Determining the equilibrium structures of nanoalloys by computational methods

  • Riccardo FerrandoEmail author
Part of the following topical collections:
  1. 20th Anniversary Issue: From the editors


Nanoalloys are bi- or multi-metallic nanoparticles with sizes in the range between 1 and 100 nm. They are the subject of intense research activity in the last decades, both in experiments and in theory/modelling. From a theoretical point of view, determining the equilibrium structure of nanoalloys at different temperatures is a quite complex task, which has stimulated the developments of specifically tailored methods and algorithms. Here, we review some recent developments in this field, considering first methods for the global optimization of nanoalloys, and then methods for studying their finite-temperature equilibrium properties.


Nanoalloys Global optimization Thermodynamics 


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Conflict of interests

The author declares that they have no conflict of interest


  1. Akbarzadeh H, Abbaspour M (2016) Investigation of melting and freezing of Ag-Au alloy nanoclusters supported on carbon nanotube using molecular dynamics simulations. J Mol Liq 216:671–682CrossRefGoogle Scholar
  2. Alloyeau D, Ricolleau C, Mottet C, Oikawa T, Langlois C, Le Bouar Y, Braidy N, Loiseau A (2009) Size and shape effects on the order-disorder phase transition in copt nanoparticles. Nat Mater 8:940–946CrossRefGoogle Scholar
  3. Alloyeau D, Mottet C, Ricolleau C (eds) (2012) Nanoalloys–synthesis, structure and properties. Springers, BerlinGoogle Scholar
  4. Asgari M, Behnejad H (2013) Molecular dynamics simulation of the melting process in Ag27Cu13 core-shell nanoalloy. Chem Phys 423:36–42CrossRefGoogle Scholar
  5. Aslan M, Davis JBA, Johnston RL (2016) Global optimization of small bimetallic pd-co binary nanoalloy clusters: a genetic algorithm approach at the DFT level. Phys Chem Chem Phys 18:6676–6682CrossRefGoogle Scholar
  6. Atanasov I, Ferrando R, Johnston RL (2014) Structure and solid solution properties of Cu-Ag nanoalloys. J Phys Condens Matter 26:235701CrossRefGoogle Scholar
  7. Barcaro G, Fortunelli A, Polak M, Rubinovich L (2011) Patchy multishell segregation in pd-pt alloy nanoparticles. Nano Lett 11:1766–1769CrossRefGoogle Scholar
  8. Barcaro G, Sementa L, Fortunelli A (2014) A grouping approach to homotop global optimization in alloy nanoparticles. Phys Chem Chem Phys 16:24256–24265CrossRefGoogle Scholar
  9. Berg BA (2003) Multicanonical simulations step by step. Comput Phys Commun 153(3):397–406CrossRefGoogle Scholar
  10. Bochicchio D, Ferrando R (2010) Size-dependent transition to high-symmetry chiral structures in AgCu, AgCo, AgNi, and AuNi nanoalloys. Nano Lett 10:4211–4216CrossRefGoogle Scholar
  11. Bochicchio D, Ferrando R (2012) Structure and thermal stability of AgCu chiral nanoparticles. Eur Phys J D 66:115CrossRefGoogle Scholar
  12. Bochicchio D, Ferrando R (2013) Morphological instability of core-shell metallic nanoparticles. Phys Rev B 87:165435CrossRefGoogle Scholar
  13. Bochicchio D, Ferrando R, Panizon E, Novakovic R, Rossi G (2014) Chemical ordering in magic-size Ag-Pd nanoparticles. Phys Chem Chem Phys 16:26478–26484CrossRefGoogle Scholar
  14. Bochicchio D, Ferrando R, Panizon E, Rossi G (2016) Structures and segregation patterns of Ag-Cu and Ag-Ni nanoalloys adsorbed on mgo(0 0 1). J Phys Condens Matter 28(6):064005CrossRefGoogle Scholar
  15. Bohra M, Grammatikopoulos P, Singh V, Zhao J, Toulkeridou E, Steinhauer S, Kioseoglou J, JFmc Bobo, Nordlund K, Djurabekova F, Sowwan M (2017) Tuning the onset of ferromagnetism in heterogeneous bimetallic nanoparticles by gas phase doping. Phys Rev Materials 1:066001CrossRefGoogle Scholar
  16. Bonventre D, Panizon E, Ferrando R (2018) Phase separation in AgCu and agni core–shell icosahedral nanoparticles: A harmonic thermodynamics study. Part Part Syst Charact 35:1700425CrossRefGoogle Scholar
  17. Calvo F (2008) Solid-solution precursor to melting in onion-ring Pd-Pt nanoclusters: a case of second-order-like phase change? Fadaray Discuss 138:75CrossRefGoogle Scholar
  18. Calvo F (ed) (2013) Nanoalloys from fundamentals to emergent applications. Elsevier, AmsterdamGoogle Scholar
  19. Calvo F, Wales D (2015) Harmonic superposition method for grand-canonical ensembles. Chem Phys Lett 623:17–21CrossRefGoogle Scholar
  20. Calvo F, Cottancin E, Broyer M (2008) Segregation, core alloying, and shape transitions in bimetallic nanoclusters: Monte carlo simulations. Phys Rev B 77:121406CrossRefGoogle Scholar
  21. Cerbelaud M, Barcaro G, Fortunelli A, Ferrando R (2012) Theoretical study of AuCu nanoalloys adsorbed on mgo(001). Surf Sci 606:938CrossRefGoogle Scholar
  22. Chantry RL, Atanasov I, Siriwatcharapiboon W, Khanal BP, Zubarev ER, Horswell SL, Johnston RL, Li ZY (2013) An atomistic view of the interfacial structures of aurh and aupd nanorods. Nanoscale 5(16):7452–7457CrossRefGoogle Scholar
  23. Cheng D, Huang S, Wang W (2006a) Thermal behavior of core-shell and three-shell layered clusters: Melting of \({\text {Cu}}_{1}{\text {Au}}_{54}\) and \({\text {cu}}_{12}{\text {Au}}_{43}\). Phys Rev B 74:064117CrossRefGoogle Scholar
  24. Cheng DJ, Wang WC, Huang SP (2006b) The onion-ring structure for pdpt bimetallic clusters. J Phys Chem B 110:16193–16196CrossRefGoogle Scholar
  25. Darby S, Mortimer-Jones TV, Johnston RL, Roberts C (2002) Theoretical study of cu-au nanoalloy clusters using a genetic algorithm. J Chem Phys 116:1536CrossRefGoogle Scholar
  26. Delfour L, Creuze J, Legrand B (2009) Exotic behavior of the outer shell of bimetallic nanoalloys. Phys Rev Lett 103:205701CrossRefGoogle Scholar
  27. Dieterich JM, Hartke B (2016) Error-safe, portable, and efficient evolutionary algorithms implementation with high scalability. J Chem Theory Comput 12(10):5226–5233CrossRefGoogle Scholar
  28. Doye JPK, Calvo F (2001) Entropic effects on the size dependence of cluster structure. Phys Rev Lett 86:3570–3573CrossRefGoogle Scholar
  29. Faken D, Jónsson H (1994) Systematic analysis of local atomic structure combined with 3d computer graphics. Comput Mater Sci 2:279–286CrossRefGoogle Scholar
  30. Fan TE, Liu TD, Zheng JW, Shao GF, Wen YH (2016) Structure and stability of fe-pt bimetallic nanoparticles: Initial structure, composition and shape effects. J Alloys Compd 685:1008–1015CrossRefGoogle Scholar
  31. Fan TE, Demiroglu I, Hussein HA, Liu TD, Johnston RL (2017) DFT Study of the structure, chemical ordering and molecular adsorption of pd-ir nanoalloys. Phys Chem Chem Phys 19:27090–27098CrossRefGoogle Scholar
  32. Ferrando R (2015) Symmetry breaking and morphological instabilities in core-shell metallic nanoparticles. J Phys Condens Matter 27:013003CrossRefGoogle Scholar
  33. Ferrando R (2016) Structure and properties of nanoalloys. frontiers of nanoscience, vol 10. Elsevier, AmsterdamGoogle Scholar
  34. Ferrando R, Fortunelli A, Johnston RL (2008a) Searching for the optimum structures of alloy nanoclusters. Phys Chem Chem Phys 10:640–649CrossRefGoogle Scholar
  35. Ferrando R, Jellinek J, Johnston RL (2008b) Nanoalloys: from theory to applications of alloy clusters and nanoparticles. Chem Rev (Washington, DC) 108:845–910CrossRefGoogle Scholar
  36. Frenkel D, Smit B (2002) Understanding molecular simulation from algorithms to applications. Academic Press, CambridgeGoogle Scholar
  37. Goh JQ, Akola J, Ferrando R (2017) Geometric structure, chemical ordering and electronic properties of large AuCu clusters–a computational study. J Phys Chem C 121:10809–10816CrossRefGoogle Scholar
  38. Heard CJ, Johnston RL, Schön JC (2015) Energy landscape exploration of sub-nanometre copper-silver clusters. ChemPhysChem 15:1461–1469CrossRefGoogle Scholar
  39. Heiles S, Johnston RL (2013) Global optimization of clusters using electronic structure methods. Int J Quantum Chem 113:2091–2109CrossRefGoogle Scholar
  40. Heiles S, Logsdail AJ, Schafer R, Johnston RL (2012) Dopant-induced 2d-3d transition in small au-containing clusters: DFT-global optimisation of 8-atom au-ag nanoalloys. Nanoscale 4:1109–1115CrossRefGoogle Scholar
  41. Jellinek J, Krissinel EB (1996) Nina1m alloy clusters: analysis of structural forms and their energy ordering. Chem Phys Lett 258:283–292CrossRefGoogle Scholar
  42. Johnston RL (2003) Evolving better nanoparticles: genetic algorithms for optimising cluster geometries. Dalton Trans 2003:4193CrossRefGoogle Scholar
  43. Kennedy J, Eberhart R (1995) Theoretical surface science and catalysis—calculations and concepts. In: International conference on neural networks, 1995. Proceedings, IEEEGoogle Scholar
  44. Kovács G, Kozlov SM, Neyman KM (2017) Versatile optimization of chemical ordering in bimetallic nanoparticles. J Phys Chem C 121(20):10803–10808CrossRefGoogle Scholar
  45. Kozlov SM, Kovács G, Ferrando R, Neyman KM (2015) How to determine accurate chemical ordering in several nanometer large bimetallic crystallites from electronic structure calculations. Chem Sci 6:3868–3880CrossRefGoogle Scholar
  46. Krissinel EB, Jellinek J (1997) 13-atom Ni-Al alloy clusters: structures and dynamics. Int J Quantum Chem 62:185–197CrossRefGoogle Scholar
  47. Kuntová Z, Rossi G, Ferrando R (2008) Melting of core-shell ag-ni and ag-co nanoclusters studied via molecular dynamics simulations. Phys Rev B 77:205431CrossRefGoogle Scholar
  48. Laasonen K, Panizon E, Bochicchio D, Ferrando R (2013) Competition between icosahedral motifs in AgCu, agni, and agco nanoalloys: a combined atomistic-dft study. J Phys Chem C 117:26405–26413CrossRefGoogle Scholar
  49. Lai X, Xu R, Huang W (2011) Geometry optimization of bimetallic clusters using an efficient heuristic method. J Chem Phys 135(16):164109CrossRefGoogle Scholar
  50. Lazauskas T, Sokol AA, Woodley SM (2017) An efficient genetic algorithm for structure prediction at the nanoscale. Nanoscale 9:3850–3864CrossRefGoogle Scholar
  51. Leary RH (2000) Global optimization on funneling landscapes. J Glob Optim 18(4):367–383CrossRefGoogle Scholar
  52. Lequien F, Creuze J, Berthier F, Legrand B (2006) Superficial segregation in nanoparticles: from facets to infinite surfaces. J Chem Phys 094707:125Google Scholar
  53. Lequien F, Creuze J, Berthier F, Braems I, Legrand B (2008) Superficial segregation, wetting, and dynamical equilibrium in bimetallic clusters: a monte carlo study. Phys Rev B 78:075414CrossRefGoogle Scholar
  54. Li Z, Scheraga HA (1987) Monte-carlo-minimization approach to the multiple-minima problem in protein folding. Proc Natl Acad Sci USA 84:6611–6615CrossRefGoogle Scholar
  55. Liao TW, Yadav A, Hu KJ, van der Tol J, Cosentino S, D’Acapito F, Palmer RE, Lenardi C, Ferrando R, Grandjean D, Lievens P (2018) Unravelling the nucleation mechanism of bimetallic nanoparticles with composition-tunable core-shell arrangement. Nanoscale 10:6684–6694CrossRefGoogle Scholar
  56. Lv J, Wang Y, Zhu L, Ma Y (2012) Particle-swarm structure prediction on clusters. J Chem Phys 137(8):084104CrossRefGoogle Scholar
  57. Lysgaard S, Myrdal JSG, Hansen HA, Vegge T (2015) A dft-based genetic algorithm search for AuCu nanoalloy electrocatalysts for co2 reduction. Phys Chem Chem Phys 17:28270–28276CrossRefGoogle Scholar
  58. Marques J, Pereira F (2010) An evolutionary algorithm for global minimum search of binary atomic clusters. Chem Phys Lett 485(1–3):211–216CrossRefGoogle Scholar
  59. Mottet C, Tréglia G, Legrand B (1997) New magic numbers in metallic clusters: an unexpected metal dependence. Surf Sci 383:L719–L727CrossRefGoogle Scholar
  60. Mottet C, Rossi G, Baletto F, Ferrando R (2005) Single impurity effect on the melting of nanoclusters. Phys Rev Lett 95:035501CrossRefGoogle Scholar
  61. Müller M, Albe K (2005) Lattice monte carlo simulations of fept nanoparticles: influence of size, composition, and surface segregation on order-disorder phenomena. Phys Rev B 72:094203CrossRefGoogle Scholar
  62. Negreiros FR, Barcaro G, Kuntová Z, Rossi G, Ferrando R, Fortunelli A (2011) Structures of AgPd nanoclusters adsorbed on mgo(100): a computational study. J Chem Phys 605:483–488Google Scholar
  63. Negreiros FR, Sementa L, Barcaro G, Vajda S, Aprà E, Fortunelli A (2012) Co oxidation by subnanometer AgxAu3−x supported clusters via density functional theory simulations. ACS Catal 2:1860–1864CrossRefGoogle Scholar
  64. Oderji HY, Behnejad H, Ferrando R, Ding H (2013) System-dependent melting behavior of icosahedral anti-mackay nanoalloys. RSC Adv 3:21981–21993CrossRefGoogle Scholar
  65. Paiva MAM, Peluzo BMTC, Belchior JC, Galvao BRL (2016) Structure and stability of neutral Al-Mg nanoclusters up to 55 atoms. Phys Chem Chem Phys 18:31579–31585CrossRefGoogle Scholar
  66. Palomares-Baez JP, Panizon E, Ferrando R (2017) Nanoscale effects on phase separation. Nano Lett 17(9):5394–5401CrossRefGoogle Scholar
  67. Panizon E, Ferrando R (2015) Solid-solid transitions in Pd-Pt nanoalloys. Phys Rev B 92:205417CrossRefGoogle Scholar
  68. Panizon E, Ferrando R (2016) Strain-induced restructuring of the surface in core@shell nanoalloys. Nanoscale 8:15911–15919CrossRefGoogle Scholar
  69. Polak M, Rubinovich L (2014) Stabilization and transformation of asymmetric configurations in small-mismatch alloy nanoparticles: the role of coordination dependent energetics. Phys Chem Chem Phys 16:1569–1575CrossRefGoogle Scholar
  70. Rambukwella M, Chang L, Ravishanker A, Fortunelli A, Stener M, Dass A (2018) Au36(seph)24 nanomolecules: synthesis, optical spectroscopy and theoretical analysis. Phys Chem Chem Phys 20:13255–13262CrossRefGoogle Scholar
  71. Rapallo A, Rossi G, Ferrando R, Fortunelli A, Curley BC, Lloyd LD, Tarbuck GM, Johnston RL (2005) Global optimization of bimetallic cluster structures. I. size-mismatched Ag-Cu, Ag-Ni, and Au-Cu systems. J Chem Phys 122:194308CrossRefGoogle Scholar
  72. Rapallo A, Olmos-Asar JA, Oviedo OA, Luduena M, Ferrando R, Mariscal MM (2012) Thermal properties of Co/Au nanoalloys and comparison of different computer simulation techniques. J Phys Chem C 116:17210–17218CrossRefGoogle Scholar
  73. Rondina GG, Da Silva JLF (2013) Revised basin-hopping monte carlo algorithm for structure optimization of clusters and nanoparticles. J Chem Inf Model 53:2282–2298CrossRefGoogle Scholar
  74. Rossi G, Ferrando R (2006) Global optimization by excitable walkers. Chem Phys Lett 423:17–22CrossRefGoogle Scholar
  75. Rossi G, Ferrando R (2007) Freezing of gold nanoclusters into poly-decahedral structures. Nanotechnology 18:225706CrossRefGoogle Scholar
  76. Rossi G, Ferrando R (2009) Searching for low-energy structures of nanoparticles: a comparison of different methods and algorithms. J Phys Cond Mat 21:084208CrossRefGoogle Scholar
  77. Rossi G, Ferrando R (2017) Combining shape-changing with exchange moves in the optimization of nanoalloys. Comput Theor Chem 1107:66–73CrossRefGoogle Scholar
  78. Rossi G, Rapallo A, Mottet C, Fortunelli A, Baletto F, Ferrando R (2004) Magic polyicosahedral core-shell clusters. Phys Rev Lett 93:105503CrossRefGoogle Scholar
  79. Rossi G, Ferrando R, Rapallo A, Fortunelli A, Curley BC, Lloyd LD, Johnston RL (2005) Global optimization of bimetallic cluster structures. I. Size-matched Ag-Pd, Ag-Au, and Pd-Pt systems. J Chem Phys 122:194309CrossRefGoogle Scholar
  80. Rossi G, Ferrando R, Mottet C (2008) Structure and chemical ordering in CoPt nanoalloys. Faraday Discuss 138:193CrossRefGoogle Scholar
  81. Rubinovich L, Haftel MI, Bernstein N, Polak M (2006) Compositional structures and thermodynamic properties of Pd-Cu, Rh-Pd, and Rh-Pd-Cu nanoclusters computed by a combined free-energy concentration expansion method and tight-binding approach. Phys Rev B 74:035405CrossRefGoogle Scholar
  82. Schebarchov D, Wales DJ (2013) Communication: a new paradigm for structure prediction in multicomponent systems. J Chem Phys 139:221101CrossRefGoogle Scholar
  83. Schebarchov D, Wales DJ (2014) Structure prediction for multicomponent materials using biminima. Phys Rev Lett 113:156102CrossRefGoogle Scholar
  84. Schebarchov D, Wales DJ (2015) Quasi-combinatorial energy landscapes for nanoalloy structure optimisation. Phys Chem Chem Phys 17:28331–28338CrossRefGoogle Scholar
  85. Shao GF, Wang TN, Liu TD, Chen JR, Zheng JW, Wen YH (2015) Structural optimization of Pt-Pd alloy nanoparticles using an improved discrete particle swarm optimization algorithm. Comput Phys Commun 186:11–18CrossRefGoogle Scholar
  86. Shao GF, Zhu M, Shangguan YL, Li WR, Zhang C, Wang WW, Li L (2017) Structural optimization of Au-Pd bimetallic nanoparticles with improved particle swarm optimization method. Chin Phys B 26:063601CrossRefGoogle Scholar
  87. Shayeghi A, Goetz D, Davis JBA, Schafer R, Johnston RL (2015) Pool-bcga: a parallelised generation-free genetic algorithm for the ab initio global optimisation of nanoalloy clusters. Phys Chem Chem Phys 17:2104–2112CrossRefGoogle Scholar
  88. Shukla R, Ray D, Sarkar K, Kumar Dixit M, Prasad Bhattacharyya S (2017) Flying onto global minima on potential energy surfaces: a swarm intelligence guided route to molecular electronic structure. Int J Quantum Chem 117(5):e25328–n/aCrossRefGoogle Scholar
  89. Stillinger FH (1999) Exponential multiplicity of inherent structures. Phys Rev E 59:48CrossRefGoogle Scholar
  90. Stillinger FH, Weber TA (1982) Hidden structure in liquids. Phys Rev A 25:978CrossRefGoogle Scholar
  91. Stillinger FH, Weber TA (1984) Packing structures and transitions in liquids and solids. Science 225:983–989CrossRefGoogle Scholar
  92. Taherkhani F, Akbarzadeh H, Rezania H (2014) Chemical ordering effect on melting temperature, surface energy of copper-gold bimetallic nanocluster. J Alloys Compd 617:746–750CrossRefGoogle Scholar
  93. Trebst S, Huse DA, Troyer M (2004) Optimizing the ensemble for equilibration in broad-histogram monte carlo simulations. Phys Rev E 70:046701CrossRefGoogle Scholar
  94. Wales DJ (2003) Energy landscapes. Cambridge University Press, CambridgeGoogle Scholar
  95. Wales DJ, Doye JPK (1997) Global optimization by basin-hopping and the lowest energy structures of Lennard-Jones clusters containing up to 110 atoms. J Phys Chem A 101:5111–5116CrossRefGoogle Scholar
  96. Wang LL, Tan TL, Johnson DD (2014) Configurational thermodynamics of alloyed nanoparticles with adsorbates. Nano Lett 14(12):7077–7084CrossRefGoogle Scholar
  97. Wang Y, Hou M (2012) Ordering of bimetallic nanoalloys predicted from bulk alloy phase diagrams. J Phys Chem C 116:10814CrossRefGoogle Scholar
  98. Wolfbeisser A, Kovács G, Kozlov SM, Föttinger K, Bernardi J, Klötzer B, Neyman KM, Rupprechter G (2017) Surface composition changes of CuNi-ZrO2 during methane decomposition: an operando NAP-XPS and density functional study. Catal Today 283:134–143CrossRefGoogle Scholar
  99. Yang Y, Zhao Z, Cui R, Wu H, Cheng D (2015) Structures, thermal stability, and chemical activity of crown-jewel-structured Pd-Pt nanoalloys. J Phys Chem C 119(20):10888–10895CrossRefGoogle Scholar
  100. Zanvettor C, Marques J (2014) On the lowest-energy structure of binary Zn-Cd nanoparticles: size and composition. Chem Phys Lett 608:373–379CrossRefGoogle Scholar
  101. Zhao J, Shi R, Sai L, Huang X, Su Y (2016) Comprehensive genetic algorithm for ab initio global optimisation of clusters. Mol Simul 42(10):809–819CrossRefGoogle Scholar

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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Chemistry and Industrial Chemistry DepartmentUniversity of GenoaGenoaItaly

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