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At least 379 records · Page 21
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Formation and surface melting of nanoparticle superlattices in a solution

The wisdom in the saying of “There are no two snowflakes alike” lies in the importance of history or kinetic pathways in the phase transitions of solids. Likewise, “artificial solids,” namely superlattices consisting of functional nanoparticles, have lattice size, surface morphology, crystallinity, symmetry, and structural reconfiguration (for example, transition into a disordered state) highly dependent on the kinetic pathways as the nanoparticles interact with each other in solution [1]. Great progresses have been made in understanding the formation pathways of superlattices using liquid-phase transmission electron microscopy (TEM) [2-4]. For example, by tracking single nanoparticle’s trajectories, especially aided by U-net neural network-based machine learning, previous studies mapped the fundamental nanoparticle interactions at nanometer resolution [5]. Nonclassical, two-step nucleation pathway has also been elucidated in the system of nanoprisms, by optimizing protocols such as loading nanoparticle suspensions over the supersaturation threshold and minimizing particle‒substrate interaction [2]. Surface morphologies or exposed facets of superlattices have been shown to follow the principles of Wulff construction rule, where the facet-dependent surface energy can be measured based on the capillary wave theory [4]. However, the reverse process of crystallization of superlattices, the conversion from crystalline to disordered state, has been much less explored. On one hand, the melting of nanoparticle superlattices can provide a preferred pathway to induce structural reorganization or shuffling of building blocks for them to transform into different types of crystal structures. On the other hand, understanding nanoscale superlattice melting and comparing such behaviors with the prevailing surface melting theories developed for atomic/molecular solids can provide a potent way to engineer phase transitions of supra- and hierarchical structures constructed from nanoscale entities (e.g., DNA-coated nanoparticles, proteins), for their applications in reprogrammable and switchable materials with multifunctional properties [6, 7]. The experimental challenges to observe melting of superlattices are twofold. Practically it is difficult to load the initial superlattice form, in an intact manner, into the highly confined liquid-phase TEM chamber for in-situ observation. Here, the triggering of melting also needs meticulous manipulation of nanoparticle concentration, interparticle interaction, and solution environment.

Kim, Ahyoung↗
NASA NTRS1996

Nonlinear Dynamics and Nucleation Kinetics in Near-Critical Liquids

The objective of our study is to model the nonlinear behavior of a near-critical liquid following a rapid change of the temperature and/or other thermodynamic parameters (pressure, external electric or gravitational field). The thermodynamic critical point is manifested by large, strongly correlated fluctuations of the order parameter (particle density in liquid-gas systems, concentration in binary solutions) in the critical range of scales. The largest critical length scale is the correlation radius r(sub c). According to the scaling theory, r(sub c) increases as r(sub c) = r(sub 0)epsilon(exp -alpha) when the nondimensional distance epsilon = (T - T(sub c))/T(sub c) to the critical point decreases. The normal gravity alters the nature of correlated long-range fluctuations when one reaches epsilon approximately equal to 10(exp -5), and correspondingly the relaxation time, tau(r(sub c)), is approximately equal to 10(exp -3) seconds; this time is short when compared to the typical experimental time. Close to the critical point, a rapid, relatively small temperature change may perturb the thermodynamic equilibrium on many scales. The critical fluctuations have a hierarchical structure, and the relaxation involves many length and time scales. Above the critical point, in the one-phase region, we consider the relaxation of the liquid following a sudden temperature change that simultaneously violates the equilibrium on many scales. Below T(sub c), a non-equilibrium state may include a distribution of small scale phase droplets; we consider the relaxation of such a droplet following a temperature change that has made the phase of the matrix stable.

Patashinski, Alexander Z.↗
DOE OSTI2025

Diffusion behavior of lanthanide fission products in bcc Fe cladding: A first-principles study

Fuel-cladding chemical interaction poses significant challenges in nuclear reactors, where fission products generated from nuclear fuel interact with Fe-based cladding materials, potentially compromising their structural integrity. This study investigates the diffusion behavior of lanthanide fission products, Lanthanum (La), Cerium (Ce), Praseodymium (Pr), and Neodymium (Nd), within body-centered cubic (bcc) Fe cladding using the density functional theory, nudged elastic band method, and self-consistent mean field theory. Our results reveal significant vacancy binding energies, particularly with the 1st and 2nd nearest neighbors, which diminish beyond the 5th nearest neighbor, with La exhibiting the strongest binding affinity, followed by Nd, Ce, and Pr. The nudged elastic band calculations indicate significant high barriers for the dissociation of 1st nearest neighbor vacancy-solute pairs for all fission products. The tracer diffusion coefficients of these fission products were derived in an Arrhenius form, with a magnetic correction that accounts for the high-temperature paramagnetic state. The significant trapping effect of vacancies caused by a very dilute concentration of fission products reduces vacancy mobility, potentially leading to modifications in point defect supersaturation, void nucleation, and swelling under irradiation. These represent critical challenges for irradiated cladding materials. The tracer diffusion coefficients indicate that Nd diffuses the fastest, followed by La, Ce, and Pr. Furthermore, this study provides essential insights for understanding fission product transport in cladding materials and informs future design strategies to mitigate fuel-cladding chemical interaction, ultimately enhancing nuclear reactor safety and performance.

Diffusion↗
NASA NTRS1982

Stratospheric aerosols - Observation and theory

Important chemical and physical roles of aerosols are discussed, and properties of stratospheric aerosols as revealed by experimental data are described. In situ measurements obtained by mechanical collection and scattered-light detection yield the overall size distribution of the aerosols, and analyses of preserved aerosol precursor gases by wet chemical, cryogenic and spectroscopic techniques indicate the photochemical sources of particle mass. Aerosol chemical reactions including those of gaseous precursors, those in aqueous solution, and those on particle surfaces are discussed, in addition to aerosol microphysical processes such as nucleation, condensation/evaporation, coagulation and sedimentation. Models of aerosols incorporating such chemical and physical processes are presented, and simulations are shown to agree with measurements. Estimates are presented for the potential aerosol changes due to emission of particles and gases by aerospace operations and industrial consumption of fossil fuels, and it is demonstrated that although the climatic effects of existing levels of stratospheric aerosol pollution are negligible, potential increases in those levels might pose a future threat.

Turco, R. P.↗
NASA NTRS1982

Noctilucent clouds - Simulation studies of their genesis, properties and global influences

A numerical model is presented for testing theories of the physical mechanisms of noctiluminescent clouds. The time-dependent, one-dimensional model describes the formation, evolution, and properties of the clouds as interactive ice crystals, meteoric dust, water vapor, and ionized air. Mesopause temperatures below 140 K are found to be necessary for the formation of the clouds, conditions existing only at high latitudes in the summer. No predominant nucleation particle could be identified for the formation of the clouds, although a time period of up to a day was determined as necessary for materialization, which lasts several days. Several atmospheric and environmental conditions were characterized which enhance the appearance of the noctiluminescent clouds. One conclusion reached is that the numerous launches necessary to build a solar power satellite system would not significantly exacerbate noctiluminescent cloud formation.

Turco, R. P.↗
DOE OSTI2022

A reaction mechanism for plasma electrolysis of AgNO 3 forming silver nanoclusters and nanoparticles

In plasma-driven solution electrolysis (PDSE), gas-phase plasma-produced species interact with an electrolytic solution to produce, for example, nanoparticles. An atmospheric pressure plasma jet (APPJ) directed onto a liquid solution containing a metallic salt will promote reduction of metallic ions in solution, generating metallic clusters that nucleate to form nanoparticles. In this article, results from a computational investigation are discussed of a PDSE process in which a radio-frequency APPJ sustained in helium impinges on a silver nitrate solution, resulting in growth of silver nanoparticles. A reaction mechanism was developed and implemented in a global plasma chemistry model to predict nanoparticle growth. To develop the reaction mechanism, density functional theory was used to generate probable silver growth pathways up to Ag 9 . Neutral clusters larger than Ag 9 were classified as nanoparticles. Kinetic reaction rate coefficients for thermodynamically favorable growth pathways were estimated based on an existing, empirically determined base reaction mechanism for smaller Ag particle interactions. These rates were used in conjunction with diffusion-controlled reaction rate coefficients that were calculated for other Ag species. The role of anions in reduction of Agn ions in forming nanoparticles is also discussed. Oxygen containing impurities or admixtures to the helium, air entrainment into the APPJ, and dissociation of saturated water vapor above the solution can produce additional reactive oxygen species in solution, resulting in the production of anions and O 2 – in particular. For a given molarity, delivering a sufficient fluence of reducing species will produce similar nanoparticle densities and sizes for all applied power levels. In conclusion, comparisons are made to alternate models for nanoparticle formation, including charged nanoparticles and use of direct current plasmas.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Graphene Nanopattern for Single-Crystal Film Growth, Defect Reduction and Layer Transfer

Thin film heterostructures are key building blocks for advanced electronic and optoelectronic devices. For this, direct heteroepitaxy has been pursued for decades, although it has been challenging to reduce crystal defects stemming from lattice mismatches and thermal mismatches between materials. The layer transfer method has been proposed as an alternative approach, wherein dissimilar materials are separately grown and then hetero-integrated. However, the applicability of layer transfer techniques is limited by several technical challenges, such as controllability, throughput, and damage to the substrate. Remote epitaxy, which is a recently developed method to produce single-crystalline membranes, is a promising approach but cannot be applied to elemental materials such as Si and Ge. In this work, we report graphene nanopattern as a universal template for the growth of single-crystal thin films that can be exfoliated as a freestanding form. This is realized by the chemical inertness of graphene, which allows selective nucleation at the exposed region, followed by lateral overgrowth onto graphene to form a planarized thin film. By employing graphene nanopattern, both group IV and III-V materials are utilized as the substrate as well as the epilayer. The epilayer can be exfoliated at the graphene interface because partially covered graphene effectively weakens the interface, which is corroborated by theoretical analyses of spalling theory. We reveal that graphene nanopattern not only works as a weakened interface for exfoliation, but also allows for dislocation reduction in heteroepitaxial films. This is because of the flexibility and the dangling-bond-free nature of graphene, which provides an additional path for strain relaxation. Therefore, these results represent a meaningful step toward production of high-quality single-crystal membranes that can be hetero-integrated.

Kim, Hyunseok↗
DOE OSTI2022

Graphene Nanopattern for Single-Crystal Film Growth, Defect Reduction and Layer Transfer

Thin film heterostructures are key building blocks for advanced electronic and optoelectronic devices. For this, direct heteroepitaxy has been pursued for decades, although it has been challenging to reduce crystal defects stemming from lattice mismatches and thermal mismatches between materials. The layer transfer method has been proposed as an alternative approach, wherein dissimilar materials are separately grown and then hetero-integrated. However, the applicability of layer transfer techniques is limited by several technical challenges, such as controllability, throughput, and damage to the substrate. Remote epitaxy, which is a recently developed method to produce single-crystalline membranes, is a promising approach but cannot be applied to elemental materials such as Si and Ge. In this work, we report graphene nanopattern as a universal template for the growth of single-crystal thin films that can be exfoliated as a freestanding form. This is realized by the chemical inertness of graphene, which allows selective nucleation at the exposed region, followed by lateral overgrowth onto graphene to form a planarized thin film. By employing graphene nanopattern, both group IV and III-V materials are utilized as the substrate as well as the epilayer. The epilayer can be exfoliated at the graphene interface because partially covered graphene effectively weakens the interface, which is corroborated by theoretical analyses of spalling theory. We reveal that graphene nanopattern not only works as a weakened interface for exfoliation, but also allows for dislocation reduction in heteroepitaxial films. This is because of the flexibility and the dangling-bond-free nature of graphene, which provides an additional path for strain relaxation. Therefore, these results represent a meaningful step toward production of high-quality single-crystal membranes that can be hetero-integrated.

Kim, Hyunseok↗
NASA NTRS1993

Homogeneous ice nucleation and supercooled liquid water in orographic wave clouds

This study investigates ice nucleation mechanisms in cold lenticular wave clouds, a cloud type characterized by quasi-steady-state air motions and microphysical properties. It is concluded that homogeneous ice nucleation is responsible for the ice production in these clouds at temperatures below about -33 C. The lack of ice nucleation observed above -33 C indicates a dearth of ice-forming nuclei, and hence heterogeneous ice nucleation, in these clouds. Aircraft measurements in the temperature range -31 to -41 C show the following complement of simultaneous and abrupt changes in cloud properties that indicate a transition from the liquid phase to ice: disappearance of liquid water; decrease in relative humidity from near water saturation to ice saturation; increase in mean particle size; change in particle concentration; and change in temperature due to the release of latent heat. A numerical model of cloud particle growth and homogeneous ice nucleation is used to aid in interpretation of our in situ measurements. The abrupt changes in observed cloud properties compare favorably, both qualitatively and quantitatively, with results from the homogeneous ice nucleation model. It is shown that the homogeneous ice nucleation rates from the measurements are consistent with the temperature-dependent rates employed by the model (within a factor of 100, corresponding to about 1 C in temperature) in the temperature range -35 deg to -38 C. Given the theoretical basis of the modeled rates, it may be reasonable to apply them throughout the -30 to -50 C temperature range considered by the theory.

Heymsfield, Andrew J.↗
NASA NTRS2016

Growth Mechanism of Nanowires: Binary and Ternary Chalcogenides

Semiconductor nanowires exhibit very exciting optical and electrical properties including high transparency and a several order of magnitude better photocurrent than thin film and bulk materials. We present here the mechanism of nanowire growth from the melt-liquid-vapor medium. We describe preliminary results of binary and ternary selenide materials in light of recent theories. Experiments were performed with lead selenide and thallium arsenic selenide systems which are multifunctional material and have been used for detectors, acousto-optical, nonlinear and radiation detection applications. We observed that small units of nanocubes and elongated nanoparticles arrange and rearrange at moderate melt undercooling to form the building block of a nanowire. Since we avoided the catalyst, we observed self-nucleation and uncontrolled growth of wires from different places. Growth of lead selenide nanowires was performed by physical vapor transport method and thallium arsenic selenide nanowire by vapor-liquid-solid (VLS) method. In some cases very long wires (>mm) are formed. To achieve this goal experiments were performed to create situation where nanowires grew on the surface of solid thallium arsenic selenide itself.

Singh, N. B.↗
DOE OSTI2025

Site-specific surface reactivity on SnO 2 : Evaluating selective atomic layer deposition processes

Area selective atomic layer deposition (AS-ALD) is a bottom-up synthesis approach with potential for deposition with molecular level precision. Here, the site-specific hydration of metal oxide substrates, combined with surface H 2 O-selective ALD processes, provides a potentially powerful path to targeted synthesis. Density functional theory (DFT) calculations are used to predict the thermodynamics of ALD precursor reactivity and hydration for (001), (101), (110), and (100) rutile SnO 2 facets as a function of temperature. Trimethylaluminum (TMA) and dimethyl aluminum isopropoxide (DMAI) dimers are predicted to react with both dehydrated and hydrated SnO 2 (001), (101), and (110) facets at ALD-relevant temperatures, while the SnO 2 (100) facet is predicted to be uniquely unreactive with TMA and DMAI monomers as well as dehydrate near 177 °C making this facet more amenable to targeted ALD. In situ ellipsometric studies of Al 2 O 3 ALD on polycrystalline SnO 2 at 150 °C are consistent with the computational predictions of rapid and unselective nucleation, in stark contrast to inhibited and selective ALD on isostructural rutile TiO 2 .

Atomic Layer Deposition↗
DOE OSTI2024

Composition-Dependent Reconstructions of Titanium Oxide Clusters and Cu(111) Support via Cluster-Adatom Interactions

Mass-selected cluster deposition and scanning tunneling microscopy (STM) were used to investigate the surface structure and thermal stability of Ti 3 O y (y = 5, 6) clusters on a Cu(111) surface. STM imaging shows that the substoichiometric Ti 3 O 5 clusters aggregate into large dendritic assemblies at step edges, while the stoichiometric Ti 3 O 6 clusters are highly dispersed as single or small groupings of clusters. Cluster deposition also results in extensive reconstruction of the Cu(111) surface. The Ti 3 O 5 /Cu(111) surface exhibits one Cu-layer deep pits that are ringed by cluster assemblies that nucleate and grow at the perimeter step edges. By comparison, the Ti 3 O 6 /Cu(111) surface consists of irregular step edges and small one Cu-layer islands that are decorated with clusters. The restructuring of the Cu(111) surface is attributed to strong Cu-cluster interactions that release Cu adatoms from the step edges. This mechanism is supported by density functional theory (DFT) calculations, which predict that the Cu adatom attachment to the clusters is energetically favorable. Annealing the surfaces at elevated temperatures (400-700 K) results in higher densities of irregular steps, pits and isolated Cu islands as well as increased cluster aggregation. In conclusion, this work highlights adatom-cluster interactions as another manifestation of strong cluster-support interactions that can significantly alter the nature of the oxide-metal interface.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2026

Electropolishing-induced topographic defects in niobium: insights and implications for superconducting radio frequency applications

Electropolishing (EP) is the premier surface preparation method for high-Q, high-gradient superconducting RF cavities made of Nb. This leaves behind an apparently smooth surface, yet the achievable peak magnetic fields fall well below the superheating field of Nb, in most cases. Here, in this work, the ultimate surface finish of EP was investigated by studying its effect on highly polished Nb samples. EP introduces high slope angle sloped-steps at grain boundaries. The magnetic field enhancement and superheating field suppression factors associated with such a geometry are calculated in the London theory. Despite the by-eye smoothness of electropolished Nb, such defects compromise the stability of the low-loss Meissner state, likely limiting the achievable peak accelerating fields in superconducting RF cavities. Finally, the impact of surface roughness on impurity diffusion is investigated which can link surface roughness to the effectiveness of heat treatments like low-temperature baking or nitrogen infusion in the vortex nucleation or hydride hypotheses. Surface roughness tends to decrease the effective dose of impurities as a result of the expansion of impurities into regions with greater internal angle. The effective dose of impurities can be protected by minimizing slope angles and step heights, ensuring uniformity.

Hryhorenko, Oleksandr [Thomas Jefferson National A↗
DOE OSTI2026

Electropolishing-induced topographic defects in niobium: Insights and Implications for SRF

Electropolishing (EP) is the premier surface preparation method for high-Q, high-gradient superconducting RF cavities made of Nb. This leaves behind an apparently smooth surface, yet the achievable peak magnetic fields fall well below the superheating field of Nb, in most cases. In this work, the ultimate surface finish of EP was investigated by studying its effect on highly polished Nb samples. EP introduces high slope angle sloped-steps at grain boundaries. The magnetic field enhancement and superheating field suppression factors associated with such a geometry are calculated in the London theory. Despite the by-eye smoothness of electropolished Nb, such defects compromise the stability of the low-loss Meissner state, likely limiting the achievable peak accelerating fields in superconducting RF cavities. Finally, the impact of surface roughness on impurity diffusion is investigated which can link surface roughness to the effectiveness of heat treatments like low-temperature baking or nitrogen infusion in the vortex nucleation or hydride hypotheses. Surface roughness tends to decrease the effective dose of impurities as a result of the expansion of impurities into regions with greater internal angle. The effective dose of impurities can be protected by minimizing slope angles and step heights, ensuring uniformity.

Lechner, Eric [Thomas Jefferson National Accelerat↗
DOE OSTI2023

Characterization of dissipative regions of a N-doped superconducting radio-frequency cavity

We report radio-frequency measurements of quality factors and temperature mapping of a nitrogen doped Nb superconducting RF cavity. Cavity cutouts of hot and cold spots were studied with low temperature scanning tunneling microscopy and spectroscopy, X-ray photoelectron spectroscopy and secondary electron microscopy. Temperature mapping revealed a substantial reduction of the residual resistance upon cooling the cavity with a greater temperature gradient and hysteretic losses at the quench location, pointing to trapped vortices as the dominant source of residual surface resistance. Analysis of the tunneling spectra in the framework of a proximity effect theory shows that hot spots have a reduced pair potential and a wider distribution of the contact resistance between the Nb and the top Nb oxide. Alone, these degraded superconducting properties account for a much weaker excess dissipation as compared with the vortex contribution. Based on the correlation between the quasiparticle density of states and temperature mapping, we suggest that degraded superconducting properties may facilitate vortex nucleation or settling of trapped flux during cooling the cavity through the critical temperature.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2025

Facet-Dependent Doping and Dopant-Dependent Faceting in Si-Doped GaAsSb Nanowires

Here, we correlate the spatial distributions of Si, Sb, and rotational twins in Si-doped GaAs 1-x Sb x nanowires. GaAs 1-x Sb x nanowires were grown epitaxially on Si(111) substrates by tuning process conditions to achieve repeated nucleation of rotational twins and growth along the [111]B direction; dilute Sb and Si fluxes were chosen to create a sufficient twin density to achieve high yield while avoiding growth of the wurtzite phase. While the impact of Si and Sb on twin density and nanowire growth rate has been previously reported, the facet-dependent incorporation of these species has not been established. Scanning transmission electron microscopy was used to confirm that Sb incorporates preferentially on the (111)B facets relative to {1 ̅1 ̅0} facets prior to nucleation of a rotational twin. With periodic twinning, this facet dependence leads to alternating regions of enriched and depleted Sb concentration attributed to a growth rate-dependent Sb-As-exchange mechanism. Atom probe tomography measurements establish that while Si doping is not perturbed by twinning on (111)B facets, Si and Sb concentrations are anti-correlated for growth on non-(111)B facets. Density functional theory calculations underpin a thermodynamic model that explains the observed anisotropies in dopant incorporation.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Anomalies in the electromagnetic response and peculiarities of the domain structure in the magnetic Weyl semimetal Co 3⁢ Sn 2 ⁢S 2

In this paper, we present a comprehensive study of magnetic properties of Co 3 ⁢Sn 2 ⁢S 2 (CoSnS) crystals using macroscopic characterization and observations of the domain structure (DS) in a wide range of easy- and hard-axis fields (𝐻) and temperatures (𝑇). From macroscopic measurements, we derive temperature dependences of the basic magnetic parameters of the material [saturation magnetization 𝑀 𝑠 ⁡(𝑇), uniaxial anisotropy constant 𝐾⁡(𝑇), and exchange stiffness 𝐴⁡(𝑇)] and, based on them, calculate the thermodynamic magnetization 𝑀⁡(𝐻,𝑇) curves and DS parameters for pinning-free samples. We find important qualitative and quantitative differences between the theory and experiment defined by the efficient pinning of domain walls (DWs) in our samples. It turns out that, already at temperatures close to the ferromagnetic transition 𝑇 𝑐 , the DW dynamics falls into the heavy creep regime, resulting in a strong deferral of the DS adjustment into the equilibrium state. Here, we suggest that specific magnetic defects, responsible for pinning and causing field-tuned reproducible domain nucleation patterns observed in our high-quality samples, are pointlike. Recently found magnetic polarons formed around vacancies and impurities, which carry strong diamagnetic moments of spin-orbit nature and are intrinsic for CoSnS and expected in other Weyl semimetals, are a possible source of pinning yielding peculiar 𝑀⁡(𝐻,𝑇) response of CoSnS.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Recent Advances in Nonclassical Crystallization: Fundamentals, Applications, and Challenges

We report crystals are ubiquitous and play an important role in our daily life. Recent studies on properties and formation of crystals have proven the attachment of particle ranging from ion pairs to well-crystallized nanocrystal is one of the most important ways for crystallization. Compared with the monomer-by-monomer (i.e., atoms, ions, or molecules) addition described in longstanding classical theories, so-called nonclassical crystallization pathways are more complex as the non-specific interaction of variation in system free energy and reaction kinetics. In view of the detailed insights into nonclassical crystallization pathways has broadened the scope of research across various disciplines such as geological events, biomineralization mechanisms, environmental remediation, and the development of functional materials, this paper reviews the current state of the art in nonclassical nucleation (the prenucleation clusters pathway, aggregation pathway, etc.) and growth pathways (oriented attachment and random attachment) based on several spotlights. In addition, the observed specific phenomena on crystallization in the last 10 years as well as recent advancements and achievements made on the synthesis of mesocrystals are also elucidated. With implications and perspectives of nonclassical crystallization researches proposed in this paper, this review aims to summarize research advancement regarding crystallizing systems. Emphasis will be placed on novel insights into nonclassical crystallization of materials, which are expected to provide completely new perspectives on the underlying crystallization mechanisms.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗