The stability of hexagonal lattices with a simple law of force

1952 ◽  
Vol 48 (2) ◽  
pp. 316-328 ◽  
Author(s):  
F. R. N. Nabarro ◽  
J. H. O. Varley

AbstractA hexagonal lattice bound by central forces between nearest neighbours is always close-packed. If there is in addition an energy which, like the Fermi energy of free electrons, depends only on the volume, a close-packed equilibrium structure is still possible, but there may be another hexagonal structure of lower energy. A numerical example is given in which this occurs, the lattice spacing, binding energy and elastic constants being comparable with those of Zn, and the law of force showing no obvious peculiarities.

Author(s):  
M. Born

The theory of lattice deformations is presented in a new form, using the tensor calculus. The case of central forces is worked out in detail, and the results are applied to some simple hexagonal lattices. It is shown that the Bravais hexagonal lattice is unstable but the close-packed hexagonal lattice stable. The elastic constants of this lattice are calculated.


Author(s):  
Akhileshwar Srivastava ◽  
Divya Singh

Presently, an emerging disease (COVID-19) has been spreading across the world due to coronavirus (SARS-CoV2). For treatment of SARS-CoV2 infection, currently hydroxychloroquine has been suggested by researchers, but it has not been found enough effective against this virus. The present study based on in silico approaches was designed to enhance the therapeutic activities of hydroxychloroquine by using curcumin as an adjunct drug against SARS-CoV2 receptor proteins: main-protease and S1 receptor binding domain (RBD). The webserver (ANCHOR) showed the higher protein stability for both receptors with disordered score (<0.5). The molecular docking analysis revealed that the binding energy (-24.58 kcal/mol) of hydroxychloroquine was higher than curcumin (-20.47 kcal/mol) for receptor main-protease, whereas binding energy of curcumin (<a>-38.84</a> kcal/mol) had greater than hydroxychloroquine<a> (-35.87</a> kcal/mol) in case of S1 receptor binding domain. Therefore, this study suggested that the curcumin could be used as combination therapy along with hydroxychloroquine for disrupting the stability of SARS-CoV2 receptor proteins


Energies ◽  
2021 ◽  
Vol 14 (11) ◽  
pp. 3105
Author(s):  
Mohamed Zbair ◽  
Simona Bennici

To improve the proficiency of energy systems in addition to increasing the usage of renewable energies, thermal energy storage (TES) is a strategic path. The present literature review reports an overview of the recent advancements in the utilization of salt hydrates (single or binary mixtures) and composites as sorbents for sorption heat storage. Starting by introducing various heat storage systems, the operating concept of the adsorption TES was clarified and contrasted to other technologies. Consequently, a deep examination and crucial problems related to the different types of salt hydrates and adsorbents were performed. Recent advances in the composite materials used in sorption heat storage were also reviewed and compared. A deep discussion related to safety, price, availability, and hydrothermal stability issues is reported. Salt hydrates display high theoretical energy densities, which are promising materials in TES. However, they show a number of drawbacks for use in the basic state including low temperature overhydration and deliquescence (e.g., MgCl2), high temperature degradation, sluggish kinetics leading to a low temperature rise (e.g., MgSO4), corrosiveness and toxicity (e.g., Na2S), and low mass transport due to the material macrostructure. The biggest advantage of adsorption materials is that they are more hydrothermally stable. However, since adsorption is the most common sorption phenomenon, such materials have a lower energy content. Furthermore, when compared to salt hydrates, they have higher prices per mass, which reduces their appeal even further when combined with lower energy densities. Economies of scale and the optimization of manufacturing processes may help cut costs. Among the zeolites, Zeolite 13X is among the most promising. Temperature lifts of 35–45 °C were reached in lab-scale reactors and micro-scale experiments under the device operating settings. Although the key disadvantage is an excessively high desorption temperature, which is problematic to attain using heat sources, for instance, solar thermal collectors. To increase the energy densities and enhance the stability of adsorbents, composite materials have been examined to ameliorate the stability and to achieve suitable energy densities. Based on the reviewed materials, MgSO4 has been identified as the most promising salt; it presents a higher energy density compared to other salts and can be impregnated in a porous matrix to prepare composites in order to overcome the drawbacks connected to its use as pure salt. However, due to pore volume reduction, potential deliquescence and salt leakage from the composite as well as degradation, issues with heat and mass transport can still exist. In addition, to increase the kinetics, stability, and energy density, the use of binary salt deposited in a porous matrix is suitable. Nevertheless, this solution should take into account the deliquescence, safety, and cost of the selected salts. Therefore, binary systems can be the solution to design innovative materials with predetermined sorption properties adapted to particular sorption heat storage cycles. Finally, working condition, desorption temperature, material costs, lifetime, and reparation, among others, are the essential point for commercial competitiveness. High material costs and desorption temperatures, combined with lower energy densities under normal device operating conditions, decrease their market attractiveness. As a result, the introduction of performance metrics within the scientific community and the use of economic features on a material scale are suggested.


Leaving out of consideration those nuclei of small atomic number it is possible to develop a statistical theory of nuclei. Bethe and Bacher (1936, p. 149), as well as many other writers, have treated this subject in great detail starting from the Hartree approximation. All these investigations were mainly concerned with the binding energy, and not much attention has been paid so far to the stability of nuclei according to the statistical theory, except the determination of the most stable nucleus with a given atomic number: this is due to the fact that previous investigators have always neglected to distinguish between quantum states with opposite spin, thereby losing the distinction between “odd” and “even” nuclei, which is essential for stability considerations.


Quantum 20/20 ◽  
2019 ◽  
pp. 303-322
Author(s):  
Ian R. Kenyon

It is explained how plateaux are seen in the Hall conductance of two dimensional electron gases, at cryogenic temperatures, when the magnetic field is scanned from zero to ~10T. On a Hall plateau σ‎xy = ne 2/h, where n is integral, while the longitudinal conductance vanishes. This is the integral quantum Hall effect. Free electrons in such devices are shown to occupy quantized Landau levels, analogous to classical cyclotron orbits. The stability of the IQHE is shown to be associated with a mobility gap rather than an energy gap. The analysis showing the topological origin of the IQHE is reproduced. Next the fractional QHE is described: Laughlin’s explanation in terms of an IQHE of quasiparticles is presented. In the absence of any magnetic field, the quantum spin Hall effect is observed, and described here. Time reversal invariance and Kramer pairs are seen to be underlying requirements. It’s topological origin is outlined.


Author(s):  
Max Born

The stability of lattices is discussed from the standpoint of the method of small vibrations. It is shown that it is not necessary to determine the whole vibrational spectrum, but only its long wave part. The stability conditions are nothing but the positive definiteness of the macroscopic deformation energy, and can be expressed in the form of inequalities for the elastic constants. A new method is explained for calculating these as lattice sums, and this method is applied to the three monatomic lattice types assuming central forces. In this way one obtains a simple explanation of the fact that the face-centred lattice is stable, whereas the simple lattice is always unstable and the body-centred also except for small exponents of the attractive forces. It is indicated that this method might be used for an improvement of the, at present, rather unsatisfactory theory of strength.


2013 ◽  
Vol 1492 ◽  
pp. 15-23
Author(s):  
Chih-Hsing Leu ◽  
Shu-Yuan Chuang ◽  
Kan-Lin Hsueh ◽  
Jia-Ming Huang ◽  
Chia-Chun Chung ◽  
...  

ABSTRACTThe electrode materials for VRFB should possess higher electric conductivity, corrosion resistance and hydrophilic properties in sulfuric acid. The characteristics of the electrode materials affect the stability and the energy efficiency of VRFB. Carbon materials are the best suited for VRFB applications. In this study, the calcined treatment, acid treatment and ozone treatment were used to modify the surface of carbon papers. The redox reaction of [VO]2+/[VO2]+ on the modified carbon papers was evaluated by cyclic voltammetry (CV). The surface compositions of carbon materials were analyzed by X-ray photoelectron spectrometry (XPS). The experimental results reveal that three oxidative methods enhance the redox reaction of [VO]2+/[VO2]+. The calcined treatments and acid treatments also enhanced hydrolysis reaction. The mole ratio of O/C apparently increased, but the binding energy of C1s and O1s were not chemically shifted in the acid treatment. The intensity of binding energy of O1s, between 532 eV and 534 eV, apparently increased in the ozone and calcined treatments. The Ox treated samples were more hydrophilic than the Oz treated samples. In the Ox treated samples, the decrease of Rct value indicates that was contributed from the redox reaction of [VO]2+/[VO2]+ and hydrolysis reaction. It does not completely benefit the energy efficiency of VRFB. The 5 x 5 cm2 modified carbon papers were used as electrode materials in the VRFB. The voltage efficiency, coulomb efficiency and energy efficiency reached 93 %, 90 % and 83 %, respectively, at a current density of 12 mA.cm-2 at 0.8-1.8 V.


1979 ◽  
Vol 57 (2) ◽  
pp. 136-146 ◽  
Author(s):  
S. Luryi ◽  
J. Van Kranendonk

The anisotropic displacement–displacement correlation function for the two types of pairs of nearest neighbours in solid hep hydrogen and deuterium is studied. Two mechanisms contributing to the deviation of the pair distribution function from axial symmetry around the pair axis are identified. The one is due to the anisotropy of the phonon dispersion relations and is treated in a generalized Debye model parameterized in terms of the elastic constants. The elasticity tensor is decomposed into rotationally irreducible parts, and certain new relations between the elastic constants of hep crystals with central forces are derived. The other mechanism arises from the immediate, anisotropic environment of a pair and is treated using a generalized Einstein model. The relevance of these results for the interpretation of the microwave spectrum of pairs of orthohydrogen molecules in parahydrogen is also discussed.


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