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Gold−Copper Nano-Alloy, “Tumbaga”

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Gold−Copper Nano-Alloy, “Tumbaga” This is an open access article published under an ACS AuthorChoice License, which permits copying and redistribution of the article or any adaptations for non-commercial purposes. Letter pubs.acs.org/NanoLett Gold−Copper Nano-Alloy, “Tumbaga”, in the Era of Nano: Phase Diagram and Segregation † ‡ † † Gregorý Guisbiers,*, Sergio Mejia-Rosales, Subarna Khanal, Francisco Ruiz-Zepeda, † † Robert L. Whetten, and Miguel Jose-Yacamań † Department of Physics & Astronomy, University of Texas at San Antonio, One UTSA Circle, San Antonio, Texas 78249, United States ‡ Center for Innovation, Research and Development in Engineering and Technology (CIIDIT) and CICFIM-Facultad de Ciencias Fisico-Matematicas, Universidad Autonoma de Nuevo Leon, San Nicolaś de los Garza, Nuevo Leon 66450, Mexico *S Supporting Information ABSTRACT: Gold−copper (Au−Cu) phases were employed already by pre-Columbian civilizations, essentially in decorative arts, whereas nowadays, they emerge in nanotechnology as an important catalyst. The knowledge of the phase diagram is critical to understanding the performance of a material. However, experimental determination of nanophase diagrams is rare because calorimetry remains quite challenging at the nanoscale; theoretical investigations, therefore, are welcomed. Using nanothermody- namics, this paper presents the phase diagrams of various polyhedral nanoparticles (tetrahedron, cube, octahedron, decahe- dron, dodecahedron, rhombic dodecahedron, truncated octahe- dron, cuboctahedron, and icosahedron) at sizes 4 and 10 nm. One finds, for all the shapes investigated, that the congruent melting point of these nanoparticles is shifted with respect to both size and composition (copper enrichment). Segregation reveals a gold enrichment at the surface, leading to a kind of core−shell structure, reminiscent of the historical artifacts. Finally, the most stable structures were determined to be the dodecahedron, truncated octahedron, and icosahedron with a Cu-rich core/Au-rich surface. The results of the thermodynamic approach are compared and supported by molecular-dynamics simulations and by electron- microscopy (EDX) observations. KEYWORDS: nanothermodynamics, binary phase diagram, nanoalloy, size effect, polyhedra, congruent melting “Tumbaga” was the name given by the Conquistadors to the chemical properties11,12 at the nanoscale. Although the Au−Cu gold−copper alloy perfected by pre-Columbian civilizations in alloy has been extensively studied in the literature both at the − − − Central and South America.1 3 The proportion of gold to bulk4,13 18 and nanoscales,10,11,19 29 the prediction of phase copper varies widely and sometimes silver was even found as an diagrams at the nanoscale is still missing. The objective of this impurity. The popularity of this alloy comes from its congruent paper is to present the phase diagram of Au−Cu at the melting point. Congruency denotes that at a particular nanoscale for the relevant distinct polyhedral morphologies of composition, the alloy behaves like a pure element (i.e., it nanoparticles namely the tetrahedron, cube, octahedron, fi melts at a de nite temperature rather than over a range) and decahedron, dodecahedron, rhombic dodecahedron, truncated also the melting point of the alloy is reduced as compared to octahedron, cuboctahedron, and icosahedron. the two pure elements. For bulk Au−Cu, the congruent melting ° 4 To predict the solid solubility of two metals, there exist the point occurs at 44% copper composition and 910 C, well empirical Hume−Rothery rules.30,31 These rules indicate that below the gold melting point (1064 °C) and the copper the alloy is preferred when the atomic radii, crystal structure, melting point (1084 °C). In contrast to this high-temperature valence, and electronegativity of the elements are similar. The regime, wherein the alloy exists in the form of a solid solution Au−Cu combination fulfills three of the four Hume−Rothery over the entire range of composition; at reduced temperatures, it forms ordered phases Au Cu (L1 ), AuCu (L1 ) and AuCu rules, and hence, it forms at high temperature a random 3 2 0 3 substitutional solid solution; that is, Au and Cu atoms (L12) depending on the alloy composition. Nowadays, besides its continued use in jewelry, the Au−Cu substitute for each other in the crystal lattice without structural alloys have emerged prominently in the nanosciences, mostly for catalysis; they catalyze a wide range of chemical reactions Received: September 13, 2014 − from carbon monoxide oxidation5 8 to selective oxidation of Revised: October 17, 2014 alcohols.9,10 In fact, this alloy exhibits novel physical and Published: October 22, 2014 © 2014 American Chemical Society 6718 dx.doi.org/10.1021/nl503584q | Nano Lett. 2014, 14, 6718−6726 Nano Letters Letter − changes, whereas at low temperature it forms several substitu- the experimental data points34 37 of Au−Cu alloy are well fi − tionally ordered solid solutions (Au3Cu, AuCu, AuCu3). In fact, described by this model. Speci cally, the solidus liquidus the relative difference between the atomic radii of gold and curves of a regular solution model are given by38 copper is less than 15%; they share common crystal structures ⎧ (face centered cubic, fcc) and valences (+1), but their ⎛ ⎞ ⎪ ⎜ xsolidus ⎟ electronegativities are quite disconnected, the relative difference RTln⎜ ⎟ ⎪ ⎝ x ⎠ in their Mulliken electronegativity values being around 29% (cf. ⎪ liquidus ⎛ ⎞ Table 1). Nonetheless, it has been shown that, at the nanoscale, ⎪ T =ΔH A⎜1(1) −⎟ +Ω −x 2 ⎪ m⎝ A ⎠ lliquidus ⎪ Tm Table 1. Material Properties Used to Calculate the Phase ⎪ 2 ⎨ −Ωssolidus(1 −x ) Diagrams at the Nanoscale ⎪ ⎪ ⎛ ⎞ material properties Au Cu ⎜ 1 − xsolidus ⎟ 53 ⎪RTln⎜ ⎟ crystal structure fcc fcc ⎪ ⎝1 − x ⎠ 53 liquidus Tm,∞ (K) 1337 1357 ⎪ ⎛ ⎞ 53 T ΔH ∞ (J/mol) 12 552 13 263 ⎪ B⎜ ⎟ 2 2 m, =ΔHm 1 − +Ωlliquidusxx −Ωssolidus γ 2 53 ⎪ ⎝ B ⎠ l (J/m ) 1.128 1.300 ⎩ Tm (1) γ 2 44 s,111 (J/m ) 1.283 1.952 γ 2 44 s,100 (J/m ) 1.627 2.166 Here, xsolidus (xliquidus) denote the compositions of the solid γ 2 44 A B s,101 (J/m ) 1.700 2.237 (liquid) phases at given temperature T; Tm and Tm, the size- Ω 62 − l (J/mol) 27 230 dependent melting temperatures of gold (A) and copper (B); Ω 62 − Δ A Δ B s (J/mol) 20 290 Hm and Hm, their respective size-dependent melting 53 Ω Ω atomic radii (pm) 134 117 enthalpies; l and s, the respective size-dependent electronic affinity (eV)53 2.31 1.24 interactions parameters in the liquid and solid phases; and R, first ionization energy (eV)53 9.23 7.73 the characteristic ideal gas constant. χ, Mulliken electronegativity (eV)a 5.77 4.49 Figure 1 presents the bulk phase diagram wherein the Δ 53 Hv,∞, molar heat of vaporization (J/mol) 334 400 300 700 congruent melting point is the intersection between the aThe Mulliken electronegativity is defined as the mean value between liquidus and solidus curves, at this particular composition, the the electronic affinity and the first ionization energy. two-component solution behaves like a pure element. In the Au−Cu alloy, the congruent melting point is lower than either this fourth (electronegativity) Hume−Rothery rule should be the gold and copper melting points, implying that the liquid replaced by one based on the molar heat of vaporization,32,33 solution is stabilized more than the solid one. This is which is related to the cohesive energy of the material and, rationalized within the regular solution model (above) by the thus, is better adapted to describe the alloy behavior. Applying interaction parameters, which are both negative (A−B this new rule, the relative difference between the molar heat of interactions are stronger than A−AorB−B interactions, i.e., vaporization of gold and copper is only 11% indicating a strong mixing is favored), leading to the inequality, indicative of preference for mixing. Therefore, as usually given for a binary greater stability of the liquid solution compared to the solid isomorphous system, that is, a two-component system A and B one. in which A and B are completely miscible in both solid and To calculate the phase diagram at the nanoscale, the size- liquid phases, the phase diagram can be predicted within a dependent parameters must be evaluated. The size-dependent thermodynamic approach employing a regular solution model melting temperature is calculated according to eq 239 (i.e., a quasichemical model). Figure 1 demonstrates clearly that ⎛ ⎞⎛ ⎞ T N 1 γγ− m =+1 ⎜ surf ⎟⎜ ls⎟ Tmhkl,∞∞⎝ NXtot ( ) a⎠⎝ Δ Hm, ⎠ (2) √ √ Here, X(hkl) denotes a set of factors equal to {1/2, 2/4, 3/ γ γ 3} for the {100, 110, 111} faces, respectively. l and s are the respective surface energies in the liquid and solid state; a is the bulk lattice parameter; and Nsurf/Ntot is the ratio of surface to total atoms. The size-dependence of the interactions and melting enthalpy are also calculated consistently by the same relationship. This is justified by quantum physics consideration where all thermodynamic quantities are approximately a linear functions of 1/D (where D denotes the length edge of the polyhedron) corresponding to the nanoparticle’s surface-to- volume.38,40 Once we have used eq 2 to obtain the set of size-dependent A B Δ A Δ B Ω Ω parameters {Tm,Tm, Hm, Hm, l, s} for any sizes selected (here, 10 and 4 nm), we can introduce these parameters into eqs 1 to generate the Au−Cu phase diagram at the nanoscale (Figure 2). All phase diagrams, presented in Figure 2 at two distinct sizes (10 and 4 nm), show that the liquid region is Figure 1. Bulk binary phase diagram of Au−Cu alloy. enlarged and the solid solution area is narrowed. As usual, 6719 dx.doi.org/10.1021/nl503584q | Nano Lett. 2014, 14, 6718−6726 Nano Letters Letter Figure 2.
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