The thermoelectric properties of pure and doped UO2, namely the thermal and electrical conductivities and the thermopower, are assessed. We adopt the small polaron theory of the Mott type insulators, wherein the charge carriers, the electron and hole on the U3+ and U5+ ions, are treated as small polarons. For the thermal conductivity, the small polaron theory is applicable at temperatures above 1500 K. A review of the experimental data on the temperature dependence of the aforementioned transport properties is made. The data include UO2 with dopants such as Cr2O3, Gd2O3, Y2O3 and Nb2O5. We compare the applications of the theory with the data. Two limiting regimes, adiabatic and nonadiabatic, with the ensuing expressions for the conductivities and the thermoelectric power are considered. We discuss both the merits and shortcomings of the putative small polaron model and the simplification thereof as applied to pure and doped uranium dioxide. (C) 2017 Elsevier B.V. All rights reserved.

General properties of directed ordering near line defects, in particular an edge dislocation, in elastic crystals undergoing phase transition are studied using the two-component time-dependent Ginzburg-Landau equation in two dimensions or 2D-XY model. The associated Landau potential comprises a sixth-order term, cubic anisotropy terms and the field of the dislocation. In thermodynamic equilibrium, the phase diagram for the model is delineated. Upon quenching the system below its transition point, the temporal evolution of the order parameter components in the vicinity of the defect is numerically evaluated. The development of vortices, emanated from the model, is explored and their interaction with the dislocation is examined. The dislocation produced a vortex free circular region whose diameter grew almost linearly with time. The time-dependence of vortex density for various settings of the Landau potential coefficients are evaluated. The vortex density ( in 2D) decreased inversely with time, albeit faster in the absence of dislocation. By computing the two-point correlation function, we established that the dynamic scaling law is satisfied for the considered model if the distance is scaled by L = t(1/2) or by its half-width L-1/2 for a dislocation free crystal. Finally, phase transitions in improper ferroelectrics in the context of the model are discussed.

We report the results of an ab initio -based density functional theory study of the thermodynamic and structural properties of titanium hydrides. The thermodynamic modelling contains contributions from both vibrational and electronic excitations to the free energy and is conducted using the quasi-harmonic approximation (QHA). The enthalpy, entropy and heat capacity are computed over a wide range of temperature (0≲T⩽1000 K) and found to concur well with available experimental data. The simulations show that the Debye temperature varies significantly with temperature below about 50 K demonstrating that the Debye model is too simplistic for thermodynamic modelling throughout the entire temperature spectrum. Comparing the Debye temperature from QHA with that calculated from low temperature elastic constants reveals limited agreement, which suggests that the actual frequency distribution characteristics do not comply with that of the Debye model. The calculated thermodynamic properties are found to show many similarities to those of zirconium hydrides, which are discussed.

Vi söker i rapporten systematisera data avseende zirkoniumbaserade bränslekapslingsrörs brottbeteende under haverifall med kylmedelsförlust (LOCA), som rapporterats från ex- perimentella studier sedan slutet av 1970-talet. Vårt mål är att fastställa användbara data och utvärdera dessa gentemot de brottkriterier som är tillgängliga i QT/SSM:s version av beräkningsprogrammet FRAPTRAN. Detta program beräknar transientbeteendet hos kärn- bränslestavar i lättvattenreaktorer under reaktortransienter och hypotetiska olyckor, såsom LOCA. Databasen omfattar kapslingsmaterialen Zircaloy-4, ZIRLO och legeringar med sammansättningen Zr-1wt%Nb. Rapporten sammanfattar databasen, beräkningsmetodiken och uttrycken för de olika brottkriterierna, samt presenterar resultaten av vår utvärdering genom att jämföra beräkningsresultat med mätdata i diagram över tid till kapslingsbrott, brottemperatur, och kapslingens brottspänning och brottöjning. Dessutom ges en kort över- sikt av osäkerheterna i beräkningarna. Vi har funnit att Rosingers spänningsbaserade brottkriterium, vilket ursprungligen utvecklades för “best-estimate”-prediktering av kapslings- brott i Zircaloy-4, är tillämpbart för såväl Zircaloy-4 som ZIRLO-kapsling, om en bästa skattning av kapslingsbrott erfordras. Vad gäller ZIRLO-kapsling, kan nämnda brottkriterium förbättras ytterligare, under förutsättning att en tillräcklig mängd mätdata avseende brott- och materialegenskaper är tillgänglig.

We attempt to systematize the zirconium-base fuel cladding burst data obtained under loss- of-coolant accident (LOCA) conditions that have been reported from various experimental programs since the late 1970’s. Our objective is to assess the usable data and evaluate them with the various burst criteria that are available in the QT/SSM version of the FRAPTRAN computer program. The FRAPTRAN program computes the transient behavior of light-water reactor fuel rods during reactor transients and hypothetical accidents, such as LOCAs. The cladding materials in the data base include Zircaloy-4, ZIRLO and Zr- 1wt%Nb type alloys. The report summarizes the data base, the method of computation, the expressions for the various burst criteria, and the outcome of our assessment in the form of measured versus calculated plots: cladding time-to-burst, cladding burst tempera- ture and cladding burst stress/strain. A summary of the uncertainties in the computations is also provided. We have found that the stress-based Rosinger best-estimate burst criterion, originally developed for Zircaloy-4 cladding, is suitable for applications to Zircaloy and ZIRLO claddings on a best-estimate basis. For the ZIRLO cladding, additional improve- ments of this burst criterion can be made, provided sufficient amount of measured data on burst properties and material characteristics would be available.

Downward axial relocation of fuel fragments within distending fuel rods may occur during loss-of-coolant accidents (LOCAs) in light water reactors. The fuel relocation may localize the heat load to “ballooned” parts of the rod, thereby increasing the risk for cladding failure and aggravating local oxidation. It may also increase the amount of fuel dispersed into the coolant, should the cladding fail. Recent LOCA tests have revived interest in the relocation and dispersion phenomena, since the test results suggest that high burnup UO2 fuel pellets may pulverize into very fine fragments, with a higher potential for axial relocation and subsequent dispersal than observed earlier for low to medium burnup fuel. To improve our understanding of these phenomena, a computational model for axial relocation of fuel fragments during LOCA and its effects on the fuel rod heat load and failure processes has been developed and introduced in the FRAPTRAN-1.5 computer program. The axial fuel relocation is calculated on the basis of estimated fuel fragment size distributions and the calculated cladding distension along the fuel rod, and its effects on the axial redistribution of fuel mass, stored heat and power are accounted for in FRAPTRAN’s calculations of the fuel rod thermo-mechanical behaviour. The model has been validated against the IFA-650.4 integral LOCA test in the Halden reactor, Norway, which was done on a very high burnup UO2 fuel rodlet and resulted in extensive fuel pulverization, axial relocation and fuel dispersal into the coolant. Our simulations of this test suggest that thermal feedback effects from axial fuel relocation are strong enough to significantly affect the dynamics of cladding ballooning and rupture, even though the calculated duration of these processes is no more than 7–8 seconds. Moreover, for the considered LOCA test, the axial relocation has a strong effect on the calculated peak cladding temperature and oxidation after rupture.

The creep of UO2 doped with Nb2O5 or Cr2O3 has been assessed using a point defect model based on the law of mass action, and the diffusional creep according to the Nabarro-Herring mechanism, which relates the creep rate to the lattice self-diffusivity, the inverse of grain area and the applied stress. The self-diffusion coefficients of cation (U) and anion (O) are directly proportional to the ion concentrations, which in turn are functions of dopant concentrations. The model has been used to evaluate past creep experiments on doped UO2 that were made as a function of dopant concentration (up to about 1 mol%) with a varying grain size at different temperatures and applied stresses. The creep rate increases significantly with the dopant concentration and the model, after a modification of the creep rate coefficient, retrodict the measured data satisfactorily.

The creep of UO2 doped with Nb2O5 and Cr2O3 has been assessed using a point defect model based on the law of mass action, and the diffusional creep according to the Nabarro-Herring mechanism, which relates the creep rate to the lattice self-diffusivity, the inverse of grain area and the applied stress. The self-diffusion coefficients of cation (U) and anion (O) are directly proportional to the concentrations of ions, which in turn are functions of dopant concentrations. The model has been used to evaluate past creep experiments on UO2 doped with Nb2O5 and Cr2O3 in concentrations up to about 1 mol%, with a varying grain size at different temperatures and applied stresses. The creep rate increases significantly with the dopant concentration and the putative model, after a modification of the creep rate coefficient, retrodict the measured data satisfactorily. A number of factors affecting creep rate and thereby our model computations are discussed.

General properties of directed ordering near line defects in elastic crystals undergoing phase transition are studied using the two-component time-dependent Ginzburg-Landau equation. Upon quenching the system below its transition point, the temporal evolution of the order parameter in the vicinity of the defect is evaluated. The development of vortices is explored and their interaction with the structural defect is examined. Finally, phase transitions in improper ferroelectrics in the context of the model are discussed.

Downward axial relocation of fuel pellet fragments may occur when overheated and internally overpressurized cladding tubes of light water reactor fuel rods distend due to creep during a loss-of-coolant accident (LOCA). The relocation is of safety concern, since it changes the axial distribution of heat load along the rod and also has the potential to increase the amount of fuel material dispersed into the reactor coolant, should the cladding fail. Here, we present a computational model that calculates the fuel relocation on the basis of estimated fuel fragment size distributions and the calculated cladding distension along the fuel rod. The model has been implemented and fully integrated with the FRAPTRAN-1.5 computer program, such that thermal feedback effects of fuel relocation on the axial redistribution of fuel mass, stored heat and power are accounted for in FRAPTRAN’s calculations of the fuel rod thermo-mechanical behaviour. The model has been validated against the IFA-650.4 integral LOCA test in the Halden reactor, Norway, which was done on a very high burnup UO2 fuel rodlet and resulted in extensive fuel pellet pulverization, axial relocation and dispersal into the coolant. Our simulations of this test suggest that thermal feedback effects from axial fuel relocation are strong enough to significantly affect the dynamics of cladding ballooning and rupture, in spite of the short duration of these processes. Moreover, for the considered LOCA test, the axial relocation has a strong effect on the calculated peak cladding temperature and oxidation after rupture.

Haverifall med kylmedelsförlust (LOCA) i lättvattenreaktorer kan leda till överhettning av bränslestavar, utvidgning av stavarnas kapslingsrör, samt axiell omflyttning av brän- slekutsfragment i de delar av stavarna som expanderat. Bränsleomflyttningen kan kon- centrera värmebelastningen till en begränsad del av stavarna och därigenom öka risken för kapslingsskador och förvärra kapslingsrörens oxidation lokalt. Den kan också medföra att mängden bränsle som sprids ut i kylvattnet ökar i händelse av kapslingsskada. Nyligen genomförda LOCA-experiment har återuppväckt tillsynsmyndigheternas intresse för dessa fenomen, då provresultaten antyder att högutbränt (> 65 MWd/kgU) UO2- bränsle kan pulveriseras till mycket små (< 0.2 mm) fragment, vilket leder till en större risk för omflyttning och efterföljande utspridning i kylvattnet än vad som tidigare observerats för bränsle med låg eller medelhög utbränning. För att analysera dessa frågor utvecklas här en beräkningsmodell för axiell omflyttning av bränslefragment under LOCA och dess effekter på bränslestavens värmebelastning och skadeprocesser. Modellen införs i SSM:s version av FRAPTRAN-1.5, ett beräknings- program avsett för termomekanisk analys av bränslestavar under transienter och olyckor. Bränsleomflyttningen beräknas på grundval av uppskattad storleksfördelning för bränsle- fragmenten samt kapslingsrörets beräknade deformationsprofil längs bränslestaven, och bränsleomflyttningens inverkan på axiell omfördelning av effekt och lagrad värme beaktas i termomekaniska analyser av bränslestaven. Vår modell tar således full hänsyn till termiska återkopplingseffekter av bränsleomflyttningen, i motsats till existerande beräkningsmodeller. Den tillhandahåller även uppskattningar av den bränslemängd som potentiellt kan spridas ut i kylvattnet vid kapslingsbrott i någon del av staven. Modellen valideras genom jämförelser mot mätdata och diskuteras mot bakgrund av experimentella resultat. I synnerhet studerar vi LOCA-experiment IFA-650.4, som genomförts i Haldenreaktorn, Norge. Provet gjordes på en högutbränd (92.3 MWd/kgU) UO2-provstav, och resulterade i omfattande bränslepulverisering, axiell omflyttning och bränsleutspridning i kylvattnet. Våra simuleringar av detta prov antyder att termiska återkopplingseffekter från den axiella bränsleomflyttningen är tillräckligt starka för att märkbart påverka dynamiken för kapslingens deformation och brott, trots att den beräknade varaktigheten hos dessa processer är högst 7–8 sekunder. Dessutom har den axiella bränsleomflyttningen stor inverkan på kapslingens beräknade maximala temperatur och oxidation efter kapslingsbrottet för det beaktade LOCA-experimentet. Avslutningsvis skall nämnas att vårt arbete pekar mot att ovan nämnda pulveriserings- mekanism för högutbränt bränsle är betydelsefull för axiell bränsleomflyttning, då den kan öka bränslefragmentens packningstäthet. Pulveriseringen underlättar därmed axiella rörelser hos bränslekutspelaren och ökar den lokala värmebelastningen i områden där kutsfragment ansamlas. Våra beräkningar antyder att bränsle med en genomsnittlig kutsutbränning runt 70–75 MWd/kgU torde vara särskilt benäget för axiell omflyttning, på grund av dess förväntade fragmentstorleksfördelning.

Loss-of-coolant accidents (LOCAs) in light water reactors may lead to over- heating of the fuel rods, significant distension of the cladding tubes and axial relo- cation of fuel pellet fragments inside the “ballooned” part of the fuel rods. The fuel relocation may localize the heat load to a particular part of the rod, there- by increasing the risk for cladding failure and aggravating local oxidation of the cladding. It may also increase the amount of fuel dispersed into the coolant, should the cladding fail. Recent LOCA tests have revived interest in the relocation and dispersion phenomena among nuclear regulators, since the test results suggest that high burnup (> 65 MWd/kgU) UO2 fuel pellets may pulverize into very fine (< 0.2 mm) fragments, with a higher potential for axial relocation and subsequent dispersal than observed earlier for low to medium burnup fuel. To analyse these issues, a computational model for axial relocation of fuel frag- ments during LOCA and its effects on the fuel rod heat load and failure processes is developed and introduced in SSM’s version of FRAPTRAN-1.5, a computer program intended for fuel rod thermo-mechanical analyses of transients and acci- dents. The fuel relocation is calculated on the basis of estimated fuel fragment size distributions and the calculated cladding distension along the fuel rod, and its ef- fects on the axial redistribution of stored heat and power are accounted for in thermo-mechanical analyses of the fuel rod. Hence, our model fully considers thermal feedback effects from the fuel relocation, in contrast to existing relocation models. It also provides estimates of the amount of fuel that may potentially be ejected into the coolant upon cladding failure anywhere along the fuel rod. The model is validated by comparisons with measured data and discussed in light of tests and experiments. In particular, we study the IFA-650.4 integral LOCA test in the Halden reactor, Norway. This test was done on a very high burnup (92.3 MWd/kgU) UO2 fuel rodlet and it resulted in extensive fuel pulverization, axial relocation and fuel dispersal into the coolant. Our simulations of this test suggest that thermal feedback effects from axial fuel relocation are strong enough to sig- nificantly affect the dynamics of cladding ballooning and rupture, even though the calculated duration of these processes is no more than 7–8 seconds. Moreover, for the considered LOCA test, the axial relocation has a strong effect on the calculat- ed peak cladding temperature and oxidation after rupture. Finally, our work suggests that the aforementioned pulverization mechanism of high burnup fuel is important to axial fuel relocation during LOCA as it may in- crease the packing fraction of crumbled fuel. The pulverization thereby eases axial movements of the fuel pellet column and raises the local heat load in regions where fuel fragments accumulate. Our calculations indicate that fuel with a pellet average burnup around 70–75 MWd/kgU would be particularly prone to axial relocation, due to its expected fragment size distribution.