Elasticity of grossular-andradite solid solution: an ab initio investigation

Area of Science:

• Geophysics
• Materials Science
• Computational Chemistry

Background:

• Grossular and andradite are garnet end-members found in the upper mantle.
• Understanding their solid solution properties is crucial for geophysics.

Purpose of the Study:

• To investigate the bulk modulus dependence on chemical composition in the grossular-andradite solid solution (Ca3Fe(2-2x)Al(2x)(SiO4)3).
• To provide accurate computational data for this geologically significant mineral system.

Main Methods:

• Utilized ab initio simulations with all-electron local basis sets of Gaussian-type orbitals.
• Employed the hybrid B3LYP density functional for electronic structure calculations.
• Computed the bulk modulus across the entire composition range (0 ≤x≤ 1) using two independent methods: equation-of-state fitting and elastic tensor calculations.

Main Results:

• Predicted a linear relationship between bulk modulus and chemical composition for the grossular-andradite solid solution.
• Estimated maximum deviation from linearity to be approximately 0.5 GPa at ambient conditions, decreasing to <0.2 GPa at 20 GPa.
• Achieved excellent agreement between the two computational approaches, confirming high numerical accuracy.

Conclusions:

• The study establishes a clear, linear modulus-composition trend, challenging prior experimental interpretations.
• The findings offer reliable computational data for grossular-andradite garnets under various pressures.
• This work refines our understanding of garnet mechanical properties relevant to upper mantle conditions.