View source for Modified embedded-atom method interatomic potentials for the Mg-Al alloy system

== Abstract ==

[[File:MEAM_Mg_Al_Fig_1.gif|thumb|right|500px|Fig. 1. Atomic energies  as a function
of the atomic volume for Al atoms in fcc, hcp,
bcc, and simple cubic crystal structures. The energies are measured
from the equilibrium atomic energy of fcc structure. Volumes
are scaled by the equilibrium atomic volume of the fcc structure
V0
fcc.]]

We developed modified embedded-atom method (MEAM) interatomic potentials for the Mg-Al alloy system using a first-principles method based on density functional theory (DFT). The materials parameters, such as the cohesive energy, equilibrium atomic volume, and bulk modulus, were used to determine the MEAM parameters. Face-centered cubic, hexagonal close packed, and cubic rock salt structures were used as the reference structures for Al, Mg, and MgAl, respectively. The applicability of these MEAM potentials to atomistic simulations for investigating Mg-Al alloys was demonstrated by performing simulations on Mg and Al atoms in a variety of geometries. These MEAM potentials were used to calculate the adsorption energies of Al and Mg atoms on Al (111) and Mg (0001) surfaces. The formation energies and geometries of various point defects, such as vacancies, interstitial defects, and substitutional defects, were also calculated. We found that the MEAM potentials give a better overall agreement with DFT calculations and experiments when compared against the previously published MEAM potentials.
Full Article:http://prb.aps.org/abstract/PRB/v75/i5/e054106



== Introduction ==

Magnesium alloys are becoming increasingly important in
many technological areas, including aerospace and automotive
industries. The usage of magnesium die castings, for
example, is increasing in the automotive industry1–3 due to
the lower mass densities of magnesium alloys compared with
steel and aluminum, higher temperature capabilities and improved
crash worthiness over plastics. The primary magnesium
alloys for die-casting applications are the magnesium-aluminum
alloys such as AM50 and AM60B.4–6
To meet the industrial demand for high-strength lightweight
magnesium alloys, it is essential to obtain detailed
understanding of the effect of individual alloying elements
on the properties of magnesium alloys, especially among the
main constituent elements, Mg and Al. The alloying elements
can form interstitial or substitutional defects, or can precipitate
into small particles creating complex interface structures.
The interactions between these alloying elements need to be
investigated using atomistic simulation techniques such as
molecular dynamics or Monte Carlo simulations. These atomistic
simulations require accurate atomic interaction potentials
to compute the total energy of the system. First principles
calculations certainly can provide the most reliable
interatomic potentials. However, realistic simulations of alloy
systems often require a number of atoms that renders
these methods impractical—they either require too much
computer memory or take too long to be completed in a
reasonable amount of time. One alternative is to use semi-
empirical interaction potentials that can be evaluated efficiently,
so that the atomistic approaches that use them can, in
certain cases, handle systems with more than a million atoms.

== Validation ==

[[File:MEAM_Mg_Al_Fig_2.gif|thumb|right|500px|Fig. 2. Atomic energies of Mg as a function of the atomic
volume in fcc, hcp, and bcc cubic crystal structures. The energies
are measured from the equilibrium atomic energy of the hcp structure.
Volumes are scaled by the equilibrium atomic volume of the
hcp structure V0
hcp.]]

To test the validity of the MEAM potentials for single
elements, each element was put into fcc, hcp, body-centered
cubic (bcc), and simple cubic (sc) crystal structures. The
atomic energies for several atomic volumes near equilibrium
atomic volume were calculated. The results were compared
with those of DFT calculations, as shown in Fig. 1. As expected,
the curve for the fcc structure produced by the
MEAM potential retraces the results of DFT calculations
nearly perfectly since fcc was used as the reference structure
during the potential construction process. The agreement between
the MEAM potential and DFT for the hcp structure is
also remarkable. The most important result, however, is the
fact that the new MEAM potential correctly identified fcc as
the most stable structure for Al. Furthermore, the sequence of
the structures is correctly predicted in the order of stability
by the Al MEAM potential. The relative cohesive energies,
with respect to the one for the fcc structure, are also in good
agreement with the DFT calculations, although the result for
the simple cubic structure is slightly underestimated. The
relative equilibrium atomic volumes, with respect to the one
for the fcc structure, are also well reproduced. We point out
that the equilibrium atomic volume for fcc Al, obtained by
the MEAM potential (16.61 Å^3), is slightly different from
the one predicted by DFT (15.76 Å^3). This is due to the fact
that the MEAM parameters are fitted to reproduce the experimental
volume, while DFT within LDA tends to underestimate
the equilibrium lattice constants by roughly 1%.
Figure 2 shows the atomic energy plot for Mg atoms in
different crystal structures compared with the results of the
DFT calculations. The hcp structure was used as the reference
structure for the Mg MEAM potential, and the DFT
data points for this structure are accurately reproduced. The
sequence of the structures is again predicted correctly in the
order of stability by the Mg MEAM potential. The relative
atomic energies, with respect to the one for the hcp structure,
are also in good agreement with the DFT calculations. Note
that the scale of the vertical axis of Fig. 2 is six times larger
than that of Fig. 1, and that the largest error in relative
atomic energies is in the order of 0.01 eV. Similar
to the Al potential, equilibrium atomic volume for hcp Mg in
the MEAM is set to the experimental value of 23.16 Å^3,
while DFT predicts a smaller value of 21.54 Å^3. Both the
MEAM and the DFT methods prefer a c/a ratio close to
0.994 of the ideal c/a ratio.

== Conclusion ==

In this study we developed a set of MEAM potentials for
Al, Mg, and their alloy systems using first-principles calculations
based on DFT. The validity and transferability of
these MEAM potentials were tested rigorously by calculating
physical properties of the Mg-Al alloy systems in many different
atomic arrangements such as bulk, surface, and point
defect structures. These MEAM potentials show a significant
improvement over the previously published potentials, especially
for the surface formation, stacking faults, and point
defect calculations. The Mg-Al alloy potentials, however,
failed to predict the stability of the Mg17Al12 alloy intermetallic
phase, suggesting the need for further improvements.

[[Category:Research Paper]]
[[Category:Electronic Scale]]
[[Category:VASP]]
[[Category: Modified Embedded Atom Method]]