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Results for “Normalized enthalpy”

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 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Exploring laser-material interactions of zirconium carbide under additive manufacturing conditions

Zirconium carbide (ZrC) is an ultra-high temperature ceramic with a melting temperature above 3000°C and a broad range of high temperature applications. Given the high melting and sintering temperatures of pure ZrC, producing near-net shape and fully dense parts remains challenging with conventional techniques. In this study, we investigate the fundamental laser-material interactions of ZrC under laser powder bed fusion (LPBF) additive manufacturing (AM) conditions. Normalized enthalpy, a scaling law term that is used in welding and AM literature for detailing laser-material interactions in metallic alloys, was calculated to determine the predictive capabilities of melt pool features in ZrC. Further, the melt pool quality of laser irradiated ZrC was used to compare LPBF relevant laser parameter combinations of laser power, scan speed, and beam diameter. Laser build parameters that resulted in desirable melt pool morphologies were applied to the fabrication of ZrC coupons using LPBF AM. A custom LPBF system was used to determine hatch spacing and layer height parameters that resulted in a fabricated sample with a density of 85% as measured by Archimedes and a Vicker's microhardness of 20.9 ± 1.9 GPa. This investigation reveals the laser-material interactions of ZrC under AM relevant conditions and is the first step towards LPBF fabrication of ZrC parts.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Energetics of oxidation and formation of uranium monocarbide

To enable better implementation of uranium monocarbide (UC) as an advanced nuclear fuel for future high-temperature reactors, it is essential to have a thorough knowledge of its thermal and thermodynamic properties under reactor operational conditions. In this work, we studied thermal bulk oxidation of UC by simultaneous thermal analysis consisting of thermogravimetric analysis – differential scanning calorimetry coupled with evolved gas mass spectrometry (TGA-DSC-MS), and we examined the thermodynamic stability of UC using high temperature oxide melt drop solution calorimetry. Further, in air, our studied UC sample (which contains ~5 mol% UO 2 ) was found to undergo a step-wise thermal oxidation process consisting of consecutive oxidations and thermal decomposition reactions: 0.95UC·0.05UO 2 → UO 3 ·0.29(C x O y ) + 0.66CO 2 → UO 3 ·0.20(C x O y ) + 0.09CO 2 → UO 3 ·0.03(C x O y ) + 0.17CO 2 → U 3 O 8 + 0.03CO 2 + 0.166O 2 . DSC was further used to determine the enthalpies of reactions associated with this series of oxidation reactions. Synchrotron X-ray diffraction (XRD) and extended X-ray absorption spectroscopy (EXAFS) were performed to characterize both the long- and short-range structures of UC. The standard enthalpy of formation (ΔH° f ) of UC was determined to be –50.7 ± 10.8 kJ/mol·atom, in good agreement with previous values measured by bomb calorimetry. Lastly, the enthalpic landscape of U-C compounds, including UC, U 2 C 3 , and α-UC 1.94 , were established based on the enthalpy normalized per mole atom, which suggests that U-C phases are thermodynamically stable at lower C/U ratios.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2025

A Review of the Influence of Processing Parameters on ODS Steels Produced via Additive Manufacturing Techniques

Abstract This paper reviews current observations regarding processing conditions for oxide dispersion-strengthened steels consolidated through additive manufacturing techniques. Variations in ODS steels observed across process parameters include changes in grain size, grain texture, oxide size, density of oxides, porosity, melt pool characteristics, and mechanical properties. These properties were then compared across techniques to understand which techniques and processing conditions lead to the highest strength, ductility, and oxide density. Current literature suggests that a mix of grain types, in the form of either morphology or phase, can significantly increase the strength of printed ODS steels. Meanwhile, the most ductile samples, regardless of consolidation technique or matrix material, were made from feedstock with oxide additions located on the powder surface. Reported grain and oxide sizes were plotted against the ratio of laser power to scan speed, volumetric energy density, and normalized enthalpy. No strong correlation between these values and microstructural features was observed. The plots that were made suggest that a larger data set, more in-depth representative equations, and more defined material properties as a function of specific feedstock used are necessary to determine a value that can be correlated to the printed ODS steel microstructure.

deJong, Matthew↗
DOE OSTI2021

The causal relationship between melt pool geometry and energy absorption measured in real time during laser-based manufacturing

During laser powder bed fusion additive manufacturing, laser power absorption is governed by a pro -tean pool of molten metal that can present as a highly reflective surface, a deeply absorbing cavity, or some amalgamation thereof. These melt pool dynamics have been linked to defect creation, porosity, and surface finish quality. Although these are therefore critical for determining final part quality, their in-stantaneous influence on laser absorption have only been explored through simulation. To date, direct real-time observations have been elusive due to the locally extreme environment. In this work, we fo-cus a laser on Ti-6Al-4V powder and bare plate while quantifying the time-dependent, absolute energy absorption by monitoring omnidirectional backscattered laser intensity. We also simultaneously record the projective melt pool geometries with high-speed synchrotron x-ray imaging. We find that laser ab-sorption strongly reflects the stability of the vapor depression over a wide range of applied laser powers, oxygen content in the processing atmosphere, and with the presence of powder. During laser scanning of a powder bed surface, we find a significant absorption reduction after 400 mu s due to a dramatic change in the vapor depression aspect ratio-an event known to create porosity. Furthermore, as several industrial scan strate-gies necessitate thousands of these events during a build, their identification and control is of significant practical importance. Lastly, a normalized enthalpy model is demonstrated to be effective in quantifying the relationship between the laser absorption and cavity depth, even under transient conditions. In addi-tion to providing vital quantitative data for simulation calibration, the correlation of melt pool geometry with laser absorption during realistic processing conditions suggests the use of a total backscattered light detection system for real-time process control.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Effect of LPBF Processing Parameters on Inconel 718 Lattice Structures: Geometrical Characteristics, Surface Morphology, and Mechanical Properties

Laser Powder Bed Fusion (LPBF) enables the additive manufacturing of complex lattice structures. However, the fabrication of lattice structures via LPBF poses challenges in achieving the intended geometrical accuracy due to their inherent complexity. This study investigates the effects of LPBF processing parameters, specifically laser power and scanning speed, on the geometrical characteristics, surface quality, and mechanical behavior of Inconel 718 lattices structures. The results reveal that processing parameters required for the fabrication of near-full dense structures do not translate effectively to lattice configurations, as variations in energy input influence lattice geometry and surface quality. In this work, strut thickness, open-pore size, open-cell porosity, and surface roughness were measured, and the mechanical properties of the lattices were evaluated under shear loading. The findings indicate that lower energy inputs, achieved by reducing laser power and increasing scanning speed, yield porous structures but lead to mechanical degradation. In contrast, high energy inputs lead to lattices with enhanced strength but result in undesirable open-pore blockage and dimensional inaccuracies. These findings provide insights into tailoring LPBF parameters for dimensional accuracy in lattices and correlating the processing parameters to mechanical performance and surface roughness.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Comptonization by reconnection plasmoids in black hole coronae – III. Dependence on the guide field in pair plasma

ABSTRACT We perform non-radiative two-dimensional particle-in-cell simulations of magnetic reconnection for various strengths of the guide field (perpendicular to the reversing field), in magnetically dominated electron–positron plasmas. Magnetic reconnection under such conditions could operate in accretion disc coronae around black holes. There, it has been suggested that the transrelativistic bulk motions of reconnection plasmoids containing inverse-Compton-cooled electrons could Compton-upscatter soft photons to produce the observed non-thermal hard X-rays. Our simulations are performed for magnetizations 3 ≤ σ ≤ 40 (defined as the ratio of enthalpy density of the reversing field to plasma enthalpy density) and guide field strengths 0 ≤ Bg/B0 ≤ 1 (normalized to the reversing field strength B0). We find that the mean bulk energy of the reconnected plasma depends only weakly on the flow magnetization but strongly on the guide field strength – with Bg/B0 = 1 yielding a mean bulk energy twice smaller than Bg/B0 = 0. Similarly, the dispersion of bulk motions around the mean – a signature of stochasticity in the plasmoid chain’s motions – is weakly dependent on magnetization (for σ ≳ 10) but strongly dependent on the guide field strength – dropping by more than a factor of two from Bg/B0 = 0 to Bg/B0 = 1. In short, reconnection in strong guide fields (Bg/B0 ∼ 1) leads to slower and more ordered plasmoid bulk motions than its weak guide field (Bg/B0 ∼ 0) counterpart.

Astronomy & Astrophysics↗
DOE OSTI2020

High-throughput investigation of the formation of double spinels

Spinel compounds, with the general chemical formula AB 2 O 4 , are a wide class of materials, where A and B can be a variety of cations, providing this structure with a great deal of functional flexibility and giving rise to its considerable scientific interest. Recently, a spinel with the general formula ABB'O 4 has been predicted, increasing the possible usability of the spinels due to the higher cation diversity in the so-called double spinel structure. In this study, we use density functional theory calculations to predict if double spinels can be formed between experimentally synthesized normal and inverse single spinels. Our computations reveal that 49 double spinels have negative mixing enthalpies and are thus thermodynamically stable, with most of the stable compounds being formed from one of two distinct cation orderings. We show that the 17 different cations that form the different double spinels have a preferred site, tetrahedral or octahedral, except for Mn, Fe and Co which can occupy both sites interchangeably. We also study the relation between mixing enthalpies and cation-specific properties, as well as ways to classify the double spinels into distinct types and spinel groups depending on the cation ordering and cation oxidation states, respectively. Furthermore, by applying the Sure Independence Screening and Sparsifying Operator (SISSO) approach on the coordination-dependent ionic radii of the elemental constituents, we show that an interplay of local strain and electrostatic dominated terms can be used to separate the double spinels into distinct structural types depending on the cation order and their oxidation states.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Low- and high-temperature heat capacity of metallic technetium

The heat capacity of technetium metal has been measured from 2.1 K to 293 K using relaxation calorimetry and the enthalpy increment up to 1700 K using drop calorimetry. The low-temperature calorimetry measurements revealed a superconducting transition temperature of T C = (7.76 ± 0.08) K. The zero-degree Debye temperature(θ E ) and the electronic heat capacity coefficient ($γ_{e}$) of the normal state were derived as (307 ± 5) K and (4.22 ± 0.20) mJ·K –2 ·mol –1 , respectively. The standard entropy of the superconducting standard state was derived as $S^{°}_{m}$ (298.15) = (36.8 ± 1.3) J·K –1 ·mol –1 . The fitting of enthalpy-increment data together with high-temperature heat capacity data reported in literature yielded a heat capacity equation up to 1700 K.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Determination of the enthalpy of adsorption of hydrogen in activated carbon at room temperature

The development of high-performance materials for hydrogen storage by adsorption requires detailed understanding of the adsorbate-adsorbent interactions, e.g., the enthalpy of adsorption ΔH, which measures the interaction strength. The determination of ΔH for a weakly adsorbing gas such as hydrogen in a carbonaceous porous material is difficult experimentally, normally requiring measuring two cryogenic adsorption isotherms. Here we demonstrate a calculation of ΔH based on ca. room temperature adsorption isotherms at 273 K and 296 K using the Clausius-Clapeyron equation. This requires an estimation of the volume of the adsorbed film (~40%, ~12% of the total pore volume at 77 K, 296 K, respectively) obtained from fits of the excess adsorption isotherms to an Ono-Kondo model with the auxiliary use of a fixed point corresponding to the saturation film density (estimated as 100 ± 20 g/L) which appears to be remarkably sample and temperature independent, i.e., a property of the adsorbate. The calculated room temperature enthalpy of adsorption ΔH = 8.3 ± 0.4 kJ/mol is in excellent agreement with the low-coverage cryogenic determination of ΔH. The methodology hereby proposed facilitates reliable calculations of the enthalpy of adsorption at room temperatures for weakly-adsorbing gases.

08 HYDROGEN↗
DOE OSTI2021

Effect of Temperature and FEC on Silicon Anode Heat Generation Measured by Isothermal Microcalorimetry

Isothermal microcalorimetry (IMC) was used to better understand parasitic reactions and heat generation from Si electrodes in the first 10 cycles using Li/Si half cells. Heat generation from cell polarization (ohmic heat), entropy changes (reversible heat), and parasitic reactions (parasitic heat) are separated and quantified. The effect of temperature and fluoroethylene carbonate (FEC) as an electrolyte additive are also explored. Our results show that at the C/10 cycling rate used here, ohmic heat makes the largest contribution to overall heat generation while reversible heat is the smallest. Ohmic heat generation increases with cycle number due to increasing internal resistance, though the effect is smaller for cells with FEC. Interestingly, capacity-normalized parasitic heat generation is largely unaffected by changes in temperature despite differing reaction kinetics. We show that this is caused by a decrease in average parasitic reaction enthalpy as temperature is increased. Further, cells with FEC display higher average parasitic reaction enthalpy than cells without. The average parasitic reaction enthalpies for all the Si electrodes we tested were lower than previously reported values for graphite, indicating that the SEI formed on Si is less stable.

25 ENERGY STORAGE↗
DOE OSTI2023

Stability Criteria for Self-Propagating Reaction Waves in Co/Al Multilayers

The propagation of self-sustained formation reactions in sputter-deposited Co/Al multilayers is known to exhibit a design-dependent instability. Multilayers having thin bilayers (<55 nm period) exhibit stable propagating waves, whereas those with a larger period react unstably. The specific two-dimensional (2D) instability observed involves the transverse propagation of a band in front of a stalled front commonly referred to as a “spin band.” Previous finite-element studies have shown that these instabilities are thermodynamically driven by the forward conduction of heat away from the flame front. However, the magnitude of that loss is inherently tied to the bilayer design in traditional bimetallic multilayers, which couples any proposed stability criteria to a varying critical diffusion distance. Here, this work utilizes a recently developed class of materials known as “inert-mediated reactive multilayers” to decouple the thermodynamic and kinetic contributions to propagating wave stability by reducing the stored chemical energy density in normally stable bilayer designs. By depositing an inert product phase (B2-CoAl) within the mid-plane of Co and Al reactant layers, spin instabilities arise as a function of both diluted volume and critical diffusion distance. From there, a stability criterion is determined for Co/Al multilayers based on enthalpy loss from the reaction zone, and its physical significance is explored.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Glass transition temperature studies of planetary ball milled glasses: Accessing the rapidly cooled glassy state in Na 4 P 2 S 7-x O x , 0 ≤ x ≤ 7, Oxy-thio phosphate glasses

This paper details the very first in-depth study of the glass transition temperature (T g ) for planetary balled milled (PBM) Na 4 P 2 S 7-x O x (NaPSO), where 0 ≤ x ≤ 7, glasses. For 0 ≤ x ≤ 5, fully amorphous, homogeneous, and chemically reacted compositions can be prepared. For samples with 5 < x ≤ 7, partially amorphous but fully chemically reacted glass-ceramics can be produced. The reproducible, thermally cyclable onset T g and the onset crystallization temperature, T c , were investigated as a function of the composition and of the short-range order (SRO) structures of the glasses. Additionally, we examined the extreme sub-T g exothermic relaxations present due to the high energy milling processing and correspondingly high effective quenching rate. Using a differential scanning calorimeter (DSC) and scanning from well below the onset T g , the glasses are observed to relax exothermally below T g . The integrated relaxation enthalpy, ΔH rel , is ~ 0 for the x = 2 glass, but is significantly exothermic for lower and higher values of x. Once the high fictive state of these glasses has been erased by scanning to above the T g , but below the T c of the glass, the DSC scans of the glasses recover normal behavior for a normally cooled glass without any relaxation exotherm. The T g s of these glasses remain relatively constant for 0 ≤ x ≤ 3, but for glasses with 3 < x ≤ 5, T g increases sharply following the combined effects of the phosphate chain length increasing caused by the formation of bridging oxygens and the increasing concentration of more charge dense non-bridging oxygens (NBOs). For x > 5, both T g and Tc decrease sharply, becoming nearly identical at x = 7 where glass formation essentially ceases. For smaller values of x, T c increases with both chain length and the structural complexity of the composition but decreases sharply for glass-ceramics of x > 5.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Molecular-level understanding of gibbsite particle aggregation in water

Using molecular dynamics simulations, we investigate the molecular scale origin of crystal face selectivity when one gibbsite particle attaches to another in water. A comparison of the free energy per unit surface area of particle–particle attachment indicates that particle attachment through edge surfaces, where the edge surfaces are either (1 0 0) or (1 1 0) crystal faces, is more energetically favorable compared to attachment between two basal surfaces (i.e., (0 0 1) crystal faces) or between the basal surface of one particle and the edge surface of another. This result suggests that gibbsite crystals with low basal/edge surface area ratio will preferentially attach through edge surfaces, potentially helping the crystals grow laterally. However, for larger gibbsite particles (high basal/edge surface area ratio) the total free energy, not normalized by surface area, of particle attachment through the basal surfaces is lower (more negative) than attachment through the edge surfaces, indicating that larger gibbsite particles will preferentially aggregate through basal surface attachments. The short-range electrostatic interactions including the interparticle hydrogen bonds from surface –OH groups drive particle attachment, and the dominant contribution to the free energy minimum is enthalpic rather than entropic. However, the enthalpy of basal-edge attachment is significantly offset by the entropy leading to a higher free energy (less negative) compared to that of basal-basal attachment. Study of the free energy for a few imperfect attachments of two particles indicates a higher free energy (i.e., less negative, less stable), compared to a perfect attachment

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

Thermal mechanical assessment of a SiC-SiC-composite clad fuel pin concept in a light water reactor environment

Accident Tolerant Fuels (ATFs) are designed to increase coping time following an accident scenario while preserving or improving current steady state reactor operational performance. A potential ATF concept is SiC-SiC composite claddings. Fuel performance simulations were conducted on a SiC-SiC based cladding concept utilizing a multilayered approach for improved performance. This cladding concept referred to as the Duplex concept is a duplex structure composed of a monolithic SiC layer placed on the outside of a SiC-SiC composite. A liquid metal is added to fuel-cladding gap for improved heat dissipation from the fuel. The monolithic SiC layer is used to improve the coolant corrosion characteristics and protect the SiC-SiC composite layer from exposure to the coolant. The fuel performance code BISON was used to conduct fuel performance simulations on the cladding concepts. Comparisons are made with a current prototypic fuel rod design (UO 2 fuel enclosed in Zircaloy-4 cladding). Representative steady-state cases were considered for normal power and two cycle power histories. Additionally, a PCI ramp case was simulated to analyze potential anticipated operational occurrences. Transient response during a Loss of Coolant Accident and a Reactivity Initiated Accident were also simulated. This computational study demonstrated that for normal operating conditions, the SiC concept cladding performed as well as the baseline for the standard power cases evaluated. The ramping evaluations indicate potential fracturing of the SiC-SiC composite of the composite cladding compared to the Zircaloy-4 cladding due to the temperature gradient and the subsequent differential thermal conductivity degradation and swelling across the composite thickness. In conclusion, the rod fails early at low enthalpy for RIA but survives a LOCA with minimal material loss due to high temperature steam corrosion.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2024

Phase equilibria of advanced technology uranium silicide-based nuclear fuel

The phases in uranium-silicide binary system were evaluated in regards to their stabilities, phase boundaries, crystal structures, and phase transitions. The results from this study were used in combination with a well assessed literature to optimize the U-Si phase diagram using the CALPHAD method. A thermodynamic database was developed, which could be used to guide nuclear fuel fabrication, could be incorporated into other nuclear fuel thermodynamic databases, or could be used to generate data required by fuel performance codes to model fuel behavior in normal or off-normal reactor operations. The U 3 Si 2 and U 3 Si 5 phases were modeled using the Compound Energy Formalism model with 3 sublattices to account for the variation in composition. The crystal structure used for the USi phase was the tetragonal with an I4/mmm space. Above 450°C, the U 3 Si 5 phase was modeled. The composition of the USi 2 phase was adjusted to USi 1.84 . The calculated invariant reactions and the enthalpy of formation for the stoichiometric phases were in agreement with experimental data.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2021

Process Engineering to Increase the Layered Phase Concentration in the Immediate Products of Flame Spray Pyrolysis

Flame-spray-pyrolysis (FSP) is a robust and scalable process to synthesize particles at the commodity-scale. FSP has been used to produce the precursor powders which were converted to the layered structure $(R\bar{3m} \text { phase})$ by a postannealing step in making nickel-rich cathode materials (NCMs). Theoretically, the high flame temperature (normally >1500 K) in FSP can provide adequate energy for the phase conversion from rock-salt to layered structures and potentially enables one-step synthesis. However, the high flame temperature is a critical issue to cause lithium loss and structural degradation, preventing the formation of the layered phase. Here, guided by the gaseous nucleation theory, we implemented several FSP processes with different solution recipes. The layered phase concentration in the as-burned products can be increased with the solution enthalpies. By adding a rapid quench step to suppress the lithium loss and phase degradation, the layered phase can be further increased. This work contributes new ideas to innovating process regarding the process efficiency and throughput of manufacturing cathode materials at a large scale.

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

Interactions of Polar and Nonpolar Groups of Alcohols in Zeolite Pores

Understanding the quantitative interactions among zeolite pore walls, Bro̷nsted acid sites, and molecules with both polar and nonpolar regions is essential for scoping out the potential of zeolites as sorbents and catalysts. Purely siliceous zeolites (MFI and Beta in the present study) are hydrophobic, whereas those containing aluminum are considered hydrophilic, preferentially adsorbing organic molecules even in aqueous environments. To characterize these interactions, we use primary alcohols of increasing molecular weight, quantifying their specific interactions in the confined pore space of the alkyl (CH x ) and OH groups. Three types of interactions were identified: (i) alkyl CH x groups interacting with the zeolite pore walls (approximately 10 kJ mol −1 per carbon), (ii) alcohol OH groups interacting with the pore walls (30−35 kJ mol −1 ), and (iii) alcohol OH groups interacting with Bro̷nsted acid sites (37 kJ mol −1 ). All three interactions were well mirrored by computational simulations. The contribution of the alkyl CH x groups was inferred from the incremental increase in sorption enthalpy with increasing molecular weight; the interaction strength of the OH groups was determined by extrapolating the global adsorption enthalpy of the alcohols to a hypothetical OH group without an alkyl group. This value was identical to the adsorption enthalpy of water. The experiments demonstrated that only water has an adsorption enthalpy on zeolite pore walls lower than its condensation enthalpy (30−35 kJ mol −1 vs 45 kJ mol −1 ), limiting the concentration of water that can be adsorbed.

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

Extracting meaningful standard enthalpies and entropies of activation for surface reactions from kinetic rates

While analyses based on the Arrhenius kinetic model have been successfully applied since its introduction, the Arrhenius model neglects to describe pre-exponential factor in a scientifically meaningful fashion. Since the 1930s, transition-state theory (TST), has met with success in interpreting the pre-exponential factor’s value, allowing a standard entropy of activation to be estimated. However, analyses based on TST’s assumptions have been applied inconsistently in the literature, particularly in corrosion science, leading to difficulty in comparison of standard entropy of activations from different studies. In this work, the foundational principles of TST and standard states are discussed and a standard method to apply TST in analyzing rates of surface reactions is recommended. When full details are not available, reacting species’ concentrations should be normalized to the concentration of active surface sites. For corrosion reactions, conversion relationships are given to convert from units of corrosion rate to surface reaction rate, consistent with TST. This method is dubbed a surface reactant equi-density approximation. Application of this standard to reported data results in adjustments of the standard entropy of activation between - 65 and +50 J/mol K and brings reported entropies into a narrower range of values.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗