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.

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.

Grüneisen parameter of quartz, quartzite, and fluorite at high pressures

1979 ◽  
Vol 84 (B7) ◽  
pp. 3527-3531 ◽  
Author(s):  
R. Boehler ◽  
A. Skoropanov ◽  
D. O'Mara ◽  
G. C. Kennedy
Keyword(s):  
High Pressures ◽  
Grüneisen Parameter ◽  
Gruneisen Parameter

scholarly journals Volume derivatives of the Grüneisen parameter in the limit of infinite pressure

2019 ◽  
Vol 97 (1) ◽  
pp. 114-116 ◽  
Author(s):  
A. Dwivedi
Keyword(s):  
Boundary Condition ◽  
Fourth Order ◽  
Fundamental Theorem ◽  
High Pressures ◽  
Grüneisen Parameter ◽  
Third Order ◽  
Gruneisen Parameter ◽  
The Third ◽  
Properties Of Materials ◽  
Derivatives Of

Expressions have been obtained for the volume derivatives of the Grüneisen parameter, which is directly related to the thermal and elastic properties of materials at high temperatures and high pressures. The higher order Grüneisen parameters are expressed in terms of the volume derivatives, and evaluated in the limit of infinite pressure. The results, that at extreme compression the third-order Grüneisen parameter remains finite and the fourth-order Grüneisen parameter tends to zero, have been used to derive a fundamental theorem according to which the volume derivatives of the Grüneisen parameter of different orders, all become zero in the limit of infinite pressure. However, the ratios of these derivatives remain finite at extreme compression. The formula due to Al’tshuler and used by Dorogokupets and Oganov for interpolating the Grüneisen parameter at intermediate compressions has been found to satisfy the boundary condition at infinite pressure obtained in the present study.

scholarly journals Thermoelastic properties of magnesiowüstite, (Mg1−xFex)O: determination of the Anderson–Grüneisen parameter by time-of-flight neutron powder diffraction at simultaneous high pressures and temperatures

2008 ◽  
Vol 41 (5) ◽  
pp. 886-896 ◽  
Author(s):  
Ian G. Wood ◽  
Lidunka Vočadlo ◽  
David P. Dobson ◽  
G. David Price ◽  
A. D. Fortes ◽  
...  
Keyword(s):  
Equation Of State ◽  
Powder Diffraction ◽  
High Pressures ◽  
Equations Of State ◽  
Time Of Flight ◽  
Neutron Powder Diffraction ◽  
Grüneisen Parameter ◽  
Gruneisen Parameter ◽  
Measured State

The ability to perform neutron diffraction studies at simultaneous high pressures and high temperatures is a relatively recent development. The suitability of this technique for determiningP–V–Tequations of state has been investigated by measuring the lattice parameters of Mg1−xFexO (x= 0.2, 0.3, 0.4), in the rangeP < 10.3 GPa and 300 <T< 986 K, by time-of-flight neutron powder diffraction. Pressures were determined using metallic Fe as a marker and temperatures were measured by neutron absorption resonance radiography. Within the resolution of the experiment, no evidence was found for any change in the temperature derivative of the isothermal incompressibility, ∂KT/∂T, with composition. By assuming that the equation-of-state parameters either varied linearly or were invariant with composition, the 60 measured state points were fitted simultaneously to aP–V–T–xequation of state, leading to values of ∂KT/∂T= −0.024 (9) GPa K−1and of the isothermal Anderson–Grüneisen parameter δT= 4.0 (16) at 300 K. Two designs of simultaneous high-P/Tcell were employed during this study. It appears that, by virtue of its extended pressure range, a design using toroidal gaskets is more suitable for equation-of-state studies than is the system described by Le Godec, Dove, Francis, Kohn, Marshall, Pawley, Price, Redfern, Rhodes, Ross, Schofield, Schooneveld, Syfosse, Tucker & Welch [Mineral. Mag.(2001),65, 737–748].

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.

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.

Thermoelastic parameters of crystals

1984 ◽  
Vol 62 (2) ◽  
pp. 109-114 ◽  
Author(s):  
V. B. L. Mehrotra ◽  
R. M. Misra ◽  
Ram Singh ◽  
D. D. Shukla ◽  
M. N. Sharma ◽  
...  
Keyword(s):  
Experimental Data ◽  
Temperature Variation ◽  
Theoretical Estimate ◽  
Pressure Variation ◽  
Potential Functions ◽  
Ionic Crystals ◽  
Grüneisen Parameter ◽  
Gruneisen Parameter ◽  
Realistic Potential ◽  
Interaction Approach

The parameters C1 = [∂(1/KT)/∂P]T, which describes the pressure variation of the compressibility, δT, the isothermal Anderson–Grüneisen parameter, and mT = (∂ ln KT/∂T)P, which describes the temperature variation of the compressibility, have been investigated for some face-centred cubic (f.c.c.) and body-centred cubic (b.c.c.) types of ionic crystals using a central force, rigid-ion interaction approach employing fewer approximations than has been usual heretofore. A theoretical estimate of these parameters is made by using thermodynamic relationships, including the expression for the parameter q that describes the volume variation of the Grüneisen parameter, and choosing a few modified and realistic potential functions. The results compare well with the available experimental data and exhibit an essential improvement over other theoretical determinations.

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.

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