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Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company,!
for the United States Department of Energy"s National Nuclear Security Administration !
under contract DE-AC04-94AL85000.#
Sandia is a multi-program laboratory operated by Sandia corporation, a fully owned subsidiary of Lockheed Martin Corporation, for the United States Department of Energy’s National Nuclear Security Administration under
contract DE-AC04-94AL85000.
Molten salt eutectics from atomistic alchemical simulations
Sai Jayaraman1,*, Aidan Thompson1 and Anatole von Lilienfeld2
1Advanced Device Technologies, Sandia National Laboratories2Leadership Computing Facility, Argonne National Laboratory
Lammps workshopAugust 11, 2011
*sjayara@sandia.gov
Common tangent at eutectic point between liquid and solid phases
Chemical thermodynamics of Materials - C. H. P. LupisNorth-Holland, 1983
2
Computing the free energy of a liquid mixture
Free energy of binary mixture at
T, P, xA, xB
Free energy of Pure
species A at T,P
Free energy of Pure
species B at T,P
Free energy contribution arising from entropy of mixing
Residual contribution from energetic
interaction between molecules of A and B.
Gmix = xAGA + xBGB + RT�
i=A,B
xi lnxi + Gexcess
3
B
NA, NB
λ = 0
NA+1, NB-1A
λ = 1
Alchemical Transformation
∂Gexcess
∂x≈ ∆G
∆x
∆µAB =1�
0
dλ
�∂U
∂λ
�
λ
=1�
0
dλ
��
i
(uiA − uiB)
�
λ
4
uij(λ) = λuiA + (1− λ)uiB
B
NA, NB
λ = 0
NA+1, NB-1A
λ = 1
Alchemical Transformation
∂Gexcess
∂x≈ ∆G
∆x
∆µAB =1�
0
dλ
�∂U
∂λ
�
λ
=1�
0
dλ
��
i
(uiA − uiB)
�
λ
4
uij(λ) = λuiA + (1− λ)uiB
0 0.2 0.4 0.6 0.8 1!
-80
-60
-40
-20
0"#U/#!$
!
LiNO3-KNO3
Reversibility of transformation: Red (Li K) and Black (K Li)
coincide.
xLiNO3 = 0.5
B
NA, NB
λ = 0
NA+1, NB-1A
λ = 1
Alchemical Transformation
∂Gexcess
∂x≈ ∆G
∆x
∆µAB =1�
0
dλ
�∂U
∂λ
�
λ
=1�
0
dλ
��
i
(uiA − uiB)
�
λ
4
uij(λ) = λuiA + (1− λ)uiB
fix 1 all adapt 1 pair lj/cut epsilon 5 * v_lj scale yescompute 1 all ti lj/cut 5 v_lj v_dlj tail v_lj v_dlj
gex� (xA, xB) =
xA�
0
dx�A ∆µAB(x�
A)− xA
1�
0
dx�A∆µAB(x�
A)
gex� (xA, xB, xC) =
xA�
0
dx�A∆µAB(x�
A, xC)− xA
xA + xB
xA+xB�
0
dx�A∆µAB(x�
A, xC)
+xA
xA + xBgexAC�(xC) +
xB
xA + xBgexBC�(xC)
Excess free energies from ∆μAB
Binary:
Ternary: Area under ∆μAB
C
A B
x A=
1−x C
xB
=1−
xC
At each xC, alchemical changes conducted at xA mesh points
5
gex� (xA, xB) =
xA�
0
dx�A ∆µAB(x�
A)− xA
1�
0
dx�A∆µAB(x�
A)
gex� (xA, xB, xC) =
xA�
0
dx�A∆µAB(x�
A, xC)− xA
xA + xB
xA+xB�
0
dx�A∆µAB(x�
A, xC)
+xA
xA + xBgexAC�(xC) +
xB
xA + xBgexBC�(xC)
Excess free energies from ∆μAB
Binary:
Ternary: Area under ∆μAB
C
A B
x A=
1−x C
xB
=1−
xC
At each xC, alchemical changes conducted at xA mesh points
0 0.2 0.4 0.6 0.8 1xLiNO3
-27
-26.5
-26
-25.5
-25
-24.5
-24
!µ
AB (k
cal/m
ol) LiNO3-KNO3
5
LiNO3-KNO3 mixture - Free energy vs composition
0 0.2 0.4 0.6 0.8 1xLiNO
3
-1.5
-1
-0.5
0
Fre
e en
ergy (
kca
l/m
ol)
400 K423 K450 K
KNO3 LiNO3
�
i
xi∆s�g◦i
gmix� (xA) = gid(xA) + gex
� (xA)
• Approximation: “Simple Eutectic” - Solid phases approximated by pure solids.
• Location of eutectic : Point of tangency between liquid free energy of mixing and solid-liquid connecting line
410 K
M.J. Maeso and J. Largo, Thermochimica Acta, 223, 145-156 (1993)
6
Jayaraman et al. IECR (2010)
LiNO3-NaNO3-KNO3 ternary
S. Jayaraman, A. P. Thompson and O. A. von Lilienfeld, PRE rapid communication, accepted (2011)
7
1M.J. Maeso and J. Largo, Thermochimica Acta, 223, 145-156 (1993) - Binaries
2A.G. Bergman and K. Nogoev, Zh. Neorg. Khim., 9 1423 (1964) - Ternary 3H. R. Carveth, J. Phys. Chem., 2, 209 (1898) -
Conclusions
• Thermodynamic integration based method developed to compute free energies of mixing from MD simulations
• Tangent method extended to compute approximations of eutectic compositions assuming a “simple eutectic”
• Need per-atom contributions from pppm!
8
fix 1 all adapt 1 pair lj/cut epsilon * 5 v_lj scale yescompute 1 all ti lj/cut 5 v_lj v_dlj tail v_lj v_dlj
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