Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “disordered solids”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 415 records · Page 23
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Chemical durability of multicomponent lanthanide zirconate solid solutions

Multicomponent zirconate solid solutions A 2 Zr 2 O 7 (A= (Sm,Yb), (Sm,Yb,Gd), (Sm,Yb,Gd,Er), and (Sm,Yb,Gd,Er,Dy)) were synthesized through spark plasma sintering and their chemical durability was investigated via semi-dynamic leaching tests in pH = 1 nitric acid at 90°C. Incongruent dissolution occurred for all samples with the preferential elemental release of zirconium in all A 2 Zr 2 O 7 except for high entropy (Sm,Yb,Gd,Er,Dy)Zr 2 O 7 which displays a congruent release of the A-site elements and Zr. A strong positive correlation was found between the lanthanide elemental release rates and the A-site cation size disorder, whereas a negative correlation was observed between the elemental release rates and mixing entropy.

36 MATERIALS SCIENCE↗
DOE OSTI2026

From high-entropy ceramics to compositionally complex ceramics and beyond

Over the past decade, the field of high-entropy ceramics (HECs) has expanded rapidly to encompass a broad range of oxides, borides, silicides, and other ceramic solid solutions. In 2020, we proposed extending HECs to compositionally complex ceramics (CCCs), where non-equimolar compositions and the presence of long- or short-range order, although reducing configurational entropy, create new opportunities to tailor and enhance properties, often surpassing those of higher-entropy counterparts. Along these lines, several fundamental scientific questions arise. Is the entropy in HECs truly high? Is maximizing entropy always desirable? In this perspective article, I revisit key concepts and terminologies and highlight emerging directions, including dual-phase CCCs, ultrahigh-entropy phases, and novel processing routes such as ultrafast reactive sintering. I propose that exploring compositional complexity across vast non-equimolar spaces, together with exploiting correlated disorder (coupled chemical and structural short-range order), represents a transformative strategy for designing ceramics with superior performance.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Preserving the Josephson Coupling of Twisted Cuprate Junctions via Tailored Silicon Nitride Circuits Boards

Controlled fabrication of twisted van der Waals heterostructures is essential to unlock the full potential of moiré materials. However, achieving reproducibility remains a major challenge, particularly for air-sensitive materials such as Bi 2 Sr 2 CaCu 2 O 8 + δ (BSCCO), where it is crucial to preserve the intrinsic and delicate superconducting properties of the interface throughout the entire fabrication process. Here, a dry, inert and cryogenic assembly method is presented that combines silicon nitride nanomembranes (NMBs) with pre-patterned electrodes and the cryogenic stacking technique (CST) to fabricate high-quality twisted BSCCO Josephson junctions (JJs). This protocol prevents thermal and chemical degradation during both interface formation and electrical contact integration. It is also found that asymmetric membrane designs, such as a double cantilever, effectively suppress vibration-induced disorder due to wire bonding, resulting in sharp and hysteretic current–voltage characteristics. The junctions exhibit a twist-angle-dependent Josephson coupling with magnitudes comparable to the highest-performing devices reported to date, but achieved through a straightforward and versatile contact method, offering a scalable and adaptable platform for future applications. These findings highlight the importance of both interface and contact engineering in addressing reproducibility in superconducting van der Waals heterostructures.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Comparing the Effects of Side Chain Dipole–Dipole Interactions and Hydrogen Bonding on the Mechanical and Electrical Properties of Poly(3-hexylthiophene)

Poly(3-alkylthiophenes) are simple conjugated polymers with good electrical properties, but tend to be brittle, limiting their application. Here, we investigate how side chain modifications can improve their toughness without compromising their charge transport. Specifically, we compare a weak dipole–dipole interaction of ester groups with a stronger hydrogen-bonding interaction of the hydroxyl groups. Two copolymers with targeted 5 and 10 mol % ester-functionalized side chains were synthesized and hydrolyzed in the solid state to introduce hydroxyl groups. Both hydrolyzed polymers became insoluble in most organic solvents, providing a path to layer-by-layer solution processing. All polymers’ optical, thermal, structural, electrical, and mechanical properties were investigated. Optical spectroscopy revealed that functionalization at these low levels did not significantly affect aggregation or π–π stacking. Differential scanning calorimetry indicated reduced crystallinity in the functionalized copolymers compared to that of P3HT. Grazing-incidence wide-angle X-ray diffraction data showed that functionalization led to an increase in lamellar spacing without altering molecular orientation or π–π stacking. Mechanical testing highlighted that at the lower functionalization level, both ester and hydroxyl groups similarly enhanced toughness, suggesting that disorder, rather than the specific nature of the functional group, was responsible for these improvements. At the higher functionalization level, hydroxyl groups significantly increased the elastic modulus while also negatively impacting charge carrier mobility. This study suggests that with stronger hydrogen-bonding groups, only very small amounts can improve P3HT’s toughness. For a wider tunable range, it may be a better strategy to use weak interactions such as dipole–dipole interactions of ester groups.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Van Hove singularity in the magnon spectrum of the antiferromagnetic quantum honeycomb lattice

In quantum magnets, magnetic moments fluctuate heavily and are strongly entangled with each other, a fundamental distinction from classical magnetism. Here, with inelastic neutron scattering measurements, we probe the spin correlations of the honeycomb lattice quantum magnet YbCl 3 . A linear spin wave theory with a single Heisenberg interaction on the honeycomb lattice, including both transverse and longitudinal channels of the neutron response, reproduces all of the key features in the spectrum. In particular, we identify a Van Hove singularity, a clearly observable sharp feature within a continuum response. The demonstration of such a Van Hove singularity in a two-magnon continuum is important as a confirmation of broadly held notions of continua in quantum magnetism and additionally because analogous features in two-spinon continua could be used to distinguish quantum spin liquids from merely disordered systems. These results establish YbCl 3 as a benchmark material for quantum magnetism on the honeycomb lattice.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Building [U IV 70 (OH) 36 (O) 64 ] 4– oxocluster frameworks with sulfate, transition metals, and U V

Uranium (IV) oxide clusters, colloids, and materials are designed and studied for 1) nuclear materials applications, 2) understanding environmental fate and transport of actinides, and 3) exploring the complex bonding behavior of open-shell f-elements. U IV -oxyhydroxsulfate clusters are particularly relevant in industrial processes and in nature. Recent studies have shown that counter-cations to these polynuclear anions differentiate rich structural topologies in the solid-state. Here we present nine different structures with wheel-shaped [U 70 (OH) 36 (O) 64 (SO 4 ) 60 ] 4- (U 70 ) linked into 1-dimensional and 2-dimensional frameworks with sulfate, divalent transition metals (Cr II , Fe II , Co II , Ni II ) and U V . Here, the small-angle X-ray scattering of these phases dissolved in butylamine reveals differing supramolecular assembly of U 70 clusters, controlled primarily by sulfates. However, observed trends in transition metal linking guide future design of U 70 -materials with different topologies. Finally, U 70 linking via U IV -O-U V -O-U IV bridges presents a rare example of mixed oxidation state uranium oxides without disorder.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1994

Diagenetic Microcrystalline Opal Varieties from the Monterey Formation, CA: HRTEM Study of Structures and Phase Transformation Mechanisms

Microcrystalline opal varieties form as intermediary precipitates during the diagenetic transformation of biogenically precipitated non-crystalline opal (opal-A) to microquartz. With regard to the Monterey Formation of California, X-ray powder diffraction studies have shown that a decrease in the primary d-spacing of opal-CT toward that of cristobalite occurs with increasing diagenesis. The initial timing of opal-CT/quartz formation and the value of the primary opal-CT d-spacing, are influenced by the sediment. lithology. Transmission electron microscopy methods (CTEM/HRTEM) were used to investigate the structure of the diagenetic phases and establish transformation mechanisms between the varieties of microcrystalline opals in charts and porcelanites from the Monterey Formation. HRTEM images revealed that the most common fibrous varieties of microcrystalline opals contain varying amounts of structural disorder. Finite lamellar units of cristobalite-and tridymite-type. layer sequences were found to be randomly stacked in a direction perpendicular to the fiber axis. Disordered and ordered fibers were found to have coprecipitated within the same radial fiber bundles that formed within the matrix of the Most siliceous samples. HRTEM images, which reveal that the fibers within radial and lepispheric fiber bundles branch non-crystallographically, support an earlier proposal that microspheres in chert grow via a spherulitic growth mechanism. A less common variety of opal-CT was found to be characterized by non-parallel (low-angle) stacking sequences that often contain twinned lamellae. Tabular-shaped crystals of orthorhombic tridymite (PO-2) were also identified in the porcelanite samples. A shift in the primary d-spacing of opal-CT has been interpreted as an indication of solid-state ordering g toward a predominantly cristobalite structure, (opal-C). Domains of opal-C were identified as topotactically-oriented overgrowths on discrete Sections of opal-CT fibers and as lamellar domains within relict opal-CT fibers. These findings indicate that the type of transformation mechanism depends upon the primary structural characteristics of the authigenic opaline. varieties that are in turn influenced by the sediment lithology.

Cady, Sherry L.↗
NASA NTRS2002

Stability of Pseudobrookite-Type Titanium Oxides

Orthorhombic, (Bbmm), (Al, Fe, Cr, Ti)(sub 2) TiO5-(Mg, Fe)Ti2O5 solid solutions (pseudobrookites, s.l.) are found either as an oxidation product of ilmenite and/or spinel or a primary crystallizing phase in igneous and metamorphic rocks on Earth (e.g., basalt flows, crustal and mantle xenoliths, hornfels), and basaltic rocks on the Moon. Moreover, orthorhombic oxides are often part of the crystalline matrix in glass/ceramics with useful applications, and play a major role in the industrial production of TiO2. To fully exploit the potential of these compounds as petrogenetic indicators and/or useful materials we need to quantitatively understand the factors controlling their properties and stability, and thus, to extrapolate beyond the calibrating experiments. For that purpose, we need to combine thermochemistry, phase equilibrium, and in situ P-V-T-cation disorder experimental data that presently either are incomplete or lacking. Perhaps, the most complete data set is that for MgTi2O5 (karrooite) which allows the calibration of models for the Gibbs free energy of the MgTi2O5 as a function of pressure, temperature, and the Mg2+-Ti4+ distribution between the two nonequivalent octahedral sites. Consequently, the effect of cation disorder on MgTi2O5 stability, and the phase relations among MgTi2O5, other titanium oxides, and silicate minerals can be examined. Calculated phase relations in the Mg-Ti-Si-O system and phase equilibrium experiments in Fe-bearing compositions suggest that pseudobrookite-type oxides may be a more common in rocks than previously realized. However, homogeneous and heterogeneous equilibria, and crystallization paths likely affect their stability. For example, isobaric increases in temperature favor disordering and thus entropy-stabilization, in contrast, isothermal increases in pressure have the opposite effect. Although, currently, the potential effect of composition to cation disorder cannot be fully explored, it appears that enrichment in trivalent cations probably enhances entropy-stabilization and thus may increase the stability of (Al, Fe, Cr, Ti)-rich pseudobrookites relative to that of (Mg, Fe)-rich ones. In addition, high-temperature, nearly isothermal, decompression paths of olivine+orthopyroxene+oxide assemblages may favor pseudobrookites (s.l.) over rutile and/or ilmenite, in contrast, cooling at low pressures seems to favor ilmenite and/or rutile. In the case of crustal and mantle xenoliths, the presence or absence of orthorhombic oxides is probably controlled by reactions with olivine, orthopyroxene, ilmenite, and rutile. In oceanic mantle xenoliths such reactions may also involve a TiO2-enriched but not SiO2-enriched melt/fluid, because pseudobrookites (s.l.) would react with the SiO2-enriched melt/fluid to form orthopyroxene and rutile. Parenthetically, experiments and model calculations in the Mg-Ti-Si-O system suggest that low degree partial melting of low-TiO2 bulk compositions may produce Ti-enriched liquids in equilibrium with olivine, orthopyroxen ad=nd MgTi2O5, rutile or ilmenite.

Xirouchakis, Dimistrios↗
DOE OSTI2024

Exploring Li-Ion Transport Properties of Li 3 TiCl 6 : A Machine Learning Molecular Dynamics Study

We performed large-scale molecular dynamics simulations based on a machine-learning force field (MLFF) to investigate the Li-ion transport mechanism in cation-disordered Li 3 TiCl 6 cathode at six different temperatures, ranging from 25°C to 100°C. In this work, deep neural network method and data generated by ab − initio molecular dynamics (AIMD) simulations were deployed to build a high-fidelity MLFF. Radial distribution functions, Li-ion mean square displacements (MSD), diffusion coefficients, ionic conductivity, activation energy, and crystallographic direction-dependent migration barriers were calculated and compared with corresponding AIMD and experimental data to benchmark the accuracy of the MLFF. From MSD analysis, we captured both the self and distinct parts of Li-ion dynamics. The latter reveals that the Li-ions are involved in anti-correlation motion that was rarely reported for solid-state materials. Similarly, the self and distinct parts of Li-ion dynamics were used to determine Haven’s ratio to describe the Li-ion transport mechanism in Li 3 TiCl 6 . Obtained trajectory from molecular dynamics infers that the Li-ion transportation is mainly through interstitial hopping which was confirmed by intra- and inter-layer Li-ion displacement with respect to simulation time. Ionic conductivity (1.06 mS/cm) and activation energy (0.29eV) calculated by our simulation are highly comparable with that of experimental values. Overall, the combination of machine-learning methods and AIMD simulations explains the intricate electrochemical properties of the Li 3 TiCl 6 cathode with remarkably reduced computational time. Thus, our work strongly suggests that the deep neural network-based MLFF could be a promising method for large-scale complex materials.

Selvaraj, Selva Chandrasekaran (ORCID:000000029023↗
DOE OSTI2023

A Graph Dynamical neural network approach for decoding dynamical states in ferroelectrics.

Ferroelectric materials such as BaTiO 3 show tremendous potential for emerging advances in memory devices, particular neuromorphic type devices. High density of memory can be obtained by stabilising polar domain walls at the nanoscale, regions of discontinuity between the well-defined polarization order parameter, but little is known about what controls their structure and dynamics in real nanoscale materials. Indeed, chiral polar domain walls have been observed in heterogeneous ferroelectrics, such as oxygen-deficient BaTiO 3 , but very little is known about how such polar-domains walls interact with defects. Indeed, a critical understanding of how dynamics of domain-walls depend on point-defects is crucial to create engineered ferroelectric memory devices. For this work, we perform large-scale simulations of nansocale domain-wall dynamics in pristine and defective BaTiO 3 using reactive force-field developed by us earlier (Phys. Chem. Chem. Phys., 2019, 21, 18240–18249), and capture their dynamical dependence on point defects using a graph dynamical neural-network approach, which we adapted to interrogate solids with well-defined order-parameters, and implemented using Pytorch based libraries. Our machine learning (ML) approach goes beyond the traditional post-processing methods to capture both spatial and temporal heterogeneities of large-scale molecular dynamics simulations of complex defective ferroelectric oxide materials. We crucially find that isolated oxygen vacancies introduce very localized spatial regions (~1–2 unit-cell in length) that show slow dipole relaxation due to formation of defect-dipoles, and that these defect-dipoles in turn slow the intrinsic dynamics of domain walls. Further, the roughness of domain walls, also influenced by vacancies, introduce dynamic heterogeneity along the domain-wall. As such we find a novel mechanism by which quenched disorder due to defects introduce dynamic heterogeneity thereby influencing response to external fields (particularly time varying fields) in a ferroelectric. Our study also emphasizes the need for creating digital twins of dynamical quantities to achieve autonomous in operando control of nanoscale switching.

42 ENGINEERING↗
DOE OSTI2024

Probing Interactions between Adsorbed Polymers and γ-Al 2 O 3 Using Solid-State NMR

The interactions between polymers and metal oxide surfaces affect the physical properties of polymer composites and the selectivity of catalysts used for plastic conversion. Gauging the strengths of these interactions and how they depend on adsorption conformations and polymer structure is nevertheless quite challenging. Herein, we evaluate whether a recently introduced dynamic nuclear polarization-based surface-to-atom distance measurement method can be used to gauge the specific interactions between five vinyl polymers and an oxide support (alumina). The adsorption conformations of polymer monolayers were studied using site-specific 13 C{ 27 Al} rotational-echo saturation-pulse double-resonance (RESPDOR) experiments. The method is effective in revealing the average distance between the adsorbed polymer and the surface, as well as the fraction of the monomers that are adsorbed. Polymers that possess larger side chains are more weakly adsorbed, as evidenced by their formation of more numerous loop and tail structures. In conclusion, the measured RESPDOR dephasing data further reveals that polymer adsorption conformations are largely disordered and involve few hydrogen bonding interactions.

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

Single Crystals of Vanadium Oxides as a Lens for Understanding Structural and Electronic Phase Transformations, Ion Transport, Chemo-Mechanical Coupling, and Electrothermal Neuronal Emulation

Vanadium oxides cystallize in a diverse array of structures and compositions arising from the redox versatility of vanadium, variable covalency of V−O bonds, and myriad coordination geometries. Their open frameworks present abundant interstitial sites that enable insertion of guest-ions. In such compounds, V3d electron and spin localization and disorder couple strongly to structural preferences. The rich structural diversity manifests as a “rugged” free energy landscape with multiple interconvertible polymorphs. Such a landscape sets up structural, electronic, and magnetic transitions that underpin the promise of these materials as ion-insertion battery electrodes; compact primitives for brain-inspired computing, and heterogeneous catalysts. Here, we examine the structural and compositional diversity, electronic instabilities, defect dynamics, structure transformations, mechanical properties, and surface structure of vanadium oxides using single crystals as a distinctive lens. Single crystals enable the measurement of structure−function correlations without the ensemble and orientational averaging inevitable in polycrystalline materials. Their well-defined surfaces further enable examination of facet-dependent reactivity toward molecular adsorbates, ion fluxes, and lattice (mis)matched solids. We provide a comprehensive account of vanadium-oxide single-crystal studies, from delineation of common structural motifs to single-crystal growth techniques, topochemical modification strategies, mechanisms underpinning electronic instabilities, and implementation as electrothermal neurons and battery electrode materials.

Ponis, John [Texas A&M University, College Station↗
DOE OSTI2024

Tutorial: Defects in topological semimetals

Three-dimensional topological semimetals are a class of electronic materials in which their bulk and surface states contain linear band touching nodes near the Fermi level. Like semiconductors, their properties will be affected by point and extended defects in their crystal structures, although the extent to which defects and disorders influence topological semimetals may differ in key ways due to their unique electronic structures. In this Tutorial, we provide an overview of the defects in topological semimetals, covering both computational and experimental methods for exploring defect-property relationships. We also include a discussion on open questions that still need to be explored further.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Analysis of Intermediates and Products from the Dehydrogenation of Mg(BH 4 ) 2

The thermodynamic properties of key compounds, Mg(B 3 H 8 ) 2 , MgB 2 H 6 , MgB 10 H 10 , Mg(B 11 H 14 ) 2 , Mg 3 (B 3 H 6 ) 2 , and MgB 12 H 12 , proposed to be formed in the release of hydrogen from magnesium borohydride Mg(BH 4 ) 2 and uptake of hydrogen by MgB 2 , have been investigated using solid–state density functional theory (DFT) calculations. Further, more accurate treatment of cell–size effects to the entropies were also investigated, in order to improve the accuracy of the thermodynamic properties of complex borohydrides. We find that the zero–point energy corrections can lower the electronic energies of reaction by 20–30 kJ/(mol H 2 ) for these intermediates, while adding the thermal and entropy contributions results in the total decrease up to ~50 kJ/(mol H 2 ). Although our treatment lowers the calculated formation energy of Mg(B 3 H 8 ) 2 , it is still too high to explain the experimental observation of B 3 H 8 – . We discuss possible reasons for this disparity and propose that the formation of B 3 H 8 – and H – in a disordered amorphous phase has a large energy difference compared to the phase–separated Mg(B 3 H 8 ) 2 and MgH 2 considered in calculations. Comparison of the experimental and NMR chemical shifts calculated within a DFT approach for known species Mg(BH 4 ) 2 , Mg(B 3 H 8 ) 2 , Mg(B 11 H 14 ) 2 , MgB 10 H 10 and MgB 12 H 12 provides validation for predicting the chemical shifts of the other compounds which are yet to be confirmed experimentally. These include MgB 2 H 6 and the proposed tri–anion species Mg 3 (B 3 H 6 ) 2 that both have favorable thermodynamics for reversible hydrogen storage in Mg(BH 4 ) 2 without the formation of MgH 2 as a co–product which could phase–separate and inhibit rehydrogenation.

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

Hybrid microstructure of smectite clay gels revealed using neutron and synchrotron X-ray scattering

Aqueous suspensions of swelling clays display a nematic sol-gel transition at very low solid concentrations. The underlying microstructure of the gel has remained a point of contention since the time of Irving Langmuir and has been a major obstacle to fully realizing the potential of clays for practical applications. Here, we comprehensively probe the microstructure of a smectite clay suspension using ultra-small angle neutron/X-ray scattering and find that the nematic gel is structurally ordered and contains entities that are at least an order of magnitude larger than the individual particles. Complementary cryo-electron microscopy shows the presence of domains having particle-particle ordering responsible for nematic texture and regions of particle-particle aggregation responsible for gel-like behavior. We find that the smectic clay gels have a hybrid microstructure with co-existing repulsive nematic domains and attractive disordered domains.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Spectroscopic fingerprint of charge order melting driven by quantum fluctuations in a cuprate

Copper oxide high-T C superconductors possess a number of exotic orders that coexist with or are proximal to superconductivity. Quantum fluctuations associated with these orders may account for the unusual characteristics of the normal state, and possibly affect the superconductivity. Yet, spectroscopic evidence for such quantum fluctuations remains elusive. Here in this paper, we use resonant inelastic X-ray scattering to reveal spectroscopic evidence of fluctuations associated with a charge order in nearly optimally doped Bi 2 Sr 2 CaCu 2 O 8+δ . In the superconducting state, while the quasielastic charge order signal decreases with temperature, the interplay between charge order fluctuations and bond-stretching phonons in the form of a Fano-like interference increases, an observation that is incompatible with expectations for competing orders. Invoking general principles, we argue that this behaviour reflects the properties of a dissipative system near an order–disorder quantum critical point, where the dissipation varies with the opening of the pseudogap and superconducting gap at low temperatures, leading to the proliferation of quantum critical fluctuations, which melt charge order.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Correlated States of 2D Electrons near the Landau Level Filling ν = 1 / 7

The ground state of two-dimensional electron systems (2DESs) at low Landau level filling factors ( ν ≲ 1 / 6 ) has long been a topic of interest and controversy in condensed matter. Following the recent breakthrough in the quality of ultrahigh-mobility GaAs 2DESs, we revisit this problem experimentally and investigate the impact of reduced disorder. In a GaAs 2DES sample with density n = 6.1 × 10 10 / cm 2 and mobility μ = 25 × 10 6 cm 2 / V s , we find a deep minimum in the longitudinal magnetoresistance ( R x x ) at ν = 1 / 7 when T ≃ 104 mK . There is also a clear sign of a developing minimum in R x x at ν = 2 / 13 . While insulating phases are still predominant when ν ≲ 1 / 6 , these minima strongly suggest the existence of fractional quantum Hall states at filling factors that comply with the Jain sequence ν = p / ( 2 m p ± 1 ) even in the very low Landau level filling limit. The magnetic-field-dependent activation energies deduced from the relation R x x ∝ e E A / 2 k T corroborate this view and imply the presence of pinned Wigner solid states when ν ≠ p / ( 2 m p ± 1 ) . Similar results are seen in another sample with a lower density, further generalizing our observations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗