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At least 325 records · Page 18

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DOE OSTI2026

Scalable Upcycling of Spent Lithium-Ion Battery Anodic Graphite to Electronic-Grade Graphene

Recycling processes for lithium-ion batteries (LIBs) are imperative to support the sustainable growth of global energy storage systems. This study introduces a scalable method for the upcycling of spent graphite anodes from LIBs to produce electronic-grade graphene nanoplatelets. In addition to comprehensive materials characterization, the electronic quality of the upcycled graphene is demonstrated by formulating it into a screen printing ink that achieves high-resolution patterning and thin-film electrical conductivity exceeding 104 S m−1. This screen printing ink is also used to print planar micro-supercapacitors with exceptional areal capacitance (1.78 mF cm−2), areal energy density (0.247 µWh cm−2), and cycling stability (> 10 000 cycles). Life cycle assessment (LCA) and techno-economic analysis (TEA) highlight the environmental benefits and cost reductions attainable through upcycling of graphite from LIBs. By capturing economic value from spent LIBs, this work fosters a sustainable battery supply chain and provides an abundant and geographically distributed raw material for electronic-grade graphene.

energy storage↗

DOE OSTI2020

Direct Recycling of Spent NCM Cathodes through Ionothermal Lithiation

Ionic liquids (ILs) are a family of nonconventional molten salts that offer many advantages, such as negligible vapor pressures, negligible flammability, wide liquidus ranges, good thermal stability, and much synthesis flexibility. The unique solvation environment of these ILs provides new reaction or flux media for controlling formation of solid-state materials with a minimum perturbation of morphologies. A successful lithiation via ionothermal synthesis using a cost-effective Li halide as Li source and recyclable ILs as solvents is reported in this study for the direct recycling of LiNi 1/3 Co 1/3 Mn 1/3 O 2 (NCM 111) cathodes. In addition, the ionic liquids can be readily recycled and reused after ionothermal lithiation. The lithiation of spent cathodes can enable the direct recycling of spent cathode materials in lithium-ion batteries.

25 ENERGY STORAGE↗

DOE OSTI2013

Geant4 Model Validation of Compton Suppressed System for Process monitoring of Spent Fuel

Nuclear material accountancy is of continuous concern for the regulatory, safeguards, and verification communities. In particular, spent nuclear fuel reprocessing facilities pose one of the most difficult accountancy challenges: monitoring highly radioactive, fluid sample streams in near real-time. The Multi-Isotope Process monitor will allow for near-real-time indication of process alterations using passive gamma-ray detection coupled with multivariate analysis techniques to guard against potential material diversion or to enhance domestic process monitoring. The Compton continuum from the dominant 661.7 keV 137Cs fission product peak obscures lower energy lines which could be used for spectral and multivariate analysis. Compton suppression may be able to mitigate the challenges posed by the high continuum caused by scattering. A Monte Carlo simulation using the Geant4 toolkit is being developed to predict the expected suppressed spectrum from spent fuel samples to estimate the reduction in the Compton continuum. Despite the lack of timing information between decay events in the particle management of Geant4, encouraging results were recorded utilizing only the information within individual decays without accounting for accidental coincidences. The model has been validated with single and cascade decay emitters in two steps: as an unsuppressed system and with suppression activated. Results of the Geant4 model validation will be presented.

Bender, Sarah↗

DOE OSTI2018

Recovery of Platinum Group Metals from Spent Catalysts Using Iron Chloride Vapor Treatment

The recovery of platinum group metals (PGMs) from spent automobile catalysts is a difficult process because of their relatively low contents in the scrap. In this study, to improve the efficiency of the existing recycling techniques, a novel physical concentration method involving treatment with FeCl{sub 2} vapor has been examined. The reactions occurring between typical catalyst components and FeCl{sub 2} vapor are discussed from the thermodynamic point of view, and the validity of the proposed technique was experimentally verified. The obtained results indicate that the vapor treatment at around 1200 K (927 °C) can effectively alloy PGMs (Pt, Pd, and Rh) with Fe, resulting in the formation of a ferromagnetic alloy. It was also confirmed that cordierite and alumina (the major catalyst components) remained unreacted after the vapor treatment, while ceria species were converted into oxychlorides. The samples simulating the automobile catalyst were also subjected to magnetic separation after the treatment with FeCl{sub 2} vapor; as a result, PGMs were successfully extracted and concentrated in the form of a magnetic powder. Thus, the FeCl{sub 2} vapor treatment followed by magnetic separation can be utilized for recovering PGMs directly from spent catalysts as an effective pretreatment for the currently used recycling methods.

36 MATERIALS SCIENCE↗

DOE OSTI2018

Soluble Graphene Nanosheets from Recycled Graphite of Spent Lithium Ion Batteries

Soluble graphene nanosheets are fabricated from recycled graphite of spent lithium ion batteries through a modified Hammers process followed by deoxygenation with NaOH–KOH eutectic. Ultrasonic exfoliation in N-methyl-pyrrolidone indicates the loosened graphene layers in recycled graphite are prone to exfoliation. Reduction of the exfoliated graphene oxide sheets was conducted in molten NaOH–KOH eutectic at different temperatures. The results show that molten NaOH–KOH effectively eliminates the unsaturated oxygen-containing moieties from the exfoliated graphene oxide sheets while creating more hydroxyl functional groups. Higher temperature treatment is more prone to remove hydroxyls while producing the shrinkage on the surface of graphene sheets. Graphene sheet with a good solubility is produced when the graphene oxide is heat-treated at 220 °C for 10 h. After reduction, the graphene oxide sheets exhibit excellent dispersibility or solubility in water, ethanol and other polar solvents, therefore being highly desirable for solution processing of graphene materials. Such study not only identifies a high-quality stockpile to prepare soluble graphene but also paves a feasible alternative of graphite recycling from spent lithium batteries.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Hydrometallurgical Recycling of Black Mass of Spent Lithium-Ion Batteries Using Methanesulfonic Acid: Leaching, Kinetic Studies, and Potential for Total Recovery of Valuable Components

Methanesulfonic acid (MSA) exhibits several advantageous properties rendering it a promising candidate for circular hydrometallurgical processes. These properties include a high acidity (pKa = - 1.9) comparable to that of classical mineral acids as well as biodegradability, high stability, and high solubility of metal-MSA complexes in aqueous solutions. In this study, MSA was employed as a lixiviant for the leaching of metals (lithium, nickel, cobalt, and manganese) from the black mass of spent lithium-ion batteries (LIBs). The effect of various parameters, including MSA concentration, H 2 O 2 concentration, temperature, and pulp density, was systematically investigated. Under the optimized conditions (1.5 M MSA, 0.2 M H 2 O 2 , 60 °C, and 50 g/L pulp density), quantitative leaching of lithium was achieved within 30 min, while for nickel and cobalt it was after 2 h, and 4 h for manganese leaching. The leaching kinetics of Li, Ni, Co, and Mn were studies using the shrinking particle models (SPM) and the Avrami model. The results indicated that the Avrami model provided the best fit to the kinetic data, with apparent activation energies of 46.81 kJ/mol for Li, 58.61 kJ/mol for Ni, 59.69 kJ/mol for Co, and 58.86 kJ/mol for Mn, within the temperature range of 25-70 °C (except for Li, which was analyzed in the range of 25-60 °C), consistent with chemical reaction control. Subsequently, residual contaminants in the leaching residue were eliminated through pyrolysis. The quantitative leaching of metals in MSA solution (a green lixiviant), combined with the pyrolytic treatment of leaching residues, represents a circular strategy for the total recovery of valuable components from the black mass of spent LIBs.

25 ENERGY STORAGE↗

DOE OSTI2024

Scale effects on core design, fuel costs, and spent fuel volume of pressurized water reactors

The desire to improve the economic competitiveness and deployment pace of nuclear energy through modularization, manufacturing, and series production had led to the development of smaller size reactors. As the standard 17x17 fuel technology is mainly maintained in the pressurized water reactors (PWRs) category, this translates into a lower number of fuel assemblies in the core and sometimes a reduced fuel height. To assess the impact of such scale change in core design on fuel cycle cost and spent fuel volume, a scoping analysis tool is developed based on infinite lattice calculations, leakage, fuel management reduced models, and levelized unit cost of electricity (LCOE) estimate. As such, cost dynamics driven by fuel specific power, burnup, core leakage, feed, cycle length, fuel assembly height as well as uranium market data are captured with consistent set of assumptions and analysis methods. A selection of 5 reactor designs representative of leading PWR developers is assessed and compared. Pursuing higher specific powers and optimal burnups are highlighted as the main fuel cost reduction drivers, nevertheless, practical limitations and opportunities must be evaluated to establish the feasibility of such enhanced fuel operation. In consequence, a detailed core design is performed using SIMULATE3 code for 5 PWR variations including natural and forced coolant circulation modes, two reactor scales, power densities of 73, 112, and 123 kW/l and higher discharge burnups. Design and optimization are performed at the lattice level, for the reflector, and at the core loading level. Satisfactory steady-state operation including power distribution, coolant operating limits, and reactivity requirements are analyzed and reported in this paper. The fuel economics of the detailed core designs confirm the scoping analysis findings. Despite the unlocked power uprates in small PWRs, the achievable burnup for a given fuel specific power requires more enrichment and shorter fuel height results in higher fabrication costs per mass of fuel, which makes scaling down core size a more expensive endeavor on the fuel cycle front. Spent fuel volumes are reported for the PWRs designed in this paper. Furthermore, these volumes are driven by the core average discharge burnup regardless of the scale in consideration. Additional cost and core performance aspects related to heavy reflector gains, fuel-reflector substitution, and disposal cost policy in the U.S. are examined.

42 ENGINEERING↗

DOE OSTI2022

Oxidation of glucose to glycolic acid using oxygen and pyrolyzed spent Li-ion battery electrode material as catalyst

A search for non-noble catalysts for biomass processing led to the discovery that pyrolyzed electrode coating of spent Li-ion batteries can be used as an excellent catalyst for oxidation of D-glucose to glycolic acid. New no/low-cost catalyst was prepared by pyrolyzing black electrode coatings of 18,650 Li-ion cells from a spent DELL 1525 laptop battery at 600 ºC. Catalyst was characterized using SEM, EDX and X-ray and was shown to contain lithium nickel manganese cobalt oxide (Li a Ni b Mn c Co d O e ) on carbon with Ni: Mn: Co 4.12: 2.10: 1.50. Here, the catalytic activity of this material was evaluated for oxidation of D-glucose in aq. NaOH and water; glycolic, tartaric, malic, succinic and 2-hydroxybutaric acid were identified as key degradation products. The highest glycolic acid yield of 94% was obtained for oxidation of D-glucose under 3.4 Atm. oxygen, 120 °C, 2.0 h in 0.5 M aq. NaOH using 10 g catalyst/mol glucose.

25 ENERGY STORAGE↗

DOE OSTI2024

Progress in direct recycling of spent lithium nickel manganese cobalt oxide (NMC) cathodes

With the widespread use of lithium-ion batteries (LIBs) in portable electronics and electric vehicles (EVs), the end-of-life (EOL) LIBs are projected to reach 1336 GWh by 2040 under the sustainable development scenario. Proper recycling is urgently needed to minimize the release of hazardous waste and reduce mining activities by reintroducing critical minerals into the supply chain. Lithium nickel manganese cobalt oxide (LiNi x Mn y Co z O 2 , NMCs) cathodes have become dominant in the LIB market, especially with the increasing production of EVs, which are also the most valuable components in EOL LIBs. Unlike pyrometallurgical and/or hydrometallurgical methods, which convert spent NMCs into metals or metal compounds, direct recycling technologies aim to maximize the value of spent cathodes by restoring their degraded structure and composition. Furthermore, this review summarizes direct recycling methods for NMC cathodes published in the last decade and provides insights into the challenges and future development of direct recycling techniques.

Cathode↗

DOE OSTI2025

Upcycling Mixed Spent Ni-Lean Cathodes into Ni-Rich Polycrystalline Cathodes

Sustainable battery recycling is vital for conserving resources and reducing environmental impacts. Current open- and closed-loop recycling strategies often focus on recovering individual components, making the reuse of mixed cathode materials a complex challenge. Meanwhile, the research on upcycling has been limited to using pristine cathode feedstocks and virgin materials for synthesis. Here, to address this issue, we present an upcycling approach for spent Ni-lean mixed cathode materials that integrate an upcycling hydrometallurgical recycling process with traditional hydrometallurgical methods. This strategy achieves a utilization of 92.31 mol % of recycled materials, enabling the regeneration of Ni-rich cathode materials while significantly reducing the reliance on virgin resources. The regenerated 83Ni cathode materials demonstrate physical properties comparable to those produced from virgin materials. Electrochemical evaluations using single-layer pouch cells show that both recycled and virgin cathodes exhibit initial specific capacity close to 201.1 mAh/g and maintain approximately 88 % capacity retention after 500 cycles. Additionally, 2Ah cells confirmed these findings, delivering 85 % capacity retention after about 900 cycles. Techno-economic analysis demonstrates notable environmental benefits, including reductions in greenhouse gas emissions and energy consumption, achieving 232.75 MJ/kg of product, which is 8.6 % lower than traditional methods and comparable to direct upcycling. Furthermore, the upcycling hydrometallurgical recycling process generates the highest profit, proving its economic viability. This scalable and versatile process is adaptable to varying transition metal compositions, facilitating a closed-loop recycling system that bridges mixed spent cathodes with next-generation cathode materials, and offers a sustainable solution for managing waste battery materials.

Hydrometallurgical recycling↗

DOE OSTI2017

Helium interactions with alumina formed by atomic layer deposition show potential for mitigating problems with excess helium in spent nuclear fuel

Helium gas accumulation from alpha decay during extended storage of spent fuel has potential to compromise the structural integrity the fuel. We report results obtained with surrogate nickel particles which suggest that alumina formed by atomic layer deposition can serve as a low volume-fraction, uniformly-distributed phase for retention of helium generated in fuel particles such as uranium oxide. Thin alumina layers may also form transport paths for helium in the fuel rod, which would otherwise be impermeable. Micron-scale nickel particles, representative of uranium oxide particles in their low helium solubility and compatibility with the alumina synthesis process, were homogeneously coated with alumina approximately 3–20 nm by particle atomic layer deposition (ALD) using a fluidized bed reactor. Particles were then loaded with helium at 800 °C in a tube furnace. Subsequent helium spectroscopy measurements showed that the alumina phase, or more likely a related nickel/alumina interface structure, retains helium at a density of at least 10 17 atoms/cm 3 . High resolution transmission electron microscopy revealed that the thermal treatment increased the alumina thickness and generated additional porosity. Results from Monte Carlo simulations on amorphous alumina predict the helium retention concentration at room temperature could reach 10 21 atoms/cm 3 at 400 MPa, a pressure predicted by others to be developed in uranium oxide without an alumina secondary phase. This concentration is sufficient to eliminate bubble formation in the nuclear fuel for long-term storage scenarios, for example. Finally, measurements by others of the diffusion coefficient in polycrystalline alumina indicate values several orders of magnitude higher than in uranium oxide, which then can also allow for helium transport out of the spent fuel.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2025

In-situ ion irradiation induced nanograin growth in a spent UO 2 fuel

This study investigates the irradiation-driven evolution of nanograins in the early-stage restructured rim region of medium burnup spent uranium dioxide (UO 2 ) fuel. Transmission electron microscopy (TEM) lamellas prepared from Belgium Reactor 3 (BR-3) fuel were subjected to in-situ 300 keV Xe ion irradiations under varying doses, fluxes, and temperatures to evaluate their effect on the evolution of the nanograins. Our results reveal that the nanograins grow during ion irradiation. Additionally, the growth is most pronounced at elevated temperatures (300 °C), moderate at room temperature, and negligible at cryogenic temperature (−223 °C). This behavior indicates that thermal activation, alongside irradiation effects, is essential to overcome grain boundary pinning by fission gas bubbles, metallic precipitates, and porosity. Furthermore, while nanograins (<200 nm) consistently coarsened under irradiation, larger grains did not undergo further restructuring, which can be attributed to the strong defect annihilation at TEM lamella surfaces combined with the limited electronic stopping power of low energy Xe ions used in this work. These findings highlight the roles of thermal spike effects, defect mobility, and impurity pinning in governing grain evolution in the rim region of spent UO 2 fuel during ion irradiation, providing key insights for predictive models of restructuring and performance of the high burnup nuclear fuel.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2018

Structural, optical and photocatalytic properties of zinc oxides obtained from spent alkaline batteries

Highlights: • Zinc oxides were synthetized using spent alkaline batteries as raw materials. • Both prepared samples present the wurzite structure and exhibits good optical properties. • The decrease in lattice parameters and the narrow band gap are associated with the formation of oxygen vacancies. • Recovered zinc oxides were active for photodegradation of methylene blue by UV irradiation. • The photocatalytic was correlates to the bulk/surface defects ratio. - Abstract: The structural, optical and photocatalytic properties of two zinc oxides prepared from spent alkaline batteries were analysed. After leaching the anode of alkaline batteries, zinc was precipitated from the leachate liquor by introducing oxalic acid (O-ZnO) or sodium carbonate (C-ZnO). The structure of ZnO samples were analysed by X-ray diffraction (XRD), scanning electron microscopy (SEM), transmission electron microscopy (TEM), S{sub BET}, DRS-UV-vis spectroscopy and positron annihilation lifetime spectroscopy (PALS). Both oxides present the ZnO wurzite structure and similar morphology. C-ZnO presents a cell lower lattice parameters and bang gap energy (2.99 eV) than O-ZnO (3.05 eV), possibly due to higher concentration of oxygen vacancies. The photocatalytic activity in the degradation of methylene blue (MB) of O-ZnO (achieving 70% MB degradation at 90 min) was superior to C-ZnO, due to its higher surface area and degree of crystallinity and lower bulk/surface defects ratio.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Life-cycle analysis of battery metal recycling with lithium recovery from a spent lithium-ion battery

Demand for critical materials (nickel, cobalt, manganese [NCM], and lithium) for use in batteries is increasing rapidly due to the expansion of the battery-electric vehicles market. Battery metal recycling (BMR) is an important technology that can potentially realize environmental and economic benefits in cathode active material (LiNi x Mn y Co z O 2 ) production using recycled materials. While current major battery recycling technologies recover cathode materials (NCM) and other metals (steel, aluminum, copper, etc.) from the spent battery, the lithium (Li) recovery rate is less than 1% in the world. In this study, we analyze the environmental benefits of a BMR process that recovers lithium in the form of lithium hydroxide monohydrate (LiOH∙H 2 O) along with other cathode materials. Using life-cycle analysis (LCA), we evaluate the life-cycle greenhouse gas (GHG) emissions, criteria air pollutant emissions, and water consumption of the new BMR technology in terms of lithium hydroxide production and cathode active material production. The LCA results show that the life-cycle GHG emissions recycled LiOH are 37–72% lower than those of virgin LiOH production from Chilean brine and Australian ore, respectively. In addition, the life-cycle GHG emissions of NCM811 produced using the recycled materials are 40–48% lower compared to virgin cathode active material production. Furthermore, recovering lithium from the spent batteries reduces associated air pollutant emissions and water consumption relative to using the virgin materials or materials from other recycling technologies without LiOH recovery.

25 ENERGY STORAGE↗

DOE OSTI2022

Electrification and decarbonization of spent Li-ion batteries purification by using an electrochemical membrane reactor

The expanding electric vehicle market brings with it exponential growth in the use of lithium (Li)-ion batteries (LIB) for which a wave of spent LIB is expected to come within the next 5 to 10 years. Due to the economic and strategic value imbedded within the metals contained in LIB, different recycling technologies, including hydrometallurgy, pyrometallurgy and direct recycling, are under development. Being different from previous hydrometallurgical methods, which may have high chemical consumption and negative environmental impact, an electrochemical membrane reactor is designed and validated for the first time, to electrify and decarbonize the impurity removal process. This reactor electroplates copper (Cu) and electrochemically precipitates aluminum (Al) and iron (Fe) from simulated spent LIB leachates, by consuming only air, water, and electricity, and the impurities are reduced to <1 ppm. The purified leachate maintains 99.5 % of the nickel (Ni), 95.4 % of the cobalt (Co) and 99.14 % of manganese (Mn) from the original leachate solution, and then can be directly applied for cathode precursor synthesis. Additionally, the purification process doesn’t introduce extra impurity, and the reactor restoration process generates valuable by-product hydro sulfate (H2SO4). This electrochemical process can reduce the cost, because of the much less chemical consumption and the valuable by-product generation, and mitigates the waste emissions, because of no extra impurity introduced and no greenhouse gas (GHG) produced. In conclusion, the chemical precipitation method uses significant amount of NaOH, which induced GHG emission during the manufacturing process.

25 ENERGY STORAGE↗

DOE OSTI2024

Actinide Elemental Ratios of Spent Nuclear Fuel Samples by Resonance Ionization Mass Spectrometry

While resonance ionization mass spectrometry (RIMS) has demonstrated utility in measuring isotopic compositions of elements in complex matrices without the need for chemical separation to remove isobaric interferences, it has had limited application in measuring elemental compositions. The ability to determine elemental compositions via an in situ method like RIMS would be an exceptional asset in spent nuclear fuel analysis, where they are important in assessing reactor histories and whose chemical separation presents a radiological hazard. However, quantitative elemental analysis by RIMS requires special considerations because each element is ionized by its own set of lasers tuned to element specific resonant ionization wavelengths. We present the first comprehensive study of measuring elemental ratios by RIMS in spent nuclear fuel. All actinides produced by neutron capture are enhanced significantly radially from the center to the edge of a fuel pellet. This edge effect is not readily accessible by conventional bulk measurements.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2024

Characterization of spent nuclear fuel canister surface roughness using surface replicating molds

In this study we present a replication method to determine surface roughness and to identify surface features when a sample cannot be directly analyzed by conventional techniques. As a demonstration, this method was applied to an unused spent nuclear fuel dry storage canister to determine variation across different surface features. In this study, an initial material down-selection was performed to determine the best molding agent and determined that non-modified Polytek PlatSil23-75 provided the most accurate representation of the surface while providing good usability. Other materials that were considered include Polygel Brush-On 35 polyurethane rubber (with and without Pol-ease 2300 release agent), Polytek PlatSil73-25 silicone rubber (with and without PlatThix thickening agent and Pol-ease 2300 release agent), and Express STD vinylpolysiloxane impression putty. The ability of PlatSil73-25 to create an accurate surface replica was evaluated by creating surface molds of several locations on surface roughness standards representing ISO grade surfaces N 3 , N 5 , N 7 , and N 8 . Overall, the molds were able to accurately reproduce the expected roughness average (R a ) values, but systematically over-estimated the peak-valley maximum roughness (R z ) values. Using a 3D printed sample cell, several locations across the stainless steel spent nuclear fuel canister were sampled to determine the surface roughness. These measurements provided information regarding variability in normal surface roughness across the canister as well as a detailed evaluation on specific surface features (e.g., welds, grind marks, etc.). The results of these measurements can support development of dry storage canister ageing management programs, as surface roughness is an important factor for surface dust deposition and accumulation. This method can be applied more broadly to different surfaces beyond stainless steel to provide rapid, accurate surface replications for analytical evaluation by profilometry.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2022

A green closed-loop process for selective recycling of lithium from spent lithium-ion batteries

As the economy started to recover from the COVID pandemic, the price of Li 2 CO 3 skyrocketed to its highest. This situation has aggravated concerns about the supply chain for lithium-ion batteries (LIBs). Recycling spent LIBs is a potential solution to alleviate the bottleneck of the supply chain and prevent environmental pollution, and has attracted lots of attention. However, lithium recycling is generally disregarded because of the complex recycling process and its low recycling efficiency. Here, in this work we developed a sustainable lithium recovery process, which can selectively leach and recover lithium with formic acid before recycling valuable metals. With the reported method, lithium can be 99.8% recovered from layered oxide cathode materials with 99.994% purity. In addition, this lithium recovery process is affordable, compared to the typical hydrometallurgical process, by saving 11.15% per kilogram of spent LIBs. Therefore, this research provided a new solution to eliminating the effects of lithium ions on valuable metal separation and the co-precipitation reaction and precluding the influence of other metal ions on lithium recovery. Finally, this simplified lithium recovery process provides new opportunities for sustainable recycling of LIBs and economical restoration of the lithium supply chain.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗