Molten salt eutectics from atomistic alchemical simulations · 2017. 2. 7. · Lammps workshop...
Transcript of Molten salt eutectics from atomistic alchemical simulations · 2017. 2. 7. · Lammps workshop...
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
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