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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 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Structural and electronic properties of rare-earth chromites: A computational and experimental study

Here, in this work, the structural, optical, and electronic properties of rare-earth perovskites of the general formula R⁢ CrO 3 , where R⁢ represents the rare-earth Gd, Tb, Dy, Ho, Er, and Tm, have been studied in detail. These compounds were synthesized through a facile citrate route. X-ray diffraction, Raman spectroscopy, and UV-Visible spectroscopy were utilized to reveal the structural evolutions in R⁢ ⁢CrO 3 . The lattice parameters, Cr 3+ –O 2 –Cr 3+ bond angle, and CrO 6 octahedral distortions were found to strongly depend on the ionic radii of R⁢ . First-principles calculations based on density-functional theory within the generalized gradient approximation (GGA) of Perdew-Burke-Ernzerhof (PBE) and strongly constrained and appropriately normed (SCAN) meta-GGA were also employed to calculate the structural and electronic properties of R⁢ ⁢CrO 3 . The ground-state energy, lattice constants, electronic structures, and density of states of R⁢ ⁢CrO 3 were calculated. These provide some insights into the electronic characteristics of the R⁢ ⁢CrO 3 compounds. The calculated values of lattice parameters and band gaps with Hubbard U correction (SCAN+ U ) agree well with values measured experimentally and show more accuracy in predicting the ground-state crystal structure and band structure compared to PBE+ U approximation. The band gap of R⁢ ⁢CrO 3 is found to be independent of the ionic radii of R⁢ from both experiments and calculations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Research on Deformation Law of Deep Foundation Pit of Station in Core Region of Saturated Soft Loess Based on Monitoring

Saturated soft loess has a large pore structure, high compressibility, low strength, fluid plastic state, and poor engineering properties. It is still one of the key problems that engineering needs to solve. In order to study the influence of deep foundation pit excavation in the saturated soft loess area on the deformation of foundation pits, the deformation laws of ground settlement, enclosure structure, and supporting axial force were clarified based on the field tests on the deformation characteristics of deep foundation pits in areas with the high-water level in saturated soft loess, combined with geological conditions and on-site construction procedures. The results indicate the following: water supply and construction process were found to be the main factor in changing the surface settlement curve of deep foundation pits in saturated soft loess; increasing the construction speed of the pit bottom floor, inverted braces, floor frame beams, and sidewall frame beams to close the structure, which is conducive to restraining the deformation of the continuous underground wall and foundation pits in similar areas. In the initial stage of support layout, the axial force of steel support tends to increase too fast or even exceed the standard control value. Therefore, a reasonable preadding axial force is an effective means to control the deformation of the continuous underground wall and the axial force of the steel support. The current research results may provide a reference for constructing deep foundation pits in similar areas.

Wang, Xueyan↗
DOE OSTI2022

Simulations of frustrated Ising Hamiltonians using quantum approximate optimization

Novel magnetic materials are important for future technological advances. Theoretical and numerical calculations of ground-state properties are essential in understanding these materials, however, computational complexity limits conventional methods for studying these states. Here we investigate an alternative approach to preparing materials ground states using the quantum approximate optimization algorithm (QAOA) on near-term quantum computers. We study classical Ising spin models on unit cells of square, Shastry-Sutherland and triangular lattices, with varying field amplitudes and couplings in the material Hamiltonian. We find relationships between the theoretical QAOA success probability and the structure of the ground state, indicating that only a modest number of measurements (≲100) are needed to find the ground state of our nine-spin Hamiltonians, even for parameters leading to frustrated magnetism. We further demonstrate the approach in calculations on a trapped-ion quantum computer and succeed in recovering each ground state of the Shastry-Sutherland unit cell with probabilities close to ideal theoretical values. The results demonstrate the viability of QAOA for materials ground state preparation in the frustrated Ising limit, giving important first steps towards larger sizes and more complex Hamiltonians where quantum computational advantage may prove essential in developing a systematic understanding of novel materials.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Dirac's equation and its implications for density functional theory based calculations of materials containing heavy elements

Electronic structure calculations based on density functional theory (DFT) give quantitatively accurate predictions of properties of most materials containing light elements. For heavy materials, and in particular for f -electron systems, DFT based methods can fail both qualitatively and quantitatively for two distinct reasons: their failure to describe confinement effects arising from localized f -electron behavior and their incomplete or approximate treatment of relativity. In addition, different methods for incorporating relativistic effects, which give identical results in most light materials, can give different predictions in heavy elements. In order to develop a quantitative capability for calculating the properties of these materials, it is essential to separate the predictions of the underlying equations from the uncertainty introduced in approximations used in computation. Working toward that goal, here we have developed a code, called dirac-fp , which is based directly on solving the Dirac-Kohn-Sham equations and uses the full-potential linear muffin-tin orbital (FP-LMTO) approach to electronic structure. In order to assess the performance of dirac-fp , we perform calculations on three different face-centered cubic materials using different approximate treatments of relativity: the scalar relativistic (SR) approach commonly used in most solid-state DFT codes, the scalar relativistic plus spin-orbit coupling corrections (SR+SO) approach which includes spin-orbit coupling self-consistently using the SR states inside the muffin tins, and the Dirac-Kohn-Sham (Dirac) approach implemented in dirac-fp . Performing calculations on thorium, in which relativistic effects should be strong, aluminum, in which relativistic effects should be negligible, and gold, in which relativistic effects play an intermediate role, we find that the Dirac approach is able to provide theoretically consistent results in the electronic structure and ground-state properties across all three materials.

3-dimensional systems↗
DOE OSTI2025

Singly occupied 4⁢𝑓 antiferromagnetic insulators: CePO 4 and CeVO 4

Rare-earth containing wide band gap oxides, which provide spin-photon interface and narrow linewidth optical emission, are getting significant attention as the most promising candidate materials in advancing quantum transduction and memories. Here, in this work, from ab initio calculations, we identify antiferromagnetic ground states in structurally preferred monoclinic CePO 4 and tetragonal CeVO 4 exhibiting localized occupied and unoccupied Ce 4⁢𝑓 states with 4⁢𝑓−4⁢𝑓 transition characteristics. Interestingly, in CePO 4 , O 2⁢𝑝 and P 3⁢𝑝 states hybridize negligibly with Ce 4⁢𝑓 states, while in CeVO 4 , V 3⁢𝑑 and O 2⁢𝑝 states hybridize and appear as extended states in between the occupied and unoccupied Ce 4⁢𝑓 states. Here, phonon calculations and analysis identify and differentiate Raman active phonon modes along with the spin phonon coupling of Ce in both CePO 4 and CeVO 4 that ultimately lead to different 4⁢𝑓 ground-state crystal-field multiplets, which are critical to accurately describe electronic transitions for foundational quantum transduction and memories. Further, the identified 𝐶 1 site symmetry of Ce, lacking inversion symmetry in CePO 4 , is relevant for quantum memories and 𝐷 2⁢𝑑 site symmetry of Ce exhibiting inversion symmetry in CeVO 4 is relevant for quantum transduction.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Ground Heat Flux Reconstruction Using Bayesian Uncertainty Quantification Machinery and Surrogate Modeling

Ground heat flux (G 0 ) is a key component of the land-surface energy balance of high-latitude regions. Despite its crucial role in controlling permafrost degradation due to global warming, G 0 is sparsely measured and not well represented in the outputs of global scale model simulation. In this study, an analytical heat transfer model is tested to reconstruct G 0 across seasons using soil temperature series from field measurements, Global Climate Model, and climate reanalysis outputs. The probability density functions of ground heat flux and of model parameters are inferred using available G 0 data (measured or modeled) for snow-free period as a reference. When observed G 0 is not available, a numerical model is applied using estimates of surface heat flux (dependent on parameters) as the top boundary condition. These estimates (and thus the corresponding parameters) are verified by comparing the distributions of simulated and measured soil temperature at several depths. Aided by state-of-the-art uncertainty quantification methods, the developed G 0 reconstruction approach provides novel means for assessing the probabilistic structure of the ground heat flux for regional permafrost change studies.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Electronic Structure of the Complete Series of Gas-Phase Manganese Acetylacetonates by X-ray Absorption Spectroscopy

Metal centers in transition metal–ligand complexes occur in a variety of oxidation states causing their redox activity and therefore making them relevant for applications in physics and chemistry. The electronic state of these complexes can be studied by X-ray absorption spectroscopy, which is, however, due to the complex spectral signature not always straightforward. Here, we study the electronic structure of gas-phase cationic manganese acetylacetonate complexes Mn(acac) 1–3 + using X-ray absorption spectroscopy at the metal center and ligand constituents. The spectra are well reproduced by multiconfigurational wave function theory, time-dependent density functional theory as well as parameterized crystal field and charge transfer multiplet simulations. This enables us to get detailed insights into the electronic structure of ground-state Mn(acac) 1–3 + and extract empirical parameters such as crystal field strength and exchange coupling from X-ray excitation at both the metal and ligand sites. By comparison to X-ray absorption spectra of neutral, solvated Mn(acac) 2,3 complexes, we also show that the effect of coordination on the L 3 excitation energy, routinely used to identify oxidation states, can contribute about 40–50% to the observed shift, which for the current study is 1.9 eV per oxidation state.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

First-Principles Discovery of Novel LiInP 2 S 6 Polymorphs with Promising Optoelectronic Responses

Recent advances in two-dimensional (2D) van der Waals (vdW) metal thiophosphates have attracted considerable attention due to their promising ionic conductivity, optical characteristics, and tunable physical properties. Within this material family, LiInP 2 S 6 has emerged as an intriguing candidate, not only because of its sensitivity to air and moisture but also due to its suitable band gap within the UV−vis range, enabling potential optoelectronic and photocatalytic applications. In this study, through comprehensive first-principles investigations, we unveil two previously unreported polymorphs of LiInP 2 S 6 in the monoclinic C2/c and trigonal P3̅1c (in-gap) space groups, in addition to examining the experimentally synthesized P3̅1c (in-layer) phase. Our studies identify the C2/c structure as the ground state, lying 9 meV per unit cell lower in energy than the experimentally realized trigonal P3̅1c (in-layer) phase. Further, we systematically examine the elastic, mechanical, thermodynamical, dynamical, electronic, and optical properties of all three polymorphs, confirming their mechanical, thermal, and dynamical stability. Notably, the P3̅1c (in-gap) phase exhibits enhanced stiffness, while the calculated indirect band gaps and strong photon absorption in the UV−vis range (∼3 eV) highlight the potential of the studied LiInP 2 S 6 phases for iontronic devices and optoelectronic applications.

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

Simple hydrogenic estimates for the exchange and correlation energies of atoms and atomic ions, with implications for density functional theory

Exact density functionals for the exchange and correlation energies are approximated in practical calculations for the ground-state electronic structure of a many-electron system. An important exact constraint for the construction of approximations is to recover the correct non-relativistic large-Z expansions for the corresponding energies of neutral atoms with atomic number Z and electron number N = Z, which are correct to leading order (–0.221 Z 5/3 and –0.021 Z ln Z respectively) even in the lowest-rung or local density approximation. We find that hydrogenic densities lead to E x (N,Z) ≈ –0.354 N 2/3 Z (as known before only for Z >> N >> 1) and E c ≈ –0.02 N ln N . These asymptotic estimates are most correct for atomic ions with large N and Z >> N, but we find that they are qualitatively and semi- quantitatively correct even for small N and for N ≈ Z. The large-N asymptotic behavior of the energy is pre-figured in small-N atoms and atomic ions, supporting the argument that widely-predictive approximate density functionals should be designed to recover the correct asymptotics. Here, it is shown that the exact Kohn-Sham correlation energy, when calculated from the pure ground-state wavefunction, should have no contribution proportional to Z in the Z → ∞ limit for any fixed N.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Recent progress in low energy neutrino scattering physics and its implications for the standard and beyond the standard model physics

Neutrinos continue to provide a testing ground for the structure of the standard model of particle physics as well as hints towards the physics beyond the standard model. Neutrinos of energies spanning over several orders of magnitude, originating in many terrestrial and astrophysical processes, have been detected via various decay and interaction mechanisms. At MeV scales, there has been one elusive process, until a few years ago, known as coherent elastic neutrino-nucleus scattering (CEvNS) that was theoretically predicted over five decades ago but was never observed experimentally. The recent experimental observation of the CEvNS process by the COHERENT collaboration at a stopped pion neutrino source has inspired physicists across many subfields. This has vital implications for nuclear physics, high-energy physics, astrophysics, and beyond. CEvNS, being a low-energy process, provides a natural window to study light, weakly-coupled, new physics in the neutrino sector. In this review, we intend to provide the current status of low energy neutrino scattering physics and its implications for the standard and beyond the standard model physics. We discuss the general formalism of calculating the tree-level CEvNS cross section and present estimated theoretical uncertainties on the CEvNS cross section stemming from different sources. We also discuss the inelastic scattering of tens of MeV neutrinos that have implications for supernova detection in future neutrino experiments. We discuss how the CEvNS experiments can be used as a testing ground for the Standard Model (SM) weak physics as well as in searching for the Beyond the Standard Model (BSM) physics signals. Any deviation from the SM predicted event rate either with a change in the total event rate or with a change in the shape of the recoil spectrum, could indicate new contributions to the interaction cross-section. The SM implications include the study of weak nuclear form factor and weak mixing angle. The BSM studies include non-standard interactions, neutrino electromagnetic properties, and sterile neutrino searches. In conclusion, stopped pion facilities are also a copious source of neutral and changed mesons that allow study of several dark sector physics scenarios such as vector portal models, leptophobic dark matter as well as axion-like particle searches.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Oxygen–Chlorine Chemisorption Scaling for Seawater Electrolysis on Transition Metals: The Role of Redox

To clarify what controls species oxidation selectivity in seawater electrolysis, density functional theory (DFT) is used to identify chemisorption enthalpy trends and scaling relations for the simplest relevant adsorbates (O, Cl, and H) on relevant surfaces of 3d transition metals, as well as Pd and Pt, in face-centered-cubic and, if different, their ground-state crystal structures. Approximations are tested for electron exchange-correlation (XC) and van der Waals interactions to assess their ability to reproduce experimental adsorption enthalpies of H and O on Pt(111). The vdW-uncorrected generalized gradient approximation to XC of Perdew, Burke, and Ernzerhof (PBE) agrees most closely with experiments. Using DFT-PBE thereafter, it is determined that the O chemisorption enthalpy on this wide range of transition-metal surfaces is proportional to the sum of first and second atomic ionization energies, akin to a Born–Haber cycle for a redox reaction, indicating that metal redox activity controls O chemisorption strength. Then it is shown that the O and Cl chemisorption enthalpies are strongly correlated, suggesting that the transition metals considered will oxidize unselectively water and Cl – . This strong correlation appears also for crystal reduction potentials of binary oxides and chlorides, indicating a fundamental challenge for future seawater electrode materials design.

08 HYDROGEN↗
DOE OSTI2022

Deciphering Distinct Overpotential-Dependent Pathways for Electrochemical CO 2 Reduction Catalyzed by an Iron–Terpyridine Complex

[Fe(tpyPY2Me)] 2+ ([Fe] 2+ ) is a homogeneous electrocatalyst for converting CO 2 into CO featuring low overpotentials of <100 mV, near-unity selectivity, and high activity with turnover frequencies faster than 100 000 s -1 . To identify the origins of its exceptional performance and inform future catalyst design, we report a combined computational and experimental study that establishes two distinct mechanistic pathways for electrochemical CO 2 reduction catalyzed by [Fe] 2+ as a function of applied overpotential. Electrochemical data shows the formation of two catalytic regimes at low (η TOF/2 of 160 mV) and high (η TOF/2 of 590 mV) overpotential plateaus. We propose that at low overpotentials [Fe] 2+ undergoes a two-electron reduction, two-proton-transfer mechanism (electrochemical-electrochemical-chemical-chemical, EECC), where turnover occurs through the dicationic iron complex, [Fe] 2+ . Computational analysis supports the importance of the singlet ground-state electronic structure for CO 2 binding and that the rate-limiting step is the second protonation in this low-overpotential regime. When more negative potentials are applied, an additional electron-transfer event occurs through either a stepwise or proton-coupled electron-transfer (PCET) pathway, enabling catalytic turnover from the monocationic iron complex ([Fe] + ) via an electrochemical-chemical-electrochemical-chemical (ECEC) mechanism. Comparison of experimental kinetic data obtained from variable controlled potential electrolysis (CPE) experiments with direct product detection with calculated rates obtained from the energetic span model supports the PCET pathway as the most likely mechanism. Moreover, we build upon this mechanistic understanding to propose the design of an improved ligand framework that is predicted to stabilize the key transition states identified in our study and explore their electronic structures using an energy decomposition analysis. Finally, taken together, this work highlights the value of synergistic computational/experimental approaches to decipher mechanisms of new electrocatalysts and direct the rational design of improved platforms.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Near-Infrared Photoluminescence from Spin-Flip Excited States of π-Conjugated Tris(quinolinolate) Chromium(III) Complexes

Tuning metal–ligand covalency offers promising design strategies to tailor the photoluminescence (PL) emission energies of metal-centered, spin-flip excited states. Herein, we report a series of tris(quinolinolate) chromium(III) complexes that exhibit record-low near-infrared II emission energies in a fluid solution at room temperature, afforded by their strong metal–ligand covalencies. Appending π-conjugated arylethynyl substituents to quinolinolate ligands resulted in minimal changes to metal–ligand bond lengths, facilitating nearly indiscriminate metal–ligand covalencies for each tris(quinolinolate) chromium(III) complex. As a result, near-infrared II emission was observed across the series, while simultaneously affording careful tuning of the 4 LMCT/ 4 ( 1 ILCT) electronic transition energies across the visible region. Here, detailed analyses of ground-state electronic structures and excited-state electronic transitions revealed that PL arises from a ligand-field, 2 E excited state, admixed with charge-transfer character. This assignment was supported by solvent-dependent near-infrared emission energies and long excited-state lifetimes, consistent with spin-forbidden relaxation (ranging from 115 ± 5 to 123 ± 1 ns across the series). Utilizing spectroscopic data, ligand-field parameters were quantified, further rationalizing the role of strong metal–ligand covalency in enabling near-infrared II emission. Supported by these results, this study presents a new class of ligands that enable room-temperature near-infrared II emission in chromium(III)-based spin-flip excited states.

Absorption spectroscopy↗
DOE OSTI2022

Point Defects in Two-Dimensional Ruddlesden–Popper Perovskites Explored with Ab Initio Calculations

Two-dimensional Ruddlesden–Popper (RP) halide perovskites stand out as excellent layered materials with favorable optoelectronic properties for efficient light-emitting, spintronic, and other spin-related applications. However, properties often determined by defects are not well understood in these perovskite systems. This work investigates the ground state electronic structure of commonly formed defects in a typical RP perovskite structure by density functional theory. Our study reveals that these 2D perovskites generally retain their defect tolerance with limited perturbation of the electronic structure in the case of neutral-type point defects. In contrast, donor/acceptor defects induce deep midgap states, potentially causing harm to the material’s electronic performance. To retain positive intrinsic properties, the halide vacancies and interstitial defects should be avoided. The observed strong electron localization results in trap states and consequently leads to reduced device performance. Finally, this understanding can guide experimental efforts that aim for improved 2D halide perovskite-based device performance.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Coexisting kagome and heavy fermion flat bands in YbCr 6 Ge 6

Flat bands, electronic states with nearly dispersionless energy-momentum structure, provide fertile ground for unconventional quantum phases. Recent observations of flat bands at the Fermi level in kagome metals open the possibility of unifying topology and correlation-driven heavy-fermion physics. Here we show that topology and heavy-fermion correlations coexist in the layered kagome metal YbCr 6 Ge 6 . At high temperatures, an intrinsic kagome flat band—arising from frustrated hopping on the kagome lattice—dominates the Fermi level. Upon cooling, localized Yb 4f-states hybridize with the topological kagome flat bands, transforming this state into momentum-independent Kondo resonance states across the entire Brillouin zone. Topological analysis of the hybridization gaps reveals filling-tunable weak and strong topological Kondo-insulating regimes, and identifies a topological Dirac–Kondo semimetal. Taken together, these results identify YbCr 6 Ge 6 as a prototype of a topological heavy-fermion system and a platform where geometric frustration, strong correlations, and topology converge, with broad implications for correlated quantum matter.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Pausing ultrafast melting by timed multiple femtosecond-laser pulses

An intense femtosecond-laser excitation of a solid induces highly nonthermal conditions. In materials like silicon, laser-induced bond-softening leads to a highly incoherent ionic motion and eventually nonthermal melting. But is this outcome an inevitable consequence, or can it be controlled? Here, we performed ab initio molecular dynamics simulations of crystalline silicon after timed multiple femtosecond-laser pulse excitations with fluence above the nonthermal melting threshold. Our results demonstrate an excitation mechanism that pauses nonthermal melting and creates a metastable state instead, with an electronic structure similar to the ground state. This mechanism can be generalized to other materials, potentially enabling structural and/or electronic transitions to metastable phases in the high-excitation regime. In addition, our approach could be used to switch off nonthermal contributions in experiments, allowing reliable electron-phonon coupling constants to be obtained more easily.

47 OTHER INSTRUMENTATION↗
DOE OSTI2020

Emergent mystery in the Kondo insulator samarium hexaboride

Samarium hexaboride (SmB 6 ) is an example of a Kondo insulator, in which strong electron correlations cause a band gap to open. SmB 6 hosts both a bulk insulating state and a conductive surface state. Within a Fermi-liquid framework, the strongly correlated ground-state electronic structure can be mapped to a simple state resembling a topological insulator. Although uncertainties remain, many experiments provide compelling evidence that the conductive surface states have a topological origin. However, the bulk behavior is less well understood and some experiments indicate bulk in-gap states. This has inspired the development of many theories that predict the emergence of new bulk quantum phases beyond Landau’s Fermi-liquid model. We review the current progress on understanding both the surface and the bulk states, especially the experimental evidence for each. A mystery centres on the existence of the bulk in-gap states and why they appear in some experiments but not others. Adding to the mystery is why quantum oscillations in SmB6 appear only in magnetization but not in resistivity. Here, we conclude by elaborating on three questions: why SmB 6 is worth studying, what can be done to move forwards and what other correlated insulators could give additional insight.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Quantum machine learning for chemistry and physics

Machine learning (ML) has emerged as a formidable force for identifying hidden but pertinent patterns within a given data set with the objective of subsequent generation of automated predictive behavior. In recent years, it is safe to conclude that ML and its close cousin, deep learning (DL), have ushered in unprecedented developments in all areas of physical sciences, especially chemistry. Not only classical variants of ML, even those trainable on near-term quantum hardwares have been developed with promising outcomes. Such algorithms have revolutionized materials design and performance of photovoltaics, electronic structure calculations of ground and excited states of correlated matter, computation of force-fields and potential energy surfaces informing chemical reaction dynamics, reactivity inspired rational strategies of drug designing and even classification of phases of matter with accurate identification of emergent criticality. In this review we shall explicate a subset of such topics and delineate the contributions made by both classical and quantum computing enhanced machine learning algorithms over the past few years. We shall not only present a brief overview of the well-known techniques but also highlight their learning strategies using statistical physical insight. The objective of the review is not only to foster exposition of the aforesaid techniques but also to empower and promote cross-pollination among future research in all areas of chemistry which can benefit from ML and in turn can potentially accelerate the growth of such algorithms.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗