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 Earths
  crust constituting about 8 by weight. Silicon
  and oxygen are the only two elements more common.
• To understand aluminums 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.

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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. B 1992, 46,
  21.

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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.

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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.

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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.

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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 0.07 kJ/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.

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Solid-Liquid Gibbs Free Energy Differences
.0001 GPa (1 atm) .001 GPa 1 GPa 2 GPa 5 GPa
850 0.117
900 0.5967 0.5957 -0.0177
950 1.087 0.457 -0.107
1000 0.357
1050 0.817 -0.578
1100 -0.148
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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
p Tm (K), MDEA
0.0001 GPa 8387
0.001 GPa 8407
1 GPa 9028
2 GPa 9628
5 GPa 111610
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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.

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Acknowledgments

• Siepmann Group