Transcript Document

Melting Points of Aluminum
at Geological Pressures
Linzey Bachmeier
Divesh Bhatt
Ilja Siepmann
Chemistry Department
University of Minnesota
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.
Potential Energy Function
• The potential energy function that was
used during this project was the Mei
Davenport Embedded-Atom(MDEA).
~ U =  F( )   (v )
• MDEA was originally parameterized to
reproduce the solid-state properties of

aluminum*
N
i
i
ij
i j
*Mei, J.; Davenport, J. W. Phys. Rev. B 1992, 46, 21.
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.
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.
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.
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.
Solid-Liquid Gibbs Free Energy
Differences
.0001 GPa
(1 atm)
850
0.117
900
0.5967
950
.001 GPa
1 GPa
0.5957
-0.0177
1.087
0.457
2 GPa
-0.107
1000
0.357
1050
0.817
1100
5 GPa
-0.578
-0.148
Results
Gs - GL (kJ/mol)
• Using the Gibbs free energy differences at each
of the pressures from the last table and
reweighting
histograms
at
MDEA, 1 GPa
different
temperatures and
particular
pressures
yields
the melting point
at the pressure.
Temperature (K)
Results
p
Tm (K),
MDEA
0.0001 GPa 8387
0.001 GPa
8407
1 GPa
9028
2 GPa
9628
5 GPa
111610
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.
Acknowledgments
• Siepmann Group