Department of Nuclear Engineering, University of California, Berkeley, CA 94720-1730
Historically, uranium dioxide has been used almost exclusively in all light water reactor applications. Other forms of uranium fuel include: uranium metal, uranium carbide, uranium nitride, uranium phosphide and uranium sulfide. The main advantages in the use of uranium dioxide are its high melting point, dimensional and radiation stability and its chemical compatibility with other reactor components. The main disadvantages are its low thermal conductivity and low fuel density which leads to high centerline temperatures and large volume cores. All factors considered, oxide fuels have been the fuel of choice in light water reactor applications. As a result, much data has been accumulated on the behavior of oxide fuels in these applications.
The stable form of stoichiometric uranium dioxide, for all temperatures up to its melting point (2865C), is the Fluorite structure, shown in Figure 1. This structure may be considered as a 3 x 3 cube of simple cubic anion sublattices with an interpenetrating FCC cation sublattice. The unoccupied central positions of the simple cubic structures provide locations for the buildup of fission products or sites for interstitial oxygen. Oxide fuels may also form hyperstoichiometric and hypostoichiometric compounds depending upon the ratio of oxygen to uranium atoms (O/M) such that stoichiometric compounds have an O/M ratio of 2.00, hyperstoichiometric comounds have an O/M ratio greater than 2.00 and hypostoichiometric compounds have an O/M ratio less than 2.00. [A]
Figure 1 The Fluorite structure.
Fuel pellets
Fuel pellet fabrication begins with enriched UO2 powder. Typical enrichments of fuel for use in LWR's are from 2-6% U235. The powder is cold pressed at 150-300MPa to form "green" pellets of 50-60% theoretical density (TD), where theoretically dense UO2 is 10.96 grams per cubic centimeter. The green pellets are then sintered in a Hydrogen-Argon atmosphere at 1600-1700C for 5-10 hours to produce pellets of 95-96% TD. Further annealing in hydrogen gas ensures a final product of stoichiometric composition. Although designs vary from core to core, typical final dimensions of fuel pellets are on the order of 1cm in diameter and 1cm in height. [A]
Cladding
Fission of the fissile species in the fuel results in the production of radioactive fission products. Solid fission products are easily retained in the fuel matrix, but gaseous fission products may diffuse from the fuel and be released into the coolant system. This represents a significant hazard to the general public. Particularly radioactive isotopes of iodine, which as airborne contaminates, are readily absorbed in the body and may result in a significant dose to internal organs. It is therefore necessary to prevent the release of these fission products from the fuel. This is accomplished by sealing the fuel in "pins" of zircaloy. Zircaloy is an alloy of zirconium and is used in two principle forms, Zircaloy-2 and Zircaloy-4. Zircaloy-2 consists of a zirconium sponge with 1.5 wt.% tin, 0.12 wt.% iron, 0.01 wt.% chromium and 0.05 wt.% nickel. Zircaloy-4 is similar to Zircaloy-2, but without the addition of nickel and has an iron content of 0.18 wt. % iron. Zirconium has the advantages of having high thermal conductivity, low neutron absorption cross-sections, good multiaxial rupture strength, good creep strength and ductility. The addition of alloying elements increases the corrosion resistance of the clad in high temperature aqueous environments over that of pure zirconium. The difference between Zicraloy-2 and Zircaloy-4 is primarily due to nickel, which tends to absorb hydrogen so that Zircaloy-4 absorbs less hydrogen that Zircaloy-2 during high temperature water corrosion. Zircaloy-4 is used in pressurized light water reactor applications and Zircaloy-2 is used in boiling water reactors. [B]
Fuel Pin Construction
The basic fuel pin arrangement consists of a zircaloy tube capped at both ends, with sintered UO2 pellets stacked inside. An initial (unirradiated) gap is designed between the fuel and the clad wall to accommodate swelling of the fuel due to the build up of fission products and differential thermal expansion between the fuel and clad. The top of the fuel pin is void of fuel to create a plenum for the retention of fission product gasses through out the life of the pin, and a spring is provided at the top of the pellet stack to minimize motion of the pellets, particularly during shipping of new fuel. The rod is internally pressurized to 10 atm. of He to minimize the differential pressure experienced across the clad during operation.
The relatively low thermal conductivity of UO2 requires that large temperature gradients be established to drive the heat from the fuel. This results in a high centerline temperature which, during extreme transient conditions, can rapidly approach the melting point of the fuel. As a result, factors which affect the thermal conductivity are of great concern. Some of these factors are: temperature ,stoichiometry ,porosity , and burnup.
The temperature dependence of thermal conductivity for stoichiometric UO2 is correlated by Eqn. 1. At temperatures below 1500C, heat transfer is predominately due to lattice vibrations and is represented by the first term in eqn. 1. Above 1500C, additional heat transfer occurs due to radiation and electron transport and is reflected by the last term. [A]
Equation 1
Thermal Conductivity vs. Temperature100% TD UO2
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The effect of stoichiometry on thermal conductivity is given by eqn. 2. At beginning of life, LWR fuel has an Oxygen to Metal ratio (O/M) of 2.00. Throughout burnup, hypostoichiometric fuel is formed such that O/M ratios as low as 1.97 may be seen, depending upon the extent of burnup. Deviations of O/M from 2.00 result in increased phonon-defect interactions and thereby lower the thermal conductivity of the fuel. The chemical composition of oxide fuels also changes during burnup due to the production of plutonium from fission of uranium. Plutonium atoms are accommodated in the fluorite structure by substitution on the uranium sites with complete solid solubility. The chemical equation which describes the various compositions of the fuel is as follows: [A]
Equation 2
Thermal Conductivity vs. Temperature for various O/M ratios100% TD fuel, (0.8U, 0.2Pu)
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Porosity is a measure of the ratio of the volume of the pores in the fuel matrix to the total volume of the matrix and is controlled in the fuel fabrication process. Densities as high as 98% TD can be achieved by controlling the time during sintering. Although pores accommodate fission products produced during irradiation, they also reduce the thermal conductivity by effectively reducing the diffusional area for heat transfer. Typical values of porosity for oxide fuels are around 95% TD. The effect of porosity on thermal conductivity is given by eqn. 3. [A]
Equation 3
Fission Product Buildup Dependence
During burnup, the concentration of fission products in the fuel matrix gradually increases. Ceramic inclusions of Ba and Zr oxide reduce thermal conductivity, while inclusions of Mo, Pd, Rh, Ru, and Tc increase thermal conductivity. LWR fuel is designed to be fission gas retentive and the buildup of these gasses produces a large reduction in the thermal conductivity of the fuel. The following figure shows the result of experiments conducted on simulated fuel with fission product additives corresponding to different levels of burnup as a function of temperature. At 8 at. % burnup, a reduction in thermal conductivity of about 30% of its new fuel value is seen at temperatures in the 400 - 600 C region, corresponding to the outer perimeter of operating fuel. [A]
Thermal Conductivity vs. Temperature for simulated UO2 fuel of 95% TD at equivalent burnups of 0, 3, and 8 at. %.
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For discussion on mathematical techniques used in solving heat transfer equations for nuclear fuel elements, see paper by Gianluca Gregioriv. Contents
Diffusion is primary mechanism responsible for the operating characteristics of oxide fuels. The species involved in diffusion are typically: oxygen, uranium, fission products, and point defects. The diffusion coefficients of these species control the rates of the effects seen and are affected by the concentrations of the species, temperature distribution and irradiation flux. Diffusion affects both the thermal and mechanical properties of the fuel.
Oxygen diffuses at a much higher rate than uranium. Each fission event of uranium or plutonium produces, on average, two oxygen atoms and two other fission product atoms. The majority of these new oxygen atoms are involved in the formation of oxides with other fission products to form precipitates or soluble compounds. Only a slight increase in stoichiometry is seen during burnup. The diffusion coefficient of oxygen is dependent upon the stoichiometry of the fuel and equations 4, 5 and 6 show correlation's for this coefficient for the stoichiometric, hypostoichiometric and hyperstoichiometric cases respectively. [A]
Equation 4Diffusion of oxygen in stoichiometric UO2 as a function of temperature.
Equation 5Diffusion of oxygen in hypostoichiometric UO2 as a function of temperature.
Equation 6Diffusion of oxygen in hyperstoichiometric UO2 as a function of temperature.
Equation 7Diffusion of Uranium in stoichiometric UO2 as a function of temperature.
As discussed previously, deviations in stoichiometry result in reductions in thermal conductivity. Hyperstoichiometry also increases the rate at which creep occurs for fixed temperature and stress. Since creep involves the movement of two oxygen atoms for every uranium atom, it is ultimately the rate of diffusion of uranium which controls this process. Creep is also a thermally activated process and is therefore significant at higher temperatures. In general, an increase of 100 C increases the creep rate by a factor of 50 while an increase in O/M ratio from 2.00 to 2.10 increases the creep rate by a factor of about 10. At low temperatures, irradiation promotes a process of athermal creep called fission-induced creep while at high temperatures fission-enhanced creep dominates. [A]
Creep Rate vs. Stress at various temperatures and Creep Rate vs. Inverse Temperature for various O/M ratios
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Strain Rate vs Inverse Temperature
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For a discussion on the basic mechanisms of creep in reactor applications, see paper by Jason Rhoads.
Irradiation Swelling
Solid fission products formed during irradiation of oxide fuels accumulate in the fuel matrix and result in an increase in the volume of the fuel. Additionally, fission product gasses may be trapped at grain boundaries in the fuel also contributing to an increases in volume. As the volume of the fuel increases, the gap thickness decreases. Eventually direct contact is made between the fuel and the clad. Gasses which escape the fuel enter the plenum and further increase its pressure so that internal fuel pin pressures exceed primary system pressures. The application of these contact and gas pressures result in a net stress which acts radially outward in the clad. Relaxation of these stresses is accomplished by creep and results in outward radial displacement of the clad or swelling. The primary limitation to the lifetime of a fuel pin is based on the amount of swelling and the subsequent creep time to rupture of the clad. The following figure illustrates the swelling of UO2 compared to burnup. [C]
Irradiation swelling of UO2 vs. Burnup at various temperatures.
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Fuel restructuring
Owing to the steep temperature gradient in oxide fuels, the structure of the fuel changes radial outward according to the distribution of local temperatures. Unirradiated UO2 consists of grains of equal size with a uniform distribution of pores produced during the sintering process. Shortly after initial radiation the fuel undergoes structural changes which produce four distinct regions characterized by different grain growth processes. For a given parabolic temperature distribution with a maximum centerline temperature of 2000C and pellet surface temperature of 800C, the following regimes may be identified. In the region of 800-1500C, the original equal grain size remains. Between 1500-1800C grain growth occurs uniformly to produce equiaxed grains of larger size. From 1800-2000C grain growth of a directional nature occurs resulting in long columnar grains directed toward the center of the fuel. Pore migration to the center of the fuel occurs in this region and produces a central void. One mechanism suggested for this migration is the vaporization of fuel on the hotter side of existing pores and subsequent condensation on the cooler side resulting in the migration of pores to the highest temperature region by solid state difffusion. Removal of pores from the matrix produces a denser region of fuel with higher thermal conductivity and thereby lowers the maximum centerline temperature slightly. Another structural change which occurs in oxide fuel is the formation of cracks produced during startup and shutdown when significant transient temperatures induce thermal stresses over the radius of the fuel. Startup cracks are healed by thermally activated diffusion processes during operation. At shutdown however, cracks formed are retained due to the maintenance of a low temperature environment and are observed in crossectional samples taken from irradiated fuel. The following figure illustrates the regions developed in fuel restructuring and presence of shutdown cracks. [D]
Crossection of irradiated fuel demonstrating restructuring and crack development.
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Another phenomenon associated with structural changes in fuel is that of densification. Fuels constructed with densities in the range of 92% TD experienced on overall shortening of the length of active fuel region within the fuel pin. In several cases, this lead to collapse of the cladding in the unfueled regions from external reactor coolant pressure. Small pores produced in the sintering process are destroyed by the migration of interstitial atoms to the pores. This lead to an overall denser fuel and a reduction in volume occupied by the fuel. Newer fuel designs eliminate this failure mode by internally pressurizing the fuel pins with helium and by using sintering techniques which eliminate small pores and increasing the density of the final fuel to around 95% TD, thereby significantly reducing the degree of densification of the fuel. [D]
Fission gas release
The release of fission product gasses from the fuel matrix is dependent upon operating temperatures and the extent of burnup. The following figure shows the concentration of fission gas in the fuel as a function of fuel burnup for a fixed temperature of 1500C at low irradiation times. [C]
Fission gas concentration in UO2 as a function of burnup at 1500C.
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Curve I shows the gas retained in the fuel matrix. Curve II represents the gas contained in pores and bubbles in the fuel. Curve III is the total gas retained in the fuel. Curve D is the total fission gas produced from irradiation. The magnitude of gas release is strongly dependent on the structure of the fuel, which itself is directly related to burnup as discussed previously. In restructured fuel, in the region of 1000 to 1600C, gas is released by atomic diffusion through the lattice and diffusion along grain boundaries, cracks and pores. Fission gas bubbles formed in the matrix are immobile, but may be broken up by high energy fission products traveling through the matrix, effectively redissolving the gas in the matrix and increasing its mobility. This processes is called "resolution." During grain growth, moving grain boundaries trap gas bubbles which grow on the grain boundaries and increase in density until they touch. On shutdown, the formation of cracks provides a means of direct release of fission gas from the fuel through the lower temperature region. Below 1000C the diffusion of gas in the fuel matrix is insignificant. Release of the gas from the matrix may occur by "recoil" or "knock-out." Recoil occurs when a fission event near the surface of the fuel produces a gas atom with sufficient kinetic energy to escape from the matrix. Knock-out results when a fission fragment collides with a gas atom providing the gas atom with sufficient kinetic energy to escape the fuel. Fission gas release from these mechanisms is only on the order of 1% of the total gas produced from fission. As a result, fission gas retention decreases as temperatures increase so that at low temperatures there is high retention and at higher temperatures fission gas release occurs rapidly due to the formation of cracks. The following figure shows fission gas retention in the fuel matrix as a function of temperature for fuel burnups greater that 3%. [C]
Fission gas retention in UO2 vs. Temperature at burnups greater than 3%.
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The most prevalent failure mode for fuel rods is due to the failure of cladding from Pellet-Cladding Interactions (PCI). PCI failures are the result of mechanical interaction between the fuel and cladding in a corrosive environment. Thermal expansion mismatches between the fuel pellets and cladding material result in pellet expansion exceeding that of the clad. Direct contact between the two results. This internal stress is opposed by the external stress of the pressurized cooling system such that a tight interface between the two materials is maintained. Volatile fission products of cesium and iodine released to the gap contribute a corrosive environment to the interface and result in Stress Corrosion Cracking (SCC) of the interior surface of the cladding. Thermal shocks induced in the clad by power ramping establish stress gradients in the clad and further the contact stress caused by the mismatch in thermal expansion coefficients resulting in crack advancement through the cladding until the cladding is eventually breached. Immediately, fission product gasses retained in the fuel elements are release to the primary coolant system, where radiation monitoring equipment quickly identifies the problem. Variation of control rod positions alters the individual power production of the fuel assemblies so that identification of the affected assembly is possible by monitoring the variations in radiation levels in the coolant. The rate of PCI failures has been minimized by limiting the rates of power transients to minimize thermal stresses and by constructing pre-pressurized fuel pins (with helium to approximately 10 atmospheres) to minimize the differential pressure across the cladding due to coolant pressure. The geometric shape of the fuel also changes as burnup proceeds. Cracks in the UO2 matrix develop which can result in the formation of sharp points and edges on the exterior surface of the fuel. During pellet-clad interactions, these features act to amplify the local stress to the clad and can result in premature failure of the rod. New fuel designs make use of a pure zirconium liner on the inside surface of the clad. Pure zirconium is softer than the zircaloy and more readily accommodates the sharp features of the fuel to minimize premature failure. [A]/[D]
Fuel element failure may also occur due to the process of hydriding of the zircaloy cladding. Zircaloy has a high affinity for hydrogen and oxygen with a preference for interaction with oxygen to form zirconium oxide. On the external surface, a thin oxide film is formed by interaction of the clad with the coolant which provides a protective coating and an effective barrier to external hydriding. The internal surface of the clad are, however, subject to hydriding. Internal sources of hydrogen include: helium gas impurities, radiolytic decomposition of organic contaminants, hydrogen trapped in pores of the UO2 lattice and moisture absorbed in the fuel pellets following fabrication and prior to assembly of the fuel pins. Hydrogen is absorbed into the zircalloy ensuing in the formation of zircalloy hydride, which is less dense and more brittle than the original material. Stresses are established which nucleate blisters and cracks in the cladding which continue to grow under the formation of additional hydrided material until the cracks completely penetrate the clad. [E]
The rate of this reaction is strongly dependent upon the partial pressure of hydrogen and can only occur in regions of low oxygen content. This mode of failure is referred to as primary hydriding and a rod may be operated for years during the formation of this defect without failure. A more dramatic form of hydride failure is that of secondary hydriding. Primary clad defects on the order of micrometers, caused by PCI or primary hydriding, allow water to enter the interior portions of the rod where it flashes to steam. The influx of water and steam erode the defect, increasing its size. Radiolysis of the steam produces hydrogen gas and peroxide which is transported through the gap by differential pressures and gaseous diffusion. The cladding preferentially reacts with the oxygen in the steam to form and enhance the oxide layer on the interior surface of the clad. This oxidation results in the production of addition hydrogen thereby increasing the ratio of partial pressures of hydrogen to water. As the hydrogen-steam mixture passes the location of peak heat flux, drying out of the mixture occurs further increasing the ratio of partial pressures. Pressure equalization slows the rate of advance of the mixture and finally a critical ratio of partial pressures is reached such that at the location of an oxide defect, insufficient oxygen is available to heal the defect and hydrogen is allowed to penetrate the clad. This initiates rapid, massive hydriding of the zircaloy, consuming hydrogen and lowering the internal pressures allowing more steam to enter the reaction. This mechanism self perpetuates until massive failure of the cladding occurs. The onset of massive hydriding is of primary concern in the use of pure zirconium liners because the rate of hydriding is greater in zirconium than zircaloy. [E]
Failure of fuel rods may also occur as the result of wear at contacts points between the cladding and the spacer grid caused by flow induced vibrations. Design modifications have effectively eliminated the occurrence of these events by ensuring the use of retainer springs with sufficient strength to minimize vibration. [D]
Earlier fuel fabrication techniques resulted in a phenomena known as fuel densification. In order to promote longer burnups, fuels were fabricated with lower densities (90-92% TD) so that larger amounts of fission products could be accommodated. This resulted in the formation of a large number of small pores in the fuel. Under early irradiation, these small pores (<1 micrometer) disappear from the matrix by migration of interstitial atoms to the pores resulting in more dense fuel. The denser fuel, occupying less volume, created empty regions at the tops of the rods (some times several inches in length) which collapsed under the external coolant pressure and occasionally developing leaks. The problem was corrected by fabrication of the fuel to higher densities and by internally pressurizing the fuel rods. [D]
During operation, fuel elements tend to warp and bow from their original cylindrical configuration. This results in non-uniform flow coolant between rods which may be a consideration for heat removal during transient conditions. This is the result of the formation of texture in the zircaloy during fabrication of the tubes. During formation of the tubing, random grain orientation gives way to preferential orientations which grow anisotropically during irradiation. Additionally, variations in the axial flux and temperature distributions in the core produce uneven growth in the rods, all of which lead to bowing. These effects have not proven to be a problem in the past but are a concern for higher burn-up fuels which will experience these forces over longer time periods and can be expected to result in even more distortion. [D]
The main concern in fuel pin analysis is in the ability to accurately predict the length of time for which the cladding provides its primary function of separating the fuel from the coolant system. The primary means of cladding failure result from mechanical loading of the internal clad surface by fuel-clad interactions or from the buildup fission product gasses in the plenum to critical values. Failure in both cases is due to rupture from plastic deformation and creep. Analysis of the mechanical behavior is a very complicated task due to the complicated relationships which exist between the mechanical, thermal, chemical, and structural properties. Additionally, not all of the individual mechanisms involved are completely understood. Analysis necessarily takes the form of fuel-modeling codes which accept operational, geometric and mechanical parameters and return an estimate of the time to failure based on observed and predicted results for individual phenomena. The most sophisticated codes in used today are the LIFE (U. S. National Code) and COMETHE/CRASH (Belgo nucleaire) codes. [F]
A. Cahn, R. W., Haasen, P., Kramer, E. J., Frost, Brian R. T., Materials Science and Technology, A Comprehensive Treatment, Volume 10A, Nuclear Materials, Part I, VCH Publishers Inc., New York, NY (1994) pp 114-179.
B. Kaufmann, Albert R., Nuclear Reactor Fuel Elements, Metallurgy and Fabrication, John Wiley and Sons, Inc., New York (1962) pp 240-243.
C. Ma, Benjamin M., Nuclear Reactor Materials and Applications, Van Nostrand Reinhold Company Inc., New York (1983) pp162-182,494-502.
D. Frost, Brian R. T., Nuclear Fuel Elements, Pergamon Press, New York (1982) pp 57-70, 77-78, 184-190.
E. Ygnik, S. K., Secondary Hydriding of Defected Zircaloy-Clad Fuel Rods, Electric Power Research Institute, Inc., Palo Alto, CA (1993) pp 2-6,...,2-12.
Olander, Donald R., Fundamental Aspects of Nuclear Reactor Fuel Elements, Technical Information Center Energy Research and Development Administration, Springfield, VA (1976) pp 566.
