Response to “Comment on ‘Electrum, the Gold−Silver Alloy, from the Bulk Scale to the Nanoscale: Synthesis, Properties, and Segregation Rules’” Grégory Guisbiers,* Rubén Mendoza-Cruz, Lourdes Bazán-Díaz, J. Jesús Velázquez-Salazar, Rafael Mendoza-Perez, José Antonio Robledo-Torres, José-Luis Rodríguez-López, Juan Martín Montejano-Carrizales, Robert L. Whetten, and Miguel José-Yacamán
I
Table 1. Predictions of the Surface-Segregated Element Using the Segregation Rules Proposed by Cui et al.
n their comment, Cui et al. claim that the segregation rules we proposed in our published paper1 are questionable and therefore proposed two other segregation rules. In this response, we provide irrefutable evidence that their own segregation rules are inexact and unable to explain the surface segregation observed in several bimetallic nanoalloys. The first segregation rule we state in ref 1 is that the element with the highest bulk melting point will segregate to the surface if the difference between the bulk melting temperatures of the two elements is larger than 10% of the highest melting point. If not, the surface segregation will then be determined by the solid surface energy, promoting to the surface the element with the lowest surface energy (second rule). Before those two rules are applied, the miscibility of the alloy has to be determined, and this can be done by using the well-known Hume− Rothery’s rules.2 In the case of total immiscibility, only the second rule based on the surface energy applies. In the case of total or even partial miscibility, both rules apply (of course, they cannot be applied simultaneously as Cui et al. suggested due to their definition; therefore, there is no violation as claimed in the comment). As Pt is totally miscible with Ni all over the composition range, the first rule applies, then Pt segregates to the surface since Pt has the highest melting temperature compared to Ni. Indeed, ΔTm,bulk = 313 K (∼15% of the highest melting point between Pt and Ni, i.e., Pt) is larger than 10%; therefore, only the first rule applies. Concerning the Cu− Ni alloy, Ni segregates to the surface because of the first rule since Ni has the highest melting temperature compared to Cu, ΔTm,bulk = 371 K (∼21% of the highest melting point between Cu and Ni, i.e., Ni). In another paper published by Reyes-Nava et al.,3 two segregation rules based on the core and valence electron density of each constituent of the alloy have been formulated. These segregations rules state that (a) for adjacent elements in the periodic table (the case of Ni and Cu), the bimetallic system would be more stable if the component with the smallest valence electron density is placed on the surface; therefore, in the Cu−Ni case, nickel will be at the surface, in agreement with our prediction. The second rule concerns elements in the nanoalloy in the same group; that is, (b) for two elements within a column, the trend to be at the surface is larger for the element with the largest electron core density, and this trend increases when the alloying elements are very © 2016 American Chemical Society
alloy Cu−Ni
Pt−Ni
Au−Ag
first rule based on the surface energy12 Δγs(111) = 3% ( γs(Ni) Δγs(110) = 16% → first rule can be applied γs(Pt) > γs(Ni) Δγs(111) = 9% → first rule cannot be applied Δγs(100) = 26% → first rule can be applied γs(Au) > γs(Ag) Δγs(110) = 27% → first rule can be applied γs(Au) > γs(Ag)
second rule based on the atomic size13 aCu = 140 pm aNi = 160 pm
segregated element Ni
Cu
Ni
aPt = 170−180 pm
Ni
aNi = 160 pm Ni
Ni
aAg = 170 pm aAu = 170 pm
undetermined Ag
Ag
separated in the given group, i.e., Pt in the Pt−Ni case, the same result as in our paper.1 Let us now apply the rules proposed by Cui and co-workers. The first segregation rule they state is that the element with the lowest solid surface energy will segregate to the surface. If the difference between the solid surface energies of the two elements is less than ∼10% of the highest surface energy, then the element with the largest atomic size goes to the surface; this is the second rule. It is worth noting that this second rule has been formulated previously by Wang and Johnson,4 in a model that resulted from DFT-GGA calculations. The two segregation Received: September 7, 2016 Published: December 27, 2016 10620
DOI: 10.1021/acsnano.6b06045 ACS Nano 2016, 10, 10620−10622
Letter to the Editor
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Table 2. Comparison between Different Models alloy
Guisbiers et al.1
Au−Ag Au−Cu Pt−Pd Cu−Ni Pt−Ni Ag−Cu Au−Pt Au−Ni Ag−Ni Ag−Co
Ag Au Pd Ni Pt Ag Au Au Ag Ag
Hamilton8
Reyes-Nava et al.3
Mukherjee et al.9,10
Au Pd Ni Pt Ag Au Au Ag Ag
Ag Au Pt Cu Pt Ag Au Au Ag Ag
Ag Au none none Ag Au Au
discussing the complex surface segregation phenomena in bimetallic nanoalloys.
rules given by Wang and Johnson are qualitatively equivalent to the rules formulated independently by Reyes-Nava et al.3 By using the bulk surface energies for low-index facets (111), (110), and (100), discrepancies arise from this analysis, particularly for the Cu−Ni and Pt−Ni systems alleged by Cui and co-workers. Considering (111) facets and (110) facets in the Cu−Ni system, Ni is predicted to be at the surface, just like the result we obtained in our previous published paper. However, they claim in their comment that copper is at the surface, a result that can only be obtained by considering the difference between (100) facets (Table 1). Considering now the Pt−Ni system and applying Cui’s rules, Ni is predicted at the surface (Table 1), which is in strong disagreement with what they wrote in their comment stating that Pt was the segregated element. Consequently, there are strong discrepancies in their predictions. Obviously, Cui and co-workers forgot to consider that the surface energy is face-dependent, and consequently, it is not clear by using their segregation rules which element segregates to the surface in Cu−Ni and Au−Ag alloys. Thus, the proposed rules by Cui et al. based just on bulk surface energies and atomic size radii have shown their limitations. A comparison between different models predicting surface segregation is shown in Table 2. It is clear that that there is a good agreement between our predictions and many other theoretical models. Unquestionably, the surface energy alone cannot explain the surface segregation in nanoalloys, except when the alloy is immiscible (our second rule). However, when the alloy is miscible (totally or even partially), another material property is driving the segregation. Several material properties have then been proposed by different groups to explain the surface segregation, such as sublimation enthalpy,5 atomic size,6 melting temperature,7 electron densities,3,8 etc. As also was suggested by Mukherjee et al.,9,10 magnetism seems to play a particular role in surface segregation. It has been shown that the elements presenting higher magnetic moment segregate to the surface.11 From Table 2, one can see that this argument is not always valid because the magnetic element does not segregate to the surface for all of the bimetallic alloys where those elements are involved. However, it seems that the miscibility of the alloy, controlled by the interaction parameters (in the liquid and solid phase) of the regular solution model, plays a major role in the segregation as claimed in our paper.1 In conclusion, the segregation rules proposed by Cui et al. do not apply for all the considered alloys. On the contrary, our segregation rules proposed in ref 1 correctly predict the nature of the surface-segregated element for a large number of different bimetallic alloys and are in agreement with previously published results from different models and approaches
ACKNOWLEDGMENTS This project was supported by grants from the Welch Foundation (AX-1615 and AX-1857) the UTSA International Center for Nanotechnology and Advanced Materials (1000000321), the National Center for Research Resources (G12RR013646-12), the National Institute on Minority Health and Health Disparities (G12MD007591) from the National Institutes of Health. The authors would also like to acknowledge the NSF PREM #DMR0934218, the Mexican Council for Science and Technology, CONACYT (Mexico) through the CIAM Grants 148967 and 216315, the Ph.D. scholarship 250283 for J.A. Robledo-Torres and the postdoctoral Grant 232171. J. A. Robledo-Torres is now working at the Institute of Physics, Universidad Autónoma de San Luis Potosi, Alvaro Obregón 64000, Centro, San Luis Potosi Mexico. Finally, highperformance computing resources granted at the CNS-IPICYT are also acknowledged. REFERENCES (1) Guisbiers, G.; Mendoza-Cruz, R.; Bazan-Diaz, L.; VelazquezSalazar, J. J.; Mendoza-Perez, R.; Robledo-Torres, J. A.; RodriguezLopez, J. L.; Montejano-Carrizales, J. M.; Whetten, R. L.; JoseYacaman, M. Electrum, the Gold-Silver Alloy, from the Bulk Scale to the Nanoscale: Synthesis, Properties, and Segregation Rules. ACS Nano 2016, 10, 188−198. (2) Hume-Rothery, W.; Mabbott, G. W.; Evans, K. M. The Freezing Points, Melting Points, and Solid Solubility Limits of the Alloys of Silver, and Copper with the Elements of the B Sub-Groups. Philos. Trans. R. Soc., A 1934, 233, 1−97. (3) Reyes-Nava, J. A.; Rodriguez-Lopez, J. L.; Pal, U. Generalizing Segregation and Chemical Ordering in Bimetallic Nanoclusters Through Atomistic View Points. Phys. Rev. B. 2009, 80, 161412R. (4) Wang, L. L.; Johnson, D. D. Predicted Trends of Core-Shell Preferences for 132 Late Transition-Metal Binary-Alloy Nanoparticles. J. Am. Chem. Soc. 2009, 131, 14023−14029. (5) Williams, F. L.; Nason, D. Binary Alloy Surface Compositions from Bulk Alloy Thermodynamic Data. Surf. Sci. 1974, 45, 377−408. (6) Vanlangeveld, A. D. The Atomic Size Effect in Surface Segregation. Thin Solid Films 1985, 129, 161−180. (7) Burton, J. J.; Machlin, E. S. Prediction of Segregation to Alloy Surfaces from Bulk Phase-Diagrams. Phys. Rev. Lett. 1976, 37, 1433− 1436. (8) Hamilton, J. C. Prediction of Surface Segregation in Binary-Alloys Using Bulk Alloy Variables. Phys. Rev. Lett. 1979, 42, 989−992. (9) Mukherjee, S.; Moran-Lopez, J. L. Surface Segregation in Transition-Metal Alloys and in Bimetallic Alloy Clusters. Surf. Sci. 1987, 189, 1135−1142. 10621
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(10) Mukherjee, S.; Moran-Lopez, J. L. Theory of Surface Segregation in Transition-Metal Alloys. Surf. Sci. 1987, 188, L742− L748. (11) Modak, S.; Khanra, B. C. Surface Segregation in MagneticAlloys. Solid State Commun. 1989, 71, 693−696. (12) Vitos, L.; Ruban, A. V.; Skriver, H. L.; Kollar, J. The surface energy of metals. Surf. Sci. 1998, 411, 186−202. (13) Martienssen, W.; Warlimont, H. Springer Handbook of Condensed Matter and Materials Data; Springer: Berlin, 2005.
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