The elastic solid solution model for minerals at high pressures and temperatures.

Area of Science:

• Mineralogy
• Geophysics
• Materials Science

Background:

• Non-ideality in mineral solid solutions impacts elastic, thermodynamic, and stability properties.
• Current models using Gibbs free energy excess are limited for solutions with significant endmember lattice parameter differences, leading to errors in high-pressure extrapolations.

Purpose of the Study:

• To investigate parameterizing solid solution models using Helmholtz free energy, with volume as an independent variable.
• To explore the implications for thermodynamics and elasticity of solid solutions, particularly concerning lattice parameter mismatches.

Main Methods:

• Developed a theoretical framework for Helmholtz free energy-based solid solution models.
• Included energetic contributions from elastic deformation and chemical contributions from atomic exchange.
• Derived thermodynamic properties for n-endmember solutions.

Main Results:

• The Helmholtz free energy approach intuitively incorporates elastic deformation energies.
• Accurate predictions of excess enthalpies, entropies, and volumes are made as functions of volume and temperature.
• Demonstrated applicability to alkali halides, pyroxene, garnet, and bridgmanite solid solutions.

Conclusions:

• The Helmholtz free energy model offers a more robust approach for non-ideal solid solutions, especially those with large endmember lattice parameter variations.
• This formulation provides insights into the microscopic origins of non-ideality and can assess excess properties where experimental data is limited.
• The model is valuable for geochemical and geophysical studies of planetary bodies.