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At least 1,333 records · Page 74
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Direct Synthesis of Layer-Tunable and Transfer-Free Graphene on Device-Compatible Substrates Using Ion Implantation Toward Versatile Applications

Direct synthesis of layer-tunable and transfer-free graphene on technologically important substrates is highly valued for various electronics and device applications. State of the art in the field is currently a two-step process: a high-quality graphene layer synthesis on metal substrate through chemical vapor deposition (CVD) followed by delicate layer transfer onto device-relevant substrates. Here, we report a novel synthesis approach combining ion implantation for a precise graphene layer control and dual-metal smart Janus substrate for a diffusion-limiting graphene formation to directly synthesize large area, high quality, and layer-tunable graphene films on arbitrary substrates without the post-synthesis layer transfer process. Carbon (C) ion implantation was performed on Cu–Ni film deposited on a variety of device-relevant substrates. A well-controlled number of layers of graphene, primarily monolayer and bilayer, is precisely controlled by the equivalent fluence of the implanted C-atoms (1 monolayer ~4 × 10 15 C-atoms/cm 2 ). Upon thermal annealing to promote Cu-Ni alloying, the pre-implanted C-atoms in the Ni layer are pushed toward the Ni/substrate interface by the top Cu layer due to the poor C-solubility in Cu. As a result, the expelled C-atoms precipitate into a graphene structure at the interface facilitated by the Cu-like alloy catalysis. After removing the alloyed Cu-like surface layer, the layer-tunable graphene on the desired substrate is directly realized. The layer-selectivity, high quality, and uniformity of the graphene films are not only confirmed with detailed characterizations using a suite of surface analysis techniques but more importantly are successfully demonstrated by the excellent properties and performance of several devices directly fabricated from these graphene films. Molecular dynamics (MD) simulations using the reactive force field (ReaxFF) were performed to elucidate the graphene formation mechanisms in this novel synthesis approach. With the wide use of ion implantation technology in the microelectronics industry, this novel graphene synthesis approach with precise layer-tunability and transfer-free processing has the promise to advance efficient graphene-device manufacturing and expedite their versatile applications in many fields.

36 MATERIALS SCIENCE↗
DOE OSTI2024

The Effective Fragment Molecular Orbital Method: Achieving High Scalability and Accuracy for Large Systems

The effective fragment molecular orbital (EFMO) method has been developed to predict the total energy of a very large molecular system accurately (with respect to the underlying quantum mechanical method) and efficiently by taking advantage of the locality of strong chemical interactions and employing a two-level hierarchical parallelism. The accuracy of the EFMO method is partly attributed to the accurate and robust intermolecular interaction prediction between distant fragments, in particular, the many-body polarization and dispersion effects, which require the generation of static and dynamic polarizability tensors by solving the coupled perturbed Hartree–Fock (CPHF) and time-dependent HF (TDHF) equations, respectively. Solving the CPHF and TDHF equations is the main EFMO computational bottleneck due to the inefficient (serial) and I/O-intensive implementation of the CPHF and TDHF solvers. In this work, the efficiency and scalability of the EFMO method are significantly improved with a new CPU memory-based implementation for solving the CPHF and TDHF equations that are parallelized by either message passing interface (MPI) or hybrid MPI/OpenMP. Here, the accuracy of the EFMO method is demonstrated for both covalently bonded systems and noncovalently bound molecular clusters by systematically examining the effects of basis sets and a key distance-related cutoff parameter, R cut . R cut determines whether a fragment pair (dimer) is treated by the chosen ab initio method or calculated using the effective fragment potential (EFP) method (separated dimers). Decreasing the value of Rcut increases the number of separated (EFP) dimers, thereby decreasing the computational effort. It is demonstrated that excellent accuracy (<1 kcal/mol error per fragment) can be achieved when using a sufficiently large basis set with diffuse functions coupled with a small R cut value. With the new parallel implementation, the total EFMO wall time is substantially reduced, especially with a high number of MPI ranks. Given a sufficient workload, nearly ideal strong scaling is achieved for the CPHF and TDHF parts of the calculation. For the first time, EFMO calculations with the inclusion of long-range polarization and dispersion interactions on a hydrated mesoporous silica nanoparticle with explicit water solvent molecules (more than 15k atoms) are achieved on a massively parallel supercomputer using nearly 1000 physical nodes. In addition, EFMO calculations on the carbinolamine formation step of an amine-catalyzed aldol reaction at the nanoscale with explicit solvent effects are presented.

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

Performance of high-order Godunov-type methods in simulations of astrophysical low Mach number flows

High-order Godunov methods for gas dynamics have become a standard tool for simulating different classes of astrophysical flows. Their accuracy is mostly determined by the spatial interpolant used to reconstruct the pair of Riemann states at cell interfaces and by the Riemann solver that computes the interface fluxes. In most Godunov-type methods, these two steps can be treated independently, so that many different schemes can in principle be built from the same numerical framework. Because astrophysical simulations often test out the limits of what is feasible with the computational resources available, it is essential to find the scheme that produces the numerical solution with the desired accuracy at the lowest computational cost. However, establishing the best combination of numerical options in a Godunov-type method to be used for simulating a complex hydrodynamic problem is a nontrivial task. In fact, formally more accurate schemes do not always outperform simpler and more diffusive methods, especially if sharp gradients are present in the flow. For this work, we used our fully compressible Seven-League Hydro (SLH) code to test the accuracy of six reconstruction methods and three approximate Riemann solvers on two- and three-dimensional (2D and 3D) problems involving subsonic flows only. We considered Mach numbers in the range from 10 −3 to 10 −1 , which are characteristic of many stellar and geophysical flows. In particular, we considered a well-posed, 2D, Kelvin–Helmholtz instability problem and a 3D turbulent convection zone that excites internal gravity waves in an overlying stable layer. Although the different combinations of numerical methods converge to the same solution with increasing grid resolution for most of the quantities analyzed here, we find that (i) there is a spread of almost four orders of magnitude in computational cost per fixed accuracy between the methods tested in this study, with the most performant method being a combination of a low-dissipation Riemann solver and a sextic reconstruction scheme; (ii) the low-dissipation solver always outperforms conventional Riemann solvers on a fixed grid when the reconstruction scheme is kept the same; (iii) in simulations of turbulent flows, increasing the order of spatial reconstruction reduces the characteristic dissipation length scale achieved on a given grid even if the overall scheme is only second order accurate; (iv) reconstruction methods based on slope-limiting techniques tend to generate artificial, high-frequency acoustic waves during the evolution of the flow; and (v) unlimited reconstruction methods introduce oscillations in the thermal stratification near the convective boundary, where the entropy gradient is steep.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

All Solid-State Li/LLZO/LCO Battery Enabled by Alumina Interfacial Coating

Li 7 La 3 Zr 2 O 12 (LLZO) garnet-type lithium-ion conductors are being investigated as a promising solid electrolyte for solid-state lithium batteries. To enable a functional all-solid-state configuration intensive investigations are needed to reduce the cathode/electrolyte interfacial resistance which contributes the most to cell performance loss. Among the commercial cathode materials investigated so far, LiCoO 2 (LCO) is one of the most stable with garnet electrolytes as only a superficial reaction has been detected between the two materials. However, even this minor reaction would block the Li-ion transport through the interface, resulting in deteriorated cell performance. In this work, we demonstrate that a thin aluminum oxide layer (5 nm) can be an effective interlayer to impede the formation of a harmful interphase and enable facile Li-ion transfer between LCO and the LLZO garnet. Room-temperature-sputtered LCO thin films were employed to form an interface with the garnet electrolyte and annealed at 800 °C to reveal the effect of the interfacial reaction on the Li-ion transfer across the interface. An aluminum oxide layer was then introduced between LCO and the garnet electrolyte by sputtering a metallic aluminum layer which is then annealed together with the upper LCO layer in oxygen, or by direct atomic layer deposition of the oxide. Compared to the LCO/LLZO/Li cells without an aluminum oxide interlayer, those with the interlayer exhibited improved performance, i.e., a stable discharge capacity of up to 90 mAh/(g LCO) at a C/10 rate, a rate capability up to 1.68C and a stable galvanostatic cycling at 0.1C for over 100 cycles with a discharge capacity fade rate of 0.15% per cycle. It was determined that aluminum diffused into the LCO layer after preventing the initial detrimental reaction between LCO and the LLZO garnet from happening during high temperature annealing, suggesting that the coating does not have to remain a physically blocking layer during cycling to function.

Electrochemistry↗
NASA NTRS1998

Algebraic Nonoverlapping Domain Decomposition Methods for Stabilized FEM and FV Discretizations

We consider preconditioning methods for convection dominated fluid flow problems based on a nonoverlapping Schur complement domain decomposition procedure for arbitrary triangulated domains. The triangulation is first partitioned into a number of subdomains and interfaces which induce a natural 2 x 2 partitioning of the p.d.e. discretization matrix. We view the Schur complement induced by this partitioning as an algebraically derived coarse space approximation. This avoids the known difficulties associated with the direct formation of an effective coarse discretization for advection dominated equations. By considering various approximations of the block factorization of the 2 x 2 system, we have developed a family of robust preconditioning techniques. A computer code based on these ideas has been developed and tested on the IBM SP2 using MPI message passing protocol. A number of 2-D CFD calculations will be presented for both scalar advection-diffusion equations and the Euler equations discretized using stabilized finite element and finite volume methods. These results show very good scalability of the preconditioner for various discretizations as the number of processors is increased while the number of degrees of freedom per processor is fixed.

Barth, Timothy J.↗
NASA NTRS1995

Molecular Sieve Bench Testing and Computer Modeling

The design of an efficient four-bed molecular sieve (4BMS) CO2 removal system for the International Space Station depends on many mission parameters, such as duration, crew size, cost of power, volume, fluid interface properties, etc. A need for space vehicle CO2 removal system models capable of accurately performing extrapolated hardware predictions is inevitable due to the change of the parameters which influences the CO2 removal system capacity. The purpose is to investigate the mathematical techniques required for a model capable of accurate extrapolated performance predictions and to obtain test data required to estimate mass transfer coefficients and verify the computer model. Models have been developed to demonstrate that the finite difference technique can be successfully applied to sorbents and conditions used in spacecraft CO2 removal systems. The nonisothermal, axially dispersed, plug flow model with linear driving force for 5X sorbent and pore diffusion for silica gel are then applied to test data. A more complex model, a non-darcian model (two dimensional), has also been developed for simulation of the test data. This model takes into account the channeling effect on column breakthrough. Four FORTRAN computer programs are presented: a two-dimensional model of flow adsorption/desorption in a packed bed; a one-dimensional model of flow adsorption/desorption in a packed bed; a model of thermal vacuum desorption; and a model of a tri-sectional packed bed with two different sorbent materials. The programs are capable of simulating up to four gas constituents for each process, which can be increased with a few minor changes.

Mohamadinejad, Habib↗
NASA NTRS2019

Reliable Bonding of Composite Laminates Using Reflowable Epoxy Resins

Epoxy matrix composites assembled with adhesives maximize the performance of aerospace structures, but the possibility of forming weak bonds requires the installation of redundant fasteners, which add weight and manufacturing cost. Co-cured joints (e.g. unitized composite structures) are immune to weak bonds because the uncured resin undergoes diffusion and mixing through the joint. A means of co-curing complex structures may reduce the need for redundant fasteners in bondlines. To this end, NASA started the AERoBOND project to develop novel joining materials to enable a “secondary-co-cure” assembly process. Aerospace epoxy resin systems reformulated with offset stoichiometry prevented the resin from advancing beyond the gel point during a conventional autoclave cure cycle up to 180 °C. The offset resins were applied to the joining surfaces of laminate preforms as prepreg. Two surfaces with complimentary offset resins were joined using conventional secondary bonding techniques. Preliminary efforts have indicated that the resulting joint has no discernable interface and appears as a conventional co-cured laminate under optical magnification. This report will discuss the initial work performed regarding formulation of the epoxy resin system using calorimetry, rheology, and mechanical testing.

Palmieri, Frank L.↗
DOE OSTI2020

Ultrahigh temperature in situ transmission electron microscopy based bicrystal coble creep in Zirconia II: Interfacial thermodynamics and transport mechanisms

This work uses a combination of stress dependent single grain boundary Coble creep and zero-creep experiments to measure interfacial energies, along with grain boundary point defect formation and migration volumes in cubic ZrO 2 . These data, along with interfacial diffusivities measured in a companion paper are then applied to analyzing two-particle sintering. The analysis presented here indicates that the large activation volume, v * = v f + v m primarily derives from a large migration volume and suggests that the grain boundary rate limiting defects are delocalized, possibly due to electrostatic interactions between charge compensating defects. The discrete nature of the sintering and creep process observed in the small-scale experiments supports the hypothesis that grain boundary dislocations serve as sources and sinks for grain boundary point defects and facilitate strain during sintering and Coble creep. Model two-particle sintering experiments demonstrate that initial-stage densification follows interface reaction rate-limited kinetics.

36 MATERIALS SCIENCE↗
DOE OSTI2023

MATBOX, an Open-Source Microstructure Analysis Toolbox for Meshing, Generation, Segmentation, and Characterization of 3D Heterogenous Volumes

Battery performance is strongly correlated with electrode microstructural properties. To account for its impact, lithium-ion battery (LIB) models either abstract the microstructural heterogeneity of composite electrodes using effective macroscopic properties (macro- or meso- scale models) or directly solve the system of equations on the microstructure geometry or mesh (microstructure-scale models). Therefore, to be adequate, both families of models require information from the microstructure geometry, which can be provided by the numerical tool presented in this work. MATBOX is a MATLAB open-source application [1] developed by NREL for performing various microstructure-related tasks including microstructure numerical generation, image filtering and microstructure segmentation, microstructure characterization and correlation, visualization, and microstructure meshing. MATBOX was originally developed for the analysis of LIB electrode microstructures; however, the algorithms provided by the toolbox are widely applicable to other heterogeneous materials. The toolbox provides a user-friendly experience thanks to a Graphical-User Interface, requires no coding by the user, and is well documented. This presentation will illustrate various MATBOX features for the characterization of a LIB electrode, including a fully automated Representative Volume Element (RVE) analysis, the numerical generation of complex 'virtual' microstructure, including dual-layer electrodes and carbon-binder additive phase, and the meshing of a complex NMC/graphite full cell microstructure suitable for 3D finite-element modeling. Other modules (segmentation, visualization, and correlation) will be briefly presented. Thanks to its modular, open-source approach, MATBOX can easily incorporate third-party algorithms to eventually build a standard in the field that will benefit the whole scientific community. Effective diffusion coefficient [2], additive phase numerical generation [3], and meshing [4] third-party algorithms have been already integrated in the toolbox with more to come.

DIRECT ENERGY CONVERSION,MATHEMATICS AND COMPUTING↗
NASA NTRS1998

A Parallel Non-Overlapping Domain-Decomposition Algorithm for Compressible Fluid Flow Problems on Triangulated Domains

This paper considers an algebraic preconditioning algorithm for hyperbolic-elliptic fluid flow problems. The algorithm is based on a parallel non-overlapping Schur complement domain-decomposition technique for triangulated domains. In the Schur complement technique, the triangulation is first partitioned into a number of non-overlapping subdomains and interfaces. This suggests a reordering of triangulation vertices which separates subdomain and interface solution unknowns. The reordering induces a natural 2 x 2 block partitioning of the discretization matrix. Exact LU factorization of this block system yields a Schur complement matrix which couples subdomains and the interface together. The remaining sections of this paper present a family of approximate techniques for both constructing and applying the Schur complement as a domain-decomposition preconditioner. The approximate Schur complement serves as an algebraic coarse space operator, thus avoiding the known difficulties associated with the direct formation of a coarse space discretization. In developing Schur complement approximations, particular attention has been given to improving sequential and parallel efficiency of implementations without significantly degrading the quality of the preconditioner. A computer code based on these developments has been tested on the IBM SP2 using MPI message passing protocol. A number of 2-D calculations are presented for both scalar advection-diffusion equations as well as the Euler equations governing compressible fluid flow to demonstrate performance of the preconditioning algorithm.

Barth, Timothy J.↗
DOE OSTI2021

Sr and Co Vapor-Phase Transport from LSCF Cathodes

A series of tests were performed to differentiate between surface diffusion and vapor-phase diffusion of chemical species from LSCF cathode material at typical sintering temperatures (up to 1100°C) in SOFC production. A GDC source substrate was printed with LSCF and separated by an air gap from a YSZ target substrate. Various geometries with long surface paths were employed to reduce the possibility of surface transport. Sr and Co were detected on the target substrates via energy dispersive spectroscopy (EDS) and x-ray photoelectron spectroscopy (XPS), including spatially resolved XPS. These results support a vapor-phase transport mechanism for Sr and Co. Sintering conditions and barrier layer requirements may need to be revisited to prevent the formation of undesired strontium zirconate at cathode/electrolyte interface due to vapor-phase transport.

vapor phase transport, SOFC cathode, Sr transport↗
DOE OSTI2022

Effect of thermal oxidation on helium implanted 316L stainless steel

The effect of thermal oxide layer on He implanted 316L stainless steel was studied to evaluate experimentally how thermal oxidation affects the diffusion and distribution of He in the material. In the case of thermal oxidation of a He implanted sample, with an increase in oxidation time, the max swelling height increases logarithmically as a function of time and finally saturates for all samples except for the lowest dose of implanted He. Concerning TEM results, two void regions are identified. Similar to the calculation, the total irradiated depth was around 250 nm and the large void region was formed around 100–150 nm depth. On the other hand, the small void region was observed immediately under oxide layer from the thermal oxidation. In contrast, there were no voids in the altered zone near the metal/oxide interface in the non-thermal oxidized/He implanted sample. This description of the phenomena was justified using the Kirkendall effect and the Point Defect Model.

36 MATERIALS SCIENCE↗
NASA NTRS1991

The effect of process conditions on the performance of epitaxial InP solar cells

Indium phosphide solar cells have a higher resistance to electron irradiation than Si or GaAs cells of comparable junction depth. As a result, there is much interest in the use of this material for space applications. Cells of this material were made in bulk InP by a number of techniques, including ion implantation, direct diffusion in sealed ampoules, and by open tube diffusion. However, it is generally considered that the epitaxial approach will be superior to all of these techniques. The epitaxy of InP is considerably more difficult than that of gallium arsenide, for a number of reasons. Perhaps the most important is the fact that the native oxides of Indium are extremely difficult to remove, as compared to that of Gallium. In addition, thermal treatments for the desorption of these oxides often result in the formation of phosphorus vacancies and free indium on the surface. Thus, inadequate sample preparation before epitaxy, poor reactor cleaning procedures, or poor transition procedures between the growth of successive layers, all give rise to trap phenomena and to high interface recombination velocities. Moreover, the lifetime of the grown material is dominated by the occurrence of native defects, so that it is a strong function of growth parameters. These problems are of special interest to the fabrication of solar cells, where long life-time, combined with the absence of traps, is highly desirable. A study of this problem is described using a non-invasive diagnostic technique which was developed.

Borrego, J. M.↗
DOE OSTI2022

Spontaneous Lithiation of Binary Oxides during Epitaxial Growth on LiCoO 2

Epitaxial growth is a powerful tool for synthesizing heterostructures and integrating multiple functionalities. Interfacial mixing can readily occur at temperatures required for complete film crystallization and can significantly modify the properties of layered structures, particularly for those containing energy storage materials with smaller cations. Here we show a two-step sequence involving the growth of an epitaxial LiCoO 2 cathode layer followed by the deposition of a binary transition metal oxide (WO 3 , TiO 2 , and others) in which controlled lithiation of the binary oxide occurs. Orientation-controlled epitaxial synthesis of the model solid-state-electrolyte Li 2 WO 4 and model anode material Li 4 Ti 5 O 12 occurs as WO 3 and TiO 2 nucleate their respective host lattices and attract Li ions from the underlying cathode. The cathode layer readily provides a tunable amount of Li ions for the controlled lithiation of the subsequent layer. We demonstrate that this approach can be used for energy materials discovery and exploring different combinations of epitaxial interfaces that can serve as well-defined model systems for mechanistic studies of energy storage and conversion processes.

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

Signatures of a liquid-crystal transition in spin-wave excitations of skyrmions

Abstract Understanding the spin-wave excitations of chiral magnetic order, such as the skyrmion crystal (SkX), is of fundamental interest to confirm such exotic magnetic order. The SkX is realized by competing Dzyaloshinskii-Moriya and ferromagnetic-exchange interactions with a magnetic field or anisotropy. Here, we compute the dynamical spin structure factor, using Monte Carlo and spin dynamics simulations, extracting the spin-wave spectrum in the SkX, in the vicinity of the paramagnet to SkX transition. Inside the SkX, we find six spin-wave modes, which are supplemented by another mode originating from the ferromagnetic background. Above the critical temperature T s for the skyrmion crystallization, we find a diffusive regime, reminiscent of the liquid-to-crystal transition, revealing that topological spin texture of skyrmionic character starts to develop above T s as the precursor of the SkX. We discuss the opportunities for the detection of the spin waves of the SkX using inelastic-neutron-scattering experiments in manganite-iridate heterostructures.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Spin Decoherence Dynamics of Er 3+ in CeO 2 Films

Developing telecom-compatible spin-photon interfaces is essential towards scalable quantum networks. Erbium ions (Er 3+ ) exhibit a unique combination of a telecom (1.5 mu m) optical transition and an effective spin-1=2 ground state, but identifying a host that enables heterogeneous device integration while preserving long optical and spin coherence remains an open challenge. In this work, we explore the potential of Er 3+ :CeO 2 films on silicon and study the Er 3+ spin coherence, offering low nuclear spin density and the potential for on-chip integration. We demonstrate a 38.8 mu s spin coherence, which can be extended to 176.4 mu s with dynamical decoupling. Pairing experiments with cluster correlation expansion calculations, we identify spectral diffusion induced by bath Er 3+ spin flip-flops as the dominant decoherence mechanism and provide pathways to millisecond-scale coherence.

36 MATERIALS SCIENCE↗
NASA NTRS1990

On the possibility of an alpha-sq omega-type dynamo in a thin layer inside the sun

If the solar dynamo operates in a thin layer of 10,000-km thickness at the interface between the convection zone and the radiative core, using the facts that the dynamo should have a period of 22 years and a half-wavelength of 40 deg in the theta-direction, it is possible to impose restrictions on the values which various dynamo parameters are allowed to have. It is pointed out that the dynamo should be of alpha-sq omega nature, and kinematical calculations are presented for free dynamo waves and for dynamos in thin rectangular slabs with appropriate boundary conditions. An alpha-sq omega dynamo is expected to produce a significant poloidal field which does not leak to the solar surface. It is found that the turbulent diffusity eta and alpha-coefficient are restricted to values within about a factor of 10, the median values being eta of about 10 to the 10th sq cm/sec and alpha of about 10 cm/sec. On the basis of mixing length theory, it is pointed out that such values imply a reasonable turbulent velocity of the order 30 m/s, but rather small turbulent length scales like 300 km.

Choudhuri, Arnab Rai↗
DOE OSTI2026

Aluminum Based Solvent-Free Organic–Inorganic Hybrid Materials

In emerging materials, molecular hybrids are especially promising, as they have molecular level mixing of the organic and inorganic components, producing homogeneous materials without interfaces that can deteriorate properties. However, the current methods of manufacturing molecular hybrids are based on solution processing, which is impractical for bulk materials such as may be used for optically clear radiation and electromagnetic shielding components or photonics. Here we examine molecular hybrids composed of aluminum isopropoxide (AIP) and epoxy resins aiming to understand the molecular scale chemistry and manufacturability of these hybrid materials. DSCmonitored cure revealed the ideal cure temperature for these materials is 160−170 °C and demonstrated that an AIP concentration of 16.7 wt % maximizes the extent of reaction. Kinetic analysis of the curing reaction showed the Sestak−Berggren autocatalytic model is effective at temperatures over 140 °C but the reaction has diffusion limitations at a temperature of 120 °C. Mechanical testing with custom resin molds revealed a decrease in properties of the bulk samples with increasing AIP content due to an increase in defects but further testing with nanoindentation demonstrated comparable or improved mechanical properties of AIP-epoxy hybrids compared to epoxy resin with a standard hardener. Ultimately, this work lays the foundation for hardener-free epoxy-aluminum inorganic/organic hybrids and presents opportunities to expand on properties for specific applications such as thermal conductivity, optical clarity, and dielectric constant.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗