Abstract
Nanostructured materials exhibit remarkable properties significantly different from their bulk counterparts. Metal alloys at the nanoscale show an impressive potential to produce new systems having well-designed functionalities. By using a nanothermodynamic approach, here, we present the effects of the size and shape of the nanoparticles (NPs) on the phase diagrams (PDs) of the Mo-M (M = Nb, Ta, and W) alloys. A well-known group of morphologies at 50, 20, and 10 nm in diameter was considered, which are as follows: tetrahedron, cube, octahedron, decahedron, dodecahedron, cuboctahedron, rhombic dodecahedron, sphere, icosahedron, and truncated octahedron. From an examination of the liquidus and solidus curves, we calculated the expansion or contraction of the coexistence solid-liquid region of the PDs and how these changes are related to the size and shape of the NPs. Through a detailed Gibbs free energy (GFE) analysis, we also determined the thermal stability of the three Mo-based nanoalloys as a function of the size (10–50 nm) of the mentioned polyhedra, by fixing the temperature and the chemical composition. Finally, the surface segregated element was predicted in each bimetallic system.
Graphical abstract
Similar content being viewed by others
Abbreviations
- NP:
-
Nanoparticle
- PD:
-
Phase diagram
- GFE:
-
Gibbs free energy
- MD:
-
Molecular dynamics
References
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 8:940–946
Andrews MP, O’Brien SC (1992) Gas-phase “molecular alloys” of bulk immiscible elements: iron-silver (FexAgy). J Phys Chem 96:8233–8241. https://doi.org/10.1021/j100200a007
Ashcroft NW, Mermin ND (1976) Solid state physics. Brooks/Cole, Cengage Learning
Atanasov I, Ferrando R, Johnston RL (2014) Structure and solid solution properties of Cu–Ag nanoalloys. J Phys Condens Matter 26:275301. https://doi.org/10.1088/0953-8984/26/27/275301
Baccolo G (2015) Tantalizing tantalum. Nat Chem 7:854. https://doi.org/10.1038/nchem.2350
Calvo F (2015) Thermodynamics of nanoalloys. Phys Chem Chem Phys 17:27922–27939. https://doi.org/10.1039/C5CP00274E
Che C, Xu H, Wen H, Gou G, Cheng D (2019) Theoretical study on the structural, thermal and phase stability of Pt–Cu alloy clusters. J Clust Sci 31:615–626. https://doi.org/10.1007/s10876-019-01753-y
Chen CBC, Rossi G, Johnston RL (2007) Structure, melting, and thermal stability of 55 atom Ag−Au nanoalloys. J Phys Chem C 111:9157–9165. https://doi.org/10.1021/jp0717746
Chepkasov IV, Gafner YY, Vysotin MA, Redel’ L V. (2017) A study of melting of various types of Pt–Pd nanoparticles. Phys Solid State 59:2076–2081. https://doi.org/10.1134/S1063783417100109
Chepulskii RV, Curtarolo S (2011) Ab initio insights on the shapes of platinum nanocatalysts. ACS Nano 5:247–254. https://doi.org/10.1021/nn102570c
Cho SJ, Kang SK (2004) Structural transformation of PdPt nanoparticles probed with X-ray absorption near edge structure. Catal Today 93–95:561–566
Christensen A, Stoltze P, Norskov JK (1995) Size dependence of phase separation in small bimetallic clusters. J Phys Condens Matter 7:1047–1057. https://doi.org/10.1088/0953-8984/7/6/008
Cobelo-García A, Filella M, Croot P, Frazzoli C, du Laing G, Ospina-Alvarez N, Rauch S, Salaun P, Schäfer J, Zimmermann S (2015) COST action TD1407: network on technology-critical elements (NOTICE)—from environmental processes to human health threats. Environ Sci Pollut Res 22:15188–15194. https://doi.org/10.1007/s11356-015-5221-0
Darling KA, Rajagopalan M, Komarasamy M, Bhatia MA, Hornbuckle BC, Mishra RS, Solanki KN (2016) Extreme creep resistance in a microstructurally stable nanocrystalline alloy. Nature 537:378–381. https://doi.org/10.1038/nature19313
Fedoseev VB, Shishulin AV (2018) Shape effect in layering of solid solutions in small volume: bismuth–antimony alloy. Phys Solid State 60:1398–1404. https://doi.org/10.1134/S1063783418070120
Ferrando R, Jellinek J, Johnston RL (2008) Nanoalloys: from theory to applications of alloy clusters and nanoparticles. Chem Rev 108:845–910. https://doi.org/10.1021/cr040090g
Foster DM, Pavloudis T, Kioseoglou J, Palmer RE (2019) Atomic-resolution imaging of surface and core melting in individual size-selected Au nanoclusters on carbon. Nat Commun 10:2583. https://doi.org/10.1038/s41467-019-10713-z
Franke P, Neuschütz D (2006) Binary systems. Part 4: binary systems from Mn-Mo to Y-Zr. Springer-Verlag Berlin Heidelberg. https://doi.org/10.1007/b76778
Freeman Y (2018) Tantalum and niobium-based capacitors : science, technology, and applications. Springer International Publising, Switzerland
Frisk K, Gustafson P (1988) An assessment of the Cr-Mo-W system. Calphad 12:247–254. https://doi.org/10.1016/0364-5916(88)90004-1
Goya P, Martín N, Román P (2011) W for tungsten and wolfram. Nat Chem 3:336. https://doi.org/10.1038/nchem.1014
Guenther G, Guillon O (2014) Models of size-dependent nanoparticle melting tested on gold. J Mater Sci 49:7915–7932. https://doi.org/10.1007/s10853-014-8544-1
Guisbiers G (2019) Advances in thermodynamic modelling of nanoparticles. Adv Phys X 4:1668299. https://doi.org/10.1080/23746149.2019.1668299
Guisbiers G, Buchaillot L (2009a) Modeling the melting enthalpy of nanomaterials. J Phys Chem C 113:3566–3568. https://doi.org/10.1021/jp809338t
Guisbiers G, Buchaillot L (2009b) Universal size/shape-dependent law for characteristic temperatures. Phys Lett A 374:305–308. https://doi.org/10.1016/j.physleta.2009.10.054
Guisbiers G, José-Yacaman M (2018) Use of chemical functionalities to control stability of nanoparticles. In: Wandelt K (ed) Encyclopedia of interfacial chemistry. Elsevier, pp 875–885
Guisbiers G, Mejia-Rosales S, Khanal S, Ruiz-Zepeda F, Whetten RL, José-Yacaman M (2014) Gold–copper nano-alloy, “tumbaga”, in the era of nano: phase diagram and segregation. Nano Lett 14:6718–6726. https://doi.org/10.1021/nl503584q
Guisbiers G, Mendoza-Cruz R, Bazán-Díaz L, Velázquez-Salazar JJ, Mendoza-Perez R, Robledo-Torres JA, Rodriguez-Lopez JL, Montejano-Carrizales JM, Whetten RL, José-Yacamán M (2016) Electrum, the gold-silver alloy, from the bulk scale to the nanoscale: synthesis, properties, and segregation rules. ACS Nano 10:188–198. https://doi.org/10.1021/acsnano.5b05755
Guisbiers G, Mendoza-Pérez R, Bazán-Díaz L, Mendoza-Cruz R, Velázquez-Salazar JJ, José-Yacamán M (2017) Size and shape effects on the phase diagrams of nickel-based bimetallic nanoalloys. J Phys Chem C 121:6930–6939. https://doi.org/10.1021/acs.jpcc.6b09115
Halperin WP (1986) Quantum size effects in metal particles. Rev Mod Phys 58:533–606. https://doi.org/10.1103/RevModPhys.58.533
Hamilton JC (1979) Prediction of surface segregation in binary alloys using bulk alloy variables. Phys Rev Lett 42:989–992. https://doi.org/10.1103/PhysRevLett.42.989
Haynes WM, Lide DR, Bruno TJ (2013) CRC handbook of chemistry and physics: a ready-reference book of chemical and physical data, 97th edn. CRC Press, Boca Raton
Hill TL (2001a) A different approach to nanothermodynamics. Nano Lett 1:273–275. https://doi.org/10.1021/nl010027w
Hill TL (2001b) Perspective: nanothermodynamics. Nano Lett 1:111–112. https://doi.org/10.1021/nl010010d
Hill TL (1962) Thermodynamics of small systems. J Chem Phys 36:3182–3197. https://doi.org/10.1063/1.1732447
Hourlier D, Perrot P (2010) Au-Si and Au-Ge phases diagrams for nanosystems. Mater Sci Forum 653:77–85. https://doi.org/10.4028/www.scientific.net/MSF.653.77
Hu J, Shi YN, Sauvage X, Sha G, Lu K (2017) Grain boundary stability governs hardening and softening in extremely fine nanograined metals. Science 355:1292–1296. https://doi.org/10.1126/science.aal5166
Jang M-H, Kizilkaya O, Kropf AJ, Kurtz RL, Elam JW, Lei Y (2020) Synergetic effect on catalytic activity and charge transfer in Pt-Pd bimetallic model catalysts prepared by atomic layer deposition. J Chem Phys 152:24710. https://doi.org/10.1063/1.5128740
Jellinek J (2008) Nanoalloys: tuning properties and characteristics through size and composition. Faraday Discuss 138:11–35. https://doi.org/10.1039/B800086G
Jiang Q, Yang CC, Li JC (2002) Melting enthalpy depression of nanocrystals. Mater Lett 56:1019–1021. https://doi.org/10.1016/S0167-577X(02)00667-5
Jiao ZB, Schuh CA (2018) Nanocrystalline Ag-W alloys lose stability upon solute desegregation from grain boundaries. Acta Mater 161:194–206. https://doi.org/10.1016/j.actamat.2018.09.014
Kaptay G (2012) Nano-Calphad: extension of the Calphad method to systems with nano-phases and complexions. J Mater Sci 47:8320–8335
Kaptay G (2018) On the solid/liquid interfacial energies of metals and alloys. J Mater Sci 53:3767–3784. https://doi.org/10.1007/s10853-017-1778-y
Kaptay G (2014) A method to estimate interfacial energy between eutectic solid phases from the results of eutectic solidification experiments. Mater Sci Forum 790–791:133–139. https://doi.org/10.4028/www.scientific.net/MSF.790-791.133
Kaufman L (1991) Coupled thermochemical and phase diagram data for tantalum based binary alloys. Calphad 15:243–259. https://doi.org/10.1016/0364-5916(91)90004-4
Kim DH, Kim HY, Ryu JH, Lee HM (2009) Phase diagram of Ag–Pd bimetallic nanoclusters by molecular dynamics simulations: solid-to-liquid transition and size-dependent behavior. Phys Chem Chem Phys 11:5079–5085. https://doi.org/10.1039/B821227A
Koči L, Ma Y, Oganov AR, Souvatzis P, Ahuja R (2008) Elasticity of the superconducting metals V, Nb, Ta, Mo, and W at high pressure. Phys Rev B 77:214101. https://doi.org/10.1103/PhysRevB.77.214101
Koinov Z, Mendoza R, Fortes M (2011) Rotonlike Fulde-Ferrell collective excitations of an imbalanced Fermi gas in a two-dimensional optical lattice. Phys Rev Lett 106:3–6. https://doi.org/10.1103/PhysRevLett.106.100402
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 77:205431. https://doi.org/10.1103/PhysRevB.77.205431
Lee J, Lee J, Tanaka T et al (2005) Phase diagrams of nanometer-sized particles in binary systems. JOM 57:56–59. https://doi.org/10.1007/s11837-005-0235-6
Lennartson A (2014) Made by molybdenum. Nat Chem 6:746. https://doi.org/10.1038/nchem.2011
Li M, Zhu TS (2016) Modeling the melting temperature of nanoscaled bimetallic alloys. Phys Chem Chem Phys 18:16958–16963. https://doi.org/10.1039/c6cp01742h
Liang LH, Zhao M, Jiang Q (2002) Melting enthalpy depression of nanocrystals based on surface effect. J Mater Sci Lett 21:1843–1845. https://doi.org/10.1023/A:1021532311219
Lim B, Jiang M, Camargo PHC, Cho EC, Tao J, Lu X, Zhu Y, Xia Y (2009) Pd-Pt bimetallic nanodendrites with high activity for oxygen reduction. Science 324:1302–1305. https://doi.org/10.1126/science.1170377
Lopes A, Tréglia G, Mottet C, Legrand B (2015) Ordering and surface segregation in ${\mathrm{Co}}_{1\text{\ensuremath{-}}c}{\mathrm{Pt}}_{c}$ nanoparticles: a theoretical study from surface alloys to nanoalloys. Phys Rev B 91:35407. https://doi.org/10.1103/PhysRevB.91.035407
Lu HM, Jiang Q (2004) Size-dependent surface energies of nanocrystals. J Phys Chem B 108:5617–5619. https://doi.org/10.1021/jp0366264
Magnin Y, Zappelli A, Amara H, Ducastelle F, Bichara C (2015) Size dependent phase diagrams of nickel-carbon nanoparticles. Phys Rev Lett 115:205502. https://doi.org/10.1103/PhysRevLett.115.205502
McNamara K, Tofail SAM (2015) Nanosystems: the use of nanoalloys, metallic, bimetallic, and magnetic nanoparticles in biomedical applications. Phys Chem Chem Phys 17:27981–27995. https://doi.org/10.1039/C5CP00831J
Mendoza-Pérez R, Bahrami A, Calderón-Olvera RM, Romero-Ibarra JE, Álvarez-Zauco E, Huerta L, Muhl S (2020) Surpassing Cu–Ta miscibility barriers using a high-current pulsed arc. Adv Mater Interfaces 2000921. https://doi.org/10.1002/admi.202000921
Mendoza-Pérez R, Guisbiers G (2019) Bimetallic Pt–Pd nano-catalyst: size, shape and composition matter. Nanotechnology 30:305702. https://doi.org/10.1088/1361-6528/ab1759
Mendoza R, Fortes M, Solís MA (2014) Collective excitations of an imbalanced fermion gas in a 1D optical lattice. J Low Temp Phys 175:265–271. https://doi.org/10.1007/s10909-013-0926-2
Mendoza R, Fortes M, Solís MA, Koinov Z (2013) Superfluidity of a spin-imbalanced Fermi gas in a three-dimensional optical lattice. Phys Rev A - At Mol Opt Phys 88:1–8. https://doi.org/10.1103/PhysRevA.88.033606
Mints RG, Rakhmanov AL (1981) Critical state stability in type-II superconductors and superconducting-normal-metal composites. Rev Mod Phys 53:551–592. https://doi.org/10.1103/RevModPhys.53.551
Mondal S, Phukan M, Ghatak A (2015) Estimation of solid–liquid interfacial tension using curved surface of a soft solid. Proc Natl Acad Sci 112:12563–12568. https://doi.org/10.1073/pnas.1502642112
Monji F, Jabbareh MA (2017) Thermodynamic model for prediction of binary alloy nanoparticle phase diagram including size dependent surface tension effect. Calphad Comput Coupling Phase Diagrams Thermochem 58:1–5. https://doi.org/10.1016/j.calphad.2017.04.003
Nagender-Naidu SV, Sriramamurthy AM, Rao PR (1984) The Mo−W (molybdenum-tungsten) system. Bull Alloy Phase Diagr 5:177–180. https://doi.org/10.1007/BF02868956
Nagender-Naidu SV, Sriramamurthy AM, Rao PR (1985) Mo–W system. Bull Alloy Phase Diagr 6:113. https://doi.org/10.1007/BF02869216
Nanda KK (2009) Size-dependent melting of nanoparticles: hundred years of thermodynamic model. Pramana 72:617–628. https://doi.org/10.1007/s12043-009-0055-2
Nelli D, Ferrando R (2019) Core–shell vs. multi-shell formation in nanoalloy evolution from disordered configurations. Nanoscale 11:13040–13050. https://doi.org/10.1039/C9NR02963J
Okamoto H (1991) Mo-Nb (molybdenum-niobium). J Phase Equilibria 12:616–617. https://doi.org/10.1007/BF02645086
Panizon E, Ferrando R (2016) Strain-induced restructuring of the surface in core@shell nanoalloys. Nanoscale 8:15911–15919. https://doi.org/10.1039/c6nr03560d
Pohl J, Stahl C, Albe K (2012) Size-dependent phase diagrams of metallic alloys: a Monte Carlo simulation study on order–disorder transitions in Pt–Rh nanoparticles. Beilstein J Nanotechnol 3:1–11
Purja Pun GP, Darling KA, Kecskes LJ, Mishin Y (2015) Angular-dependent interatomic potential for the Cu-Ta system and its application to structural stability of nano-crystalline alloys. Acta Mater 100:377–391. https://doi.org/10.1016/j.actamat.2015.08.052
Qi W (2016) Nanoscopic thermodynamics. Acc Chem Res 49:1587–1595. https://doi.org/10.1021/acs.accounts.6b00205
Rahm JM, Erhart P (2018) Understanding chemical ordering in bimetallic nanoparticles from atomic-scale simulations: the competition between bulk, surface, and strain. J Phys Chem C 122:28439–28445. https://doi.org/10.1021/acs.jpcc.8b10874
Ramírez G, Rodil SE, Arzate H, Muhl S, Olaya JJ (2011) Niobium based coatings for dental implants. Appl Surf Sci 257:2555–2559. https://doi.org/10.1016/j.apsusc.2010.10.021
Rodríguez-Proenza CA, Palomares-Báez JP, Chávez-Rojo MA, García-Ruiz A, Azanza-Ricardo C, Santoveña-Uribe A, Luna-Bárcenas G, Rodríguez-López J, Esparza R (2018) Atomic surface segregation and structural characterization of PdPt bimetallic nanoparticles. Materials 11:1882. https://doi.org/10.3390/ma11101882
Romero-Freire A, Santos-Echeandía J, Neira P, Cobelo-García A (2019) Less-studied technology-critical elements (Nb, Ta, Ga, In, Ge, Te) in the marine environment: review on their concentrations in water and organisms. Front Mar Sci 6:532
Shishulin AV, Fedoseev VB (2019) Effect of initial composition on the liquid–solid phase transition in Cr–W alloy nanoparticles. Inorg Mater 55:14–18. https://doi.org/10.1134/S0020168519010138
Shishulin AV, Fedoseev VB, Shishulina AV (2019) Melting behaviour of fractal-shaped nanoparticles (the example of Si–Ge system). Tech Phys 64:1343–1349. https://doi.org/10.1134/S1063784219090172
Sim K, Lee J (2014) Phase stability of Ag-Sn alloy nanoparticles. J Alloys Compd 590:140–146. https://doi.org/10.1016/j.jallcom.2013.12.101
Simnad MT (2001) Nuclear reactors: shielding materials. In: KHJ B, Flemings MC, Kramer EJ et al (eds) Encyclopedia of materials: science and technology, 2nd edn. Elsevier, pp 6377–6384
Snead LL, Hoelzer DT, Rieth M, Nemith AAN (2019) Refractory alloys: vanadium, niobium, molybdenum, tungsten. In: Odette GR, Zinkle SJ (eds) Structural alloys for nuclear energy applications. Elsevier, pp. 585–640
Sopoušek J, Kryštofová A, Premović M, Zobač O, Polsterová S, Brož P, Buršík J (2017) Au-Ni nanoparticles: phase diagram prediction, synthesis, characterization, and thermal stability. Calphad 58:25–33. https://doi.org/10.1016/j.calphad.2017.05.002
Sopoušek J, Vřeš’ál J, Zemanova A, Bursik J (2012) Phase diagram prediction and particle characterisation of Sn-Ag nano alloy for low melting point lead-free solders. J Min Metall Sect B Metall 48:419–425. https://doi.org/10.2298/JMMB120121032S
Sui M, Pandey P, Li M-Y, Zhang Q, Kunwar S, Lee J (2017) Au-assisted fabrication of nano-holes on c-plane sapphire via thermal treatment guided by Au nanoparticles as catalysts. Appl Surf Sci 393:23–29. https://doi.org/10.1016/j.apsusc.2016.09.163
Sundaram D, Yang V, Yetter RA (2017) Metal-based nanoenergetic materials: synthesis, properties, and applications. Prog Energy Combust Sci 61:293–365. https://doi.org/10.1016/j.pecs.2017.02.002
Tarselli M (2015) Subtle niobium. Nat Chem 7:180. https://doi.org/10.1038/nchem.2164
Turnlund JR, Friberg LT (2007) Chapter 34—molybdenum. In: Nordberg GF, Fowler BA, Nordberg M, Friberg LT (eds) Handbook on the toxicology of metals, 2nd edn. Academic Press, Burlington, pp 731–741
Vahl A, Strobel J, Reichstein W, Polonskyi O, Strunskus T, Kienle L, Faupel F (2017) Single target sputter deposition of alloy nanoparticles with adjustable composition via a gas aggregation cluster source. Nanotechnology 28:175703. https://doi.org/10.1088/1361-6528/aa66ef
Vallée R, Wautelet M, Dauchot JP, Hecq M (2001) Size and segregation effects on the phase diagrams of nanoparticles of binary systems. Nanotechnology 12:68–74. https://doi.org/10.1088/0957-4484/12/1/312
Velázquez-Salazar JJ, Bazán-Díaz L, Zhang Q, Mendoza-Cruz R, Montaño-Priede L, Guisbiers G, Large N, Link S, José-Yacamán M (2019) Controlled overgrowth of five-fold concave nanoparticles into plasmonic nanostars and their single-particle scattering properties. ACS Nano 13:10113–10128. https://doi.org/10.1021/acsnano.9b03084
Vitos L, Ruban AV, Skriver HL, Kollár J (1998) The surface energy of metals. Surf Sci 411:186–202. https://doi.org/10.1016/S0039-6028(98)00363-X
Wang F, Wu Z, Shangguan X, Sun Y, Feng J, Li Z, Chen L, Zuo S, Zhuo R, Yan P (2017) Preparation of mono-dispersed, high energy release, core/shell structure Al nanopowders and their application in HTPB propellant as combustion enhancers. Sci Rep 7:5228. https://doi.org/10.1038/s41598-017-05599-0
Wang H, Zepeda-Ruiz LA, Gilmer GH, Upmanyu M (2013) Atomistics of vapour-liquid-solid nanowire growth. Nat Commun 4:1956. https://doi.org/10.1038/ncomms2956
Warlimont H, Martienssen W (2018) Springer handbook of materials data, 2nd edn. Springer Nature, Switzerland
Wu CH, Liu C, Su D, Xin HL, Fang HT, Eren B, Zhang S, Murray CB, Salmeron MB (2019) Bimetallic synergy in cobalt–palladium nanocatalysts for CO oxidation. Nat Catal 2:78–85. https://doi.org/10.1038/s41929-018-0190-6
Wu G, Chan KC, Zhu L, Sun L, Lu J (2017) Dual-phase nanostructuring as a route to high-strength magnesium alloys. Nature 545:80–83. https://doi.org/10.1038/nature21691
Zhang X, Vo NQ, Bellon P, Averback RS (2011) Microstructural stability of nanostructured Cu-Nb-W alloys during high-temperature annealing and irradiation. Acta Mater 59:5332–5341. https://doi.org/10.1016/j.actamat.2011.05.009
Zhao Z, Fisher A, Cheng D (2016) Phase diagram and segregation of Ag–Co nanoalloys: insights from theory and simulation. Nanotechnology 27:115702. https://doi.org/10.1088/0957-4484/27/11/115702
Acknowledgments
We thank Roxana M. Calderón-Olvera for her assistance in making the graphs.
Availability of data and material
The data generated during the current study are available from the corresponding author on reasonable request.
Code availability
Not applicable.
Funding
This work was supported by the PAPIIT Project IN113017. RMP also would like to acknowledge financial support from the DGAPA-UNAM postdoctoral grant.
Author information
Authors and Affiliations
Contributions
RMP conceptualized the study and performed the calculations. Both authors analyzed the results; wrote, reviewed, and edited the original draft; and read and approved the final manuscript.
Corresponding author
Ethics declarations
Conflict of interests
The authors declare that they have no conflict of interests.
Additional information
Publisher’s note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Mendoza-Pérez, R., Muhl, S. Phase diagrams of refractory bimetallic nanoalloys. J Nanopart Res 22, 306 (2020). https://doi.org/10.1007/s11051-020-05035-x
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11051-020-05035-x