Comparative Analysis of Grüneisen Parameters for Selected Geophysical Minerals Using Advanced Equations of State

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ABSTRACT

The Grüneisen parameter (γ) is a critical dimensionless quantity that provides insights into the thermal and elastic properties of geophysical minerals under high-pressure conditions. In this study, we investigate the Grüneisen parameter for three key geophysical minerals—MgO, Al₂O₃, and Mg₂SiO₄—using three advanced equations of state (EOS): Vinet-Rydberg, modified Lennard-Jones (mL-Jones), and Brennan-Stacey. The study employs Stacey’s formulation to calculate γ, offering a comprehensive evaluation of the parameter across varying compression ratios (V/V₀). The results reveal a consistent decrease in the Grüneisen parameter as the compression ratio declines from 1 to 0.9 for all three minerals. Among the EOS models, the modified Lennard-Jones equation consistently shows the least sensitivity to compression, followed by the Vinet-Rydberg equation, while the Brennan-Stacey equation exhibits the highest sensitivity. For MgO, the Grüneisen parameter decreases from 1.125 to 1.01245, 1.11012, and 0.98935 for Vinet-Rydberg, mL-Jones, and Brennan-Stacey EOS, respectively. Similar trends are observed for Al₂O₃ and Mg₂SiO₄, with notable differences in sensitivity between the EOS models. These findings underscore the importance of selecting the appropriate EOS model when studying thermodynamic properties, as the sensitivity of γ to compression can significantly influence theoretical predictions. The results also highlight the utility of the Grüneisen parameter in modeling geophysical phenomena, including mantle convection, seismic wave propagation, and phase transitions within Earth’s interior. This study contributes to a deeper understanding of the thermoelastic behavior of geophysical minerals under extreme conditions.

Significance of the Study:

This study provides a comparative analysis of the Grüneisen parameter for geophysical minerals (MgO, Al2O3, Mg2SiO4) using three different Equations of State (EOS): Vinet-Rydberg, modified Lenard-Jones, and Brennan-Stacey. By examining material responses to compression, it aids in understanding the thermodynamic behavior of these minerals under high-pressure conditions. This research contributes to advancements in geophysics, materials science, and planetary studies, offering insights into mineral stability and the selection of appropriate EOS models for various applications.

Summary of the Study:

This theoretical study investigates the Grüneisen parameter of MgO, Al2O3, and Mg2SiO4 using Vinet-Rydberg, modified Lenard-Jones, and Brennan-Stacey EOS. Results show a consistent decrease in the Grüneisen parameter with increasing compression, with the modified Lenard-Jones EOS displaying the least sensitivity and the Brennan-Stacey EOS showing the highest. This analysis highlights the critical role of EOS models in predicting thermodynamic properties and informs future research on high-pressure material behavior.