Dependence of the ratio of squares of the velocity of acoustic waves in solids on the Gruneisen parameter

2021 ◽  
pp. 32-37
Author(s):  
D.S. Sanditov ◽  
◽  
S.S. Badmaev ◽  
A.A. Mashanov ◽  
◽  
...  
Keyword(s):  
Experimental Data ◽  
Acoustic Wave ◽  
Acoustic Waves ◽  
Interatomic Bond ◽  
Grüneisen Parameter ◽  
Theoretical Dependence ◽  
Gruneisen Parameter ◽  
Normal Stiffness ◽  
Wave Velocities ◽  
The Right

It is found that in the Leont'ev and Belomestnykh-Tesleva formulas for the Grüneisen parameter, the right-hand sides of the equalities depend on anharmonicity through the dependence of the ratio of the squared acoustic wave velocities ( v L2 / v S2) on the Grüneisen parameter γ. The theoretical dependence of ( v L2 / v S2) on γ generally agrees with experimental data for both crystals and glassy solids. The quantity ( v L2 / v S2) turns out to be a single-valued function of the ratio of the tangential and normal stiffness of the interatomic bond.

scholarly journals Упругие свойства и ангармонизм твердых тел

2022 ◽  
Vol 64 (2) ◽  
pp. 241
Author(s):  
Д.С. Сандитов
Keyword(s):  
Acoustic Waves ◽  
Lattice Vibration ◽  
Interatomic Bond ◽  
Vibration Modes ◽  
Grüneisen Parameter ◽  
Gruneisen Parameter ◽  
Normal Lattice ◽  
Transverse Acoustic ◽  
Definition Of ◽  
The Relationship

The squares of the velocities of the longitudinal and transverse acoustic waves separately are practically not associated with anharmonicity, and their ratio (vL2 / vS2) turns out to be a linear function of the Grüneisen parameter γ - the measure of anharmonicity. The obtained dependence of (vL2 / vS2) on γ is in satisfactory agreement with the experimental data. The relationship between the quantity (vL2 / vS2) and anharmonicity is explained through its dependence on the ratio of the tangential and normal stiffness of the interatomic bond λ, which is a single-valued function of the Grüneisen parameter λ (γ). The relationship between Poisson's ratio μ and Grüneisen parameter γ, established by Belomestnykh and Tesleva, can be substantiated within the framework of Pineda's theory. Attention is drawn to the nature of the Leont'ev formula, derived directly from the definition of the Grüneisen parameter by averaging the frequency of normal lattice vibration modes. The connection between Grüneisen, Leontiev and Belomestnykh-Tesleva relations is considered. The possibility of a correlation between the harmonic and anharmonic characteristics of solids is discussed.

The mathematical modeling for bulk acoustic wave propagation velocities in transversely isotropic piezoelectric materials

2015 ◽  
Vol 22 (4) ◽  
pp. 823-836 ◽  
Author(s):  
Abo-el-nour N Abd-alladan ◽  
Abdelmonam M Hamdan ◽  
Adel A Almarashi ◽  
Antonio Battista
Keyword(s):  
Acoustic Wave ◽  
Acoustic Waves ◽  
Piezoelectric Effect ◽  
Piezoelectric Materials ◽  
Transversely Isotropic ◽  
Bulk Acoustic Wave ◽  
Acoustic Wave Propagation ◽  
Wave Velocities ◽  
Saw Devices ◽  
Propagation Velocities

The objective of this paper is to study the bulk acoustic wave (BAW) propagation velocities in transversely isotropic piezoelectric materials, aluminum nitride, zinc oxide, cadmium sulfide and cadmium selenide. The bulk acoustic wave velocities are computed for each direction by solving the Christoffel’s equation based on the theory of acoustic waves in anisotropic solids exhibiting piezoelectricity. These values are calculated numerically and implemented on a computer by Bisection Method Iterations Technique (BMIT). The modification of the bulk acoustic wave velocities caused by the piezoelectric effect are graphically compared with the velocities in the corresponding non-piezoelectric materials. The results obtained in this study can be applied to signal processing, sound systems and wireless communication in addition to the improvement of surface acoustic wave (SAW) devices and military defense equipment.

MELTING BEHAVIOR AND THE GRÜNEISEN PARAMETER OF NaCl AT HIGH PRESSURE: A MOLECULAR DYNAMICAL STUDY

2010 ◽  
Vol 24 (03) ◽  
pp. 331-341
Author(s):  
SHOUXIN CUI ◽  
LINGCANG CAI ◽  
HAIQUAN HU ◽  
ZIZHENG GONG ◽  
JIJUN ZHAO
Keyword(s):  
Experimental Data ◽  
Molecular Dynamics ◽  
Pressure Range ◽  
Melting Curve ◽  
Pair Potential ◽  
Melting Behavior ◽  
Grüneisen Parameter ◽  
Dynamical Study ◽  
Gruneisen Parameter ◽  
Approximate Power

The improved Tosi–Fumi pair potential has been employed to simulate the melting behavior and Grüneisen parameters of sodium chloride ( NaCl ) using molecular dynamics (MD) method at constant volume. The melting curve of NaCl is compared with the experimental data and other calculations in a pressure range from 0 to 144 GPa. The simulated results validate the amount of 20% superheating of the NaCl solid and yield an approximate power law dependence of the Grüneisen parameter (γ) on compression γ = γ0(V/V0)q, with q ≈ 1.078, in the temperature range from 298 to 1073 K and pressure range from 0 to 60 GPa.

A Study and Comparison of Calculating Grüneisen Parameter Using Different Methods

2010 ◽  
Vol 146-147 ◽  
pp. 1102-1107
Author(s):  
Ting Zhang ◽  
Meng Qiang Wu ◽  
Ming He ◽  
Jie Xiong ◽  
Song Chen
Keyword(s):  
Experimental Data ◽  
High Pressures ◽  
Measured Data ◽  
Grüneisen Parameter ◽  
Gruneisen Parameter

Some attempts for getting Grüneisen parameter are discussed. After comparing, the Grüneisen parameter got from Grüneisen EOS and Vinet EOS is consistent with the experimental data. However, we are not sure which method can describe the behavior of the Grüneisen parameter good under high pressures, because of the lack of directly measured data for Grüneisen parameter under high pressures. So, the technology for directly measuring Grüneisen parameter should be developed for clarifying this problem by experiments.

Grüneisen parameter and propagation velocities of acoustic waves in vitreous solids

2012 ◽  
Vol 54 (8) ◽  
pp. 1643-1647 ◽  
Author(s):  
D. S. Sanditov ◽  
S. B. Munkueva ◽  
D. Z. Batlaev ◽  
S. Sh. Sangadiev
Keyword(s):  
Acoustic Waves ◽  
Grüneisen Parameter ◽  
Gruneisen Parameter ◽  
Propagation Velocities

Pressure dependence of the Grüneisen parameter and melting temperature of some metals

2021 ◽  
pp. 2150255
Author(s):  
K. Sunil ◽  
D. Ashwini ◽  
Vijay S. Sharma
Keyword(s):  
Experimental Data ◽  
Molecular Dynamics ◽  
Equation Of State ◽  
Pressure Dependence ◽  
High Pressures ◽  
Grüneisen Parameter ◽  
Thermal Equation ◽  
Gruneisen Parameter ◽  
Melting Temperatures ◽  
Volume Dependence

We have used a method for determining volume dependence of the Grüneisen parameter in the Lindemann law to study the pressure dependence of melting temperatures in case of 10 metals viz. Cu, Mg, Pb, Al, In, Cd, Zn, Au, Ag and Mn. The reciprocal gamma relationship has been used to estimate the values of Grüneisen parameters at different volumes. The results for melting temperatures of metals at high pressures obtained in this study using the Lindemann law of melting are compared with the available experimental data and also with the values calculated from the instability model based on a thermal equation of state. The analytical model used in this study is much simpler than the accurate DFT calculations and molecular dynamics.

Analysis of melting curves of MgO and LiF using the Lindemann law

2018 ◽  
Vol 32 (30) ◽  
pp. 1850339 ◽  
Author(s):  
K. Sunil ◽  
S. B. Sharma ◽  
B. S. Sharma
Keyword(s):  
Experimental Data ◽  
Equation Of State ◽  
Finite Difference ◽  
Bulk Modulus ◽  
Melting Temperature ◽  
Pressure Dependence ◽  
Grüneisen Parameter ◽  
Gruneisen Parameter ◽  
Melting Temperatures ◽  
Volume Dependence

We have determined the melting slopes as a function of pressure for MgO up to a pressure of 135 GPa, and for LiF up to a pressure of 100 GPa using the Lindemann law. Values of melting temperature have also been calculated from the melting slopes using Euler’s finite difference calculus method. It is found that the melting slope decreases continuously with the increase in pressure giving a nonlinear pressure dependence of the melting temperature. Values of bulk modulus and the Grüneisen parameter appearing in the Lindemann law of melting have been determined using the Stacey reciprocal K-primed equation of state and the Shanker reciprocal gamma relationship. The results for melting temperatures of MgO and LiF at different pressures are compared with the available experimental data. Values of melting temperatures at different pressures determined from the Al’tshuler relationship for the volume dependence of the Grüneisen parameter have also been included in the comparison presented.

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