Geometric frustration is an approach to the glass transition based upon the consideration of locally favoured structures (LFS), which are geometric motifs which minimise the local free energy. Geometric frustration proposes that a transition to a crystalline state is frustrated because these LFS do not tile space. However, this concept is based on icosahedra which are not always the LFS for a given system. The LFS of the popular Kob-Andersen (KA) model glassformer are the bicapped square antiprism, which does tile space. Such a LFS-crystal is indeed realised in the Al2Cu structure, which is predicted to be a low energy state for the KA model with a 2:1 composition. We, therefore, hypothesise that upon changing the composition in the KA model towards 2:1, geometric frustration may be progressively relieved, leading to larger and larger domains of LFS which would ultimately correspond to the Al2Cu crystal. Remarkably, rather than an increase, upon changing composition we find a small decrease in the LFS population, and the system remains impervious to nucleation of LFS crystals. We suggest that this may be related to the composition of the LFS, as only a limited subset is compatible with the crystal. We further demonstrate that the Al2Cu crystal will grow from a seed in the KA model with 2:1 composition and identify the melting temperature to be 0.447(2).
REFERENCES
1.
A.
Cavagna
, Phys. Rep.
476
, 51
(2009
).2.
L.
Berthier
and G.
Biroli
, Rev. Mod. Phys.
83
, 587
(2011
).3.
G.
Adam
and J.
Gibbs
, J. Chem. Phys.
43
, 139
(1965
).4.
V.
Lubchenko
and P.
Wolynes
, Annu. Rev. Phys. Chem.
58
, 235
(2007
).5.
G.
Parisi
and F.
Zamponi
, Rev. Mod. Phys.
82
, 789
(2010
).6.
G.
Tarjus
, S. A.
Kivelson
, Z.
Nussinov
, and P.
Viot
, J. Phys.: Condens. Matter
17
, R1143
(2005
).7.
D.
Chandler
and J. P.
Garrahan
, Annu. Rev. Phys. Chem.
61
, 191
(2010
).8.
T.
Hecksler
, A. I.
Nielsen
, N.
Boye Olsen
, and J. C.
Dyre
, Nat. Phys.
4
, 737
(2008
).9.
J. C.
Mauro
, Y.
Yue
, A. J.
Ellison
, P. K.
Gupta
, and D. C.
Allan
, Proc. Natl. Acad. Sci. U. S. A.
106
, 19780
(2009
).10.
C. P.
Royall
and S. R.
Williams
, Phys. Rep.
560
, 1
(2015
).11.
A.
Di Cicco
, A.
Trapananti
, S.
Faggioni
, and A.
Filipponi
, Phys. Rev. Lett.
91
, 135505
(2003
).12.
D.
Coslovich
, J. Chem. Phys.
138
, 12A539
(2013
).13.
F. C.
Frank
, Proc. R. Soc. A.
215
, 43
(1952
).14.
M.
Leocmach
, J.
Russo
, and H.
Tanaka
, J. Chem. Phys.
138
, 12A515
(2013
).15.
16.
M.
Mosayebi
, E.
Del Gado
, P.
Ilg
, and H. C.
Öttinger
, Phys. Rev. Lett.
104
, 205704
(2010
).17.
C.
Cammarota
and G.
Biroli
, Proc. Natl. Acad. Sci. U. S. A.
109
, 8850
(2012
).18.
C.
Cammarota
and G.
Biroli
, Europhys. Lett.
98
, 36005
(2012
).19.
F.
Sausset
and D.
Levine
, Phys. Rev. Lett.
107
, 045501
(2011
).20.
A. J.
Dunleavy
, K.
Wiesner
, and C. P.
Royall
, Phys. Rev. E
86
, 041505
(2012
).21.
S.
Mossa
and G.
Tarjus
, J. Non-Cryst. Solids
352
, 4847
(2006
).22.
23.
24.
J. F.
Sadoc
, J. Non-Cryst. Solids
44
, 1
(1981
).25.
D. R.
Nelson
, Defects and Geometry in Condensed Matter Physics
(Cambridge University Press
, 2002
), p. 392
.26.
D. R.
Nelson
, Phys. Rev. Lett.
50
, 982
(1983
).27.
J. P.
Straley
, Phys. Rev. B
30
, 6592
(1984
).28.
C. D.
Modes
and R. D.
Kamien
, Phys. Rev. Lett.
99
, 235701
(2007
).29.
F.
Sausset
, G.
Tarjus
, and P.
Viot
, Phys. Rev. Lett.
10
, 155701
(2008
).30.
F.
Sausset
and G.
Tarjus
, Phys. Rev. Lett.
104
, 065701
(2010
).31.
G.
Tarjus
, F.
Sausset
, and P.
Viot
, Advances in Chemical Physics
(Wiley
, New York
, 2010
), Chap. Statistical Mechanics of liquids and fluids in curved space.32.
F.
Sausset
, G.
Tarjus
, and D.
Nelson
, Phys. Rev. E
81
, 031504
(2010
).33.
D.
Coslovich
and G.
Pastore
, J. Chem. Phys.
127
, 124504
(2007
).34.
G. M.
Hocky
, D.
Coslovich
, A.
Ikeda
, and D.
Reichman
, Phys. Rev. Lett.
113
, 157801
(2014
).35.
C. P.
Royall
, A.
Malins
, A. J.
Dunleavy
, and R.
Pinney
, J. Non-Cryst. Solids
(2014
).36.
B.
Charbonneau
, P.
Charbonneau
, and G.
Tarjus
, Phys. Rev. Lett.
108
, 035701
(2012
).37.
P.
Charbonneau
and G.
Tarjus
, Phys. Rev. E
87
, 042305
(2013
).38.
B.
Charbonneau
, P.
Charbonneau
, and G.
Tarjus
, J. Chem. Phys.
138
, 12A515
(2013
).39.
A. J.
Dunleavy
, K.
Wiesner
, R.
Yamamoto
, and C. P.
Royall
, Nat. Commun.
6
, 6089
(2015
).40.
A.
Malins
, J.
Eggers
, H.
Tanaka
, and C. P.
Royall
, Faraday Discuss.
167
, 405
(2013
).41.
A.
Malins
, J.
Eggers
, C. P.
Royall
, S. R.
Williams
, and H.
Tanaka
, J. Chem. Phys.
138
, 12A535
(2013
).42.
H.
Tanaka
, T.
Kawasaki
, H.
Shintani
, and K.
Watanabe
, Nat. Mater.
9
, 324
(2010
).43.
K.
Kawasaki
and H.
Tanaka
, J. Phys.: Condens. Matter
22
, 232102
(2010
).44.
M.
Leocmach
and H.
Tanaka
, Nat. Commun.
3
, 974
(2012
).45.
U. R.
Pedersen
, T. B.
Schroder
, J. C.
Dyre
, and P.
Harrowell
, Phys. Rev. Lett.
104
, 105701
(2010
).46.
S.
Punnathanam
and P. A.
Monson
, J. Chem. Phys.
125
, 024508
(2006
).47.
S.
Jungblut
and C.
Dellago
, Phys. Rev. E
87
, 012305
(2013
).48.
A.
Evteev
, A. T.
Kosilov
, and E. V.
Levtchenko
, Acta Mater.
51
, 2665
(2003
).49.
Y. Q.
Cheng
and E.
Ma
, Prog. Mater. Sci.
56
, 379
–473
(2011
).50.
J. R.
Fernández
and P.
Harrowell
, Phys. Rev. E
67
, 011403
(2003
).51.
A.
Bannerjee
, S.
Chakrabarty
, and S. M.
Bhattacharyya
, J. Chem. Phys.
139
, 104501
(2013
).52.
S.
Toxvaerd
, U. R.
Pedersen
, T. B.
Schroder
, and J. C.
Dyre
, J. Chem. Phys.
130
, 224501
(2009
).53.
L.-C.
Valdes
, F.
Affourad
, J.
Descamps
, and M.
Habasaki
, J. Chem. Phys.
130
, 154505
(2009
).54.
J. R.
Fernández
and P.
Harrowell
, J. Phys. Chem. B
108
, 6850
(2004
).55.
B.
Weber
and F.
Stillinger
, Phys. Rev. B
31
, 1954
(1985
).56.
W.
Kob
and H. C.
Andersen
, Phys. Rev. E
51
, 4626
(1995
).57.
S.
Plimpton
, J. Comput. Phys.
117
, 1
(1995
).58.
A.
Malins
, S. R.
Williams
, J.
Eggers
, and C. P.
Royall
, J. Chem. Phys.
139
, 234506
(2013
).59.
M.
Tanemura
, Y.
Hiwatari
, H.
Matsuda
, T.
Ogawa
, N.
Ogita
, and A.
Ueda
, Prog. Theor. Phys.
58
, 1079
(1977
).60.
L.
Berthier
and G.
Tarjus
, Phys. Rev. Lett.
103
, 170601
(2009
).61.
See http://www-wales.ch.cam.ac.uk/GMIN/ for details and implementations of the GMIN minimization method.
62.
D. J.
Wales
and J. P. K.
Doye
, J. Phys. Chem. A
101
, 5111
(1997
).63.
A. K.
Jain
and R. C.
Dubes
, Algorithms for Clustering Data
(Prentice-Hall, Inc.
, Upper Saddle River, NJ, USA
, 1988
).64.
R.
Richert
and C. A.
Angell
, J. Chem. Phys.
108
, 9016
(1998
).65.
A. C.
Pan
, J. P.
Garrahan
, and D.
Chandler
, Phys. Rev. E
72
, 041106
(2004
).66.
K.
Ito
, C. T.
Moynihan
, and C. A.
Angell
, Nature
398
, 492
(1999
).67.
K. L.
Ngai
and O.
Yamamuro
, J. Chem. Phys.
111
, 10403
(1999
).68.
L.-M.
Martinez
and C. A.
Angell
, Nature
410
, 663
(2001
).69.
D.
Huang
and G. B.
McKenna
, J. Chem. Phys.
114
, 5621
(2001
).70.
T.
Bauer
, P.
Lunkenheimer
, and A.
Loidl
, Phys. Rev. Lett.
111
, 225702
(2013
).71.
D.
Coslovich
and G.
Pastore
, J. Chem. Phys.
127
, 124505
(2007
).72.
R. L.
Jack
, A. J.
Dunleavy
, and C. P.
Royall
, Phys. Rev. Lett.
113
, 095703
(2014
).73.
E. P.
Bernard
and W.
Krauth
, Phys. Rev. Lett.
107
, 155704
(2011
).74.
M.
Engel
, J. A.
Anderson
, S. C.
Glotzer
, M.
Isobe
, E. P.
Bernard
, and W.
Krauth
, Phys. Rev. E
87
, 042134
(2013
).75.
A.
Malins
, S. R.
Williams
, J.
Eggers
, H.
Tanaka
, and C. P.
Royall
, J. Phys.: Condens. Matter
21
, 425103
(2009
).76.
H.
Shintani
and H.
Tanaka
, Nat. Phys.
2
, 200
(2006
).77.
T.
Kawasaki
, T.
Araki
, and H.
Tanaka
, Phys. Rev. Lett.
99
, 215701
(2007
).78.
E.
Sanz
, C.
Valeriani
, E.
Zaccarelli
, W. C. K.
Poon
, P. N.
Pusey
, and M. E.
Cates
, Phys. Rev. Lett.
106
, 215701
(2011
).79.
© 2015 AIP Publishing LLC.
2015
AIP Publishing LLC
You do not currently have access to this content.