Chemical Ordering in Pt-Au, Pt-Ag and Pt-Cu Nanoparticles from Density Functional Calculations Using a Topological Approach

. Bimetallic alloys are actively investigated as promising new materials for catalytic and other energy-related applications. However, the stable arrangements of the two metals in prevailing nanostructured systems, which define their structure and surface reactivity, are seldom addressed. The equilibrium chemical orderings of bimetallic nanoparticles are usually different from those in the corresponding bulk phases and hard to control experimentally, which hampers assessment of the relations between composition, structure, and reactivity. Herewith, we study mixtures of platinum —an essential metal in catalysis— alloyed with coinage metals gold, silver, and copper. These systems are interesting, for instance, for reducing the costly Pt content and designing improved multifunctional catalysts, but the chemical orderings in such mixtures at the nanoscale are still debated. We therefore explore chemical orderings and properties of Pt-containing nanoalloys by means of a topological method based on density functional calculations. We determine the lowest-energy chemical orderings in 1.4 to 4.4 nm large Pt-Au, Pt-Ag, and Pt-Cu particles with different contents of metals. Chemical ordering, bonding, and charge distribution in the nanoparticles are analyzed, identifying how peculiar structural motifs relevant for catalysis and sensing applications, such as monometallic skins and surface single-atom sites, emerge. We compare these results with previous data for the corresponding Pd-based particles, identifying trends in chemical ordering, deepening understanding of the behaviour of catalytically relevant bimetallic compositions, and establishing appropriate models for studying the bimetallic nanoalloys.


Introduction
Studies of materials containing bimetallic nanoparticles (NPs), often referred to as nanoalloys, is a dynamically developing research area. The latter is interrelated to diverse applications of nanoalloy particles ranging from optics and magnetism to medicine and catalysis. 1,2 Properties of a bimetallic NP are defined, besides its geometric structure and size, by the relative amount (composition) of the two constituting metals. Tuning the composition extends the preparation means of materials containing bimetallic NPs tailor-made for the desired applications to function better, often at reduced cost.
The size, shape, and composition of bimetallic NPs can be quite well controlled by the preparation conditions. At variance, such elusive degree of complexity as chemical (or atomic) ordering, i.e. a distribution pattern of metal atoms of two types among lattice positions of an alloy NP, is hard to precisely control experimentally. The reactivity of metal NPs is directly related to their surface arrangement. The chemical ordering defines what types and how many surface sites are exposed by a bimetallic NP of a given size, shape, and composition. This is key information for catalysis, sensing, and many other applications. Yet, it remains barely accessible experimentally at the atom-by-atom level even for the most modern structure characterization techniques.
Computational modeling using Density Functional Theory (DFT) can provide detailed information about the structure and properties of bimetallic NPs complementing experimental data. DFT calculations of bimetallic NPs with over a hundred atoms and sizes of ~1.5 nm, which are required to realistically represent larger particles dealt with in catalysis, [3][4][5] are feasible since two decades. 6 However, the presence of more than one type of atoms in nanoalloys severely hinders their comprehensive DFT simulation, often restricting it to quite small particles and considering only several chemical orderings (homotops). [7][8][9][10][11][12] In fact, a direct search for the equilibrium chemical ordering in a ~2 nm large bimetallic crystallite comprising ~200 atoms requires calculating energies of a colossal number of 10 50 homotops (including symmetry-equivalent ones), 13 which is excessive for any computational method.
This challenge can be dealt with by a Topological (TOP) approach, 14,15 which enables determining equilibrium chemical orderings in bimetallic nanocrystallites containing 10 2 - 10 4 atoms of different metals across the Periodic Table from a small number of DFT calculations.
Briefly, the TOP method divides all homotops of a bimetallic nanocrystallite with a given stoichiometry and shape into groups with the same topologies. Definition of the latter depends on how atomically detailed the resulting ordering needs to be. For instance, for studying the catalytic activity of a bimetallic M' m M n NP comprising m+n atoms it is essential to know how many active surface sites of each type the NP exposes. These data are related to the propensity of M' and M atoms to segregate on the surface and define which atoms occupy surface positions of the NP with different coordination numbers, e.g. in corner, edge, and terrace sites.
Since all homotops of the NP under scrutiny share the same crystal lattice and composition, it suffices to specify atomic positions for just one of the two metals. The types of the exposed  Successfully determined chemical orderings in NPs of various metal combinations, such as Pd-Au, [13][14][15]17 Pd-Ag, 14 Pd-Cu, 14 Pd-Zn, 14 Pd-Rh, 16 Pt-Ag, 18 Pt-Co, 19,20 Pt-Ni, 21 Pt-Sn, 22 and Ni-Cu, 23  deepening the knowledge of the accuracy and applicability of the Topological approach; iv) identifying equilibrium chemical orderings in Pt-Au, Pt-Ag, and Pt-Cu particles at common for catalysis sizes over 4 nm, also at elevated temperatures.

Computational methods
All DFT calculations were performed using the plane-wave code VASP. 27

Results and discussion
In the following we present and discuss results for model Pt-X (X = Au, Ag, Cu) NPs   increasing Pt:Au content from 1:3 to 1:1, and to 3:1 suggests that the location of Pt atoms in facets of Pt-Au NPs is less energetically penalized at lower Pt concentrations than at higher ones. The surface segregation of Au atoms in the 201-atomic Pt-Au NPs with the lowestenergy orderings is illustrated in Figure 2 and additionally detailed in Table 2  These two examples demonstrate that the TOP method, beyond providing adequate relative energies of different chemical orderings of a bimetallic NP, also allows rationalizing the energy differences in such important terms as propensities of their two types of metal atoms to form heterometallic bonds and to occupy differently coordinated surface sites.

DFT data for chemical orderings of Pt-Au nanoparticles
Pt 70 Au 70 nanoparticle. The size-sensitivity of the interactions governing equilibrium orderings in Pt-Au NPs at a given Pt:Au composition can be explored by comparing the ordering of the Pt 101 Au 100 particle with that of the smaller Pt 70 Au 70 particle sketched in Fig. 1.
One can see from Table 1  Pt -Au BOND the same quantity for Pt 101 Au 100 , indicating that quite low immiscibility of Pt and Au atoms is almost independent of the particle size in this size range. Surface segregation of Au atoms is strongly energetically preferred also in the Pt 70 Au 70 particle. There, the energy gain by displacement of an inner atom Au to a corner without changing the number of Pt-Au bonds (i.e. ) is 619 meV, exceeding that for Pt 101 Au 100 particle, 530 meV. At variance, the

Charge distribution. Only a minor charge redistribution occurs between Pt and Au atoms in
Pt-Au NPs. According to the Bader charge analysis, see Table 3   feature a strong stabilization in surface sites that decreases with increasing their coordination numbers, from 625 meV in the 6-coordinated corner site, to 336 meV in the 7-coordinated edge site and to 195 meV in the 9-coordinated facet (terrace) site, see Table 1. The equilibrium ordering in Pt 70 Ag 70 NP, see Figure 1 and Table 2 Ag surface sites on Pt-Ag NPs should also differ from reactivity of these sites on Ag NPs. The energy terms ε in Table 1 reveal that Cu atoms being smaller than Pt ones (and Au and Ag atoms) are destabilized in the surface positions of Pt-Cu NPs. This occurs despite the propensity to separate of two metal components in the Pt-Cu systems compared to the Pt-Au and Pt-Ag analogues, see Table 2 and Figures 1 and 2.

DFT data for chemical orderings of Pt-Cu nanoparticles
At the lowest studied Cu content (3:1 Pt:Cu), all 50 Cu atoms of Pt 151 Cu 50 NP are energetically driven to be located inside the monolayer Pt skin and to form 412 bonds with inner and surface Pt atoms, see Table 2

Miscibility of Pt atoms with Au, Ag, and Cu atoms at the nanoscale
As already mentioned, Pt atoms in bulk alloys are immiscible at common conditions with Au and Ag atoms, but they mix with Cu atoms. These miscibility relations in the bulk are properly reflected in the terms of the studied Pt-X NPs, see Table 1, manifesting relative a Pt m X n particle is calculated as: where a negative sign of E exc indicates favorable mixing of Pt and X atoms in the particle.
The DFT excess energies of 201-atom Pt-X NPs are plotted in

Comparison of Pt-X and Pd-X nanoparticles (X = Au, Ag, Cu)
To better understand differences and similarities in the catalytic behavior of Pt-and Pd-based nanomaterials we compare the chemical ordering and related properties of the Pt 70 X 70 NPs with the previously calculated data for the Pd 70 X 70 NPs. 14 The main qualitative difference of changing Pt to Pd in the nanoalloys with Au and Ag, see   In the cases of Pd-Cu and Pt-Cu NPs Pd and Pt atoms show a strong preference to be located in the surface skin and to form stabilizing heterometallic bonds, see Tables 1 and 2. Thus, the presence of Pd and Pt on the surface of these nanoalloys as unique single-atom catalytic sites is conceivable only at very low concentration of the platinum-group metals.

Performance of the Topological method to describe chemical orderings
The present TOP method 14 To evaluate the correctness of some of these assumptions we randomly generated ≥10 different homotops for several selected topologies of Pt-Au and Pt-Cu NPs and locally optimized those by DFT; see results in Table S1. The DFT energy splits for the homotops belonging to each of the considered low-energy topologies of 201-atomic Pt-Au NPs are very A similar procedure could be applied to go beyond the topology approach, when a more precise energetic representation of chemical orderings is required for assessing notably higher-lying homotops. One can see from Table S1 a  respectively; see structures of the homotops with minimum and maximum DFT energies of these topologies in Figure S1, are notably larger than those for the 201-atom Pt-Au and Pt-Cu NPs. Again, the Pt-Cu homotops split more than the Pt-Au homotops. Our detailed analysis of this splitting reveals that not all atoms of one type (Pt-Pt, Pt-X, or X-X bonds) are equivalent, i.e. that the energy of bonds formed by Pt or X atoms to each of their first neighbours is partially dependent on the identity (and quantity) of the rest of first neighbours. This challenges the convenient assumption that all bonds between a given pair of atoms are equally strong. In addition, certain structural motifs (such as {111} facets solely composed of Au) seem to become stable for some compositions due to elusive long-range interactions neglected by the employed topological description.
Although the  values in Table 1 may seem large, they correspond to average prediction errors 1 to 6 meV/atom. The large size of the studied particles obviously increases the errors in total energies, but changes in energy caused by permuting atoms are, on average, rather well approximated. This means that irrespective of possible inaccuracies of the present TOP approach based on the DFT structure optimization, the equilibrium chemical orderings in bimetallic nanoalloys provided by this approach approximate reasonably well those obtained with the employed DFT exchange-correlation functional. The calculated atomic-level data, which are notably more detailed than those currently accessible experimentally, are very useful for rationalizing surface reactivity of bimetallic catalysts and related applications.

Larger Pt-based nanoparticles and temperature effects on the chemical ordering
Chemical orderings with the lowest-energy topology were also determined for ca. 4.4 nm large fcc truncated octahedral Pt 732 X 731 NPs using the energies ε obtained for 140-atomic Pt 70 X 70 and for 201-atomic Pt 101 X 100 NPs, see Table 1. Orderings of these homotops at 0 K, denoted as Pt 732 X 731 (140) and Pt 732 X 731 (201) , respectively, are shown in Figure 4 and occupations of various atomic positions in them are quantified in Table 4.  Table 4 and Figure 5 for the results corresponding to 300, 600, and 1000 K. In Pt 732 Cu 731 NP the number of stabilizing Pt-Cu bonds slightly decreased at higher temperatures, from 58% at 0 K to 54% at 1000 K. Cu atoms migrate upon the temperature increase from corner and edge positions most populated at 0 K primarily to surface terrace positions.

Summary and conclusions
We The results presented in this work are relevant for studies in which structure and surface properties of a large number of bimetallic compositions are simulated using machine-learning and/or high-throughput approaches. Such studies often relied on models produced by directly cutting bulk structures, 58,59 without considering that due to the stability of particular chemical orderings inherently different sites can be exposed on the surface.

Author contributions
L

Conflicts of interest
There are no conflicts to declare. b When several homotops were optimized by DFT for one of the selected ≥10 low-energy topologies, see Section 3.6, all these E DFT values were also used in the calculations of δ.