Mutual diffusion in the system zirconium-15 at. % uranium

The author has studied mutual diffusion in the system zirconium— 15 at. % uranium. The diffusion coefficients in the body-centered high-temperature phase were determined at 950–1450° C with -radiation of uranium. It is shown that alloying zirconium with uranium reduces the diffusion mobility throughout the whole of the investigated temperature range and increases the activation energy. The temperature dependence of the diffusion coefficient of uranium in zirconium, obtained by extrapolating the diffusion parameters to zero uranium concentration, is represented by the equation D= 1.40·10^–4 exp (–27,700/RT) cm²/sec.Translated from Atomnaya Énergiya, Vol.22, No.4, pp.290–292, April, 1967.     

Determination of the solubility of metals in lithium

The solubility of uranium, zirconium, iron, nickel, titanium, molybdenum, niobium and beryllium in lithium at temperatures of 700–1000 ° C was determined to assess the stability of metals in lithium and establish the mechanism of corrosion. It was found that nickel and beryllium have a high solubility (of the order of 1%), iron, zirconium, titanium and uranium are slightly soluble (from hundredths to thousands of one percent) and niobium and molybdenum have a very low solubility (less than l^–4%). Crucibles of the lithium to be tested were filled in a special still with distilled lithium and hermetically sealed in a container in a medium of argon. The solubility of the metal to be tested was determined by chemical analysis of rapidly cooled lithium fusions after they had been kept for 50–100 hours in the container at a predetermined temperature. The presence of isothermal transfer of aluminum, beryllium, zirconium and silicon via lithium to steel and iron was discovered. Under these conditions maximum solubility of the metal in lithium was reached far more slowly than in the absence of transfer. Lithium can be purified by getters — uranium and zirconium — slightly soluble in lithium.     

Dancoff Factor in Arrayed-Type Cladded Fuel Lattice

The initial-stage sintering mechanism of hyperstoichiometric urania prepared by sol-gel process was determined in relation to temperature during constant rate heating (CRH). The urania powder used in this experiment was prepared by crushing in Ar atmosphere the micro- spheric gel of UO₂ obtained by sol-gel process, and reducing the resulting powder by heating in H₂ for 1 hr at 500°C. The results obtained from densification measurements indicated that the initial-stage sintering proceeded in two phases governed by different shrinkage mechanisms, as follows.

1. The sintering up to 675°C would be due to a mechanism such as rearrangement of grains and/or plastic flow.

2. Sintering from 750° to 800°C was interpreted as being controlled by uranium volume diffusion.

The estimated diffusion coefficient D = 1.42×10^?6 exp(-52,500/RT) cm²/sec. This value agreed in order of magnitude with the uranium diffusion coefficients measured by other workers for hyperstoichiometric urania.     

Tritium diffusion in zircaloy-2 in the temperature range −78 to 204° C

Tritium diffusion measurements in Zircaloy-2 were carried out over the temperature range ?78 to 204 °C by direct measurement of tritium diffusion gradients. The ⁶Li (n, α)³H reaction was used to inject tritium into the specimens and to produce initial tritium concentration in the range 0.0065 ppm to 0.013 ppm ³H by weight. Two diffusion components were identified from the concentration profiles: a surface trapping region approximately 5 μm thick and a normal diffusion profile characteristics of bulk diffusion. Surface release measurements of tritium verified the existence of a surface trapping layer. The bulk diffusion component was consistent with classical diffusion solutions and was given by: D = 0.00021_?0.00018^+0.005 exp?(8500 ± 200 cal/RT) cm² · sec^?1.The surface trapping was attributed to oxide films formed on the Zircaloy-2 at room temperature. The apparent diffusion coefficients for the surface region were consistent with: D = 4.0_?3.3^+19.7 × 10^?14 exp?(7200 ± 1500 cal/RT) cm² · sec^?1 over the temperature range 25 to 411°C.     

Diffusion of Neptunium in Simulated High Level Waste Glass

Neptunium in high level radioactive wastes has to be retained in glasses through geological period from the point of biological toxicity for more than million years. Neptunium-237 diffusion in borosilicate glass with simulated wastes of 26.4% was investigated in the temperature range of 400–600°C by the use of α-degradation method. The energy loss rate dE/dx of α-particles, which is necessary in order to determine diffusion coefficients by the α-degradation method, was calculated for the waste glass.

The penetration depth of α-particle with 4.787MeV from ²³⁷Np was 17 μm, which gives a limit in applying the α-degradation method in the waste glass. The temperature dependence of the diffusion coefficient of Np in the waste glass was given by

D _Np=3.67 exp(-55,900/RT) (cm²/s), in which the activation energy of the diffusion was 55.9 kcal/mol. It was clarified that Np is one of the elements with the lowest mobility in waste glasses.     

In-Pile and Out-of-Pile Grain Growth Behavior of Sintered UO2 and (U,Gd)O2 Pellets

Grain growth behavior of UO₂ and (U, Gd)O₂ fuel pellets was investigated with the data from the out-of-pile isothermal heating experiments and the irradiation test at the Halden Boiling Water Reactor. The laboratory data gave best-fitted equations by employing the following fourth power rate equations :

UO₂ : D²-D⁴ ₀=3.79×10¹⁸ exp(-142,000/RT)t,

(U, Gd) : D²-D⁴ ₀=4.98×10¹⁷ exp(-140,000/RT)t,

where, D ₀ and D are initial and final three-dimensional diameters (μm), respectively, R the gas constant (=1.987 cal/mole/K), T the absolute temperature (K) and t the time (h) (gadolinia content: 3~10%, temperature range: 1,700~2,000°C).

The calculated grain diameter with the above equations revealed an overestimation on specimens which involved noticeable fission gas bubbles on their grain boundaries. It was demonstrated that the in-pile grain growth model, as was given in the following equation, which took account of the retarding effects of growth by precipitated intergranular bubbles could describe the grain growth of the irradiated samples :

where f: Grain boundary fractional coverage (-).     

Oxidation kinetics and oxygen diffusion in low-tin Zircaloy-4 up to 1523 K

This paper deals with the study of oxidation kinetics and the identification of oxygen diffusion coefficients of low-tin Zy-4 alloy at intermediate (973 K ? T ? 1123 K) and high temperatures (T ? 1373 K). Two different cases were considered: dissolution of a pre-existing oxide layer in the temperature range 973 K ? T ? 1123 K and oxidation at T ? 1373 K. The results are the following ones: in the temperature range 973-1123 K, the oxygen diffusion coefficient in α_Zr phase can be expressed as D_α = 6.798 exp(−217.99 kJ/RT) cm²/s. In the temperature range 1373-1523 K, the oxygen diffusion coefficients in α_Zr, β_Zr and ZrO₂, were determined using an ‘inverse identification method’ from experimental high temperature oxidation data (i.e., ZrO₂, and α_Zr(O) layer thickness measurements); they can be expressed as follows: D_α = 1.543 exp(−201.55 kJ/ RT) cm²/s, D_β = 0.0068 exp(−102.62 kJ/ RT) cm²/s and D_ZrO2=0.115exp(−143.64kJ/RT)cm²/s. Finally an oxygen diffusion coefficient in α_Zr in the temperature range 973 K ? T ? 1523 K was determined, by combining the whole set of results: D_α = 4.604exp(−214.44 kJ/RT) cm²/s. In order to check these calculated diffusion coefficients, oxygen concentration profiles were determined by Electron Probe MicroAnalysis (EPMA) in pre-oxidized low-tin Zy4 alloys annealed under vacuum at three different temperatures 973, 1073 and 1123 K for different times, and compared to the calculated profiles. At last, in the framework of this study, it appeared also necessary to reassess the Zr-O binary phase diagram in order to take into account the existence of a composition range in the two zirconia phases, α_ZrO2 and β_ZrO2.     

Tritium release from neutron-irradiated Li2O: Diffusion in single crystal

The release of tritium from neutron-irradiated Li₂O single crystal particles with sizes of 150 to 840 μm was measured by isothermal annealings. Time dependence of the release rate of tritium for various sizes of particles was well analyzed by a model of classical diffusion in a solid sphere. The diffusivity of tritium obtained was expressed in the temperature range from 573 to 950 K by (D_T/cm²·s⁻¹) = 0.116 exp(−(101±2) × 10³J/RT).     

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.     

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.     

Review of liquid metal corrosion issues for potential containment materials for liquid lead and lead–bismuth eutectic spallation targets as a neutron source

Lead (Pb) and lead–bismuth eutectic (44Pb–56Bi) have been the two primary candidate liquid metal target materials for the production of spallation neutrons. Selection of a container material for the liquid metal target will greatly affect the lifetime and safety of the target subsystem. For the liquid lead target, niobium–1 wt% zirconium (Nb–1Zr) is a candidate containment material for liquid lead, but its poor oxidation resistance has been a major concern. In this paper, the oxidation rate of Nb–1Zr was studied based on the calculations of thickness loss resulting from oxidation. According to these calculations, it appeared that uncoated Nb–1Zr may be used for a 1-year operation at 900°C at P_O2=1×10^–6 Torr, but the same material may not be used in argon with 5-ppm oxygen. Coating technologies to reduce the oxidation of Nb–1Zr are reviewed, as are other candidate refractory metals such as molybdenum, tantalum, and tungsten. For the liquid lead–bismuth eutectic target, three candidate containment materials are suggested, based on a literature survey of the materials’ compatibility and proton irradiation tests: Croloy 2-1/4, modified 9Cr–1Mo, and 12Cr–1Mo (HT-9) steel. These materials seem to be used only if the lead–bismuth is thoroughly deoxidized and treated with zirconium and magnesium.     

Techniques de mesure des coefficients d'heterodiffusion dans le plutonium. Application a la diffusion du cobalt dans le plutonium ϵ(cc)

The diffusion of ⁶⁰Co in bec ? plutonium has been studied by the sectioning method, and the following results have been obtained: D = 1.4 × 10^?3 exp (?9900/RT) cm²/sec over the temperature range 484–621°C. Cobalt diffuses rapidly in ? Pu. Since the diffusion coefficient does not change across the phase transition ? Pu (fcc) → ? (bcc), the diffusion mechanism must be dissociative in the two phases.     

The separation of Zr95, Nb95, and Ru106 from a mixture of fission products by extraction with tributyl phosphate

We have studied methods for preparing radiochemically pure isotopes of Zr⁹⁵, Nb⁹⁵, and Ru¹⁰⁶ by a previously described [1] general scheme for the separation of fragmentary radioactive elements.We mainly consider regularities which were established in a study of the extraction of zirconium, niobium, and ruthenium by tributyl phosphate (TBP).Ruthenium is extracted by TBP after preliminary concentration on the sulfides of metals.Niobium and zirconium are separated by successive reextraction of niobium by hydrogen peroxide and zirconium by oxalic acid.Translated from Atomnaya Énergiya, Vol. 15, No. 1, pp. 23–30, July, 1963     

Oxygen diffusion in β-Zircaloy

The diffusion of oxygen in β-Zircaloy-4 has been studied from 900 to 1500°C with survey measurements for β-zirconium and β-Zircaloy-2. The tracer diffusivity was measured over the entire temperature range and the chemical diffusivity from 1100 to 1450°C. The experiments were performed by using oxygen-18 as the tracer and activating it by proton bombardment. Some complementary measurements were made using Auger Electron Spectroscopy. The results indicated that the tracer and chemical diffusivity of oxygen in β-Zircaloy-4 are statistically identical, and that there is no oxygen concentration dependence over the oxygen concentration range studied, 0.1 to 0.6 wt.%. The temperature dependence of the diffusivity of ¹⁸O from 1000 to 1500°C is given by D = 2.48 × 10^?2 exp(?28200/RT) cm²/sec. The results for the β-zirconium and β-Zircaloy-2 indicated that the compositional differences between the three host materials exert no influence upon the oxygen diffusivity. An examination of the activation entropy, calculated assuming that Snoek's model describes the diffusion process, indicates that this model probably is not appropriate.     

Diffusion of Cesium in Stainless Steel under Condition of Oxygen Potential Controlled by Mo/MoO2 or NbO2/Nb2O5 Oxygen Buffer

The kinetic behaviors of cesium migration in SUS-316 stainless steel for a cladding material of fast breeder reactor were studied using radioactive ¹³⁴Cs as a tracer. The oxygen potential in the atmosphere surrounding the specimen was controlled by Mo/MoO₂or NbO₂/Nb₂O₅ oxygen buffer, which corresponds approximately to the one in fuel-cladding gap during irradiation. The concentration profile of Cs in the specimen was analyzed on the basis of diffusion theory. The temperature dependences of diffusion coefficients of Cs in SUS-316 stainless steel were expressed in the range of 650~800°C by the following equations:

In the oxygen potential controlled by Mo/MoO₂ oxygen buffer

D = 0.15 exp (?63,500/RT) (cm²/s).

In the oxygen potential controlled by NbO₂/Nb₂O₅ oxygen buffer

D = 9.0×10-⁵exp(?50,300/RT) (cm²/s)

where the activation energy is expressed in terms of cal/mol.     

Reactivity feedback coefficients of a material test research reactor fueled with high-density U3Si2 dispersion fuels

The reactivity feedback coefficients of a material test research reactor fueled with high-density U₃Si₂ dispersion fuels were calculated. For this purpose, the low-density LEU fuel of an MTR was replaced with high-density U₃Si₂ LEU fuels currently being developed under the RERTR program. Calculations were carried out to find the fuel temperature reactivity coefficient, moderator temperature reactivity coefficient and moderator density reactivity coefficient. Nuclear reactor analysis codes including WIMS-D4 and CITATION were employed to carry out these calculations. It is observed that the average values of fuel temperature reactivity feedback coefficient, moderator temperature reactivity coefficient and moderator density reactivity coefficient from 20 °C to 100 °C, at the beginning of life, followed the relationships (in units of Δk/k × 10⁻⁵ K⁻¹) −2.116 − 0.118 ρ_U, 0.713 − 37.309/ρ_U and −12.765 − 34.309/ρ_U, respectively for 4.0 ≤ ρ_U (g/cm³) ≤ 6.0.     

Thermal Diffusion of Hydrogen in Zircaloy-2 Containing Hydrogen beyond Terminal Solid Solubility

The thermal diffusion of hydrogen is one of causes of uneven hydride precipitation in zircaloy fuel cladding tubes that are used in water reactors. In the diffusion model of hydrogen in zircaloy, the effects of the hydride on the diffusibility of hydrogen has been regarded as negligibly small in comparison with that of hydrogen dissolved in the matrix. Contrary to the indications given by this model, phenomena are often encountered that cannot be explained unless hydride platelets have considerable ostensible diffusibility in zircaloy.

In order to determine quantitatively the diffusion characteristics of hydrogen in zircaloy, a thermal diffusion experiment was performed with zircaloy-2 fuel cladding tubes containing hydrogen beyond the terminal solid solubility. In this experiment, a temperature difference of 20°–30°C was applied between the inside and outside surfaces of the specimen in a thermal simulator.

To explain the experimental results, a modified diffusion model is presented, in which the effects of stress are introduced into Markowitz's model with the diffusion of hydrogen in the hydride taken into account. The diffusion equation derived from this model can be written in a form that ostensibly represents direct diffusion of hydride in zircaloy. The apparent diffusion characteristics of the hydride at around 300°C are D_p = 2.3×10⁵exp(?32,000/RT), (where R: gas constant, T: temperature) and the apparent heat of transport Q _p *=?60,000 cal/mol. The modified diffusion model well explains the experimental results in such respects as reaches a steady state after several hours.     

The Behavior of Uranium Dioxide in Various Gases

The behavior of uranium dioxide in an oxidative medium in air and a neutral medium in argon for several thousands of hours was studied. Negligible additional oxidation of pellets occurred at room temperature; this was indicated by an increase of the stoichiometric mixture ratio of uranium dioxide near the surface. The oxidation rate constant at 295 K was k = 2.77·10^–7 in air and 5·10^–8 g/(cm²·h) in argon. For oxidation in air at 295–503 K only solid solutions of oxygen in uranium dioxide were formed. The temperature dependence of the oxidation rate constant was determined. The threshold temperature above which higher oxides of uranium form was determined. The stoichiometric mixture ratio has no effect on the oxidation rate constant of uranium dioxide in air. 1 figure, 3 tables, 9 references.     

Model representation of the physicochemical and diffusion properties during thermal extraction of gas from alloyed uranium dioxide

The release of the process gases H₂, H₂O, CO, CO₂, and Ar from alloyed samples of uranium dioxide by oxides of Nb, Ce, Al, Si, and Fe has been studied by means of thermal extraction in vacuum at 1873 K. The niobium concentration in U_1−yNb_yO₂ was 0.06–0.2 mass % (y = 0.001–0.004), the cerium content was 0–25 mass% (y = 0–0.3434), and the content of mullite or Indian red did not exceed 0.25 mass%, the oxygen potential Δ̄G_O2 of the surface of the samples ranged from −400 to −300 kJ/mole at 1873 K. It was determined that the specific gas release from alloyed samples of uranium dioxide depends on the content of niobium, cerium, and impurity carbon as well as the porosity and the radial gradient of the departure from stoichiometry. A model is proposed for the physicochemical and diffusion processes accompanying the thermal extraction of gas from alloyed uranium dioxide.