Chapter 22. Waterside Corrosion and Hydriding of Zr Alloy Cladding

Transcription

1 Chapter 22. Waterside Corrosion and Hydriding of Zr Alloy Cladding 22.1 Introduction Influence of Alloying Additions on Zirconium Alloy Corrosion Uniform Corrosion Mechanism and Oxide Structure... 4 Uniform Corrosion Mechanism... 4 Oxide structure Corrosion Kinetics in the Protective oxide: Parabolic Law... 9 Parabolic Scaling Law Deviation from parabolic corrosion Lateral Cracking in Oxide Linear scaling: the oxide transition In-Reactor Corrosion Uniform Corrosion under heat flux Example 22.1: Example 22.2 Variation of oxide thickness with height CRUD deposition Localized Corrosion: Nodular Corrosion and Shadow Corrosion Nodular corrosion Crud Induced Localized corrosion Shadow Corrosion Hydrogen Behavior Hydrogen Pickup Example 22.3: Hydrogen Redistribution in the Cladding Formation of hydride rim Problems References

2 22.1 Introduction Zr alloys are highly resistant to corrosion in common media and are used for that reason in the chemical industry [1]. However in the high temperature water environment found in a power reactor ( ºC at MPa), waterside corrosion (thus referred to distinguish from corrosion in the inner cladding diameter, see chapter 25 and 28) can control the design life of fuel rods and other components. The principal problem is that waterside corrosion is normally accompanied by the ingress of hydrogen into the cladding. The hydrogen that enters the cladding can form hydride precipitates that embrittle the Zr alloy cladding and can lead to failure (see chapter 27). The hydrogen accumulated in the cladding can also concentrate in particular locations, such as crack tips or the outer cladding surface as a result of temperature or stress gradients. This hydrogen concentration can allow failure mechanisms such as delayed hydride cracking (DHC) [2] or low-ductility failures as a result of pellet-cladding mechanical interaction. For these reasons, the commercial nuclear fuel industry devotes major technological efforts to limit waterside corrosion. This chapter discusses the mechanisms of corrosion and hydriding in nuclear fuel cladding. Early in the development of the U.S. Nuclear Navy program, waterside corrosion was recognized as a major obstacle to the development of Zr alloy nuclear fuel cladding. This is because at the temperatures of interest, the corrosion rate of pure Zr in water was too high and exhibited too great a degree of variability from heat to heat for successful application in nuclear fuel cladding [3]. It was soon discovered that alloying elements improved the corrosion resistance of these alloys [3]. Alloy development proceeded in two alloy systems: Zr-Sn alloys (such as the Zircaloys) and Zr-Nb alloys (such as Zr- 2.5%Nb, M5) or a combination Zr-Sn-Nb (ZIRLO). By combining these alloying elements with other alloying elements such as Cr, Fe and Ni, several commercial alloys were developed, including Zircaloy [3, 4], and, more recently, ZIRLO [5] and M5 [6], all of which exhibit very good corrosion resistance. Nevertheless, uniform waterside corrosion is one of the principal in-reactor degradation mechanisms of Zr alloys in PWR environments and can limit fuel rod design. This is, in part, because economics have driven the operation of nuclear power plants to more severe fuel duty cycles, including higher coolant temperatures, higher discharge burnups, longer cycles, and longer in-core residence times [7]. Higher coolant or cladding temperatures result in greater thermal efficiency, while extended fuel cycles result in increased plant capacity factors. The use of higher burnup fuel reduces both the costs of power plant operation and the volume of stored waste, and reducing the amount of fuel handling operations decreases occupational exposure to radiation. However as the burnup (and consequently reactor exposure) increases, so does the extent of cladding corrosion. Thus, there is a great economic incentive to minimize the amount of corrosion that the fuel cladding experiences in service. Thus, increased high burnup fuel reliability requires high performance cladding with improved resistance to in-reactor degradation [8]. 2

3 22.2 Influence of Alloying Additions on Zirconium Alloy Corrosion The oxide formed on the cladding surface is zirconium dioxide (ZrO 2 ). When the oxide is protective, it is slightly sub-stochiometric, so that the actual formula is ZrO 2-x. The protective, sub-stochiometric oxide has a shiny black appearance and adheres tightly to the substrate metal. In contrast, the non-protective oxide is white, nearly stoichiometric and tends to flake off. As mentioned above, the corrosion behavior of unalloyed zirconium is poor. The amount of corrosion is normally measured by weighing the sample after autoclave exposure. The mass gained by the oxidation reaction (in the form of oxygen) is a good measure of the overall corrosion, as long as the oxide remains adherent and as long as the oxygen absorbed into the metal without forming an oxide is a small fraction of the weight gain. In that case the weight gain provides a measure of the growth of the protective oxide scale, and thus a description of the corrosion kinetics. Figure 22.1 shows the weight gain (in mg/dm 2 ) plotted against exposure time for pure Zr tested in water. Figure 22.1: Schematic log-log plot of weight gain versus exposure time for pure Zr tested in water at various temperatures, as indicated [3]. It can be seen in Figure 22.1 that the oxides formed in pure Zr became non-protective and tended to flake off. Not illustrated in the figure is the fact that pure Zr samples also exhibited large variations in their corrosion behavior. As discussed in Chapter 17, this corrosion behavior is greatly improved by alloying additions such as Sn, Fe, Cr and Ni,. Coupled with a better control of impurities and optimization of the thermo-mechanical processing route (which greatly reduced heat-to-heat variability) this led to alloys with improved corrosion behavior and that can withstand in-reactor exposure for significant amounts of time. We now describe a simple model of the waterside uniform corrosion process. 3

4 22.3 Uniform Corrosion Mechanism and Oxide Structure Uniform Corrosion Mechanism Waterside corrosion refers to the oxidation of the outer wall of the cladding tube by the primary coolant water, in which the fuel elements are immersed. The relevant oxidation reaction is: Zr + H O ZrO + 2H ( ) (22.1) g The free energy for the reaction in equation 22.1 may be negative or positive, depending on the H 2 O / H 2 ratio in the water. The free energy for equation 22.1 is given by: Δ G = ΔG ZrO ΔG H (22.2) 2 2O When thermodynamics are favorable (ΔG < 0), the corrosion kinetics depend on the properties of the oxide scale. A protective oxide scale limits the access of the corrosion species to the metal. Generally, a protective oxide can form if the Pilling-Bedworth ratio (defined as the ratio of the oxide volume and the volume of the metal consumed) is higher than 1. For Zr, this ratio is about 1.56 (i.e. a large volume expansion upon oxidation) and thus it can form a protective oxide. Most of this volume change is accommodated by an expansion in the direction of film growth, that is, consumption of 1 micron of Zr metal yields an oxide approximately 1.56 microns thick. However, such an accommodation process is not perfect, and, as a result, lateral compressive stresses accumulate as the oxide thickness increases. It is thought that such stresses can break up the oxide layer and cause it to become non-protective. Figure 22.2 shows the weight gain kinetics of three different alloys: pure Zr, Zircaloy-4 and a model alloy. For the three curves, initially the rate of weight increase decreases with exposure time, indicating a protective oxide. In Zircaloy-4 the corrosion rate abruptly increases when the oxide thickness reaches about 40 mg/dm 2, which corresponds to a little less than 3 microns of oxide. However, the protective behavior is re-established shortly thereafter, causing the corrosion rate to decrease, in effect recreating the start of the corrosion process, which began on virgin material. This momentary loss of oxide protectiveness is termed the oxide transition. This process occurs cyclically, and the increased corrosion rate associated with the second transition is visible in Fig This protective behavior can continue indefinitely. Figure 22.3 shows transmission optical micrographs taken from two thick oxide layers formed in Zircaloy-4 and in ZIRLO tested in water. The pictures show alternating black and white bands, with a period equivalent to the oxide transition measured by weight gain. The layers are very regular laterally and the period is quite constant. For Zircaloy-4, 17 transitions can be discerned in the picture, which yields a transition thickness of 1.8 microns while for ZIRLO, 9 cycles can be seen, indicating a transition thickness of 2.25 microns. 4

5 In contrast, for pure Zr the initial protective behavior is destabilized after about 50 days of exposure, at which point the corrosion rate increases abruptly. In contrast to Zircaloy- 4, once the protective character of the layer is lost, it is not recovered. This is termed breakaway corrosion. Breakaway corrosion is normally coincident with a dramatic change in the oxide appearance from a black, protective oxide to a white, non-protective oxide. In contrast, the model alloy studied in this test showed no transition during the corrosion period observed (500 days). 200 Crystal bar Zr Weight gain (mg/dm 2 ) Zircaloy-4 Zr-0.4Fe-0.2Cr model alloy Exposure time (days) Figure 22.2: Weight gain versus exposure time in 360ºC water for three alloys. 5

6 Zr4 Zr4 20 microns 20 microns ZIRLO ZIRLO Fig. 22.3: Optical micrographs of oxide layers formed in Zircaloy-4 and in ZIRLO TM, in reflected (left) and transmitted light (right). The regular periods formed during the cyclic corrosion process correspond to the oxide transitions in the two alloys (photo courtesy of G. Sabol, Westinghouse Electric Co.). Because the oxide growth varies slightly across the surface of the sample, different regions of the sample start to exhibit slight differences in the transition time for the later transitions, thus eventually smoothing out the cyclic curves initially observed, as illustrated in the scheme below: 6

7 Weight Gain post-transition rate alloy A post-transition rate alloy B Oxide transitions for alloys A and B Exposure time Figure 22.4: Schematic illustration of the corrosion kinetics as measured by the weight gain; arrows indicate the first oxide kinetic transitions. As a result of the averaging of various regions, a nearly linear post-transition weight gain results. The nature of the loss of protectiveness at transition is still a matter of active research. Oxide structure The microstructure of the oxide layer in Zircaloy (phases present, grain size, grain shape, cracking patterns, absorbed intermetallic precipitates) is complex and changes with oxide thickness. The monoclinic crystal structure of ZrO 2 is stable at room temperatures, successively transforming to tetragonal and cubic structures as the temperature increases. The oxide films that form on Zr alloy components are mostly monoclinic, but contain various amounts of tetragonal phase, stabilized by a combination of small grain size, stresses, and stoichiometry. The newly formed oxide has a higher percentage of tetragonal phase that eventually transforms to the monoclinic phase as the grains grow. 7

8 (a) Cubic Tetragonal Monoclinic (b) Figure 22.5 The three allotropic forms of ZrO 2.[9] The oxide that forms on the bare metal consists of small equiaxed grains, out of which grow columnar grains that are mostly monoclinic, and oriented in a manner that is most favorable for minimizing stress accumulation in the oxide layer [10]. Several studies have shown that the oxide layer consists of a mixture of monoclinic and tetragonal zirconium dioxide. These oxide phases are present in a mix of equiaxed and columnar grains, varying with distance from the oxide metal interface. The overall oxide structure varies as corrosion proceeds, such that there is an alternation of small equiaxed and columnar grains in the layer. An electron micrograph illustrating this variation of grain morphology with distance from the oxide-metal interface is shown in Figure 22.6 Columnar Equiaxed Columnar Oxide growth direction 200 nm 8

9 Figure 22.6 Transmission electron micrograph of oxide formed on Zircaloy-4. The arrow indicates the direction of oxide growth. (micrograph courtesy of Sylvie Doriot, CEA- Saclay) The equiaxed grain region corresponds to the oxide formed right after an oxide transition while the columnar grain region corresponds to the region in between transitions where protective behavior is observed Corrosion Kinetics in the Protective oxide: Parabolic Law Since the oxide that forms on Zr alloys is protective, after the formation of the oxide there is no direct contact between the metal and the water. As a result, the reaction shown in equation 22.1 cannot occur directly, but requires either the cations or the anions to be transported through the protective oxide layer (that is, for the cathodic reaction either the oxygen atoms have to travel to the oxide-metal interface or the zirconium ions have to travel to the oxide-water interface and in addition either the H moves into the oxide o electrons move out). Which ion is more mobile varies from metal system to metal system. For the case of Zr alloys, the oxygen anions are the mobile species in the oxide layer and thus they migrate through the protective layer, to arrive at the oxide-metal interface where the new oxide is formed. The counterpart is that the oxide should have enough conductivity to allow the electrons to migrate through to complete the anodic reaction at the oxide-water interface. The overall reaction can be broken down into several intermediate reactions, which take an oxygen atom bound to a water molecule, to eventually combine with zirconium to form new oxide, as illustrated in Figure

10 Figure 22.5 illustrates schematically the process: Water O 2 in water (1) adsorption 85% H 2 combines with electrons at O/W interface 15% H 2 O 2 ZrO 2 O/W interface ZrO 2 oxide layer Zr metal O vac (3) Oxidation of Zr: (4) 2 e - transport -2 O H diffusion 2 in oxide (2) O diffusion δ Zr Zr 4e 2 e - H pickup ZrO 2-x O/M interface Figure 22.7: Schematic illustration of the reactions taking place during uniform corrosion of Zr alloys. At the oxide-water interface, oxygen dissolved in the water is adsorbed onto the oxide layer surface (this is the first reaction or (1)). These adsorbed atoms undergo charge exchange with electrons and can then penetrate the oxide layer. These oxygen ions then diffuse through the oxide layer by a vacancy mechanism (2), either through the bulk of the oxide or through the grain boundary. Because the oxygen ions exchange places with vacancies in migrating through the lattice, the flux of oxygen ions is balanced by a flux of vacancies in the opposite direction. When they arrive at the oxide-metal interface they can react with Zr atoms (3) thus forming new oxide, which releases electrons. These electrons then migrate through the oxide to react with hydrogen atoms in the outer layer (4). The scheme above allows for the possibility of any of the steps being rate-limiting. These component reactions are all in series, and as a result, the slowest reaction among the four listed determines the overall reaction rate. 1) Surface reaction and charge exchange: 2 2e + H 2 O O + H 2 ( dissolved in water) or 2H absorbed in metal 2 2 2) Oxygen ion diffusion in oxide : O ( surface) O ( interface) 4 3) Oxidation reaction at the oxide-metal interface: Zr Zr + + 4e 4) Electron transport in oxide: e ( interface) e ( surface) For surface reactions such as 1 and 3, the reaction rate is proportional to the gradient of the reacting species across the interface and is roughly independent of oxide layer 10

11 thickness. For example, reaction 1 is proportional to the partial pressure of oxygen in the water. However, it has been observed experimentally that the corrosion rate is more or less independent of the partial pressure of oxygen. Further, as shown in Figure 22.2, the corrosion rate decreases as the thickness of the oxide layer increases, so its is unlikely that the surface reactions are the rate-limiting step. Consequently, the crucial step is the transport of species (either electrons or ions) through the oxide layer. The two fluxes have to be balanced for charge neutrality. The assumption that the rate-limiting step is the oxygen ion diffusion through the oxide layer results in a parabolic scaling law (following section.) However, it is also possible that the ratelimiting step is the transport of electrons through the oxide layer. In case the transport of electrons is not fast enough, an electrical gradient would build in the oxide layer that would slow down the migration of oxygen ions. Parabolic Scaling Law In the situation described above, the oxide hampers the ingress of further oxygen ions, so the oxide is formed at the oxide-metal interface at the lowest possible O/Zr ratio, given by the lower limit of stability of the monoclinic/tetragonal ZrO 2 oxide. In the case of a protective growing oxide, although the oxide is known to be sub-stoichiometric because of its black color, the exact degree of sub-stoichiometry is not known, as the conditions in which the oxide grows (under compression, small grain size, etc.) are quite far from equilibrium and the exact mixture of tetragonal and monoclinic also varies. For the tetragonal phase, the equilibrium phase diagram shows a lower range of stability 66.5 at%. For the monoclinic phase, although it is known that the oxide forms with some substoichiometry, the equilibrium sub-stoichiometry is too small to be easily detected. In the following derivation a certain degree of sub-stoichiometry is simply assumed. At the oxide-water interface the oxygen concentration is high, so that the oxide is nearly stoichiometric (this concentration is defined as C w ). At the oxide-metal interface, the oxide is sub-stoichiometric ZrO 2-x (this concentration is defined as C m ) and forms at the lower limit of oxide stability given by the phase diagram. The ratio of the two is given by Cm Cw = 2 - x 2 (22.3) Given that the oxide/water interface concentration is kept constant at C w, and C m is the concentration at the oxide/metal interface, a diffusion flux of oxygen through an oxide layer of thickness δ results from the concentration gradient C w - C m. According to Fick's law, the oxygen flux in such a layer is: J DO = (Cw - Cm ) (22.4) δ 11

12 where Do is the oxygen diffusion coefficient in the oxide layer (cm2 /s). Once this flux is established, Jdt atoms of oxygen reach an unit area of the oxide-metal interface in an increment of time dt. Because the new oxide formed at the interface is formed at the concentration C m, for the scale thickness to increase by dδ, the number of atoms required is C m. dδ. This condition is expressed as: C m. dδ = Jdt (22.5) And substituting Fick s law for the flux dδ dt J Do = = Cm δ [Cw - Cm ] Cm (22.6) The equation above can be integrated to yield: 2 ( Cw Cm ) δ = 2Do t (22.7) Cm or, 1/ 2 δ = K p t (22.8) where the parabolic scaling constant K p is given by 1 2 ( ) 2 C w Cm K p = Do (22.9) Cm A typical value for K p is inserted into equation 22.9b below: δ( μm) = exp 12 T t (22.9b) where the thickness is in microns, the temperature in K and the time in days. The parabolic law above is characteristic of diffusion-controlled processes, in this case, the solid-state diffusion of oxygen ions by a vacancy mechanism through the oxide layer to arrive at the oxide-metal interface where fresh oxide is being formed. Corrosion studies performed at different temperatures have shown that the activation energy for oxygen migration is 1.4 ev/atom or 32.3 kcal/mole (close to the measured migration energy of oxygen in ZrO 2 ). However this activation energy is lower than the measured activation energy (formation energy plus migration energy) for diffusion of oxygen in monoclinic zirconia. This has led researchers to propose that the diffusion of oxygen into the protective oxide layer occurs through the grain boundaries [11]. Another possibility, 12

13 however, is that the sub-stoichiometric oxide provides enough vacancies to reduce the activation energy to close to the oxygen migration energy in ZrO Deviation from parabolic corrosion It is observed experimentally that the growth kinetics of the oxide layer do not follow a parabolic law but exhibit instead slower kinetics, closer to a cubic law. The reason for this is that the diffusion process in the oxide layer does not take place in a defect-free, homogeneous medium. The presence of these oxide defects hampers diffusion, such that corrosion takes place more slowly. The exact way in which oxide defects cause this deviation is still under study, but two possible models are presented here. In the first, lateral cracks impede diffusion and in the second grains grow in the oxide layer, reducing the relative area for grain boundary diffusion. Lateral Cracking in Oxide As the oxide grows, compressive stresses accumulate as a result of imperfect accommodation of the volume expansion associated with oxide formation. As a result of these stresses the oxide layer can crack laterally (i.e. forming crack surfaces parallel to the oxide-metal interface). These cracks effectively reduce the diffusional area so that the oxygen flux is reduced, reducing, in turn, the corrosion rate. This behavior can be modeled by assuming that the oxide is intact until a critical * thickness for transition from parabolic to cubic, δ pc is reached. Beyond this thickness, the oxygen flux through the layer is reduced proportionally to the diffusional area covered by the lateral cracks. (a) (b) Figure 22.9 (a) Schematic showing transition from parabolic to cubic scaling law caused by lateral cracks formed during oxide growth; (b) Lateral cracks observed in oxide layer in a TEM sample. 13

14 The presence of the lateral cracks reduces the oxygen flow through the oxide layer by J c α = J (22.10) δ where α is a proportionality constant. As the thickness of the oxide increases, the oxygen flux J c is reduced proportionately. If equation 22.4 is substituted for J in and the same procedure followed as was used for parabolic kinetics, we arrive at a cubic law: 13 δ( μ m) = Kct( days) (22.11) with ( ) 3 C w Cm Kc = α Do Cm 1/ 3 For typical values K c = 535exp( 4533 T ) (22.12) where the time is in days, the temperature in K and the thickness of the layer in microns Linear scaling: the oxide transition Whatever the corrosion kinetics in the protective oxide, at a given thickness, the oxide undergoes rate transition, as explained in section 22.4 and shown in Fig This transition thickness varies from alloy to alloy, in a given environment. The mechanism for the oxide transition is not yet completely understood, but, at transition, the corrosion rate temporarily increases, until the protective oxide re-forms and the process continues (by mechanisms also not understood, in some instances the loss of protectiveness is permanent, leading to breakaway oxide growth.) Although at the microscopic level the oxide undergoes periodic transitions, over the whole exposed surface this behavior is masked. This is because after the first transition different regions undergo transitions at slightly different times (i.e. the transitions get out of phase) so that the average weight gain follows linear kinetics. That is: δ = KL ( t t * ) where K L is the linear post-transition coefficient and t* is the transition time. Since the post transition corrosion rate is an average of various regions in the sample undergoing pre-transition kinetics, the linear coefficient can be given by 14

15 K L * δ = * t Thus, after the first transition, the oxide growth rate follows a linear law (as in the linear approximations of the scalloped curves in figure 22.4). The variation of the critical time t* and thickness for the transition δ* can be approximately given by: δ * ( μ m) = A*exp( B* / T) (22.17) where the temperature is in K and A* and B* are empirical constants. During autoclave testing of Zircaloy-4 and ZIRLO in 360ºC water, the transition thicknesses δ* were found to be equal to 1.8 and 2.2 microns respectively. These values can be well fit using B*=550 and A*=4.35 for Zircaloy-4 and 5.1 for ZIRLO. Alloys that are more protective have higher values of the pre-exponential in As the temperature increases, the critical thickness increases, but the kinetics are much faster, and as a result, the critical thickness is arrived at much earlier. Assuming cubic kinetics, it is possible to calculate the transition times for each alloy. 3 δ * t* = Kc For example for Zircaloy-4 with a transition thickness of 1.8 microns we have * 7 t ( days) = exp(11950/ T) (22.18) As an example, the transition calculated by the equations and above will occur at a thickness of 2.14 microns, after 108 days exposure at 360º C and at a thickness of 2.5 microns, after only 3.5 days exposure at 500ºC (assuming the same cubic law is applicable in both cases and the transition mechanism is the same). Thus, if the transition occurs at time t* and a critical thickness δ*, the subsequent linear growth law is: * * δ = δ + K L ( t t ) (22.19) where the temperature is in K, the time in days, and the thickness δ in microns. and where if the pre-transition regime is cubic, the K L is given by K L 3 c 2 K = (22.20) δ * Substituting equations and for Zircaloy-4 15

16 KL 6 = exp( 12500/ T) It should be noted that linear kinetics are also the mathematical description of a process whereby the barrier layer thickness is constant in time. Over the length of the sample this is effectively what occurs as the periodic transitions in the different locations get out of phase, creating an effective steady state thickness of the barrier layer equal to about 1.5 times the transition thickness In-Reactor Corrosion Many reasons exist why the in-reactor corrosion rate should be different from the out of reactor rate. Firstly, irradiation alters the chemical potential of the solution by radiolysis, as discussed in Chapter 21. Irradiation can alter the structure and transport properties of the oxide layer (enhanced solid state diffusion) or the conductivity of the protective oxide layer by creating radiation defects. Finally irradiation alters the as-fabricated microstructure of the alloy, through irradiation damage and microstructure evolution, such that the corrosion susceptibility is also altered. The net result is an increase in the corrosion rate in the reactor compared to that outside irradiation. Many of these effects are poorly understood, as they involve a complex interplay of several mechanisms. Chapter 24 provides a description of one such irradiation induced transformation leading to precipitate dissolution in Zircaloy-4. In this case, the base material is being altered by irradiation even as the oxide advances. An approximate way of dealing with this problem is to consider that the corrosion rate is altered to the value corresponding to the newly formed irradiation-induced microstructure. Similarly, if the irradiation altered chemical potential of the solution can be calculated, and the change in the corrosion rate follows. There is, however, no complete model of in-reactor corrosion that takes into account all of the mechanisms above. In addition during in-reactor corrosion, power is produced within the fuel rod, and so corrosion occurs under conditions of heat flux. The resulting thermal gradients can cause redistribution of hydrogen, and local variations of corrosion rate. In addition the chemistry in the reactor is altered, especially in the case of high burnup cores, in which burnable poisons such as soluble B have to be added, necessitating the addition of Li for ph control, which has a deleterious effect on corrosion. Finally one of the most important effects is the overall decrease in fuel cladding thermal conductivity because of the presence of corrosion products such as the uniform oxide and the CRUD. This raises the temperature of the oxide-metal interface, which increases the corrosion rate. Uniform Corrosion under heat flux As the oxide layer increases, the transmission of heat from the fuel to the coolant is degraded, since the thermal conductivity of the oxide is much lower than that of the metal. The oxide adds an additional thermal resistance that increases with time. The temperature drop across the oxide is given by: 16

17 q' ' δ q' ' w Δ T = TOM TOW = = (22.21) κ ox γκ ox where T OM is the temperature at the oxide-metal interface, T OW is the temperature at the oxide-water interface, q is the heat flux (W/cm 2 ), δ is the oxide thickness, w the weight gain, γ is a conversion factor (14.7 x 10 4 (mg/dm 2 )/cm) and κ ox is the thermal conductivity of the oxide (W/cm.K) (a typical value is 0.02 W/cm.K). ************************* Example 22.1: Calculate the temperature rise across a 100-micron oxide layer, formed on a section of the cladding where the linear power is 25 W/cm. The inner radius of the cladding tube is 4.1 mm. If the coolant temperature is 340ºC (613 K), and the oxide layer is growing in the linear regime, how much does the temperature rise increase the linear oxide scaling constant? The linear power is related to the heat flux P through P 25 q'' = = = 9.7 W/cm 2 2 R 2π 0.41 π c and ΔT q'' δ = = = 4.85 K κ 0.02 ox According to equation the scaling constant increases by: exp( / ) exp( / 613) = 1.17 as a consequence of the temperature rise induced by the presence of the oxide. ********************** This loss of heat transfer ability is a self reinforcing process. Since as seen above the corrosion rate increases with temperature, and the barrier layer is located next to the oxide-metal interface, this in turn causes an increase in the corrosion rate and so on. It is possible to estimate the effect of this increasing oxide layer on the corrosion process. The temperature dependence of the linear corrosion rate can be expressed as: dw dt = K = K exp( Q / T ) (22.22) L OL L 17

18 For a temperature increase of T OM = T OW +ΔT, we can write dw = K L = KOL exp( QL /( TOW + ΔT )) (22.23) dt Since ΔT << T OM, the exponential argument can be linearized to give: dw K Q T Q T T K T Q T T 2 2 OL exp( L / OW )exp( L / OW ) L ( w )exp( L / OW ) dt = Δ = Δ (22.24) Substituting ΔT from equation dw = K L ( TOW )exp( Bw) (22.25) dt QLq'' with B = (22.26) γκ 2 T ox OW Integrating from time t* to time t gives: 1 w = w* ln[1 K L ( TOW ) B( t t*)exp( Bw*)] (22.27) B The result of equation is plotted for typical values in Figure For zero heat flux, equation reduces to the linear behavior shown in equation As the heat flux increases, the departure from linear behavior becomes more pronounced. For the curves in which the heat flux is non-zero the curve starts to take an exponential character, and the corrosion rate increases constantly. 18

19 100 Oxide Thickness (δ-δ*) (microns) no heat flux 100 W/cm2 150 W/cm Exposure time (t-t*) (days) Figure Oxide thickness as a function of exposure time for various heat fluxes. ********************************************* The corrosion rate increases with coolant temperature such that it is lowest in the lower spans of the fuel assembly and highest at the top, where the hotter coolant exits the core. The reason for the increase is the increase in cladding surface temperature, which increases with coolant temperature. In addition, the cladding surface temperature decreases if the film heat transfer coefficient increases. As explained in Chapter 17 the fuel assembly has mixing vanes after each grid spacer, which make the flow more turbulent, thus increasing the heat transfer coefficient. Figure shows the oxide thickness measured along the axial length of the rod. There is an overall increase of oxide thickness with axial height, but sharp decreases in corrosion rate after each grid spacer. The mixing vanes cause the temperature variations which are reflected in the variations of oxide thickness. Example 22.2 Variation of oxide thickness with height Using the data from example 22.2 and figure 22.12, estimate the percent change in heat transfer coefficient brought about by the mixing vanes for an improved Zircaloy 4 cladding if the coolant temperature when exiting the core is 340ºC, assuming each cycle is 1.5 years. 19

20 Figure Oxide thickness as a function of axial elevation measured for fuel rods clad with three different alloys (conventional Zircaloy-4, improved (low-sn) Zircaloy-4 and ZIRLO) and irradiated for three cycles to 52 MWd/kg [12] The maximum oxide thickness will be achieved at the maximum coolant temperature in the core, as indicated in Figure For that location, the measured oxide thickness is 105 micron. The material has been in the reactor for three 18 month cycles. If the time and thickness at transition is given by equations and 22.18, this means that the linear constant is: * δ δ ( ) K L = = = * t t ( ) Using equation 22.20, the oxide-cladding temperature at that oxide location is then 404ºC (677 K), and the temperature drop is 4.85 K, so the outer oxide temperature is K. For the low point nearby the oxide thickness is about 58 microns and thus for that location K L * δ δ (58 2.1) = = = * t t ( ) which corresponds to a temperature of 655 K or 382ºC, or = C outer oxide temperature. For both locations the heat transfer to the cladding is given by 20

21 q'' = h( T T ) w coolant Since the two locations are close by, we assume the heat fluxes are equal and thus h1δ T1 = h2δ T2 h2 T1 T If the coolant temperature is similar in both places then = h T T 1 2 coolant coolant Assuming the coolant at that location is at 340ºC the ratio h 2 /h 1 is 1.51, or an improvement in the heat transfer coefficient of 51% induced by the mixing vanes. ********************************************************** CRUD deposition In particular reactor cores another cause of fuel cladding temperature increase originates from another type of corrosion product that deposits on the fuel rods. This type of deposit is named CRUD (said to be an acronym for Chalk River Undesirable Deposit, after the Canadian laboratory where it was initially discovered). CRUD is a mixture of various iron and nickel oxides formed as a result of the deposition of corrosion products originating from the corrosion of the steam generator, steel pipes, valves, etc. and which get transported via the primary coolant to the core. These elements have retrograde solubility, that is, their solubility in water decreases with temperature. As a result, they tend to deposit on the hottest point of the primary circuit, which is on the upper regions of the fuel, where the coolant exits the core. CRUD may have a very low thermal conductivity, depending on whether it is high density (tenacious) or porous ( fluffy ), and as result increases the cladding temperature. The ingress of primary water into the pores of the CRUD can cause boiling and results in the deposition of soluble boron (burnable poison) onto the pore walls (boron hideout). The resulting high concentration of boron causes a local neutron flux depression, compared to the normal axial flux profile. This is called an axial offset anomaly (AOA), and is another reason to minimize CRUD deposition. Additionally CRUD may contain cobalt, which under neutron irradiation activates to form Co 60. The release of this radionuclide to the coolant increases the primary circuit activity and results in additional radiation dose to the maintenance and outage personnel. The increase in cladding corrosion occurs by an increase in temperature due to the extra thermal resistance. The thermal conductivity of the CRUD is given by: κ = ( 1 ε ) κ + εκ (22.28) CRUD ox w where ε is the porosity (high for fluffy CRUD, low for tenacious CRUD). The water penetrates the pores of the CRUD and causes its thermal conductivity to be a composite of the conductivity of water κ W and that of the iron and nickel oxides. The tenacious 21

22 CRUD contains a larger percentage of Cu, while fluffy CRUD contains mostly Fe and Ni oxides. The conductivity of the trapped water is about W/cm.K and that of the oxides that form CRUD is ****. T OM = T OW + ΔT ZrO δ δ CRUD + ΔTCRUD = TOW + q'' + (22.29) 2 κ OX κ CRUD The temperature at the oxide CRUD interface increases until it reaches the saturation temperature of 346ºC at 15 MPa. At this point the phenomenon of wick boiling limits further temperature increases. The CRUD deposition rate is highest at the upper elevations of the core, and so is the uniform oxidation rate. This combination of the two depositions exacerbates the problem of loss of thermal conductivity Localized Corrosion: Nodular Corrosion and Shadow Corrosion The uniform corrosion process described in the previous sections is more of a concern in PWRs. Largely because of the lower core coolant temperatures (about 288 C compared to up to 340 C), typical oxide thicknesses from uniform corrosion are smaller in BWRs than in PWRs. As mentioned in Chapter 21, in a PWR the high dissolved hydrogen concentrations in the water eliminate galvanic potential differences. In BWRs, even under hydrogen water chemistry the hydrogen content is much lower. As a result, galvanic processes become important. These localized galvanic effects would be expected in situations where there are nearby components made of different metals (shadow corrosion) or on a more micro scale between different locations in a metallic alloy (such as precipitates and matrix in Zircaloy). These galvanic effects are to be distinguished from crevice corrosion which results from the different chemical environments in the bulk of the solution and inside the crevice such as a crack tip. Nodular corrosion In cases where the amount of dissolved hydrogen in the coolant is low, such as in high temperature steam or in boiling water reactors, a form of localized corrosion is observed that is named nodular corrosion. In this type of corrosion lens-shaped nodules form on the external surface of the cladding during corrosion, due to higher local corrosion rate. These nodules are white and porous, indicating non-protective corrosion of the oxide. The main concern with nodular corrosion is that it can induce a leak in the cladding but it also can lead to a more severe form of corrosion, namely crud induced localized corrosion. The mechanism of nodular corrosion is not understood, but it is likely to arise from galvanic potentials between different regions in the metal (such as regions in the alloy with higher or lower concentration of intermetallic precipitates) leading to instabilities in oxide growth. The propensity for nodular corrosion can be significantly decreased by 22

23 appropriate thermomechanical processing. For Zircaloys this means a low annealing parameter (Chapter 17), achieved by a late quench from the beta phase in the fabrication process. The resulting microstructure exhibits small intermetallic precipitates and, it is thought, a higher solute content in the matrix. Figure shows the nodular corrosion rate plotted versus annealing parameter. As the annealing parameter (defined in Chapter 17) increases above h, so does the propensity for nodular corrosion. This annealing parameter corresponds to a precipitate size of ~ 0.1 μm. In the beta quench microstructure the alloying elements are more evenly distributed, which decreases the galvanic potentials forming between different regions in the alloy and reduces nodular corrosion. The nucleation of nodules also tends to be enhanced in situations of high radiation fields at low heat flux, typical of gadolinia rods ((U,Gd)O 2 ), since they tend to depress the heat flux in the beginning of the cycle. It is curious to note that the dependence of uniform corrosion on precipitate size is exactly the opposite of localized corrosion (decreases with increasing annealing parameter or precipitate size). The general appearance of the nodules and their cross section is shown in Figure Figure Weight gain versus annealing parameter for uniform corrosion in PWR or nodular corrosion at high temperature [13]. 23

24 Figure 22.14: General appearance of nodules formed on zirconium alloy following a 500ºC steam test at 10.3 MPa (photo courtesy of R.Ploc and NFIR (Nuclear Fuel Industry Research Group)) Crud Induced Localized corrosion The interaction of nodular corrosion and the presence of Cu impurities in the coolant circuit can lead to crud induced localized corrosion (CILC). The Cu appears in the BWR environment from components such as condenser tubes and feedwater heaters. This form of accelerated localized corrosion can cause cladding failure by through-wall pitting. As a result of poor heat conduction in the nodule, the heat flux in the region nearby the nodule is diverted to the nodule rim and the tenacious CuO based crud tends to deposit in this region, also in between the laminations of the ZrO 2 in the nodule. Many fuel failures have been attributed to CILC. This issue is addressed by minimizing Cu sources in the primary circuit. Shadow Corrosion Shadow corrosion is a localized corrosion process by which a locally thicker oxide layer forms in the shape of a shadow of a nearby galvanically coupled component. Figure shows a region of thicker oxide in the shape of a nearby control rod handle. The mechanism is not well known but it is known to require oxidizing conditions, the presence of a galvanically coupled dissimilar alloy in close proximity, (such as could occur in grid spacers), and the presence of irradiation. Shadow corrosion is absent in PWRs due to the high dissolved hydrogen concentration causing every surface to be at the reversible hydrogen potential [14]. The corrosion enhancement has been linked to 24

25 channel deformation in BWRs, resulting in incomplete rod insertion, and as a result this phenomenon is being closely studied. \ Figure 22.15: The shadow of a control blade handle is apparent on a BWR fuel channel. The shadow region corresponds to a region of greater oxide thickness [15] Hydrogen Behavior Hydrogen Pickup The absorption of hydrogen into the cladding is probably the most deleterious consequence of waterside corrosion in zirconium alloys, since it significantly degrades the mechanical properties of the cladding. This occurs because hydrogen precipitates into brittle hydrides, which reduce the overall ductility of the cladding. There are many sources of hydrogen for the nuclear cladding: 1. Hydrogen left over in the Zircaloy tubing after fabrication or from residual moisture due to surface preparation. 2. Desorption of water from incompletely dried up fuel 3. Hydrogen produced by (n,p) reactions in the cladding. 4. Hydrogen ingress from the coolant water into the cladding during reactor exposure. This hydrogen exists in the coolant water from three sources: Hydrogen added to the coolant water to reduce corrosion potential through hydrogen water chemistry. Hydrogen formed as a result of radiolysis. Hydrogen generated during waterside corrosion. The initial concentrations of hydrogen in the cladding are on the order of 40 wt. ppm, so that the first three are comparatively smaller than the fourth. Although the hydrogen in the coolant water comes from three sources, the hydrogen pickup is normalized to the last source (hydrogen from corrosion) as that is easier to quantify. The hydrogen pickup fraction is defined as the ratio of hydrogen absorbed in the cladding to the hydrogen produced in the corrosion reaction. 25

26 H abs Hcorr f = (22.30) The hydrogen pickup fraction depends on the corrosion conditions and on the alloy. A typical value of hydrogen pickup for common Zr alloys is about 15%. Because for each oxygen atom involved in the corrosion reaction there are two hydrogen atoms, the flux of hydrogen into the cladding is given by: J H = 2 fj O (22.31) ********************************** Example 22.3: A cladding with an initial thickness of 600 microns that initially has 40 wt.ppm H undergoes corrosion to a total oxide thickness of 80 microns. What is the overall hydrogen content in wt. ppm if the hydrogen pickup fraction is 15%? An 80 micron oxide layer corresponds to a weight gain of 14.7 x 80 = 1176 mg/dm 2. This mass corresponds to x /16 atoms of oxygen = 4.42 x atoms/dm 2. If the pickup fraction is 15% then the ingress of hydrogen will be 0.15 x 2 x 4.42 x =1.33 x atoms of hydrogen/dm 2, or g of H/dm 2. After corrosion the cladding is 600-(80/1.56)=549 microns thick, so the volume of zirconium absorbing this hydrogen is 549 x 10-4 (cm) x 10 x 10 =5.49 cm 3. The weight of zirconium in that volume is: 6.5 x 5.49 =35.7 g/dm 2. Thus the hydrogen concentration is 0.022/35.7 =6.18x10-4 = 618 wt. ppm, which, added to the original 40 wt. ppm, is 658 wt. ppm. Such a high hydrogen concentration can severely degrade the mechanical properties of the cladding. ************************************* Following the example above the hydrogen content in the cladding after a thickness of oxide δ has formed and where the pickup fraction is f is: C clad H δ 4 f m = ( t δ ) 1.56 m clad H Zr Hydrogen Redistribution in the Cladding At reactor operating temperatures, the stable phases in the Zr-H phase diagram are (i) hcp-zr with dissolved hydrogen and the delta hydride ZrH x, where x varies between 1.45 and 1.2 at high temperature. The terminal solid solubility of H in hcp-zr is: 26

27 H Zr Cα = Aexp( EH T ) (22.32) where A is a constant equal to 1.2x10 5 wt. ppm (or 0.8 mole H/cm 3 ), and the activation energy for solid solution is 4300 K. Hydrogen is very mobile in alpha-zr and once it is absorbed in the cladding it migrates easily in response to concentration, temperature and stress gradients. The diffusion coefficient of H in Zr is D H Zr H o H m = D exp( E / k T ) (22.33) B where Em H = 0. 47eV and the pre-exponential factor is 7x10-3 cm 2 /s. This is a very high diffusion coefficient at the reactor operating temperatures, so that hydrogen responds quickly to changed conditions to quickly establish a new steady state. The characteristic time to attain significant hydrogen ingress by diffusion is given by 2 L t = (22.34) 4D H Zr At 355 C (average cladding temperature), the diffusion coefficient is 1.1 x 10-6 cm 2 /s, so the characteristic time for the hydrogen to travel through the thickness of the cladding is (0.06 (cm)) 2 /(4 x 1.1 x 10-6 ) cm 2 /s =881 s=12 minutes, which is much smaller than normal reactor exposure times. This means that at any given time the hydrogen distribution in the cladding can be considered quasi-steady state, i.e. we do not have to consider temporal variations. Because of this, when the hydrogen is in solid solution (before hydride precipitation) the hydrogen concentration in the cladding is essentially homogeneous. ZrO 2 Zr metal T ic T OM J H x J H =0 C α (T OM ) C α (T ic ) increasing H concentration 27

28 Figure 22.16: Schematic plot of the distribution of hydrogen picked up from the corrosion process in the cladding. Formation of hydride rim Since from equation the hydrogen solubility in Zircaloy decreases with temperature, the outer cladding arrives at the solubility limit before the inner cladding does. For an outer cladding temperature of 325ºC and an inner cladding temperature of 385ºC, the hydrogen solubilities are respectively 90 and 170 wt ppm. This causes hydrides to form preferentially at the outer cladding. Metallographic examinations performed on cladding hydrided below the solubility limit show a more or less homogeneous hydride distribution through the thickness of the cladding. These hydrides presumably have precipitated out during the cooling from operation temperature, so that at reactor temperature the hydrogen is in solution. As the overall hydrogen content increases as a result of increased corrosion, eventually the outer layer of the cladding reaches saturation and a hydride rim starts to form, whose thickness will increase with increasing reactor exposure. 100 μm Figure 22.17: Optical metallograph of hydrides in Zircaloy, showing (a) homogeneously distributed hydrides and (b) a hydride rim (photos courtesy R. Daum Argonne National Laboratory) If we make the assumption that the hydride distribution does not affect heat transfer characteristics of the cladding then as the hydrogen concentrations increase the thickness of the rim also increases because saturation is reached at ever higher temperatures. The condition expressed above is that C clad H H C α Zr = (22.35) Substituting the equations above 28

29 we obtain δ 4 f m Aexp( B/ T) = ( t δ ) 1.56 m clad H Zr (22.36) Assuming a linear temperature profile q'' T( x) = Tout + x (22.37) k where q is the heat flux, k Zr the heat conductivity of Zr and T out is the cladding outer temperature and substituting: Zr EH δ exp = C T( x) ( tclad δ ) (22.38) where C is a constant given by 4 f mh C = 1.56 m A Zr (22.39) which yields and finally x rim EH q'' = Tout + Cδ kzr ln ( tclad δ ) EH = T Cδ ln ( tclad δ ) out kzr q'' x (22.40) rim (22.41) The hydride distribution response to stress and temperature gradients is at the root of several degradation mechanisms, such as delayed hydride cracking, secondary hydriding and the degradation of cladding ductility from oxide spalling. These will be discussed in Chapters 23 and