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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

High pO2 Flux Growth and Characterization of NdNiO3 Crystals

Single crystals of the perovskite nickelate NdNiO3 with dimensions of up to 50 μm on edge have been successfully grown using the flux method at a temperature of 400 °C and oxygen pressure of 200 bar. The crystals were investigated by a combination of techniques, including high-resolution synchrotron X-ray single-crystal and powder diffraction and physical property measurements such as magnetic susceptibility and resistivity. Resistivity measurements revealed a metal-insulator transition (MIT) at TMIT~180 K with apparent thermal hysteresis; however, no superlattice peaks or peak splitting below TMIT, which corresponds to a structural transition from Pbnm to P21/n, was observed. The successful growth of NdNiO3 crystals at relatively low temperatures and oxygen pressure provides an alternative approach for preparing single crystals of interesting perovskites such as RNiO3 (R = Sm-Lu) and parent phases of superconducting square planar nickelates.

Wang, Xiaoli↗
DOE OSTI2022

Energy dispersive x-ray diffraction of luminescent powders: A complement to visible phosphor thermometry

Energy-dispersive x-ray diffraction of thermographic phosphors has been explored as a complementary temperature diagnostic to visible phosphor thermometry in environments where the temperature-dependent optical luminescence of the phosphors is occluded. Powder phosphor samples were heated from ambient to 300°C in incremental steps and probed with polychromatic synchrotron x rays; scattered photons were collected at a fixed diffraction angle of 3.9°. Crystal structure, lattice parameters, and coefficients of thermal expansion were calculated from the diffraction data. Finally, of the several phosphors surveyed, YAG:Dy, ZnO:Ga, and GOS:Tb were found to be excellent candidates for diffraction thermometry due to their strong, distinct diffraction peaks that shift in a repeatable and linear manner with temperature.

47 OTHER INSTRUMENTATION↗
DOE OSTI2022

All-Inorganic Open-Framework Chalcogenides, A 3 Ga 5 S 9 · x H 2 O ( A = Rb and Cs), Exhibiting Ultrafast Uranyl Remediation and Illustrating a Novel Post-Synthetic Preparation of Open-Framework Oxychalcogenides

Fast and effective uranyl sequestration is of interest to the nuclear industry. Recently layered chalcogenide materials have demonstrated fast, selective, and efficient sorption properties towards uranyl cations and the development and investigation of new types of chalcogenide materials continues to be of interest and represents an intriguing option for uranyl remediation. Three new all-inorganic A 3 Ga 5 S 9 ·xH 2 O (A = Rb, Rb/Cs, and Cs) open-framework chalcogenides were obtained via an in-situ alkali carbonate to alkali sulfide conversion process achieved under mild hydrothermal conditions. The structures of the all-inorganic open framework chalcogenides consist of a 2-fold interpenetrated diamond-like 3D framework containing pseudo-T 3 [Ga 10 S 20 ] 10– supertetrahedra. 48% of the structural volume is occupied by A + cations and water species, as established by single-crystal X-ray diffraction (SCXRD), infrared (IR) and energy-dispersive (EDS) spectroscopies. The dynamic nature of the A + cations and water molecules within the pores was investigated via single crystal X-ray diffraction as well as by IR spectroscopy monitored H 2 O to D 2 O exchange experiments. Framework stability was probed with post-synthetic treatment of A 3 Ga 5 S 9 ·xH 2 O (A = Rb and Cs) samples in acidic solutions that resulted in the formation of the oxysulfide (A/H) 3 Ga 5 S 9–y O y ·xH 2 O (A = Rb and Cs; y = 0–1), as shown by SCXRD and IR. Ion-exchange studies on A 3 Ga 5 S 9 ·xH 2 O (A = Rb and Cs) samples were carried out utilizing a uranyl acetate solution. The presence of the UO 2 2+ species in the ion-exchanged product was supported by IR and EDS spectroscopies. Batch method ion-exchange experiments on Cs 3 Ga 5 S 9 ·xH 2 O powder demonstrated fast kinetics with 95% uranyl removal from the uranyl acetate solution during the first minute, a maximum uranyl uptake capacity of 15mg/g, and the subsequent elution of uranyl species with KCl solution. Furthermore, the porous and dynamic nature of the A 3 Ga 5 S 9 ·xH 2 O framework coupled with effective UO 2 2+ ···S 2– bonding interactions makes it a good potential sorbent for uranyl remediation from aqueous media.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Thermal loading on self-seeding monochromators in x-ray free electron lasers

One approach to achieve longitudinally coherent hard X-ray free electron laser (XFEL) radiation is to introduce a single-crystal monochromator in the beam path to generate a co-propagating, time-synchronized self-seeding radiation pulse. For modern high-repetition rate XFELs, however, thermal loading on the crystal can degrade the quality of the seed pulse. To assess limitations on the maximum XFEL pulse repetition rate imposed by the seeding crystal, a comprehensive study of thermomechanical, and X-ray diffraction effects within the crystal is presented in this paper for two consecutive self-amplified spontaneous emission pulses incident on both reflective and transmissive crystal monochromators.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2021

Structural, Vibrational, and Electronic Properties of 1D-TlInTe 2 under High Pressure: A Combined Experimental and Theoretical Study

Analogous to 2D layered transition-metal dichalcogenides, the TlSe family of quasi-one dimensional chain materials with the Zintl-type structure exhibits novel phenomena under high pressure. In the present work, we have systematically investigated the high-pressure behavior of TlInTe 2 using Raman spectroscopy, synchrotron X-ray diffraction (XRD), and transport measurements, in combination with first principles crystal structure prediction (CSP) based on evolutionary approach. We found that TlInTe2 undergoes a pressure-induced semiconductor-to-semimetal transition at 4 GPa, followed by a superconducting transition at 5.7 GPa (with T c = 3.8 K). An unusual giant phonon mode (A g ) softening appears at ~10–12 GPa as a result of the interaction of optical phonons with the conduction electrons. The high-pressure XRD and Raman spectroscopy studies reveal that there is no structural phase transitions observed up to the maximum pressure achieved (33.5 GPa), which is in agreement with our CSP calculations. In addition, our calculations predict two high-pressure phases above 35 GPa following the phase transition sequence as I4/mcm (B37) → Pbcm → Pm$\bar{3}$m (B2). Electronic structure calculations suggest Lifshitz (L1 & L2-type) transitions near the superconducting transition pressure. Furthermore, our findings on TlInTe 2 open up a new avenue to study unexplored high-pressure novel phenomena in TlSe family induced by Lifshitz transition (electronic driven), giant phonon softening, and electron–phonon coupling.

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

Crystal Structures, Optical Behavior, and Magnetic Properties in Hydrated Lanthanide Iron Sulfates

Single crystals of LnFe(SO 4 ) 3 (H 2 O) 2 (Ln = La, Ce, Pr, Nd, Sm, Eu, Gd, Dy, Ho, Er, Tm; compounds 1–11) and LnFe(SO 4 ) 3 (H 2 O) (Ln = Tm, Yb, Lu; compounds 12–14) were synthesized under hydrothermal conditions. Single-crystal X-ray diffraction (SCXRD) analysis revealed that the dihydrated compounds (1–11) crystallize in centrosymmetric (CS) structures, with the lanthanide ions adopting eight-coordinate geometries. In contrast, the monohydrated compounds (12–14) exhibit noncentrosymmetric (NCS) structures, where the lanthanide ions are seven-coordinated. Vibrating sample magnetometry (VSM) confirmed that compounds 2, 4, and 7–11 are paramagnetic below 400 K, with compound 8 displaying the highest magnetic susceptibility. Compounds 1, 5, 6, 13, and 14 show a sharp increase in magnetic susceptibility at Néel temperatures ( T N ) of approximately 72, 76, 70, 58, and 56 K, respectively, indicating antiferromagnetic ordering. High-temperature magnetic susceptibility measurements further support the presence of antiferromagnetic transitions in these compounds. Second harmonic generation (SHG) measurements showed that the noncentrosymmetric Yb (compound 13) and Lu (compound 14) compounds exhibit SHG intensities of 0.3× and 1.6× that of potassium dihydrogen phosphate (KDP), respectively.

anions↗
DOE OSTI2020

Li 4 Ru 2 OCl 10 ·10H 2 O: crystal structure, magnetic properties and bonding interactions in ruthenium-oxo complexes

The results of the structural determination, magnetic characterization, and theoretical calculations of a new ruthenium-oxo complex, Li 4 [Ru 2 OCl 10 ]·10H 2 O, are presented. Single crystals were grown using solvent methods and the crystal structure was characterized by single crystal X-ray diffraction. Li 4 [Ru 2 OCl 10 ]·10H 2 O crystallizes into a low-symmetry triclinic structure ($P\bar1$) due to the much smaller Li + cation compared to K + cation in the tetragonal complex K 4 [Ru 2 OCl 10 ]·H 2 O. The X-ray photoelectron spectra confirm only the single valent Ru 4+ in Li 4 [Ru 2 OCl 10 ]·10H 2 O even though two distinct Ru sites exist in the crystal structure. Magnetic measurements reveal the diamagnetic property of Li 4 [Ru 2 OCl 10 ]·10H 2 O with unpaired electrons existing on Ru 4+ . Furthermore, the molecular orbital analysis matches well with the observed UV and magnetic measurements.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Synthesis of Lanthanide-Based Intermetallic Silicides

Lanthanide-containing materials are of interest because of their useful magnetic and electronic behavior. To study this intrinsic behavior, researchers need high-quality single crystals to avoid interference from grain boundaries or defects commonly found in polycrystalline samples. One method for growing single crystals is metal-flux synthesis, an approach that promotes crystal growth at lower reaction temperatures thus providing access to complex intermetallic phases. My project focuses on synthesizing novel lanthanide-containing intermetallic silicides related to previously reported f-element compounds with the Gd1??Fe4Si10?? structure type. I investigated reactions targeting lanthanum, praseodymium, neodymium, samarium, europium, and gadolinium-containing products, and used scanning electron microscopy with energy-dispersive X-ray spectroscopy (SEM-EDS) to identify promising lanthanide-containing phases. I prepared reactions by loading lanthanide oxides, Co, Si, Al, and Ga into alumina crucibles in a 0.2:1:1:10:10 Ln2O3/Co/Si/Al/Ga mmol ratio, where Ln = La, Nd, Pr, Sm, Eu, or Gd. The reactions were sealed in quartz tubes, heated in a furnace, and centrifuged to separate crystals from excess flux. Afterwards, I mechanically isolated single crystals and prepared them for characterization. Pr-, Nd-, and Sm-containing reactions were confirmed through SEM-EDS to have formed the targeted quaternary phase. Single crystal X-ray diffraction (SC-XRD) data showed the Nd-containing crystals exhibited a hexagonal unit cell associated with the Gd1??Fe4Si10?? structure type. La- and Eu-containing reactions instead formed competing Co(Al/Ga/Si)3 phase crystals. Single-crystal XRD, powder XRD, and magnetic susceptibility and heat-capacity measurements will be collected for the remaining lanthanide-containing crystals. This data will help determine the complete crystal structure of the lanthanide analogues, their phase purity and whether they exhibit localized magnetic behavior, magnetic ordering, or other electronic signatures that can be compared with the previously reported actinide analogues. The disordered structure of this intermetallic family is associated with unusual magnetic and electronic behavior meaning lanthanide analogues may show potential as thermoelectric materials. Developing new thermoelectric candidate materials is relevant to energy efficiency and waste-heat recovery, which supports DOE’s broader goal of advancing science and technology solutions for America’s energy needs.

37 - INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL C↗
DOE OSTI2020

Clathrate XI K 58 Zn 122 Sb 207 : A New Branch on the Clathrate Family Tree

Abstract The compositional screening of K‐Zn‐Sb ternary system aided by machine learning, rapid exploratory synthesis using KH salt‐like precursor and in situ powder X‐ray diffraction yielded a novel clathrate type XI K 58 Zn 122 Sb 207 . This clathrate consists of a 3D Zn‐Sb framework hosting K + ions inside polyhedral cages, some of which are reminiscent of known clathrate types while others are unique to this structure type. The complex non‐centrosymmetric structure in the tetragonal space group was solved by means of single crystal X‐ray diffraction as a 6‐component twin due to pseudocubic symmetry and further confirmed by high‐resolution synchrotron powder X‐ray diffraction and state‐of‐the‐art scanning transmission electron microscopy. The electron‐precise composition of this clathrate yields narrow‐gap p ‐type semiconductor with extraordinarily low thermal conductivity due to displacement or “rattling” of K cations inside oversized cages and as well as to twinning, stacking faults and antiphase boundary defects.

Cox, Tori↗
DOE OSTI2020

Clathrate XI K 58 Zn 122 Sb 207 : A New Branch on the Clathrate Family Tree

Abstract The compositional screening of K‐Zn‐Sb ternary system aided by machine learning, rapid exploratory synthesis using KH salt‐like precursor and in situ powder X‐ray diffraction yielded a novel clathrate type XI K 58 Zn 122 Sb 207 . This clathrate consists of a 3D Zn‐Sb framework hosting K + ions inside polyhedral cages, some of which are reminiscent of known clathrate types while others are unique to this structure type. The complex non‐centrosymmetric structure in the tetragonal space group was solved by means of single crystal X‐ray diffraction as a 6‐component twin due to pseudocubic symmetry and further confirmed by high‐resolution synchrotron powder X‐ray diffraction and state‐of‐the‐art scanning transmission electron microscopy. The electron‐precise composition of this clathrate yields narrow‐gap p ‐type semiconductor with extraordinarily low thermal conductivity due to displacement or “rattling” of K cations inside oversized cages and as well as to twinning, stacking faults and antiphase boundary defects.

Cox, Tori↗
DOE OSTI2025

Flux-Assisted Boron Chalcogen Mixture (BCM) Method for Synthesizing Mixed Chalcogenide Semiconductors (AkRE 2 Si 2 Se x S 8– x and CaRE 2 Si 2 Se 8 ) ( Ak = Ca and Sr; RE = La, Ce, Pr, Nd, and Sm): Investigation of Their Magnetic and Optical Properties

We report a detailed structural analysis of a series of ten quaternary rare-earth-containing seleno-thiosilicates AkRE 2 Si 2 Se x S 8-x and selenosilicates, CaRE 2 Si 2 Se 8 (Ak = Ca and Sr; RE = La, Ce, Pr, Nd, and Sm). Single crystals were obtained by using the flux-assisted boron chalcogen mixture (BCM) method and single crystal X-ray diffraction was used to determine their structures. All members of the AkRE 2 Si 2 Se x S 8-x and CaRE 2 Si 2 Se 8 series crystallize in the space group R$\bar{3}$c (space group number 167) of the trigonal crystal system. The single-crystal X-ray diffraction analysis revealed a strong preference for Se/S atoms to occupy one vs. the other of the two available sites. Polycrystalline samples were used for magnetic susceptibility and UV–visible diffuse reflectance measurements. Magnetic measurements show that CaCe₂Si₂Se₁.₇₃S₆.₂₇ and CaNd₂Si₂Se₂.₅S₅.₅ are paramagnetic with negative Weiss constants (θ = –60.1 and –26.2). Diffuse reflectance analysis gives optical band gaps of 2.7(1) eV (CaLa₂Si₂Se₂.₃₈S₅.₆₂), 2.2(1) eV (CaCe₂Si₂Se₁.₇₃S₆.₂₇), 2.5(1) eV (CaNd₂Si₂Se₂.₅S₅.₅), and 2.0(1) eV (CaCe₂Si₂Se₈), consistent with density functional theory calculations. By partially or fully replacing S sites with Se it was possible to achieve band gap tuning. Photoluminescence behavior was also investigated for CaCe 2 Si 2 Se 1.73 S 6.27 via irradiation with 375 nm ultraviolet light.

BCM method↗
DOE OSTI2021

Suppression of antiferromagnetic order and strong ferromagnetic spin fluctuations in Ca(Co 1-x Ni x ) 2-y As 2 single crystals

CaCo 2–y As 2 is a unique itinerant system having strong magnetic frustration. Here, we report the effect of electron doping on the physical properties resulting from Ni substitutions for Co. The single crystals of Ca(Co 1–x Ni x ) 2–y As 2 were characterized by single-crystal x-ray diffraction, energy-dispersive x-ray spectroscopy, magnetization M versus temperature T, magnetic field H, time t, and heat capacity C p (H, T) measurements. The A-type antiferromagnetic (AFM) transition temperature T N = 52 K for x = 0 decreases to 22 K with only 3% Ni substitution and is completely suppressed for x > 0.16. For 0.11 ≤ x ≤ 0.52 strong ferromagnetic (FM) fluctuations develop as revealed by magnetic susceptibility χ(T) = M(T) / H measurements. For x = 0.11 and 0.16 competing AFM and FM interactions result in a reentrant spin-glass behavior below T N , as evidenced by the observations of thermomagnetic hysteresis and magnetic relaxation. Enhanced FM fluctuations are also found for the x = 0.21 and 0.31 crystals, where χ c increases significantly at low T. A large χ anisotropy in these compositions where χ c is up to a factor of two larger than χ ab suggests that the FM spin fluctuations are quasi-1D in nature. Weak ferromagnetic contributions to the magnetization are found at T = 2 K for x = 0.11 –0.31. Heat-capacity Cp(T) measurements reveal the presence of FM quantum spin fluctuations for 0.11 ≤ x ≤ 0.52, where a logarithmic T dependence of Cp(T) / T is observed at low T. Here, the suppression of AFM order by the development of strong FM fluctuations in Ca(Co 1–x Ni x ) 2–y As 2 crystals suggests the presence of a FM quantum-critical point at x ≈ 0.20. Our density-functional theory (DFT) calculations confirm that FM fluctuations are enhanced by Ni substitutions for Co in CaCo 2–y As 2 . The Sommerfeld electronic heat-capacity coefficient is enhanced for x = 0, 0.21, and 0.42 by about a factor of two compared to DFT calculations of the density of states (DOS) at the Fermi energy, suggesting an enhancement of the DOS from electron-phonon and/or electron-electron interactions. The crystals with x > 0.52 do not exhibit FM spin fluctuations or magnetic order at T ≥ 1.8 K, which was found from the DFT calculations to arise from a Stoner transition. Superconductivity is not observed above 1.8 K for any of the compositions. Neutron-diffraction studies of crystals with x = 0.11 and 0.16 in the crossover regime (0.1 ≲ x ≲ 0.2) show no evidence of A-type ordering as observed in the parent compound with x = 0. Furthermore, no other common magnetic structures, such as ferromagnetic (FM), helical stacking of in-plane FM layers, or in-plane AFM structure, are found with an ordered moment greater than the uncertainty of 0.05 μ B per transition-metal atom.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Synthesis and structure of carbon-doped H 3 S compounds at high pressure

Understanding of recently reported putative close-to-room-temperature superconductivity in C-S-H compounds at 267 GPa demands a reproducible synthesis protocol as well as knowledge of the compounds' structure and composition. Here, we synthesized C-S-H compounds with various carbon compositions at high pressures from elemental carbon C and methane CH 4 , sulfur S, and molecular hydrogen H 2 . Here, we focus on compounds synthesized using methane as these allow a straightforward determination of their structure and composition by combining single-crystal x-ray diffraction and Raman spectroscopy. We applied a two-stage synthesis of [(CH 4 ) x (H 2 S) (1-x) ] 2 H 2 compounds with various compositions by first reacting sulfur and mixed methane-hydrogen fluids and forming CH 4 -doped H 2 S crystals at 0.5-3 GPa and then by growing single crystals of the desired hydrogen-rich compound. Raman spectroscopy applied to this material shows the presence of CH 4 molecules incorporated into the lattice and allows the determination of the CH 4 content, while single-crystal x-ray diffraction results suggest that the methane molecules substitute H 2 S molecules. The structural behavior of these compounds is very similar to the previously investigated methane-free crystals demonstrating a transition from Al 2 Cu type I4/mcm molecular crystal to a modulated molecular structure at 20-30 GPa and back to the same basic I4/mcm structure in an extended modification with greatly modified Raman spectra. This latter phase demonstrates a distortion into a Pnma structure at 132-159 GPa and then transforms into a common Im$\bar{3}$m H 3 S phase at higher pressures; however, no structural anomaly is detected near 220 GPa, where a sharp upturn in T c has been reported.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Radiation-Induced Solid-State Transformations of Uranyl Peroxides

Single-crystal X-ray diffraction studies of pristine and γ-irradiated Ca 2 [UO 2 (O 2 ) 3 ]·9H 2 O reveal site-specific atomic-scale changes during the solid-state progression from a crystalline to X-ray amorphous state with increasing dose. Following γ-irradiation to 1, 1.5, and 2 MGy, the peroxide group not bonded to Ca 2+ is progressively replaced by two hydroxyl groups separated by 2.7 Å (with minor changes in the unit cell), whereas the peroxide groups bonded to Ca 2+ cations are largely unaffected by irradiation prior to amorphization, which occurs by a dose of 3 MGy. The conversion of peroxide to hydroxyl occurs through interaction of neighboring lattice H 2 O molecules and ionization of the peroxide O–O bond, which produces two hydroxyls, and allows isolation of the important monomer building block, UO 2 (O 2 ) 2 (OH) 2 4– , that is ubiquitous in uranyl capsule polyoxometalates. Steric crowding in the equatorial plane of the uranyl ion develops and promotes transformation to an amorphous phase. In contrast, γ-irradiation of solid Li 4 [(UO 2 )(O 2 ) 3 ]·10H 2 O results in a solid-state transformation to a well-crystallized peroxide-free uranyl oxyhydrate containing sheets of equatorial edge and vertex-sharing uranyl pentagonal bipyramids with likely Li and H 2 O in interlayer positions. The irradiation products of these two uranyl triperoxide monomers are compared via X-ray diffraction (single-crystal and powder) and Raman spectroscopy, with a focus on the influence of the Li + and Ca 2+ countercations. Highly hydratable and mobile Li+ yields to uranyl hydrolysis reactions, while Ca 2+ provides lattice rigidity, allowing observation of the first steps of radiation-promoted transformation of uranyl triperoxide.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Influence of heterocyclic N-donors on the structural topologies and vibrational spectra of uranyl selenate phases

Uranyl (U(VI)O 2 2+ ) selenate compounds represent a well-studied family of structures with diverse structural arrays. Differences in the overall topology and bonding with the uranyl cation combined with additional intermolecular interactions can lead to variation in the resulting spectroscopic signals. Here, in the current study, we evaluated the structural chemistry and vibrational spectroscopy for uranyl selenates crystallized with heterocyclic N-donors. Five compounds ((C 4 H 12 N 2 )[(UO 2 )(SeO 4 ) 2 (H 2 O)]·H 2 O (USe_pip), (C 4 H 5 N 2 ) 2 [(UO 2 )(SeO 4 ) 2 (H 2 O)] (USe_pyrdz), (C 5 H 5 N) 2 [(UO 2 ) 2 (SeO 4 ) 3 (H 2 O)] ∙ 3H 2 O (USe_pyrmd), (H 3 O) 2 (C 4 H 5 N 2 ) 2 [(UO 2 ) 3 (SeO 4 ) 5 (H 2 O)]·H 2 O (USe_pyrz), and (C 5 H 6 N) 2 [(UO 2 ) 2 (SeO 4 ) 3 (H 2 O)] ∙ 3H 2 O (USe_pyr)) were characterized using X-ray diffraction (single-crystal and powder) and vibrational (Raman and IR) spectroscopy. Two one-dimensional (1-D) chain and three two-dimensional sheet (2-D) topologies were identified and classified based upon previous graphical representations. Overall, the arrangement of the heteroatoms could be linked to the hydrogen bonding network associated with the heterocycles and selenate anions. Vibrational spectra of the solid-state compounds were complex, with multiple bands associated with the uranyl cation, selenate anion, and heteroatoms. The ν 1 symmetric stretching band of the uranyl was relatively consistent across all compounds, whereas differences were observed for the ν 3 asymmetric band between the 1-D and 2-D structural topologies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗