ARTICLE pubs.acs.org/JPCC
Tailoring Electronic Structure Through Alloying: The AgnCu34 (n = 0 34) Nanoparticle Family
n
Handan Yildirim,*,† Abdelkader Kara, and Talat S. Rahman Physics Department, University of Central Florida, Orlando, Florida, United States
bS Supporting Information ABSTRACT:
Electronic structures of the free-standing core shell (Cu@Ag) AgnCu34 n (n = 0 34) nanoalloy family are studied as a function of stoichiometry using ab initio total energy electronic structure calculations. Our calculations show that progressive alloying significantly alters the coordination distribution, bond lengths, formation energies, and the electronic densities of states. Changes in coordination and elemental environment are reflected in the electronic densities of states, which broaden or narrow as a result of hybridization between the Cu and the Ag atoms. The densities of states of Ag atoms in Ag-rich nanoparticles show large broadening when a single Cu atom is introduced, followed by substantial deviation of the position of the center of d states from that of the pristine (Ag34) nanoparticle. Such deviation is found to persist for nonsymmetric nanoparticles. The calculated HOMO LUMO gaps vary between 0.2 and 0.9 eV within the family. The magnitude of the gaps is found to be strongly dependent on the geometric structure determined by the species ratio: the particles belonging to two ends of the NP family have relatively small gaps, and no overriding symmetry, whereas those toward the middle of the family exhibit high symmetry and larger gaps. The calculated ionization energies show no monotonic dependence on the Cu-to-Ag ratio and fluctuate within 500 meV as the stoichiometry changes.
I. INTRODUCTION In recent years, nanoalloying has become an important tool in nanoengineering for several technologically promising fields, for example, in catalysis.1 Most of the studies so far have focused mainly on the changes observed in chemical activity or in magnetic and optical properties with changes in particle size. Although alloying in bulk systems is well-understood, alloying at the nanoscale has been little explored. Such questions as what controls the structural, electronic, chemical, and vibrational properties of the bimetallic nanoparticles (NPs)—vital in their own right for efficient nanoengineering design—remain unanswered. Several difficulties have stood in the way of the desired progress in this important field. When a NP is composed of two elements with different radii, that difference determines the conceivable arrangements of the atoms within the NP. In addition, the relative positions of the constituent atoms within the given stoichiometry increase the number of abstractly possible structures. The resulting picture becomes challenging r 2011 American Chemical Society
to explore, because many equilibrium structures—ranging from quasicrystals through amorphous conglomerations, through well-ordered superlattices and onion-like multishell structures, to core shell arrangements2,3—may be feasible. Recent studies on bimetallic transition-metal (TM) NPs have shown that the icosahedral structure is preferred over the other available phases.4 Of particular interest to us is a recent study on bimetallic TM NPs ranging in size from 30 to 40 atoms.4 The initial structure for each NP was obtained from an earlier study in which the genetic algorithm approach5 was applied to search for the lowest-energy configuration. In that study, a semiempirical model potential6 was used for the optimization of a wide range of bimetallic nanoclusters.4 Further optimization of these initial structures with the first principles leads to the same structures. This study Received: September 5, 2011 Revised: November 10, 2011 Published: December 14, 2011 281
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finds the most stable structures to be core shell polyicosahedra (pIh) in which the element of smaller radius occupies the core of the NP (whose atoms are thus highly coordinated), while the one of larger radius forms the NP’s shell (which is relevant for catalytic activity). Further insights into such controlling factors as size mismatch, tendency toward alloying (as compared to the bulk phase), and likelihood for surface segregation are arrived at in the study performed by Rapallo et al.7 of six binary systems. The most interesting nanoalloy families among these systems reported are those with a wide miscibility gap in the bulk, such as Ag Cu.8 Although these NPs have not been studied extensively experimentally, a few experimental studies9 have confirmed the core shell arrangement in the NP, in which Cu atoms form the core surrounded by a shell consisting of Ag atoms. Both molecular dynamics simulations and density functional theory (DFT) calculations for chosen stoichiometries speak to the relative stability of this 34-atom NP family.10 Our results11 on the vibrational and thermodynamical properties of this family predict their strong stoichiometry dependence, which can be derived from atomically resolved properties. The stoichiometry dependence of the vibrational properties is qualitatively consistent with experimental results for Fe Pt NPs of about 2 nm.12 The structure of large Ag Cu clusters was shown experimentally to exhibit Janus-like patterns, in which the core is located either on the center or off-center; while theoretical studies have confirmed the spontaneous occurrence of these patterns.13 Note that, in our investigation, we study only one isomer, whose structure was provided by an earlier study. Exploring differences in the properties of different isomers of a given NP is beyond the scope of our paper. The efforts so far devoted to exploring how the interplay between size and chemical characteristics affects the properties of single-element NPs have led to a good understanding of the key features. Understanding the properties of bimetallic NPs, however, requires additional dimensionality because of composition effects. These properties are dictated by the combined effects of size, the ratio of atoms of constituent species, the relative positions of atoms, and the species environment of the atoms. Studies conducted so far on the core shell NPs have mostly been focused on revealing stoichiometry effects on optical,14 catalytic,15 thermodynamical,16,17 magnetic,18 and electronic19 properties. The electronic structure of core shell NPs is affected by the chemical composition of the core, shell, and interface.19 Catalytic activities are enhanced for bimetallic NPs as compared with those of monometallic NPs.15 These studies have revealed the importance of nanoscale, and the effect of an NP’s structure on its properties. Following up on them, increasing efforts have recently been devoted to revealing the effects beyond those of stoichiometry. A recent DFT study of the electronic and magnetic properties of Ni3nAln NPs highlights the role of nanoscale on the magnetic properties by showing that the magnetic moment per atom is significantly higher for those NPs than for either species of atoms in the bulk20 and that the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) gaps are affected by the size of these NPs. That study also shows that the distribution of magnetic charge is inhomogeneous, depending on the number of Al and Ni neighbors. Although the effect of size on the magnetic properties was clearly revealed in this study, the composition effect was not taken into account in detail as an important contributor for shaping the properties of this nanoalloy. The effect of composition has been addressed by a DFT study of the
CoPd NPs.21 It shows that, for a fixed-size NP, metallicity decreases almost monotonically with increasing Co concentration. Still, another recent DFT study reports that the electronic and magnetic properties of Pt12 nCun NPs (with n = 0, 1...12) depend on the number of Cu atoms, thus highlighting the composition effect on the electronic and magnetic properties.22 However, though the composition effect on the properties of this nanoalloy was discussed, an atom-based analysis—which has the potential to offer further insights into the effects wrought by composition—was not provided. This study also reports that there is an important interplay between structure and the reactivity of the NPs. Although these studies provide insights into size and composition effects on the physical and chemical properties of bimetallic NPs, there is more to be discovered by studying the combined effects on the electronic properties of the species ratios together with the effects of the chemical characteristics of the constituent atoms, the relative positions of atoms within the NPs, and their immediate environment. In the present study, we explore the role of stoichiometry in shaping key electronic properties within the AgnCu34 n NP family. As a first analysis of the role of progressive alloying, we have calculated—starting from the pristine NPs and proceeding systematically throughout the family—the change, with stoichiometry, in the position of the center of the d bands (for purposes of understanding the catalytic activity), in the HOMO LUMO gaps (for exploring metal-to-nonmetal transitions), and in the ionization potential (for enabling comparison with potential experiments). In our second approach, we undertake to reveal the atomically resolved contributions to the electronic structure of these NPs. For each member of the family, we calculate the average bond length of each type (Cu Cu, Ag Ag, Cu Ag), the average coordination of Cu and Ag atoms, and the formation energy and then compare these across the entire family. For each stoichiometry, we derive the total and partial electronic densities of states (EDOS), in order to elucidate how increasing the ratio of Cu to Ag affects the latter. We analyze changes in the shape of the EDOS and the position of the center of the d states, in order to trace the role of coordination and elemental environment, and compare these features to those for the atoms in extended systems (i.e., surfaces and bulk). Our results show how, among the various properties discussed so far, it is the composition and corresponding shape that mostly govern the diversity in the gaps. From the second part of the analysis, we find that increasing the number of Cu atoms in the neighborhood of Ag atoms in the Ag-rich NPs drastically perturbs the electronic structure of Ag atoms. We also find that, for the atoms with a similar coordination and elemental environment, those in the NPs, as compared with those in the bulk and/or surfaces, show distinct features in their EDOS. Our results show also that, especially for the NPs at the two ends of the NP family, the distinct features of a single atom in the NP can control the overall properties of the NP.
II. COMPUTATIONAL DETAILS We performed calculations using DFT as implemented in the Vienna Ab initio Simulation Package (VASP).23 We employed generalized-gradient approximation (GGA) for the exchangecorrelation functional provided by PW91.24 We set the kinetic energy cutoff to 273 eV, and for the purpose of comparison, we repeated calculations for some NPs using a higher energy cutoff (400 eV). We obtained integrations over the BZ using Γ point. 282
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Figure 1. Geometric structure of sample NPs: (a) Ag34; (b) Ag29Cu5; (c) Ag27Cu7; (d) Ag20Cu14; (e) Ag19Cu15; (f) Ag17Cu17; (g) Ag11Cu23; (h) Ag10Cu24; (i) Ag9Cu25; (j) Ag8Cu26; (k) Ag7Cu27; (l) Cu34.
We used a cubic supercell with a side length of 21 Å. The atomic positions are all relaxed until the forces are less than 2 10 3 eV/Å. We obtained the center of d states for each atom by calculating the centroid of the density of states.
core (and are highly coordinated), while Ag atoms form the shell (and are low-coordinated). The average coordination of Cu and Ag atoms is shown in Figure 2c as a function of Ag atoms in the NPs. The figure shows that an increase in the number of Ag atoms leads to a monotonic increase in the average coordination of Cu atoms for up to the Ag27Cu7 NP. This can be understood as the Ag-to-Cu ratio increases (from 0 to 34), Cu atoms are further incorporated into the core, resulting in an increase in their coordination; in contrast, as the number of Ag atoms increases, their average coordination does not vary as significantly as that of Cu atoms (it varies only between 4 and 7.5). The Ag27Cu7 NP is considered as the “magic” nanoalloy because of its high electronic and thermodynamic stability.4 This structure contains a compact decahedral nucleus of Cu atoms in the core, and all the Ag atoms are arranged in an anti-Mackay shell. As one would expect, the diversity in coordination, elemental environment, and the relative positions of the constituent atoms results in contraction and/or expansion of the Cu Cu, Cu Ag, and Ag Ag bond lengths, which leads, in turn, to dissimilarities in the electronic structure. Figure 2d presents a global picture of the changes in the bond lengths: the average Cu Cu, Cu Ag, and Ag Ag bond lengths are plotted as a function of Ag atom content. For Cu34 NPs, we find the average Cu Cu bond length to be 2.52 Å, whereas for Ag34, the Ag Ag bond length is 2.84 Å. The bond lengths are shorter by 3% and 4%, respectively, than those of the nearest-neighbor distances in the bulk. This is expected since the increase in the number of surface atoms leads to contraction of the bonds associated with the decrease in neighboring atoms. For the alloy NPs, we find that, as the Ag content increases, the average Cu Cu bond length stays virtually the same (ranging from 2.53 to 2.55 Å) for all the NPs except for Ag32Cu2 (in which it is 2.69 Å). The average Cu Ag bond lengths are found to fluctuate between 2.68 and 2.72 Å as the Ag atom content increases, except for the Ag-rich NPs (those above Ag30Cu4), for which the bond length gradually increases to 2.79 Å. The shortest average Ag Ag bond length is found to be 2.84 Å (Ag34 NP), whereas the largest is 2.99 Å (Ag32Cu2). As compared with Ag Ag bond lengths in the bulk, the Ag Ag bond lengths in these NPs experience both contraction (∼4%) and expansion (∼1.5%). To discover the relative energetic stability of these alloys, we calculate the formation energy per atom, which is a measure of the NP cohesive energy and is defined as EForm(AgN1CuN2) = [E(AgN1CuN2) N1E(Agiso) N2E(Cuiso)]/N. The first term
III. RESULTS AND DISCUSSIONS A. Geometric Structures, Coordination and Bond Length Distributions. The introduction of a foreign atom into a NP and
the position of that atom within the bonding environment of any other atom in that NP can bring about significant change in the geometric and electronic structures. A thorough understanding of the effects requires exploring the coordination and elemental environment of each atom in any given stoichiometry. We begin by examining the diversity in the geometric structures in order to categorize the NPs with respect to their distinct shapes. Figure 1 shows the structures of some selected bimetallic NPs ranging from pristine Ag34 to pristine Cu34 NPs. We classify the 35 NPs into four distinct groups: (1) nonsymmetric Ag-rich NPs (from Ag34 to Ag28Cu6) and Cu-rich NPs (from Ag4Cu30 to Cu34), (2) symmetric NPs with complete Ag shells (from Ag27Cu7 to Ag16Cu18), (3) symmetric NPs with mixed Cu Ag shells (from Ag15Cu19 to Ag11Cu23), and (4) symmetric NPs with noncomplete mixed Cu Ag shells (from Ag10Cu24 to Ag5Cu29). For the NPs with small Cu-to-Ag ratios (see Figure 1b), Cu atoms form a core. Once the number of Cu atoms reaches seven, a Cu ring is formed, resulting in a defined symmetry (see Figure 1c f) with complete Ag shells, whereas further Cu addition leads to segregation of Cu atoms to the shell (see Figure 1g,i). As we proceed toward Cu-rich NPs, the core shell structure is maintained. We find that, for some NPs, the mixed Cu Ag shells become incomplete (see Figure 1h,j,k). As we proceed toward the NPs with fewer than five Ag atoms to pristine Cu34 NP, the symmetry is lost. Within the family, only Ag27Cu7 and Ag17Cu17 NPs have mirror symmetry. As we shall see later, the geometric structure of the NPs and the relative positions of their components are the key factors in shaping their electronic structure. For determining the dominant coordination of Cu and Ag atoms within the NP family, we calculate the coordination number density. Results are shown in Figure 2a,b. The figure indicates that Cu atoms with a coordination of 12 and Ag atoms with a coordination of 6 are dominant. This analysis also reflects the core shell arrangement of the NPs: Cu atoms occupy the 283
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Figure 2. (a) Number density as a function of coordination for Cu atoms. (b) Number density as a function of coordination for Ag atoms. (c) Average coordination of Cu and Ag atoms as a function of the number of Ag atoms in the NPs. (d) Average Cu Cu, Cu Ag, and Ag Ag bond lengths as a function of the number of Ag atoms in the NPs. (e) Formation energy as a function of the number of Ag atoms in the NPs. The bond length distribution for each NP studied is reported in the Supporting Information.
in the equation is the total energy of the NP, N1 and N2 are the number of Ag and Cu atoms, and E(Agiso) and E(Cuiso) are the energies of isolated Ag and Cu atoms, respectively. In Figure 2e, we plot the formation energies per atom in each NP as a function of the number of Ag atoms. As shown there, the formation energy per atom decreases monotonically from 2.88 eV (Cu34 NP) to 2.09 eV (Ag34 NP) as the number of Ag atoms mounts. The increase in the Ag-to-Cu ratio weakens the average bond strength, decreasing, in turn, the binding energy per atom. This results from the fact that increasing the number of Ag atoms decreases the number of Cu Cu bonds, replacing them with relatively weak Cu Ag and Ag Ag bonds: weaker because the cohesive energy of Ag (2.73 eV) is lower than that of Cu (3.73 eV) atom. B. Alloying Effect on the Total Electronic Densities of States (EDOS). The impact of the differences in the elemental environment, coordination, and bond length of constituent atoms in these NPs can be traced in their EDOSs. However, even before entering into our atom-based analyses, we can see the effect of progressive alloying on the total EDOS throughout the family. To illustrate the changes in the EDOS upon increase in the Cu-to-Ag ratio, we present in Figure 3a f, the total EDOS of six chosen NPs from pristine Ag34 to Cu34 NPs, with a plot of the particle’s EDOS as a background at each figure. The figure indicates that the EDOS of both Ag34 and Cu34 NPs has narrowed in comparison with those for Ag and Cu bulk atoms. This is understandable, as the average coordination of the Ag and Cu atoms in Ag34 and Cu34 NPs is much less than 12 (see Figure 2c), and it is well established that, for TMs, a decrease in coordination narrows the EDOS. As compared with Cu34 NPs, we find Ag34 to experience the most narrowing, owing to the positions occupied by Ag atoms within the NPs. As the figure makes clear, starting from Ag32Cu2 (Figure 3a) and progressing
to Ag2Cu32 (Figure 3f), there is a successive shift in the EDOS toward that for the Cu34 NP. Let us now turn our attention to some striking features observed within these plots for individual NPs. In Ag32Cu2 (Figure 3a), the presence of only two Cu atoms considerably broadens the total EDOS: the calculated center of the d states for the Ag atoms is 4.29 eV, whereas that for the Cu atoms is 2.60 eV, a shift, for the Ag atoms (in comparison with those of the pristine Ag NP), of over 700 meV toward higher binding energy. The EDOS of Ag27Cu7 (see Figure 3b) shows strong hybridization between Cu and Ag states: with respect to that for Ag34, it broadens, and we witness the appearance of new states in both higher and lower binding energy regions: the average position of the center of the d states for Ag atoms is at 3.79 eV, very similar to that for Ag34. The effect of increasing Cu atoms in the NPs becomes apparent as we analyze the EDOS of Ag17Cu17 (see Figure 3c), which shows a shift toward lower binding energy, reflecting the increase in the Cu-to-Ag ratio. The figure shows a splitting in the EDOS into two regions, each of which exhibits the characteristics of Cu and Ag atoms, indicating hybridization between Cu and Ag states. The average position of the center of d states of the Cu atoms is at 2.17 eV, a shift of 700 meV toward lower binding energy relative to that for Cu bulk atoms. However, in comparison with that of the Cu atoms in Cu34 NPs, the change turns out to be small (∼200 meV). For Ag atoms, the position of the center of d states is located at 3.79 eV, also lower (by 600 meV) than that for Ag bulk atoms. A more detailed understanding can be gained by exploring the differences in coordination, elemental environment, and alloying on the coordination and species environment of individual atoms within each NP. For now, we defer discussion of the results of our atom-based analysis below. 284
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Figure 3. Effect of progressive alloying on the total EDOS for (a) Ag32Cu2, (b) Ag27Cu7, (c) Ag17Cu17, (d) Ag10Cu24, (e) Ag7Cu27, and (f) Ag2Cu32.
Figure 4. Average position of the center of d states of Cu and Ag atoms in the NP family. The dashed lines represent the average center of the d states for Cu and Ag atoms in the Cu34 and Ag34 NPs.
Figure 5. Schematic representation of the three parameters (stoichiometry, alloying, and coordination) contributing to the properties of the AgnCu34 n NP family.
The analysis so far indicates that the characteristics of the EDOS are altered as the Cu-to-Ag ratio changes. Since d states predominate over both s and p states for the system of interest here, these alterations can be quantitatively analyzed by calculating the average position of the center of the d states. In Figure 4, these are plotted as a function of the number of Ag atoms. As the figure shows, the average position of the center of d states of Cu atoms in these NPs are very similar to that for Cu34 NPs, whereas for Ag atoms, there is a substantial deviation (∼1 eV) from that of Ag34 at both low and high Ag concentrations. The deviation from the pristine NPs is found to be small for those NPs with a similar number of Cu and Ag atoms. The results suggest that there is structural dependence as well. C. Analysis of the Local Electronic Densities of States. The physical and chemical properties of pristine NPs can, in many cases, be rationalized in terms of coordination differences
between particular atoms. Some of the physical properties of small NPs (nanometer range) may be qualitatively derived from those of low-coordinated atoms in extended systems.25 For the atoms in nanoalloys, however, caution is required, as more factors have to be taken into consideration. For a bimetallic NP of a fixed size, two additional parameters beyond coordination have to be included in the analysis. These are stoichiometry (S), the ratio of the constituent species, and alloying (A), or elemental environment (the number of neighbors of other species). In addition to these new parameters, we will also show that, in some cases, the electronic properties of the atoms in these nanoalloys differ from those of their counterparts in an extended system. This fact makes obsolete the correlation between the characteristics of low-coordinated atoms in extended systems, and those in an alloy NP. To put into perspective the parameters we take into account, we construct a stoichiometry-alloying-coordination “SAC box” 285
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Figure 6. (a) EDOS of Ag atoms in bulk, on Ag(100), and on Cu(100). (b) Effect of the Cu-to-Ag ratio on the EDOS of 4-coordinated Ag atoms. (c) Effect of the Cu-to-Ag ratio on the EDOS of 8-coordinated Ag atoms. (d) Effect of elemental environment (number of Cu neighbors) on the EDOS of Ag atoms. (e) EDOS of Ag atoms in Ag-rich NPs. (f) EDOS of 4-coordimated Ag atoms in different elemental environments. (g) EDOS of 8-coordinated Ag atoms in different environments. The EDOS of the Ag bulk atom is represented as a gray background.
(see Figure 5) with parameters corresponding to those of the AgnCu34 n family. The parameters in this box will be partially explored while discussing the “local” (atom-based) and “global” (simple stoichiometry-based) properties. As the SAC box is not continuous—inasmuch as not every combination of coordination and alloying is available in all NPs—our analysis proceeds by following a series of well orchestrated “walks” (i.e., along segments of lines) inside the SAC box. Before we delve into the details of our atom-based electronic structure analysis, let us recall the effect of coordination on the EDOS of atoms in extended systems. For a TM with more than half-filled d states, the atoms with lower coordination than that of the bulk exhibit d-band narrowing along with an increase in intensity, so as to maintain a fixed occupation number. For highly coordinated atoms, the d band becomes broader relative to that of low-coordinated atoms. A change in coordination rearranges bond lengths that are reflected in the distribution of the EDOS. Narrowing of the EDOS may lead to a shift in the position of the center of d states, an alteration that has proved suitable as a
descriptor for exploring adsorbate-induced reactivity on several metal systems.26 In the following, we monitor the change in the position of the center of d states of the atoms that are exposed to different elemental environments and have varying coordinations in order to asses the changes wrought by both parameters. Let us note that, in the figures reported below, the EDOS are continuous, owing to the 0.2 eV width of the Gaussian functions, as described in the previous section. To put into perspective the changes in EDOS owing to the nanoscale, we show, in Figure 6a, the EDOS of Ag atoms in bulk (background), on Ag(100) (in red), and on Cu(100) (in blue). The comparison of the EDOS of the atoms in the Ag27Cu7 NP and those in the (111) surface is reported in an earlier study using DFT.27 From Figure 6a, we find that the d band of a Ag adatom on Ag(100) shows substantial narrowing compared with its counterpart in the bulk, and the center of its d band shifts toward the Fermi level. When a Ag atom is absorbed on Cu(100), its d band has a much narrower distribution, and the center of its d band shifts away from the Fermi level, in comparison with that of 286
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the Ag on Ag(100). These analyses might lead one to predict that alloying with Cu would introduce further narrowing of the d band. However, as we shall later see, the EDOS of the atoms with the same coordination and elemental environment (in nanoalloys) present some surprising characteristics. Certain economies are in order. As we have in mind the catalytic properties of these core shell NPs, we devote more attention to exploring the EDOS of Ag atoms, which form the shells. Moreover, Cu atoms show a small deviation in their positions of the center of d states throughout all stoichiometries in the family. For these reasons, we restrict our EDOS analysis to Ag atoms with a coordination of 4 and 8 and with zero alloying (i.e., all neighbors are Ag atoms), for various stoichiometries. These analyses allow us to follow a segment of a line that is in the CS plane (at A = 0), and parallel to the S axis with the intercept at C = 4 and 8 (see Figure 5). In Figure 6b,c, we plot the EDOS of 4-coordinated (Figure 6b) and 8-coordinated (Figure 6c) Ag atoms in Ag34, Ag33Cu1, Ag32Cu2, and Ag31Cu3 NPs. For Ag34 (see Figure 6b,c) the difference in coordination is reflected in the EDOS as the noticeable change in width (narrower for 4-coordinated Ag). Moreover, with respect to that of the bulk, the center of d states of 4-coordinated Ag atoms shifts toward the Fermi level. Introducing a single Cu atom (Ag33Cu1 NP) broadens the EDOS of both 4- and 8-coordinated Ag atoms. We thus expect that, for these small-sized NPs, any small perturbation to the bonding environment of a given atom at a proximity to all the others will induce a similarly noticeable effect. What is surprising though is that the changes are not gradual upon increase in the number of Cu atoms (see Figure 6b,c). To isolate the direct influence of alloying on the EDOS, we turn now to examining, for a given stoichiometry (Ag31Cu3), the change in the EDOS of 8-coordinated Ag atoms with Cu neighbors ranging from zero to three: constant C, constant S, and variable A (recall Figure 5). As can be noticed from Figure 6d, the presence of Cu in the immediate neighborhood does not change the observations described in the previous paragraph: we see a substantial broadening of the EDOS regardless of the number of Cu atoms. The redistribution of the EDOS when three Cu atoms are part of the bonding neighborhood results in a shift in the position of the center of d states away from the Fermi level. The analysis of the position of the center of d states of Ag atoms in Ag-rich NPs predicts a sharp drop in the position of the center of d states at the transition from the Ag27Cu7 to the Ag28Cu6 NP (see Figure 5). To understand the underlying reason for this change, we analyze the EDOS of 8-coordinated Ag atoms in the targeted NPs (Ag26Cu8, Ag27Cu7, Ag28Cu6, and Ag29Cu5) when the number of Cu neighbors is kept the same (two), that is, with constant C, constant A, and variable S (recall again Figure 5). We plot the EDOS of these Ag atoms in Figure 6e. As is evident from the figure, the EDOS of Ag atoms in the Ag29Cu5 and Ag28Cu6 NPs are similar, and the position of the center of d states is shifted away from the Fermi level, in comparison with those for Ag27Cu7 and Ag26Cu8. As we move from Ag28Cu6 to Ag27Cu7, we note that, whereas the width of the EDOS seems to remain more or less the same, the position of the center of d states changes noticeably. What emerges from this analysis is that the characteristics of a single atom in such small NPs can be representative of the electronic properties of the NP itself. Comparison between the geometric structures of the Ag28Cu6 and Ag27Cu7 NPs suggests that the change in the position of the center of d states may originate from the differences in shapes.
As shown above, when alloyed with Ag in Ag-rich NPs, Cu atoms induce substantial broadening of the EDOS of Ag atoms. The broadening is also accompanied by a shift in the position of the center of d states of those Ag atoms (see, in particular, the series of NPs from Ag33Cu1 to Ag28Cu6), extending the drop from the position of the center of d states from that of Ag34 to that of Ag33Cu1 (see Figure 4). Note that the above analyses are performed for Ag atoms by fixing two variables out of three (C, A, S). For Cu-rich NPs, the position of the center of d states of Ag atoms also deviates from that of Ag34 NPs (see Figure 4). However, for these NPs, it is not possible to find Ag atoms with the same coordination and/or elemental environment in order to follow any segment of a line in the SAC box to repeat a corresponding analysis as for the Ag-rich end. We now embark on a comparison between the EDOS of lowcoordinated Ag atoms in an extended system (4-coordinated adatom on (100) surface, and 8-coordinated surface atoms of (100)), with those atoms in the alloy NPs with the same coordination. In Figure 6f, we plot the EDOS of a 4-coordinated Ag atom on Ag(100), in Ag34 NP, and in Ag32Cu2 NP, using the EDOS of bulk Ag as a reference. For such a Ag atom in the bulk, the EDOS is broad and becomes noticeably narrower in the Ag34 NP (with a substantial shift in the position of the center of d states toward the Fermi level). When a 4-coordinated Ag atom adsorbs on Ag(100), its EDOS is also narrower than that of the bulk; however, with respect to that of Ag34 NPs, it is smaller. This may be an indication of the finite-size effect. As we examine the EDOS of the 4-coordinated Ag atom in an alloyed NP (Ag32Cu2), we find that alloying induces widening of the EDOS that approaches that of an adsorbate. For the 8-coordinated Ag atom (see Figure 6g), the result is similar for the EDOS as compared to that of the bulk Ag and to that in the Ag34 NP. However, for a surface atom of Ag(100), the EDOS is slightly narrower than that of the bulk, indicative of its being lower in coordination, whereas the EDOS of the 8-coordinated Ag atom in Ag32Cu2 NP becomes wider than that of the bulk. D. Effect of Stoichiometry on the HOMO LUMO Gaps and Ionization Energies. Small single-element metal NPs exhibit striking size-dependent variations in chemical reactivity.28 For determining the key sizes, the energy difference between the HOMO and LUMO is regarded correlative to the band gap. For our bimetallic NPs, we calculate the HOMO LUMO gap for each stoichiometry to explore how progressive alloying affects the gap, and what, in particular, it brings about that works to control the gaps for these nanoalloys. In Figure 7, we plot the HOMO LUMO gaps as a function of the number of Ag atoms. The first thing we notice is the diversity in the gaps ranging from 0.2 to 0.9 eV, although the sizes of the NPs are the same. We also find that the gaps for both Ag-rich and Cu-rich NPs are small, whereas those in the middle of the NP family are large. The NPs at the two ends of the family have no particular symmetry, whereas those situated in the midregion exhibit both well-defined cores and shells and approximate mirror symmetry (except for Ag17Cu17, whose mirror symmetry is perfect). Our results indicate that, for NPs with a well-defined symmetry, the gaps are large, and for those with no symmetry, the gaps are small: a clear correlation between the shape of the NPs and the magnitude of the HOMO LUMO gaps. As it is evident from this pattern with respect to the gaps, mixing of these two metals at the nanoscale for certain stoichiometries modifies the metallic character significantly. Small gaps 287
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length between a Cu 0( atom and its nearest Cu ring+ atom is 2.46 Å; that between the former and its nearest Cu ring atom is 4.08 Å. The bond length (2.48 Å) between neighboring atoms within either of the chain Cu atoms (Cu 0( ) is much shorter than in the bulk, indicating a stiffening of the bonds in the core of the NP. The bond lengths between the atoms in the Cu ring0 are much shorter than those in the Cu ring+. The bond lengths between neighbors within the Ag rings are 4.18, 4.23, and 5.01 Å for Ag ring+, Ag ring0, and Ag ring , respectively. We also find that the bond length between an atom in either of the chain Cu atoms (Cu 0( ) and the nearest atom in the Ag chain atom (Ag 0+) is 2.51 Å, which is also shorter than the bond length for the Cu Ag dimer. In addition to the stiffening of the bond within the Cu ring atoms, there is also stiffening of the bonds between the atoms in the chain. The shortest Cu Cu, Cu Ag, and Ag Ag bond lengths are found to be 2.46, 2.52, and 2.98 Å, respectively. The large contraction of the bond lengths between the atoms in the core of the NP also appears in the vibrational dynamics12 and in the local EDOS. To determine the region with the highest charge accumulation within the NP, we calculate the charge density distribution by subtracting the charge density of each atom from the total charge density of the NP while keeping the positions of the atoms exactly the same as they are in the NP. We present our results in Figure 8c. The figure suggests that the charge density accumulates in the core (red area), which is where the stiffening of the bonds is found to be the highest. This stiffening originates from the high coordination of Cu core atoms, each with a large number of Cu neighbors. To trace the effect of coordination, bond lengths, and the local species environment on the electronic structure, we examine the EDOS of each atom as these variables change. In Figure 8d f, we plot the partial EDOS (d states only) of the three Cu atoms, together with the partial EDOS of the Cu bulk atom. Notice that the EDOS of the chain atoms (Cu 0( ) show broadening with respect to that for bulk atoms. The bond length with its 11 Cu neighbors of ). the 12-coordinated chain atom residing at the core is short (2.46 Å The partial DOS (PDOS) of the highly coordinated inner Cu ring atoms (Cu ring0) also shows slight broadening, and the bond length , which is between the neighboring Cu atoms in the ring is 2.55 Å ) slightly shorter than that in the bulk. The short bond length (2.53 Å between atoms in the Cu ring0 and their nearest Ag ring( neighbors signals strong hybridization between the Cu and Ag states. For the chain atoms, the overlap between Cu Cu states originates from the short Cu Cu bond lengths, which, in turn, are due to high coordination, together with a large number of Cu neighbors. The PDOS of the outer Cu ring atoms (Cu ring( ) shows a narrowing with respect to that of the bulk (Figure 8f). This is attributable to their low coordination (9). Figure 8g i shows the PDOS for the three Ag atoms. The PDOS of the Ag chain atoms (Ag 0+) shows narrowing as compared with that for the Ag bulk atom. The Ag chain atom is 6-coordinated and has no Ag neighbors. The hybridized states can be understood as resulting from the presence of a large number of Cu neighbors. In contrast to the PDOS of the chain atoms, that of the inner Ag ring atom (Ag ring0) shows broadening, reflecting its high coordination (8). Figure 8i summarizes the electronic DOS of the outer Ag ring atoms (Ag ring( ). There is narrowing relative to Ag bulk owing to its low coordination (5). The existence of three Cu neighbors in the bonding environment leads to the emergence of new states. In Figure 8j, we report the change in the average position of the d states for both Cu and Ag atoms. We find that only highly
Figure 7. HOMO LUMO gaps as a function of the number of Ag atoms. The inset figures show the geometric structures of the selected NPs.
suggest chemical activity, whereas large gaps indicate chemical inactivity. We first notice that those NPs with completely closed shells (see Figure 7) have large HOMO LUMO gaps. This may be understood by the fact that high symmetry increases hybridization by way of strong overlapping of the wave functions. In contrast, in those NPs with open shells and low or no symmetry, the overlap between wave functions is small, resulting in creation of new states close to the Fermi level: hence, the much smaller gaps exhibited by these less regularly structured NPs (see Figure 7). As it is a measurable quantity and potentially accessible to experiment, we also calculated the ionization energy for each stoichiometry, that is, the energy required to remove an electron from the system. Our calculations predict that ionization energies vary between 4.05 and 4.50 eV. To put this into perspective, the calculated ionization energies are close to those of the work functions of the extended systems Cu(100) and Ag(100), which are 4.50 and 4.27 eV, respectively. Our results show that there is no monotonic dependence of the ionization energies on change in the Cu-to-Ag ratio; rather, the ionization energies fluctuate between the values reported above. E. Ag17Cu17 NP: Structural Characteristics, EDOS, and Charge Density Distribution. We proceed now to the analysis of the bond lengths between each atom and every one of its neighbors, its charge-density distribution, and its EDOS for that instance within the family that has the most pronounced mirror symmetry (see Figure 8a) and the highest HOMO LUMO gap. This NP is made of three Ag and three Cu rings, each consisting of five atoms (see Figure 8b). Additionally, the chain has two Ag (Ag 0( ) and two Cu atoms. For ease of reference, we classify the rings from the mirror plane as Cu ring0, Cu ring( , Ag ring0, and Ag ring ( (see Figure 8b). The Cu 0+ and Cu ring0 (inner ring) atoms are 12-coordinated (with 11 Cu and 8 Cu neighbors, respectively). The atoms in the Cu ring+ are 9-coordinated (with five Cu neighbors). The coordination of Ag ring0, Ag 0+, and Ag ring+ atoms are 8, 6, and 5, respectively. Ag 0+ atoms have six Cu neighbors, Ag ring0 atoms four Cu, and Ag ring+ three Cu neighbors. The bond length between a Cu 0( atom and its nearest Cu ring0 (inner ring) atom is found to be 2.49 Å, which is 3.3% shorter than that of the bulk nearest-neighbor distance. The bond 288
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Figure 8. (a) Schematic view of the Ag17Cu17 NP. (b) Schematic view of the rings of the Ag17Cu17 NP. (c) Charge density distribution. (d) EDOS of Cu 0+. (e) EDOS of Cu ring0. (f) EDOS of Cu ring(. (g) EDOS of Ag 0+. (h) EDOS of Ag ring0. (i) EDOS of Ag ring(. (j) Position of the center of d states. (k) Coordination distribution. (l) Distribution of average bond lengths.
We find that, as the Ag-to-Cu ratio increases, the average coordination increases more rapidly for Cu atoms than for Ag ones, as a result of the fact that the core (Cu) shell (Ag) structure is energetically favored in this family of NPs. We find that the average bond length of a given NP increases with increasing Ag atom content, while the formation energy decreases with increasing Ag atom content. This is attributable to the fact that the number of Cu Cu bonds decreases as these are replaced by Cu Ag and Ag Ag bonds, with strengths relatively lower than those of Cu Cu, reflecting the hierarchy in the bond, as dictated by the relative cohesive energies of Cu (the larger) and Ag. Analysis of the electronic structure for the AgnCu34 n NP family reveals the importance of understanding atomically
coordinated atoms show distinct values for the position of the centers of the d states. The broadening observed for Cu 0+ atoms relative to what is characteristic of the bulk is in agreement with the change in the position of its center of d states. As to the Ag atoms, since their coordination distribution is not broad and there are no highly coordinated Ag atoms with short bond lengths, the centers of their d states do not show distinct values.
IV. CONCLUSION We carried out DFT calculations of the atomic and electronic structures of the AgnCu34 n NP, analyzing the latter both globally and locally. 289
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The Journal of Physical Chemistry C resolved contributions to the overall electronic structure of each NP. As we compare the EDOS of the bimetallic NPs with those of the two pristine NPs, we observe shifts toward either higher or lower binding energies as well as hybridization between the states of Cu and Ag atoms. Our analysis shows that these changes can be understood by examining the characteristics of individual atoms as the overall properties of such (small) finite-sized systems may be governed by just a few atoms with distinct properties. We have performed detailed local analyses of the EDOS using three parameters, namely, the stoichiometry, the relative elemental environment, and the average coordination (SAC) of the two elemental species. We performed the analysis by fixing two of these parameters and varying the third one within the limits allowed by the structure of the particular alloy NPs. We find that, for the silver-rich NPs, the presence of a single copper atom in the NP induces a substantial broadening of the EDOS of the Ag atoms, accompanied by a shift of the position of the center of the d states. The latter is strongly dependent on the stoichiometry, inasmuch as the number of silver atoms in a given NP substantially changes its shape. At the Ag- and Cu-rich ends, the NPs present nonsymmetric shapes, inducing shifts of the position of the d states’ center. This fact is also reflected in the HOMO LUMO gap. The correlation between the magnitude of the gap and the geometric structure persists throughout the whole family. The effect of coordination is similar to that for single-element systems, namely, a narrowing of the EDOS with a decrease in the average coordination. Detailed analysis of one of the most symmetric NPs (Ag17Cu17) shows that the charge density distribution explicitly correlates with the accumulation of charge and the stiffening of bond lengths. In comparison with the outer Cu ring atoms, there is a stronger charge accumulation among the inner Cu ring atoms. This is in agreement with the hierarchy of bond lengths between the atoms within each ring, as reflected in our calculated charge density differences, which show a charge accumulation at the core of the NP. The stiffening of the bond lengths between the core atoms reaches up to 4% with respect to that in the bulk, causing the Cu core atoms to be “over-coordinated.” The EDOSs of these particular atoms show a broadening of the band relative to that of a bulk atom: short bond lengths induce strong overlap between the d orbitals, followed by hybridization between the states. The Ag atoms in the NPs are rarely as highly coordinated as the Cu atoms, owing to the fact that they form the shell. Hence, the relatively few highly coordinated Ag atoms that appear only in Ag-rich NPs—from Ag34 to Ag28Cu6—and the position of their center of the d states are also shifted toward higher binding energy. Because the d band of Cu is much closer to the Fermi level than that of Ag, it is to be expected that Cu is more reactive than Ag, as indeed it is known to be. In terms of reactivity of these NPs, our analysis shows that mixing of Ag with Cu does not seem to affect the overall reactivity of Ag atoms. Rather, only those NPs with a relatively large number of Cu atoms at the shell (which are low-coordinated) are expected to be chemically active. In summary, the extensive electronic structure analysis indicates that physical and chemical properties of this core shell NP family can be tuned by controlling the chemical composition and thereby the relative sizes of the core and the shell.
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’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected]. Present Addresses †
Center for Nanoscale Materials, Argonne National Laboratory, Argonne, IL 60439.
’ ACKNOWLEDGMENT We thank Lyman Baker for careful reading of the manuscript and many constructive comments. We also thank R. Ferrando for providing the initial configurations of the NPs. This work was supported, in part, by DOE Grant DE-FG02-07ER46354. ’ REFERENCES (1) (a) Ferrando, R.; Jellinek, J.; Johnston, R. L. Chem. Rev. 2008, 108, 845. (b) Bonnemann, H.; Richards, R. M Eur. J. Inorg. Chem. 2001, 10, 2455. (c) Jellinek, J. Faraday Discuss. 2008, 138, 11. (d) Haruta, M. Catal. Today 1997, 36, 153. (e) Valden, M.; Lai, X.; Goodman, D. W. Science 1998, 281, 1647. (2) (a) Enache, D.; et al. Science 2006, 311, 362. (b) Gaudry, M.; Cottancin, E.; Pellarin, M.; Lerme, J.; Arnaud, L.; Huntzinger, J. R.; Vialle, J. L.; Broyer, M.; Rousset, J. L.; Treilleux, M.; Melinon, P. Phys. Rev. B 2003, 67, 155409. (3) (a) Baletto, F.; Mottet, C.; Ferrando, R. Phys. Rev. Lett. 2003, 90, 135504. (b) Pratti, R.; Rossi, M. J. Catal. 1998, 176, 552. (c) Toshima, N.; Kanemaru, M.; Shiraishi, Y.; Koga, Y. J. Phys. Chem. B 2005, 109, 16326. (d) Li, Z. Y.; Yuan, J.; Chen, Y.; Palmer, R. E.; Wilcoxon, J. P. Microsc. Microanal. 2005, 11, 1450. (4) (a) Baletto, F.; Ferrando, R. Rev. Mod. Phys. 2005, 77, 371. (b) Rossi, G.; Rapallo, A.; Mottet, C.; Fortunelli, A.; Baletto, F.; Ferrando, R. Phys. Rev. Lett. 2004, 93, 105503. (c) Barcaro, G.; Fortunelli, A.; Rossi, G.; Nita, F.; Ferrando, R. J. Phys. Chem. B 2006, 110, 23197. (d) Calleja, M.; Rey, C.; Alemany, M. M. G.; Gallego, L. J.; Ordejon, P.; SanchezPortal, D.; Artacho, E.; Soler, J. M. Phys. Rev. B 1999, 60, 2020. (5) (a) Darby, S.; Mortimer-Jones, T. V.; Johnston, R. L.; Roberts, C. J. Chem. Phys. 2002, 116, 1536. (b) Johnston, R. L. Dalton Trans. 2003, 4193. (c) Roberts, C.; Johnston, R. L.; Wilson, N. T. Theor. Chem. Acc. 2000, 104, 123. (6) (a) Rosato, V.; Guillope, M.; Legrand, B. Philos. Mag. A 1989, 59, 321. (b) Guillope, M.; Legrand, B. Surf. Sci. 1989, 215, 577. (c) Cleri, F.; Rosato, V. Phys. Rev. B 1993, 48, 22. (7) Rapallo, A.; Rossi, G.; Ferrando, R.; Fortunelli, A.; Curley, B. C.; Lloyd, L. D.; Tarbuck, G. M.; Johnston, R. L. J. Chem. Phys. 2005, 122, 194308. (8) Pearson, W. B. The Crystal Chemistry and Physics of Metals and Alloys; Wiley: New York, 1972. (9) (a) Belloni, J.; Mostafavi, M.; Remita, H.; Marignier, J.-L.; Delcourt, M.-O. New J. Chem. 1998, 22, 123. (b) Cazayous, M.; Langlois, C.; Oikawa, T.; Ricolleau, C.; Sacuta, A. Phys. Rev. B 2006, 73, 113402. (c) Janssens, E.; Neukermans, S.; Wang, X.; Veldeman, N.; Silverans, R. E.; Lievens, P. Eur. Phys. J. D 2005, 34, 23. (10) Ferrando, R.; Fortunelli, A.; Rossi, G. Phys. Rev. B 2005, 72, 085449. (11) Yildirim, H.; Kara, A.; Rahman, T. S. J. Phys.: Condens. Matter 2009, 21, 084220. (12) (a) Roldan Cuenya, B.; Croy, J. R.; Ono, L. K.; Naitabdi, A.; Heinrich, H.; Keune, W.; Zhao, J.; Sturhahn, W.; Alp, E. E.; Hu, M. Phys. Rev. B 2009, 80, 125412. (b) Naitabdi, A.; Roldan Cuenya, B. Appl. Phys. Lett. 2007, 91, 113110. (13) (a) Cazayous, M.; Langlois, C.; Oikawa, T.; Ricolleau, C.; Sacuto, A. Microelectron. Eng. 2007, 84, 419. (b) Parsina, I.; Baletto, F. J. Phys. Chem. C 2010, 114, 1504. (c) Calvo, F.; Cottancin, E.; Broyer, M. Phys. Rev. B 2008, 77, 121406. (14) (a) Barber, D. J.; Freestone, I. C. Archaeometry 1990, 32, 33. (b) Benten, W.; Nilius, N.; Ernst, N.; Freund, H.-J. Phys. Rev. B 2005, 72, 045403.
’ ASSOCIATED CONTENT
bS
Supporting Information. The bond length distribution for each NP studied. This material is available free of charge via the Internet at http://pubs.acs.org. 290
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