Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “ATOMIC DISPLACEMENTS”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 559 records · Page 31
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Molecular-Level Behavior of Imidazolium-Based Ionic Liquid Mixtures

Understanding the molecular-level organization of anions and cations in a mixture of different ionic liquids (ILs) is challenging, but it can be very important for designing solvents and IL-based membrane materials. In this work, we perform all-atom molecular dynamics (MD) simulations to understand the intermolecular interactions and structuring of both neat and mixed IL compositions containing 1-benzyl-3-methylimidazolium [ZMIM + ], 1-butyl-3-methylimidazolium [BMIM + ], bistriflimide [Tf 2 N – ], and tetrafluoroborate [BF 4 – ]. We observe very strong underlying molecular-level migrations in these mixtures, and this tends to mainly involve the anion species. As compared to the systems with a single anion, the mixed anions lead to large increases/decreases in the radial distribution function peak heights, whereas the cation mixing is relatively benign. The [BF 4 – ] anions have a strong tendency to displace the [Tf 2 N – ] anions in the mixtures, and this is seen with respect to both [BMIM + ] and [ZMIM + ].

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Infrared Optical Anisotropy in Quasi‐1D Hexagonal Chalcogenide BaTiSe 3

Polarimetric infrared (IR) detection bolsters IR thermography by leveraging the polarization of light. Optical anisotropy, i.e., birefringence and dichroism, can be leveraged to achieve polarimetric detection. Recently, giant optical anisotropy is discovered in quasi-1D narrow-bandgap hexagonal perovskite sulfides, A 1+x TiS 3 , specifically BaTiS 3 and Sr 9/8 TiS 3 . In these materials, the critical role of atomic-scale structure modulations in the unconventional electrical, optical, and thermal properties raises the broader question of the nature of other materials that belong to this family. To address this issue, for the first time, high-quality single crystals of a largely unexplored member of the A 1+x TiX 3 (X = S, Se) family, BaTiSe 3 are synthesized. Single-crystal X-ray diffraction determined the room-temperature structure with the P31c space group, which is a superstructure of the earlier reported P6 3 /mmc structure. The crystal structure of BaTiSe 3 features antiparallel c-axis displacements similar to but of lower symmetry than BaTiS 3 , verified by the polarization dependent Raman spectroscopy. Fourier transform infrared (FTIR) spectroscopy is used to characterize the optical anisotropy of BaTiSe 3 , whose refractive index along the ordinary (E ⊥ c) and extraordinary (E ‖ c) optical axes is quantitatively determined by combining ellipsometry studies with FTIR. With a giant birefringence Δn ∼ 0.9, BaTiSe 3 emerges as a new candidate for miniaturized birefringent optics for mid-wave infrared to long-wave infrared imaging.

optical anisotropy↗
NASA NTRSDate not supplied

Seeding Mechanism for High-Pressure Nozzles

NASA tests new launch and entry vehicle configurations in wind tunnels, where flow visualizations and quantitative flow field measurements are often desired. Some of these vehicles have rocket motors for propulsion, retro-propulsion, or reaction control. Unseeded,high-pressure air is often used to simulate these rocket motor plumes. However, it is difficult to make off-body measurements in these regions, for several reasons. First, the plumes themselves are usually unseeded and at such low pressures that the flow velocity cannot currently be measured. Second, the plumes displace seeded tunnel air, preventing measurements such as laser sheet visualizations. Third, they force shock waves ahead of the vehicle, which melts the ice crystal fog commonly used for many visualization and measurement techniques. The Virginia Tech Advanced Propulsion and Power Lab has designed and tested a novel method for seeding the flow in these small-scale, high-pressure nozzles to allow quantitative measurement with a particle-based measurement such as particle image velocimetry (PIV). The method involves a Venturi contraction to draw the seed liquid out of a reservoir and into the nozzle channel, wherein shearing forces atomize the seed into particles. The concept was tested with a laser sheet visualization, which showed the nozzle spray pattern and the controllability of the seeding flow rate. This relatively inexpensive and simple technique may prove useful in wind tunnel experiments involving particle-based laser diagnostics and small, high-pressure nozzles.

particle image velocimetry↗
NASA NTRS2009

A Method for Combining Experimentation and Molecular Dynamics Simulation to Improve Cohesive Zone Models for Metallic Microstructures

Fracture processes within a material begin at the nanometer length scale at which the formation, propagation, and interaction of fundamental damage mechanisms occur. Physics-based modeling of these atomic processes quickly becomes computationally intractable as the system size increases. Thus, a multiscale modeling method, based on the aggregation of fundamental damage processes occurring at the nanoscale within a cohesive zone model, is under development and will enable computationally feasible and physically meaningful microscale fracture simulation in polycrystalline metals. This method employs atomistic simulation to provide an optimization loop with an initial prediction of a cohesive zone model (CZM). This initial CZM is then applied at the crack front region within a finite element model. The optimization procedure iterates upon the CZM until the finite element model acceptably reproduces the near-crack-front displacement fields obtained from experimental observation. With this approach, a comparison can be made between the original CZM predicted by atomistic simulation and the converged CZM that is based on experimental observation. Comparison of the two CZMs gives insight into how atomistic simulation scales.

Hochhalter, J. D.↗
DOE OSTI2020

Leiomodin creates a leaky cap at the pointed end of actin-thin filaments

Improper lengths of actin-thin filaments are associated with altered contractile activity and lethal myopathies. Leiomodin, a member of the tropomodulin family of proteins, is critical in thin filament assembly and maintenance; however, its role is under dispute. Using nuclear magnetic resonance data and molecular dynamics simulations, we generated the first atomic structural model of the binding interface between the tropomyosin-binding site of cardiac leiomodin and the N-terminus of striated muscle tropomyosin. Our structural data indicate that the leiomodin/tropomyosin complex only forms at the pointed end of thin filaments, where the tropomyosin N-terminus is not blocked by an adjacent tropomyosin protomer. This discovery provides evidence supporting the debated mechanism where leiomodin and tropomodulin regulate thin filament lengths by competing for thin filament binding. Data from experiments performed in cardiomyocytes provide additional support for the competition model; specifically, expression of a leiomodin mutant that is unable to interact with tropomyosin fails to displace tropomodulin at thin filament pointed ends and fails to elongate thin filaments. Together with previous structural and biochemical data, we now propose a molecular mechanism of actin polymerization at the pointed end in the presence of bound leiomodin. In the proposed model, the N-terminal actin-binding site of leiomodin can act as a “swinging gate” allowing limited actin polymerization, thus making leiomodin a leaky pointed-end cap. Results presented in this work answer long-standing questions about the role of leiomodin in thin filament length regulation and maintenance.

2D-NMR↗
DOE OSTI2024

Dust and Ions: Self Organization and Stability (Final Report)

This project explores the stability and structure of systems with non-reciprocal interactions, challenging the traditional understanding based on Newton's third law, which states that every action has an equal and opposite reaction. Reciprocal forces are fundamental to the stability of systems ranging in size from atomic nuclei to galactic clusters. Our research investigates what happens when the forces between two objects are not equal and opposite. We used dusty plasmas as a model system to study non-reciprocal interactions. In a plasma chamber, micron-sized dust particles acquire a negative charge and form 2D planar "dust crystals" when levitated by the electric field present in the plasma sheath at the interface between the plasma and the lower surface of the chamber. This electric field also drives a vertical ion flow, creating a positively charged "plasma wake" downstream of the dust grains. While horizontally aligned dust grains interact reciprocally, a slight vertical displacement causes non-reciprocal interactions due to the attraction of the lower dust grain to the upper dust grain’s ion wake. Our experiments investigated the range of plasma conditions (gas pressure and system power) where stable dusty plasma structures are able to self-organize, aided by the ion wake. We studied systems ranging from pairs of dust particles to large 2D crystals, providing insights into the conditions that lead to stable or unstable structures. We used numerical simulations to investigate how ion wakes changed in response to changes in the operating conditions as well as how the wakes of separate grains interact when dust grains are in close proximity.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRSDate not supplied

Particle Seeding Method for Small-Scale, High-Pressure Nozzles

NASA tests new launch and reentry vehicle configurations in wind tunnels, where flow visualizations and quantitative flowfield measurements are often desired. Some of these vehicles have rocket motors for propulsion, retro-propulsion, or reaction control. High-pressure air is used to supply these rocket motor plumes. However, it is difficult to make off-body measurements in these regions, for several reasons. First, the plumes themselves lack seeding particles for flow diagnostics, and at the low pressures after expansion, Rayleigh scattering or other molecular techniques yield insufficient signal for flow velocity measurements. Second, the plumes displace particle-seeded tunnel air, preventing measurements in the vicinity of the plume. Third, the plumes force shock waves ahead of the vehicle, which melts the ice crystal fog commonly used for visualization and measurement techniques in certain facilities. In the current work, a novel method for seeding the flow in these small-scale, high-pressure nozzles has been devised and initially demonstrated, potentially enabling quantitative and qualitative measurements with particle-based instruments such as Doppler global velocimetry or particle image velocimetry. The method involves a Venturi contraction to draw the seed liquid out of a reservoir and into the nozzle channel, wherein shearing forces atomize the seed into particles. The concept was tested with a laser sheet visualization, which demonstrated that the flow rate of liquid spray was controllable; a valve could be adjusted to drop the flow rate by up to 65%. This relatively inexpensive and simple technique may prove useful in wind tunnel experiments involving particle-based laser diagnostics and small, high-pressure nozzles.

Aditya S. Acharya↗
NASA NTRSDate not supplied

Particle Seeding Method for Small-Scale, High-Pressure Nozzles

NASA tests new launch and reentry vehicle configurations in wind tunnels, where flow visualizations and quantitative flowfield measurements are often desired. Some of these vehicles have rocket motors for propulsion, retro-propulsion, or reaction control. High-pressure air is used to supply these rocket motor plumes. However, it is difficult to make off-body measurements in these regions, for several reasons. First, the plumes themselves lack seeding particles for flow diagnostics, and at the low pressures after expansion, Rayleigh scattering or other molecular techniques yield insufficient signal for flow velocity measurements. Second, the plumes displace particle-seeded tunnel air, preventing measurements in the vicinity of the plume. Third, the plumes force shock waves ahead of the vehicle, which melts the ice crystal fog commonly used for visualization and measurement techniques in certain facilities. In the current work, a novel method for seeding the flow in these small-scale, high-pressure nozzles has been devised and initially demonstrated, potentially enabling quantitative and qualitative measurements with particle-based instruments such as Doppler global velocimetry or particle image velocimetry. The method involves a Venturi contraction to draw the seed liquid out of a reservoir and into the nozzle channel, wherein shearing forces atomize the seed into particles. The concept was tested with a laser sheet visualization, which demonstrated that the flow rate of liquid spray was controllable; a valve could be adjusted to drop the flow rate by up to 65%. This relatively inexpensive and simple technique may prove useful in wind tunnel experiments involving particle-based laser diagnostics and small, high-pressure nozzles.

lasers↗
DOE OSTI2022

Optimization of Extended-Surface PtNi Nanowire Oxygen Reduction Electrocatalysts Produced via Atomic Layer Deposition

Polymer electrolyte membrane fuel cells (PEMFCs) produce electricity with only heat and water as byproducts, but sluggish kinetics of the oxygen reduction reaction (ORR) at the cathode and durability limitations restrict widespread commercialization, motivating the development of advanced catalysts. In this research, extended-surface platinum nickel (PtNi) nanowires (NWs) synthesized using the scalable atomic layer deposition (ALD) technique are investigated with the goal of exploring the durability benefits of high-aspect-ratio electrocatalysts and the tunability of beneficial kinetic properties. The surface and bulk composition and the structure of the PtNi NWs were investigated as a function of a series of postsynthesis modifications. The results from a combination of electron microscopy and X-ray spectroscopy characterization techniques were correlated to electrochemical performance to gain a comprehensive understanding of the structure-property-performance relationships. The robust structure of the ALD-derived NWs enabled additional postsynthesis optimization steps, which were not possible with previous-generation materials synthesized via spontaneous galvanic displacement, resulting in a catalyst with beneficial properties for catalyst kinetics as well as improved durability. Our study demonstrates potential pathways toward further improving the performance of this class of materials through optimization of bulk and surface properties of the catalyst.

30 DIRECT ENERGY CONVERSION↗
DOE OSTI2025

Fermi surface reconstruction due to orthorhombic distortion in the Dirac semimetal YbMnSb 2

A Dirac semimetal with magnetic atoms as constituents delivers an interesting platform to investigate the interplay of Fermi surface (FS) topology, electron correlation, and magnetism. One such family of semimetals is YbMn⁢ 𝑃⁢𝑛 2 (𝑃⁢𝑛 = Sb,Bi), which is being actively studied due to the intertwined spin and charge degrees of freedom. Here, in this study, we investigate the relationship between the magnetic/crystal structures and FS topology of YbMnSb 2 using single crystal x-ray diffraction, neutron scattering, magnetic susceptibility, magnetotransport measurements, and complimentary density functional theory (DFT) calculations. Contrary to previous reports, the x-ray and neutron diffraction reveal that YbMnSb 2 crystallizes in an orthorhombic 𝑃⁢𝑛⁢𝑚⁢𝑎 structure with a notable antiphase displacement of the magnetic Mn ions that increases in magnitude upon cooling. As a result of this orthorhombicity, first-principles DFT calculation reveals a reduced Brillouin zone and more anisotropic FS of YbMnSb 2 compared to YbMnBi 2 . Moreover, the hole-type carrier density drops by two orders of magnitude as YbMnSb 2 orders antiferromagnetically, indicating band folding in a magnetic ordered state. In addition, the Landau level fan diagram yields a nontrivial nature of the Shubnikov–de Haas quantum oscillation frequency arising from the Dirac-like Fermi pocket. These results imply that YbMnSb 2 is an ideal platform to explore the interplay of subtle lattice distortion, magnetic order, and topological transport arising from relativistic quasiparticles.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Facile Tensile Testing Platform for In Situ Transmission Electron Microscopy of Nanomaterials

In situ tensile testing using transmission electron microscopy (TEM) is a powerful technique to probe structure-property relationships of materials at the atomic scale. In this work, a facile tensile testing platform for in situ characterization of materials inside a transmission electron microscope is demonstrated. The platform consists of: 1) a commercially available, flexible, electron-transparent substrate (e.g., TEM grid) integrated with a conventional tensile testing holder, and 2) a finite element simulation providing quantification of specimen-applied strain. The flexible substrate (carbon support film of the TEM grid) mitigates strain concentrations usually found in free-standing films and enables in situ straining experiments to be performed on materials that cannot undergo localized thinning or focused ion beam lift-out. The finite element simulation enables direct correlation of holder displacement with sample strain, providing upper and lower bounds of expected strain across the substrate. The tensile testing platform is validated for three disparate material systems: sputtered gold-palladium, few-layer transferred tungsten disulfide, and electrodeposited lithium, by measuring lattice strain from experimentally recorded electron diffraction data. The results show good agreement between experiment and simulation, providing confidence in the ability to transfer strain from holder to sample and relate TEM crystal structural observations with material mechanical properties.

2D materials↗
DOE OSTI2025

Predicting interface structure using the minima hopping method

Here, we adapt the minima hopping method (MHM) to the problem of interfacial structure prediction and apply it to study a canonical problem, the tilt grain boundaries in SrTiO 3 . Our method employs a hybrid approach by first exploring the potential energy surface (PES) of different grain boundary samplings with an empirical force field, among which the fifteen candidates with lower energies are then refined using ab initio density functional theory (DFT) calculations. During the exploratory stage, we bias the search using a local order parameter to primarily sample various reconstructions in the vicinity of the interface, while preserving the crystallinity of the bulk regions. We further enhance the search by incorporating initial structures with rigid body displacements to account for translational variations between bulk phases, enabling the MHM to effectively generate both stoichiometric and nonstoichiometric SrTiO 3 Σ⁢3(111)[110] and Σ⁢3(112)[110] grain boundaries. From an algorithmic standpoint, MHM outperforms earlier studies based on genetic algorithms (GA) by identifying more stable interfacial structures of several SrTiO 3 grain boundaries. The performance of the present implementation of the MHM approach is primarily limited by exploring an approximate description of the PES with a rather simple Buckingham potential. This limitation leads to variations in performance when compared to approaches utilizing more advanced surrogate PES models, such as direct DFT-PES sampling or GA with the embedded atom method (EAM). Despite the present limitations, the MHM approach is able to yield interfacial structures with comparable or lower interfacial energies in specific cases, such as Σ⁢3(111)[110] Γ=1, ±0.5 and Σ⁢3(112)[110] Γ= ±1, −2, underscoring the robustness of the MHM approach even with a simple approximation of the DFT PES. The MHM interfacial structure prediction method thus offers an efficient approach to understanding the grain boundaries and heterointerfaces at the atomic scale, providing an important prerequisite for effective materials design.

density functional theory↗
DOE OSTI2025

The interaction of edge dislocations with hydrogen-helium bubbles in tungsten

In fusion reactors, plasmas-facing components undergo degradation due to displacement damage and injection of gas impurities. Significant amounts of hydrogen (H) and helium (He) impurities can be introduced into materials through plasma exposure and nuclear transmutation, and their synergistic effects lead to the formation of mixed He/H bubbles under irradiation, changing their hardening mechanisms. In this study, molecular dynamics (MD) models were developed to study the interaction between ½<111> edge dislocations with mixed He/H-bubbles in W. The critical resolved shear stress (CRSS) that is required for dislocation breakaway increases with He/H-to-vacancy ratio at 600 K, indicating strong pinning effects of mixed He/H bubbles. However, as the temperature increases up to 1400 K, the mixed He/H bubbles become unstable as the H atoms are increasingly emitted from the mixed He/H bubbles and migrate into W matrix, which lowers bubble pressure and CRSS. Overall, these results highlight the synergistic effects of He and H on dislocation behavior in irradiated W during deformation.

36 - MATERIALS SCIENCE↗
DOE OSTI2021

Spectral Denoising for Accelerated Analysis of Correlated Ionic Transport

Computation of correlated ionic transport properties from molecular dynamics in the Green-Kubo formalism is expensive, as one cannot rely on the affordable mean square displacement approach. We use spectral decomposition of the short-time ionic displacement covariance to learn a set of diffusion eigenmodes that encode the correlation structure and form a basis for analyzing the ionic trajectories. This allows systematic reduction of the uncertainty and accelerate computations of ionic conductivity in systems with a steady-state correlation structure. We provide mathematical and numerical proofs of the method’s robustness and demonstrate it on realistic electrolyte materials.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2020

Nanoscale serration characteristics of additively manufactured superalloys

Structural elements made of nickel-based superalloys usually operate at high temperatures. Many surface failure mechanisms such as creep, fatigue, fretting fatigue, corrosion, and stress corrosion cracking start from the surface. Thus, studying the surface mechanical properties and deformation behavior of materials is vital in order to draw a correlation between the surface properties and failures. Herein, a nanoindentation technique was implemented to characterize surface properties of a widely used additively manufactured (AM) superalloy, i.e., Inconel 625. The specimens were tested in a range of temperatures in a vacuum chamber. Serrated plastic flow characterized by pop-in events during nanoindentation, known as Portevin-Le Chatelier (PLC) effect, was observed in all three tested elevated temperatures. This phenomenon depicts itself as bursts of plasticity in the loading section of the load-displacement curves. These bursts were studied comprehensively to explore incipient plasticity. Hertzian contact mechanics were implemented to extract the maximum shear stress beneath the indenter from the pop-in loads. The results show that the initial pop-in load increases as the temperature increases. The average initial pop-in load increases by almost four times from 300 °C to 650 °C. This was attributed to the formation of strengthening precipitates. The average size of the serrations and the magnitude of dislocation nucleation increase from 300 °C to 500 °C and decrease from 500 °C to 650 °C. Finally, the serrations are attributed to the dislocation generation and movement as well as their interaction with the solute atoms and precipitates.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Modeling the effect of MHD activity on runaway electron generation during SPARC disruptions

Magnetohydrodynamic (MHD) instabilities and runaway electrons (REs) interact in several ways, making it important to self-consistently model these interactions for accurate predictions of RE generation and the design of mitigation strategies, such as massive gas injection (MGI). Using M3D-C1 – an extended MHD code with a RE fluid model – we investigate the effects of 3-D nonlinear MHD activity, material injection, and 2-D axisymmetric vertical displacement events (VDEs) on RE evolution during disruptions on SPARC – a high-field, high-current tokamak designed to achieve a fusion gain Q > 1. Several cases, comprising different combinations of neon (Ne) and deuterium (D 2 ) injection, are considered. Here, our results demonstrate key effects that arise from the self-consistent RE + MHD coupling, such as an initial increase in RE generation due to MHD instability growth, decreased saturation energies of the m/n = 1/1 mode driving sawteeth-like activity, RE losses in stochastic magnetic fields, and subsequent RE confinement and plateau formation due to re-healing of flux surfaces. Large RE plateaus (>5 MA) are obtained with Ne-only injection (2-5 × 10 21 atoms), while combined D 2 + Ne injection (2 × 10 21 Ne atoms; 1.8 × 10 22 D 2 molecules) produces a lower RE current (<2 MA). With D 2 + Ne injection, a post thermal quench "cold" VDE terminates the RE beam, preventing a steady plateau. These simulations couple REs, 3-D MHD instabilities, MGI, and axisymmetric VDEs for the first time in SPARC disruption simulations and represent a crucial step in understanding RE generation and mitigation in high-current devices like SPARC.

Datta, Rishabh [Massachusetts Inst. of Technology ↗
DOE OSTI2020

Low-frequency Raman spectrum of 2D layered perovskites: Local atomistic motion or superlattice modes?

We report the low-frequency Raman spectrum (ω = 10 cm -1 –150 cm -1 ) of a wide variety of alkylammonium iodide based 2D lead halide perovskites (2D LHPs) as a function of A-site cation (MA = methylammonium and FA = formamidinium), octahedral layer thickness (n = 2–4), organic spacer chain length (butyl-, pentyl-, hexyl-), and sample temperature (T = 77 K–293 K). Using density functional theory calculations under the harmonic approximation for n = 2 BA:MAPbI, we assign several longitudinal/transverse optical phonon modes between 30 cm -1 and 100 cm -1 , the eigen displacements of which are analogous to that observed previously for octahedral twists/distortions in bulk MAPbI. Additionally, we propose an alternative assignment for low-frequency modes below this band (<30 cm -1 ) as zone-folded longitudinal acoustic phonons corresponding to the periodicity of the entire layered structure. Furthermore, we compare measured spectra to predictions of the Rytov elastic continuum model for zone-folded dispersion in layered structures. Our results are consistent across the various 2D LHPs studied herein, with energetic shifts of optical phonons corresponding to microscopic structural differences between materials and energetic shifts of acoustic phonons according to changes in the periodicity and elastic properties of the perovskite/organic subphases. This study highlights the importance of both the local atomic order and the superlattice structure on the vibrational properties of layered 2D materials.

2D materials↗
DOE OSTI2024

Teaching Nonradiative Transitions with MATLAB and Python

Nonradiative transitions are changes in energy states of atoms, ions, or molecules that do not involve the emission or absorption of photons. Despite their importance in understanding luminescent properties and photochemical reaction mechanisms, nonradiative transitions are rarely given more than a qualitative overview in undergraduate and even graduate physical chemistry curricula. To supplement the coverage of nonradiative transition topics, we provide here a set of active learning exercises to help students develop an intuitive understanding of the factors that determine the rate of nonradiative transitions. Here, we start by outlining the theoretical background through the formulations of the Franck–Condon factor and its relation to the rate of nonradiative transition. We then introduce three teaching modules, with associated MATLAB and Python codes, to explore how (1) the excited state nuclear displacement, (2) the electronic energy gap between excited and ground state and (3) the excited/ground state vibrational mode frequencies affect the magnitude of the Franck–Condon factor and thereby the rate of nonradiative transitions. The wave function overlap plots that accompany all teaching modules provide direct visualization of the effect of input parameters on the magnitude of Franck–Condon overlap integral.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗