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At least 919 records · Page 51

Induction Heating Model of Cermet Fuel Element Environmental Test (CFEET)

Deep space missions with large payloads require high specific impulse and relatively high thrust to achieve mission goals in reasonable time frames. Nuclear Thermal Rockets (NTR) are capable of producing a high specific impulse by employing heat produced by a fission reactor to heat and therefore accelerate hydrogen through a rocket nozzle providing thrust. Fuel element temperatures are very high (up to 3000 K) and hydrogen is highly reactive with most materials at high temperatures. Data covering the effects of high‐temperature hydrogen exposure on fuel elements are limited. The primary concern is the mechanical failure of fuel elements due to large thermal gradients; therefore, high‐melting‐point ceramics‐metallic matrix composites (cermets) are one of the fuels under consideration as part of the Nuclear Cryogenic Propulsion Stage (NCPS) Advance Exploration System (AES) technology project at the Marshall Space Flight Center. The purpose of testing and analytical modeling is to determine their ability to survive and maintain thermal performance in a prototypical NTR reactor environment of exposure to hydrogen at very high temperatures and obtain data to assess the properties of the non‐nuclear support materials. The fission process and the resulting heating performance are well known and do not require that active fissile material to be integrated in this testing. A small‐scale test bed; Compact Fuel Element Environmental Tester (CFEET), designed to heat fuel element samples via induction heating and expose samples to hydrogen is being developed at MSFC to assist in optimal material and manufacturing process selection without utilizing fissile material. This paper details the analytical approach to help design and optimize the test bed using COMSOL Multiphysics for predicting thermal gradients induced by electromagnetic heating (Induction heating) and Thermal Desktop for radiation calculations.

Gomez, Carlos F.↗

Characterization of Fe and Cr Dissolution and Reaction Product Formation in Molten Chloride Salts With and Without Impurities

There is considerable interest in molten chloride salts for several applications including thermal storage and next-generation molten salt reactors (MSRs). Several studies have concluded that Cl salts are highly corrosive to structural materials. Using Oak Ridge National Laboratory’s established methodology, Cl salt compatibility was assessed for candidate Ni-based alloys 230, 600 and 740 H at 600°–800°C in static welded capsules and in flowing thermal convection loop (TCL) salt experiments. Simply drying commercial Cl salt at 550°–650°C and adding~0.05 wt.%Mg was able to produce small specimen mass changes and limited surface attack after 100–1000 h exposures. Intentional additions of H 2 O, NiCl 2 and undried salt were used to better understand the role of impurities and achieve the>50 µm levels of attack reported in other studies. Further, characterisation of Cr depletion and oxide formation in conjunction with pre- and post-test salt chemistry measurements are being used to understand salt compatibility of structural materials.

36 MATERIALS SCIENCE↗

Pulsed Thermal Tomography Nondestructive Examination of Additively Manufactured Reactor Materials (Second Annual Progress Report)

Additive manufacturing (AM) is an emerging method for cost-efficient fabrication of nuclear reactor parts. AM of metallic structures for nuclear energy applications is currently based on laser powder bed fusion (LPBF) process, which can introduce internal material flaws, such as pores and anisotropy. Integrity of AM structures needs to be evaluated nondestructively because material flaws could lead to premature failures due to exposure to high temperature, radiation and corrosive environment in a nuclear reactor. Thermal tomography (TT) provides a capability for non-destructive evaluation of sub-surface defects in arbitrary size structures. Thermal tomography is a computational method for heat diffusion-based imaging of solids, which provides 3D visualization of data from flash thermography measurements. We investigate thermal tomography imaging and nondestructive evaluation of stainless steel and nickel super alloy metallic structures produced with laser powder bed fusion (LPBF) additive manufacturing (AM) process. Metallic structures produced with LPBF contain defects, and there are limited capabilities to evaluate these structures non-destructively. Thermal tomography reconstruction of 3D apparent spatial effusivity provides information about AM structure geometry and internal material flaws. We study performance of thermal tomography in imaging of metallic structures through COMSOL computer simulations of transient heat transfer, and through reconstruction of data obtained from experimental measurements. Reconstruction of internal defects is investigated using a stainless steel 316L specimen with flat bottom hole (FBH) indentations, and Inconel 718 plate produced with laser powder bed fusion (LPBF) method, which contains imprinted hemispherical shape low density regions containing non-sintered metallic powder. The FBH’s have the same sizes as the imprinted defects in the LPBF specimens, but offer better imaging contrast. Thermal tomography reconstructions provide visualizations of internal defects, and allow for estimation of their sizes and locations. Detection sensitivity of TT is limited by noises. We investigate separation of signal from noise in thermography images using several machine learning (ML) methods, including new spatio-temporal blind source separation (STBSS) and spatio-temporal sparse dictionary learning (STSDL) methods. Performance of the ML methods is benchmarked using thermography data obtained from imaging stainless steel 316L and Inconel 718 specimens produced LPBF method with imprinted calibrated porosity defects. The ML methods are ranked by F-score and execution runtime. Finally, we investigate TT of AM stainless steel 316L specimen with imprinted internal porosity defects using relatively low-cost, small form factor infrared (IR) camera based on uncooled micro bolometer detector. Sparse coding related K-means singular value decomposition (SVD) machine learning, image processing algorithms are developed to improve quality of TT images through removal of Additive white Gaussian noise without blurring the images. Following initial qualification of an AM component for deployment in a nuclear reactor, a compact TT can also be used for in-service nondestructive evaluation (NDE). With capability to perform in-service NDE of the AM component lifecycle, TT data can be used for development of a component digital twin.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Experimental and Simulation Analysis of Binary Mixtures of Biomass and Inert Material

A literature review was conducted to identify experiments on various scales of biomass combustion specific to circulating fluidized bed (CFB) combustors. Typical feedstock and inert bed material characteristics for biomass combustion in a CFB were gathered. This information was used to design laboratory-scale, non-reacting experiments on biomass-inert bed material mixtures in a 1-in. cylindrical test rig in the Multiphase Flow Analysis Laboratory (MFAL) in Morgantown, WV. The biomass chosen was a hardwood. Pellets from the hardwood were milled and sieved to obtain three size ranges—small, medium, and large. Three mass loadings of each of the biomass samples were fluidized with glass beads as the inert bed material to study the mixing characteristics under varying fluidizing gas velocities. Hydrodynamic data including pressure drop measurements at select vertical locations and video recordings of the mixture behavior were generated in this effort.

09 BIOMASS FUELS↗

SPC-3185 Rev 5 Guard Vessel Build to Print Fabrication Specification

Idaho National Laboratory (INL) is developing a microreactor to produce electrical power utilizing a small nuclear core and Stirling engines under the Microreactor Application Research Validation and Evaluation (MARVEL) program. This procurement specification defines the requirements for fabrication of the Guard Vessel.

21 - SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLAN↗

Experimental and numerical studies of seismic fluid-structure interaction in a base-supported cylindrical vessel

Seismic design and qualification of advanced reactors will rely heavily on the use of verified and validated numerical models capable of capturing the interaction of the vessel, its contained fluid, and the internal equipment: fluid-structure interaction (FSI) analysis. Analytical solutions can be used for preliminary sizing and design of such vessels but their application is limited to simple geometries and boundary conditions, and small amplitude, translational (and rotational) inputs. To validate numerical models for seismic FSI analysis in finite element codes, a comprehensive set of experiments was performed on a liquid-filled cylindrical vessel, using a 6 degree-of-freedom earthquake simulator. Results in terms of sloshing frequency, damping ratio in sloshing modes, and hydrodynamic responses (wave height, hydrodynamic pressure, base shear, and base moment) for multi-directional earthquake simulator inputs are reported and compared with analytical solutions for liquid-filled vessels. The impact of seismic (base) isolation on hydrodynamic responses was studied using earthquake simulator inputs generated using a virtual isolation system. Data from the experiments are used to validate a numerical model of the fluid-filled vessel using the Arbitrary Lagrangian Eulerian (ALE) solver in the commercial finite element program LS-DYNA. Validation studies are presented for multi-directional seismic inputs, including rocking motions. Lagrangian modeling approaches using an elastic material formulation for the fluid are also investigated and their limitations and possible applications are identified. Here, the results are broadly applicable to the seismic response of base supported, liquid-filled vessels.

58 GEOSCIENCES↗

Investigating effects of soil chemicals on density of small mammal bioindicators using spatial capture-recapture models

Monitoring the ecological impacts of environmental pollution and the effectiveness of remediation efforts requires identifying relationships between contaminants and the disruption of biological processes in populations, communities, or ecosystems. Wildlife are useful bioindicators, but traditional comparative experimental approaches rely on a staunch and typically unverifiable assumption that, in the absence of contaminants, reference and contaminated sites would support the same densities of bioindicators, thereby inferring direct causation from indirect data. We demonstrate the utility of spatial capture-recapture (SCR) models for overcoming these issues, testing if community density of common small mammal bioindicators was directly influenced by soil chemical concentrations. By modeling density as an inhomogeneous Poisson point process, we found evidence for an inverse spatial relationship between Peromyscus density and soil mercury concentrations, but not other chemicals, such as polychlorinated biphenyls, at a site formerly occupied by a nuclear reactor. Although the coefficient point estimate supported Peromyscus density being lower where mercury concentrations were higher (β = –0.44), the 95% confidence interval overlapped zero, suggesting no effect was also compatible with our data. Estimated density from the most parsimonious model (2.88 mice/ha; 95% CI = 1.63–5.08), which did not support a density-chemical relationship, was within the range of reported densities for Peromyscus that did not inhabit contaminated sites elsewhere. Environmental pollution remains a global threat to biodiversity and ecosystem and human health, and our study provides an illustrative example of the utility of SCR models for investigating the effects that chemicals may have on wildlife bioindicator populations and communities.

36 MATERIALS SCIENCE↗

Microtructure and Low-Cycle Fatigue Behavior of Additively Manufactured 316L Stainless Steel at 300°C

Metal additive manufacturing (AM) or 3D printing has the potential to transform the nuclear industry by producing high quality components faster and cheaper, thus enhancing the operating performance of current plants and advanced reactors. Two AM 316L tubes - intended to act as surrogates for complex components where nuclear equipment vendors are more likely to consider AM technologies - were printed using a Renishaw AM400 Laser Powder Bed Fusion (L-PBF) system. The porosity of the as-built material was found to be small, 0.06%. In prior research, the fatigue and corrosion fatigue crack growth rate (CGR) response of the AM specimens in the as-built condition was found to be similar to that expected for conventional alloys, and extremely resistant to stress corrosion cracking (SCC). The present research demonstrates that the low-cycle fatigue behavior of the AM material in air is similar to that of wrought stainless steel at LWR temperature. The data suggest that low porosity levels do not have a significant effect on the fatigue performance of AM materials. Taken together, all data generated to date demonstrate that the use of AM alloys in a nuclear environment is plausible. Additional research on environmental fatigue, crack initiation, and SCC needs to be conducted to provide the performance information needed to qualify AM materials for LWR applications.

36 MATERIALS SCIENCE↗

Scaled up Process Report – Apparatus and Model

Advanced voloxidation with NO 2 is a proposed process for used nuclear fuel head-end reprocessing scheme that converts UO 2 to higher oxides, and it also converts partitioning volatile fission products into the gas phase, thus facilitating fuel dissolution and actinide recovery. NO 2 voloxidation is being studied on small batches of UO 2 Simfuel, but the real test of process feasibility will be when it is scaled up to work with >100 g of irradiated material. This report discusses the aspects of scale-up that must be considered for NO 2 voloxidation, including development of a stirred reactor to promote agitation of the mixture during processing, online process monitoring, and automation controls. Brief details on parallel efforts are also provided in this report, including (a) demonstration of iodine release from Simfuel made by Spark Plasma Sintering, and (b) development of an order-of-magnitude scale-up to react 100 g of UO 2 Simfuel in a metal reactor.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Effect of inlet temperature on the performance of a catalytic reactor

A 12 cm diameter by 15 cm long catalytic reactor was tested with No. 2 diesel fuel in a combustion test rig at inlet temperatures of 700, 800, 900, and 1000 K. Other test conditions included pressures of 3 and 6 x 10 to the 5th power Pa, reference velocities of 10, 15, and 20 m/s, and adiabatic combustion temperatures in the range 1100 to 1400 K. The combustion efficiency was calculated from measurements of carbon monoxide and unburned hydrocarbon emissions. Nitrogen oxide emissions and reactor pressure drop were also measured. At a reference velocity of 10 m/s, the CO and unburned hydrocarbons emissions, and, therefore, the combustion efficiency, were independent of inlet temperature. At an inlet temperature of 1000 K, they were independent of reference velocity. Nitrogen oxides emissions resulted from conversion of the small amount (135 ppm) of fuel-bound nitrogen in the fuel. Up to 90 percent conversion was observed with no apparent effect of any of the test variables. For typical gas turbine operating conditions, all three pollutants were below levels which would permit the most stringent proposed automotive emissions standards to be met.

Anderson, D. N.↗

Effect of inlet temperature on the performance of a catalytic reactor

A 12-cm-diameter by 15-cm-long catalytic reactor was tested with No. 2 diesel fuel in a combustion test rig at inlet temperatures of 700, 800, 900, and 1000 K. Other test conditions included pressures of 300,000 and 600,000 Pa, reference velocities of 10, 15, and 20 m/s, and adiabatic combustion temperatures in the range from 1100 to 1400 K. The combustion efficiency was calculated from measurements of carbon monoxide and unburned hydrocarbon emissions. Nitrogen oxide emissions and reactor pressure drop were also measured. At a reference velocity of 10 m/s, the CO and unburned hydrocarbons emissions and, therefore, the combustion efficiency were independent of inlet temperature. At an inlet temperature of 1000 K, they were independent of reference velocity. Nitrogen oxides emissions resulted from conversion of the small amount of fuel-bound nitrogen in the fuel. Up to 90% conversion was observed with no apparent effect of any of the test variables. For typical gas-turbine operating conditions, all three pollutants were below levels which would permit the most stringent proposed automotive emissions standards to be met.

Anderson, D. N.↗

Simulation of a TRISO MiniFuel irradiation experiment with data-informed uncertainty quantification

An irradiation experiment using tristructural isotropic (TRISO) fuel particles and the miniature fuel (MiniFuel) irradiation vehicle was performed in Oak Ridge National Laboratory’s High Flux Isotope Reactor (HFIR) to support development of the Kairos Power fluoride salt–cooled, high-temperature reactor (KP-FHR). Here, this paper describes modeling predictions of temperatures and fuel burnup for the as-built experiment. An uncertainty quantification (UQ) analysis was performed to determine the effect of TRISO particle volume and position on the temperature predictions at various fuel heat generation rates (HGRs). This UQ study utilized fuel kernel position and volume measurements previously collected using X-ray computed tomography (XCT) techniques and Monte Carlo sampling methods to generate fuel compact cases that were then analyzed using a finite element thermal model. The UQ analysis indicated that uncertainty in calculated temperatures caused by varying TRISO particle arrangement is relatively small, even at high fuel HGR. Final predictions of particle temperatures throughout the irradiation are shown to be relevant to KP-FHR normal and off-normal operating conditions and to previous TRISO irradiation experiments. The combination of XCT with UQ analyses will inform post-irradiation examination (PIE) of the irradiated fuel compacts, and these analyses can be used to develop fuel performance models for coated particle fuel forms. Both PIE of separate-effects irradiation data and enhanced fuel performance modeling support accelerated qualification of TRISO fuels for a broad range of advanced reactor applications. The novel approach demonstrated here of measuring TRISO particle configurations with XCT methods and generating representative fuel compacts for finite element modeling and UQ analysis could be leveraged by the broader particle fuel community in the development of other TRISO fuel experiments in which these variables may have a significant impact on key outcomes.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Using Generative AI to implement the discrepancy checker for a Nearly Autonomous Management and Control System for Advanced Reactors

Developments related to generative artificial intelligence (AI) have brought a major breakthrough in AI. These developments are rapidly accelerating developments in different science and engineering applications. Nearly Autonomous Management and Control (NAMAC) system provides recommendations to the operator for maintaining the safety and performance of the reactor. The discrepancy checker (DC) is an important component of the NAMAC) system, whose goal is to determine if the plant is moving towards the expected system state after the control actions are injected. In this work, we explore generative AI methods, particularly, a generative pretrained transformer (GPT) for implementing the DC function in NAMAC. The GPT-based DC aims to alert the operator in situations outside NAMAC’s scope and act as a chatbot the operator can use to retrieve relevant information. This study involves two versions of GPT developed by OpenAI: GPT-3.5 and GPT-4. These GPTs are trained on huge amounts of undisclosed general domain datasets. We explored two methods to adapt GPTs for DC implementation in NAMAC: fine-tuning and retrieval augmented generation. A small knowledge base (information file) that encompasses rules for DC implementation and some general information related to NAMAC has been created to support DC implementation using GPT. In this work, the GPT-based DC implementations have been tested for their reasoning abilities, comprehension, information retrieval, and extraction abilities. It should be noted that this paper only presents a preliminary study to test the feasibility of DC implementation using generative AI technology. Given the potential risks and severe consequences associated with nuclear reactor applications, combined with the black-box nature of AI, extensive offline and online testing and reliability analyses of GPT-based DCs are needed for further developing such capabilities.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Neutronic Consideration of TREAT Facility Fuel SiC Recladding

The Transient Reactor Test (TREAT) Facility is an air-cooled reactor composed of graphite-urania fuel encapsulated in zirconium alloy canisters and surrounded by ~2 ft (~61 cm) of nuclear grade graphite. The primary role of TREAT is to provide in-pile nuclear-heated safety research via transient testing [1]. Benchmark efforts have demonstrated sensitivity of TREAT neutronics models to graphite cross section data and key neutron poisons found in the fuel assemblies [2]. During fabrication of TREAT fuel assemblies, a small concentration of boron was inadvertently introduced with variable concentration into the aggregate of fuel blocks prepared for TREAT use. The concentration of boron, and its respective uncertainty, represent the most sensitive component in a neutronics study; unfortunately, nothing can be done to reduce or otherwise mitigate its impact. Hydrogen in the fuel blocks reduces the mean free path of the core and its true quantity and uncertainty is approximated. The hydrogen remains from pitch binder used in the fuel fabrication process and was not completely released due to incomplete fuel graphitization. Destructive fuel testing is necessary to quantify the actual hydrogen content and to improve benchmark model quality. A third neutron poison of some significance is the hafnium impurity in the Zircaloy-3 (Zry-3) assembly cladding. The quantity of hafnium is expected to be within nominal manufacturing limits for nuclear grade zircaloy. Recladding the fuel assemblies with material that is less neutron absorbing is expected to benefit reactor neutron economy. Moreover, TREAT’s total transient energy is restricted based on the rate of Zry-3 oxidation in TREAT’s air coolant environment. Hence, cladding with more benign air reaction kinetics could dramatically uprate the facility’s experimental capability. Silicon carbide (SiC) has been proposed as a candidate material for recladding TREAT assemblies, as SiC/SiC demonstrate favorable properties within nuclear environments [3]. The current operational limits of TREAT are restricted by the oxidation of Zry-3. Change of the cladding to SiC could feasibly double the current temperature limitation. Recladding opportunities allow for previously damaged fuel assemblies to be returned to service, as Zry-3 is not commercially available. The initial effort required to consider proceeding with any recladding effort is to neutronically characterize key reactor parameters while replacing Zry-3 with SiC. A characterization summary, with respective results, is provided herein.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Immortal rays: Rethinking random ray neutron transport on GPU architectures

The Random Ray Method (TRRM) is a recently developed adaptation of the Method of Characteristics for neutral particle transport simulations. TRRM has demonstrated excellent performance on 3D nuclear reactor benchmark problems using CPU-based compute systems. When porting to GPU-based systems, however, new performance challenges arise that are unique to processors targeting massive fine-grained parallelism. For smaller problems, or for large problems that are domain decomposed across many computational nodes, the problem size per node has insufficient parallelism to saturate GPU node resources, thus greatly limiting speedup. In this study, we report on a newly developed “immortal ray” variant of TRRM. Here, the immortal ray technique exposes significantly more fine-grained parallelism by fundamentally reformulating the numerical details of ray discretization, resulting in performance tradeoffs with significant overall benefit on GPUs. For very small 2D simulation problems we found the new immortal ray variant allowed for up to a 4.4x speedup when run on a single GPU. For larger 3D simulation problems we found the new variant improved strong scaling by 3x when run on the Summit supercomputer.

97 MATHEMATICS AND COMPUTING↗

The Monolithic Heat Pipe Microreactor Reference Plant Model

This work introduces a reference plant model for a generic monolithic heat-pipe-cooled microreactor. The model will serve as a springboard to develop future evaluation models in the licensing process of similar microreactor designs at the U.S. Nuclear Regulatory Commission. This model has been developed with the Comprehensive Reactor Analysis Bundle and its specifications are based on open literature publications for the eVinci TM design. BlueCRAB is the U.S. Nu- clear Regulatory Commission non-light-water reactor analysis system based on the Multiphysics Object-Oriented Simulation Environment framework, which can couple the Griffin, BISON, and Sockeye applications to resolve the various physics that are essential for the safety analysis of this type of reactor system. The core specifications includes tristructural isotropic fuel, graphite monolith, graphite reflectors, and drums composed of graphite and B 4 C. No moderator or burnable poison pins are used in the design. The fuel enrichment is reduced to control excess reactivity in the core. This core design is not optimized and only serves for testing purposes, since the primary objective of this work is to exercise the multiphysics coupling for this type of reactor system. A three dimensional (3D) core heterogeneous Griffin discrete ordinates (SN) transport model allows the precise calculation of the flux distribution and pin powers. Griffin transfers the power density distribution and obtains a temperature distribution to and from BISON. The BISON model com- putes the 3D core temperature distribution and is coupled to 876 Sockeye subapplications running a heat pipe model. This 3D conduction model is coupled to the various heat pipes via heat flux boundary conditions. The model includes a small gap between the heat pipe and the monolith. Convective heat transfer boundaries with either ambient temperature or condenser temperature as heat sinks are imposed at the model boundaries. The 2D Sockeye heat pipe model uses a vapor- only methodology, which provides the needed resolution for transient calculations and allows the determination of various heat pipe limits. This approach is superior to the superconductor model traditionally used in steady-state calculations. BlueCRAB computes steady-state power and temperature distributions that serve as the initial condition for a loss-of-heat-sink transient simulation. The steady-state results show significant peaking due to the position of the control drum, but this is a characteristic of the particular design used, which is not optimized at this stage. The transient results show the reactor power slowly stabilizing towards a 3% power level after the partial loss of secondary heat removal. Several recriticalities are observed due to cooling through the secondary system but the reactor is self-stabilizing and behaves as expected.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

A density functional theory and neutron diffraction study of the ambient condition properties of sub-stoichiometric yttrium hydride

Several mechanical and thermophysical properties are required as a function of non-stoichiometry for the successful implementation of YH 2-x for nuclear reactor moderator applications. Density functional theory calculations, in combination with neutron diffraction experiments, were used to study the structural and mechanical properties of YH 2-x . Point defect analysis indicated H occupation primarily at the tetrahedral site within an fcc Y sub-lattice, confirming a fluorite YH 2 structure. The small positive formation energy for H vacancies under Y-rich conditions predicted that hypo-stoichiometry is accommodated by Y+YH 2 at ambient conditions and by H vacancies in the YH 2-x single phase that is relevant to high temperatures. Neutron diffraction studies were used to confirm both the occupation of H on tetrahedral sites and the near-stoichiometric composition of the hydride phase in the two-phase Y+YH 2 region of the phase diagram that dominates at room temperature. Energy minimized special-quasirandom-structures of H vacancies were used to calculate lattice parameters, elastic constants, and several other properties as a function of composition for the single phase YH 2-x . The lattice parameter of YH 2-x decreased by only 0.004 Å with increasing H/Y for the range 1.31 ≤ H / Y ≤ 2.0 indicating a negligible effect on lattice parameters due to vacancy formation. In the two-phase region, however, calculations predicted the density of z Y + ( 1 - z ) Y H 2 - x to increase with decreasing H/Y at lower temperatures due to the increased fraction of high-density Y metal. Additionally, for the high temperature single phase, decreasing H/Y reduced the density as a consequence of the lattice expansion associated with vacancy formation. All elastic constants and moduli increased with increasing hydrogen content in single-phase YH 2-x .

36 MATERIALS SCIENCE↗