LXXXI.Note on Dr. Wheeler's discussion of the Madelung constants for some cubic crystal lattices

1932 ◽  
Vol 14 (93) ◽  
pp. 745-746 ◽  
Author(s):  
J. Sherman
Keyword(s):  
Crystal Lattices ◽  
Cubic Crystal

The thermodynamics of crystal lattices

1943 ◽  
Vol 39 (2) ◽  
pp. 104-113 ◽  
Author(s):  
Max Born ◽  
Mary Bradburn
Keyword(s):  
Thermodynamic Properties ◽  
General Type ◽  
Crystal Lattices ◽  
Cubic Crystal ◽  
Lattice Sums ◽  
Lattice Sum ◽  
The Stability ◽  
The Waves

In previous papers by Misra(1) and by Born and Misra(2) lattice sums of the type required in discussing the stability of a cubic crystal of the Bravais type in which the forces are central have been calculated. In the investigation of the thermodynamic properties of crystals a more general type of lattice sum occurs, which involves the phases of the waves. In the present paper a method of calculating these sums is developed and tables are computed.

scholarly journals On the equation of state for solids

1944 ◽  
Vol 183 (992) ◽  
pp. 87-110 ◽  
Keyword(s):  
High Pressure ◽  
Thermal Expansion ◽  
Melting Point ◽  
Equation Of State ◽  
Potential Energy ◽  
Mechanical Instability ◽  
Crystal Lattices ◽  
Cubic Crystal ◽  
Sublimation Energy ◽  
Very High

The problem of the thermodynamics of crystal lattices has been treated by rigorous methods recently in a series of papers by Born and collaborators. In particular, Bradburn succeeded in deriving the equation of state for a solid cubic crystal, consisting of identical atoms, under the assumption that the mutual potential energy of a pair of atoms satisfies a law of the form ɸ = — ar -m + br -n . In the present paper a method is developed which makes it possible to determine the exponents m and n in the force law for a given element from measurements of the sublimation energy, the compressibility, the thermal expansion coefficient, and the dependence of these quantities on pressure and temperature. The method is applied to a large number of elements, and it is shown that the compression and the thermal expansion of these substances, as predicted by the theory, are in satisfactory agreement with the measured values of these quantities up to very high pressure and up to temperatures near the melting-point. The question whether melting is caused by the mechanical instability of the lattice is also investigated, and a certain rule connecting the two phenomena is found which is closely related to Lindemann’s law.

Traveling waves of the solidification and melting of cubic crystal lattices

2020 ◽  
Vol 102 (6) ◽  
Author(s):  
V. Ankudinov ◽  
K. R. Elder ◽  
P. K. Galenko
Keyword(s):  
Traveling Waves ◽  
Crystal Lattices ◽  
Cubic Crystal

Molecular dynamics modeling and simulation of lubricant between sliding solids

2017 ◽  
Vol 02 (02) ◽  
pp. 1750009 ◽  
Author(s):  
Mir Ali Ghaffari ◽  
Yan Zhang ◽  
Shaoping Xiao
Keyword(s):  
Modeling And Simulation ◽  
Hydrodynamic Lubrication ◽  
Molecular Model ◽  
Embedded Atom Method ◽  
Dynamics Modeling ◽  
Crystal Lattices ◽  
Jones Potential ◽  
Cubic Crystal ◽  
Embedded Atom ◽  
Molecular Dynamics Modeling

This paper presents molecular dynamic modeling and simulation of lubricant between sliding solids. Linear [Formula: see text]-alkanes with united atoms were used to model lubricant while iron sliding solids were modeled with body-centered cubic crystal lattices. We employed various potential functions, including the embedded atom method, the multibody force field and the Lennard–Jones potential, to approximate the interatomic interactions in the molecular model. Hydrodynamic lubrication was considered in this paper. We found that the temperature and the chain length of alkanes had effects on the friction between lubricated sliding solids. In addition, one debris, modeled as a nanoparticle, was added in the lubricant to study its effect on the friction. It was observed that nanoparticles would increase the friction in hydrodynamic lubrication.

scholarly journals Морфология и структурное состояние частиц нанопорошков, полученных измельчением природного алмаза и методом детонационного синтеза

2020 ◽  
Vol 46 (3) ◽  
pp. 46
Author(s):  
П.П. Шарин ◽  
А.В. Сивцева ◽  
В.И. Попов
Keyword(s):  
High Resolution ◽  
Detonation Synthesis ◽  
Complex Structures ◽  
Interatomic Distances ◽  
Crystal Lattices ◽  
Cubic Crystal ◽  
Noticeable Increase ◽  
Diamond Crystals ◽  
Primary Particles ◽  
Large Diamond

A complex of high-resolution methods has revealed that the nanopowder particles obtained by milling natural diamonds have a wider variety of sizes and predominantly of lamellar shape in contrast to detonation synthesis nanopowder, which consists mainly of similar-sized and isometric particles. The primary particles of the nanopowder obtained by milling, as well as detonation synthesis nanodiamonds, consist of diamond nuclei with cubic crystal lattices surrounded by shells with complex structures, which are formed from carbon atoms in the sp2-state and impurities. A noticeable increase in interatomic distances in nanodispersed diamond crystals has been established compared with those for large diamond crystals.

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