Melting Points of Aluminum at Geological Pressures

1. Melting Points of Aluminum at Geological Pressures Linzey Bachmeier Divesh Bhatt Ilja Siepmann Chemistry Department University of Minnesota

2. Introduction • Aluminum is a major element inside the Earth’s crust constituting about 8% by weight. Silicon and oxygen are the only two elements more common. • To understand aluminum’s properties inside the surface of the Earth requires knowledge of the phase behavior under the pressure conditions that are present in the crust. • This project evaluates one potential energy function with respect to its accuracy in predicting the solid/liquid phase behavior of aluminum at geological pressures.

3. Potential Energy Function • The potential energy function that was used during this project was the Mei Davenport Embedded-Atom(MDEA). ~ U = • MDEA was originally parameterized to reproduce the solid-state properties of aluminum* *Mei, J.; Davenport, J. W. Phys. Rev. B1992, 46, 21.

4. Thermodynamics • The Gibbs free energy difference between the liquid and solid phase is determined at a single pressure using thermodynamic integration along a pseudo-supercritical path.* • Also, the Gibbs free energy differences between the two phases is determined at other temperatures using the Multiple Histogram Reweighting (MHR) technique.** *Grochola, G. J. Chem. Phys. 2004, 120, 2122. **Ferrenberg, A. M.; Swendsen, R. H. Phys Rev. Lett.1988, 61, 2635.

5. Simulation Details • NPT (constant pressure/constant temperature) simulations for the face-centered cubic solid and the disordered liquid were performed at a few different temperatures and many pressures up to 20 Gpa using the MDEA potential. • 256 atoms were used in a three dimensional periodic cubic box. • Energy-volume and energy-pressure histograms at different temperatures and at different pressures were combined using MHR, so calculations of the Gibbs free energies at different pressures and temperatures is allowed.

6. More Simulation Details • Subsequently, the melting point as a function of pressure, as well as temperature, can be determined. • For each pressure, a few different temperatures, at 50K intervals, were performed. • These simulations were done at increasing temperatures as the pressure increased in anticipation of the melting point of aluminum increasing with pressure.

7. Results • Explicit thermodynamic integration along a pseudo-supercritical path was performed at 850 K and 1 atm for the MDEA potential, and the Gibbs free energy difference between the solid and liquid phase was obtained as 0.11 ± 0.07kJ/mol. • With one Gibbs free energy difference between the FCC solid and the liquid phase known, other energy differences could be obtained via the MHR procedure.

8. Solid-Liquid Gibbs Free Energy Differences

9. Results • Using the Gibbs free energy differences at each of the pressures from the last table and reweighting histograms at different temperatures and particular pressures yields the melting point at the pressure. MDEA, 1 GPa Gs - GL (kJ/mol) Temperature (K)

10. Results

11. Conclusion • The Gibbs free energy differences show that the solid becomes increasingly more stable relative to the liquid at higher temperatures as the pressure is increased. • With increased stability of the solid phase at higher pressure, the melting point increases with pressure.

12. Acknowledgments • Siepmann Group