scholarly journals The First Principle Approach in Estimating Bulk Modulus Based on Explicit Expression of Canonical Partition Function

2020 ◽  
Vol 21 (1) ◽  
pp. 61-67
Author(s):  
H. Mangelli ◽  
M. Vafaeei ◽  
N. Mansoori Oghaz ◽  
B. Haghighi
Keyword(s):  
Partition Function ◽  
Bulk Modulus ◽  
Input Data ◽  
First Principle ◽  
Grüneisen Parameter ◽  
Canonical Partition Function ◽  
Gruneisen Parameter ◽  
Statistical Mechanical ◽  
Characteristic Features ◽  
Hexagonal Closed Packed

The bulk modulus is one of the most important characteristic features of solids. Accordingly, we have developed a statistical-mechanical treatment based on an equation which enables us to calculate the bulk modulus for solids with the minimum manifold of input data. In our model, a conjunction between Gruneisen parameter and canonical partition function has been established. We have found out that the volume dependency of Gruneisen parameter is critical in estimating bulk modulus. The result for hexagonal closed- packed (hcp) iron is very good and commensurate with the best measurements. This framework can be extended to the other elemental solids or a variety of compounds.

scholarly journals Higher order derivatives of bulk modulus of materials at infinite pressure

2016 ◽  
Vol 94 (8) ◽  
pp. 748-750 ◽  
Author(s):  
A. Dwivedi
Keyword(s):  
Bulk Modulus ◽  
Higher Order ◽  
Grüneisen Parameter ◽  
Third Order ◽  
Pressure Derivative ◽  
Basic Principles ◽  
Gruneisen Parameter ◽  
The Third ◽  
The Status ◽  
Derivatives Of

Pressure derivatives of bulk modulus of materials at infinite pressure or extreme compression have been studied using some basic principles of calculus. Expressions for higher order pressure derivatives at infinite pressure are obtained that are found to have the status of identities. A generalized formula is derived for the nth-order pressure derivative of bulk modulus in terms of the third-order Grüneisen parameter at infinite pressure.

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.

HIGHER ORDER THERMOELASTIC PROPERTIES OF THE EARTH LOWER MANTLE AND CORE

2010 ◽  
Vol 24 (09) ◽  
pp. 1187-1200 ◽  
Author(s):  
S. S. KUSHWAH ◽  
N. K. BHARDWAJ
Keyword(s):  
Bulk Modulus ◽  
Lower Mantle ◽  
Inner Core ◽  
Outer Core ◽  
Higher Order ◽  
Grüneisen Parameter ◽  
Free Volume Theory ◽  
Gruneisen Parameter ◽  
The Earth ◽  
Derivatives Of

We have used some of the most reliable high pressure equations of state (EOS) to determine the thermoelastic Grüneisen parameter and its higher order volume derivatives for the lower mantle, outer core and inner core of the Earth. The cross derivatives of bulk modulus with respect to pressure and temperature have also been obtained for the deep interior of the Earth using the results based on the modified free volume theory for the Grüneisen parameter. We have used five EOS viz. (a) modified Rydberg EOS, (b) modified Poirier–Tarantola EOS, (c) Hama–Suito EOS, (d) Stacey EOS, and (e) Kushwah EOS to determine pressure derivatives of bulk modulus. The results for thermoelastic parameters obtained in the present study show systematic variations with the increase in pressure.

Comments on the paper entitled “Pressure variation of melting temperatures of alkali halides”

2019 ◽  
Vol 33 (17) ◽  
pp. 1975001 ◽  
Author(s):  
A. Vijay
Keyword(s):  
Bulk Modulus ◽  
High Pressures ◽  
Equations Of State ◽  
Alkali Halides ◽  
Pressure Variation ◽  
Grüneisen Parameter ◽  
Gruneisen Parameter ◽  
Melting Temperatures ◽  
Melting Curves

The expressions for the pressure dependences of bulk modulus and the Grüneisen parameter used by Arafin and Singh [Int. J. Mod. Phys. B 30, 1750031 (2016)] in the Lindemann law for determining melting curves of 14 alkali halides have been found to yield no results which are consistent with the recent studies on equations of state. It is demonstrated here that Arafin–Singh’s expressions are physically not acceptable as they are shown here to give unrealistic values of bulk modulus and Grüneisen parameter for the materials at high pressures.

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