The oxygen snoek damping and an abnormal peak of neutron-irradiated vanadium

Measurements of low-frequency internal friction and electron microscope observations were made on neutron-irradiated vanadium with various oxygen contents. Irradiation was carried out at about 60°C to a fast fluence of $\text{2 × 10}{}^{17}$ or $\text{5 × 10}{}^{19}$ n/cm² ($\text{E ? 1 MeV}$). The oxygen Snoek damping was decreased by irradiation and post-irradiation annealing below 200 or 250° C, while it began to recover by annealing above this temperature. Complete recovery was attained by 30 min anneal at 450°C in the case of the lower fluence, whereas in the other case it was not observed after the same treatment. The results of electron microscope observations were consistent with those of internal friction measurements. The specimens irradiated to $\text{5 × 10}{}^{19}$ n/cm² showed an abnormal peak after annealing above 250°C near the nitrogen Snoek temperature. The height of this peak, $\text{P}{}^{\mathrm{?1}}{}_{\mathrm{<mtext>max</mtext>}}$, was expressed as $\text{P}{}^{\mathrm{?1}}{}_{\mathrm{<mtext>max</mtext>}}$ ∝ exp ($\text{2.72 × 10}{}^3\text{/RT}$) $\text{Q}{}^{\mathrm{?1}}{}_{\mathrm{<mtext>max</mtext>}}$, where $\text{Q}{}^{\mathrm{?1}}{}_{\mathrm{<mtext>max</mtext>}}$ the heiβht of the oxygen Snoek damping after each annealing. The mechanism for radiation-anneal hardening and the abnormal peak were considered in the light of these experiments.     

Fluage du pyrocarbone sous irradiation

Three massive samples of pyrocarbon were irradiated at 1100°C for a maximum fast-neutron dose of $\text{1.6 × 10}{}^{21}$ DNE. They were subjected to stresses in the range $\text{1.33 × 10}{}^2\text{–2 × 10}{}^2$ Kg/cm². The pyrocarbon was deposited from methane in a rotating furnace. Its density, its isotropy, its structure according to X-rays and TEM relate closely to its homologue deposited from methane in fluidised conditions. A study of creep under irradiation showed that a brief stage of primary creep is followed by a stage which is linear with respect to both stress and fast-neutron dose. Creep is thus well represented by an expression of the form $\text{? = Kσφ}$, where $\text{K}$ is $\text{2 × 10}{}^{\mathrm{?25}}$ (Kg · cm^?2. DNE)^?1, which is a value ten times greater than previously estimated. Irradiation is accompanied by densification, a slight increase in anisotropy and a reduction in $\text{L}{}_{\mathrm{c}}$ (apparent crystallite size measured along the $\text{c}$ axis). The variation of these parameters with dose does not, however, differ appreciably between the three creep samples and the unstressed sample.     

Grain-boundary diffusion in uranium dioxide: The correlation between sintering and creep and a reinterpretation of creep mechanism

Previously published data on the final stage sintering kinetics of stoichiometric uranium dioxide are correlated with a reinterpretation of low-stress creep behaviour of identical material (data on both processes by the present authors). For both processes the rate-controlling diffusional flux is considered to be that of uranium ions along grain boundaries. The effective diffusion coefficient for uranium ion diffusion along grain boundaries, $\text{D}{}_{\mathrm{GB}}$, is estimated to be: $\text{D}{}_{\mathrm{GB}}\text{= 1.38(}{}_{\mathrm{÷}}{}^{\mathrm{x}}\text{5) × 10}{}^{\mathrm{?6}}\text{exp ? [(2.39 ± 0.8) × 10}{}^5\text{/8.31T] m}{}^2\text{/s}$. Comparisons are made between this value and those previously measured by radio-tracer methods.     

Density,thermal expansion of stainless steel and interfacial properties of UO2-stainless steel above 1690 K

The sessile drop method was used for the determination of the density in liquid state. The results for stainless steel 1.4970 using uranium dioxide as substrate material in the temperature range 1690 K (liquidus temperature $\text{T}{}_1$) $\text{< T < 2120 K}$ are $\text{ρ = 6.82 × 10}{}^3\text{? 10.25 × 10}{}^{\mathrm{?1}}\text{(T ? T}{}_1\text{) kg/m}{}^3$, and $\text{α = 1.50 × 10}{}^{\mathrm{?4}}\text{K}{}^{\mathrm{?1}}$. Below 1690 K the linear thermal expansion is given by $\text{Δl/l}{}_0\text{= 0.002}{}_{04}\text{+ 7.11}{}_0\text{× 10}{}^{\mathrm{?6}}\text{T + 7.734 × 10}{}^{\mathrm{?9}}\text{T}{}^2$. Using the same method but not correlated with the density measurements the following interfacial properties of the system UO₂-stainless steel have been determined: surface energy of liquid steel $\text{γLv = 1.19 ? 0.57 × 10}{}^{\mathrm{?3}}\text{(T ? T}{}_1\text{) J/m}{}^2$ and interfacial energy of liquid steel against UO₂$\text{γSL = 1.57 ? 2.01 × 10}{}^{\mathrm{?3}}\text{(T ? T}{}_1\text{) J/m}{}^2$, the results yield a contact angle $\text{θ = 0°}$ at $\text{T= 2515 K}$. Using literature data for the compressibility of liquid UO₂, an estimate of the surface energy of UO₂ in liquid state was performed. The estimated value at the melting point is: $\text{γLV = 0.522 J/m}{}^2$. The mean value of the experimental data given by several authors is $\text{0.513 ± 0.085 J/m}{}^2$. The estimated temperature dependence of the surface energy of liquid UO₂ is given by $\text{dγLV/dT = ?0.19 × 10}{}^{\mathrm{?3}}\text{J/m}{}^2$.     

The diffusion of fission products in thorium metal

A study was performed of the diffusion in α-thorium of fission products representing impurity atoms with a diversity of size and valance differences with respect to the solvent lattice. The atoms were recoil injected into thorium disks. Diffusion coefficients were determined for ¹³³Xe by monitoring its release during annealing, and for the other isotopes by post-annealing concentration profile analysis. The Arrhenius constants $\text{d}{}_{\mathrm{o}}\text{(cm}{}^2\text{/sec)}$, resp. $\text{Q(kcal/mole)}$ were obtained for the diffusion coefficients where. $\text{D = D}{}_{\mathrm{o}}$exp$\text{(?Q/RT)}$;${}^{99}\text{Mo: 7.6 × 10}{}^{\mathrm{?4}}$ and $\text{37.6;}{}^{132}\text{Te: 1.32 × 10}{}^6$ and $\text{95.6;}{}^{133}\text{I: 2.7 × 10}{}^{\mathrm{?1}}$ and $\text{66.2;}{}^{133}\text{Xe: 3.6 × 10}{}^2$ and $\text{82.3;}{}^{140}\text{Ba: 2.3 × 10}{}^{\mathrm{?2}}$ and $\text{59.4;}{}^{141}\text{Ce ?}{}^{143}\text{Ce: 1.8 × 10}{}^{\mathrm{?2}}$ and 60.0. The fission product diffusion behavior, in general, fit either the vacancy or the substitutional-interstitial diffusion mechanisms for impurity atoms in a fcc metal. Both valence and ionic radius correlations were found. The data indicate low rates of diffusion for the operating temperatures at which α-thorium-based fuel might be used.     

Diffusion of carbon in zirconium and some of its alloys

Diffusion of carbon in zirconium, zircaloy-2 and Zr- 2.5% Nb has been studied in the temperature range 873–1523K for zirconium and zircaloy-2 and 753–1523K for Zr-2.5% Nb alloy, using the residual activity technique. The diffusivities (in m²/s) in the α and β phases could be represented by $\text{D}{}_{\mathrm{C/\alpha -Zr}}\text{(873–1123K) = (2.00 ± 0.37) × 10}{}^{\mathrm{?7}}\text{exp [}\text{?(151.59 ± 2.51)}\text{RT}\text{]}$$\text{D}{}_{\mathrm{C/\alpha -Zircaloy-2}}\text{(873–1043K) = (1.41 ± 0.32) × 10}{}^{\mathrm{?7}}\text{exp [}\text{?(158.99 ± 3.14)}\text{RT}\text{]}$$\text{D}{}_{\mathrm{C/\alpha -Zr-Nb-alloy}}\text{(753–873K) = (4.68 ± 0.88) × 10}{}^{\mathrm{?7}}\text{exp [}\text{?(159.98 ± 2.91)}\text{RT}\text{]}$$\text{D}{}_{\mathrm{C/\beta \; Zr}}\text{((1143–1523K) = (8.90 ± 1.60) × 10}{}^{\mathrm{?6}}\text{exp [}\text{?(133.05 ± 1.46)}\text{RT}\text{]}$$\text{D}{}_{\mathrm{C/\beta \; Zircaloy-2}}\text{(1263–1523K) = (2.45 ± 0.61) × 10}{}^{\mathrm{?5}}\text{exp [}\text{?(150.29 ± 1.72)}\text{RT}\text{]}$$\text{D}{}_{\mathrm{C/\beta \; Zr-Nb\; alloy}}\text{(1143–1523) = (1.70 ± 0.42) × 10}{}^{\mathrm{?5}}\text{exp [}\text{?(158.20 ± 2.09)}\text{RT}\text{]}$The activation energies are given in kJ/mole. In the phase transition region, the diffusivities could be represented by the empirical relation: D = D_α^Cα · D_β^Cβ, where C_α, C_β are the concentrations of the two phases in the alloy and D_α, D_β are the extrapolated values of diffusion co-efficients in the α and β phases respectively.The results have been explained in terms of the interstitial mechanism of diffusion.     

Steady-state creep of zircaloy-4 fuel cladding from 940 to 1873 K

Steady-state creep rates of as-received zircaloy-4 fuel cladding have been determined from 940 to 1073 K in the α-Zr range, from 1140 to 1190 K in the mixed (α + β) phase region and from 1273 to 1873 K in the β-Zr phase region. Strain rates of between 10^?6 and 10^?2/s were determined under constant uniaxial load conditions. Assuming that creep rates can be described by a power law-Arrhenius equation, the creep rate for α-phase zircaloy-4 is given by: $\text{ge}{}_{\mathrm{ss}}\text{?}\text{= 2000 σ}{}^{5.32}\text{exp}\text{(?284 600/kT) s}{}^{\mathrm{?1}}$; for the β-phase zircaloy-4 by: $\text{ge}{}_{\mathrm{ss}}\text{?}\text{= 8.1 σ}{}^{3.79}\text{exp}\text{(?142 300/kT) s}{}^{\mathrm{?1}}$; and for the mixed (α + β) phase of zircaloy-4 (for creep rates ?3 × 10^?3 s^?1) by: $\text{ge}{}_{\mathrm{ss}}\text{?}\text{= 6.8 × 10}{}^{\mathrm{?3}}\text{σ}{}^{1.8}\text{exp}\text{(?56 600/kT) s}{}^{\mathrm{?1}}$. For the both the α and β phases, the activation energies for creep are in agreement with those of self-diffusion. For the mixed (α + β) phase region, the low creep rate range is controlled by grain boundary sliding at the α/(α + β) phase boundary.     

Thermally activated deformation of Zircaloy-4

Tensile tests were carried out on Zircaloy-4 over the temperature range 298–798 K. Yield stress values at the strain rates $\text{1.33 × 10}{}^{\mathrm{?4}}\text{s}{}^{\mathrm{?1}}$ and $\text{6.67 × 10}{}^{\mathrm{?4}}\text{s}{}^{\mathrm{?1}}$ were used to determine the activation parameters. A peak in activation volume ($\text{V}{}_{\mathrm{app}}\text{= 3100 b}{}^3$) was observed at about 690 K; outside this temperature range the activation volumes became almost independent of temperature ($\text{V}{}_{\mathrm{app}}\text{= 200?300 b}{}^3$). The peak in activation volume was explained in terms of a basic rate controlling mechanism and dynamic strain aging. This analysis indicated that the peak could be ascribed to the negative value of the strain rate sensitive solute strengthening term $\text{M}$ and that the mechanism based on the non-conservative motion of jogs appeared to be more favored as the basic rate controlling mechanism of Zircaloy-4 than an impurity mechanism     

Contribution a l'etude des cinetiques de l'oxydation a l'air du hafnium

The oxidation kinetics in air of Van Arkel hafnium were studied between 750 and 950°C. Comparison of the results obtained by thermogravimetry and microhardness measurements has allowed us to characterise the overall oxidation kinetics which are of parabolic type and also the two separate kinetics, likewise parabolic, of growth of the oxide film and of dissolution of oxygen in the metal underlying the oxide. For each of these three kinetics the rate constants are respectively given by the following relations: $\text{K}{}_{\mathrm{p}}\text{= 3.1 × 10}{}^8\text{exp (?46 000/RT)}$, $\text{K}{}_1\text{= 1.4 × 10}{}^6\text{exp (?36 000/RT)}$, $\text{K}{}_2\text{= 3.4 × 10}{}^{10}\text{exp (?59 000/RT)}$.These results are in agreement with a classical diffusion model of oxygen, both in the oxide and in the metal, set up on the basis of Wagner's general theory. The activation energy of diffusion of oxygen in hafnium is $\text{53.0 ± 2}$ kcal/mole.     

Study of 3He+-bombarded palladium using nuclear magnetic resonance techniques

The nuclear magnetic resonance (NMR) from ion-implanted ³He atoms has been observed in ³He⁺-bombarded palladium. Two 1 μm palladium thin films, one on each side of a copper foil substrate, were bombarded at 75°C with 75 and 140 keV ³He⁺-ions to a fluence of $\text{～10}{}^{18}{}^3\text{He}{}^{\mathrm{+}}\text{/}\text{cm}{}^2$ for each energy. Spin-lattice ($\text{T}{}_1$) and spin-spin ($\text{T}{}_2$) relaxation times were measured at 10, 20, and 35 MHz in the temperature range 1–4K. The ³He nuclear relaxation data indicate that the implanted atoms after the 75°C bombardment are situated in small clusters within the Pd thin films.     

Beryllium diffusion in zirconium

The diffusion coefficients of ⁷Be in both α and β phases of Zr, are reported. The temperature dependence of the diffusion coefficient in the α phase may be expressed by $\text{D}{}^{\mathrm{Be}}{}_{\mathrm{\alpha -Zr}}\text{= 0.33 exp(?31900/RT) cm}{}^2\text{/s}$. The measured values in the β phase are in agreement with previously literature reported data, which give a temperature dependence expressed by $\text{D}{}^{\mathrm{Be}}{}_{\mathrm{\beta -Zr}}\text{= 8.33 × 10}{}^{\mathrm{?2}}\text{exp(?31800/RT) cm}{}^2\text{/s}$. Be diffusion in Zr, which is consistent with an interstitial-like behavior, is analyzed in terms of the Anthony and Turnbull conditions, and atomic size criteria. It is concluded that the latter is a very important parameter when assessing the possibility of significant interstitial-like dissolution.     

Room temperature aging effects of blistering and surface roughening after Ar+ ion bombardment on Mo single crystals

300 keV Ar⁺ ions are bombarded on the surface of Mo single crystals to doses of $\text{1 × 10}{}^{17}$, $\text{6.2 × 10}{}^{17}$, $\text{1 × 10}{}^{18}$ and $\text{2.8 × 10}{}^{18}$ ions/cm². After bombardment with $\text{6.2 × 10}{}^{17}$ ions/cm², blistering is observed after room-temperature aging of less than 100 days, in spite of the large sputtering yield. Disappearance of the formed blisters and concurrent surface roughening are observed with further aging. For higher dose bombardments, only surface roughening is observed without prior formation of blisters. Distribution of the injected ions associated with large sputtering yield is derived. From this distribution, the critical amount of injected ions required for blistering to occur is estimated to be equal to or less than $\text{3.4 × 10}{}^{17}$ ions/cm².     

Existence of hypostoichiometric chromium sesquioxide at low oxygen partial pressures

The nonstoichiometric composition of $\text{Cr}{}_2\text{O}{}_{\mathrm{3\pm x}}$ was measured by means of thermogravimetry in the range of $\text{1173 ≦ T/K ≦ 1318}$ and . The compositional deviation from stoichiometry, $\text{x}$, in the hyperstoichiometric Cr₂O_3+x phase was observed to be smaller than 2 × 10^?4, irrespective of temperatures, provided that the hyperstoichiometric Cr₂O_3+x exists. The existence of the hypostoichiometric Cr₂O_3?x phase was first established in this study in the region of low oxygen partial pressure below 10^?5 Pa. From the oxygen partial pressure dependence of $\text{x}$ in Cr₂O_3?x, the defect structure was discussed with the neutral chromium interstitials in the composition near stoichiometry and with the triply charged ones far from stoichiometry. The partial molar enthalpy and entropy of oxygen of Cr₂O_3?x showed the complex compositional dependences, suggesting the change of the type of the predominant defect.     

Heterodiffusion de l'or,de l'argent et du cuivre dans les phases cubiques δ et ε du plutonium

The solute diffusion at infinite dilution of ¹⁹⁸Au and ^110mAg in cubic phases of Pu has been studied using the serial sectroning method. The solute diffusion coefficients in the b.c.c. ? phase can be expressed by: $\text{D}{}^{\mathrm{Au}}{}_{\mathrm{?Pu}}\text{= 5,7 × 10}{}^{\mathrm{?5}}$ exp(?10300/RT) cm²/s and $\text{D}{}^{\mathrm{Ag}}{}_{\mathrm{?Pu}}\text{= 4,9 × 10}{}^{\mathrm{?5}}\text{exp(?9600/RT) cm}{}^2\text{/s}$. The solute diffusion mechanism is interstitial of the dissociative type in both cases. These experiments confirm the activated interstitial model which has been proposed for self diffusion of ?Pu. Indeed the solute diffusion coefficients of Au and Ag are near of the self diffusion coefficients of Pu. The mechanisms are therefore interstitial in both cases. In the f.c.c. δ phase of Pu where self diffusion takes place by a vacancy mechanism, the solute diffusion coefficients of Au and Ag are near of the self diffusion coefficients of δ Pu. Solute diffusion takes place also by a vacancy mechanism. On the other hand, the extrapolation at infinite dilution of experiments of solute diffusion of Cu in ?Pu (Matano-Wagner coupling) gives the following results: $\text{D}{}^{\mathrm{Cu}}{}_{\mathrm{?Pu}}\text{= 1 × 10}{}^{\mathrm{?3}}\text{exp(?12300/RT)}$ cm²/s. The solute diffusion mechanism is interstitial of the dissociative type. In the ? phase the smaller the atomic radius the faster the migration: r_Co < r_Cu < r_?Pu < r_Ag = r_Au, and D^Co_?Pu > D^Cu_?Pu >D^Pu_?PU > D^Ag_?Pu ≈ D^Au_?Pu.     

Irradiation creep in Zr single crystals

A single crystal of crystal bar Zr was irradiated, unstressed, at 570 K in a fast (> 1 MeV) neutron flux of $\text{5.5 × 10}{}^{16}\text{n/m}{}^2\text{-s}$. After a dose of $\text{6 × 10}{}^{23}\text{n/m}{}^2$ a tensile stress of 25 MPa was applied during a period of steady reactor power. The loading strain was an order of magnitude smaller than that observed when an identical, unirradiated, crystal was loaded to the same stress. There followed a period of primary creep during which the creep rate decreased to a value of $\text{5 × 10}{}^{\mathrm{?6}}\text{h}{}^{\mathrm{?1}}$ in the first 24 hours of the test. For the final 2000 hours of the test the specimen was observed to creep at a rate of $\text{1 × 10}{}^{\mathrm{?6}}\text{h}{}^{\mathrm{?1}}$ when the reactor was at full power. During shutdowns, the creep rate decreased with time. The results will be discussed and compared with predictions from current theories for the mechanism of irradiation enhanced creep in light of the micro-structures observed.     

Damage in neutron-irradiated molybdenum: (I). Characterization of as-irradiated microstructure

The as-irradiated microstructure of molybdenum, irradiated in the EBR-II reactor at six different temperatures in the range 430–1000°C (0.24–0.44 $\text{T}{}_{\mathrm{m}}$) to a fast neutron fluence of ≈ 1 × 10²² n · cm^?2 ($\text{E > 1 MeV}$), has been characterized as black spot clusters, loops, rafts, voids (random and ordered) and dislocations. Present results show that both the void density, $\text{N}$_v and the void size, $\text{d}{}_{\mathrm{v}}$, are independent of irradiation temperature in the range 430–700° C. Above the 700° C irradiation temperature the void density decreases and the void size increases exponentially with increasing irradiation temperature and they have been expressed empirically as $\text{N}{}_{\mathrm{<mtext>v</mtext>}}\text{= 3.6 × 10}{}^{20}\text{exp}\text{(?26.9 T/T}{}_{\mathrm{<mtext>m</mtext>}}\text{)}$, $\text{d}{}_{\mathrm{<mtext>v</mtext>}}\text{= 1.5}\text{exp}\text{(9.44 T/T}{}_{\mathrm{<mtext>m</mtext>}}\text{)}$, where $\text{T/T}{}_{\mathrm{<mtext>m</mtext>}}$ is the irradiation temperature presented as a fraction of the melting point. The void density of all available published data has been used to show that the void density is (a) a strong function of irradiation temperature for a constant number of displacements per atom (dpa) and (b) a function of reactor power and spectrum when normalized to dpa.     

Radiation and anneal hardening in neutron-irradiated vanadium

Vanadium samples were neutron irradiated at the reactor ambient temperature to fluences in the range from 2.0 × 10⁷ to 1.0 × 10²⁰ n/cm² ($\text{E}{}_{\mathrm{n}}\text{? 1 MeV}$). The radiation hardening measured at the ambient temperature increased linearly with the square root of the neutron fluence, up to a fluence of about 2.5 × 10¹⁹ n/cm², to approximately $\text{25 kg/mm}{}^2$ for the highest fluence. The radiation-anneal hardening phenomenon was clearly observed in samples irradiated at a low fluence (2.0 × 10¹⁷ and 1.0 × 10¹⁸ n/cm²) and the hardening was accompanied by changes in the density and size distribution of the radiation-produced defect clusters. The radiation hardening induced during irradiation to 1.0 × 10²⁰ n/cm² recovered monotonically as the annealing temperature increased. Defect clusters invisible in the electron microscope played an important role in the radiation and anneal hardening except when radiation hardening was induced at the highest fluence.     

Consideration of the simulation of in-pile radial temperature profiles in mixed-oxide fuel pins

Temperature profiles similar to those existing in fuel rods under irradiation have been simulated by passing electrical current through cylindrical pellets. The comparison between calculated and measured temperatures in pellets heated in a thermal gradient shows: (1) The values of thermal conductivity obtained by different authors in isothermal experiments and extrapolated to temperatures up to 2700°C are not in agreement. Therefore, the calculation of the temperature of the fuel leads to errors which vary between 1 and 16% depending on the data for λ used. For central temperatures above 1900°C the values of Schmidt better suit the calculations, especially if the oxygen content of the fuel is smaller than 2.00. (2) The published data of electrical conductivity are in open disagreement. The values of activation energy are generally higher than those deduced from the present investigation. It has been assumed that the activation energy $\text{E}$ in the equation $\text{σ = A exp(?E(T)/kT)}$ varies with temperature as $\text{E(T)= E}{}_0\text{(1?1.94 × 10}{}^{\mathrm{?4}}\text{T)}$ when $\text{E}{}_0\text{= 0.58}$ eV if O/M = 2.00, and $\text{E(T) = E}{}_0\text{(1?2.21× 10}{}^{\mathrm{?4}}\text{T)}$ when $\text{E}{}_0\text{=0.91}$ eV if O/M = 1.94.     

Annealing behavior of neutron irradiated β-SiC

The post-irradiation annealing behavior of β-SiC for use as a monitor of irradiation temperature is discussed. Powder and rods of polycrystalline β-SiC were irradiated to $\text{1.5 × 10}{}^{17}$ to $\text{5.0 × 10}{}^{19}\text{n/cm}{}^2\text{(E > 0.18 MeV)}$ at temperatures between 290 and 500°C. The estimated temperatures deduced from the changes in lattice constant and specific electric resistivity during progressive annealing, and from thermal expansion measurement by high-temperature X-ray diffraction agreed with values determined by means of a thermocouple. Thermal expansion measurement in a conventional dilatometer resulted in an over estimate of the irradiation temperature, and further improvement of this method is required for experimental application.