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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Updates to Nek5000: RANS wall functions, NRC support, and documentation

As a key part of the U.S. Department of Energy’s Nuclear Energy Advanced Modeling and Simulation program (NEAMS), the next generation of tools for nuclear reactor design are being developed. A primary metric for success of this program is the adoption of those tools by industry stakeholders. To help meet this metric for Nek5000, development efforts this year have focused on the expansion of the available Reynolds-averaged Navier-Stokes (RANS) turbulence models to include wall function models, continued support of the U.S. Nuclear Regulatory Commission in simulating a hydrogen mitigation benchmark experiment, and expansion of the Nek5000 documentation to enhance the code’s usability. The implementation of wall functions is intended to significantly decrease time to-solution for a wide range of problems and it has been identified as an important feature by stakeholders across the nuclear community. The initial implementation of standard and pressure corrected wall functions has been tested in Nek5000 on the classical problems of channel flow and a backward facing step. It has also been tested on a 2D molten salt fast reactor core and a T-junction. The recommended formulation of choosing y + = 30 as a boundary value combined with a Neumann-Neumann formulation of the boundary condition for k and τ produces the most consistent results compared to a wall resolved approach. The collaboration with the NRC is a continuing exercise that has been ongoing for multiple years. This year we have concluded investigations into appropriate inlet conditions, showing that fully developed turbulent conditions are adequate for the full PANDA domain. We have also concluded simulations for an unobstructed jet and are now refocusing to the original obstructed jet case. The expansion of the code documentation has also been an ongoing effort over the past few years to address feedback from the various stakeholders. The documentation now more fully covers many of the available features and closes identified SQA gaps. Finally we report on three training sessions that were offered over the past year in an effort to expand the Nek5000 user base.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Application of Raman Spectroscopy to Determine Uranium Content in ADUN Solution

The work presented in this report is part of the ongoing efforts to address the nuclear material control and accounting needs for advanced reactor fuel fabrication facilities. This work was supported by the Materials Protection, Accounting, and Control Technologies (MPACT) program under the US Department of Energy Office of Nuclear Energy‘s Nuclear Fuel Cycle and Supply Chain program. The activities and engagements under the MPACT program are designed to support a robust US civilian nuclear energy enterprise. In the work described in this report, we supported MPACT objectives by developing measurement techniques that could be used for material accounting and process monitoring and by working with industry partners to identify existing gaps and areas for improvement. Oak Ridge National Laboratory has been working with commercial tristructural isotropic (TRISO) fuel fabricators such as Standard Nuclear to develop technology for rapid and cost-effective uranium content assessment. This work has focused on demonstrating advanced measurement techniques (e.g., Raman spectroscopy) that can be used for rapid, reliable, and cost-effective routine measurements of uranium content in feed solutions and liquid waste streams as well as for monitoring in-line process measurements and product streams. Specifically, this report explores techniques for accurately determining uranium content in acid-deficient uranyl nitrate (ADUN) solutions and detecting low uranium concentrations in ammonia solutions. Developing such measurement techniques will benefit TRISO fuel fabrication facilities, facilities involved in other parts of the fuel cycle that require online monitoring of aqueous solutions, and potentially molten salt fuel reactors. This work supports developing Raman spectroscopy procedures to determine uranium concentrations in ADUN solutions, which are used as feedstock in the sol–gel process for creating TRISO fuel. Some additional benefits of using Raman spectroscopy for uranium quantification in fabrication facilities include enabling online monitoring of the chemical process, which would provide near real-time feedback; eliminating the need for sample transfers, preparation, or dilution; providing nondestructive measurements; and user friendliness. In this fiscal year, FY25, we determined the identity of the unknown Raman band at approximately 853 cm−1 that was discovered in ADUN Raman spectra in FY24, created calibration curves and determined uranium concentrations of two ADUN solutions, and compared the Raman results to results obtained from inductively coupled plasma mass spectrometry and Davies–Gray titration. Furthermore, we have identified focus areas for experimentation in future fiscal years. A key result is that the accuracy of using Raman can provide accuracy comparable to destructive analysist techniques, With a well-developed calibration curve, using standards and a large number of samples (more than five samples), uncertainty on the order of 1%–3% is achievable. Given that the uncertainties achieved by Raman spectroscopy were on the order of the uncertainties achieved using ICP-MS, we conclude that with a well-developed procedure Raman spectroscopy can be used to determine uranium concentrations in ADUN solutions for NMC&A applications. The benefits of such an approach are that the time and effort will be less than that of comparable destructive analysis techniques, with approximately the same level of technical expertise. This will be attractive to operators of fuel fabrication facilities as it will lower costs and improve efficiencies.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2021

X-ray absorption spectroscopy of trivalent Eu, Gd, Tb, and Dy chlorides and oxychlorides

Growing interest in next generation molten salt nuclear reactors necessitates a fundamental understanding of the chemical and physico-chemical properties of fission products, including elements of the lanthanide series. In this study, we probed coordination environment of Eu, Gd, Tb, and Dy in their chloride salts with both laboratory and synchrotron scale X-ray absorption spectroscopy (XAS). Here the aerobic melting was carried out with LnCl 3 ·nH 2 O, where Ln is Eu, Gd, Tb, and Dy, and yielded predominant formation of oxychlorides (LnOCl), that was confirmed by extended X-ray absorption fine structure (EXAFS) analysis and X-ray diffraction (XRD). Density functional theory (DFT) and time-dependent density functional theory (TDDFT) computations were performed to obtain ground state structures, lattice parameters, and to simulate L 3 -edge XANES (X-ray absorption near edge structure) spectra of the LnCl 3 ·nH 2 O and LnOCl. A blue shift, initially predicted by our calculations, was also observed for the experimental Ln L 3 -edge XANES spectra of the hydrated trichlorides vs oxychlorides, highlighting the power of combining the predictive ability of theory with experiment to elucidate the properties of the compounds of interest. The blue shift is indicative of structural stabilization of LnCl 3 ·nH 2 O due to higher symmetry compared with LnOCl. To the best of knowledge, this is a first study providing the framework for fundamental insights into the structure of Ln trichlorides and oxychlorides in support of future characterization of lanthanides in the molten salt environment.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Analysis and Thermal Property Investigations into Ternary Actinide Chloride Salt Systems Containing UCl3 and PuCl3

While regulators, the scientific community, and MSR developers still lack access to literature data on the thermal properties of clean fuel salts, even less information is available on the properties of fuel salts containing impurities. It is essential to understand, benchmark, and predict crucial data on the changes in thermal properties of fuel salt systems due to impurities arising from moisture, corrosion, and reactor operation (i.e., fission products). This research focuses on two actinide fuel salts (1) to investigate a worst-case scenario buildup of actinide fission product in a NaCl-UCl3 eutectic fuel salt and (2) to investigate NaCl-PuCl3 eutectic salt after 1000 hours of operation in a natural circulation flow loop flow to determine if corrosion or atmospheric (moisture/oxygen) products are present. For the first salt, a conservative assumption or worst-case scenario, for fission product buildup in a fuel salt was investigated by adding PuCl3 to eutectic 67 mol% NaCl – 33 mol% UCl3 salt resulting in a ternary salt having a composition of 61 mol% NaCl – 30 mol% UCl3 – 9mol% PuCl3. Addition of PuCl3 to eutectic NaCl-UCl3 resulted in a ternary salt that had a higher melting temperature than either the NaCl-PuCl3 or NaCl-UCl3 binary eutectic mixture. Addition of PuCl3 also resulted in an increase in density which was expected. The second salt was extracted from a micro loop. The composition of the fuel (primary) salt prior to flow loop operations was determined to be 64 mol% NaCl – 36 mol% PuCl3, however, the post-flow loop salt showed increased levels of MgCl2 and NaCl changing the salt composition to 10 mol% MgCl2 – 63mol% NaCl – 26mol% PuCl3) indicating the primary salt interacted with the rinse salt. Analysis of the post flow loop salt detected low concentrations of Al, Ni, Co, Nb, and Zr, most likely corrosion products from the flow loop material of construction. Contamination of the fuel salt (with the rinse salt NaCl-MgCl2) decreased the density by approximately 10% and reduced the onset of melting temperature by 50 °C, from 451 °C to approximately 400 °C. Results from the fission product simulated salt (61 mol% NaCl – 30 mol% UCl3 – 9mol% PuCl3) and the corrosion product salt (10 mol% MgCl2 – 63mol% NaCl – 26mol% PuCl3) will be included in two separate manuscripts for submission to peer-reviewed journals.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2020

Molten Chloride Thermophysical Properties, Chemical Optimization, and Purification

Next-generation concentrating solar power (CSP) technology requires high-temperature heat-transfer fluids and thermal energy storage that can operate in the temperature range of 500°–720°C. This high temperature demands a new chemistry for the heat-transfer fluids that must have high-temperature thermal and chemical stabilities, high energy density, and low corrosion rate on metallic materials used in the heat exchangers, piping, and thermal energy storage tanks. A ternary MgCl 2 -KCl-NaCl chloride-salt system has been proposed to achieve such goals, given its high-temperature thermal stability. The chloride-salt-based systems have been used by the metallurgy industry as the electrolyte to electrolytically extract metallic magnesium. They have also attracted attentions from the nuclear industry for developing the molten salt fast reactors that can operate at close to atmospheric pressure and at higher temperature than traditional light-water reactors. However, the corrosion properties of the ternary salt are not well known. The corrosion mechanism is believed to be correlated to the presence of MgOHCl impurity at the operation temperature. MgOHCl is fundamentally caused by the hygroscopic nature of the MgCl 2 component. Therefore, the first key objective of this project is to understand the nature of the corrosiveness of the ternary chloride-salt system and its prevention by designing new lab-scale purification processes. Because of its importance, a working group called the Chloride Salt Collective across multiple U.S. Department of Energy national laboratories is established to gain experimental agreement on the corrosion behaviors. In addition, water generation during salt dehydration could lead to highly corrosive HCl/water mixture via a hydrolysis process between water and anhydrous MgCl 2 or MgCl 2 hydrates. MgOHCl will eventually be converted to MgO particulates regardless of the chemical path chosen (i.e., by thermal decomposition, chemical purification with an active metal, or electrochemical purification utilizing the reduction power of electron flows). Large MgO particles with high hardness can wear out bearing and bushing and even clog the delicate channels in the primary heat exchanger. Because of this, a second objective is to understand the chemistry behind salt purification and transfer the scientific understanding to a set of engineering know-how for large-scale salt melter design. Because there is limited information on the thermophysical properties and the sensitivity of these properties around the targeted salt composition, a third objective is to measure thermophysical properties relevant to system and component design and support Topic 1 Liquid Pathway development. For example, composition shift due to salt reaction with water can be a potential issue because it can lead to changes of thermophysical properties, such as (1) melting point (or freeze point), which can jeopardize safe operation of the supercritical CO 2 power cycle proposed for next-generation CSP, and (2) heat capacity and density, which can decrease the overall power-generation capability of the plants. The value of the thermal conductivity of the selected salt composition is also a critical criterion for the solar receiver design.

14 SOLAR ENERGY↗
DOE OSTI2024

Development of Segregated Thermal-Hydraulics Solvers in MOOSE

The simulation of fluid flows is an essential part of the design and analysis of nuclear systems. Algorithms able to simulate flows at different fidelity levels are available in the Multiphysics Object-Oriented Simulation Environment (MOOSE) and MOOSE-based applications such as Pronghorn \cite{novak2018pronghorn}, Pronghorn-Subchannel, RELAP-7, and SAM. Currently, significant effort is being invested in the development of coarse-mesh Computational Fluid Dynamics (CFD) capabilities within MOOSE and Pronghorn for the simulation of Generation IV nuclear reactors. Traditionally, the solution algorithms in MOOSE have relied on Newton or quasi-Newton methods (such as the preconditioned Jacobian-free Newton-Krylov method) where residuals and Jacobians (or approximations thereof) are constructed. Both Newton and quasi-Newton methods require the solution of a linear system at each nonlinear Newton iteration with the Jacobian as the system matrix. The Jacobian contains blocks originating from all variables in the problem (i.e., for thermal-hydraulics at least pressure, velocities, and temperature). Due to the formulation of the problem in a general multiphysics setting on unstructured mesh, creating a good preconditioner for the linear system can be challenging, thus many fluid applications have utilized direct solver-based methods such as LU factorization. However, with increasing system size and complexity in multi-dimensional problems, the direct solution of linear systems becomes computationally expensive both in execution time and and memory. For this reason, recent effort has focused on adapting segregated solution algorithms for CFD problems in MOOSE. These algorithms use fixed-point iteration between segregated systems whose assembly and preconditioning are easier those of the monolithic system. Initial results show that the segregated solution algorithm outperforms the monolithic approach in terms of memory usage and for large 3D problems in terms of CPU time as well.

42 ENGINEERING↗
DOE OSTI2024

Design, Fabrication and Testing of Surveillance Test Articles for MSR Materials Degradation Management

This report details the design, fabrication, and testing of surveillance test articles aimed at assessing material damage in reactor-relevant environments for effective degradation management. Two types of surveillance test articles with reduced sizes were developed based on design algorithms and finite element modeling: welded design and interlocking design. A furnace heating setup was adopted to apply multiple thermal cyclic loading profiles on the test articles with a temperature range of 500°C - 700°C, while the strain response was monitored using a digital image correlation technique. The testing results demonstrated the successful capturing of expected strain range for welded design while machining tolerance should be improved to engage strain coupling in the interlocking design. Mid-term (500 hours) and long-term (1500 hours) cyclic tests were conducted on welded test articles. A constant strain range of ~0.6% was observed at the specimen with testing under 500 hours, while a gradual decrease of strain at specimen was observed after 500 hours. Non-destructive evaluation through X-ray computed tomography confirmed the microcracks in the welds at specimen-driver joints after cyclic test that caused the strain change. Creep testing of the specimen after long-term cyclic test revealed a short creep life than expected. A multi-profile cyclic test was also conducted on a test article and demonstrated consistent strain response under different temperature ramp rates. The report also briefly discussed the challenges and future research efforts to advance test article development for material surveillance.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2025

Quantifying uncertainty in uranium concentration measurements via K-edge densitometry

This study quantifies the uncertainty in uranium concentration predictions of fluoride and chloride-based salts within a steel pipe using K-edge densitometry. Modeling and simulation was conducted with the Monte Carlo N-Particle Transport (MCNP) code. The quality of of this technique’s prediction in a pipe requires proper characterization of the pipe’s thickness, which is dependent on the source size and axial offset from the pipe centerline. The thickness was determined as either the center-line thickness seen by the X-ray source or an average value determined through random sampling. Generally, the predicted concentrations were slightly better at lower offset with the random sampling thickness and using the center-line thickness for the highest offsets. For a line-beam source and varying axial offsets, the relative error of concentration was within 1% of the true value but uncertainty increased by 2 orders of magnitude. Similarly, for no axial offset, the relative error was significantly less than 1% while no trend for uncertainty was found. However, at the largest possible offset for a given source size, the concentrations become erroneous and greater than the allowable 1% relative error. Furthermore, high offsets tended to increase the variance of the transmission spectra by 3 orders of magnitude.

Characterization and Analytical Technique↗
DOE OSTI2025

Viewing is understanding: Graphite microstructure effects on infiltrated molten salt distribution revealed by 3D neutron tomography

Molten salt infiltration in the pore network of nuclear graphite may cause unwanted changes to graphite's local structure and mechanical and thermal properties. A detailed and comprehensive understanding of molten salt intrusion (distribution across sample cross section and penetration depth) is needed to assess its effects. Here, in this work, we report on an improved methodology for the use of neutron imaging (computed tomography) to evaluate salt penetration and distribution of a wide range of graphite grades with diverse microstructures. Neutron tomography data were acquired on the same graphite sample before and after salt intrusion; the 3D reconstructed volumes were digitally co-registered and subtracted. The difference in neutron attenuation coefficient represents direct visualization of FLiNaK (LiF–NaF–KF) salt distribution in the salt-impregnated graphite samples. This improved methodology was applied to investigate the effect of exposure times (12 h and 336 h) and of graphite microstructure when exposed to FLiNaK at 750 °C and 3 bar (gauge) pressure, starting from flowing argon at near atmospheric pressure. The results show that medium-grained and fine-grained graphites evolve to equilibrium at significantly different rates: fast salt uptake in medium-grained graphites produces salt deposits throughout the volume of graphite specimens, whereas salt infiltration in fine-grained graphites is much slower and limited to exposed surfaces.

FLiNaK infiltration↗
DOE OSTI2021

Effect of excess Mg to control corrosion in molten MgCl 2 and KCl eutectic salt mixture

Structural alloys may experience corrosion when exposed to molten chloride salts due to selective dissolution of active alloying elements. One way to prevent this is to make the molten salt reducing. For the KCl + MgCl 2 eutectic salt mixture, pure Mg can be added to achieve this. However, Mg can form intermetallic compounds with nickel at high temperatures, which may cause alloy embrittlement. This work shows that an optimum level of excess Mg could be added to the molten salt which will prevent corrosion of alloys like 316 H, while not forming any detectable Ni-Mg intermetallic phases on Ni-rich alloy surfaces.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Effect of tellurium concentration on the corrosion and mechanical properties of 304 stainless steel in molten FLiNaK salt

In this study, the effect of Te concentration in molten FLiNaK salt on the corrosion and mechanical properties of 304 stainless steel was investigated. The corrosion depth of samples after the immersion tests for 48 h at 600 °C decreased with increasing Te concentration. Likewise, the sample after the immersion test containing 1.0 wt% of Te (1.0 wt% Te sample) showed less reduction in mechanical properties than the 0.1 wt% Te sample. We hypothesize that the condition for a Cr-oxide layer that has the protective property is fulfilled underneath the Ni-Fe rich layer which is formed by the selective leaching of Cr.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Pressure drop and heat transfer characteristics of nitrate salt and supercritical CO 2 in a diffusion-bonded heat exchanger

A lab-scale 316/L stainless steel diffusion-bonded heat exchanger was examined within a coupled high-temperature test facility consisting of an atmospheric-pressure nitrate salt loop and a supercritical carbon dioxide (sCO 2 ) loop operating between 10 and 16 MPa. Pressure loss measurements collected for flow rates up to 0.55 kg/s of Solar Salt and up to 0.6 kg/s of carbon dioxide were used to generate friction factor correlations for the respective circular and semicircular zig-zag flow passages. Heat transfer measurements were also performed over a wide range of conditions to produce Nusselt correlations for the CO 2 and nitrate salt geometries. The Nusselt number is deduced from a heat transfer resistance network and overall conductance measurements collected across the operating envelope of the coupled sCO 2 – nitrate salt test facility. The CO 2 side correlation showed excellent agreement with existing correlations in the literature. Further, the salt side, having nearly circular channels with a different zig-zag angle and hydraulic diameter, yielded a new correlation applicable to the laminar flow regime. To examine the similitude of the friction correlations, pressure drop testing with water was performed on both sides of the component as well. Finally, results from non-destructive examination are discussed to provide insights regarding inspection methods and draining performance of high-temperature liquids in compact heat exchangers.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Thermodynamic evaluation and modeling of the CeF 3 -LaF 3 -LiF-NaF system

The thermodynamic properties of the LiF-NaF-CeF 3 -LaF 3 pseudo-quaternary system have been evaluated, and models for the relevant phases have been revised or newly developed. The solid solubility of NaF in LaF 3 and CeF 3 was described in the model based on reported phase-equilibria observations and results from density functional theory calculations. The Gibbs energy functions for the NaCeF 4 and NaLaF 4 phases have been updated with recently reported thermochemical measurements. The Gibbs energy functions and model relations for the LiF-NaF-LaF 3 and LiF-NaF-CeF 3 pseudo-ternary systems were successfully optimized based on thermochemical properties and phase equilibria observations.

CALPHAD↗
DOE OSTI2020

Electrochemical behavior and separation of iodide in molten LiF-NaF-KF melt

This work studied the electrochemical behavior of iodide in molten LiF-NaF-KF mixture and the separation of iodide from the molten salt at 973 K using a graphite working electrode. The cyclic voltammetry (CV) and chronoamperometry (CA) measurements indicated an anodic passivation layer was formed on the graphite electrode in this melt and the layer blocked the charge transfer across the electrolyte/electrode interface. However, the added I- ions could pass through the passivation layer and were oxidized at the graphite electrode. The characterization of the obtained products proved that iodide ions was efficiently oxidized to I2 gas during electrolysis. Furthermore, the graphite anode showed excellent stability without any obvious change in dimensions after electrolysis, which showed the high current efficiency of I2 evolution reaction. Thus, the graphite electrode was possible to be served as an excellent anode to separate other anions (such as Br) from molten fluoride salts.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Validating modern methods for impurity analysis in fluoride salts

Salt impurities directly affect degradation of structural materials in molten salt environments, so impurity quantification and analysis of salts is important for the deployment of next generation molten salt nuclear reactors. Despite the importance of moisture and other oxygen containing impurities, reliable methods of measuring these impurities are not well qualified or commonly used. Herein, we present two methods for analysis of oxygen content and one method for analysis of hydrogen content in fluoride salts demonstrated on two batches of LiF-NaF-KF (FLiNaK) salt with differing purity levels. The intentional addition of varying amounts of oxygen and hydrogen to the FLiNaK salt as internal standards produced a linear response using a commercial combustion analysis instrument, and measured amounts were consistent with the standards. Overall, these results indicate the technique is a valid method for measuring oxygen and hydrogen content in fluoride salts. Corrosion studies of 316H in FLiNaK revealed 5 times more mass loss in the salt containing more impurities including hydrogen and transition metals.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Corrosion of 316H stainless steel in flowing FLiNaK salt

In this report type 316H stainless steel samples were exposed to flowing FLiNaK salt for 1000 h in a monometallic thermal convection loop (TCL) with a maximum temperature of 650 °C and a minimum of 540 °C. Samples in the hottest part of the TCL lost mass, with a maximum mass loss of 1.4 mg/cm 2 , while samples in the coldest parts of the TCL gained mass, with a maximum mass gain of 1.0 mg/cm 2 . Analysis of the samples that gained mass showed an Fe-rich layer on the sample surfaces, indicating that Fe, not Cr, was the primary deposition product in the TCL. Cr loss was apparent to a depth of ~5 µm in the hot leg. Post-exposure analysis of the salt showed major increases in the Cr, Fe, and Mn contents. The TCL was modeled using the TRANSFORM code. Modeled values matched the experimental temperature measurements showing that TRANSFORM is capable of accurately simulating the TCL conditions.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Ab initio molecular dynamics (AIMD) simulations of NaCl, UCl 3 molten salts

Ab initio molecular dynamics (AIMD) simulations are used to calculate select thermophysical and thermodynamic properties of NaCl, UCl and NaCl-UCl 3 molten salts. Following established approaches, the AIMD simulations include a model for Van der Waals interactions. The Langreth & Lundqvist (vDW-DF2), DFT-D3, and density-dependent energy correction (DFT-dDsC) dispersion models are first tested for molten NaCl in order to assess their accuracy for density and heat capacity predictions across a range of temperatures. Based on the NaCl results, the vdW-DF2 and DFT-dDsC methods are extended to the UCl 3 system and compared to available experimental data. Next, mixtures of NaCl-UCl 3 are investigated and analyzed with respect to the deviation from ideal solution behavior. For the DFT-dDsC simulations, density deviates by up to 2% from an ideal mixture, with the maximum occurring close to the eutectic composition. The mixing energy also deviates from an ideal solution and exhibits a minimum of about -0.074 to eV per formula unit, again close to the eutectic composition. Finally, the compressibility and species diffusivity of the pure and mixed salt systems are calculated. The diffusivities are slightly reduced in the mixed compared to the pure systems and the compressibilities loosely follow a linear correlation as a function of the UCl 3 composition. The trends observed for mixing properties are rationalized by correlating them to the coordination chemistry, which emphasizes the importance of maintaining the extended network formed by U and Cl ions as the NaCl concentration increases. The concentration at which breakdown of the extended network occurs, roughly coincides with the minimum of both the mixing energy and the deviation from ideal solution behavior for density.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗