M. Kumar

High pressure equation of state for solids

Abstract A useful general equation of state based on thermodynamic analysis is proposed to investigate the properties of solids under the effect of high pressures. It is shown that the Murnaghan equation of state widely used in the literature is a particular case of the proposed equation of state. The equation of state is applied to investigate the compression behaviour of solids up to their transition pressures. The results are found to present a better agreement with the experimental data as compared with the Murnaghan equation of state of high pressures. It is concluded that the Murnaghan equation of state holds good only in the low pressure range, ∼ 40 kbar, while the equation of state proposed in the present paper is fairly applicable from atmospheric pressure up to the transition pressures of solids.

Application of high pressure equation of state for different classes of solids

Abstract The application of the high pressure equation of state recently proposed by Kumar is discussed for different classes of solids such as ionic, metallic, covalent and rare gases. The variation of the unit cell volume under the effect of pressure which presents a good agreement with the experimental data is reported. It is concluded that the Kumar equation of state is superior to those used by earlier workers viz. Murnaghan, Birch and also to the Universal equation of state. A simple and straightforward method for the determination of bulk modulus as a function of pressure is also pointed out. A good agreement between theory and experiment demonstrates the validity of the present work.

Temperature dependence of interatomic separation and bulk modulus for ionic solids

Abstract The temperature dependence of the interatomic separation and bulk modulus is investigated from room temperature up to melting temperature for sixteen ionic solids. A phenomenological relation is derived to investigate the interatomic separations as a function of temperature. The results thus obtained are used to predict values of the bulk modulus at different temperatures. The results are compared with the available experimental data and are discussed in the view of recent research in the field of high temperature physics. A good agreement between theory and experiment demonstrates the validity of the present work.

Thermal expansivity and equation of state up to transition pressure and melting temperature: NaCl as an example

Abstract The thermodynamic relation recently proposed by Kumar for thermal expansivity is used to compute the coefficient of volume thermal expansion for NaCl from atmospheric pressure upto the structural transition pressure at the temperatures ranging from room temperature upto the melting temperature. The formula requires the values of interatomic separations as a function of pressure and temperature which are evaluated from the theory of interionic potential recently developed in the field of high pressure and high temperature physics. The results obtained are in good agreement with the available experimental

Application of high pressure–high temperature equation of state for elastic properties of solids

Abstract The theory of high pressure–high temperature equation of state recently developed is used to investigate the elastic properties of solids under the effect of temperature as well as pressure. The calculated values of temperature dependence of bulk modulus of NaCl are found to present a better agreement with the experimental data as compared with earlier relation. The results obtained for second-order elastic constants are found to present a good agreement with experimental data. It is concluded that the present approach is very simple and far better compared with the theory of lattice dynamics and two-body central potential. It makes the situation very simple and straightforward as compared with earlier investigations. The results are reported for NaCl, KCl, CaF2, MgO, CaO, Mg2SiO4 and Al2O3.

Electronic polarizabilities, potential functions, and spectroscopic constants for diatomic molecules of alkali halides and alkali hydrides

The two different approaches for the evaluation of molecular state electronic polarizabilities of ions based on Seitz–Ruffa (SR) energy level analysis and Wilson–Curtis–Coker model are critically analyzed by calculating the values of dipole moments within the framework of the original Rittner and the modified T‐Rittner models. It is found that the polarizabilities based on SR energy level analysis along with the T‐Rittner model are distinctly superior. These polarizabilities are used for determining spectroscopic constants for diatomic molecules of alkali halides and alkali hydrides. Various potential functions for the overlap repulsive energy proposed so far are used to estimate the binding energy and its various order derivatives. A comparison of calculated values with the experimental data shows that the modified Varshni–Shukla potential, among seven traditional potentials, and the Narayan–Ramaseshan (NR) potential, among three ion‐dependent potentials, yield the best agreement with experimental data. ...

Author's reply on the remark of Prieto and Renero on Kumar equation of state

It is found that the comparison presented by Prieto and Renero (PR) between the theories of high-pressure equation of state due to Kumar and PR is useful for readers. But several ideas in the study of PR are not adequate. A detailed analysis is presented along with the comments on the several concepts presented by PR.

Temperature dependence of bulk modulus and equation of state for minerals

A simple method based on basic thermodynamic functions is presented to investigate the temperature dependence of bulk modulus for minerals. The method requires the values of unit cell volumes at corresponding temperatures which are investigated using the equation of state more recently proposed by Kumar. The results are reported for six minerals. Good agreement between theory and experiment demonstrates the validity of the present approach. The present work thus verifies the experimental measurements performed by Anderson and coworkers.

Relationship between solid state parameters and melting parameters for alkali halides

Abstract In the present communication we report some interesting relationships found between solid state parameters and melting parameters for alkali halides. Values of the melting temperatures and relative changes in volume after melting are found to exhibit systematic trend of variation with the Phillips ionicity parameter defining the amount of fractional ionic character. An empirical analysis is presented for determining the nearest-neighbour distances in alkali halide melts. The predictions made in the present work are shown to be consistent with available X-ray diffraction measurements.

Analysis of the Pressure Dependence of Thermal Expansivity

Various relations for the determination of thermal expansivity under the effect of pressure, used by Thomas and Shanker are discussed. The claim of earlier workers that the relations are new on the basis of their different mathematical forms is not correct. It is found that all the relations which are based on the approximation that δ T is a constant, as compiled by Thomas and Shanker, are the same well known Anderson formula given in 1967.