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At least 1,603 records · Page 89
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Coupled crystal orientation-size effects on the strength of nano crystals

We study the combined effects of grain size and texture on the strength of nanocrystalline copper (Cu) and nickel (Ni) using a crystal-plasticity based mechanics model. Within the model, slip occurs in discrete slip events exclusively by individual dislocations emitted statistically from the grain boundaries. We show that a Hall-Petch relationship emerges in both initially texture and non-textured materials and our values are in agreement with experimental measurements from numerous studies. We find that the Hall-Petch slope increases with texture strength, indicating that preferred orientations intensify the enhancements in strength that accompany grain size reductions. These findings reveal that texture is too influential to be neglected when analyzing and engineering grain size effects for increasing nanomaterial strength.

36 MATERIALS SCIENCE↗
DOE OSTI2014

Size-dependent stability toward dissociation and ligand binding energies of phosphine-ligated gold cluster ions

The stability of sub-nanometer size gold clusters ligated with organic molecules is of paramount importance to the scalable synthesis of monodisperse size-selected metal clusters with highly tunable chemical and physical properties. For the first time, a Fourier transform ion cyclotron resonance mass spectrometer (FT-ICR-MS) equipped with surface induced dissociation (SID) has been employed to investigate the time and collision energy resolved fragmentation behavior of cationic doubly charged gold clusters containing 7-9 gold atoms and 6-7 triphenylphosphine (TPP) ligands prepared by reduction synthesis in solution. The TPP ligated gold clusters are demonstrated to fragment through three primary dissociation pathways: (1) Loss of a neutral TPP ligand from the precursor gold cluster, (2) asymmetric fission and (3) symmetric fission and charge separation of the gold core resulting in formation of complementary pairs of singly charged fragment ions. Threshold energies and activation entropies of these fragmentation pathways have been determined employing Rice-Ramsperger-Kassel-Marcus (RRKM) modeling of the experimental SID data. It is demonstrated that the doubly charged cluster ion containing eight gold atoms and six TPP ligands, (8,6)2+, exhibits exceptional stability compared to the other cationic gold clusters examined in this study due to its large ligand binding energy of 1.76 eV. Our findings demonstrate the dramatic effect of the size and extent of ligation on the gas-phase stability and preferred fragmentation pathways of small TPP-ligated gold clusters.

Environmental Molecular Sciences Laboratory↗
DOE OSTI2017

Nature of peptide wrapping onto metal nanoparticle catalysts and driving forces for size control

Colloidal metal nanocrystals find many applications in catalysis, energy conversion devices, and therapeutics. However, the nature of ligand interactions and implications on shape control have remained uncertain at the atomic scale. Large differences in peptide adsorption strength and facet specificity were found on flat palladium surfaces versus surfaces of nanoparticles of 2 to 3 nm size using accurate atomistic simulations with the Interface force field. Folding of longer peptides across many facets explains the formation of near-spherical particles with local surface disorder, in contrast to the possibility of nanostructures of higher symmetry with shorter ligands. The average particle size in TEM correlates inversely with the surface coverage with a given ligand and with the strength of ligand adsorption. The role of specific amino acids and sequence mutations on the nanoparticle size and facet composition is discussed, as well as the origin of local surface disorder that leads to large differences in catalytic reactivity.

Chemistry↗
DOE OSTI2018

Two mechanisms of nanoparticle generation in picosecond laser ablation in liquids: the origin of the bimodal size distribution

The synthesis of chemically clean and environmentally friendly nanoparticles through pulsed laser ablation in liquids has shown a number of advantages over conventional chemical synthesis methods and has evolved into a thriving research field attracting laboratory and industrial applications. The fundamental understanding of processes leading to the nanoparticle generation, however, still remains elusive. In particular, the origin of bimodal nanoparticle size distributions in femto- and picosecond laser ablation in liquids, where small nanoparticles (several nanometers) with narrow size distribution are commonly observed to coexist with larger (tens to hundreds of nanometers) ones, has not been explained so far. In this paper, joint computational and experimental efforts are applied to understand the mechanisms of nanoparticle formation in picosecond laser ablation in liquids and to explain the bimodal nanoparticle size distributions. The results of a large-scale atomistic simulation reveal the critical role of the dynamic interaction between the ablation plume and the liquid environment, leading to the generation of large nanoparticles through a sequence of hydrodynamic instabilities at the plume-liquid interface and a concurrent nucleation and growth of small nanoparticles in an expanding metal-liquid mixing region. The computational predictions are supported by a series of stroboscopic videography experiments showing the emergence of small satellite bubbles surrounding the main cavitation bubble generated in single pulse experiments. Lastly, carefully timed double pulse irradiation triggers expansion of secondary cavitation bubbles indicating, in accord with the simulation results, the presence of localized sites of laser energy deposition (possibly large nanoparticles) injected into the liquid at the early stage of the bubble formation.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Influence of dopant size and electron affinity on the electrical conductivity and thermoelectric properties of a series of conjugated polymers

Here, chemical doping is widely used to manipulate the electrical and thermoelectric properties of organic semiconductors, yet intelligent design of polymer–dopant systems remains elusive. It is challenging to predict the electrical and thermoelectric properties of doped organic semiconductors due to the large number of variables impacting these properties, including film morphology, dopant and polymer energetics, dopant size, and degree of polaron delocalization. Herein, a series of dopants with varying sizes and electron affinities (EAs) are combined with polymers of differing ionization energies (IEs) to investigate how the difference between polymer IE and dopant EA influences the doping efficiency and electrical conductivity, and how the dopant size influences the thermoelectric properties. Our experiments demonstrate that at low doping levels the doping efficiency strongly depends on the difference between the polymer IE and dopant EA; the effectiveness of doping on increasing electrical conductivity drastically decreases at high loadings for the molybdenum dithiolene complexes, while FeCl 3 remains effective at high loadings; and the large molybdenum complexes lead to more delocalized polarons as compared to FeCl 3 . To take advantage of the complementary doping characteristics of the molybdenum complexes and FeCl 3 , both dopants are employed simultaneously to reach high power factors at relatively low dopant concentrations.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Molecular dynamics simulations of alkaline earth metal ions binding to DNA reveal ion size and hydration effects

The identity of metal ions surrounding DNA is key to its biological function and materials applications. In this work, we compare atomistic molecular dynamics simulations of double strand DNA (dsDNA) with four alkaline earth metal ions (Mg 2+ , Ca 2+ , Sr 2+ , and Ba 2+ ) to elucidate the physical interactions that govern DNA–ion binding. Simulations accurately model the ion–phosphate distance of Mg 2+ and reproduce ion counting experiments for Ca 2+ , Sr 2+ , and Ba 2+ . Our analysis shows that alkaline earth metal ions prefer to bind at the phosphate backbone compared to the major groove and negligible binding occurs in the minor groove. Larger alkaline earth metal ions with variable first solvation shells (Ca 2+ , Sr 2+ , and Ba 2+ ) show both direct and indirect binding, where indirect binding increases with ion size. Mg 2+ does not fit this trend because the strength of its first solvation shell predicts indirect binding only. Ions bound to the phosphate backbone form fewer contacts per ion compared to the major groove. Within the major groove, metal ions preferentially bind to guanine–cystosine base pairs and form simultaneous contacts with the N7 and O6 atoms of guanine. Overall, we find that the interplay among ion size, DNA–ion interaction, and the size and flexibility of the first solvation shell are key to predicting how alkaline earth metal ions interact with DNA.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

A new metric to control nucleation and grain size distribution in hybrid organic–inorganic perovskites by tuning the dielectric constant of the antisolvent

In perovskite research, there is a widely exploited but poorly explained phenomenon in which the addition of “antisolvents (ATS)” to precursor solutions results in higher-quality films. We explain the mechanism and driving force underlying an antisolvent-driven solvent extraction process. Density functional theory calculations uncover the defining effects of antisolvent choice on the extent of complexation between a lead salt and a methylammonium cation in solution. We experimentally validate the computational results using ultraviolet-visible spectroscopy and 207 Pb nuclear magnetic spectroscopy of methylammonium lead iodide solutions, containing both a processing solvent and an antisolvent. Furthermore, we uncover, and subsequently identify, the appearance of new species in solution as a result of the addition of the antisolvent. Furthermore, we observe that the choice of antisolvent has a substantial effect on the nature of the complexation of the methylammonium lead iodide (MAPbI 3 ) precursor species, whose origin we explain at an atomic level; specifically, the lower the dielectric of the antisolvent, the stronger the intermolecular binding energy between methylammonium cation (MA + ) cation and PbI 3 - plumbate, independent of the solvent or antisolvent interaction with the lead salt. Thin films were characterized using scanning electron microscopy; images of the films show how the addition of an antisolvent influences and, importantly, can be used to alter thin-film grain size. Grain size and distribution in thin films is reflected by the choice of antisolvent, promoting slower nucleation rates, a lower nucleation density, and hence larger final grain size.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Inverse size-dependent Stokes shift in strongly quantum confined CsPbBr 3 perovskite nanoplates

Colloidal semiconductor nanocrystals (NCs) are used as bright chromatic fluorophores for energy-efficient displays. Here we focus here on the size-dependent Stokes shift for CsPbBr 3 nanocrystals. The Stokes shift, i.e., the difference between the wavelengths of absorption and emission maxima, is crucial for display application, as it controls the degree to which light is reabsorbed by the emitting material reducing the energetic efficiency. One major impediment to the industrial adoption of NCs is that slight deviations in manufacturing conditions may result in a wide dispersion of the product's properties. A data-driven analysis of over 2000 reactions comparing two data sets, one produced via standard colloidal synthesis and the other via high-throughput automated synthesis is discussed. We show that differences in the reaction conditions of colloidal CsPbBr 3 nanocrystals yield nanocrystals with opposite Stokes shift size-dependent trends. These match the morphologies of two-dimensional nanoplatelets (NPLs) and nanocrystal cubes. The Stokes shift size dependence trend of NPLs and nanocubes is non-monotonic indicating different physics is at play for the two nanocrystal morphologies. For nanocrystals with cubic shape, with the increase of edge length, there is a significant decrease in Stokes shift values. However, for NPLs with the increase of thickness (1–4 ML), Stokes shift values will increase. The study emphasizes the transition from a spectroscopic point of view and relates the two Stokes shift trends to 2D and 0D exciton dimensionalities for the two morphologies. Our findings highlight the importance of CsPbBr 3 nanocrystal morphology for Stokes shift prediction.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Influence of the molecular weight and size distribution of PSS on mixed ionic-electronic transport in PEDOT:PSS

The commercially available polyelectrolyte complex poly(3,4-ethylenedioxythiophene):poly(styrene sulfonate) (PEDOT:PSS) is ubiquitous in organic and hybrid electronics. As such, it has often been used as a benchmark material for fundamental studies and the development of new electronic devices. Yet, most studies on PEDOT:PSS have focused on its electronic conductivity in dry environments, with less consideration given to its ion transport, coupled ionic-electronic transport, and charge storage properties in aqueous environments. These properties are essential for applications in bioelectronics (sensors, actuators), charge storage devices, and electrochromic displays. Importantly, past studies on mixed ionic-electronic transport in PEDOT:PSS neglected to consider how the molecular structure of PSS affects mixed ionic-electronic transport. Herein, we therefore investigated the effect of the molecular weight and size distribution of PSS on the electronic properties and morphology of PEDOT:PSS both in dry and aqueous environments, and overall performance in organic electrochemical transistors (OECTs). Using reversible addition–fragmentation chain transfer (RAFT) polymerization with two different chain transfer agents, six PSS samples with monomodal, narrow (D = 1.1) and broad (D = 1.7) size distributions and varying molecular weights were synthesized and used as matrices for PEDOT. We found that using higher molecular weight of PSS (Mn = 145 kg mol –1 ) and broad dispersity led to OECTs with the highest transconductance (up to 16 mS) and [μC*] values (~140 F cm –1 V –1 s –1 ) in PEDOT:PSS, despite having a lower volumetric capacitance (C* = 35 ± 4 F cm –3 ). The differences were best explained by studying the microstructure of the films by atomic force microscopy (AFM). We found that heterogeneities in the PEDOT:PSS films (interconnected and large PEDOT- and PSS-rich domains) obtained from high molecular weight and high dispersity PSS led to higher charge mobility (μOECT ~4 cm 2 V –1 s –1 ) and hence transconductance. Furthermore, these studies highlight the importance of considering molecular weight and size distribution in organic mixed ionic-electronic conductor, and could pave the way to designing high performance organic electronics for biological interfaces.

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

Do not forget the electrons: Extending moderately-sized nuclear networks for multidimensional hydrodynamic codes

Context.Nuclear networks are widely used coupled with hydrodynamical simulations of explosive scenarios to account for the change of nuclear species and energy generation rate due to nuclear reactions. In this way, there is a feedback mechanism between the hydrodynamical state and the nuclear processes. Unfortunately, the timescale of nuclear reactions is orders of magnitude smaller than the dynamical timescale that drives hydrodynamical simulations. Therefore, these nuclear networks are usually very small, reduced in most cases to a dozen elements, especially when simulations are carried out in more than one dimension. Aims.We present here an extended nuclear network, with 90 species, designed for being coupled with hydrodynamic simulations, which includes neutrons, protons, electrons, positrons, and the corresponding neutrino and anti-neutrino emission. This network is also coupled with temperature, making it extremely robust and, together with its size, unique of its kind. The inclusion of electron captures on free protons makes the network very appropriate for multidimensional studies of Type Ia supernova explosions, especially when the exploding object is a massive white dwarf. Methods.We perform several tests that are relevant to simulate explosive scenarios, such as Type Ia supernovae and core-collapse supernovae. We compare the results of the 90 nuclei network with a standardα-chain network with 14 elements to evaluate the differences in the energy generation rate. We also evaluate the relevance of including the electrons in the network in terms of generated yields and how it affects the pressure of a degenerate fluid such as that of white dwarfs. The results obtained with the 90-nuclei network have been verified with a much larger 2000-nuclei network built from REACLIB (WinNet), in terms of nuclear energy generation rate, pressure, and produced yields. Results.The results obtained with the proposed medium-sized network compare fairly well, to a few percent, with those computed withWinNetin scenarios reproducing the gross physical conditions of current Type Ia supernova explosion models. In those cases where the carbon and oxygen fuel ignites at high density, the high-temperature plateau typical of the nuclear statistical equilibrium regime is well defined and stable, allowing large integration time steps. We show that the inclusion of electron captures on free protons substantially improves the estimation of the electron fraction of the mixture. Therefore, the pressure is better determined than in networks where electron captures are excluded, which will ultimately lead to more reliable hydrodynamic models. Explosive combustion of helium at low density, occurring near the surface layer of a white dwarf, is also better described with the proposed network, which gives nuclear energy generation rates much closer toWinNetthan typical reduced alpha networks. Conclusions.A nuclear network withN= 90 species, including electrons, aimed at multidimensional calculations of supernova explosions is described and verified. The proposed network is suitable for the study of Type Ia supernova explosions because it provides better values of pressure and electron abundance than other existing networks with smaller or even a similar size but without including electron capture processes.

Astronomy & Astrophysics↗
DOE OSTI2023

Spherical powders: Control over the size and morphology of powders for additive manufacturing and enriched stable isotope nuclear targets

Metal powders are a fundamental starting point for fabricating many types of nuclear targets. Elemental powder properties can differ drastically between batches, even when using the same method. Therefore, the variation in morphology and the size of metal powders can cause variable quality and produce inconsistent results with what are otherwise proven target manufacturing techniques. Additive manufacturing has additional requirements for higher quality and more uniform feedstock. The production of spheroidized powders with uniform, reproducible properties and a narrow size distribution represents unexplored opportunities for experiments. These opportunities include experimenting with solid metals that can now flow like liquids, new options for powder handling and dispensing, and new target fabrication methods using additive manufacturing. The Stable Isotope Materials and Chemistry Group at Oak Ridge National Laboratory obtained an AMAZEMET rePowder ultrasonic metal atomization tool for creating limited batches of fully dense, free flowing, spherical powders with a narrow size distribution of extremely rare materials. Early results are presented with materials that were produced. The team explores the anticipated limits of this instrument with extremely rare materials (e.g., enriched stable isotopes) and highlights research into new fabrication techniques that provide additional options benefitting the international nuclear target community.

Zach, Mike↗
DOE OSTI2012

Influence of laser irradiated spot size on energetic electron injection and proton acceleration in foil targets

The influence of irradiated spot size on laser energy coupling to electrons, and subsequently to protons, in the interaction of intense laser pulses with foil targets is investigated experimentally. Proton acceleration is characterized for laser intensities ranging from 2x10{sup 18}-6x10{sup 20} W/cm{sup 2}, by (1) variation of the laser energy for a fixed irradiated spot size, and (2) by variation of the spot size for a fixed energy. At a given laser pulse intensity, the maximum proton energy is higher under defocus illumination compared to tight focus and the results are explained in terms of geometrical changes to the hot electron injection.

43 PARTICLE ACCELERATORS↗
DOE OSTI2012

Inhomogeneous linewidth broadening and radiative lifetime dispersion of size dependent direct bandgap radiation in Si quantum dot

The SiO{sub x} (SiO{sub x}:Si-QDs) with buried Si quantum dots (Si-QDs) is synthesized by plasma-enhanced chemical vapor deposition (PECVD), and the size-dependent wave-function of Si-QDs embedded in Si-rich SiO{sub 2} matrix is experimentally and theoretically analyzed to reformulate its bandgap energy as E{sub g}(d) = 1.12+5.83/d{sup 1.78}. The photoluminescent lifetime of Si-QDs is dominated by the non-phonon assisted radiative recombination. Shrinking the Si-QD size from 4.3 to 1.9 nm increases the overlapping probability of electron-hole wave-functions in Si-QD to shorten the non-phonon assisted radiative lifetime from 6.3 {mu}s to 83 ns. Fitting the time-resolved photoluminescence trace with a stretched exponential decay function reveals a lifetime dispersion factor. The lifetime dispersion greatly reduced from 0.8 to 0.39 by enlarging the size distribution of Si-QDs from 0.2 to 1.1 nm, which elucidates the inhomogeneous linewidth broadening feature of Si-QDs. Based on the simulation of non-phonon assisted recombination process, the full-band stretched exponential decay analysis confirms the correlation between inhomogeneous linewidth broadening and lifetime dispersion in Si-QDs.

36 MATERIALS SCIENCE↗
DOE OSTI2013

Size-dependent transition of deformation mechanism, and nonlinear elasticity in Ni{sub 3}Al nanowires

A size-dependent transition of deformation mechanism is revealed in Ni{sub 3}Al nanowire under atomistic uniaxial tension. Deformation twinning is replaced by phase transformation when the diameter of Ni{sub 3}Al nanowire reduces to a critical value near 4 nm. Enhanced size-dependent nonlinear elasticity is observed in the nanowires, in comparison to their bulk counterpart which is benchmarked by combined density functional and atomistic study. This study provide fundamental understanding on the size-dependent deformation mechanisms of nanostructured alloys.

36 MATERIALS SCIENCE↗
DOE OSTI2013

Radiation thermometer size-of-source effect testing using aperture

Size-of-source effect is an important attribute of any radiation thermometer. The effects of this attribute may be quantified in a number of different ways to include field-of-view, distance ratio, or size-of-source effect. These parameters provide needed information for the user of a radiation thermometer, as they aid in determining whether the measured object is large enough for adequate radiation thermometry measurement. Just as important, these parameters provide needed information for calibration. This information helps to determine calibration geometry, and it is needed for calibration uncertainty determination. For determination of size-of-source effect, there are a limited number of test methods furnished by the standards available today. The test methods available may be cumbersome to perform due to the cost of the required equipment and the time needed to set-up and perform the test. Other methods have been proposed. This paper discusses one such method. This method uses a circular aperture such as that used in radiation thermometer calibration. It describes the method both theoretically and mechanically. It then discusses testing done to verify this method comparing the results to those obtained while performing steps in current standards. Finally, based on this testing, the basis for a new standard test method is presented.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2013

Structural and optical properties of size controlled Si nanocrystals in Si{sub 3}N{sub 4} matrix: The nature of photoluminescence peak shift

Superlattices of Si{sub 3}N{sub 4} and Si-rich silicon nitride thin layers with varying thickness were prepared by plasma enhanced chemical vapor deposition. After high temperature annealing, Si nanocrystals were formed in the former Si-rich nitride layers. The control of the Si quantum dots size via the SiN{sub x} layer thickness was confirmed by transmission electron microscopy. The size of the nanocrystals was well in agreement with the former thickness of the respective Si-rich silicon nitride layers. In addition X-ray diffraction evidenced that the Si quantum dots are crystalline whereas the Si{sub 3}N{sub 4} matrix remains amorphous even after annealing at 1200 °C. Despite the proven Si nanocrystals formation with controlled sizes, the photoluminescence was 2 orders of magnitude weaker than for Si nanocrystals in SiO{sub 2} matrix. Also, a systematic peak shift was not found. The SiN{sub x}/Si{sub 3}N{sub 4} superlattices showed photoluminescence peak positions in the range of 540–660 nm (2.3–1.9 eV), thus quite similar to the bulk Si{sub 3}N{sub 4} film having peak position at 577 nm (2.15 eV). These rather weak shifts and scattering around the position observed for stoichiometric Si{sub 3}N{sub 4} are not in agreement with quantum confinement theory. Therefore theoretical calculations coupled with the experimental results of different barrier thicknesses were performed. As a result the commonly observed photoluminescence red shift, which was previously often attributed to quantum-confinement effect for silicon nanocrystals, was well described by the interference effect of Si{sub 3}N{sub 4} surrounding matrix luminescence.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2013

Nature of size-dependent lattice distortions in doped CeO{sub 2}

Electron paramagnetic resonance spectroscopy of Gd{sup 3+} probe ions is used to investigate the nature of size dependent lattice distortions in bulk and nanocrystalline CeO{sub 2} with crystallite sizes of 600 and 10 nm, respectively, and doped with 0.5 and 1 cation% Y. The Gd{sup 3+} ions in bulk CeO{sub 2} are primarily located in almost perfect cubic crystal field, and the presence of the nearest neighbor vacancies results in trigonal distortion of this crystal field. In contrast, for nanocrystalline ceria, although the long-range symmetry remains unchanged, decreasing size results in local distortion of the crystal-field that is significantly different than that induced by the presence of nearest-neighbor oxygen vacancies. Different types of distortions are observed for the cation sites in the core and the surface regions of the nanocrystallites. Such lattice distortions at short-range are fundamental to the nanocrystalline state, being related to the increased ratio of the surface:bulk energy at nanometer length scales and provides mechanistic understanding of previously reported lattice parameter changes and phase transitions in nanocrystalline oxides.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Finite size effects in L1{sub o}-FePt nanoparticles

Finite size effects on the temperature dependence of the uniaxial magnetic anisotropy, longitudinal and transverse susceptibilities and specific heat are examined for L1{sub o}-ordered FePt nanoparticles using an atomistic model based on an effective classical spin Hamiltonian. At low temperatures below criticality, we study the intrinsic uniaxial magnetic anisotropy energy (MAE) K{sub 1} and its scaling with magnetization K{sub 1}(T)∼M{sub s}(T){sup δ} and using Langevin dynamics simulations we show that the dependence of the exponent δ on the size L and aspect ratio of the grain arises from decomposition of the MAE into bulk and surface dependent terms. Monte Carlo simulations in the critical regime near the Curie temperature T{sub c}, show that the temperature variation of the specific heat and longitudinal susceptibility is given by finite size scaling relations c=L{sup α/ν}c{sup ~}(L{sup 1/ν}ϵ) and χ=L{sup γ/ν}χ{sup ~}(L{sup 1/ν}ϵ), respectively, where ϵ=(T−T{sub c})/T{sub c} is the reduced temperature, and the susceptibility scaling function χ{sup ~} can be approximated by a Lorentzian. Our estimates of the critical exponents α,γ, and ν appear to be in agreement with the universality class of the 3D Ising model.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗