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At least 55 records · Page 3

Highly-Active and Contaminant-Tolerant Cathodes for Durable Solid Oxide Fuel Cells

The objective of this project is to investigate the fundamental degradation methods occurring in solid oxide fuel cell (SOFC) cathodes when exposed to chromium and carbon dioxide contamination and to rationally design alkaline earth-based catalysts to increase stability and tolerance to contaminate poisoning. With a mechanistic and fundamental understanding of the degradation methods, advanced catalytic surface modifications can be applied to reduce degradation. The specific technical objectives are: (1) To identify/develop new catalysts (alkaline-earth based-) that are compatible chemically with the state-of-the-art cathode materials at high temperatures required for fabrication and with contaminates commonly encountered under operating conditions; (2) To improve the infiltration process for optimal control of the thickness, composition, and uniformity of the catalyst coatings; (3) To evaluate the electro-catalytic activity toward ORR of the chemically-stable materials when exposed to different types of contaminants using electrical conductivity relaxation measurements on bar samples and performance evaluation of catalyst-infiltrated cathodes; (4) To unravel the contamination-tolerant mechanisms of the new catalyst coatings under realistic environmental conditions (with different types of contaminants) using powerful in situ and in operando characterization techniques performed on model cells with thin-film/pattern electrodes, as guided by modeling and simulation; (5) To establish scientific basis for rational design of new catalysts of high tolerance to contaminants; (6) To validate the long term stability of modified LSCF cathodes in commercially available cells/stacks under ROC. Alkaline earth-based catalysts have been systematically explored and tested under various contamination conditions. BaCoO 3-δ (BCO) was shown to produce the best catalytic activity enhancement as well as stability in a variety of contaminating conditions, including CO 2 and chromium. The microstructural evolution was investigated with SEM, EDS, and Raman spectroscopy, showing the BCO catalyst prevents the formation of insulating SrCrO 4 by forming electrically conductive BaCrO 4 . Electrochemical relaxation measurements determined the BCO catalyst coatings increased the surface diffusion coefficient but did not significantly affect the diffusion coefficient and determined an optimum surface modification layer of 100 nm. A novel Ba 0.9 Co 0.7 Fe 0.2 Nb 0.1 O x (BCFN) catalyst was also shown to have excellent stability in chromium containing atmospheres. A novel surface sol-gel (SSG) surface modification, which offers superior thickness and compositional control, was applied to SOFCs to produce BaO catalyst coatings. SSG BaO coatings were shown to produce conformal coatings on the electrode surface, greatly 4 increasing stability in chromium containing atmospheres. An atomic level mechanistic approach was applied to investigate the stability of PrBa 0.8 Ca 0.2 Co 2 O 5+δ (PBCC) with respect to a variety of common contaminants, demonstrating thermodynamically its superior stability in CO 2 containing atmospheres. Finally, the best catalyst coatings demonstrated in this project, BCO and PBCC, were applied to full cells which demonstrated superior stability for over 300 hours in CO 2 and Cr atmospheres

01 COAL, LIGNITE, AND PEAT↗

Acceptable Knowledge Technologist Procedure

Process acceptable knowledge (AK) is a waste stream characterization method that can be used to meet all or part of the waste analysis requirements appropriate for the waste. The method may include documented knowledge of process (KOP), additional characterization data, and/or facility records of analysis. LANL will use process AK to ensure chemical compatibility; assign matrix parameter categories and Environmental Protection Agency (EPA) hazardous waste numbers (HWNs) commonly referred to as EPA codes to waste streams; and determine the waste material parameters and radionuclides present in waste streams.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Alternative Liquid DSA Containers for Sludge Slurry Storage in the SRNL Shielded Cells

A pending revision of the Documented Safety Analysis (DSA) for the Savannah River National Laboratory (SRNL) defines “DSA containers'’ for liquid sludge slurries as containers not susceptible to a flashing spray release in a fire and requires that a list of DSA containers be maintained. High Level Waste (HLW) samples are typically received from the Savannah River Site (SRS) tank farm after retrieval from the storage tanks. Glass bottles are preferred for long-term storage of radioactive liquid sludge slurry samples but are not on the DSA container list. An evaluation has been conducted to identify vessel lids for the glass bottles that would vent prior to pressurization and liquid superheating in a fire event. Low melting Field's Metal eutectic alloy with a melting point of 62°C has been identified as a preferred material of construction for vessel lids for this application because the material is resistant to puncture and is expected to have good chemical compatibility and radiation stability in the shielded cells environment. A test vessel was designed to evaluate the alloy and confirm that it would melt before the water in the vessel reaches the boiling point. The tests confirmed: 1) that the reported melting point of the alloy was accurate, 2) that a top fashioned from this material will melt creating an open atmosphere in the vessel headspace prior to sample boiling under moderate and fast heating rates, and 3) that nonuniform heating of the bottle from the bottom also results in melting of the alloy prior to boiling. Based on the results, neither an engulfing fire with standing or toppled bottles or a fire producing localized heat at the vessel bottom would result in flashing spray conditions. It is recommended that glass vessels of various volumes ranging from 125 mL to 1 gallon with modified tops containing the specified Field's Metal eutectic alloy which are appropriately designed to avoid flashing spray material releases be added to the DSA container list. These vessels will be utilized in the Shielded Cells for the storage of radioactive liquid samples of sludge slurries. Use of these vessels will also be advantageous for other liquid samples containing accountable amounts of nuclear material throughout other SRNL laboratories. Similarly constructed paraffin vessel lids could also potentially be added to the approved list, though additional testing would be required.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Alternative Liquid DSA Containers for Sludge Slurry Storage in the SRNL Shielded Cells

A pending revision of the Documented Safety Analysis (DSA) for the Savannah River National Laboratory (SRNL) defines “DSA containers” for liquid sludge slurries as containers not susceptible to a flashing spray release in a fire and requires that a list of DSA containers be maintained. High Level Waste (HLW) samples are typically received from the Savannah River Site (SRS) tank farm after retrieval from the storage tanks. Glass bottles are preferred for long-term storage of radioactive liquid sludge slurry samples but are not on the DSA container list. An evaluation has been conducted to identify vessel lids for the glass bottles that would vent prior to pressurization and liquid superheating in a fire event. Low melting Field’s Metal eutectic alloy with a melting point of 62 °C has been identified as a preferred material of construction for vessel lids for this application because the material is resistant to puncture and is expected to have good chemical compatibility and radiation stability in the shielded cells environment. A test vessel was designed to evaluate the alloy and confirm that it would melt before the water in the vessel reaches the boiling point. The tests confirmed: 1) that the reported melting point of the alloy was accurate, 2) that a top fashioned from this material will melt creating an open atmosphere in the vessel headspace prior to sample boiling under moderate and fast heating rates, and 3) that nonuniform heating of the bottle from the bottom also results in melting of the alloy prior to boiling. Based on the results, neither an engulfing fire with standing or toppled bottles or a fire producing localized heat at the vessel bottom would result in flashing spray conditions.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Electrical-Discharge-Machining Contamination Removal from Metal Additively Manufactured Components

The use of an electrochemical dissolution process is shown to remove the recast layer contamination from the surfaces of electrical-discharge-machining cut components, as well as the interior exposed surfaces of the structure. The solution chemistry, cell potential, and exposure time are all relevant interdependent variables. Optimization of the electrode geometry should be made for each type of component. For the case of Cu-Zn recast contamination of 300-series alloy components, surface composition analysis indicates that complete electrochemical dissolution is achieved using a dilute solution of nitric acid (HNO 3 ). For example, electrochemical dissolution of the Cu-Zn recast is accomplished at 1.2 V cell potential using a 20% nitric solution and an exposure time of 4 h. The use of a nitric acid bath was specifically chosen since it’s chemically compatible and will not degrade the host alloy or the component. In sum, an electrochemically driven dissolution process can be tailored to remove of the recast contamination without affecting the integrity of the host component structure and its dimensional tolerances.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Downselection of Cladding Materials for Zirconium Hydride Moderator

This report complete Milestone M3.1.1 — “Cladding downselection: Team will report to ARPA-E on at least two down-selected cladding options—one metallic and one ceramic.” In this milestone, we systematically assess FeCrAl alloys and SiC-based cladding options for a zirconium hydride (ZrHx) moderator in terms of their neutronics, radiation stability, hydrogen permeability, chemical compatibility, and fabricability. The analysis shows that FeCrAl alloys are excellent candidate cladding materials for a ZrHx moderator given their proven radiation stability, acceptable compatibility with ZrHx, and industrially established fabricability. The relative high hydrogen permeability is manageable by introducing a thin layer of an Al 2 O 3 hydrogen permeation barrier on the external surface. The SiC-cladded ZrHx moderator is promising because of its outstanding neutronics performance, excellent radiation stability, and extremely low intrinsic hydrogen permeability. However, potential interactions of SiC and Zr and the challenge in achieving a hermetic SiC-based cladding require further investigation.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

A Multiscale Investigation of the Mechanisms Controlling Materials Degradation in the Fusion Energy Environment (DE-SC0006661: Final Report)

Realizing the promise of fusion as a commercially attractive energy source requires the development of advanced structural materials capable of sustained operation in an incredibly hostile environment. The fusion environment presents many challenges associated with high cyclic thermal-mechanical loadings, welding and joining disparate materials, and achieving chemical compatibility with coolants and tritium breeders. Yet, the overarching concern is the degradation of physical and mechanical properties, resulting from a neutron energy spectrum peaked at 14 MeV. The high-energy fusion neutron irradiation produces both displacement damage and high levels of hydrogen and helium through transmutation reactions. Advanced materials development for use in such a hostile environment is predicated on understanding the underlying mechanisms responsible for physical and material property degradation. This project has closely combined computational, theoretical and experimental techniques within a multiscale materials science paradigm to determine the mechanisms controlling material degradation in the fusion environment.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Van de Graaff Irradiation Studies of Oxygen Sensor and Hydrated Zirconia Sorbent

Commercial-scale production of Mo-99 demands a facility-wide assessment of radiation-induced degradation across process equipment, instrumentation, and purification media. Key factors— total ionizing dose, dose rate, radiolysis-driven chemistry, thermal loads, activation, and any neutron-related effects—should inform material selection, shielding, and component layout. Purification materials (sorbents, resins, filters, seals, housing) require particular attention to ensure that irradiation does not alter selectivity or capacity, generate fines, or introduce leachables that could compromise Mo-99 purity or downstream Tc-99m generator performance. Dose mapping, accelerated irradiation testing, and studies of extractables/leachables together provide the basis for setting maintenance, calibration, and replacement intervals and for qualifying materials that retain mechanical integrity, chemical compatibility, and radiopurity over their service life.

36 MATERIALS SCIENCE↗

High Entropy Rare-earth Oxide (HERO) Coatings for Refractory Alloys

The HERO coating was developed to protect refractory alloys for application in the harsh hot section of the turbine engine environment addressing ARPA-E ULTIMATE Project Topic 2: Coating Development. The effort was both innovative in its utilization of high entropy rare earth oxides as well as transformational in our approach: holistic design of a single layer thermal/environmental barrier coating (T/EBC) for refractory alloys, with an excellent coefficient of thermal expansion (CTE) match to the alloy substrate, chemical compatibility with the underlying alloy, low oxidant permeability, stability in combustion environments, low thermal conductivity, thermal shock resistance, and resistance to degradation by siliceous debris (calcium magnesium alumino-silicates-CMAS). The high entropy rare earth oxide approach enables two critical coating properties: tailoring CTE match to the substrate and, most significantly, substantially reduced thermal conductivity. The summation of these proposed coating capabilities goes well beyond the technical requirements specified in the ULTIMATE program objectives, and additionally is essential for a successful first stage turbine blade application.

36 MATERIALS SCIENCE↗

Density Functional Theory Analysis of Candidate Tritium Permeation Barriers for Vanadium Alloys as a Fusion Structural Material

Vanadium alloys are being considered as a candidate structural material for the breeder blanket component of future fusion reactors due to their good thermal conductivity, low activation, and chemical compatibility with FLiBe. However, vanadium has a high hydrogen solubility, resulting in hydrogen diffusion and trapping in the vanadium structural alloy and lower than expected tritium breeding ratios. To mitigate the permeation of hydrogen into the structural alloy, a tritium permeation barrier will be coated onto the vanadium alloy. Multiple materials have been proposed as candidate tritium permeation barriers, but the extent to which each of these materials impacts hydrogen diffusion and trapping is still unknown. In this project, we perform atomic-scale calculations to narrow down the list of potential tritium permeation barrier candidates and to understand the mechanisms through which hydrogen diffusion is affected in these materials.

36 MATERIALS SCIENCE↗

A Micelle Electrolyte Enabled by Fluorinated Ether Additives for Polysulfide Suppression and Li Metal Stabilization in Li-S Battery

The Li-S battery is a promising next-generation technology due to its high theoretical energy density (2600 Wh kg -1 ) and low active material cost. However, poor cycling stability and coulombic efficiency caused by polysulfide dissolution have proven to be major obstacles for a practical Li-S battery implementation. In this work, we develop a novel strategy to suppress polysulfide dissolution using hydrofluoroethers (HFEs) with bi-functional, amphiphlic surfactant-like design: a polar lithiophilic "head" attached to a fluorinated lithiophobic "tail." A unique solvation mechanism is proposed for these solvents whereby dissociated lithium ions are readily coordinated with lithiophilic "head" to induce self-assembly into micelle-like complex structures. Complex formation is verified experimentally by changing the additive structure and concentration using small angle X-ray scattering (SAXS). These HFE-based electrolytes are found to prevent polysulfide dissolution and to have excellent chemical compatibility with lithium metal: Li||Cu stripping/plating tests reveal high coulombic efficiency (>99.5%), modest polarization, and smooth surface morphology of the uniformly deposited lithium. Li-S cells are demonstrated with 1395 mAh g-1 initial capacity and 71.9% retention over 100 cycles at >99.5% efficiency-evidence that the micelle structure of the amphiphilic additives in HFEs can prohibit polysulfide dissolution while enabling facile Li + transport and anode passivation.

25 ENERGY STORAGE↗

Fabrication and Evaluation of Large Alumina Crucibles by Vat Photopolymerization Additive Manufacturing for High-Temperature Actinide Chemistry

Additive manufacturing (AM) offers opportunities to advance the design and function of ceramic tooling in high temperature actinide pyrochemistry. In technical ceramics such as alumina, conventional forming techniques often restrict design flexibility and can limit experimental progress. In this study, we investigate the use of vat photopolymerization (VP) with commercial resins to fabricate large-scale alumina crucibles, reaching dimensions up to 125 mm, which is significantly larger than typically reported for dense VP ceramics. Notably, these additively manufactured components are produced using consumer-grade hardware, which limits process control, but offers significant upside in scalability and accessibility. Using microscopy and X-ray computed tomography, the VP alumina parts have high bulk densities above 95%, but also the prevalence of AM-induced artifacts and surface defects. Mechanical testing showed these defects to significantly reduce flexural strength and compromise part reliability. Electrorefining trials under sustained exposure to molten salts and metals reveal mixed results, with the AM material exhibiting high chemical compatibility, but mechanical failures due to the reduced strength were prevalent. Our findings illustrate both the promise and current limitations of AM ceramics for actinide chemistry, and point toward future improvements in process optimization, design strategies, and part screening to enhance performance and reliability.

Materials science↗

A Computational Fluid Dynamic Study on Polymer Heat Exchangers

Polymer heat exchangers have been developed for the applications involving weight restrictions or chemical compatibility and fouling issues owing to the low density, anticorrosive properties, and low thermal expansion of polymers. Recently development of additive manufacturing also brings new opportunities to make polymer heat exchangers with desired design that was hard to realize before. However, due to the lower thermal conductivity polymer composite, the overall heat transfer performance is still a challenge in the polymer heat exchanger technology. In present work, a computational fluid dynamic (CFD) model has been developed to study the overall heat transfer performance of additively manufactured polymer heat exchangers. The CFD results offer an insight of fluid flow and temperature distribution in the polymer heat exchangers. This study provides a guidance not only on the polymer material selection but also on the design of polymer heat exchangers. The conclusions will be helpful to design a polymer heat exchanger whose overall heat transfer performance is comparable to a metal heat exchanger.

Zhang, Mingkan↗

DuPont Nomex 410 Datasheet

Nomex 410 is a type of electrical insulation paper that can be found in a large variety of electrical applications. It exhibits a combination of good thermal stability, mechanical toughness, abrasion resistance, dielectric strength, broad chemical compatibility, and flame resistance. Nomex 410 is a high-density variety of a broader class of Nomex insulation papers, which makes it suitable for applications where high mechanical resilience is more important than impregnability or saturability.

Pingree, Richard↗

Final report on assessment of molten salt corrosion testing of unirradiated and ion irradiated advanced manufactured high entropy alloys

Generation IV reactors and future fusion reactor designs have led to more demanding materials performance requirements due to their increased operating temperatures, corrosive coolants, and increased radiation doses compared to the current light-water reactor fleet. Among the innovative nuclear technologies under development, molten salt reactors stand out for their potential to offer superior fuel utilization, intrinsic safety characteristics, and economic viability. Of the proposed Generation IV designs, the gas fast reactor operates at 450 to 850°C and the molten salt reactor operates at 565 to 850°C, with the molten salt reactor design needing molten salt corrosion resistant materials [1, 2]. These increased temperatures and more extreme corrosion environments necessitate higher material performance, such as creep strength, radiation-tolerant microstructures, corrosion resistance, and high-temperature tensile properties. Hastelloy-N, a nickel-based alloy with additions of molybdenum and chromium, has been successfully employed to contain molten fluoride salt at temperatures up to 705°C. However, Hastelloy-N becomes embrittled upon neutron irradiation, primarily due to the accumulation of helium produced by (n,a) transmutation reactions. Furthermore, the corrosive nature of molten fluoride and chloride salts presents a formidable challenge, as these salts can react with and dissolve alloying elements such as Cr, Mo, and Fe, leading to selective leaching, loss of protective oxide layers, and accelerated degradation. High entropy alloys (HEAs) and refractory high entropy alloys (RHEAs) have emerged as a prominent area of interest, due to their ability to achieve tailored chemical compositions for specific applications. Unlike conventional alloys, HEAs are characterized by having multiple principal elements in equimolar or near equimolar ratios, leading to an unconventional alloying strategy [3]. This alloying strategy is believed to promote unique properties, such as single-phase stabilization of chemically compatible elements, lattice distortion effects due to atomic radius differences, and proposed sluggish diffusion effects. For extreme-environment applications, RHEAs have garnered much research interest because of the possibility of creating relatively ductile materials that can operate in extremely high-temperature environments, beyond the operating temperatures where other Ni-based superalloys begin to lose strength [4-6]. Idaho National Laboratory (INL) initiated a joint international effort with the Czech Republic to explore the feasibility of manufacturing HEAs for high-temperature nuclear applications using advanced manufacturing. This effort was funded at INL by the United States Department of Energy's Office of Nuclear Energy under the Advanced Reactor Technologies and Advanced Materials and Manufacturing Technologies (AMMT) Program. The HEAs were specifically designed for the corrosive and irradiation environments experienced in gas-cooled fast reactors, molten salt reactors, and fusion power. These alloys have been manufactured by multiple processes to determine the impact of manufacturing processes on the performance of the alloys in corrosive and irradiation environments. Preliminary molten salt corrosion testing showed that equimolar MoNbTiV and MoNbTi alloys exhibit exceptional performance, with arc-melted variants demonstrating only minimal degradation after 1000 hours of exposure to molten chloride salt at 700°C. Conversely, Nb2TiVZr2 showed significant molten salt corrosion susceptibility and microstructural instability during high-temperature molten salt exposures, and was, therefore deemed unfit for molten salt reactor applications. The MoNbTiV, MoNbTi, and Nb2TiVZr2 alloys were further evaluated through ion irradiation experiments conducted at the Michigan Ion Beam Laboratory at the University of Michigan. The microstructural stability and the evolution of irradiation-induced defects were characterized to assess the irradiation resistance of each of these alloys.

36 - MATERIALS SCIENCE↗

Chemical and Radiological Compatibility Testing of 3D Printed Materials

To dramatically increase the adaptability, performance, and safety of processes in support of the Defense Waste Processing Facility (DWPF), Savannah River National Lab (SRNL) plans to perform chemical and radiological compatibility testing on a wide variety of 3D printed materials of interest. The 3D printing process provides numerous strategic operational benefits such as rapid prototyping of complex designs and geometry specific to the needs of the nuclear waste disposition process, as well as on-demand rapid prototyping and iteration with materials that aren’t as accessible through traditional manufacturing methods. Reaction chemistry in simulated waste batches can be matched closely to its radioactive counterpart, but glass reactor vessels have limitations. Vessel geometry can play a big factor in mixing transport limitations, process chemistry, and degradation reaction kinetics. In addition, additive manufacturing allows for much more detailed vessel design than traditional alternatives. Waste processing techniques in DWPF also encounter extreme chemical environments including high pH, strong acids, abrasive slurries, and significant irradiation. To meet these challenges, a matrix of various polymer, ceramic, and metal additive manufacturing materials have been exposed to a suite of chemical environments of interest as well as radioactive dose (such as gamma radiation from 60 Co) to properly test their durability under these conditions. Mass change has been monitored over a period of up to a week in these conditions, as well as added characterization for surface modification through Scanning Electron Microscopy/Electron Dispersive X-ray analysis (SEM/EDX). Further chemical characterization has been monitored through Fourier-Transform InfraRed Spectroscopy (FTIR), with planned investigation via thermal and tensile strength degradation. While the direct product of this research is identification of material(s) that can withstand specific hazardous environments encountered by the mercury water wash tank in DWPF process simulation experiments, the reference base of materials will be used for many other nuclear processes in the pursuit of rapidly developed, cost-efficient, and highly specific devices for environmental remediation and much more.

Wilson, Nathan W. [Savannah River National Laborat↗

Predicting the chemical reactivity of organic materials using a machine-learning approach

Stability and compatibility between chemical components are essential parameters that need to be considered in the selection of functional materials in configuring a system. In configuring devices such as batteries or solar cells, not only the functionality of individual constituting materials such as electrodes or electrolyte but also an appropriate combination of materials which do not undergo unwanted side reactions is critical in ensuring their reliable performance in long-term operation. While the universal theory that can predict the general chemical reactivity between materials is long awaited and has been the subject of studies with a rich history, traditional ways proposed to date have been mostly based on simple electronic properties of materials such as electronegativity, ionization energy, electron affinity and hardness/softness, and could be applied to only a small group of materials. Moreover, prediction has often been far from accurate and has failed to offer general implications; thus it was practically inadequate as a selection criterion from a large material database, i.e. data-driven material discovery. Herein, we propose a new model for predicting the general reactivity and chemical compatibility among a large number of organic materials, realized by a machine-learning approach. As a showcase, we demonstrate that our new implemented model successfully reproduces previous experimental results reported on side-reactions occurring in lithium–oxygen electrochemical cells. Furthermore, the mapping of chemical stability among more than 90 available electrolyte solvents and the representative redox mediators is realized by this approach, presenting an important guideline in the development of stable electrolyte/redox mediator couples for lithium–oxygen batteries.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Cell design for laser-induced breakdown spectroscopy measurements on reactive gas samples

Uranium hexafluoride (UF 6 ) is the primary material used for the enrichment of uranium in the production of light water nuclear reactor fuels worldwide. Accurate, rapid quantification of uranium isotopic composition in nuclear materials is required for safeguards programs and nonproliferation purposes. One potential technique for isotopic measurements in uranium species in the field is laser induced breakdown spectroscopy (LIBS). Safe and effective application of LIBS to UF 6 for enrichment measurements is uniquely challenging due to the chemical and physical properties of UF 6 , which necessitate specific handling procedures. The objective of this work is to design a cell for isotopic analysis of UF 6 that is (1) compatible with chemical and physical properties of UF 6 , (2) compatible with LIBS laser, and (3) portable-sized for nuclear safeguards applications. Along with cell design, initial testing of the cell for basic performance and chemical compatibility is performed. As designed and constructed, the portable gas cell was gas-tight, chemically compatible with UF 6 , and withstood long-duration laser exposure. In this work, the cell has proven capability for handling reactive gasses, such as UF 6 , with specification application to isotopic analysis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗