U2O7] is pre­cipitated by passing ammonia gas. Following the separation of diuranate, it is dried and reduced to uranium dioxide in hydrogen at 650 °C. In another process (Dryway process), ammonium diuranate can be converted to uranium trioxide (UO3) by heating it to remove ammonia and steam. Uranium trioxide is then treated with hydrogen at ~600 °C to produce uranium dioxide and then this dioxide is reacted with anhydrous hydrogen fluoride to obtain the uranium tetrafluoride (UF4) that can then be reduced with either calcium or magnesium to produce metallic ura­nium. Some of the reactions involved in the Dryway process are given below:

UO3 + H2 ! UO2 + H2O (7.5)

UO2 + 4HF! UF4 + 2H2O (7.6)

UF4 + 2Mg! U + 2MgF2 (7.7a)

UF4 + 2Ca! U + 2CaF2 (7.7b)

For enrichment of uranium (i. e., to increase the amount of fissile atom U235 den­sity), there are specific methods like membrane separation, centrifuging, and so on, using UF6. Depending on the condition of uranium (unenriched, slightly enriched, or highly enriched), specific details of the process may change to avoid any possibility of obtaining critical mass for fission chain reaction.

The strength (both yield and ultimate tensile stress) of metals/alloys increases along with appreciable reduction in ductility coupled with reduction in strain

hardening exponent. For example, strain hardening exponent of Zircaloy-2 has been found to vary between 0.1 to 0.15 in annealed condition. However, after irradiation, the exponent may decrease to 0.02 to 0.01 depending on the extent of radiation damage, thus affecting the uniform elongation of the alloy (as described in Chapter 5.1). Radiation hardening can occur due to the multitude of defect cre­ation in irradiated materials: (i) point defects (vacancies and self-interstitials), (ii) impurity atoms, (iii) small defect clusters, (iv) dislocation loops, (v) dislocation lines, (vi) cavities (voids/bubbles), and (vii) precipitates. Generally, radiation hard­ening effect starts to appear at temperatures less than <0.4Tm (where in situ recov­ery effect is less) and at radiation damage of >0.1 dpa.

Figure 6.23a-c shows tensile stress-strain curves of irradiated (increasing flu — ence) BCC-based alloy (A533B — low-alloy ferritic steel), an FCC-based alloy (316- type stainless steel), and a HCP-based alloy (zircaloy-4), respectively. Generally, FCC — and HCP-based alloys do not show discontinuous behavior in unirradiated state. However, in irradiated state they exhibit yield point-like behavior, as shown in Figure 6.23b and c.

In BCC metals where yield points appear along with Luders strain before expo­sure to high-energy radiation, Luders strain increases following irradiation and at high neutron fluxes (>1019 ncm~2) fracture occurs during Luders strain itself. Figure 6.24 depicts a series of stress-strain curves in mild steel tested at ambient temperature following neutron radiation exposures.

An actual example of the effect of neutron irradiation on tensile strength and ductility properties is shown in Figure 6.25. Here, we describe one example from

9Cr-1MoVNb steel (T91) on the radiation effect in F/M steels. Irradiation exposure dose of 9 dpa resulted in appreciable radiation hardening due to the formation of a wide range of radiation-produced defects in a temperature range of 425-450 °C (Figure 6.25a). Figure 6.25b shows the corresponding ductility as a function of test temperature. Hardening causes a decrease in ductility at the lowest temperature. However, interestingly, the ductility of the irradiated alloy increases at 450 °C com­pared to that of the aged alloy. It is interesting to note that the aged alloy shows a maximum strength at a temperature where the irradiated alloy shows much higher

ductility. However, note that the ductility data of the unirradiated alloy are not avail­able at 450 °C. Radiation hardening saturates by around 10dpa. For irradiation above 425-450 °C, there may be enhanced softening due to increased recovery and coarsening.

Understanding radiation hardening would need our understanding of the dislo­cation theories and strengthening mechanisms. First, we will discuss the two major components of radiation hardening — source hardening and friction harden­ing. As discussed in Chapter 5, yield stress (ty) can be regarded as composed of source hardening (ts) and friction hardening (т;) terms, representing the hardening due to solute atoms locking dislocation sources and due to subsequent dislocation movement through the lattice.

800

Figure 6.25 Variation of (a) yield strength and (b) total elongation as a function of test temperature in aT91 steel Ref. [16].

a) Source Hardening (ts) This hardening can increase the stress required to start a dislocation moving on its glide plane. This can be found in irradiated FCC met­als, and in both unirradiated and irradiated BCC metals. In case of FCC metal — s/alloys and most HCP metals/alloys, the unirradiated materials do not show source hardening behavior. This is shown by continuous stress-strain curve without yield point phenomenon (note in Section 5.1). However, the unirradi­ated BCC metals (low-alloy ferritic steels) manifest a source hardening-like phe­nomenon that occurs due to the dislocation-interstitial impurity interaction as seen in the yield point phenomenon (Figure 6.23a). Source hardening observed in irradiated FCC metals is due to the formation of irradiation-produced defect clusters near the Frank-Read sources, consequently raising the stress (tFR = Gb/L) required to activate the loop by decreasing the pinning point dis­tance (L). However, once the loop starts forming, it sweeps away the defect clus­ters and the stress drops.

In a polycrystalline material, majority of the dislocation sources are on or near the grain boundaries and the dislocation pileups create stress concentration at the boundaries to activate dislocation sources and generate dislocations in the other grain. Basically, the Hall-Petch strengthening (fcyd~1/2) effect, discussed in Section 5.1 contributes profusely to the source hardening term in poly­crystalline materials.

b) Friction Hardening (ti) After being generated from the source, the dislocation encounters a number of obstacles that lie on the slip plane or near the slip plane while moving on it. This raises the stress needed to move dislocations on the slip plane and in aggregate is called friction hardening. Friction stress (t) consists of two components: long-range stresses (tLR) and short-range stresses (tSR):

ti = tLR + tSR, (6.3)

The long-range stresses generally arise from the repulsive interaction between a moving dislocation and the dislocation network. This effect is termed as long range as it works over a distance from the gliding dislocation (Taylor Equation).

tLR = aGbg1/2,

where gd is the dislocation density.

The short-range stresses may have two origins — athermal and thermally activated. The short-range stresses may arise out of precipitates, such as precipitate hardening in terms of Orowan bowing and particle cutting, in the presence of voids/bubbles (void hardening) and dislocation loops. One general way of expressing the short-range stresses is the summation of the contributions of precipitation hardening (tp), void hardening (tv), and loop hardening (tl):

tSR — tp + tv + tl.

If it is assumed that these obstacles are dispersed in a random fashion, it can be shown that the average interparticle spacing (l) between the defects characteristics (number density N and average diameter d) can be described as Eq. (6.6):

l = (Nd)~1/2. (6.6)

Thus, the general form of tSR can be given by

rSR = aGb(Nd)1/2. (6.7)

At a very low dose, the irradiated microstructure would contain defect clusters and small loops. With increasing dose, the loop microstructure saturates at a particular number density and size as the loops unfault and become part of the dislocation line network, thus increasing dislocation density. At higher tempera­tures, voids/bubbles would be present and irradiation-induced precipitation can also contribute to the radiation hardening effect.

There are six allotropes of plutonium. Given the melting temperature of just ~640 °C, it means the various allotropes are stable only in limited temperature ranges. In plutonium, the narrow conduction bands and high density of states of 5f electrons make it energetically favorable for the ground-state crystal structure to distort to a low-symmetry monoclinic lattice at lower temperatures. Plutonium adopts more typical symmetric structures only at elevated temperatures or with suitable alloying.

Up to ~122 °C, plutonium is known as alpha phase (a-Pu) and has a simple monoclinic crystal structure. The density of this phase at 21 °C is 19.816 gcm~3, and the lattice parameters are a = 6.1835 A, b = 4.8244A, c = 10.973 A, and b = 101.81°. Figure 7.11a illustrates the (020) plane of the a-plutonium monoclinic lattice, which resembles an HCP plane. In Figure 7.11b, two stacked (020) planes of the crystal contain four unit cells. The bond lengths, however, can be categorized into two groups (long bonds ~3.19-3.71 A, and short bonds ~2.57-2.78 A); each of the eight numbered sites is crystallographically unique. Lawson et al. [7] showed that there are 16 atoms per unit cell with 8 distinct lattice positions.

From ~122 °C to ~206 °C, plutonium assumes a body-centered monoclinic lat­tice structure (34 atoms per unit cell) and is known as b-Pu. At 190 °C, the density of b-Pu is 17.70gcm~3 and the lattice parameters are a = 9.284A, b = 10.463 A, c = 7.859A and b = 92.13°.

From ~206 °C to ~319 °C, plutonium assumes a face-centered orthorhombic (8 atoms per unit cell) crystal structure. This phase is also known as gamma — plutonium (y-Pu). At 235 °C, the density of y-Pu is 17.14 gcm~3 and the lattice parameters are a = 3.1587 A, b = 5.7682 A, and c = 10.162 A

From ~319 °C to ~451 °C, plutonium takes up a face-centered cubic (FCC) crys­tal structure with usual 4 atoms per unit cell, and is known as delta-plutonium (6-Pu). At 320 °C, the density of 6-Pu is 15.92 gcm~3 and the lattice constant is a = 4.6871 A

From ~451 ° C to ~476 °C, plutonium assumes a body-centered tetragonal lattice structure with usual 2 atoms per unit cell. This phase is known as delta-prime (6′-Pu). At 465 °C, the density of 6′-Pu is 16.00 gcm~3 and the lattice constants are a = 3.327 A and c = 4.482 A.

From ~476 °C to just before the melting point (639.5 °C), plutonium maintains a body-centered cubic structure (2 atoms per unit cell) and is called “epsilon” phase.

The lattice constant and the physical density of this phase are 3.6361 A and 16.51 g cm~3, respectively.

The allotropic (or polymorphic) transformation kinetics is very sensitive to prior processing history and presence of impurities. In case of pure metal, significant hysteresis occurs on cooling. Plutonium has many anomalous characteristics. For instance, the transformation from b-Pu to a-Pu is very slow and generally other high temperature phases are found to be retained even below the transformation temperature except under application of high pressures. So, generally high strain is retained at room temperature in a-Pu when cooled at atmospheric pressure. So, martensitic type of transformation modes can also occur in plutonium, such as transformations from the delta phase to the gamma phase and from the gamma phase to the beta phase. Linear thermal expansion coefficient of plutonium as a function of temperature follows the trend as shown in Figure 7.12 from dilatometry

experiment. The temperature is generated due to its alpha-emitting characteristics with about 1.923 W g-1. A specimen of plutonium bit larger than a foil or a wire can be used as an adiabatic self-heater in the thermal expansion measurement so that no external heat needs to be provided for experimentation. The thermal expansion coefficient increases in the alpha-, beta-, and gamma-phase regimes. However, the delta phase contracts as the temperature rises. It also has positive temperature coefficient of resistivity. The delta-prime phase shows anomalous thermal expan­sion behavior. The electrical resistivity of plutonium is one of the highest in all met­als with much like semiconductors. Thermal conductivity and specific heat of plutonium increase with increasing temperature. Interestingly, plutonium has the largest low-temperature specific heat of any pure element [8].

From various theoretical calculations, it has been noted that point defects created during irradiation may affect the elastic constants (elastic modulus and shear mod­ulus). Interstitials are noted to have the greatest effect. Experimental results have not readily shown much changes. Also, point defect diffusion and annihilation lessen the effect. Higher fluences tend to show some effect. However, as defect insensitive properties, elastic constants do not change significantly with change in microstructure.

6.3.3

Fabrication

Uranium dioxide production can follow the same methods described in Section 7.1.1.1, except the steps involved to produce metallic uranium. UO2 can also be processed into bulk shapes such as pellets, tubes, rods, etc. by usual ceramic proc­essing methods, including powder metallurgy. Sintering of UO2 must be done

under an atmosphere either inert or reducing since sintering in air has conse­quences. The UO2 can exist in the form of a wide range of variable compounds depending on temperature and environment. U3O7 (2UO2 + UO3) in an unstable state of mixture forms at ~150-190 °C and U3O8 at about 375 °C. Figure 7.18 shows thermal analysis curves of UO2 as a function of temperature, showing the evolution of U3O8 is unstable above ~500 °C and converts back to UO2 at higher temperatures (1100-1300 °C).

UO2 + 2UO3 ! U3O8 ! 3UO2 + O2 (7.13)

The change in density with all the phase changes causes disruption during sin­tering in air. That is why sintering in hydrogen at 1700-1725 °C for 8-10h pro­duces bulk UO2 with 93-95% of the theoretical density. Minor additions of titanium dioxide (TiO2) or cerium dioxide (CeO2) can act as sintering additives and help to reduce the sintering temperature. However, there are now different kinds of sintering process that may allow better processing characteristics.

If the oxygen to uranium atom ratio is 2.0, the UO2 is stoichiometric. If an oxy­gen-deficient or excessive uranium exists (i. e., O/U < 2.0), the fuel is called super­stoichiometric fuel (UO2_x). If O/U > 2.0, UO2+x is called hypostoichiometric fuel (x is a small fraction). The departures from stoichiometry influence self-diffusion behavior in fuel itself and interdiffusion between fuel and cladding materials to form hyperstoichiometric or hypostoichiometric fuel during the reactor operation complicating the chemical composition of UO2. It can also affect fuel density, melt­ing point, and other physical and temperature-dependent properties.

The nuclear properties of uranium are summarized in Table 7.1. U235 and U233 nuclides have substantial fission cross sections at the thermal neutron energy level (average energy of 0.025 eV), but U238 has negligible fission cross section as it is not fissile (rather fertile). Natural uranium contains only 0.7% U235. So, as the enrich­ment of U235 is increased, the fission cross section increases. The absorption cross section in Table 7.1 is the sum of fission and capture cross sections.

According to the discussion above, the yield strength increase should be propor­tional to N1/2. In the absence of annihilation mechanisms of obstacles, N is propor­tional to fluence and thus radiation hardening should be proportional to (Wt)1/2. But this is not the case in reality. It has been shown that the radiation hardening does not increase with neutron fluence indefinitely, but seems to saturate as shown in Figure 6.26.

Makin and Minter [23] postulated a theory to explain the observation. According to their model, as the defect concentration increases, it becomes harder to form

new zones because of the reduced volume available for new zone formation. The time rate change of the zone density (N) is given by

dNr = zXsW(1 — VN), (6.8)

where f is the number of zones created per neutron collision (~1), Ss is the macro­scopic scattering cross section, and ф is the fast neutron flux. The term in parenthe­ses represents the fraction of solid volume available for creation of new zones. Radiation saturation takes place because of the dynamic balance reached between creation and annihilation of obstacles.

Studies on mild steel by Murty and Oh [25] revealed that the yield stress increases with fluence raised to 1/3 rather than 1/2; Luders strain also increased correspond­ingly as (ф4)1/3 as expected since in mild steel the Luders strain is proportional to the yield stress (Figure 6.27). They analyzed the results to determine the effect of neutron radiation fluence on friction and source hardening terms and demon­strated that while friction hardening (т;) increases as (ф4)1/2, the source hardening (ts) decreases (Figure 6.28), so the yield stress increases with fluence raised to a power less than 0.5.

Plutonium is mainly produced by reprocessing of spent fuels since it is not a natu­rally occurring element. Recycling of dismantled nuclear weapons could also pro­vide some plutonium! Here, we will not discuss those details, rather we will focus on the fabrication of plutonium. Fabrication of plutonium needs to be carried out with extreme caution as plutonium may cause extreme health hazard. A host of techniques, including casting, rolling, extrusion, drawing, and machining can be used. The characteristics of plutonium, such as low melting point, high fluidity, small-volume change, and high density, all are favorable for casting. However, the inherent differences between different forms of allotropes make precision casting of plutonium practically implausible. Generally, plutonium is melted and cast under controlled environment (under vacuum or inert gas) in a resistively heated or induction furnace. A number of materials can be used for the crucibles (for melting) and molds (for casting).

Alpha plutonium is relatively brittle and can be fabricated using machining or press forging. The beta and gamma phases also show brittle behavior, but can be plastically worked with due care. On the contrary, delta phase is relatively ductile and can be formed by traditional mechanical working techniques. Although ele­vated temperature working gives better deformation characteristics, oxidation is a problem. So, working at temperatures that has limited oxidation is desired. How­ever, the large volume changes associated with allotropic transformation may intro­duce distortions in the components. The delta phase can be extruded in the temperature range of 320-400 °C with care.

As noted in Chapter 1, thermal conductivity is a very important property of fuel cladding materials as it is needed to take the heat away from the fuel to the coolant. Theory indicates that one would expect a decrease in the thermal conductivity due to increased phonon scattering in the irradiated materials. However, in actual reactor operating conditions, the changes have been insignificant.

308 I 6 Radiation Effects on Materials

6.3.4

The crystal structure of uranium dioxide is of fluorite type, as described in Section 2.1. Theoretical density (TD) of UO2 is 10.96gcm~3 at room temperature.

The melting point of UO2 is about 2850 °C (the literature gives a variety of values). However, it has appreciable vapor pressure at lower temperatures leading to weight losses during sintering. Fuel pellets of UO2 are generally produced using powder metallurgy techniques. The properties of UO2 often depend on the processing. The actual density (AD) of UO2 fuel may vary from 80% to 95% of the TD depending on the size/crystallite shape of the powder particles and the actual fuel fabrication pro­cess. However, there are more fabrication techniques that have come to improve fuel fabrication. High density of UO2 fuel fabricated has the following advantages: (a) high uranium density, (b) higher thermal conductivity, (c) high capability to con­tain and retain fission product gases in the fuel, and (d) large linear power rating of the fuel element. Figure 7.19 shows the bulk density of UO2 fuels with respect to oxygen/uranium ratio. In general, UO2 has a lower thermal conductivity compared to other uranium-based metallic and ceramic fuels, and its thermal expansion coefficient is relatively high. However, it got a smaller specific heat.

The thermal conductivity of UO2 has been measured repetitively since the late 1940s; however, modern measurement techniques have produced a significant insight into the transport mechanisms within the UO2 fuel. At temperatures rang­ing from room temperature to about 1800 K (1527 °C), the transport of energy within UO2 is controlled by lattice vibrations that cause a temperature-based decrease in the thermal conductivity trend. However, above 1800 K and up to the melting temperature, a small ambipolar polaron contribution reverses the trend and begins to increase the thermal conductivity. UO2 is a ceramic that is dominated by phonon-phonon interactions and as such the thermal conductivities are low at all temperatures. Figure 7.20 shows the thermal conductivity as a function of temperature.

Both UO2 and UN exhibit very similar temperature-dependent specific heats (Cp) that rise much more rapidly at elevated temperatures than typical ceramic materials (Figure 7.21). Both fuels exhibit a behavior that presents specific heat values nearly twice the Dulong-Petit value near their melting points. Significant research has shown that at low temperatures, the specific heat of both UO2 and UN is governed by lattice vibrations that can be predicted based on the Debye model. Over the range of 1000 (727 °C)-1500 K (1227 °C), the specific heat is governed by the har­monic lattice vibrations and above this temperature the specific heat is governed by crystal defects such as Frenkel pairs up to 2670 K (2397 °C). Above 2670 K, Schottky

TEMPERATURE C)

Figure 7.22 The variation of total thermal expansion and linear thermal expansion coefficients of UO2 as a function oftemperature Ref. [2].

defects become a dominant component in the specific heat for both ceramic materials.

The thermal expansion coefficients of both stoichiometric and nonstoichiometric uranium dioxide vary with temperature, as shown in Figure 7.22.

Mechanical Properties

Uranium dioxide has a tensile strength of just ~35 MPa and Young’s modulus of ~172 GPa. Strength increases with temperature most probably due to closure of pores (sintering effect). Above 1400 °C, it rapidly loses strength and can be subject to plastic deformation.

Irradiation Effects

UO2 is dimensionally stable to high-radiation exposure (>1020ncm~2) and rela­tively high burnup. Under neutron irradiation of sufficient flux, the fuel pellets may fragment by radial cracking. Furthermore, axial and circumferential cracking can also be observed. It is noted that the pellet cracks only in the initial period into few pieces and then stay that way for prolonged duration, implying that the cracking is related to thermal stresses and is not due to mechanical degradation. However, displacement damage caused by fission fragments may enhance the cracking effect.

Uranium dioxide also tends to release volatile fission products from free sur­faces. Fission gases could include Br, I, Te, Xe, Kr, and other related nuclides [17]. The amount of fission gas a depends on many factors, such as porosity, other microstructural characteristics, irradiation time, and irradiation temperature.

Figure 7.23 shows the radiation swelling as a function of fuel burnup at different irradiation temperatures.

The creep rates of a stoichiometric UO2 fuel as a function of stress in both uni­rradiated and irradiated conditions are shown in Figure 7.24. The in-reactor creep rate in the temperature regime of 800-900 °C does not depend much on tempera­ture, but it depends on neutron flux and stress. So, radiation-induced creep oper­ates in this temperature regime. However, in the higher temperature regime (>1200 °C), the creep rate becomes strongly temperature dependent.

7.3.2