The anharmonic phenomena in Zirconium Hydrides and Deuterides, including ε-ZrH2, γ-ZrH, and γ-ZrD, have been investigated from aspects of inelastic neutron scattering (INS) and lattice dynamics calculations within the framework of density functional theory (DFT). The observed multiple sharp peaks below harmonic multi-phonon bands in the experimental spectra of all three materials did not show up in the simulated INS spectra based on the harmonic approximation, indicating the existence of strong anharmonicity in those materials and the necessity of further explanations. We present a detailed study on the anharmonicity of zirconium hydrides/deuterides by exploring the 2D potential energy surface of hydrogen/deuterium atoms, and solving the corresponding 2D single-particle Schrodinger equation to get the eigenfrequencies. The obtained results well describe the experimental INS spectra and show harmonic behavior in the fundamental modes and strong anharmonicity at higher energies.
Zirconium alloys are widely used in the nuclear industry because of their high strength, good corrosion resistance and low neutron absorption cross-section. However, zirconium has strong affinity for hydrogen which leads to hydrogen concentration build-up over time. It is well known that the formation of hydrides will degrade the material and leads to, for example, delayed hydride cracking during high burn up. Even though zirconium hydrides have been studied for several decades, there still remain some controversies regarding the formation mechanisms, exact crystal structure, and stability of …
The effects of applied load on the formation and reorientation of delta hydrides in alpha-zirconium matrix are studied by a multiphase field model. Simulations with only one hydride seed indicate that the hydride reorientation occurs only when a tensile or compressive strain of ~0.02 is applied along [112-0] (hoop or circumferential direction) or [0001] (radial direction aligned with the basal pole direction), respectively. However, two-seed and multi-seed hydride simulations show the significant influence of neighboring hydrides on the required load for reorientation, reducing it by more than…
A model for precipitation of the plate-shaped second-phase under applied stress is presented. The precipitates in the matrix-precipitate system are represented by their local volume fraction and an orientation parameter that defines the alignment of a precipitate platelet in a given direction. Kinetic equations, based on diffusion theory and classical nucleation theory, are used to describe the time evolution of these two parameters. The model is used to describe the stress orientation of hydrides in Zr-alloys in light of experiments.
Hydrogen embrittlement in Zr alloy fuel cladding is a primary safety concern for water based nuclear reactors. Here we investigated the stabilisation of planar defects within the forming hydrides by Sn, the primary alloying element of Zircaloy-4 used in the cladding. In order to explain formation of hydrides and planar defects observed in our experiments, we performed atomic-scale ab initio calculations focusing on the solute interactions with generalized stacking faults in hcp $α$-Zr and fcc zirconium hydrides. Our calculations showed that an increase in Sn concentration leads to a stabilisat…
The formation of precipitated zirconium (Zr) hydrides is closely related to the hydrogen embrittlement problem for the cladding materials of pressured water reactors (PWR). In this work, we systematically investigated the crystal structures of zirconium hydride (ZrHx) with different hydrogen concentrations (x = 0~2, atomic ratio) by combining the basin hopping algorithm with first principles calculations. We conclude that the P3m1 ζ-ZrH0.5 is dynamically unstable, while a novel dynamically stable P3m1 ZrH0.5 structure was discovered in the structure search. The stability of bistable P42/nnm Zr…
Zirconium alloys are used as nuclear fuel cladding material due to their mechanical and corrosion resistant properties together with their favorable cross-section for neutron scattering. At running conditions, however, there will be an increase of hydrogen in the vicinity of the cladding surface at the water side of the fuel. The hydrogen will diffuse into the cladding material and at certain conditions, such as lower temperatures and external load, hydrides will precipitate out in the material and cause well known embrittlement, blistering and other unwanted effects. Using phase-field methods…
We have performed a detailed x-ray diffraction structural study of Zr under pressure and unambiguously identify the existence of a first-order isostructural bcc-to-bcc phase transition near 58 GPa. First-principles quantum molecular dynamics lattice dynamics calculations support the existence of this phase transition, in excellent agreement with experimental results, triggered by anharmonic effects. Our results highlight the potential ubiquity of anharmonically driven isostructural transitions within the periodic table under pressure and calls for follow-up experimental and theoretical studies…
The integrity of irradiated zirconium based nuclear fuel cladding is related to the precipitation of hydrides which is closely connected with the solubility of hydrogen. A review on the development of measurement technologies is given and the resulting terminal solid solubilities are reflected with respect to the established model of hydrogen solubility in zirconium alloys. The results often allow for a different interpretation than the established model. An alternative qualitative approach is proposed in which the fixed TSSp for the precipitation of zirconium hydrides is replaced by a kinetic…
The interaction of hydrogen and metals continues to be industrially relevant and is a critical part of creating and supporting a safety case for nuclear reactor operation. In the present work, we explore hydrogen storage and hydride formation in a zirconium alloy. We characterise the structure and interfaces of fine scale hydrides using scanning transmission electron microscopy (STEM) including energy dispersive spectroscopy (EDS/EDX), electron energy loss spectroscopy (EELS), and high-resolution STEM. Chemical characterisation is supported further with atom probe tomography (APT). Samples wer…
Zircaloy-4 is used as a fuel cladding material for water reactors, as it has good mechanical properties, corrosion resistance, and a low thermal neutron absorption cross section. However, the mechanical performance of Zircaloy-4 can be reduced during service due to hydrogen uptake and hydride formation. These hydrides are brittle, and often reduce the strength and toughness of materials as well as increase susceptibility to delayed hydride cracking (DHC). In this work, large grain Zircaloy-4 with hydrides was prepared and then cross sectioned using cryo-ion beam polishing, using plasma focused…
The variational stochastic self-consistent harmonic approximation is combined with the calculation of third-order anharmonic coefficients within density-functional perturbation theory and the "$2n+1$" theorem to calculate anharmonic properties of crystals. It is demonstrated that in the perturbative limit the combination of these two methods yields the perturbative phonon linewidth and frequency shift in a very efficient way, avoiding the explicit calculation of fourth-order anharmonic coefficients. Moreover, it also allows calculating phonon lifetimes and inelastic neutron scattering spectra …
The long-term safety of water-based nuclear reactors relies in part on the reliability of zirconium-based nuclear fuel. Yet the progressive ingress of hydrogen during service makes zirconium alloys subject to delayed hydride cracking. Here, we use a combination of electron back-scattered diffraction and atom probe tomography to investigate specific microstructural features from the as-received sample and in the blocky-alpha microstructure, before and after electrochemical charging with hydrogen or deuterium followed by a low temperature heat treatment at 400C for 5 hours followed by furnace co…
Zirconium and its alloys are extensively used as cladding material in nuclear reactors. They are vulnerable to hydrogen degradation under the harsh service conditions of the reactors, which necessitates continuous monitoring for the hydride concentration. The presence of hydride denuded zones in the latter stages of the pressure tube's life hinders the monitoring process, which is carried out by scrape samples taken from the surface of pressure tubes. We investigated the effect of oxygen on diffusivity of hydrogen in hcp-Zr, to check the hypothesis that oxygen slows the diffusion of hydrogen a…
A recent experimental work on palladium hydrides suggested that metastable structures with hydrogen atoms occupying tetrahedral sites could lead to superconductivity above 50 K, a huge increase compared to the 10 K critical temperature of the stable structure with all hydrogen atoms occupying octahedral sites. By generating many structures with hydrogen atoms randomly occupying the octahedral and tetrahedral sites of the face-centered cubic lattice and calculating their energy at different theoretical levels from first principles, we determine that metastable structures with partial or full oc…
Realistic prediction of the superconducting transition temperature (Tc) for PdH is a long-standing challenge, because it depends on robust calculations of the electron and phonon band structures to obtain the electron-phonon scattering matrix element. To date, first-principles calculations employing density functional theory (DFT) have been based on selected exchange-correlation and core-electron approximations. Incorporating anharmonicity produced a more realistic value of Tc that nevertheless still disagreed strongly with experiment unless adjustable parameters were introduced. Here we consi…
The structural phase behaviors of pure zirconium metal under compressions up to $160$ GPa at room temperature are investigated from the perspective of ensemble theory where the partition function is solved by our recently proposed method with \emph{ab initio} precision. The derived Gibbs free energy is employed as the very criterion to determine phase transitions and the calculated transition pressures of the $α\rightarrowω\rightarrowβ$ are $6.93$ and $24.83$ GPa respectively, the former one of which is so far the only theoretical result agreeing with multiple experimental measurements to our …
Deuteride phases in the zirconium-deuterium system in the temperature range 25-286$\celsius$ have been studied in-situ by high resolution neutron diffraction. The study primarily focused on observations of $δ\rightarrow γ$ transformation at 180$\celsius$, and the peritectoid reaction $α+ δ\leftrightarrow γ$ at 255$\celsius$ in commercial grade Zr powder that was deuterated to a deuterium/Zr ratio of one to one. A detailed description of the zirconium deuteride preparation route by high temperature gas loading is also described. The lattice parameters of $α$-Zr, $δ$-ZrD$_x$ and $ε$-ZrD$_x$ were…
Analysis and understanding of the role of hydrogen in metals is a significant challenge for the future of materials science, and this is a clear objective of recent work in the atom probe tomography (APT) community. Isotopic marking by deuteration has often been proposed as the preferred route to enable quantification of hydrogen by APT. Zircaloy-4 was charged electrochemically with hydrogen and deuterium under the same conditions to form large hydrides and deuterides. Our results from a Zr hydride and a Zr deuteride highlight challenges associated to accurate quantification of hydrogen and de…
Harmonic calculations based on density-functional theory are generally the method of choice for the description of phonon spectra of metals and insulators. The inclusion of anharmonic effects is, however, delicate as it relies on perturbation theory requiring a considerable amount of computer time, fast increasing with the cell size. Furthermore, perturbation theory breaks down when the harmonic solution is dynamically unstable or the anharmonic correction of the phonon energies is larger than the harmonic frequencies themselves.We present a stochastic implementation of the self-consistent har…
