From the Ising model and the Lennard-Jones fluid to water and the iron-carbon system, phase diagrams are an indispensable tool to understand phase equilibria. Despite the effort of the simulation community, the calculation of a large portion of a phase diagram using computer simulation is still today a significant challenge. Here, we propose a method to calculate phase diagrams involving liquid and solid phases by the reversible transformation of the liquid and the solid. To this end, we introduce an order parameter that breaks the rotational symmetry and we leverage our recently introduced method to sample the multithermal-multibaric ensemble. In this way, in a single molecular dynamics simulation, we are able to compute the liquid-solid coexistence line for entire regions of the temperature and pressure phase diagram. We apply our approach to the bcc-liquid phase diagram of sodium and the fcc-bcc-liquid phase diagram of aluminum.
REFERENCES
1.
D.
Frenkel
and B.
Smit
, Understanding Molecular Simulation: From Algorithms to Applications
(Academic Press
, 2001
), Vol. 1.2.
A. Z.
Panagiotopoulos
, “Direct determination of phase coexistence properties of fluids by Monte Carlo simulation in a new ensemble
,” Mol. Phys.
61
(4
), 813
–826
(1987
).3.
D.
Frenkel
and A. J. C.
Ladd
, “New Monte Carlo method to compute the free energy of arbitrary solids. Application to the fcc and hcp phases of hard spheres
,” J. Chem. Phys.
81
(7
), 3188
–3193
(1984
).4.
G.
Grochola
, “Constrained fluid λ-integration: Constructing a reversible thermodynamic path between the solid and liquid state
,” J. Chem. Phys.
120
(5
), 2122
–2126
(2004
).5.
L. B.
Pártay
, A. P.
Bartók
, and G.
Csányi
, “Efficient sampling of atomic configurational spaces
,” J. Phys. Chem. B
114
(32
), 10502
–10512
(2010
).6.
R. J. N.
Baldock
, L. B.
Pártay
, A. P.
Bartók
, M. C.
Payne
, and G.
Csányi
, “Determining pressure-temperature phase diagrams of materials
,” Phys. Rev. B
93
(17
), 174108
(2016
).7.
P. M.
Piaggi
and M.
Parrinello
, “Multithermal-multibaric molecular simulations from a variational principle
,” Phys. Rev. Lett.
122
(5
), 050601
(2019
).8.
P.
Steinhardt
, D.
Nelson
, and M.
Ronchetti
, “Bond-orientational order in liquids and glasses
,” Phys. Rev. B
28
, 784
–805
(1983
).9.
J. S.
Van Duijneveldt
and D.
Frenkel
, “Computer simulation study of free energy barriers in crystal nucleation
,” J. Chem. Phys.
96
(6
), 4655
–4668
(1992
).10.
W.
Lechner
and C.
Dellago
, “Accurate determination of crystal structures based on averaged local bond order parameters
,” J. Chem. Phys.
129
(11
), 114707
(2008
).11.
P. M.
Piaggi
, O.
Valsson
, and M.
Parrinello
, “Enhancing entropy and enthalpy fluctuations to drive crystallization in atomistic simulations
,” Phys. Rev. Lett.
119
(1
), 015701
(2017
).12.
H.
Niu
, P. M.
Piaggi
, M.
Invernizzi
, and M.
Parrinello
, “Molecular dynamics simulations of liquid silica crystallization
,” Proc. Natl. Acad. Sci. U. S. A.
115
(21
), 5348
–5352
(2018
).13.
S.
Angioletti-Uberti
, M.
Ceriotti
, P. D.
Lee
, and M. W.
Finnis
, “Solid-liquid interface free energy through metadynamics simulations
,” Phys. Rev. B
81
(12
), 125416
(2010
).14.
A. P.
Bartók
, R.
Kondor
, and G.
Csányi
, “On representing chemical environments
,” Phys. Rev. B
87
(18
), 184115
(2013
).15.
S.
De
, A. P.
Bartók
, G.
Csányi
, and M.
Ceriotti
, “Comparing molecules and solids across structural and alchemical space
,” Phys. Chem. Chem. Phys.
18
(20
), 13754
–13769
(2016
).16.
F.
Martelli
, H.-Y.
Ko
, E. C.
Oğuz
, and R.
Car
, “Local-order metric for condensed-phase environments
,” Phys. Rev. B
97
, 064105
(2018
).17.
P. R.
ten Wolde
, M. J.
Ruiz-Montero
, and D.
Frenkel
, “Numerical calculation of the rate of crystal nucleation in a Lennard-Jones system at moderate undercooling
,” J. Chem. Phys.
104
(24
), 9932
–9947
(1996
).18.
O.
Valsson
and M.
Parrinello
, “Variational approach to enhanced sampling and free energy calculations
,” Phys. Rev. Lett.
113
(9
), 090601
(2014
).19.
S. R.
Wilson
, K. G. S. H.
Gunawardana
, and M. I.
Mendelev
, “Solid-liquid interface free energies of pure bcc metals and B2 phases
,” J. Chem. Phys.
142
(13
), 134705
(2015
).20.
P.
Raiteri
, A.
Laio
, F. L.
Gervasio
, C.
Micheletti
, and M.
Parrinello
, “Efficient reconstruction of complex free energy landscapes by multiple walkers metadynamics
,” J. Phys. Chem. B
110
(8
), 3533
–3539
(2006
).21.
Y.
Mishin
, D.
Farkas
, M. J.
Mehl
, and D. A.
Papaconstantopoulos
, “Interatomic potentials for monoatomic metals from experimental data and ab initio calculations
,” Phys. Rev. B
59
(5
), 3393
(1999
).22.
A. R.
Oganov
and C. W.
Glass
, “Crystal structure prediction using ab initio evolutionary techniques: Principles and applications
,” J. Chem. Phys.
124
(24
), 244704
(2006
).23.
P. M.
Piaggi
and M.
Parrinello
, “Predicting polymorphism in molecular crystals using orientational entropy
,” Proc. Natl. Acad. Sci. U. S. A.
115
(41
), 10251
–10256
(2018
).24.
S.
Plimpton
, “Fast parallel algorithms for short-range molecular dynamics
,” J. Comput. Phys.
117
(1
), 1
–19
(1995
).25.
G. A.
Tribello
, M.
Bonomi
, D.
Branduardi
, C.
Camilloni
, and G.
Bussi
, “PLUMED 2: New feathers for an old bird
,” Comput. Phys. Commun.
185
(2
), 604
–613
(2014
).26.
VES Code, a library that implements enhanced sampling methods based on Variationally Enhanced Sampling written by
O.
Valsson
, for the current version, see http://www.ves-code.org.27.
G.
Bussi
, D.
Donadio
, and M.
Parrinello
, “Canonical sampling through velocity rescaling
,” J. Chem. Phys.
126
(1
), 014101
(2007
).28.
M.
Parrinello
and A.
Rahman
, “Polymorphic transitions in single crystals: A new molecular dynamics method
,” J. Appl. Phys.
52
(12
), 7182
–7190
(1981
).29.
O.
Valsson
and M.
Parrinello
, “Well-tempered variational approach to enhanced sampling
,” J. Chem. Theory Comput.
11
(5
), 1996
–2002
(2015
).© 2019 Author(s).
2019
Author(s)
You do not currently have access to this content.