A competing-rates model is presented to account for operational changes in the metastable β-Zr phase of the Zr-2.5Nb alloy used to make CANDU reactor pressure tubes and is used to predict temperature gradients at the outlet rolled joints using the decomposition of the β-Zr phase as a proxy for temperature. High temperatures decompose the β phase by enhancing the formation of small particles of ω and α phases. Fast neutron flux causes the ω and α phases to shrink. This process is assumed to depend on the total volume of the particles, because they are comparable to, or smaller than, the size of the neutron displacement cascades. The barrier energy for thermal growth was determined to be 2.43 eV, when an Arrhenius A factor of 1013/s was assumed. The cross section for (ω+α)-phase shrinkage is 24.5 barns for Zr-2.5Nb irradiated in CANDU reactors. Assuming that the shrinkage is dominated by the migration of self-interstitial point defects, a defect production efficiency of 1.4% was found.

Hydrogen diffuses in zirconium alloys in response to gradients in hydrogen concentration, temperature, and stress. This essay discusses the results of several evaluations of the coefficient describing the effects of temperature gradients called the heat of transport. The values distinguish between when hydrogen is in solution, (25 +/- 3) kJ/mol, and when stable hydrides are present, (116 +/- 17) kJ/mol.

Hydrogen moves in zirconium because of forces associated with gradients in concentration and stress. When solubility limits are reached, stable hydrides form within control volumes that include stabilizing clouds and Cottrell atmospheres of hydrogen in solution, otherwise unstable hydrides form that can continue to grow as observed in delayed hydride cracking and predicted by the Diffusion First Model written in terms of hydrogen partial molar volume, diffusivity, and solvus, matrix yield strength, and sink strength for hydrogen moving under the influence of a hydrostatic stress gradient. This model predicts cracking rates following heating and cooling to temperatures where the hydride that is found on the crack fracture face is a mixture of delta and gamma hydride. A graphical representation is provided to illustrate the temperature history of hydride nucleation and growth. The effects of neutron irradiation and athermal hydrides are discussed. Other models of delayed hydride cracking are critically reviewed.

Helium (He) isotope exchange in tungsten (W) during sequential irradiation by 3 keV 4He and 3He ions at room (RT) and elevated temperatures (700-1200 K) was investigated. The total He fluence was in the range of 5 × 1021–1.8 × 1022 He/m2 to provide a saturation of the surface layer. The amount of He retained in W after irradiation was measured using in-situ (up to 1500 K) and ex-situ (up to 2500 K) thermal desorption spectroscopy (TDS). Air exposure influenced TDS spectra, but clear were no noticeable differences between 3He and 4He TDS spectra after single irradiation. Subsequent irradiation with different He isotopes demonstrated a very efficient isotope exchange already at room temperature. The substitution of He atoms goes even faster with increasing irradiation temperature. Mechanisms of observed processes are discussed on the base of a simple model.

A diffusion model is proposed to explain high concentrations of hydrogen isotopes seen in some rolled joints of CANDU reactors. Predicted concentration profiles emanating from the rolled joints into the Zr-2.5Nb pressure tubes suggest an early ingress event happens within the first six months of operation in some tubes. This event is consistent with gettering of hydrogen from the 403 stainless steel end-fittings by the pressure tubes.

Hydrogen moves in zirconium because of forces associated with gradients in concentration and stress. When solubility limits are reached, stable hydrides form within control volumes that include stabilizing clouds and Cottrell atmospheres of hydrogen in solution, otherwise unstable hydrides form that can continue to grow as observed in delayed hydride cracking and predicted by the Diffusion First Model written in terms of hydrogen partial molar volume, diffusivity, and solvus, matrix yield strength, and sink strength for hydrogen moving under the influence of a hydrostatic stress gradient. This model predicts cracking rates following heating and cooling to temperatures where the hydride that is found on the crack fracture face is a mixture of delta and gamma hydride. A graphical representation is provided to illustrate the temperature history of hydride nucleation and growth. The effects of neutron irradiation and athermal hydrides are discussed. Other models of delayed hydride cracking are critically reviewed.

The equilibrium hydrogen solvus in the Zr-H system is still in doubt after 60 years of experiments and debate. Currently, there are two ‘equilibrium’ solvi: one for heating and one for cooling. Two solvi are not allowed at equilibrium by Gibbs’ Phase Rule: there can be only one solvus. The ‘true’ solvus is often associated with the temperature associated with the maximum slope of the differential scanning calorimetry endothermic heat flow curve, called TSSD. This association stems from isothermal experiments where hydrogen moves from a source into the metal. Previous work has concluded that hydrogen stops moving when the TSSD temperature reaches the isothermal temperature. This stoppage is interpreted to occur when equilibrium is reached and, thus, the TSSD temperature is the equilibrium solvus. In this paper, long-time isothermal experiments are presented that show hydrogen movement continues well after the TSSD temperature reaches the isothermal temperature. Implications for predicting hydrogen isotope ingress for zirconium alloys are discussed.

Two models of precipitation-dissolution hysteresis in zirconium have been discussed recently. In one an elastic model for the hydrogen flux is written as the superposition of a diffusion current and a drift current. The solvus, TSS, is defined when the currents sum to zero at a hydride interface. Stable hydrides are surrounded by a cloud of hydrogen terminating at concentration C- calculated from another zero-flux condition. The temperature difference between TSS and C- agrees with the hysteresis. The second ‘traditional’ model invokes plastic deformation in zirconium caused by differences between the crystal axes in zirconium and those of the hydride.

The Einstein flux equation is used to predict the concentrations of hydrogen in solid solution when hydrides precipitate in Zircaloy during fast cooling followed by isothermal interludes (constant hold temperatures) observed with synchrotron X-ray diffraction. A thermodynamic description is presented that challenges the current notion that precipitation is limited by kinetics. It also reinforces the claim that the solvus is closer to the temperature where precipitation starts, not to the temperature where precipitates dissolve.

Hydrogen redistribution and ingress were found to occur between metals proposed for manufacturing containers to store used nuclear fuel in deep geologic repositories. Zircaloy fuel cladding was found to getter hydrogen from steel, and through steel and copper, presumably after disappearance of metal-oxide barriers to hydrogen transport in anoxic conditions expected in-service. Long-term implications for changes in fracture toughness and delayed hydride cracking of the fuel cladding are discussed.

Delayed hydride cracking (DHC) risk can be minimized by limiting hydrogen concentration, stress intensity factor, KI, and optimizing temperature maneuvers. Understanding how thermomechanical history affects bulk hydrides and DHC hydrides is critical for predicting DHC and the mechanical properties of zirconium components. On heating from a low temperature, T1, the DHC crack growth rate reaches a maximum value with temperature, T2, and then slows with further increase in temperature until cracking effectively stops, T3. This behavior is observed despite KI being greater than a threshold value, having hydrides present and a nonzero crack growth rate on cooling to the same temperature. In this study, prior DHC models have been used to predict cracking rates for past and present DHC velocity data, including more than 200 cantilever beam test specimens machined from Zr-2.5Nb plates containing 37 to 108 ppm hydrogen subjected to a variety of thermal histories, including quenching. Differential scanning calorimetry was also performed on quenched material, revealing a shift in heat flow features that contributes to an explanation for higher T2 and T3 temperatures after quenching. Examination of DHC fracture surfaces by X-ray diffraction detects the hydrides responsible for cracking; γ hydride is dominant below 125°C and δ hydride is dominant above 225°C, with a smooth transition region between these temperatures. The temperature dependence of the DHC hydride phase is not affected by thermal history. These observations are consistent with γ-phase stability at low temperatures and suggest that inferences about DHC hydrides cannot necessarily be made by observations of bulk hydrides. The results of this study can be used to improve the understanding of the effects of thermal history on DHC and lead to improved temperature maneuvering strategies, increased confidence in the structural integrity of zirconium components, and can be applied to future mechanistic modeling efforts.

The Einstein flux equation is used to predict the apparent temperature hysteresis in hydride precipitation and dissolution in zirconium alloys first observed in 1964. The new interpretation is consistent with Gibbs’ Phase Rule: there can be only one solvus. X-ray diffraction of the remnant hydride record from fracture surfaces of Zr-2.5Nb after delayed hydride cracking showed no dependence on the approach to the test temperature, which is consistent with the predictions of the Einstein flux equation.

X-ray diffraction of fracture surfaces of Zr-2.5Nb after delayed hydride cracking revealed both γ-phase and δ-phase after testing isothermally at temperatures between 25°C and 240°C. The fraction of hydrides that are γ-phase on the fracture surfaces depends on temperature with high values of γ-phase at low test temperatures. When similar amounts of each hydride phase are observed on the same fracture surface, the γ-phase fraction should diminish to zero at the trailing end, that is, the oldest region, if γ-phase is transforming to δ-phase. The absence of such an extreme difference of the γ-phase fraction indicates that γ-phase is a stable phase.

Simple, small-scale, experiments demonstrate that the initial protium in stainless-steel end fittings contributes to the high deuterium concentrations found in the zirconium pressure tubes at CANDU rolled joints. This protium isotopically exchanges becoming deuterium that is then gettered by the zirconium pressure tube. We propose to reduce the concentration of hydrogen isotopes at the ends of pressure tubes in heavy-water nuclear reactors with yttrium getters placed in the outer regions of the stainless-steel end fittings away from the heat-transport heavy water. Simple, small-scale, experiments demonstrate the operating principle showing that yttrium can getter hydrogen isotopes from the zirconium through the stainless steel.

A probe has been developed to determine the solubility of hydrogen in metals. The method is based on mass balance and high-pressure hydrogen produced in situ partitioning between a zirconium probe and the metal. As an example, the solubility of hydrogen in copper, SH in Cu, has been determined between 350 and 450 °C: $$ S_{\text{H\,in\,Cu}} = (1000 \pm 200)\exp \left( { - \frac{43000 \pm 1300}{RT}} \right){\text{ [mol H}}_{2} /{\text{m}}^{3} \sqrt {\text{MPa}} ]. $$This solubility agrees with permeation and diffusivity measurements spanning 10 and 6 orders of magnitude, respectively.

A practical method to add hydrogen to zirconium alloys is described that works at low temperatures and short times. Fitness-For-Service predictions to support extended service of CANDU pressure tubes requires mechanical testing of tubes removed from service with end-of-life hydrogen concentrations and representative changes in alloy microstructure caused by irradiation. With the current method, (101 +/- 5) wt.ppm hydrogen has been added homogeneously to Zircaloy sheets at (201.5 +/- 4.4) degrees C within 22.3 h. These times and temperatures are well below values that would change any effects of irradiation in the alloy. The method has also been demonstrated with a Zr-2.5Nb micro-pressure tube. Crown Copyright (C) 2020 Published by Elsevier B.V. All rights reserved.

The fuel channels and fuel assemblies of all conventional nuclear reactors that generate power from the fission of uranium by thermal neutrons are made from zirconium alloys because of their low thermal neutron absorption cross-section. The dimensional stability, and the ability to predict dimensional changes, of components made from zirconium alloys is important to designers and operators of such reactors because deformation has a consequence for the operability or life of the reactor core. The dimensional changes in zirconium alloys due to neutron irradiation has been the subject of intense study since the inception of the thermal nuclear power reactor. During irradiation zirconium alloys behave differently from most other engineering alloys in that they resist swelling. They do exhibit anisotropic dimensional changes in the absence of an applied stress that depend on the microstructure; this process is called irradiation growth. Like any other material they also exhibit a dimensional response to an applied stress; this process is called irradiation creep. In this review the evolution in measurement methodologies (either from controlled experiments in materials test reactors or gauging of power reactor components) is described together with the results gleaned from such measurements. As measurements have improved and the amount of experimental and operational data has increased, the theoretical basis for modelling creep and growth has also evolved. The history of the evolution in understanding and the ability to predict dimensional changes in zirconium alloys over the past 60–70 years is described and discussed.

Knowledge of the temperature dependence of hydrogen solubility is used to define the conditions necessary for brittle hydrides to be present in reactor components during service. The terminal solid solubility (TSS) of hydrogen is affected by several factors, including irradiation, cold work, and decomposition of the beta phase in Zr-2.5Nb. TSS temperatures for specimens irradiated in Osiris, Halden, and CANDU (R) reactors are reported. TSS was measured on Zr-2.5Nb specimens using differential scanning calorimetry (DSC) to complete four heat-up/cool-down cycles (heat to a peak temperature and cool to room temperature at a rate of 10 degrees C/min) followed by a 1-h anneal at 500 degrees C, and then four more heat-up/cool-down cycles. As with Zircaloy, irradiation slightly decreases the TSS temperatures, but subsequent annealing increases them. These changes are attributed to an initial effect of irradiation damage and reconstitution of the beta phase and reversal of these effects by annealing, as indicated by X-ray diffraction data showing reduced dislocation density and higher beta-phase volume fraction after the specimens were annealed.

Delayed hydride cracking (DHC) has been responsible for cracking in zirconium alloy pressure tubes and fuel cladding and is a concern for spent fuel storage. For cracking to start, sufficient hydrogen must be present for hydride to form at a flaw tip and the local tensile stress must be sufficiently large to crack the hydride (a crack will not extend if the threshold in the stress intensity factor, K-IH, is not exceeded. A high-temperature limit exists when the yield stress of the cladding alloy becomes too low to crack the hydride. In this paper we describe measurements of K-IH and the crack growth rate, V, in unirradiated Zircaloy-4 fuel cladding containing approximately 130 ppm hydrogen in the cold-worked stress-relieved condition representing pressurized water reactors (PWRs) and pressurized heavy-water (PHWR) reactors. Four methods are used to evaluate K-IH. The test specimen and fixture used in these methods was the pin-loading tension configuration. The test temperature ranged from 227 to 315 degrees C. The mean value of K-IH below 280 degrees C had little temperature dependence; it was about 5.5 MPa root m in the PWR cladding and slightly higher at 7 MPa root m in the PHWR material. At higher test temperatures, K-IH increased dramatically to more than 12 MPa root m, whereas the crack growth rate declined toward zero. This behavior suggests that unirradiated Zircaloy-4 fuel cladding is immune from DHC above about 320 degrees C; this temperature may be increased to 360 degrees C by irradiation. The implications for spent fuel storage are that during early storage when the temperatures are high, any flaw will not extend by DHC, whereas at low temperatures, after many years of storage, flaws would have to be very large, approaching through wall, before being extended by DHC. To date, spent nuclear fuel is not known to have failed by DHC during storage, confirming the inference.