Reply [to “Discussion of paper by O. L. Anderson, ‘Elastic constants of the Central Force Model for three cubic structures: Pressure derivatives and equations of state’”]

A theory is developed which correlates the thermal expansion of crystals to the anharmonicity introduced into Born's lattice dynamics by allowing the force constants of the crystal to vary with volume. This is achieved by identifying the force constants with the elastic constants of the crystal by the method of long waves. It is then assumed that it is primarily the volume dependence of the elastic constants that give rise to their temperature variation. A central force nearest and next-nearest neighbor force model analogous to Leighton's is applied to copper. The values of the lattice thermal expansion coefficient and of Grüneisen's parameter are given as a function of the temperature and found to agree quite well with the latest experimental results. It is pointed out that the description of the interionic potential in metals by a two-body central force is certainly a serious oversimplification and that the theory is likely to be more realistic for, say, the ideal inert solid gases, as soon as the experimental data becomes available.

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Elastic constants of solids and fluids with initial pressure via a unified approach based on equations-of-state

Ultrasonics ◽

10.1016/j.ultras.2014.01.012 ◽

2014 ◽

Vol 54 (5) ◽

pp. 1323-1331 ◽

Cited By ~ 3

Author(s):

John H. Cantrell

Keyword(s):

Elastic Constants ◽

Equations Of State ◽

Initial Pressure ◽

Unified Approach

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FIRST-PRINCIPLES HIGH-PRESSURE ELASTIC AND THERMODYNAMIC PROPERTIES OF TANTALUM

International Journal of Modern Physics B ◽

10.1142/s0217979211058572 ◽

2011 ◽

Vol 25 (10) ◽

pp. 1393-1407 ◽

Cited By ~ 6

Author(s):

JING-HE WU ◽

XIAN-LIN ZHAO ◽

YOU-LIN SONG ◽

GUO-DONG WU

Keyword(s):

Thermodynamic Properties ◽

Elastic Constants ◽

First Principles ◽

Equations Of State ◽

Debye Model ◽

Thermal Expansivity ◽

Orbital Method ◽

Full Potential ◽

Body Centered Cubic ◽

Theoretical Results

The all-electron full-potential linearized muffin-tin orbital method, by means of quasi-harmonic Debye model, is applied to investigate the elastic constant and thermodynamic properties of body-centered-cubic tantalum (bcc Ta). The calculated elastic constants of bcc Ta at 0 K is consistent with the previous experimental and theoretical results. Our calculations give the correct trends for the pressure dependence of elastic constants. By using the convenient quasi-harmonic Debye model, we refined the thermal equations of state. The thermal expansivity and some other thermal properties agree well with the previous experimental and theoretical results.

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The Dependence of the Internal Vibrational Frequencies of Liquid Water on Central Force Potentials

Zeitschrift für Naturforschung A ◽

10.1515/zna-1983-0218 ◽

1983 ◽

Vol 38 (2) ◽

pp. 206-213 ◽

Cited By ~ 32

Author(s):

G. Jancsó ◽

P. Bopp

Keyword(s):

Molecular Dynamics ◽

Liquid Phase ◽

Liquid Water ◽

Md Simulations ◽

Vibrational Frequencies ◽

Central Force ◽

Intramolecular Interactions ◽

Force Model ◽

Harmonic Force ◽

Anharmonic Force

Abstract The differences in the liquid phase internal vibrational frequencies of water, obtained from molecular dynamics (MD) simulations, between the two versions of the central force model of Rahman and Stillinger (CF1 and CF2) are investigated by employing the theory of Buckingham on solvent effects. It is found that the differences can be essentially accounted for by the different O-H stretching cubic anharmonic force constants of CF1 and CF2. A significantly improved agreement between the results of MD simulations and spectroscopically observed liuqid phase frequencies could be achieved by using a harmonic force field, supplemented by a cubic stretching force constant, for the intramolecular interactions of water, and the CF2 potential for the intermolecular interactions.

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