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At least 487 records · Page 27
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Recovering Rare Earth Elements from Coal Mine Drainage Using Industrial Byproducts: Environmental and Economic Consequences

Coal mine drainage (CMD) impairs tens of thousands of kilometers of U.S. waterways each year, in part with the leaching of low concentrations of rare earth elements (REEs). REEs are essential for modern technologies, yet economically viable natural deposits are geospatially limited, thus engendering geopolitical concerns, and their mining is energy intense and environmentally destructive. This work summarizes laboratory-scale experimentalresults of a trap-extract-precipitate (TEP) process and uses the mass and energy balances to estimate the economic costs and environmental impacts of the TEP. The TEP process uses the alkalinity and filtering capacity of stabilized flue gas desulfurization (sFGD) material or water treatment plant (WTP) sludge to remediate CMD waters and extract REEs. Passive treatment systems that use WTP sludge are cheaper than those that use sFGD material ($\$$89,300/year or $\$$86/gT-REE vs. $\$$89,800/year or $\$$278/gT-REE) and have improved environmental performance across all indicators from two different impact assessment methods. These differences are largely attributable to the larger neutralizing capacity of WTP sludge in the treatment application.

01 COAL, LIGNITE, AND PEAT↗
DOE OSTI2022

Rare earth ion-adsorption clays in the presence of iron at basic pH: Adsorption mechanism and extraction method

In this work, the uptake mechanism and influence of iron (Fe) co-adsorption on the binding of rare-earth elements (REEs) on kaolinite have been investigated. REEs and varying concentrations of Fe were co-adsorbed onto kaolinite at pH 10.5. Inductively coupled plasma mass spectrometry (ICP-MS), powder X-ray diffraction (PXRD), and X-ray photoelectron spectroscopy (XPS) were used to characterize how Fe co-adsorption influenced the uptake mechanism of REEs on kaolinite. Elemental analysis by ICP-MS revealed that the REE concentrations on kaolinite were unaffected by the presence of Fe. Crystal structure of kaolinite, determined by PXRD, was not altered after REE and Fe co-adsorption. XPS suggests that the adsorbed Fe is in the form of FeOOH, while the greatly attenuated REE XPS signals upon Fe co-adsorption implies that REEs are encapsulated by Fe species. Based on these results, we conclude that FeOOH layers were formed on top of REEs on the surface of kaolinite. Synthesized REE-Fe-kaolinite samples respond poorly to ion-exchange leaching, indicating that Fe is detrimental to the REE ion-exchange efficiency. The inhibition of ion-exchange REE extraction appears to be due to the passivating FeOOH layers. In contrast to ion-exchange methods, reductive leaching was found to dissolve the FeOOH passivating layers and liberate REEs such that they became available for ion-exchange leaching.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

An ICP-OES method for the precise and accurate quantification of rare earth elements in natural water: A comparative study from mine waste sites in New Mexico, USA

Inductively coupled plasma techniques such as ICP-OES and ICP-MS are routinely used to determine the concentrations of rare earth elements (REE) in water samples. However, their performance for the determination of REE concentration in mine drainage waters from epithermal vein and porphyry copper mining districts has not been evaluated extensively. In this work, we develop an REE analysis method on an Agilent 5900 ICP-OES instrument and assess the accuracy and precision for the quantification of REE in the natural waters collected from mine adits and an acid seep of mine sites in the Steeple Rock and Hillsboro mining districts, New Mexico, USA. The total REE concentrations in the water samples were measured using the methods we developed for both ICP-OES and ICP-MS. The power of the new ICP-OES method lies in routine analysis of μg/L level concentrations normally analyzed using ICP-MS, including a U.S. Geological Survey standard reference sample, laboratory blank samples spiked with a National Institute of Standards and Technology traceable standard, and surface water samples from mine waste sites. This ICP-OES method achieves low quantification limits ranging from 0.2 to 5 μg/L and excellent analytical accuracy and precision for REE analysis. The precision of light (La-Gd) and heavy (Tb-Lu) REE analysis using this method are better than 5% at average concentrations above 5 ± 4 μg/L and 3 ± 2 μg/L, respectively, and 3% at average concentrations above 10 ± 9 μg/L and 5 ± 4 μg/L, respectively. This method also shows excellent sensitivity and reproducibility for our laboratory and field samples.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Impact of organic acids on extraction of rare earth elements: Mechanisms and optimization

Organic acids are increasingly recognized as an environmentally friendly and efficient selective leaching agent of critical minerals. However, their impact on subsequent extraction processes remains unclear. This study investigates the extraction behavior of rare earth elements (REEs), representative of critical minerals, in the presence of various organic acids, including citric acid, maleic acid, malonic acid, DL-malic acid, L(+)-tartaric acid, and L-ascorbic acid. The results show that organic acids slightly reduce the extraction of REEs but greatly increase the extraction of aluminum (Al³⁺), making it harder to separate REEs from other elements. To avoid this, it is best to keep organic acid concentrations as low as possible in practical applications. However, by optimizing extraction conditions, these negative effects can be minimized. Specifically, adjusting the contact time between solutions allows for efficient REE extraction while limiting unwanted aluminum extraction. Among the acids tested, malonic acid and L(+)-tartaric acid were found to be the most effective for selectively extracting REEs. Mechanistically, organic acids are likely to form complexes with REEs and D2EHPA during extraction, except for Y (III), offering practical guidelines for optimizing REE recovery. Beyond extraction, this study also highlights a way to recover organic acids by precipitating REEs from stripping solutions using oxalic acid, which adds both environmental and economic benefits. Furthermore, these findings provide useful insights for optimizing REE recovery and offer a reference for extracting other critical minerals from solutions containing organic acids.

D2EHPA↗
DOE OSTI2025

Synthesis of a series of rare-earth-based multi-anion chalcogenide iodides RE 3 Si 2 Se x S 8− x I (RE = La, Ce, Pr, and Nd) using the flux-assisted boron–chalcogen mixture method

Single crystals and polycrystalline powders of rare earth mixed chalcogenide iodides La 3 Si 2 Se 1.21 S 6.79 I, Ce 3 Si 2 Se 1.39 S 6.61 I, Pr 3 Si 2 Se 1.22 S 6.78 I, and Nd 3 Si 2 Se 1.18 S 6.82 I were prepared using the reactive flux-assisted boron–chalcogen mixture (BCM) method at 850 °C. All compounds crystallized in the monoclinic crystal system, space group C2/c (space group number 15). The series adopts the La 3 Si 2 O 8 Cl structure type, containing isolated SiQ 4 tetrahedra connected by REQ 8 (RE = La, Ce, Pr and Nd) polyhedra; this arrangement creates tunnels that are filled by I atoms. The partial substitution of S by Se was carried out to modulate the optical properties. Phase pure samples and uniform solid solutions were obtained for all compositions as determined using powder X-ray diffraction patterns. Polycrystalline powders were used for physical property measurements, including magnetic susceptibility and UV-Vis diffuse reflectance. The solid-state UV-Vis data for the polycrystalline La 3 Si 2 Se 1.21 S 6.79 I, Ce 3 Si 2 Se 1.39 S 6.61 I, and Pr 3 Si 2 Se 1.22 S 6.78 I samples revealed band gaps of E g = 2.5(1), 2.2(1), and 2.3(1) eV, typical of semiconductors. Magnetic measurements indicated that Ce 3 Si 2 Se 1.39 S 6.61 I and Nd 3 Si 2 Se 1.18 S 6.82 I exhibit paramagnetic behavior with slightly negative Weiss constants θ = −25 and −38. The photoluminescence spectrum of Ce 3 Si 2 Se 1.39 S 6.61 I exhibits a broad emission band around ∼493 nm.

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

Rare earth element separations by high-speed counter-current chromatography

We report that following the initial development of High-Speed Counter-Current Chromatography (HSCCC) in the 1960s, several studies have explored its applicability in the separation of rare earth elements (REEs). More recently, however, HSCCC publications have transitioned towards the separation of natural products or pharmaceuticals, leaving the application for REEs largely unexplored from a practical standpoint. Herein, we expand upon prior work in this field by evaluating the suitability of HSCCC to separation of a subset of non-radioactive REEs (Nd, Sm, Eu, Tb, and Y) at 10 -4 mol levels using di-(2-ethylhexyl)phosphoric acid (HDEHP) in n-heptane as the stationary phase and hydrochloric acid as the mobile phase. First, the effect of flow rate on the stationary phase volume retention ratio and resolution of Nd/Sm/Eu subgroup was evaluated followed by optimization of step-gradient elution profiles resulting in additional recovery of Tb and Y within a seven-hour window. The five REEs were separated at the baseline resolution level or above. Elution profiles obtained from multiple runs across two independently operated columns and across independent runs were cross analyzed. Reproducibility in elution profiles point to future applications in radioelement separation chemistry, where both chemical and radiochemical purity are of importance.

47 OTHER INSTRUMENTATION↗
DOE OSTI2025

Sorting rare earth magnets motors for recycling without opening the motors

Abstract A novel approach for sorting electric motors without dismantling them is reported in this article. This approach increases the likelihood that a motor selected from a mixture for recycling would contain rare earth elements (REEs), which are pivotal for numerous advanced green technologies. The challenge of inadvertently dismantling motors without REEs during recycling is addressed by this proposed innovative method. It relies on cogging interactions and power density for sorting motors with REEs. The process uses an algorithm introduced in this work to sort motors in two steps by (a) distinguishing induction motors from permanent magnet motors, and (b) distinguishing motors with critical REEs (e.g., Nd, Pr, Dy, Tb) from ferrite-based motors, all without opening the motors. The former was accomplished with 100% accuracy while the latter was accomplished with ~ 78% accuracy. Such high accuracy improves the recycling efficiency of critical REEs from motors, alleviating concern about supply disruption and supporting resource conservation and sustainability.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Design and Optimization of Processing Pathways for Rare Earth Element Recovery from End-of-Life Products

In this presentation, we first discuss the benefits of targeting end-of-life (EOL) products as a feedstock. We then discuss the problem statement of designing a processing facility for recovering rare earth elements (REEs) from EOL HDDs and motors from EOL EVs/HEVs. We then discuss the most profitable pathway, and then discuss the environmental impacts associated with the processing pathway, comparing it to a processing facility in China, and find it to have lower impacts overall. We also investigate the trade-off solutions for other pathways that are not as profitable, but have lower impacts by generating Pareto Fronts. In the next portion of the presentation, Critical Materials Recycling, Inc. is discussed. We discuss how their process was found to be the optimal pathway after performing superstructure optimization, and how we are currently working with them to further optimize their process to increase profits. Finally, we wrap up with conclusions summarizing the main takeaways of the presentation.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Pretreatment of Bituminous Coal By-Products for the Hydrometallurgical Extraction of Rare Earth Elements

Low-temperature plasma (LTP) oxidation has been widely used to study the mineralogy of the mineral matter existing in coal sources. The current study investigated the potential of LTP oxidation as a pre-treatment method to improve rare earth element (REE) leachability from coal and its by-products. Representative density-fractionated samples of Baker and Fire Clay coarse refuse seam materials were ground to a top size of 180 µm and subjected to low-temperature plasma oxidation. Subsequently, the treated samples were leached at 1% w/v solids concentration and 75 °C for 5 h using (i) de-ionized (DI) water, (ii) 0.1 mol/L of ammonium sulfate, and (iii) 1.2 mol/L of sulfuric acid. It was determined that LTP treatment improved REE leaching characteristics, especially the leaching of heavy REEs (HREE), existing in the lighter density fractions of the Baker seam coarse refuse material. For instance, the HREE recovery for the 1.6 specific gravity (SG) float fraction increased from 8% to 33% using 0.1 mol/L of ammonium sulfate solution after 32 h of LTP treatment. This finding indicated that HREEs associated with the organic matter were released by the LTP treatment and adsorbed onto the surfaces of highly negative charged mineral matter and was exchanged with ammonium to allow their recovery. Similarly, when using 1.2 mol/L of sulfuric acid, the HREE recovery increased from 23% to 53% for the 1.6 SG float fraction. Interestingly, LTP oxidation did not provide significant improvement in REE recovery from the 2.2 sink density fractions, which was likely due to its lower organic content. No significant benefits were observed when treating the Fire Clay coarse refuse material, which was likely due to the lack of organic affinity and the difficult-to-leach REE minerals associated with the coal source such as monazite, xenotime, and zircon. Conversely, high-temperature oxidation within a temperature range of 600–750 °C significantly improved REE leaching characteristics for both coal sources. Improvement in REE recovery was due to decarbonization of the material, clay dehydroxylation and subsequent conversion of liberated REE-bearing minerals into a more leachable form. However, increasing the temperature above 800 °C decreased REE recovery due to the conversion of meta-kaolinite into mullite, which is chemically stable.

58 GEOSCIENCES↗
DOE OSTI2024

Enhanced rare earth element recovery with cross-linked glutaraldehyde-lanthanide binding peptides in foam-based separations

Lanthanide Binding Tag (LBT) peptides that coordinate selectively with lanthanide ions can be used to replace the energy intensive processes used for the separation of rare earth elements (REEs). These surface-active biomolecules, once selectively complexed with the trivalent REE cations, can adsorb to air/aqueous interfaces of bubbles for foam-based REEs recovery. Glutaraldehyde, an organic compound that is a homobifunctional crosslinker for proteins and peptides, can be used to enhance the adsorption and interfacial stabilization of lanthanide-bound peptides films. The stability of the interfacial cross-linked films was tested by measuring their dilational and shear surface rheological properties. Surface activity of the adsorbed species was analyzed using pendant drop tensiometry, while surface density and molecular arrangement were determined using x-ray reflectivity and x-ray fluorescence near total reflection. Glutaraldehyde cross-linked REE-peptide complexes enhance the adsorption of lanthanides to air-water interfaces, resulting in thicker interfacial structures. Subsequently, these thicker layers enhance the dilational and shear interfacial rheological properties. The interfacial film stabilization and REEs extraction promoted by the cross-linker presented in this work provides an approach to integrate glutaraldehyde as a substitute of common foam stabilizers such as polymers, surfactants, and particles to optimize the recovery of REEs when using biomolecules as extractants.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Convenient Confinement: Interplay of Solution Conditions and Graphene Oxide Film Structure on Rare Earth Separations

Graphene oxide (GO) membranes are excellent candidates for a range of separation applications, including rare earth segregation and radionuclide decontamination. Understanding nanoscale water and ion behavior near interfacial GO is critical for groundbreaking membrane advances, including improved selectivity and permeability. Here, we experimentally examine the impact of solution conditions on water and lanthanide interactions with interfacial GO films and connect these results to GO membrane performance. The investigation of the confined films at the air–water interface with a combination of surface-specific spectroscopy and X-ray scattering techniques allows us to understand water and ion behaviors separately. Sum frequency generation spectroscopy reveals a dramatic change in interfacial water organization because of graphene oxide film deprotonation. Interfacial X-ray fluorescence measurements show a 17× increase in adsorbed lanthanide to the GO film from subphase pH 3 to pH 9. Liquid surface X-ray reflectivity data show an additional 2.7 $e^–$ per Å 2 for GO films at pH 9 versus pH 3 as well. These results are connected to GO membrane performance, which show increased selectivity and decreased flux for membranes filtering pH 9 solutions. We posit insoluble lanthanide hydroxides form at higher pHs. Taken together, these results highlight the importance of interfacial experiments on model GO systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Paramagnetic Properties of Rare Earth Hydroxides, Oxalates, and Dibutyl Phosphates

Magnetic separations present a promising approach for the recovery of rare earth (RE) elements from mixtures, particularly when coupled with precipitation techniques that enhance process efficiency and selectivity. However, the magnetic properties of RE materials typically encountered in the separations industry are not well characterized. Here, we synthesized a series of RE materials, combining four REs – praseodymium (Pr), neodymium (Nd), terbium (Tb), and dysprosium (Dy) – with three precipitating agents – hydroxide, oxalate, and dibutyl phosphate. All materials showed typical paramagnetic behavior consistent with the Curie-Weiss law. At low temperatures, we observed weak antiferromagnetic correlations, which were more pronounced for the lighter RE ions (Pr, Nd). Particle morphology and crystallography analyses showed that the dibutyl phosphates were well-ordered metal-organic frameworks, the oxalates were crystals with mixed hydration states, and the hydroxides were mostly amorphous. Regardless of the degree of crystallinity, the effective magnetic moments aligned well with theoretical estimates based on Hund's rules and 4f electron configurations of the corresponding RE ions. For a given RE ion, the magnetophoretic response was thus determined by the size of the particles rather than specific metal-ligand coupling, with dibutyl phosphate promoting the formation of larger crystals that were the most strongly attracted to magnets.

Wang, Qingpu (ORCID:0000000156041571)↗
DOE OSTI2025

Rare earth metals production using alternative feedstock that eliminates HF

This work reports the successful production of rare earth (RE) metal using Na-RE-F. Presently, RE metals are primarily produced using RE-fluoride due to its higher air and moisture stability compared to RE-chloride. However, its preparation requires the use of corrosive and hazardous chemicals, such as hydrofluoric acid (HF) or ammonium bifluoride (NH 4 HF 2 ). The present study demonstrates that Na-RE-F is an alternative salt to the typically used RE-fluoride. The Na-RE-F for this work is produced via a scalable hydrometallurgical approach using three different RE salts as feedstock, including acetate, nitrate, and chloride. HF is neither used nor generated during the salt preparation process. Furthermore, the Na-RE-F powder dries in air (without dry HF), and only water evolves during the drying process. Analyses of the Na-RE-F show that NaF liberates as a flux during the heating process, which lowers the salt reduction temperature to <900 °C, thus minimizing or eliminating the need for additional flux. Calciothermic reduction of the Na-RE-F salt is successfully employed to obtain RE metal. This work represents a safer, greener, and more widely deployable approach for producing the RE metals needed for permanent magnets which support the transition to a cleaner society through the decarbonization of the transportation industry.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Sustainable extraction of rare earth elements from coal fly ash leachates using a recyclable ionic liquid

The growing demand for rare earth elements (REEs) has prompted interest in their recovery from alternative sources such as coal fly ash (CFA). This study explores the ionic liquid (IL) betainium bis(trifluoromethylsulfonyl)imide, [Hbet][Tf 2 N], for selective extraction of REEs from leachates of a Class C CFA. While previous studies have demonstrated the effectiveness of using [Hbet][Tf 2 N] to extract REEs from different types of CFA in direct ash-IL systems, this study investigates four CFA leachates prepared using HCl, HNO 3 , H 2 SO 4 , and citrate. Extraction experiments were conducted across varying pH levels and with additives such as ascorbic acid and betaine. Among the systems tested, [Hbet][Tf 2 N] achieved REE recoveries of 51% and 47% from the HCl and citrate leachates, respectively, comparable to 49% REE recovery in ash-IL extraction. Co-extraction of bulk elements was significantly reduced in the leachate-IL systems. Optimal REE extraction occurred near pH 11, and addition of ascorbic acid effectively suppressed iron co-extraction without compromising REE recovery. Recycling experiments demonstrated that [Hbet][Tf₂N] retains its performance over five cycles with manageable losses. These results reveal the promise of [Hbet][Tf 2 N] for effectively recovering REEs from leachates of solid wastes, highlighting its applicability as a sustainable strategy for other aqueous REE feedstocks.

chemistry↗
DOE OSTI2023

Functionalized Mesoporous Carbon Materials for Effective Recovery of Rare Earth Elements from NdFeB Magnet Scrap

The increasing demand and high dependence on international supplies of rare earth elements (REEs) have prompted the US to explore alternative resources and sustainable technologies for domestic REE production. One potential resource is the secondary electronic and industrial wastes at DoD complexes and across the US. These hazardous wastes require high costs for the maintenance and remediation, but their high-REE contents offer unique opportunities for REE recovery. Current hydrometallurgical technologies for REE extraction are energy intensive and costly, with low REE recovery efficiency and the generation of hazardous secondary wastes. Thus, it is crucial to develop high efficiency and environmental-friendly technologies for REE extraction and recovery from the secondary wastes. This project aims to develop novel functionalized mesoporous carbon materials for effective recovery of REEs from NdFeB magnet scrap. The proposed novel functionalized materials will be applied in a solid-liquid separation platform that can effectively extract, recover and separate REEs from NdFeB magnet scrap (the current focus), but also from other secondary electronic/industrial wastes in the future, minimize the generation of secondary hazardous wastes, and offset the management costs for existing waste streams.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Bacterial Biomining Rare Earth Elements in Abandoned Coal Mine Drainage: Solubilization and Sequestration

Bacteria can be used to biomine rare earth elements (REEs) domestically from abandoned coal-mine drainage (AMD) solids. Pennsylvania has ~11,000 abandoned mines, with ~500 AMD passive remediation systems that precipitate AMD REE rich solids onsite. In passive systems, REEs, co-precipitate with manganese (Mn), accumulating as solids that can produce a valuable leachate when resolubilized. REEs like lanthanum (La) are used in battery technology. Microbial metabolic changes that co-resolubilize Mn and REEs could result in an affordable release process that does not require chemical additives and the select sequestering of REEs like La allow for the selective purification from a mixed REE composition. Currently, the microbial mechanisms that contribute to mass REE resolubilization and selective sequestration are poorly understood. We have isolated bacteria (Bacillus mycoides JR07 and Bacillus pseudomycoides KB7) that solubilize Mn oxide, La oxide, and AMD solids by acidogenesis. We have determined that isolates JR07 and KB7 solubilize the La from AMD PRS solids by their production of organic acids. Preliminary results show methylotrophic bacterial isolate B3 can take up soluble La(III), giving an avenue to purification of La from a rich REE leachate. Determining the microbial metabolism and genes involved in the mass resolubilization of REEs and selective biomining of La(III) is crucial to optimize the biomining of AMD solids. Our work addresses the growing need to develop novel REE recovery methods from domestic sources.

microbiology↗
DOE OSTI2020

Glass waste form options for rare-earth fission products from electrochemical reprocessing

Herein, we describe a first-of-a-kind study where lead tellurite (Pb-Te-O), iron phosphate (Fe-P-O), and lanthanide aluminoborosilicate (LABS) waste forms are evaluated for treating and/or immobilizing waste streams containing high rare-earth (RE) content, e.g., RECl 3 , REOCl, and/or REO x . Results from this study show that NdOCl can be immobilized in 78TeO 2 -22PbO glass at up to 10 mass%. Higher loadings of up to 15 mass% were demonstrated, but with a small fraction of crystallization. Two Fe-P-O glasses produced from either RECl 3 (RE = Nd,Ce) or NdOCl revealed products with very similar properties, demonstrating that the phosphate process can be used to chlorinate a variety of RE-containing waste streams. Two LABS glasses produced from Nd 2 O 3 or NdOCl showed similar properties, but the LABS-NdOCl glass did have some residual Cl present. Characterization is provided for all waste forms including chemical analysis, X-ray diffraction, and bulk density.

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

Discovery of Complex Binding and Reaction Mechanisms from Ternary Gases in Rare Earth Metal–Organic Frameworks

Understanding the selectivity of metal–organic frameworks (MOFs) to complex acid gas streams will enable their use in industrial applications. In this study, ab initio molecular dynamic simulations (AIMD) were used to simulate ternary gas mixtures (H 2 O-NO 2 -SO 2 ) in rare earth 2,5-dihydroxyterephthalic acid (RE-DOBDC) MOFs. Stronger H 2 O gas-metal binding arose from thermal vibrations in the MOF sterically hindering access of SO 2 and NO 2 molecules to the metal sites. Gas-gas and gas-linker interactions within the MOF framework resulted in the formation of multiple secondary gas species including HONO, HNO 2 , NOSO, and HNO 3 ⁻. Four gas adsorption sites were identified along with a new de-protonation reaction mechanism not observable through experiment. This study not only provides valuable information on competitive gas binding energies in the MOF, but it also provides important chemical insights into transient chemical reactions and mechanisms.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗