The δ′/δ phase transition in hafnium hydride and deuteride

Bulk samples of hafnium (Hf) hydride and deuteride were prepared and the thermal properties, heat capacity (C_P) and thermal conductivity (κ) were measured. In the C_P–temperature curves for both samples, typical lambda-type peaks were observed at around 350 K, which was due to the second-order phase transition from the δ′-phase to the δ-phase. In Hf hydride, it is considered that the δ′-phase and the δ-phase consist of regularly arranged and randomly arranged hydrogen atoms, respectively. Therefore, it can be said that the δ′/δ phase transition observed in both Hf hydride and deuteride is an order–disorder phase transition. The values of κ as well as C_P changed significantly at around the phase transition temperature.     

Estimation of Hydrogen Redistribution in Zirconium Hydride under Temperature Gradient

To evaluate irradiation behavior of δ-ZrH_x+U fuel, thermal migration of hydrogen under temperature gradient has been estimated according to traditional diffusion theory. Hydrogen profiles at steady state and diffusion kinetics in single-phase δ-ZrH_x have been calculated for a cylinder specimen. When a temperature gradient is imposed on the initial uniform ZrH_1.6 hydride, considerable thermal migration from the higher temperature center region to the pellet surface can be expected. Larger temperature gradient and lower temperature will cause greater inclination of the hydrogen distribution. The hydrogen transportation process in single-phase δ-ZrH_x as a function of time was simulated by a finite difference method. In the case of two-phase δ-ZrH_x+45 wt%U, the uranium phase tends to slow down the thermal migration rate of hydrogen by about 50% compared with that in single phase δ-ZrH_x though it may have little influence on the final hydrogen distribution in the δ-ZrH_x matrix. For the cylinder specimen under the temperature conditions of interest, the steady state would be reached at an early stage of the typical irradiation cycle. Finally, the engineering impact due to the redistribution was discussed.     

Characteristics of hydriding and hydrogen embrittlement of the Ti–Al–Zr alloy

The characteristics of hydriding and hydrogen embrittlement of the Ti–Al–Zr alloy were evaluated. The amount of hydrogen absorbed into the alloy at 500 °C was continuously monitored using a hydrogen pressure measurement. The rate of decrease in hydrogen pressure indicated a high absorption rate of hydrogen into the alloy, following a linear rate law. X-ray diffraction studies showed the formation of δ-phase titanium hydride (TiH_1.97) after hydriding. At room temperature, the alloy showed much sensitivity to embrittlement in ductility by hydrogen. The δ-hydrides in the grain boundaries promoted the crack propagation in the presence of stress, leading to the cleavage failure mode. However, the tensile strengths were almost independent of the hydrogen content up to 1174 ppm. It is thus concluded that the δ-hydride acts to decrease the ductility without affecting tensile strengths.     

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.     

Influence of metallurgical variables on delayed hydride cracking in Zr-Nb pressure tubes

During service, Zr-2.5Nb pressure tubes of nuclear power reactors may be prone to suffer from crack growth by delayed hydride cracking (DHC). For a given hydrogen plus deuterium concentration there is a critical temperature (T_C) below which DHC may occur. In this work, T_C was measured for specimens cut from pressure tubes made in Canada (CANDU) and in Russia (RBMK). Hydrogen was added to the specimens to get concentrations ranging from 24 to 60 wt ppm. It was found that T_C was higher than the corresponding precipitation temperature. The crack propagation velocity (V_P), measured in axial direction, increases from a minimum at T_C to a maximum at a temperature close but higher than the precipitation temperature. At lower temperatures, when hydride precipitates are present in the bulk, V_P follows an Arrhenius law: V_P = A exp(−Q/RT), with an activation energy Q of 66-68 kJ/mol for both tubes. The RBMK material presented lower velocities than CANDU one.     

Thermal and mechanical properties of hydrides of Zr–Hf alloys

Polycrystalline bulk samples of δ-phase Hf hydrides with various Zr contents were prepared and their high-temperature stability and thermal and mechanical properties were investigated. The phase structure was examined between room temperature and 973 K using high-temperature X-ray diffraction and thermogravimetric–differential thermal analysis. From room temperature to 673 K, the coefficient of linear thermal expansion, specific heat capacity, and thermal conductivity were evaluated. The Vickers hardness and sound velocity were measured at room temperature, and the elastic modulus was evaluated. The effect of the Zr content on the high-temperature stability and the thermal and mechanical properties of Hf hydrides was studied.     

Thermal transport properties of hafnium hydrides and deuterides

The thermal conductivities of δ′-, δ-, δ+ε-, and ε-phase hafnium hydrides and deuterides with various hydrogen isotope concentrations (HfH_x, 1.48 ? x ? 2.03; HfD_x, 1.55 ? x ? 1.94) were evaluated within the temperature range of 290-570 K from the measured thermal diffusivity, calculated specific heat, and density. The thermal conductivities of δ′-, δ-, δ+ε-, and ε-phase HfH_x and HfD_x are independent of the temperature within the range 300-550 K and are in the range 0.15-0.22 W/cm K and 0.17-0.23 W/cm K, respectively; these values are similar to and lower than the observed thermal conductivities of α-phase Hf. The experimental results for the electrical resistivities of δ′-, δ-, δ+ε-, and ε-phase HfH_x and HfD_x and the Lorenz number corresponding to the electronic conduction, obtained from the Wiedemann-Franz rule, indicated that heat conduction due to electron migration significantly influences the thermal conductivity values at high temperatures. On the other hand, heat conduction due to phonon migration significantly affects the isotope effects on the thermal transport properties.     

Thermodynamics and Kinetics of Deuterium Absorption in Scandium System

Thermodynamic and kinetic characteristics of the Sc-D system are investigated as a complement to the earlier studies of the Sc-H system. A Sieverts apparatus is employed to conduct the measurements. The Sc-D system is characterized by two phase regions: the metal-rich and the deuteride phases. The equilibrium plateau relationships in the two-phase regions are determined from the Van’t Hoff plots and found to be: $ \ln P({\text{Pa)}} = {{\left( {-{\text{ 16374}}{\text{.48}} \pm{\text{188}}{\text{.88}}} \right)} \mathord{\left/ {\vphantom{{\left( {{\text{ - 16374}}{\text{.48}} \pm{\text{188}}{\text{.88}}} \right)} T}} \right.\kern-0em} T} + ({\text{23}}{\text{.56}} \pm{\text{0}}{\text{.18)}}$ _. The enthalpy and entropy of reaction are calculated to be (?136.14 ± 1.57) kJ mol^?1 D₂ and (?100.06 ± 1.50) J mol^?1 K^?1 D₂, respectively. From the relationship of ln[(P₀?P_f)/(P?P_f)] and time t, the reaction of the Sc-D system is confirmed to be a first-order reaction in the temperature range of 923–1,073 K. The temperature has a negative effect on the reaction rate (k_a), which decreases from 0.0717 to 0.0130 s^?1 with the temperature increasing from 923 to 1,073 K. In addition, a minus activation energy of (?93.87 ± 6.22) kJ.mol^?1 is acquired. However, once increasing temperature up to 1,123 K, the relationship of ln[(P₀?P_f)/(P?P_f)] and time t firstly satisfies an exponential equation of y = ?0.5471exp(?x/9.1879) + 0.00272. After 50 s, it begins fitting a linear equation again, indicating the various reaction mechanisms.     

Heat capacity of hydrogenated Zircaloy-2 and high Fe Zircaloy

Heat capacities (C_p) of non-hydrogenated and hydrogenated Zircaloy-2 and high Fe Zircaloy were measured in the temperature range from 350 to 873 K, using a differential scanning calorimeter. The hydrogen concentrations in the two types of alloys ranged from 26 to 1004 ppm. The C_p values of the as-received alloys with 26-29 ppm hydrogen were in good agreement with literature data for low hydrogen Zircaloys. From this finding and observation of almost the same enthalpy changes for hydride dissolution for both alloys, it was concluded that there was no difference in C_p values between the two types of hydrogenated Zircaloys. The dissolution enthalpy of hydrides calculated from C_p data was 41.0 kJ/g-atom H. For Zircaloy-2 samples with higher hydrogen concentrations than 700 ppm, the phase transition from α+δ to α+β was observed at the eutectoid temperature of 824-827 K. Two types of models describing an additional heat capacity due to the hydride dissolution were presented based on the present C_p data and previously derived terminal solid solubility of hydrogen.     

Application of Normal Mode Expansion Method for the Thermal-Neutrons Milne Problem

Hydride directionality in zircaloy is reportedly affected by thermal cycling and stress. Experiments were performed to study these effects quantitatively. The first experiment was thermal cycling applied repeatedly on rolled zircaloy-2 plate under tensile load. It was observed that at the first cycle the hydride directionality changed by an amount depending on the stress level, and thereafter, upon repetition of the thermal cycling, the rate of change was slow and steady, and independent of the level of applied stress.

In arranging the data, a new concept, which was termed the “average precipitation angle”, is proposed to express hydride directionality, in which account is taken of the length and the angle of precipitation of the hydride platelets. This concept should at times be more suitable than the currently adopted directionality factor Fⁿ for methodically expressing hydride directionality. Based on the results of this experiment, the average precipitation angle in zircaloy-2 cladding in reactors can be estimated with the empirical formula

A_r =A_o +ασ_t+β(C-1)

where A₀ andA_r : average precipitation angles before and after reactor service, σ _t : tangential stress, C: number of thermal cycles, α and β: constants.

Another experiment was carried out to determine the constant α for zircaloy-2 tubing serving in water cooled reactors. This experiment was on thermal diffusion under internal pressure and thermal conditions simulating those of zircaloy-2 fuel cladding in water cooled reactors.

When the specimens were prepared for the foregoing experiments by hydriding, the hydride platelets did not distribute uniformly across the wall thickness. It was clarified by a third experiment that the hydride precipitated preferentially in the zones subjected to large residual tensile stress.     

Investigation of radiation swelling in the zirconium-hydrogen system

Conclusions The radiation swelling of the hydrides ZrH_1.78–ZrH_1.90 at a temperature of 50°C is due to the accumulation of zirconium vacancies and their fine pile-ups. At 430–560°C, swelling is determined by the accumulation of fine (10Å) vacancy complexes. In this case, micropores are also formed, with a diameter of 50 Å, but their total volume does not exceed one-tenth of the macroswelling.The considerable buildup of vacancies in the hydrides studied is related with the substructure of the hydride, formed by dislocation voids and the boundaries of twins, which promote an increase of concentration and dispersivity of the injection sinks or themselves serve as these sinks. In samples of the hydride obtained by dehydrogenation of the phase, the numerous dislocations remaining in the hydride after decay of the -phase substructure obviously fulfill this function. The weak tendency of the zirconium vacancies in the hydride to amalgamation in the pores during increased irradiation temperature (by comparison with the behavior of vacancies in metals) is explained by the reduction of their surface energy as a result of interaction with hydrogen atoms.The displacement of hydrogen atoms from the tetrahedral positions during irradiation and their return during annealing changes the periods of the crystal lattice of zirconium hydride in the same way as the change of hydrogen content, which enables the number of defects of the hydrogen sublattice to be estimated.Translated from Atomnaya Énergiya, Vol. 42, No. 1, pp. 16–19, January, 1977.     

Dependence of vacancy concentration on morphology of helium bubbles in oxide ceramics

Since the formation of helium bubbles degrades swelling property and thermal conductivity of minor actinide-containing mixed oxide (MA-MOX) fuel, it is essential to understand the conditions of the bubble formation. In order to examine the dependence of vacancy concentration on morphology of helium bubbles, helium was infused into (Zr,Fe)O_2?x. The oxygen vacancy concentration was controlled by addition of solute Fe³⁺ into ZrO₂. Helium was infused by hot isostatic pressing. The helium-infused specimens were observed by field emission scanning electron microscopy (FE-SEM) and field emission transmission electron microscopy (FE-TEM). In addition, X-ray fluorescence, X-ray diffraction analysis, conversion electron yield–X-ray absorption near-edge structure and FE-SEM/EDX (energy dispersive X-ray) analyses were also made to interpret the results of microstructure observations. As a result of the helium infusion treatment, numerous 0.5–10 nm bubbles were observed and its number density clearly depended on oxygen vacancy concentration. On the other hand, sizes of the helium nano-bubbles in all specimens were almost constant.     

Direct Surface Modification of Zirconium by Reactive Plasma Processing at Elevated Temperatures

This paper investigates a surface modification process for Zr to improve its durability, in order to make use of Zr in a blanket module as an effective neutron multiplier with (n, 2n) reaction. Modified ceramic layers were successfully synthesized on Zr substrates by carburizing, nitriding and oxidizing using reactive plasma processes. The microstruc- tural evolution during the plasma process is governed both by the kinetics of the diffusion and by the kinetics of the ordering to form the reaction products. In the case of carburizing, the growth rate of the carbide layer is restrained by the diffusion of C, which was clarified to exhibit high covalency with the neighboring Zr atoms by a first principles molecular orbital simulation, through the layer. By contrast, the diffusion of O which exhibits high ionicity rather than covalency with the Zr lattice is much faster than the rate of ordering to form the monoclinic ZrO₂ phase. A 20 MeV electron beam pre-irradiation process was also conducted at ambient temperatures as a pre-treatment before the plasma process. The electron beam irradiation can influence the reaction behavior during the plasma process, depending on the process conditions.     

Fabrication and characterization of uranium-thorium-zirconium hydrides

Two uranium-thorium-zirconium hydrides, (UTh₄Zr₁₀)H_1.9 and (U₄Th₂Zr₉)H_1.5, have been fabricated and characterized. Fabrication involved arc melting of the constituent pure metals to form homogenous alloys, followed by hydriding at elevated temperatures in a hydrogen gas environment. The compounds were characterized by X-ray powder diffractometry as well as scanning and transmission electron microscopy. These methods revealed a multi-phase mixture of δ-zirconium hydride (ZrH_1.6+x), thorium-zirconium hydride (ThZr₂H_7−x), and uranium metal. The elastic modulus was mapped across the microstructure using nanoscale dynamic stiffness mapping. The elastic modulus of ThZr₂H_7−x phase is found to be 172 GPa.     

Creep behaviour of δ-phase of U-Zr system by impression creep technique

In this study, the impression creep behaviour of δ-phase of U-50 wt.% Zr (U-72.29 at.% Zr) system was studied in the temperature range 525-575 °C at different stresses. The velocity of the punch at different stresses and temperatures were evaluated for the above alloy. The stress exponents and thermal activation parameters of the above alloy were determined. A power law behaviour is displayed with the stress exponents range from 6.5 to 7. The activation enthalpy for the δ-UZr₂ was found to be independent of stress with an average value of 106 kJ/mol.     

In situ ERDA measurements of hydrogen isotope concentrations in palladium at atmospheric pressure

In situ elastic recoil detection analysis (ERDA) measurements in gases at atmospheric pressure have been carried out using 15 MeV ⁴He ion beams. The beams are extracted through a molybdenum foil having a thickness of 5 μm. The maximum depth of analysis is about 4 μm for the palladium hydride and palladium deuteride (PdH_x and PdD_x, x = 0.7-0.8) samples. The temperature of the samples rises stepwise from room temperature to 180 °C. ERDA spectra are obtained every 2 min. Hydrogen and deuterium in the samples are discharged in the temperature range of 120-140 °C in a vacuum. Decrease in the hydrogen concentration in the PdH_x sample heated in a vacuum follows a first order in the value of x and an apparent activation energy of discharge of hydrogen is 1.05 eV. On the other hand, the hydrogen and deuterium concentrations decrease at about 80 °C in air. No isotope effects are observed in both a vacuum and air. The temperature at which the hydrogen concentration decreases in helium gas is almost the same as that in a vacuum. It indicates that hydrogen and deuterium atoms are discharged by chemical reactions with air and that there are no effects of cooling of the thermocouple by convection of air.     

Room-Temperature Reactor Packed with Hydrophobic Catalysts for the Oxidation of Hydrogen Isotopes Released in a Nuclear Facility

A room-temperature reactor packed with hydrophobic catalysts for the oxidation of hydrogen isotopes released in a nuclear facility will contribute to nuclear safety. The inorganic-based hydrophobic Pt catalyst named H1P has been developed especially for efficient oxidation over a wide concentration range of hydrogen isotopes at room temperature, even in the presence of saturated water vapor. The overall reaction rate constant for hydrogen oxidation with the H1P catalyst in a flow-through system using a tritium tracer was determined as a function of space velocity, hydrogen concentration in carriers, temperature of the catalyst, and water vapor concentration in carriers. The overall reaction rate constant for the H1P catalyst in the range near room temperature was considerably larger than that for the traditionally applied Pt/Al₂O₃ catalyst. Moreover, the decrease in reaction rate for H1P in the presence of saturated water vapor was slight compared with the reaction rate in the absence of water vapor due to the excellent hydrophobic performance of H1P. Oxidation reaction on the catalyst surface is the rate-controlling step in the range near room temperature and the rate-controlling step is shifted to diffusion in a catalyst substratum above 313K due to its fine porosity. The overall reaction rate constant in the range near room temperature was dependent on the space velocity and hydrogen concentration in carriers. The overall reaction rate constants in the range of 1;000=T greater than 3.2 correlated to k _overall[s^?1] = 5.59 × 10⁷ × SV[h^?1] × exp (?67.7 [kJ/mol]/R_gT), where the space velocity range was from 600 to 7,200 h^?1.     

Thermophysical properties of molten core materials: Zr–Fe alloys measured by electrostatic levitation

In order to investigate the progression of a core meltdown accident, it is necessary to understand the behavior of molten core materials. Zr–Fe alloys are one of the low-melting-temperature liquid phases that are thought to form in the early stages of bundle degradation. The objective of this study is to measure the thermophysical properties of Zr–Fe liquid alloys. Alloy samples with a composition of Zr_1?xFe_x (x = 0.12, 0.24, and 0.50) were synthesized by arc melting, and their density, viscosity, and surface tension were measured using an electrostatic levitation technique. The results indicate that the density of Zr–Fe liquid alloys can be estimated by a linear combination of the measured or extrapolated densities of pure Zr and Fe. The viscosities of the Zr–Fe liquid alloys can be roughly estimated by extrapolating those of Zr to lower temperatures, although this method tends to underestimate the viscosity of alloys, especially for eutectic compositions. The values of the Zr–Fe liquid alloys’ surface tensions are close to those of pure Zr.     

Fracture toughness of Zr-2.5 wt% Nb pressure tubes

Measurements of fracture toughness of HT Zr-2.5 wt% Nb pressure tubes have been made by studying internally pressurizing (burst) test specimens and small bending test specimens. These tests were conducted from a viewpoint of the effects of hydrogen content, hydride orientation, temperature and crack configuration on the fracture thoughness K_c. Results of the experiments showed that K_c decreased with increasing hydrogen content, but is little affecting by hydrogen content at reactor operating temperature. The value of K_c can be quantitatively evaluated by RHC defined by radial hydride content (RHC) perpendicular to the tensile stress.     

Theoretical calculation of neutron cross sections for 90,91,92,94,96Zr in the incident energy range between 200 keV and 20 MeV

Neutron cross sections of ^{90,91,92,94,96}Zr were calculated in the incident energy (E_n) range from 200 keV to 20 MeV for the revision of the 4th version of the Japanese Evaluated Nuclear Data Library (JENDL-4.0). The calculation was carried out by using conventional nuclear reaction models such as the spherical optical model, the distorted wave Born approximation, preequilibrium models, and the multi-step statistical model. Parameter values of these nuclear models were adjusted with the aid of experimental cross sections which were published after the JENDL-4.0 evaluation. Cross sections were computed for total, elastic and inelastic scattering, (n, γ), (n, 2n), (n, p), (n, α), (n, nα), and (n, x) = (n, d) + (n, np) reactions, and they were almost consistent with the experimental data. The cross sections were also estimated for the metastable states with the half-life larger than 1 sec. The obtained results well reproduced measured cross sections for the reactions ⁹⁰Zr(n, 2n)^89mZr, ⁹¹Zr(n, x)^90mY and ⁹¹Zr(n, nα)^87mSr.