Controlling Structural Transitions in AuAg Nanoparticles through Precise Compositional Design

: We present a study of the transitional pathways between high-symmetry structural motifs for AgAu nanoparticles, with a speci ﬁ c focus on controlling the energetic barriers through chemical design. We show that the barriers can be altered by careful control of the elemental composition and chemical arrangement, with core@shell and vertex-decorated arrangements being speci ﬁ cally in ﬂ uential on the barrier heights. We also highlight the complexity of the potential and free energy landscapes for systems where there are low-symmetry geometric motifs that are energetically competitive to the high-symmetry arrangements. In particular, we highlight that some core@shell arrangements preferentially transition through multistep restructuring of low-symmetry truncated octahedra and rosette-icosahedra, instead of via the more straightforward square-diamond transformations, due to lower energy barriers and competitive energetic minima. Our results have promising implications for the continuing e ﬀ orts in bespoke nanoparticle design for catalytic and plasmonic applications.

N anoparticles (NPs) consist of between a few and many thousands of atoms or molecules, interacting to form discrete particles. 1 NPs have properties that are distinct from bulk and atomic systems, which, when considered alongside their nanoscale size, make them very suitable for applications in scientific fields such as medicine, optics, and catalysis. 2−7 Recent research has shown that the nuclearity, composition and chemical ordering of bimetallic NPs can be well controlled during synthesis, 8−14 but it remains an experimental challenge to control the shape of these systems. 5,9,15 From an applied catalysis perspective, it would be beneficial if one could preferentially form greater quantities of reactive sites, such as vertices and edges, 5,8,16−21 over unreactive sites. However, synthesis, characterization, and application of the NPs is generally performed under conditions that do not aid structure stabilization: A multitude of geometric arrangements coexist on most energy landscapes, 8,22,23 possibly with similar energies and separated by transition barriers that can be overcome at room temperature. 15,24,25 The elevated operating temperatures for catalytic applications further exacerbates the problem of structural instability, and therefore understanding how to control the morphologies of NPs is of paramount importance to further their commercial applicability.
The size of NPs makes them an attractive problem to address with computational techniques, and previous work using thermodynamic sampling has identified key transition pathways and barriers between structural motifs at a range of different nuclearities, 16,26−30 as well as demonstrating how the energy barriers change with chemical ordering in bimetallic NPs. 31−34 One well-characterized pathway is the martensitic transformation between icosahedral (Ih) and cuboctahedral (CO) motifs via the so-called sextuple diamond−square−diamond (DSD) mechanism: 26,35 Triangular facets are stretched and then rotated to form a diamond one and then transformed to a square facet 26 (DS), with the reverse square−diamond process (SD) leading to reformation of the Ih from the CO. Recently, forward (SD) and backward (DS) transition pathways have been characterized at finite temperatures through molecular dynamics modeling for 147-atom Ag and AuAg NPs; 32,33 however, no such transition occurs for Au NPs, 32, 34,36 showing that structural stability or transition barriers change considerably as a function of chemical composition. From a structural design perspective, controlling these transitions via chemical methods would be ideal, but there has been limited investigation of how to use NP composition to achieve this goal. Thus we present work in this Letter that shows how the transition barriers between different geometries for bimetallic AuAg NPs can be altered by careful chemical arrangement and stoichiometric control, which could allow NP design through improved stability of certain structures.
We have focused on the transition between the Ih and CO motifs, which are high-symmetry NP morphologies with identical nuclearities but significant structural differences: The Ih has low internal volume and the surface is composed of 20 (111) facets, while the CO is an FCC fragment with greater volume and a mix of (100) and (111) surfaces. 37 The relative stability of these motifs varies with elemental composition and also depends on the number of atoms (N) in the NPs. 8,37,38 We have focused on the "magic" number of N = 147, which ensures geometric closed-shells in the structures of interest. 37 We have used a range of complementary modeling techniques, coupled to empirical potentials, 32,39,40 to investigate transition pathways between structures, and subsequent energy barriers, in both the thermodynamic and kinetic regime. A pathway-exploring doubly nudged elastic band (DNEB) algorithm, 41 as implemented in the OPTIM packages, 42,43 was used for identification of transition pathways at 0 K, while for exploration of the free-energy landscape we used the complementing discrete path-sampling (DPS) routines from OPTIM, namely, PATHSAMPLE, 42−46 as well as our own metadynamics software. 30 In particular, metadynamics includes anharmonic effects that are disregarded by DPS and also offers a quasi-agnostic exploration of the energy landscape due to the open-ended search of the conformational space. 47,48 When not identified during the transition pathway calculations, the DS/ SD pathways between local minima were tested manually using the optimization routines in GULP. 49 Initially, the stabilities of the monometallic Ag 147 and Au 147 NPs were calculated: DNEB pathways were identified with one barrier for the forward (CO → Ih) and backward (Ih → CO) transitions. The pathways follow the SD and DS routes, respectively, with the respective barrier energies, ΔE(CO → Ih) and ΔE(Ih → CO), being 0.50 (1.14) and 3.37 (2.33) eV for Ag 147 (Au 147 ).
Substitution of a single Au dopant in to the Ag 147 NP generally results in minor variation of the forward and barrier, by ±0.02 eV. Exceptional changes in ΔE(Ih → CO) occur when the Au is positioned: (i) subsurface below an edge atom (3.33 eV) and (ii) in the middle of the (111) surface facet (3.30 eV). For Ag dopants in the Au 147 NPs, slight variation was again observed: the barriers are generally reduced by at most 0.05 eV from the Au 147 values. An exception occurs when Ag is positioned at a surface vertex, with ΔE increased by 0.02 eV in both directions; however, the transition mechanism remains identical. Ag doping in the middle of the (100) facet also reduces ΔE(CO → Ih) and ΔE(Ih → CO) by 0.06 and 0.09 eV, respectively, to 1.08 and 2.24 eV.
A distinct variation occurs when Ag is positioned at the center of Au NP, akin to a core@shell arrangement. This Ag 1 @ Au 146 arrangement is the energetically least favorable for an Ag dopant, 40 and we discover that the thermodynamic pathway between CO and Ih motifs contains 44 local minima (Figure 1, top). In this case, ΔE(CO → Ih) increases to 2.03 eV and ΔE(Ih → CO) to 3.01 eV compared with Au 147 . The transition goes through a variety of truncated octahedra (TO) and rosette-Ih (r-Ih) motifs, 16,29 proceeding via sequential CO → TO → r-Ih → Ih transitions. Through the transformation, the Ag atom is maintained in the central position of the NP, and a ring of Au atoms forms at the surface to expose a subsurface atom; the lowest energy structure encountered has just one of these rosette indentations. Calculations of the SD and DS pathways for Ag 1 @Au 146 give ΔE(CO → Ih) and ΔE(Ih → CO) as 1.19 and 2.22 eV, which are lower than the r-Ih route and similar to the other values for Ag-doped Au NPs. Analysis of the r-Ih transition pathway shows that the initial energy barriers are marginally lower than for the SD mechanism ( Figure 2, top) and that the Ih and r-Ih motifs are close in energy.
We expanded our calculations to include larger cores of two and three concentric shells of atoms, corresponding to the central 13 and 55 atoms, respectively. DNEB calculations for Au 13 @Ag 134 and Au 55 @Ag 92 give ΔE(CO → Ih) as 0.40 and 0.55 eV, with all transformations via the SD mechanism. The reduction of ΔE for Au 13 @Ag 134 is matched for ΔE(Ih → CO), where the same compositions have thermodynamic barriers of 3.25 and 2.78 eV, respectively, implying that the transition state is reduced in energy.
In contrast, the DNEB pathways are more complicated for Ag 13 @Au 134 and Ag 55 @Au 92 , proceeding via the r-Ih intermediates already observed for Ag 1 @Au 146 ; ΔE(CO → Ih) is 1.52 and 3.07 eV for these compositions, respectively, while ΔE(Ih → CO) is 2.34 and 3.98 eV. It is noted that the rate of transformation is determined by the size of the Ag core: at low Ag concentration, deformation of the CO is the timeconsuming process, with the crossover point between CO-and Ih-like structures higher in energy than for the starting structures (Figure 1, top), whereas at higher Ag concentration, the transition between CO-and Ih-like motifs is via motifs that are lower in energy than the starting structures, and thus r-Ih deformation becomes rate-limiting (Figure 1, bottom). A detailed structural analysis is presented in the Supporting Information, with a distorted TO formed in each case ( Figure  3a) before transforming to an r-Ih (Figure 3b) via rotation and stretching similar to the SD mechanism. Dissection of the A key is provided in each image, with energies (ΔE) given relative to that of the CO motif, that is, akin to ΔE(CO → Ih). A vertical dashed line in each plot indicates where the transition from CO-like to Ih-like motifs occurs, and (*) indicates the lowest energy rosette-Ih minima encountered for Ag 55 @Au 92 and is illustrated in detail in Figure 3.

The Journal of Physical Chemistry Letters
Letter lowest energy NP reveals that the Ag core is an Ih motif with five-, six-, and seven-membered rosette rings formed on the NP surface (Figure 3c,d). For Ag 13 @Au 134 the low-symmetry r-Ih and high-symmetry Ih are competitive in energy, but for Ag 55 @ Au 92 the r-Ih is substantially lower in energy (Figure 1,  bottom).
Interestingly, calculations of the SD and DS pathway for Ag 13 @Au 134 and Ag 55 @Au 92 give ΔE(CO → Ih) as 1.28 and 0.90 eV and ΔE(Ih → CO) as 2.08 and 1.66 eV, respectively. These direct barriers are lower than via the r-Ih motifs, but the lower initial barriers to form the low-symmetry r-Ih motifs, especially in the case of the Ag 13 core, mean that the transformation is taken along (and trapped in) the r-Ih pathway ( Figure 2).
Next, we studied the effect of decorating the NP vertices with a secondary species, further increasing the mixing of the Au and Ag atoms. Such controlled decoration has been achieved for AuPd nanoparticles 50 and is a logical progression when trying to design chemically bimetallic NPs. Initially, the 12 vertices of pure Ag 147 were decorated to create Ag 135 Au 12 , with ΔE(CO → Ih) and ΔE(Ih → CO) calculated as 0.35 and 3.50 eV, thus showing a decrease and an increase, respectively, compared with Ag 147 . When the vertices of Au 1 @Ag 146 , Au 13 @Ag 134 , and Au 55 @Ag 92 were decorated to give Au 1 @Ag 134 Au 12 , Au 13 @ Ag 122 Au 12 , and Au 55 @Ag 80 Au 12 , similar trends were observed: ΔE(CO → Ih) universally decreases by ∼0.1 eV to give 0.38, 0.27, and 0.38 eV, respectively; for ΔE(Ih → CO), the transition barriers are 3.38, 3.40, and 2.80 eV, which is a slight increase compared with Ag 147 .
When calculations were repeated for Ag-decorated vertices on Au-rich NPs, rather different behavior was observed: Au 135 Ag 12 has forward (SD) and backward (DS) barriers of 1.27 and 2.45 eV, that is, an increase in 0.13 and 0.12 eV, respectively, compared with Au 147 . For the core@shell arrangements, Ag 1 @Au 134 Ag 12 , Ag 13 @Au 122 Ag 12 , and Ag 55 @ Au 80 Ag 12 , only the latter now transforms via the r-Ih pathway. For Ag 1 @Au 134 Ag 12 and Ag 13 @Au 122 Ag 12 , ΔE(CO → Ih) is via the SD pathway and equal to 1.17 and 1.54 eV, respectively, but for Ag 55 @Au 80 Ag 12 , ΔE(CO → Ih) is 2.37 eV, which is a large decrease of 0.70 eV compared with the initial core@shell arrangements (Figure 1, bottom). We note that the transition pathway has significantly fewer steps and that the TO → r-Ih transition is in the center of the pathway, as the complex rotation of Au atoms on the r-Ih surface is prevented.
A calculation for Ag 55 @Au 80 Ag 12 transforming via the SD pathway gives a barrier of only 0.64 eV for ΔE(CO → Ih), and so again we conclude that the r-Ih dominates the DNEB calculations due to its low initial barriers and low-energy intermediate minima (Figure 2, bottom). For the backward transition (Ih → CO), ΔE is 2.20, 2.30, and 3.31 eV for Ag 1 @ Au 134 Ag 12 , Ag 13 @Au 122 Ag 12 , and Ag 55 @Au 80 Ag 12 , respectively.
To put our results in the context of experimental investigations, we proceed to free-energy calculations, which we have achieved via both DPS and metadynamics methodologies for pure and core@shell motifs. Calculations using DPS for temperatures (T) of 100 to 500 K show an almost universal decrease in the free energy of activation for the forward transition, ΔF(CO → Ih): a drop of 0.03 to 0.04 eV occurs when going from 0 to 100 K, whereafter the rate of decrease is reduced to ∼0.01 eV per 100 K. The only exception is the complicated case of Ag 55 @Au 92 , where ΔF(CO → Ih) increases by 0.04 eV per 100 K due to the transition states increasing in energy; it is also noted that the r-Ih has high entropy with respect to the CO and Ih, making it a more favorable minima with increasing T. 51 The open-ended metadynamics simulations identify various sets of Ih-and CO-like geometries,  For the backward transition, DPS shows that ΔF(Ih → CO) decreases at varying rates depending on the composition: For Ag 147 , ΔF(Ih → CO) decreases by 0.02 eV per 100 K, but for Au 147 the rate is doubled to 0.04 eV per 100 K. For Ag-rich core@shell motifs, that is, with an Ag shell, the rate of decrease remains at 0.02 eV per 100 K, while for Au-rich motifs the clear anomaly is Ag 55 @Au 92 , for which ΔF(Ih → CO) initially decreases from 3.98 (0 K) to 3.94 eV (300 K) and then increases back up to 3.98 eV (500 K) due to the energetic variation in TO structures close to the CO motif. Again, analysis with metadynamics gives slightly lower barriers than DPS, with Ag-rich systems displaying ΔF(Ih → CO) = 2.85 ± 0.15 eV at 50 K, and these barrier heights are maintained at 100 and 150 K (Figure 4, bottom). For single atom dopants in Au 1 Ag 146 , the barriers are calculated to be 2.8 to 3.0 eV at 50 K and steady in this energy range up to 150 K.
The overall differences in barriers calculated using DPS and metadynamics are deemed insignificant with the small underestimate from metadynamics probably due to the effect of reduced dimensionality. The identical pathways and similar barrier heights identified by both methods, which include the r-Ih-assisted transformations for Ag@Au, show that anharmonic effects do not play a significant role in the SD path. In addition, the anharmonic contributions can lower energetic barriers, which explains part of the difference between our DPS and metadynamics results. Importantly, an increase in T does not change the mechanism of structural transition for either calculation method, with chemical composition and ordering having a much stronger influence on barriers.
In conclusion, we have shown that the transition barrier between high-symmetry geometric motifs for bimetallic NPs is not merely a linear interpolation between systems but instead is strongly dependent on chemical arrangements. In particular, we have highlighted the complexity of the potential and freeenergy landscapes for systems where there are low-symmetry geometric motifs energetically competitive with the "highsymmetry" arrangements often pursued by theoretical and experimental scientists alike. In addition, we have also shown that the transition pathway can be controlled via careful construction of the NP with respect to stoichiometry and chemical arrangements, specifically by the use of vertex-doping to restrict surface-based structural transformations. Our results offer potential for future work in bespoke nanocatalyst and nanoplasmonic design, where structural stability due to specific geometric features, such as surface facets and vertex decoration, could be facilitated by careful consideration of the composition of the NPs in question.

* S Supporting Information
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpclett.6b02181.