With numerical simulations of the mW model of water, we investigate the energetic stability of crystalline clusters both for Ice I (cubic and hexagonal ice) and for the metastable Ice 0 phase as a function of the cluster size. Under a large variety of forming conditions, we find that the most stable cluster changes as a function of size: at small sizes, the Ice 0 phase produces the most stable clusters, while at large sizes, there is a crossover to Ice I clusters. We further investigate the growth of crystalline clusters with the seeding technique and study the growth patterns of different crystalline clusters. While energetically stable at small sizes, the growth of metastable phases (cubic and Ice 0) is hindered by the formation of coherent grain boundaries. A fivefold symmetric twin boundary for cubic ice, and a newly discovered coherent grain boundary in Ice 0, promotes cross nucleation of cubic ice. Our work reveals that different local structures can compete with the stable phase in mW water and that the low energy cost of particular grain boundaries might play an important role in polymorph selection.
REFERENCES
1.
F. C.
Frank
, Proc. R. Soc. London, Ser. A
215
, 43
(1952
).2.
H.
Tanaka
, R.
Shi
, H.
Tong
, and J.
Russo
, Nat. Rev. Phys.
1
, 333
(2019
).3.
H.
Tanaka
, Eur. Phys. J. E
35
, 23
(2012
).4.
H.
Shintani
and H.
Tanaka
, Nat. Phys.
2
, 200
(2006
).5.
M.
Leocmach
and H.
Tanaka
, Nat. Commun.
3
, 974
(2012
).6.
C. P.
Royall
and S. R.
Williams
, Phys. Rep.
560
, 1
(2015
).7.
C. P.
Royall
, F.
Turci
, S.
Tatsumi
, J.
Russo
, and J.
Robinson
, J. Phys.: Condens. Matter
30
, 363001
(2018
).8.
J.
Russo
, F.
Romano
, and H.
Tanaka
, Phys. Rev. X
8
, 021040
(2018
).9.
J.
Russo
and H.
Tanaka
, J. Chem. Phys.
145
, 211801
(2016
).10.
11.
J.
Russo
and H.
Tanaka
, Nat. Commun.
5
, 3556
(2014
).12.
R.
Shi
, J.
Russo
, and H.
Tanaka
, J. Chem. Phys.
149
, 224502
(2018
).13.
R.
Shi
, J.
Russo
, and H.
Tanaka
, Proc. Natl. Acad. Sci. U. S. A.
115
, 9444
(2018
).14.
P. H.
Poole
, F.
Sciortino
, U.
Essmann
, and H. E.
Stanley
, Nature
360
, 324
(1992
).15.
O.
Mishima
and H. E.
Stanley
, Nature
396
, 329
(1998
).16.
P.
Gallo
and F.
Sciortino
, Phys. Rev. Lett.
109
, 177801
(2012
).17.
P.
Gallo
, K.
Amann-Winkel
, C. A.
Angell
, M. A.
Anisimov
, F.
Caupin
, C.
Chakravarty
, E.
Lascaris
, T.
Loerting
, A. Z.
Panagiotopoulos
, J.
Russo
et al, Chem. Rev.
116
, 7463
(2016
).18.
P. H.
Handle
, T.
Loerting
, and F.
Sciortino
, Proc. Natl. Acad. Sci. U. S. A.
114
, 13336
(2017
).19.
F.
Martelli
, J. Chem. Phys.
150
, 094506
(2019
).20.
J.
Russo
, F.
Romano
, and H.
Tanaka
, Nat. Mater.
13
, 733
(2014
).21.
A. V.
Brukhno
, J.
Anwar
, R.
Davidchack
, and R.
Handel
, J. Phys.: Condens. Matter
20
, 494243
(2008
).22.
E. B.
Moore
and V.
Molinero
, Nature
479
, 506
(2011
).23.
T. L.
Malkin
, B. J.
Murray
, C. G.
Salzmann
, V.
Molinero
, S. J.
Pickering
, and T. F.
Whale
, Phys. Chem. Chem. Phys.
17
, 60
(2015
).24.
J.
Shilling
, M.
Tolbert
, O.
Toon
, E.
Jensen
, B. J.
Murray
, and A. K.
Bertram
, Geophys. Res. Lett.
33
, L17801
, https://doi.org/10.1029/2006gl026671 (2006
).25.
L.
Dowell
and A.
Rinfret
, Nature
188
, 1144
(1960
).26.
I.
Kohl
, E.
Mayer
, and A.
Hallbrucker
, Phys. Chem. Chem. Phys.
2
, 1579
(2000
).27.
T.
Loerting
, I.
Kohl
, W.
Schustereder
, K.
Winkel
, and E.
Mayer
, ChemPhysChem
7
, 1203
(2006
).28.
P.
Geiger
, C.
Dellago
, M.
Macher
, C.
Franchini
, G.
Kresse
, J.
Bernard
, J. N.
Stern
, and T.
Loerting
, J. Phys. Chem. C
118
, 10989
(2014
).29.
G.
Arnold
, E.
Finch
, S.
Rabideau
, and R.
Wenzel
, J. Chem. Phys.
49
, 4365
(1968
).30.
W.
Kuhs
, D.
Bliss
, and J.
Finney
, J. Phys. Colloq.
48
, C1
(1987
).31.
T.
Hansen
, M.
Koza
, and W.
Kuhs
, J. Phys.: Condens. Matter
20
, 285104
(2008
).32.
T.
Hansen
, M.
Koza
, P.
Lindner
, and W.
Kuhs
, J. Phys.: Condens. Matter
20
, 285105
(2008
).33.
B. J.
Murray
and A. K.
Bertram
, Geophys. Res. Lett.
34
, L16810
, https://doi.org/10.1029/2007gl030471 (2007
).34.
M. A.
Carignano
, J. Phys. Chem. C
111
, 501
(2007
).35.
P.
Pirzadeh
and P. G.
Kusalik
, J. Am. Chem. Soc.
133
, 704
(2010
).36.
D.
Rozmanov
and P. G.
Kusalik
, J. Chem. Phys.
137
, 094702
(2012
).37.
M.
Seo
, E.
Jang
, K.
Kim
, S.
Choi
, and J. S.
Kim
, J. Chem. Phys.
137
, 154503
(2012
).38.
T. L.
Malkin
, B. J.
Murray
, A. V.
Brukhno
, J.
Anwar
, and C. G.
Salzmann
, Proc. Natl. Acad. Sci. U. S. A.
109
, 1041
(2012
).39.
S.
Choi
, E.
Jang
, and J. S.
Kim
, J. Chem. Phys.
140
, 014701
(2014
).40.
D.
Quigley
, J. Chem. Phys.
141
, 121101
(2014
).41.
W. F.
Kuhs
, C.
Sippel
, A.
Falenty
, and T. C.
Hansen
, Proc. Natl. Acad. Sci. U. S. A.
109
, 21259
(2012
).42.
C.
Desgranges
and J.
Delhommelle
, J. Am. Chem. Soc.
128
, 10368
(2006
).43.
A. H.
Nguyen
and V.
Molinero
, J. Chem. Phys.
140
, 084506
(2014
).44.
L.
Lupi
, A.
Hudait
, B.
Peters
, M.
Grünwald
, R.
Gotchy Mullen
, A. H.
Nguyen
, and V.
Molinero
, Nature
551
, 218
–222
(2017
).45.
E. A.
Engel
, A.
Anelli
, M.
Ceriotti
, C. J.
Pickard
, and R. J.
Needs
, Nat. Commun.
9
, 2173
(2018
).46.
M.
Matsumoto
, S.
Saito
, and I.
Ohmine
, Nature
416
, 409
(2002
).47.
R.
Radhakrishnan
and B. L.
Trout
, Phys. Rev. Lett.
90
, 158301
(2003
).48.
V.
Molinero
and E. B.
Moore
, J. Phys. Chem. B
113
, 4008
(2008
).49.
E. B.
Moore
and V.
Molinero
, J. Chem. Phys.
132
, 244504
(2010
).50.
E. B.
Moore
and V.
Molinero
, Phys. Chem. Chem. Phys.
13
, 20008
(2011
).51.
D.
Quigley
and P. M.
Rodger
, J. Chem. Phys.
128
, 154518
(2008
).52.
T.
Li
, D.
Donadio
, G.
Russo
, and G.
Galli
, Phys. Chem. Chem. Phys.
13
, 19807
(2011
).53.
A.
Reinhardt
, J. P.
Doye
, E. G.
Noya
, and C.
Vega
, J. Chem. Phys.
137
, 194504
(2012
).54.
A.
Reinhardt
and J. P.
Doye
, J. Chem. Phys.
139
, 096102
(2013
).55.
J.
Benet
, L. G.
MacDowell
, and E.
Sanz
, Phys. Chem. Chem. Phys.
16
, 22159
(2014
).56.
J.
Benet
, L. G.
MacDowell
, and E.
Sanz
, J. Chem. Phys.
141
, 034701
(2014
).57.
B.
Cheng
, G. A.
Tribello
, and M.
Ceriotti
, Phys. Rev. B
92
, 180102
(2015
).58.
J. R.
Espinosa
, C.
Vega
, and E.
Sanz
, J. Phys. Chem. C
120
, 8068
(2016
).59.
J. R.
Espinosa
, A.
Zaragoza
, P.
Rosales-Pelaez
, C.
Navarro
, C.
Valeriani
, C.
Vega
, and E.
Sanz
, Phys. Rev. Lett.
117
, 135702
(2016
).60.
M.
Ambler
, B.
Vorselaars
, M. P.
Allen
, and D.
Quigley
, J. Chem. Phys.
146
, 074701
(2017
).61.
T.
Koop
and B. J.
Murray
, J. Chem. Phys.
145
, 211915
(2016
).62.
B.
Cheng
and M.
Ceriotti
, J. Chem. Phys.
146
, 034106
(2017
).63.
B.
Cheng
, G. A.
Tribello
, and M.
Ceriotti
, J. Chem. Phys.
147
, 104707
(2017
).64.
L.
Lupi
, A.
Hudait
, and V.
Molinero
, J. Am. Chem. Soc.
136
, 3156
(2014
).65.
A.
Reinhardt
and J. P.
Doye
, J. Chem. Phys.
141
, 084501
(2014
).66.
S. J.
Cox
, S. M.
Kathmann
, B.
Slater
, and A.
Michaelides
, J. Chem. Phys.
142
, 184704
(2015
).67.
G. C.
Sosso
, G. A.
Tribello
, A.
Zen
, P.
Pedevilla
, and A.
Michaelides
, J. Chem. Phys.
145
, 211927
(2016
).68.
L.
Lupi
, B.
Peters
, and V.
Molinero
, J. Chem. Phys.
145
, 211910
(2016
).69.
J. C.
Johnston
and V.
Molinero
, J. Am. Chem. Soc.
134
, 6650
(2012
).70.
T.
Li
, D.
Donadio
, and G.
Galli
, Nat. Commun.
4
, 1887
(2013
).71.
A.
Hudait
and V.
Molinero
, J. Am. Chem. Soc.
136
, 8081
(2014
).72.
A.
Haji-Akbari
, R. S.
DeFever
, S.
Sarupria
, and P. G.
Debenedetti
, Phys. Chem. Chem. Phys.
16
, 25916
(2014
).73.
S. M.
Malek
, G. P.
Morrow
, and I.
Saika-Voivod
, J. Chem. Phys.
142
, 124506
(2015
).74.
A.
Haji-Akbari
and P. G.
Debenedetti
, J. Chem. Phys.
147
, 060901
(2017
).75.
E. B.
Moore
, E.
de la Llave
, K.
Welke
, D. A.
Scherlis
, and V.
Molinero
, Phys. Chem. Chem. Phys.
12
, 4124
(2010
).76.
E.
Gonzalez Solveyra
, E.
de la Llave
, D. A.
Scherlis
, and V.
Molinero
, J. Phys. Chem. B
115
, 14196
(2011
).77.
G.
Bullock
and V.
Molinero
, Faraday Discuss.
167
, 371
(2013
).78.
G. D.
Soria
, J. R.
Espinosa
, J.
Ramirez
, C.
Valeriani
, C.
Vega
, and E.
Sanz
, J. Chem. Phys.
148
, 222811
(2018
).79.
M.
Conde
, M.
Rovere
, and P.
Gallo
, Phys. Chem. Chem. Phys.
19
, 9566
(2017
).80.
L.
Rovigatti
, J.
Russo
, and F.
Romano
, Eur. Phys. J. E
41
, 98
(2018
).81.
B. C.
Knott
, V.
Molinero
, M. F.
Doherty
, and B.
Peters
, J. Am. Chem. Soc.
134
, 19544
(2012
).82.
N. E.
Zimmermann
, B.
Vorselaars
, D.
Quigley
, and B.
Peters
, J. Am. Chem. Soc.
137
, 13352
(2015
).83.
J. R.
Espinosa
, C.
Vega
, C.
Valeriani
, and E.
Sanz
, J. Chem. Phys.
144
, 034501
(2016
).84.
J.
Espinosa
, C.
Navarro
, E.
Sanz
, C.
Valeriani
, and C.
Vega
, J. Chem. Phys.
145
, 211922
(2016
).85.
Y.
Lifanov
, B.
Vorselaars
, and D.
Quigley
, J. Chem. Phys.
145
, 211912
(2016
).86.
J.
Russo
, K.
Akahane
, and H.
Tanaka
, Proc. Natl. Acad. Sci. U. S. A.
115
, E3333
(2018
).87.
S.
Mossa
and G.
Tarjus
, J. Phys. Chem.
119
, 8069
(2003
).88.
P. J.
Steinhardt
, D. R.
Nelson
, and M.
Ronchetti
, Phys. Rev. B
28
, 784
(1983
).89.
G.
Tarjus
, S. A.
Kivelson
, Z.
Nussinov
, and P.
Viot
, J. Phys.: Condens. Matter
17
, R1143
(2005
).90.
D.
Quigley
, D.
Alfè
, and B.
Slater
, “Communication: On the stability of ice 0, ice i, and Ih
,” J. Chem. Phys.
141
, 161102
(2014
).91.
M.
Matsumoto
, A.
Baba
, and I.
Ohmine
, J. Chem. Phys.
127
, 134504
(2007
).92.
A.
Reinhardt
and J. P.
Doye
, J. Chem. Phys.
136
, 054501
(2012
).93.
A.
Hudait
, S.
Qiu
, L.
Lupi
, and V.
Molinero
, Phys. Chem. Chem. Phys.
18
, 9544
(2016
).94.
B.
Cheng
, C.
Dellago
, and M.
Ceriotti
, Phys. Chem. Chem. Phys.
20
, 28732
(2018
).95.
F.
Romano
, J.
Russo
, and H.
Tanaka
, Phys. Rev. B
90
, 014204
(2014
).96.
J.
Wedekind
and D.
Reguera
, J. Phys. Chem. B
112
, 11060
(2008
).97.
J.
Russo
, A. C.
Maggs
, D.
Bonn
, and H.
Tanaka
, Soft Matter
9
, 7369
(2013
).98.
W.
Lechner
and C.
Dellago
, J. Chem. Phys.
129
, 114707
(2008
).99.
P.
Ronceray
and P.
Harrowell
, Phys. Rev. E
96
, 042602
(2017
).100.
D.
Wei
, J.
Yang
, M.-Q.
Jiang
, L.-H.
Dai
, Y.-J.
Wang
, J.
Dyre
, I.
Douglass
, and P.
Harrowell
, J. Chem. Phys.
150
, 114502
(2019
).© 2019 Author(s).
2019
Author(s)
You do not currently have access to this content.