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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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All sourcesNASA NTRSDOE OSTI
NASA NTRS1995

Ab Initio Characterization of Triatomic Bromine Molecules of Potential Interest in Stratospheric Chemistry

The equilibrium structures, harmonic vibrational frequencies, quadratic force fields, dipole moments, and IR intensities of several triatomic bromine compounds of known or potential importance in stratospheric ozone depletion chemistry have been determined using the CCSD(T) electron correlation method in conjunction with a basis set of triple zeta double polarized (TZ2P) quality. Specifically, the molecules included in the present study are HOBr, HBrO, FOBr, FBrO, BrNO, BrON, Br2O, BrBrO, BrCN, BrNC, ClOBr, ClBrO, and BrClO. Very accurate isomeric energy differences have also been determined at the CCSD(T) level with atomic natural orbital basis sets that include through g-type functions. In most cases, the isomer with a normal neutral Lewis dot structure is the lowest energy form, with the single exception that FBrO is predicted to be 11.1 kcal/mol (0 K) lower in energy than FOBr. In all cases, however, the hypervalent isomer is more stable relative to the isomer with a normal Lewis dot structure as compared to the chlorine analogs. Consistent with this observation, the energy of the last three molecules given above increases in the order ClOBr less than ClBrO less than BrClO. The CCSD(T)/TZ2P geometries and vibrational frequencies are in good agreement with the available experimental data. Heats of formation are determined for all species using a combination of theoretical isomeric, homodesmic, and isodesmic reaction energies. The accuracy of these quantities is ultimately dependent on the reliability of the experimental heat of formation of HOBr.

Lee, Timothy J.↗
DOE OSTI2023

Atomic motifs govern the decoration of grain boundaries by interstitial solutes

Abstract Grain boundaries, the two-dimensional defects between differently oriented crystals, tend to preferentially attract solutes for segregation. Solute segregation has a significant effect on the mechanical and transport properties of materials. At the atomic level, however, the interplay of structure and composition of grain boundaries remains elusive, especially with respect to light interstitial solutes like B and C. Here, we use Fe alloyed with B and C to exploit the strong interdependence of interface structure and chemistry via charge-density imaging and atom probe tomography methods. Direct imaging and quantifying of light interstitial solutes at grain boundaries provide insight into decoration tendencies governed by atomic motifs. We find that even a change in the inclination of the grain boundary plane with identical misorientation impacts grain boundary composition and atomic arrangement. Thus, it is the smallest structural hierarchical level, the atomic motifs, that controls the most important chemical properties of the grain boundaries. This insight not only closes a missing link between the structure and chemical composition of such defects but also enables the targeted design and passivation of the chemical state of grain boundaries to free them from their role as entry gates for corrosion, hydrogen embrittlement, or mechanical failure.

36 MATERIALS SCIENCE↗
NASA NTRS1988

Trace fossils of microbial colonization on Mars: Criteria for search and for sample return

The recent discovery of microbial trace-fossil formation in the frigid Ross Desert of Antarctica suggests that early primitive life on Mars may have left behind similar signatures. These trace fossils are apparent as chemical or physical changes in rock (or sediment) structure (or chemistry) caused by the activity of organisms. Life on Mars, if it ever existed, almost certainly did not evolve above the level of microorganisms, and this should be considered in search for fossil life. For the reasons detailed here, microbial trace fossils seem to be a better and more realistic target for search than would be true microbial fossils (remnants of cellular structures).

Friedmann, E. I.↗
NASA NTRS1998

In search of cellular control: signal transduction in context

The field of molecular cell biology has experienced enormous advances over the last century by reducing the complexity of living cells into simpler molecular components and binding interactions that are amenable to rigorous biochemical analysis. However, as our tools become more powerful, there is a tendency to define mechanisms by what we can measure. The field is currently dominated by efforts to identify the key molecules and sequences that mediate the function of critical receptors, signal transducers, and molecular switches. Unfortunately, these conventional experimental approaches ignore the importance of supramolecular control mechanisms that play a critical role in cellular regulation. Thus, the significance of individual molecular constituents cannot be fully understood when studied in isolation because their function may vary depending on their context within the structural complexity of the living cell. These higher-order regulatory mechanisms are based on the cell's use of a form of solid-state biochemistry in which molecular components that mediate biochemical processing and signal transduction are immobilized on insoluble cytoskeletal scaffolds in the cytoplasm and nucleus. Key to the understanding of this form of cellular regulation is the realization that chemistry is structure and hence, recognition of the the importance of architecture and mechanics for signal integration and biochemical control. Recent work that has unified chemical and mechanical signaling pathways provides a glimpse of how this form of higher-order cellular control may function and where paths may lie in the future.

Non-NASA Center↗
DOE OSTI2021

Understanding the local structure of disordered carbons from cellulose and lignin

An electron microscopy investigation was performed to understand the relationship between the microstructure and properties of carbonized cellulose and lignin (softwood kraft lignin) relative to the structure of the original biomass components. Structure details at micro- and molecular levels were investigated by scanning transmission electron microscopy. Atomic-resolution images revealed the presence of random disordered carbon in carbonized cellulose (C-CNC) and of large domains of well-ordered carbon with graphite sheet structure in carbonized lignin (C-Lignin). These structural differences explain why C-CNC exhibits higher surface area and porosity than C-Lignin. The presence of certain well-ordered carbon in carbonized lignin indicates some of the carbon in lignin are graphitized with heat treatment temperature up to 950 °C. This result is encouraging for future endeavors of attaining acceptable modulus of carbon fiber from lignin given suitable modifications to the chemistry and structure of lignin. The results of this research contribute to an improved understanding of the carbonization mechanism of the key cellulose and lignin components of biomass materials.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRSDate not supplied

On the Hunt for Detectable Biosignatures in Jezero Crater: What to Look for and Where

Introduction: The Perseverance rover, which is currently exploring Jezero crater on Mars, is equipped with seven instruments that allow for observation of textures, minerals, color, structure, and chemistry of rocks and sediments in order to search for signs of ancient life, understand the geologic history of the crater, and identify candidates for sample return (Farley et al. 2020). The first of these aims includes the direct detection of potential biosignatures, including textures, organic molecules, minerals, and elemental chemistries that are of biogenic origin (Mustard et al. 2013). The presence of these biosignatures will be constrained by the habitability of the local region, the preservation potential of the host rocks, and the sensitivity of the instrument suite, and their biogenicity will be investigated after return to Earth as part of the Mars Sample Return campaign. Here, we examine key targets on the three planned campaigns, potential biosignatures that may be present, and the capabilities of key rover instruments. High Potential Biosignature Sites in Jezero: To date, measurements have been made on multiple sites that both contain minerals known in terrestrial settings to preserve biosignatures and likely were habitable settings (Williford et al. 2021). Two examples include the fine-grained rocks at the base of the delta fan and the NW inner margin of the crater. Fine-grained Rocks at Base of Delta Fan. Fine-grained, clay-bearing rocks may have been deposited as muddy lake sediments that could have hosted life and preserved biosignatures settling out of the water column. The report of organic molecules by the Curiosity rover in the Sheepbed mudstone and Murray formation has highlighted this site in particular. Potential biosignatures in mudstones, especially those rich in silica (McMahon et al. 2018), microbialites and complex organics. NW Inner Margin of Crater. This unit, located along the inner margin of the crater, contains strong carbonate signatures and may have been the littoral zone of a lake (Horgan et al. 2020). The potential biosignatures here include microfossils, microbialites, biominerals, and complex organics. Detectability of Biosignatures by the Mars 2020 Instrument Suite: The Scanning Habitable Environments with Raman and Luminescence for Organics and Chemicals (SHERLOC) instrument comprises a Deep UV spectrometer, context imager, and color camera to generate spatially resolved chemical maps (Bhartia et al. 2020). It is sensitive to trace organics as well as a range of minerals and can detect native fluorescence from aromatic organics; the WATSON and ACI cameras can be used to observe morphologies such as stromatolitic laminations or filaments ranging from the tens of micron to millimeter scale. SHERLOC can detect organics that may be present in either of the high potential biosignature targets, as well as detect carbonates in the latter. However, the presence of high amounts of iron, such as in iron-rich clays, would cause attenuation of spectral response through UV absorption. The Planetary Instrument for X-ray Lithochemistry (PIXL) comprises an X-ray fluorescence spectrometer and camera that can scan rock surfaces to generate elemental maps (Allwood et al. 2020). PIXL can detect chemical biosignatures such as spatial variations of elemental abundances that may have resulted from biological activity. PIXL would be particularly useful in detecting fine textures and elemental chemistries in either high potential biosignature target, but cannot directly detect minerals such as carbonate. The SuperCam instrument performs three types of spectroscopy, color imaging, and acoustic recording to remotely examine elemental composition, minerals, organics, and textures (Maurice et al. 2021). Using laser induced breakdown spectroscopy and time resolved luminescence spectroscopy, SuperCam can detect major elemental building blocks of organics (i.e., C, H, N, O, P, S) and conjugated organic structures, respectively, which may be found in either site. While in other contexts, luminescence is a useful tool for biosignature identification, luminescence generated by the 532 nm laser may obscure the Raman signal. Conclusion: The three instruments discussed can be used collaboratively to establish the presence of potential biosignatures in samples. These high-priority samples may then be returned to Earth for detailed laboratory analysis.

S. Sharma↗
DOE OSTI2021

Microscopic and Macroscopic Characterization of Grain Boundary Energy and Strength in Silicon Carbide via Machine-Learning Techniques

Predicting the properties of grain boundaries poses a challenge because of the complex relationships between structural and chemical attributes both at the atomic and continuum scales. Grain boundary systems are typically characterized by parameters used to classify local atomic arrangements in order to extract features such as grain boundary energy or grain boundary strength. The present work utilizes a combination of high-throughput atomistic simulations, macroscopic and microscopic descriptors, and machine-learning techniques to characterize the energy and strength of silicon carbide grain boundaries. Additionally, a diverse data set of symmetric tilt and twist grain boundaries are described using macroscopic metrics such as misorientation, the alignment of critical low-index planes, and the Schmid factor, but also in terms of microscopic metrics, by quantifying the local atomic structure and chemistry at the interface. These descriptors are used to create random-forest regression models, allowing for their relative importance to the grain boundary energy and decohesion stress to be better understood. Results show that while the energetics of the grain boundary were best described using the microscopic descriptors, the ability of the macroscopic descriptors to reasonably predict grain boundaries with low energy suggests a link between the crystallographic orientation and the resultant atomic structure that forms at the grain boundary within this regime. For grain boundary strength, neither microscopic nor macroscopic descriptors were able to fully capture the response individually. However, when both descriptor sets were utilized, the decohesion stress of the grain boundary could be accurately predicted. These results highlight the importance of considering both macroscopic and microscopic factors when constructing constitutive models for grain boundary systems, which has significant implications for both understanding the fundamental mechanisms at work and the ability to bridge length scales.

36 MATERIALS SCIENCE↗
NASA NTRS2011

Correlated Microanalysis of Cometary Organic Grains Returned by Stardust

Preliminary examination (PE) of samples returned from Comet 81P/Wild 2 by the NASA Stardust mission revealed a wide variety of carbonaceous samples [e.g. 1]. Carbonaceous matter is present as inclusions, rinds, and films in polyminerallic terminal particles [2-4], as carbon-rich particles along track walls [2, 5, 6], and as organic matter in aerogel around tracks [7, 8]. The organic chemistry of these samples ranges from purely aliphatic hydrocarbons to highly-aromatic material, often modified by various organic functional groups [2, 4, 5, 9-11]. Difficulty arises when interpreting the genesis of these carbonaceous samples, since contaminants could be introduced from the spacecraft [12], aerogel [1, 8], or during sample preparation. In addition, hypervelocity capture into aerogel may have heated cometary material in excess of 1000 C, which could have significantly altered the structure and chemistry of carbonaceous matter. Fortunately, much of this contamination or alteration can be identified through correlated microanalysis with transmission electron microscopy (TEM), scanning-transmission X-ray microscopy (STXM), and nanoscale secondary ion mass spectroscopy (SIMS).

DeGregorio, B. T.↗
DOE OSTI2024

Neural network kinetics for exploring diffusion multiplicity and chemical ordering in compositionally complex materials

Diffusion involving atom transport from one location to another governs many important processes and behaviors such as precipitation and phase nucleation. The inherent chemical complexity in compositionally complex materials poses challenges for modeling atomic diffusion and the resulting formation of chemically ordered structures. Here, we introduce a neural network kinetics (NNK) scheme that predicts and simulates diffusion-induced chemical and structural evolution in complex concentrated chemical environments. The framework is grounded on efficient on-lattice structure and chemistry representation combined with artificial neural networks, enabling precise prediction of all path-dependent migration barriers and individual atom jumps. To demonstrate the method, we study the temperature-dependent local chemical ordering in a refractory NbMoTa alloy and reveal a critical temperature at which the B2 order reaches a maximum. The atomic jump randomness map exhibits the highest diffusion heterogeneity (multiplicity) in the vicinity of this characteristic temperature, which is closely related to chemical ordering and B2 structure formation. The scalable NNK framework provides a promising new avenue to exploring diffusion-related properties in the vast compositional space within which extraordinary properties are hidden.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Pulsed-laser epitaxy of metallic delafossite PdCrO 2 films

Alternate stacking of a highly conducting metallic layer with a magnetic triangular layer found in delafossite PdCrO 2 provides an excellent platform for discovering intriguing correlated quantum phenomena. Thin film growth of delafossites may enable not only the tuning of the basic physical properties beyond what bulk materials can exhibit, but also the development of novel hybrid materials by interfacing with dissimilar materials, yet this has proven to be extremely challenging. Here, we report the epitaxial growth of metallic delafossite PdCrO 2 films by pulsed laser epitaxy (PLE). The fundamental role of the PLE growth conditions, epitaxial strain, and chemical and structural characteristics of the substrate is investigated by growing under various growth conditions and on various types of substrates. While strain plays a large role in improving the crystallinity, the direct growth of epitaxial PdCrO 2 films without impurity phases was not successful. We attribute this difficulty to both the chemical and structural dissimilarities with the substrate and volatile nature of the PdO sublayer, which make nucleation of the right phase difficult. This difficulty was overcome by growing CuCrO 2 buffer layers before PdCrO 2 films were grown. Unlike PdCrO 2 , CuCrO 2 films were readily grown with a relatively wide growth window. Only a monolayer thick buffer layer was sufficient to grow the correct PdCrO 2 phase. This result indicates that the epitaxy of Pd-based delafossites is extremely sensitive to the chemistry and structure of the interface, necessitating near perfect substrate materials. The resulting films are commensurately strained and show an antiferromagnetic transition at 40 K that persists down to as thin as 3.6 nm in thickness. This work provides key insights into advancing the epitaxial growth of the broader class of metallic delafossites for both studying the basic physical properties and developing new spintronic and computing devices.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Insights into the Assembly and Conformation of Nanoparticle Organic Hybrid Materials (NOHMs) in Solution with Varying Grafting Type

Recently, nanoparticle organic hybrid materials (NOHMs) have been considered promising electrolytes for energy storage applications due to their unique combination of properties, which include high thermal stability, negligible vapor pressure, and easy synthesis. However, the structural features of NOHMs in electrochemical systems are not well understood. Hence, we investigate the impact of grafting type (ionic vs covalent) on the structure and performance of NOHMs that consist of a silica core and grafted HPE polymer (Jeffamine M2070) in aqueous solution with and without the presence of the supporting electrolyte (0.1 M KHCO 3 ) using small-angle neutron scattering. Careful analyses of the results indicate that even at low grafting density (0.8 chains nm –2 ) and concentration (1–3 wt %), ionic NOHMs solutions contain a free polymer that may interact with the grafted polymer, altering the assembly of NOHMs in solution. Our investigation also elucidates that the covalent NOHM solutions consist of both aggregated and dispersed NOHMs in the solution. Moreover, the addition of the supporting electrolyte affects the assembly and structure of the polymer in the ionic NOHMs solution significantly, whereas only a slight change in the conformation of the grafted polymer is observed for covalent NOHMs. These conformational changes alter the performance of the NOHMs solution, resulting in a dramatic change in viscosity. Careful analysis shows that this significant alteration of solution viscosity in the ionic NOHMs can be traced back to the presence of the free polymer that interacts with the grafted layer and the attenuation of this interaction between the free and grafted polymers with the addition of salt. Furthermore, these studies elucidate the impact of grafting type on the overall structure, assembly, and performance of functionalized NOHMs in aqueous solution and explicitly correlate the structure and assembly of NOHMs to their transport properties and must be considered when designing functional systems that incorporate NOHMs.

25 ENERGY STORAGE↗
DOE OSTI2024

Effect of 60 Co Irradiation on Boehmite Dissolution in Caustic Solutions

Here, in this work, we examine how radiation impacts the dissolution behavior of boehmite by subjecting dry nanoparticles of different sizes to 60 Co γ radiation and subsequently analyzing their dissolution behavior in caustic solutions as a function of temperature. The measured kinetics show that irradiation with an amount 228.24 Mrad significantly slows the dissolution rate, particularly for smaller sizes at lower temperatures. Specifically, the temperature-dependent dissolution rates of irradiated 20 nm boehmite versus pristine material in 3 M NaOH solutions were several times lower (e.g., rate constant of 0.026 vs 0.075 h –1 at 60 °C), with an apparent activation energy 40 kJ mol –1 higher. Although various imaging techniques and X-ray diffraction measurements consistently revealed no obvious differences between pristine and irradiated samples, after irradiation significant binding energy shifts were detected in the X-ray photoelectron Spectroscopy peaks of Al 2p and O 1s, and a change in their relative intensities indicated a lower O/Al ratio. This suggests that γ-irradiation may stabilize boehmite particle surfaces by driving their chemistry and structure toward more stable aluminum oxide forms. This finding may help explain slower dissolution rates of boehmite in nuclear waste and may be useful for the development of more robust predictive models and effective strategies for waste processing.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
DOE OSTI2020

The synergistic role of Mn and Zr/Ti in producing θ'/L12 co-precipitates in Al-Cu alloys

Microstructural stability is a critical factor to consider when designing new alloys for high-temperature applications. An Al-Cu alloy with Mn and Zr additions has recently been developed to withstand extended exposures of up to 350 °C. The addition of Mn in combination with Zr and their segregation to precipitate interfaces play a significant role in stabilizing the metastable θ ' precipitates responsible for the alloy's hardness; however, adding Zr and Mn separately only improves the stability to 200 °C and 300 °C, respectively. To this end, the effect of the synergistic additions on interfacial structure and chemistry was studied in detail using atom probe tomography (APT) and scanning transmission electron microscopy (STEM) for Al-Cu-Mn-Zr/Ti-containing alloys subjected to long-term annealing (up to 2,100 h) in the critical temperature range, 300 °C and 350 °C, to investigate the role of Zr/Ti in increasing the θ '-precipitate stability. The APT and STEM results reveal that Mn additions stabilize θ ' long enough for the slower diffusing Zr atoms to segregate to coherent θ ' interfaces that eventually create a θ '/ L1 2 -Al 3 (Zr x ,Ti 1-x ) co-precipitate structure. The co-precipitate is highly stable, as shown by density functional theory calculations, and is a key factor that governs microstructural stability beyond 300 °C. This study reveals how solute additions with different stabilization mechanisms can work in concert to stabilize a desired microstructure, and the results provide insights that can be applied to other high-temperature alloy systems.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Comparative Study on the Machine Learning-Based Prediction of Adsorption Energies for Ring and Chain Species on Metal Catalyst Surfaces

Computation of adsorption and transition state energies for a large number of surface intermediates for numerous active site models pose significant computational overhead in computational screening of catalysts. Machine learning (ML) techniques can be used to predict part of these energies. To predict the energies, ML models need to be fed appropriate metal and species descriptors. For complex surface chemistries, the structures of the intermediate species can vary greatly. In this paper, working with the hydrodeoxygenation of succinic acid on six different metal surfaces, we have studied the effect of linear and non-linear ML models used along with pen-and-paper based species descriptors and two categories of metal descriptors on two different categories of intermediate species: chain and ring. More specifically, our computations include the prediction of chain species when trained on only chain species and also when trained on both chain and ring species. Similar computations were performed for predictions of ring species. In each case, results of linear ML models were compared with kernel based non-linear models. Our results indicate that ring species data does not improve the prediction of chain species. Similarly, chain species data does not improve the prediction of ring species. The use of non-linear ML models, however, did help to minimize the prediction errors compared to the linear models. Furthermore, the study also shows that electronic or adsorption energy based metal descriptors along with bond count based species fingerprints can achieve a mean absolute error (MAE) of less than 0.2 eV for complex chain molecules when used with an appropriate machine learning model.

Adsorption↗
NASA NTRS1999

Quantitative Interpretation of Optical Emission Sensors for Microgravity Experiments

Microgravity flight experiments uniquely test our knowledge and understanding of the coupling between chemistry and fluid mechanics. However, compared to ground based laboratory experiments the number of useful diagnostic tools suitable for microgravity environments is severely limited by the space, weight, power consumption, and operator complexity requirements. One of the available tools is the observation of optical emission, and total emission has already proven useful for observations of stable "flame balls" on the space shuttle. Wavelength resolved tomographic measurements of flame emission offer the promise of diagnostics to test our understanding of flame chemistry and structure. Individual emissions from electronically excited radicals, e.g., CH*, OH*, and C2*, can be identified in a methane/air flame. Spatially resolved measurements of the intensity of this resolved optical emission from a specific excited molecule enable chemically resolved flame structure studies. Wavelength resolved emission measurements to determine such structure in diffusion flames are being readied for flight experiments by a group at Yale headed by Profs. Smooke and Long. A quantitative relationship between emission intensity and flame properties, as expressed by a flame model, is needed for species specific optical emission measurements to fulfill its promise. The Yale group compared models and measurements of optical emission in laboratory tests at 1-g. Unfortunately, these experiments show disagreement between measurement and state-of-the-art flame models by over a factor of 50. Therefore, an improved chemical mechanism for optical emission from flames is needed to enable quantitative tests of microgravity flame models. The connection between excited state emission and flame chemistry is not yet adequate.

Jeffries, Jay B.↗
DOE OSTI2021

Machine learning with persistent homology and chemical word embeddings improves prediction accuracy and interpretability in metal-organic frameworks

Machine learning has emerged as a powerful approach in materials discovery. Its major challenge is selecting features that create interpretable representations of materials, useful across multiple prediction tasks. We introduce an end-to-end machine learning model that automatically generates descriptors that capture a complex representation of a material’s structure and chemistry. This approach builds on computational topology techniques (namely, persistent homology) and word embeddings from natural language processing. It automatically encapsulates geometric and chemical information directly from the material system. We demonstrate our approach on multiple nanoporous metal–organic framework datasets by predicting methane and carbon dioxide adsorption across different conditions. Our results show considerable improvement in both accuracy and transferability across targets compared to models constructed from the commonly-used, manually-curated features, consistently achieving an average 25–30% decrease in root-mean-squared-deviation and an average increase of 40–50% in R 2 scores. A key advantage of our approach is interpretability: Our model identifies the pores that correlate best to adsorption at different pressures, which contributes to understanding atomic-level structure–property relationships for materials design.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Molecular Origin of Wettability Alteration of Subsurface Porous Media upon Gas Pressure Variations

Upon extraction/injection of a large quantity of gas from/into a subsurface system in shale gas production or carbon sequestration, the gas pressure varies remarkably, which may significantly change the wettability of porous media involved. Mechanistic understanding of such changes is critical for designing and optimizing a related subsurface engineering process. Using molecular dynamics simulations, in this work we have calculated the contact angle of a water droplet on various solid surfaces (kerogen, pyrophyllite, calcite, gibbsite, and montmorillonite) as a function of CO 2 or CH 4 gas pressure up to 200 atm at a temperature of 300 K. The calculation reveals a complex behavior of surface wettability alteration by gas pressure variation depending on surface chemistry and structure, and molecular interactions of fluid molecules with surfaces. As the CO 2 gas pressure increases, a partially hydrophilic kerogen surface becomes highly hydrophobic, while a calcite surface becomes more hydrophilic. Considering kerogen and calcite being the major components of a shale formation, we postulate that the wettability alteration of a solid surface induced by a gas pressure change may play an important role in fluid flows in shale gas production and geological carbon sequestration.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗