The Stability of Crystal Lattices

1941 ◽  
Vol 37 (1) ◽  
pp. 34-54 ◽  
Author(s):  
R. Fürth
Keyword(s):  
Melting Temperature ◽  
Elastic Constants ◽  
Crystal Lattices ◽  
Short Survey ◽  
The Stability ◽  
Good Agreement

A short survey of Born's theory of the thermodynamics and melting of crystals is given. It is shown that Lindemann's and Grüneisen's law for the normal melting temperature can be deduced from this theory, and that the dependence of the melting temperature on pressure, and of the compressibility and the elastic constants on pressure and temperature, as predicted by the theory, are in good agreement with experiment. Several connexions between breaking and melting, suggested by the fundamental ideas on melting and stability of crystals, are discussed and verified. Finally a relation between the heat of melting and the heat of sublimation is deduced and compared with experiment.

On the stability of crystal lattices IX. Covariant theory of lattice deformations and the stability of some hexagonal lattices

1942 ◽  
Vol 38 (1) ◽  
pp. 82-99 ◽  
Author(s):  
M. Born
Keyword(s):  
Elastic Constants ◽  
Hexagonal Lattice ◽  
Covariant Theory ◽  
Tensor Calculus ◽  
Crystal Lattices ◽  
New Form ◽  
The Stability ◽  
Central Forces

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.

The thermodynamics of crystal lattices

1943 ◽  
Vol 39 (2) ◽  
pp. 100-103 ◽  
Author(s):  
Max Born
Keyword(s):  
Melting Point ◽  
Crystal Lattice ◽  
Temperature Dependence ◽  
Elastic Constants ◽  
Original Problem ◽  
Lattice Stability ◽  
Chemical Physics ◽  
Crystal Lattices ◽  
Fundamental Difficulty ◽  
The Stability

In 1939 I published a paper in the American Journal of Chemical Physics (Born(1)) in which I tried to develop the thermodynamics of a crystal lattice in the domain of classical (Boltzmann) statistics. Definite formulae and numerical tables for the temperature dependence of the elastic constants up to the melting point were obtained; nevertheless the work was unsatisfactory not only because the approximations used were rough and their accuracy not known, but because a fundamental difficulty with respect to lattice stability turned up. This led to a series of investigations by my collaborators and myself, published in these Proceedings under the title ‘On the stability of crystal lattices’ (quoted here as S I to SIX), by which the difficulty mentioned has been removed. It is now possible to return to the original problem, to which the present series of papers is devoted. In this introduction I wish to recapitulate the whole situation and to explain the plan of the following papers which will be published by my collaborators.

Pressure dependent ultrasonic properties of hcp hafnium metal

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Ramanshu P. Singh ◽  
Shakti Yadav ◽  
Giridhar Mishra ◽  
Devraj Singh
Keyword(s):  
Elastic Constants ◽  
Pressure Range ◽  
Room Temperature ◽  
Ultrasonic Attenuation ◽  
Coupling Constants ◽  
Ultrasonic Properties ◽  
Acoustic Coupling ◽  
Third Order Elastic Constants ◽  
The Stability ◽  
The Given

Abstract The elastic and ultrasonic properties have been evaluated at room temperature between the pressure 0.6 and 10.4 GPa for hexagonal closed packed (hcp) hafnium (Hf) metal. The Lennard-Jones potential model has been used to compute the second and third order elastic constants for Hf. The elastic constants have been utilized to calculate the mechanical constants such as Young’s modulus, bulk modulus, shear modulus, Poisson’s ratio, and Zener anisotropy factor for finding the stability and durability of hcp hafnium metal within the chosen pressure range. The second order elastic constants were also used to compute the ultrasonic velocities along unique axis at different angles for the given pressure range. Further thermophysical properties such as specific heat per unit volume and energy density have been estimated at different pressures. Additionally, ultrasonic Grüneisen parameters and acoustic coupling constants have been found out at room temperature. Finally, the ultrasonic attenuation due to phonon–phonon interaction and thermoelastic mechanisms has been investigated for the chosen hafnium metal. The obtained results have been discussed in correlation with available findings for similar types of hcp metals.

OPTIMAL VELOCITY MODEL WITH RELATIVE VELOCITY

2006 ◽  
Vol 17 (01) ◽  
pp. 65-73 ◽  
Author(s):  
SHIRO SAWADA
Keyword(s):  
Nonlinear Analysis ◽  
Relative Velocity ◽  
Velocity Model ◽  
Fundamental Diagram ◽  
Optimal Velocity ◽  
Traffic Jam ◽  
Optimal Velocity Model ◽  
Linear And Nonlinear ◽  
The Stability ◽  
Good Agreement

The optimal velocity model which depends not only on the headway but also on the relative velocity is analyzed in detail. We investigate the effect of considering the relative velocity based on the linear and nonlinear analysis of the model. The linear stability analysis shows that the improvement in the stability of the traffic flow is obtained by taking into account the relative velocity. From the nonlinear analysis, the relative velocity dependence of the propagating kink solution for traffic jam is obtained. The relation between the headway and the velocity and the fundamental diagram are examined by numerical simulation. We find that the results by the linear and nonlinear analysis of the model are in good agreement with the numerical results.

Global Stability Analysis of the Wake behind a Circular Cylinder Based on the POD-Chiba Method

2011 ◽  
Vol 137 ◽  
pp. 72-76
Author(s):  
Wei Zhang ◽  
Xian Wen ◽  
Yan Qun Jiang
Keyword(s):  
Stability Analysis ◽  
Circular Cylinder ◽  
Global Stability ◽  
Dimensional Model ◽  
Global Stability Analysis ◽  
The Stability ◽  
Low Dimensional ◽  
Proper Orthogonal ◽  
Calculated Amount ◽  
Good Agreement

A proper orthogonal decomposition (POD) method is applied to study the global stability analysis for flow past a stationary circular cylinder. The flow database at Re=100 is obtained by CFD software, i.e. FLUENT, with which POD bases are constructed by a snapshot method. Based on the POD bases, a low-dimensional model is established for solving the two-dimensional incompressible NS equations. The stability of the flow solution is evaluated by a POD-Chiba method in the way of the eigensystem analysis for the velocity disturbance. The linear stability analysis shows that the first Hopf bifurcation takes place at Re=46.9, which is in good agreement with available results by other high-order accurate stability analysis methods. However, the calculated amount of POD is little, which shows the availability and advantage of the POD method.

Experimental and Theoretical Investigation of the Supersonic Boundary Layer Stability on the Swept Wing

2008 ◽  
Vol 3 (3) ◽  
pp. 34-38
Author(s):  
Sergey A. Gaponov ◽  
Yuri G. Yermolaev ◽  
Aleksandr D. Kosinov ◽  
Nikolay V. Semionov ◽  
Boris V. Smorodsky
Keyword(s):  
Boundary Layer ◽  
Three Dimensional ◽  
Leading Edge ◽  
Supersonic Boundary Layer ◽  
Mean Flow ◽  
Swept Wing ◽  
Wing Model ◽  
Dimensional Boundary ◽  
The Stability ◽  
Good Agreement

Theoretical and an experimental research results of the disturbances development in a swept wing boundary layer are presented at Mach number М = 2. In experiments development of natural and small amplitude controllable disturbances downstream was studied. Experiments were carried out on a swept wing model with a lenticular profile at a zero attack angle. The swept angle of a leading edge was 40°. Wave parameters of moving disturbances were determined. In frames of the linear theory and an approach of the local self-similar mean flow the stability of a compressible three-dimensional boundary layer is studied. Good agreement of the theory with experimental results for transversal scales of unstable vertices of the secondary flow was obtained. However the calculated amplification rates differ from measured values considerably. This disagreement is explained by the nonlinear processes observed in experiment

Stability and collapse of holes in liquid layers

2018 ◽  
Vol 855 ◽  
pp. 1130-1155 ◽  
Author(s):  
Cunjing Lv ◽  
Michael Eigenbrod ◽  
Steffen Hardt
Keyword(s):  
Liquid Film ◽  
Power Laws ◽  
Theoretical Models ◽  
Liquid Volume ◽  
Capillary Length ◽  
Minimum Thickness ◽  
The Stability ◽  
Film Profile ◽  
Hole Closure ◽  
Good Agreement

We investigate experimentally and theoretically the stability and collapse of holes in liquid layers on bounded substrates with various wettabilities. It is shown that for a liquid layer with a thickness of the order of the capillary length, a stable hole exists when the hole diameter is bigger than a critical value $d_{c}$. Consequently, a further increase of the liquid volume causes the hole to collapse. It is found that$d_{c}$increases with the size of the container, but its dependence on the contact angle is very weak. The experimental results are compared with theory, and good agreement is obtained. Moreover, we present investigations of the dynamics of the hole and the evolution of the liquid film profile after the collapse. The diameter of the hole during collapse and the minimum thickness of the liquid film shortly after the collapse obey different power laws with time. Simple theoretical models are developed which indicate that the collapse of the hole is triggered by surface tension and the subsequent closure process results from inertia, whereas the growth of the liquid column after hole closure results from the balance between the capillary force and inertia. Corresponding scaling coefficients are determined.

Physical properties of chalcopyrite-type Cu1−xAgxGaTe2 by first-principles study

2016 ◽  
Vol 30 (30) ◽  
pp. 1650373 ◽  
Author(s):  
Li Xue ◽  
Yi-Ming Ren ◽  
Zheng-Long Hu
Keyword(s):  
Thermal Conductivity ◽  
Elastic Constants ◽  
Density Functional ◽  
Lattice Thermal Conductivity ◽  
Lattice Parameter ◽  
Functional Theory ◽  
Lattice Volume ◽  
Te Material ◽  
Ag Substitution ◽  
Good Agreement

[Formula: see text] is a promising thermoelectric (TE) material for high temperature TE applications. This work systematically investigated the structural, elastic and thermodynamic properties of [Formula: see text] ([Formula: see text] = 0, 0.25, 0.5, 0.75 and 1) by density functional theory. The calculated lattice volume is expanded with the increase of Ag content, but this expansion is anisotropic. The lattice parameter along [Formula: see text]-axis is linear expansion, and along [Formula: see text]-axis is parabolic expansion, which is in good agreement with available experimental data. The phase stability of [Formula: see text] alloy is studied by analyzing the formation energy, cohesive energy and elastic constants. Shear modulus, Young’s modulus, sound velocities, Debye temperature and the minimum thermal conductivity are obtained from the calculated elastic constants. The results show that Ag substitution could reduce the lattice thermal conductivity, which is helpful for improving the TE properties of [Formula: see text].

Stability of Water-Lubricated, Hydrostatic, Conical Bearings With Spiral Grooves for High-Speed Spindles

2001 ◽  
Vol 124 (2) ◽  
pp. 398-405 ◽  
Author(s):  
S. Yoshimoto ◽  
S. Oshima ◽  
S. Danbara ◽  
T. Shitara
Keyword(s):  
High Speed ◽  
Water Pressure ◽  
Rotating Shaft ◽  
Pressurized Water ◽  
High Speeds ◽  
Theoretical Predictions ◽  
The Stability ◽  
Stability Of Water ◽  
Spiral Grooves ◽  
Good Agreement

In this paper, the stability of water-lubricated, hydrostatic, conical bearings with spiral grooves for high-speed spindles is investigated theoretically and experimentally. In these bearing types, pressurized water is first fed to the inside of the rotating shaft and then introduced into spiral grooves through feeding holes located at one end of each spiral groove. Therefore, water pressure is increased due to the effect of the centrifugal force at the outlets of the feeding holes, which results from shaft rotation. In addition, water pressure is also increased by the viscous pumping effect of the spiral grooves. The stability of the proposed bearing is theoretically predicted using the perturbation method, and calculated results are compared with experimental results. It was consequently found that the proposed bearing is very stable at high speeds and theoretical predictions show good agreement with experimental data.

scholarly journals Solid-State and Theoretical Investigations of Some Banister-Type Macrocycles with 2,2’-Aldoxime-1,1’-Biphenyl Units

2021 ◽  
Vol 9 ◽  
Author(s):  
Ioan Stroia ◽  
Ionuţ -Tudor Moraru ◽  
Maria Miclăuş ◽  
Ion Grosu ◽  
Claudia Lar ◽  
...  
Keyword(s):  
Crystal Structure ◽  
Solid State ◽  
Density Functional ◽  
Alkali Metal Ions ◽  
Functional Theory ◽  
State Data ◽  
Supramolecular Associations ◽  
Theoretical Investigations ◽  
The Stability ◽  
Good Agreement

In the context of helical chirality, bridging of biphenyl units leads to banister-type compounds and the stability of the resulted atropisomers may increase dramatically if suitable changes are performed in the linker unit that coils around the biphenyl moiety. A rigorous density functional theory (DFT) study was conducted for macrocycles containing rigid oxime ether segments connected to the biphenyl backbone in order to determine how the rotation barriers are influenced by the presence of either a flexible oligoethyleneoxide or a more rigid m–xylylene component in the macrocycle. The calculated values for the racemization barrier were in good agreement with those obtained experimentally and confirm the benefit of introducing a more rigid unit in the macrocycle on the stability of atropisomers. Solid-state data were obtained and computed data were used to assess the contribution brought by supramolecular associations observed in the lattice to the stabilization of the crystal structure. Beside introducing rigidity in the linker, complexation of flexible macrocycles with alkali metal ions is also contributing to the stability of atropisomers, leading to values for the racemization barrier matching that of the rigid macrocycle. Using diethylammonium cation as guest for the macrocycle, a spectacular increase in the barrier to rotation was observed for the resulted pseudo[2]rotaxane.

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