Atomistic understanding of thermodynamic processes such as phase transitions in nanoalloys is crucial to improve real-life applications of Pt-based nanocatalysts. In this work, we investigate the thermodynamic properties of 55-atom PtCo and PtNi nanoalloys and compare them to reference unary systems, Pt55, Co55, and Ni55. Our results are based on the combination of the parallel tempering Monte Carlo and the revised basin-hopping Monte Carlo algorithms with many-body Gupta potentials, and furthermore, density functional theory calculations were employed to validate the adopted Gupta parameters and to analyze electronic effects induced by structural changes derived from temperature effects. We identified first-order phase transitions for Pt55, Co55, Pt30Co25, Ni55, and Pt40Ni15 at 727, 1027, 1003, 914, and 1051 K, respectively. Thus, alloying unary Pt nanoclusters with Ni and Co leads to an increase in the melting temperature, indicating that the nanoalloys are able to sustain higher temperatures while maintaining their structure. A low-temperature solid-solid transition was also identified for Pt55, which is characterized by a change from a face-centered cubic like structure (putative global minimum configuration) to the icosahedron structure. The structural transformations led by the temperature increase induce small changes on the total density of states, namely, a slight shift of the d-band center toward the highest occupied molecular orbital with increasing temperature, which was found for all considered nanoclusters.

1.
D.
Alloyeau
,
C.
Ricolleau
,
C.
Mottet
,
T.
Oikawa
,
C.
Langlois
,
Y.
Le Bouar
,
N.
Braidy
, and
A.
Loiseau
, “
Size and shape effects on the order-disorder phase transition in CoPt nanoparticles
,”
Nat. Mater.
8
,
940
946
(
2009
).
2.
G.
Barcaro
,
A.
Fortunelli
,
M.
Polak
, and
L.
Rubinovich
, “
Patchy multishell segregation in Pd–Pt alloy nanoparticles
,”
Nano Lett.
11
,
1766
1769
(
2011
).
3.
F. H.
Kaatz
and
A.
Bultheel
, “
Size, shape, and compositional effects on the order-disorder phase transitions in Au-Cu and Pt-M (M = Fe, Co, and Ni) nanocluster alloys
,”
Nanotechnology
29
,
345701
(
2018
).
4.
R.
Ferrando
,
J.
Jellinek
, and
R. L.
Johnston
, “
Nanoalloys: From theory to applications of alloy clusters and nanoparticles
,”
Chem. Rev.
108
,
845
910
(
2008
).
5.
R.
Ferrando
,
Structure and Properties of Nanoalloys
(
Elsevier
,
2016
), p.
352
.
6.
W.
Yu
,
M. D.
Porosoff
, and
J. G.
Chen
, “
Review of Pt-based bimetallic catalysis: From model surfaces to supported catalysts
,”
Chem. Rev.
112
,
5780
5817
(
2012
).
7.
M. J.
Piotrowski
,
P.
Piquini
, and
J. L. F.
Da Silva
, “
Platinum-based nanoalloys PtnTM55−n (TM = Co, Rh, Au): A density functional theory investigation
,”
J. Phys. Chem. C
116
,
18432
18439
(
2012
).
8.
D.
Guedes-Sobrinho
,
R. K.
Nomiyama
,
A. S.
Chaves
,
M. J.
Piotrowski
, and
J. L. F.
Da Silva
, “
Structure, electronic, and magnetic properties of binary PtnTM55−n (TM = Fe, Co, Ni, Cu, Zn) nanoclusters: A density functional theory investigation
,”
J. Phys. Chem. C
119
,
15669
15679
(
2015
).
9.
R.
Ferrando
, “
Determining the equilibrium structures of nanoalloys by computational methods
,”
J. Nanopart. Res.
20
,
179
(
2018
).
10.
K.
Rossi
,
L.
Bartok-Pártay
,
G.
Csányi
, and
F.
Baletto
, “
Thermodynamics of CuPt nanoalloys
,”
Sci. Rep.
8
,
9150
(
2018
).
11.
K.
Hukushima
and
K.
Nemoto
, “
Exchange Monte Carlo method and application to spin glass simulations
,”
J. Phys. Soc. Jpn.
65
,
1604
1608
(
1996
).
12.
P. A.
Frantsuzov
and
V. A.
Mandelshtam
, “
Size-temperature phase diagram for small Lennard-Jones clusters
,”
Phys. Rev. E
72
,
037102
(
2005
).
13.
V. A.
Mandelshtam
and
P. A.
Frantsuzov
, “
Multiple structural transformations in Lennard-Jones clusters: Generic versus size-specific behavior
,”
J. Chem. Phys.
124
,
204511
(
2006
).
14.
H. M.
Cezar
,
G. G.
Rondina
, and
J. L. F.
Da Silva
, “
Parallel tempering Monte Carlo combined with clustering Euclidean metric analysis to study the thermodynamic stability of Lennard-Jones nanoclusters
,”
J. Chem. Phys.
146
,
064114
(
2017
).
15.
G.
Wang
,
M. A.
van Hove
,
P. N.
Ross
, and
M. I.
Baskes
, “
Monte Carlo simulations of segregation in Pt-Re catalyst nanoparticles
,”
J. Chem. Phys.
121
,
5410
(
2004
).
16.
F.
Calvo
, “
Solid-solution precursor to melting in onion-ring Pd-Pt nanoclusters: A case of second-order-like phase change?
,”
Faraday Discuss.
138
,
75
88
(
2008
).
17.
F.
Calvo
,
E.
Cottancin
, and
M.
Broyer
, “
Segregation, core alloying, and shape transitions in bimetallic nanoclusters: Monte Carlo simulations
,”
Phys. Rev. B
77
,
121406
(
2008
).
18.
F.
Calvo
and
C.
Mottet
, “
Order-disorder transition in Co-Pt nanoparticles: Coexistence, transition states, and finite-size effects
,”
Phys. Rev. B
84
,
035409
(
2011
).
19.
L.
Delfour
,
J.
Creuze
, and
B.
Legrand
, “
Exotic behavior of the outer shell of bimetallic nanoalloys
,”
Phys. Rev. Lett.
103
,
205701
(
2009
).
20.
Y.
Wang
and
M.
Hou
, “
Ordering of bimetallic nanoalloys predicted from bulk alloy phase diagrams
,”
J. Phys. Chem. C
116
,
10814
10818
(
2012
).
21.
I.
Atanasov
,
R.
Ferrando
, and
R. L.
Johnston
, “
Structure and solid solution properties of Cu-Ag nanoalloys
,”
J. Phys.: Condens. Matter
26
,
275301
(
2014
).
22.
G.
Rossi
,
A.
Rapallo
,
C.
Mottet
,
A.
Fortunelli
,
F.
Baletto
, and
R.
Ferrando
, “
Magic polyicosahedral core-shell clusters
,”
Phys. Rev. Lett.
93
,
105503
(
2004
).
23.
C.
Mottet
,
G.
Rossi
,
F.
Baletto
, and
R.
Ferrando
, “
Single impurity effect on the melting of nanoclusters
,”
Phys. Rev. Lett.
95
,
035501
(
2005
).
24.
A.
Rapallo
,
J. A.
Olmos-Asar
,
O. A.
Oviedo
,
M.
Ludueña
,
R.
Ferrando
, and
M. M.
Mariscal
, “
Thermal properties of Co/Au nanoalloys and comparison of different computer simulation techniques
,”
J. Phys. Chem. C
116
,
17210
17218
(
2012
).
25.
F.
Taherkhani
,
H.
Akbarzadeh
, and
H.
Rezania
, “
Chemical ordering effect on melting temperature, surface energy of copper-gold bimetallic nanocluster
,”
J. Alloys Compd.
617
,
746
750
(
2014
).
26.
H.
Akbarzadeh
and
M.
Abbaspour
, “
Investigation of melting and freezing of Ag-Au alloy nanoclusters supported on carbon nanotube using molecular dynamics simulations
,”
J. Mol. Liq.
216
,
671
682
(
2016
).
27.
M.
Lingenheil
,
R.
Denschlag
,
G.
Mathias
, and
P.
Tavan
, “
Efficiency of exchange schemes in replica exchange
,”
Chem. Phys. Lett.
478
,
80
84
(
2009
).
28.
T.
Okabe
,
M.
Kawata
,
Y.
Okamoto
, and
M.
Mikami
, “
Replica-exchange Monte Carlo method for the isobaric-isothermal ensemble
,”
Chem. Phys. Lett.
335
,
435
439
(
2001
).
29.
J. K.
Lee
,
J. A.
Barker
, and
F. F.
Abraham
, “
Theory and Monte Carlo simulation of physical clusters in the imperfect vapor
,”
J. Chem. Phys.
58
,
3166
3180
(
1973
).
30.
J. P.
Neirotti
,
F.
Calvo
,
D. L.
Freeman
, and
J. D.
Doll
, “
Phase changes in 38-atom Lennard-Jones clusters. I. A parallel tempering study in the canonical ensemble
,”
J. Chem. Phys.
112
,
10340
10349
(
2000
).
31.
D.
Sabo
,
D. L.
Freeman
, and
J. D.
Doll
, “
Pressure dependent study of the solid-solid phase change in 38-atom Lennard-Jones cluster
,”
J. Chem. Phys.
122
,
094716
(
2005
).
32.
R. H.
Swendsen
, “
How the maximum step size in Monte Carlo simulations should be adjusted
,”
Phys. Procedia
15
,
81
86
(
2011
).
33.
G. G.
Rondina
and
J. L. F.
Da Silva
, “
Revised basin-hopping Monte Carlo algorithm for structure optimization of clusters and nanoparticles
,”
J. Chem. Inf. Model.
53
,
2282
2298
(
2013
).
34.
D. J.
Wales
and
J. P. K.
Doye
, “
Global optimization by Basin-Hopping and the lowest energy structures of Lennard-Jones clusters containing up to 110 atoms
,”
J. Phys. Chem. A
101
,
5111
5116
(
1997
).
35.
D. J.
Wales
and
T. V.
Bogdan
, “
Potential energy and free energy landscapes
,”
J. Phys. Chem. B
110
,
20765
20776
(
2006
).
36.
N.
Metropolis
,
A. W.
Rosenbluth
,
M. N.
Rosenbluth
,
A. H.
Teller
, and
E.
Teller
, “
Equation of state calculations by fast computing machines
,”
J. Chem. Phys.
21
,
1087
1092
(
1953
).
37.
J. R.
Shewchuk
,
An Introduction to the Conjugate Gradient Method Without the Agonizing Pain
(
School of Computer Science, Carnegie Mellon University, Pittsburgh, PA
,
1994
).
38.
R. P.
White
and
H. R.
Mayne
, “
An investigation of two approaches to basin hopping minimization for atomic and molecular clusters
,”
Chem. Phys. Lett.
289
,
463
468
(
1998
).
39.
H. G.
Kim
,
S. K.
Choi
, and
H. M.
Lee
, “
New algorithm in the basin hopping Monte Carlo to find the global minimum structure of unary and binary metallic nanoclusters
,”
J. Chem. Phys.
128
,
144702
(
2008
).
40.
R. L.
Johnston
, “
Evolving better nanoparticles: Genetic algorithms for optimising cluster geometries
,”
Dalton Trans.
2003
,
4193
4207
.
41.
D.
Bochicchio
and
R.
Ferrando
, “
Size-dependent transition to high-symmetry chiral structures in AgCu, AgCo, AgNi, and AuNi nanoalloys
,”
Nano Lett.
10
,
4211
4216
(
2010
).
42.
T.
Ye
,
R.
Xu
, and
W.
Huang
, “
Global optimization of binary Lennard-Jones clusters using three perturbation operators
,”
J. Chem. Inf. Model.
51
,
572
577
(
2011
).
43.
F.
Cleri
and
V.
Rosato
, “
Tight-binding potentials for transition metals and alloys
,”
Phys. Rev. B
48
,
22
33
(
1993
).
44.
K.
Michaelian
,
N.
Rendón
, and
I. L.
Garzón
, “
Structure and energetics of Ni, Ag, and Au nanoclusters
,”
Phys. Rev. B
60
,
2000
2010
(
1999
).
45.
D. J.
Borbón-González
,
A.
Fortunelli
,
G.
Barcaro
,
L.
Sementa
,
R. L.
Johnston
, and
A.
Posada-Amarillas
, “
Global minimum Pt13M20 (M = Ag, Au, Cu, Pd) dodecahedral core-shell clusters
,”
J. Phys. Chem. A
117
,
14261
14266
(
2013
).
46.
E.
Panizon
and
R.
Ferrando
, “
Solid-solid transitions in Pd-Pt nanoalloys
,”
Phys. Rev. B
92
,
205417
(
2015
).
47.
K.
Laasonen
,
E.
Panizon
,
D.
Bochicchio
, and
R.
Ferrando
, “
Competition between icosahedral motifs in AgCu, AgNi, and AgCo nanoalloys: A combined atomistic–DFT study
,”
J. Phys. Chem. C
117
,
26405
26413
(
2013
).
48.
G.
Rossi
,
R.
Ferrando
, and
C.
Mottet
, “
Structure and chemical ordering in CoPt nanoalloys
,”
Faraday Discuss.
138
,
193
210
(
2008
).
49.
C.
Goyhenex
,
H.
Bulou
,
J.-P.
Deville
, and
G.
Tréglia
, “
Pt/Co(0001) superstructures in the submonolayer range: A tight-binding quenched-molecular-dynamics study
,”
Phys. Rev. B
60
,
2781
2788
(
1999
).
50.
P.
Andreazza
,
C.
Mottet
,
C.
Andreazza-Vignolle
,
J.
Penuelas
,
H. C.
Tolentino
,
M.
De Santis
,
R.
Felici
, and
N.
Bouet
, “
Probing nanoscale structural and order/disorder phase transitions of supported Co-Pt clusters under annealing
,”
Phys. Rev. B
82
,
155453
(
2010
).
51.
J. P.
Perdew
,
K.
Burke
, and
M.
Ernzerhof
, “
Generalized gradient approximation made simple
,”
Phys. Rev. Lett.
77
,
3865
3868
(
1996
).
52.
V.
Blum
,
R.
Gehrke
,
F.
Hanke
,
P.
Havu
,
V.
Havu
,
X.
Ren
,
K.
Reuter
, and
M.
Scheffler
, “
Ab initio molecular simulations with numeric atom-centered orbitals
,”
Comput. Phys. Commun.
180
,
2175
2196
(
2009
).
53.
R.
Gehrke
and
K.
Reuter
, “
Assessing the efficiency of first-principles basin-hopping sampling
,”
Phys. Rev. B
79
,
085412
(
2009
).
54.
J. A.
Hartigan
,
Clustering Algorithms
, 1st ed. (
John Wiley & Sons
,
New York, NY, USA
,
1975
).
55.
W.
Kabsch
, “
A solution for the best rotation to relate two sets of vectors
,”
Acta Crystallogr., Sect. A: Found. Adv.
32
,
922
923
(
1976
).
56.
H. W.
Kuhn
, “
The Hungarian method for the assignment problem
,”
Naval Res. Logist. Q.
2
,
83
97
(
1955
).
57.
R.
Hoppe
, “
The coordination number—An “Tnorganic chameleon”
,”
Angew. Chem., Int. Ed.
9
,
25
34
(
1970
).
58.
R.
Hoppe
, “
Effective coordination numbers (ECoN) and mean active fictive ionic radii (MEFIR)
,”
Z. Kristallogr.
150
,
23
52
(
1979
).
59.
J. L. F.
Da Silva
, “
Effective coordination concept applied for phase change (GeTe)m(Sb2Te3)n compounds
,”
J. Appl. Phys.
109
,
023502
(
2011
).
60.
B.
Hammer
and
J. K.
Nørskov
, “
Why gold is the noblest of all the metals
,”
Nature
376
,
238
240
(
1995
).

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