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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.

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At least 937 records · Page 52
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Computational and Experimental Investigation of Thermal-Mechanical- Chemical Mechanisms of High-burnup Spent Nuclear Fuel (SNF) Processes at Elevated Temperatures and Degradation Behavior in Geologic Repositories

The overarching goal of the combined computational and experimental R&D activities proposed in this project is to enhance understanding of the mechanisms and thermal-mechanical-chemical (TMC) parameters controlling the instant release fraction (IRF) and matrix dissolution of high-burnup (HB; burnup) spent nuclear fuels (SNFs) and the subsequent formation, stability, and phase transformations of SNF alteration products under long-term storage and geological disposal conditions. Uranium dioxide may undergo oxidative corrosion/alteration, and the IRF may be increased for HB SNF, both of which may affect environmental systems associated with SNF long-term storage and disposal. The oxidative matrix dissolution may form various complex uranyl-based phases, including a rich variety of oxides, silicates, carbonates and other secondary minerals in varied geological environments (e.g., studtite, metastudtite, amorphous uranyl peroxide, uranium trioxide, triuranium octoxide, schoepite, dehydrated schoepite, metaschoepite, becquerelite, soddyite, rutherfordine,...). These uranyl phases generally have higher mobility UO 2 +2 species than less soluble U 4+ phases. However, limited information on the thermodynamic properties and formation kinetics of these uranyl-bearing phases is available to predict explicitly paragenesis under the conditions relevant to long-term storage or disposal. The proposed project draws on complementary expertise and research backgrounds from the team members: (i) to apply a combined ab initio modeling (UNLV/UTEP and SNL) and experimental (UNLV) strategy investigating the high-temperature TMC mechanisms of alteration of SNF under α-radiolysis conditions; (ii) to investigate the mechanistic of phase transformations in UNF degradation products under various conditions expected in long-term storage systems (e.g. (UO 2 )O 2 (H 2 O) 4 → (UO 2 )O 2 (H 2 O) 2 → U 2 O 7 → UO 3 → U 3 O 8 ); (iii) to determine high-accuracy TMC parameters for complex uranyl-based phases formed in storage or geological disposal environments (e.g. UO 3 (H 2 O) 2 , Ca[(UO 2 ) 6 O 4 (OH) 8 ] 8 H 2 O, (UO 2 ) 2 (SiO 4 ) 3 2H 2 O,…). The unforeseen COVID-19 pandemic led to the laboratory/campus closure since March 2020, that resulted in a significant delay in reaching milestones in a satisfactory manner, due to (i) the statewide recommendation from stop-working to later limited work in the lab and work-from-home (WFH), (ii) no in-person interactions, and (iii) a hiring freeze at UNLV. Therefore, a no cost extension (10/01/2021- 9/30/2022) was requested to help make up the time we lost during the global pandemic in 2020-2021, leading to paradigm shifts in the focus of the project in the following three main tasks: Task 1 (Computational), Task 2 (Experimental), and Task 3 (Final report, due on 12/29/2022).

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2021

Modeling in High Temperature Corrosion: A Review and Outlook

Realizing higher operating temperatures to increase efficiency of future applications for energy conversion and storage while minimizing cost is a challenge for development of high-temperature materials. Simultaneous optimization of mechanical properties and corrosion resistance continues to be a difficult task but is essential due to the need to significantly accelerate the transition between technology readiness levels in the future. Furthermore, oxidation-induced degradation will be a critical life-limiting mechanism at increased operating temperatures. Suitable high-temperature materials cannot be solely identified by time-consuming experiments and reliable computational methods incorporating the relevant physics of processes must be considered to complement the experimental efforts. In the present work, a review of the methods employed to model oxidation-induced material degradation described in literature will be discussed. Furthermore, their capability to predict lifetime and aid in material selection will be evaluated.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Elucidating plasma dynamics in Hasegawa–Wakatani turbulence by information geometry

In this work, the impact of adiabatic electrons on drift-wave turbulence, modeled by the Hasegawa–Wakatani equations, is studied using information length. Information length is a novel theoretical method for measuring distances between statistical states represented by different probability distribution functions (PDFs) along the path of a system and represents the total number of statistically different states that a system evolves through in time. Specifically, the time-dependent PDFs of turbulent fluctuations for a given adiabatic index $A$ are computed. The changes in fluctuation statistics are then quantified in time by using information length. The numerical results provide time traces exhibiting intermittent plasma dynamics, and such behavior is identified by a rapid change in the information length. The effects of $A$ are discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Effects of Charged Solute-Solvent Interaction on Reservoir Temperature during Subsurface CO2 Injection

A short-term side-effect of CO2 injection is a developing low-pH front that forms ahead of the bulk water injectant, due to differences in solute diffusivity. Observations of downhole well temperature show a reduction in aqueous-phase temperature with the arrival of a low-pH front, followed by a gradual rise in temperature upon the arrival of a high concentration of bicarbonate ion. In this work, we model aqueous-phase transient heat advection and diffusion, with the volumetric energy generation rate computed from solute-solvent interaction using the Helgeson–Kirkham–Flowers (HKF) model, which is based on the Born Solvation model, for computing specific molar heat capacity and the enthalpy of charged electrolytes. A computed injectant water temperature profile is shown to agree with the actual bottom hole sampled temperature acquired from sensors. The modeling of aqueous-phase temperature during subsurface injection simulation is important for the accurate modeling of mineral dissolution and precipitation because forward dissolution rates are governed by a temperature-dependent Arrhenius model.

58 GEOSCIENCES↗
DOE OSTI2021

First principles calculations in support of Pu aging: calculating the effects of lattice imperfections on thermodynamics

Plutonium (Pu) has, in theory, well defined crystal structures: its atoms are arranged in regular spatial patterns. But Pu is radioactive, and as its nuclei decay those regular spatial patterns are interrupted. The interruptions are lattice imperfections, which are known to affect how materials respond to their environment. To adequately model Pu, we need to know which lattice imperfections are present, how they interact with each other, and how they affect the material’s response to its environment. The work presented here aims to use density functional theory (DFT) calculations to begin to answer the latter, in particular, how individual lattice imperfections affect measurable effects including thermal expansion (the change in volume in response to a change in temperature), heat capacity (the amount of thermal energy needed to change a material’s temperature), and elastic moduli (a material’s resistance to applied stresses). Pu poses many computational challenges. The $\textit{f}$ electrons require special attention. Of all the elements, Pu has the largest number of electrons that must be included in the calculations. Thermal effects require calculating the phonons (the lattice vibrations), which for systems containing lattice imperfections demand large, complex computational cells - but computational resources limit the size and complexity. With careful restructuring of how the calculations are performed, all these challenges have been met to enable calculations that provide insight into how lattice imperfections affect Pu’s response to its environment. Reported here are the computational challenges and the advances developed to meet them, along with the first results showing the strong effect that one prototype lattice imperfection (an interstitial Pu atom in a delta-phase Pu lattice) has on Pu’s response to its environment.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Neural Network for Principle of Least Action

The principle of least action is the cornerstone of classical mechanics, theory of relativity, quantum mechanics, and thermodynamics. Here, we describe how a neural network (NN) learns to find the trajectory for a Lennard-Jones (LJ) system that maintains balance in minimizing the Onsager–Machlup (OM) action and maintaining the energy conservation. The phase-space trajectory thus calculated is in excellent agreement with the corresponding results from the “ground-truth” molecular dynamics (MD) simulation. Furthermore, we show that the NN can easily find structural transformation pathways for LJ clusters, for example, the basin-hopping transformation of an LJ 38 from an incomplete Mackay icosahedron to a truncated face-centered cubic octahedron. Unlike MD, the NN computes atomic trajectories over the entire temporal domain in one fell swoop, and the NN time step is a factor of 20 larger than the MD time step. The NN approach to OM action is quite general and can be adapted to model morphometrics in a variety of applications.

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

A perspective on challenges and opportunities in developing high entropy-ultra high temperature ceramics

The emergence of a new class of high entropy ultra-high temperature ceramics (HE-UHTCs) is expected to possess exceptionally superior mechanical, oxidation, and erosion resistance as compared to conventional UHTCs. The improvement in the properties of HE-UHTCs is attributed to the high configurational entropy of the multi-component system stabilized into a single-phase, but with little discussion on entropy contributions. This perspective article presents a viewpoint on the critical scientific question regarding the actual role entropy plays in stabilizing and enhancing the thermo-mechanical properties of a multi-component system. The high throughput first-principle calculations, which can provide the entropy formation ability (EFA) of thermodynamically stable HE-UHTCs, can prove to be valuable toolset to this puzzle. HE-UHTCs show enhancement in the mechanical properties much higher than the predicted rule of the mixture, which cannot traditionally be explained by a mere solid solution formation effect. Additionally, isothermal oxidation studies of HE-UHTCs limited to furnace testing state remarkable oxidation resistance which is attributed to the passivity of complex, layered structure, and composition of the oxide scale. However, whether all the constituents in the HE-UHTC system react simultaneously or preferential oxidation takes place needs to be addressed. To address all these issues, an integrated computational and experimental approach has been postulated towards designing a thermal protection system (TPS) for re-entry applications. Succeeding the approach will provide new opportunities in the compositional space of HE-UHTCs with tailored properties.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Low-Pressure Electrochemical Synthesis of Complex High-Pressure Superconducting Superhydrides

There is great current interest in multicomponent superhydrides due to their unique quantum properties under pressure. A remarkable example is the ternary superhydride Li 2 MgH 16 computationally identified to have an unprecedented high superconducting critical temperature T c of ~470 K at 250 GPa. However, the very high synthesis pressures required remains a significant hurdle for detailed study and potential applications. In this Letter, we evaluate the feasibility of synthesizing ternary Li-Mg superhydrides by the recently proposed pressure-potential (P 2 ) method that uniquely combines electrochemistry and applied pressure to control synthesis and stability. Furthermore, the results indicate that it is possible to synthesize Li-Mg superhydrides at modest pressures by applying suitable electrode potentials. Using pressure alone, no Li-Mg ternary hydrides are predicted to be thermodynamically stable, but in the presence of electrode potentials, both Li 2 MgH 16 and Li 4 MgH 24 can be stabilized at modest pressures. Three polymorphs are predicted as ground states of Li 2 MgH 16 below 300 GPa, with transitions at 33 and 160 GPa. The highest pressure phase is superconducting, while the two at lower pressures are not. Our findings point out the potentially important role of the P 2 method in controlling phase stability of complex multicomponent superhydrides.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Flexocaloric effect in superelastic materials

We present a combined theoretical–experimental study of flexocaloric effects in superelastic materials exhibiting structural transitions. We study a Ginzburg–Landau model combined with a vibrational model for a beam near a ferroelastic transition loaded with a three-point bending setup. We also perform experiments on a Cu–Al–Ni single crystal undergoing a martensitic transition. We measure bent beam profiles, vertical force vs vertical deflection during a slow isothermal process, time evolution of the bending and unbending amplitudes, and the evolution of temperature profiles. We also compute the evolution of heat source and heat sink profiles. Finally, we study the location of acoustic emission events during the bending/unbending experiment. Our observations are consistent with the model predictions and allow us to identify the main physical parameters relevant for flexocaloric applications.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Melting curves of ice polymorphs in the vicinity of the liquid–liquid critical point

The possible existence of a liquid–liquid critical point in deeply supercooled water has been a subject of debate due to the challenges associated with providing definitive experimental evidence. The pioneering work by Mishima and Stanley [Nature 392, 164–168 (1998)] sought to shed light on this problem by studying the melting curves of different ice polymorphs and their metastable continuation in the vicinity of the expected liquid–liquid transition and its associated critical point. Based on the continuous or discontinuous changes in the slope of the melting curves, Mishima [Phys. Rev. Lett. 85, 334 (2000)] suggested that the liquid–liquid critical point lies between the melting curves of ice III and ice V. Herein we explore this conjecture using molecular dynamics simulations with a machine learning model based on ab initio quantum-mechanical calculations. We study the melting curves of ices III, IV, V, VI, and XIII and find that all of them are supercritical and do not intersect the liquid–liquid transition locus. We also find a pronounced, yet continuous, change in the slope of the melting lines upon crossing of the liquid locus of maximum compressibility. Finally, we analyze the literature in light of our findings and conclude that the scenario in which the melting curves are supercritical is favored by the most recent computational and experimental evidence. Although the preponderance of evidence is consistent with the existence of a second critical point in water, the behavior of ice polymorph melting lines does not provide strong evidence in support of this viewpoint, according to our calculations.

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

A combined experimental and machine learning exploration of Ti 2-x Zr x MnCrFeNi high entropy Laves hydrides

A series of high entropy AB 2 -type Ti 2-x Zr x MnCrFeNi alloys (x = 0.6, 0.7, 0.8, 0.9, 1.0, 1.1 and 1.2) were synthesized to investigate their potential for hydrogen storage and chemical compression. The influence of the Ti/Zr ratio was explored in terms of structural, microstructural and thermodynamic properties. The storage capacity together with the reaction enthalpy and entropy changes of the synthesized high entropy alloys were compared to predictions from Machine Learning (ML) to investigate changes in these properties across the explored composition space. The results revealed that a decreasing Zr content consistently lowered the hydride formation enthalpy and increased the plateau pressure from 8 to >90 bar H 2 at 25 °C, in good agreement with ML predictions. Selected compositions (x = 1.0 and 1.2) demonstrated reversible hydrogen storage capability over 150 cycles, with capacities of 1.34–1.40 wt % H 2 and remarkable reaction kinetics (<4 min) at ambient temperature. These experimental and computational findings highlight the potential of this Laves-HEA system as tuneable, stable, and cost-effective materials suitable for long-term operations in stationary hydrogen storage and compression applications.

36 MATERIALS SCIENCE↗
DOE OSTI2023

REYNO: A Reactive Hydrodynamics Modeling Suite

REYNO is a Python library that is primarily designed as a platform for the agile development and testing of novel reactive flow models. Equations of state and multi-step rate laws can be implemented using the provided class hierarchy with different thermodynamic closure conditions. The library includes a one-dimensional Lagrangian hydrodynamic solver to simulate multi-material reactive or inert problems in planar, cylindrical, or spherical coordinates. Custom time-dependent boundary conditions are also available for problems such as ramp compression. This document describes the different numerical methods and algorithms that are included in REYNO.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Quantum Ornstein-Zernike theory for two-temperature two-component plasmas

Laboratory plasma production almost always preferentially heats either the ions or electrons, leading to a two-temperature state. In this state, density functional theory molecular dynamic simulation is the state of the art for modeling bulk material properties. We construct a statistical mechanics model for the two temperature limit that is theoretically consistent with the molecular dynamics method. We proceed to derive the electron-ion multi-temperature quantum Ornstein-Zernike equations for the first time. This allows the construction of a two-temperature two-component plasma model using the average atom from which we can compute bulk material properties at a fraction of the computation time of the two-temperature density functional theory simulation. The accuracy of the model is benchmarked against ion pair correlation and self-diffusion results from ab initio simulation. Here, we proceed to compute the viscosity and ion thermal conductivity as a function of both ion and electron temperature.

Ab initio molecular dynamics↗
DOE OSTI2022

Reversible Ligand Protonation in Noninnocent Constrained-Geometry-Like Group 4 Complexes

The proligands C 5 H 5 CMe 2 CHPhOx R (R = Me 2 , CHMe 2 , and CMe 3 ) react with M(NMe 2 ) 4 (M = Ti, Zr, and Hf) to give monodeprotonated (Ox R CHPhCMe 2 C 5 H 4 )M(NMe 2 ) 3 , doubly deprotonated (C 5 H 4 CMe 2 CPhOx R )M(NMe 2 ) 2 , or a mixture of both. The observed products depend on reaction conditions, the oxazoline substituent, and the metal center, with 4-t-butyl-oxazoline or Ti giving only the monodeprotonated (Ox R CHPhCMe 2 C 5 H 4 )M(NMe 2 ) 3 . Amine elimination from (Ox R CHPhCMe 2 C 5 H 4 )M(NMe 2 ) 3 to give (C 5 H 4 CMe 2 CPhOx R )M(NMe 2 ) 2 is reversible for 4,4-dimethyl- and 4-isopropyl-oxazoline-based ligands in Zr or Hf complexes. Temperature-dependent kinetic studies of the equilibration of (C 5 H 4 CMe 2 CPhOx Me2 )Zr(NMe 2 ) 2 , HNMe 2 and (Ox Me2 CHPhCMe 2 C 5 H 4 )Zr(NMe 2 ) 3 provide the experimental thermodynamic parameters ΔS° = -17.4 ± 2.6 cal·mol –1 K –1 and ΔH° = -6.8 ± 0.8 kcal·mol –1 . An Eyring plot of the rate constants, determined from the system as it approaches equilibrium, gives the activation entropy and activation enthalpy for the addition of (C 5 H 4 CMe 2 CPhOx Me2 )Zr(NMe 2 ) 2 and HNMe 2 as -36 ± 4 cal·mol –1 K –1 and 8.9 ± 1.3 kcal·mol –1 , respectively; the elimination of HNMe 2 from (Ox Me2 CHPhCMe 2 C 5 H 4 )Zr(NMe 2 ) 3 is characterized by ΔS ‡ = -19 ± 5 cal·mol –1 K –1 and ΔH ‡ = 15.7 ± 1.5 kcal·mol –1 . DFT computational models indicate a single-step, nonlinear transfer of the H between the benzylic position of the noninnocent, oxazoline-coordinated ligand and NMe 2 . Computations also confirm the negative activation entropy and the trends in the barriers support the experimental results. Together, these studies indicate the importance of steric effects from the oxazoline ligand, metal center, ancillary ligands, and leaving group on the shuttling of the proton between HNMe 2 and the noninnocent ligand. Finally, these effects suggest that coordination of oxazoline to the metal center is a key part of the benzylic deprotonation and noninnocent behavior of the cyclopentadienyl-oxazoline ligand.

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

Discovery of a Wurtzite-like Cu 2 FeSnSe 4 Semiconductor Nanocrystal Polymorph and Implications for Related CuFeSe 2 Materials

I 2 -II-IV-VI 4 and I-III-VI 2 semiconductor nanocrystals have found applications in photovoltaics and other optoelectronic technologies because of their low toxicity and efficient light absorption into the near-infrared. Herein, we report the discovery of a metastable wurtzite-like polymorph of Cu 2 FeSnSe 4 , a member of the I 2 -II-IV-VI 4 family of semi-conductors containing only Earth-abundant metals. Density functional theory calculations on this metastable poly-morph of Cu 2 FeSnSe 4 indicate that it may be a superior semiconductor for solar energy and optoelectronics applications compared to the thermodynamically preferred stannite polymorph, since the former displays a sharper dispersion of energy levels near the conduction band minimum that can enhance electron mobility and suppress hot electron cooling. The experimental optical band gap was measured by the inverse logarithmic derivative method to be direct, in agreement with theory, and in the range of 1.48-1.59 eV. Mechanistic studies reveal that this metastable phase de-rives from intermediate Cu 3 Se 2 nanocrystals that serve as a structural template for the final hexagonal wurtzite-like product. We compare the chemistry of wurtzite-like Cu 2 FeSnSe 4 to the related CuFeSe 2 material system. Our experimental and computational comparisons between Cu 2 FeSnSe 4 and CuFeSe 2 help explain both the crystal chemistry of CuFeSe 2 that prevents it from forming wurtzite-like polymorphs and the essential role of Sn in stabilizing the metastable structure of Cu 2 FeSnSe 4 . Furthermore, this work provides insight into the importance of elemental composition when designing syntheses for metastable materials.

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

Alloying Effects on the Transport Properties of Refractory High-entropy Alloys

Additive Manufacturing (AM) has opened new frontiers for the design of refractory high-entropy alloys (HEAs) for high-temperature applications. The thermal conductivity of the AM feedstock is among the most important thermo-physical properties that control the melting and solidification process. Despite its significance, there remains a notable gap in both computational and experimental research concerning the thermal conductivity of HEAs. Here, we use density functional theory (DFT) to systematically investigate the alloying effects on the transport properties of Ti-Cr-Mo-W-V-Nb-Ta RHEAs, including electrical and thermal conductivities and Seebeck coefficient. The relaxation time of charge carriers is a key underlying parameter determining thermal conductivity that is exceedingly challenging to predict from first principles alone, and we thus follow the approach by Mukherjee, Satsangi, and Singh [Chem Mater 32, 6507 (2022)] to optimize the relaxation time for RHEAs. Here we validated thermal conductivity predictions on elemental solids, binary and ternary alloys, and RHEAs and compared them against thermodynamic (CALPHAD) predictions and our experiments with good correlations. To understand observed trends in thermal conductivity, we assessed the phase stability, electronic structure, phonon, and intrinsic- and tensile strength of down-selected RHEAs. Our electronic structure and phonon results connect well with the observed compositional trends for thermal transport in RHEAs. Our DFT assessment and CALPHAD predictions provide a unique design guide for RHEAs with tailored thermal conductivity, a critical consideration for AM and thermal-management applications.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Enhanced Twist-Averaging Technique for Magnetic Metals: Applications Using Quantum Monte Carlo

In this study, we propose an improved twist-averaging (TA) scheme for quantum Monte Carlo methods that use converged Kohn–Sham or Hartree–Fock orbitals as the reference. This TA technique is tailored to sample the Brillouin zone of magnetic metals, although it naturally extends to nonmagnetic (NM) conducting systems. The proposed scheme aims to reproduce the reference magnetization and achieves charge neutrality by construction, thus avoiding the large energy fluctuations and the postprocessing needed to correct the energies. It shows the most robust convergence of total energy and magnetism to the thermodynamic limit (TDL) when compared to four other TA schemes. Diffusion Monte Carlo applications are shown on NM Al and ferromagnetic α-Fe. The cohesive energy of Al in the TDL shows an excellent agreement with the experimental result. Furthermore, the magnetic moments in α-Fe exhibit rapid convergence with an increasing number of twists.

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

Configuration Space Integration for Adsorbate Partition Functions: The Effect of Anharmonicity on the Thermophysical Properties of CO–Pt(111) and CH 3 OH–Cu(111)

A method for computing anharmonic thermophysical properties for adsorbates on metal surfaces has been extended to include libration, or frustrated rotation. Classical phase space integration is used with Monte Carlo sampling of the configuration space to obtain the partition function of CO on Pt(111) and CH 3 OH on Cu(111). A minima-preserving neural network potential energy surrogate is used within the integration routines. Direct state counting using discrete variable representation is used to benchmark the results. We find that the phase space integration approach is in excellent agreement with the direct state counting results. Comparison with standard models such as the harmonic oscillator indicates that anharmonicity contributes significantly to the thermodynamic properties of CH 3 OH on Cu(111). We find that there is also a considerable difference between the harmonic oscillator and phase space integration for CO on Pt(111), although the discrepancy can largely be attributed to the presence of multiple binding sites within the unit cell. We demonstrate that a multisite harmonic oscillator model might be sufficient for CO-Pt(111). A more thorough description of the potential energy surface, which can be achieved with phase space integration, is necessary for weakly bound adsorbates such as CH 3 OH. In conclusion, the thermophysical properties were used to calculate free energies of adsorption on the respective metals, and subsequently the equilibrium constants and Langmuir isotherms in relevant temperature ranges. The results show that the choice of model to obtain partition functions greatly affects the resulting surface coverages in kinetic models.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗