Thermal and Elastic Properties of Solids and Geophysical Minerals at Elevated Temperatures and Pressures

Abstract

The present work deals with the thermal and elastic properties of solids and geophysical minerals at elevated temperatures and high pressures. The equation of state (EoS) for lower mantle and core regions of the Earth has also been discussed. The entire work has been divided into six chapters. Chapter 1 gives the introduction of the subject and information about the different models given by various researchers to study the thermal and elastic properties of the solids and geophysical minerals and review of the literature available. Also the background of the study is discussed. This chapter also focuses on the various terms involved in the study and their usefulness to study the behavior of solids at high temperatures and pressures. In the last section of this chapter, reason for selecting main objectives, methodology and the purpose of the present study is discussed which helps future researchers to carry out further research in the field of high temperatures and high pressures. Chapter 2 explains different theories of volume/pressure dependence of thermal expansivity. The Grüneisen theory represents the experimental data on thermal expansivity at atmospheric pressure to represent the temperature dependent thermal expansivity. Also, the Suzuki theory of thermal expansivity is discussed which yields good results with experimental data on thermal expansivity to wide temperature range for various geophysical minerals. In this section, Born and Huang method of thermal expansivity has also been described which is physically more fundamental and mathematically more convenient and is useful to predict the temperature dependence of volume of any crystal. In the last section of this chapter, a brief introduction about anharmonicity in thermal and elastic properties of solids is provided. Chapter 3 describes the details of two important dimensionless thermoelastic parameters i.e. isothermal and adiabatic Anderson-Grüneisen parameter which are having important role to study the thermal and elastic behavior of solids at high temperatures and high pressures and also the Grüneisen parameter- a very important thermodynamic quantity used to investigate the relationship between thermal and elastic properties of solids. The volume dependence of Grüneisen parameter and its higher order volume derivatives is also discussed following the expression based on thermodynamical constraints in the limit of infinite pressure. Chapter 4 deals with different forms of equations of state (EoS) for studying the high pressure behavior of solids using interatomic potentials which represents the relationship between pressure and volume. Keane equation of state is described which suggest that first pressure derivative of isothermal bulk modulus is a monotonically decreasing function with pressure and reaching a limiting value at infinite pressure. Keane EoS is useful for interpolation between shock wave data and lower pressure P-V data. In the last section of this chapter, more numerically simplified EoS given by Stacey has been described which follows the infinite pressure thermodynamics more accurately. xiii Chapter 5 describes the various models developed in the present study and their formulations, results and discussions. An inter-relationship between the Anderson-Grüneisen parameter and thermal expansivity under adiabatic and isothermal compression has been developed for insulator materials. Further, a new empirical expression has been proposed to predict the values of volume dependence of Grüneisen parameter using two different models and higher order volume derivatives of Grüneisen parameter has also been discussed. In this chapter we have also analyzed the number of thermodynamic properties in the limit of infinite pressure. A reciprocal form model for the volume dependence of thermal expansivity has also been provided for different solids and geophysical minerals. In the last section of this chapter, a new K -prime equation of state (EoS) has been presented in the form of volume dependence of isothermal bulk modulus and its higher order pressure derivatives for lower mantle and core regions of the Earth. The temperature dependence of volume expansion ratio and its second order temperature derivative for NaCl and KCl has been proposed. Chapter 6 summarizes and concludes the results of the study on thermal and elastic properties of solids and geophysical minerals at high temperature and high pressure conditions. Relationship between Anderson-Grüneisen parameter and thermal expansivity show validation for lower mantle (an insulator) and for NaCl with experimental data reported in literature. NaCl and  -Fe have been taken to check the reliability of the volume dependence of Grüneisen parameter model which gives a reasonably good agreement between calculated values and the values derived from experimental data on thermoelastic properties. Results of higher order volume derivatives of Grüneisen ratio is found consistent with Stacey and Davis relationship but the trend of third Grüneisen ratio has not been found satisfactory for NaCl and MgO. The results obtained for the analysis of thermodynamic properties in the infinite pressure limits are found consistent with the recent analysis of infinite pressure of thermoelastic properties and also based on the Stacey thermodynamics of solids at infinite pressure. Reciprocal form for volume dependence of thermal expansivity shows consistency with experimental data for NaCl and satisfies the thermodynamic constraints at infinite pressure on which it has been formulated. The newly developed EoS is found compatible to the Stacey K -prime EoS throughout the compression used. The better results for temperature dependence of volume expansion ratio and its higher order temperature derivative with the values obtained from basic thermodynamic relation exposes the validity of the expression. All the proposed models show close or better agreement with the experimental results and present a suitable model for further study to investigate the thermal and elastic properties of interior of the Earth.