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C: Physical Processes in Nanomaterials and Nanostructures

Improved Prediction of Nanoalloy Structures by the Explicit Inclusion of Adsorbates in Cluster Expansions Chenyang Li, David Raciti, Tiancheng Pu, Liang Cao, Connie He, Chao Wang, and Tim Mueller J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b03868 • Publication Date (Web): 12 Jul 2018 Downloaded from http://pubs.acs.org on July 13, 2018

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The Journal of Physical Chemistry

Improved Prediction of Nanoalloy Structures by the Explicit Inclusion of Adsorbates in Cluster Expansions Chenyang Li,1,† David Raciti,2,† Tiancheng Pu,2 Liang Cao,1 Connie He,2 Chao Wang,2,* Tim Mueller1,* 1

Department of Materials Science and Engineering, 2Department of Chemical and Biomolecular

Engineering, Johns Hopkins University, Baltimore, Maryland 21218, United States †

Equal contribution.

*Email: [email protected]; [email protected]

1

ACS Paragon Plus Environment

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Abstract. Density functional theory (DFT) is widely used to predict the properties of materials, but its direct application to nanomaterials of experimentally relevant size can be prohibitively expensive. It has previously been demonstrated that this problem can be addressed through the generation of cluster expansion models trained on DFT calculations. Here we evaluate the use of the cluster expansion method to calculate the structures of bimetallic Pt-Cu nanoparticles of varying sizes and compositions and in different chemical environments. The predicted surface composition, shape, and lattice parameters of the alloy nanoparticles are found to be in good agreement with experimental characterization. We demonstrate that to account for adsorbate-induced surface segregation, the best agreement for surface composition can be achieved by constructing a novel cluster expansion for alloy nanoparticles of varying shape and size that explicitly includes adsorbed oxygen.

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Introduction. Alloy nanoparticles are a promising class of catalysts due to their high surface-to-volume ratios and the potential for achieving high activity, selectivity and stability by tailoring the particle size, composition, shape and surface structure.1-3 The rational design of alloy catalysts is however limited by the challenges present in the prediction of surface atomic structures and structure-property relationships at the nanoscale. The catalytic performance of bimetallic nanoparticles depends on the lattice parameters (the strain effect), the effect of alloying on the electronic structures (the ligand effect), and the effect of local atomic order near the active sites (the ensemble effect).4

It is now feasible to use density functional theory

(DFT),5-6 to perform high-accuracy calculations on single-crystal surfaces and small nanoparticles (up to about 3 nm wide).7-12 However directly predicting the energies and structures of nanoparticles at larger, experimentally relevant sizes using DFT is still prohibitively expensive. One promising approach to address this challenge is to use cluster expansions.13-14 Cluster expansions are model Hamiltonians, typically fit to DFT calculations, that are capable of accurately (within about 5 meV / atom of DFT) predicting the energies of millions of nanoparticles per minute. Cluster expansions trained on small (1~2 nm diameter) nanoparticles can be used in Monte Carlo15 simulations to predict structures and thermodynamic properties of larger nanoparticles. Nanoparticle cluster expansions have demonstrated predictive accuracy relative to DFT calculations and have been used to predict nanoparticle shapes,16-19 internal atomic ordering,18, 20-23 and adsorbate binding energies on nanoparticles of fixed shape.19, 23-26 However, there has been relatively little work on directly comparing the nanoparticle structures predicted by cluster expansions with the structures of experimentally synthesized nanoparticles. Here, we compare the cluster expansion predictions for 5~10 nm Pt-Cu nanoparticles of varying shape, size and composition with experimental characterization of Pt-Cu nanoparticles. This model system is of interest because Pt-based bimetallic alloys are promising catalyst materials 3



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for the oxygen reduction reaction (ORR) from both theoretical9, 27-29 and experimental29-34 studies, and Cu-based catalysts are being extensively studied for CO and CO2 reduction.33, 35-41 Computational Methods. Cluster expansions are generalized Ising models that account for many-body interactions.13-14 Here we illustrate the cluster expansion method using a simple binary A-B alloy as an example. A more general description of our approach, including how cluster expansions are generated for ternary and higher-order systems, is provided in the Supporting Information. In a cluster expansion for a binary A-B alloy, the occupancy of the

ith

site is represented by a site variable si , where si = 1 if species “A” is present, si = −1 if species “B” is present.

A property of the material, such as the total energy, can then be

expressed as a function of these site variables:13, 42

F (s) = V0 +

∑V

cluster

cluster

∏

si

(1)

i ∈ cluster

where s is the set of all site variables and V0 and Vcluster are coefficients known as effective cluster interactions (ECI). The cluster expansion is exact when the sum is over all clusters (subsets) of sites in the material, but in practice the sum can usually be truncated to include only small, compact clusters with little loss of accuracy. Due to the loss of translational symmetry in nanoparticle systems, there are more distinct ECIs to be fitted than that in bulk materials. To address this issue, we have used a Bayesian method43 to fit the ECIs to a set of training structures calculated using DFT. In the Bayesian method, physical insights are explicitly incorporated into the fitting procedure through the prior probability distributions, which serve as an educated guess of the likelihood of ECI values before we calculate materials properties. For example, the prior probability distribution can be constructed to incorporate the expectation that clusters of sites that are close to each other should interact more strongly (and correspondingly have a larger ECI) than clusters sites that are spread far apart. The Bayesian method has been 4


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shown to greatly improve the predictive accuracy of the cluster expansion for a given training set size.18,

43

More details on building and fitting the cluster expansions are provided in the

Supporting Information. For nanoparticles, we treat the vacuum around the nanoparticle as a collection of sites that are occupied by vacancies (Figure 1) allowing us to use a training set of small (1~2 nm in diameter) nanoparticles to construct a cluster expansion that can be used to rapidly predict the energies of larger particles with varying shapes, sizes, compositions, and atomic order.24 DFT calculations have been performed using the Vienna Ab Initio Simulation Package (VASP)6 with the Perdew-Burke-Ernzerhof (PBE)44 exchange-correlation functional. The Cu, Pt_pv, and O_GW PBE projector-augmented wave (PAW)45 potentials were used, and all VASP calculations were run with accurate precision, ensuring that there were no wrap-around errors. A single k-point at the center of the Brillouin zone was used for each nanoparticle. For bulk materials (Pt and Cu), the Brillouin zone was sampled using grids generated by the k-point grid server46 with a minimum distance of 46.5 Angstrom in real space lattice. Second-order Methfessel-Paxon smearing47 with a width of 0.2 eV was used to set partial occupancies. Real space projectors were used to evaluate the non-local part of the PAW potential. The convergence criteria for the electronic self-consistent iteration and the ionic relaxation loop were set to be 10-4 eV and 10-3 eV per cell, respectively.

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Figure 1. A conceptual schematic of how the structure of a binary nanoparticle can be mapped to a lattice in a Pt-Cu-vacancy alloy cluster expansion. Gray, blue and white spheres represent Pt, Cu and vacancy, respectively. The cluster expansion in this paper uses a 3-dimensional fcc lattice rather than the 2-dimensional square lattice shown here.

Experimental Methods. Pt-Cu alloy nanoparticles were synthesized in organic phases (see Supporting Information for more details).48,49 The as-synthesized nanoparticles were loaded onto carbon and then annealed at 185 °C for 12 hours. The Pt-Cu nanoparticles were characterized using X-ray diffraction (XRD), transmission electron microscopy (TEM), energy dispersive X-ray spectroscopy (EDS) and inductively coupled plasma mass spectroscopy (ICPMS). High-angle annular dark field scanning TEM (HAADF-STEM) imaging and elemental mapping were performed on a JEOL JSM-6700F Field Emission Scanning Electron Microscope equipped with an EDS microprobe. Addition experimental details are provided in the Supporting Information. The N2O-H2 titration method used for surface composition analysis was modified from a protocol reported by Kim et al..50 Typically, the carbon supported Pt-Cu nanoparticles were loaded into a plug flow reactor (1/8” diameter) and first reduced by H2 at 300 °C. After removing the residual hydrogen in a stream of He flow, N2O was allowed to adsorb on the nanoparticles at 6


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90 °C by flowing 2000 ppm N2O. The subsequent H2 titration was performed at room temperature after physically adsorbed N2O was removed by flowing 1,000 ppm of H2 and the composition of the effluent was monitored by using a gas chromatography equipped with a barrier ionization discharge detector (GC-BID, customized by Shimadzu). The amount of consumed H2 was estimated by integrating the peak area exhibiting in the H2-titration profile. The amount of surface Pt atoms was then determined according to the stoichiometry of Pt/H2 = 1/1.5 from the measured amount of consumed H2. The total number surface atoms (Pt + Cu) was determined based on the characterized particle size. To more accurately estimate the fraction of surface atoms for a given particle size, particle shapes were assumed to be consistent with those predicted by the Monte Carlo simulations at 90 °C. The surface composition, namely ratios of Pt and Cu, was then calculated based on these two sets of numbers ( Pt% = N Pt / N total and C u % = 1 − P t % ).

Results and Discussion. We start by assessing the ability of a cluster expansion to predict the lattice parameter of a nanoparticle. To this end, we have constructed a Pt-CuVacancy cluster expansion, using the Bayesian approach43 to fit to the lattice parameters (average nearest neighbor distances) of 122 nanoparticles ranging from 90~250 atoms (1.0~1.8 nm in diameter) as calculated by DFT.

The leave-one-out cross-validation error for this

expansion, a measure of its predictive accuracy, was 0.004 Angstroms per bond. Additional details of the construction of this cluster expansion can be found in the Supporting Information. Good agreement has been obtained between cluster expansion predicted lattice parameters and experimental measurements at room temperature for ~5 nm Pt-Cu nanoparticles of varying composition (Figure 2a). The corresponding XRD patterns are shown in Figure 2b. This is not surprising as the lattice parameters largely follow the Vegard’s law.51 For Cu-rich nanoparticle, the experimentally measured PtCu3 lattice parameter has the largest deviation (~1%) from 7



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cluster expansion prediction, possibly due to aggregation of nanoparticles and formation of copper oxides. We also predict that the lattice parameter contracts with particle size (Figure 2c), which is consistent with previously reported experimental and theoretical results on size effects.52-54 For pure Cu and pure Pt, we have fit our results using the least squares method to an analytical expression derived by Qi et al.,53

aNP ( D) = abulk (1 −

where

α

1 ), 1 + α DG / γ

(2)

is a geometry factor defined as the ratio of the surface area of a non-spherical

nanoparticle to that of a spherical nanoparticle of the same volume, (1.000 for Cu sphere and 1.105 for Pt cubooctahedron), D is the diameter of the nanoparticle, G is the shear modulus and γ is the average surface energy. We find that

G / γ ratios of 45.9 and 42.4 nm-1 give the

best fit for pure Pt and Cu, with root-mean-square errors of 0.0029 and 0.0021 Angstrom, respectively. These values are comparable to ratios of 24.3 and 26.9 nm-1 previously reported in the literature.52-53

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Figure 2. (a) Lattice parameters for Pt-Cu nanoparticles predicted by cluster expansion and measured by experiments. The DFT calculated and experimental values for pure Pt and Cu bulk 9



materials are also labeled. (b) XRD powder diffraction patterns of Pt, Pt7Cu3, PtCu, Pt3Cu7 and Cu nanoparticles of varying compositions. (c) Calculated size effect on lattice parameter of Pt, PtCu and Cu nanoparticles. Horizontal lines represent bulk values predicted by the cluster expansion. Fitted curves are generated using the analytical expression by Qi et al.53

With good agreement between lattice constant prediction and experiment for the Pt-Cu nanoparticles across different Pt compositions, we move forward to predicting the shape and near-surface composition of Pt-Cu nanoparticles in vacuum (or a non-reactive environment). To this end, we used the Bayesian approach to fit a Pt-Cu-Vacancy cluster expansion to DFTcalculated energies for the same training set we used for the lattice parameter cluster expansion. The leave-one-out cross-validation error for this expansion is 3.9 meV / atom. Monte Carlo simulations were used to identify ground-state structures and take thermodynamic averages at finite temperature. Additional computational details are provided in the Supporting Information. In equilibrium at 25 °C, at lower Cu concentrations, the nanoparticles exhibit a Pt skin and with the second layer mostly occupied by Cu atoms (Figure 3 and Figure S1). This is consistent with previous experimental findings on near-surface alloys.55-56 and Cu-Pt core-shell nanoparticles after annealing in H2.57-58 At these concentrations, the nanoparticles have welldefined facets, with only Pt(100) and Pt(111) facets present, in agreement with Wulff constructions reported in the literature.59-60 When Cu concentration increases up to 50%, Cu atoms begin to segregate out to the surface, with (110) edge sites being the preferred occupied sites, as well as some of the (100) surface sites. Most of the Pt(111) surfaces are still present at this composition. We also observe a shape change from both TEM images and cluster expansion predictions (Figure 3, first and second row), in which the Pt-Cu nanoparticle becomes less faceted when overall Pt composition decreases. The predicted composition-dependent shapes are consistent with Pt-Cu nanoparticle shapes reported in the literature.61-62 Once the 10


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overall Cu content exceeds 50% the surface fraction of Cu increases rapidly. At higher Cu compositions, the (100) surface sites are all occupied by Cu atoms, whereas the (111) surface exhibits a clear pattern of L12 ordered phase with ratio of PtCu3, which is in agreement with the Pt-Cu phase diagram.63 The PtCu3 nanoparticles becomes even more spherical and less faceted than PtCu, which arises from the increasing area of (100) and (110) facets. To check the validity of the above predictions by the cluster expansion, we have performed DFT calculations on the surface energies of various facets of Cu and Pt (Table 1). It is found that the surface energies of Cu are lower than those of Pt, and the Cu surface energies for different facets are closer to each other than the Pt surface energies. Thus, the cluster-expansionpredicted surface segregation and shape change are consistent with what would be expected based on the surface energies (Figure S2). The nanoparticle shapes between 5nm and 7nm do not exhibit significant differences, indicating the calculations are well converged with respect to particle size (Figure S3). Table 1. Surface energies of (111), (110), and (100) facets for Cu and Pt. γ Cu (meV/Å2) γ Pt (meV/Å2) (111) (110) (100)

95.42 112.24 106.79

111.45 141.55 139.31

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Figure 3. (a-i) TEM/HAADF-STEM images and (j-l) cluster expansion predicted structures for ~7 nm (13,000 atoms) Pt3Cu, PtCu and PtCu3 nanoparticles. Gray and blue spheres represent Pt and Cu atoms respectively.

We compare the predicted surface compositions with those of the synthesized nanoparticles using N2O and H2 titration. To increase sensitivity when performing the N2O and H2 titration, we synthesized smaller nanoparticles with a higher surface area to volume ratio (see Supporting Information). The resulting particle sizes, surface compositions and surface composition calculation details are shown in Table 2. To calculate the number of surface atoms, the weight of the nanoparticles was first converted to total number of atoms N . Then the cluster 12


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expansion was used to calculate the ratio of surface atoms to total number of atoms n surf / n total for a single particle based on the size and composition. The total number of surface atoms in the titration experiment was calculated by taking the product of the above two numbers

N × ( nsurf / ntotal ) . We measured the number of Pt atoms on the pure Pt nanoparticles to check the validity of this calculation, and the error between calculated and measured Pt content on the pure Pt nanoparticle was only ~1.1% (Table 2).

Table 2. Information and results of Pt-Cu nanoparticles for N2O-H2 titration measurements

a

Material

Composition, Weight % a Loading

Weight of Nanoparticles for N2O-H2 titration

Average size

Calculated Total Number of Surface Atoms

Pt-C Pt3Cu-C PtCu-C PtCu3-C

Pt, 40.8% Pt3.05Cu-C, 19.6% PtCu-C, 20.4% PtCu3.01-C, 20.2%

2.28 mg 1.78 mg 2.85 mg 2.83 mg

5.0 nm 4.5 nm 4.5 nm 3.9 nm

1.76*10 19 1.72*10 19 3.45*10 19 5.80*10

19

Number of Surface Pt from titration 19

1.74*10 19 1.15*10 18 9.22*10 18 1.99*10

Percent of surface atoms that are Pt 98.86% 66.7% 26.73% 3.45%

Composition and weight percentages were determined from the ICP-MS analyses.

It has been reported that when Pt-Cu nanoparticles are exposed to oxygen (or other oxidizing agents such as CO), Cu atoms can segregate to the surface and change the surface structure significantly.64-65 The Pt-Cu-vacancy cluster expansion built in vacuum (grey bars in Figure 4a) failed to capture this oxidizing effect, and it underpredicts the Cu surface coverage by around 30% relative to experiments.

This result suggests that it is necessary to explicitly

include the presence of possible oxygen adsorbates in the cluster expansion to realistically capture the near-surface structure of the nanoparticle, which may be determined by oxygeninduced surface segregation. We note that it is also possible that the room-temperature H2 titration drives segregation of Pt to the particle surface,33, 57 but this is likely a relatively small 13



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effect due to the weak Pt-H binding energy and low temperature (room temperature) during H2 titration. The lack of H-induced segregation of Pt to the particle surface is supported by the low percentage of surface Pt observed on PtCu3 nanoparticles (light blue bars in Figure 4a).

Figure 4. (a) Cluster expansion (CE) predicted surface Pt compositions of Pt-Cu nanoparticles in vacuum and oxidizing environment as a function of overall bulk concentration. Surface atom density is defined as ratio of number of surface atoms to total number of atoms in nanoparticles based on experimentally measured sizes. (b) Structures of Pt3Cu, PtCu and PtCu3 in oxidizing environments. Gray, blue and red spheres represent Pt, Cu and O, respectively.

Previous cluster expansions of nanoparticles have either assumed the particle exists in vacuum,16,

18-21

used very small particles of fixed size and shape,18-19, 14


25-26

or estimated the

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effects of adsorbates through the use of correction terms.17,

23

Here we demonstrate that

realistic results for particles of experimentally-relevant sizes can be achieved by explicitly including adsorbates in a cluster expansion of nanoparticles of varying size and shape. Specifically, we have constructed a cluster expansion in which each site can be occupied by either Pt, Cu, O, or a vacancy, allowing us to account for metal-adsorbate and adsorbateadsorbate interactions and calculate the energies of nanoparticles with varying sizes, shapes, and levels of oxygen coverage. To our knowledge, this approach, in which metal atoms, vacuum, and adsorbates are all included in the same cluster expansion, has not been used before. Our approach makes the approximation of placing all oxygen atoms at fcc sites on the surface prior to relaxation, even when other adsorption sites may have lower energy.

Although this

introduces some error in cases in which there is another site with lower energy than the fcc site, it greatly improved the agreement between the cluster-expansion-predicted and experimentally measured surface composition relative to the assumption that the nanoparticle exists in a vacuum. The training set for this Pt-Cu-O-Vacancy cluster expansion contained 193 nanoparticles with between 90 and 344 atoms. The leave-one-out cross validation (LOOCV) error, an estimate of the prediction error for the cluster expansion, is 4.5 meV / atom. We have determined the Pt-Cu nanoparticle morphology and surface composition by running a grand canonical Monte Carlo simulation with a fixed oxygen chemical potential. In the titration experiment, the oxygen source was provided by N2O decomposition. Therefore, we calculated the chemical potential of oxygen provided by the N2O molecules at experimental partial pressure and used this chemical potential in the Monte Carlo simulations. We constrained the Monte Carlo simulations to prevent oxygen from occupying sub-surface sites, and no nanoparticles with oxygen atoms on sub-surface sites were included in the training set. To simulate the synthesis of the nanoparticles, we initially ran a Monte Carlo simulation in which the nanoparticles were annealed at a temperature of 500 °C, which is the highest temperature 15



the particles reached before titration measurements. Then we reduced the temperature to 90 °C to simulate the N2O titration experiments done at this temperature. At this temperature only the outermost three layers were allowed to be annealed, as it is likely that the core of the particle is kinetically trapped.17 Additional details of the Monte Carlo simulations are provided in the Supporting Information. From vacuum to oxidizing environment, the calculated surface Cu composition increases around 20% on average (dark blue bars in Figure 4a), partially because oxygen binds more strongly to Cu than Pt.66 Recent experimental studies also showed that a significant increase in Cu surface composition was observed in oxidizing environments.64-65 Although there was still a small gap between the cluster expansion prediction and experimental observation, the agreement with experiment is much stronger when the surface oxygen is explicitly included in the cluster expansion. With oxygen explicitly included in the cluster expansion, we also observe shape changes compared to Pt-Cu nanoparticles in vacuum (Figure 4b). For Pt3Cu, there is an increase in the area of (110) facets and decrease in the area of (100) facets, making the particle more spherical when exposed to oxygen. For PtCu, some of the Pt(111) facets become Cu-rich. At higher Cu composition, Pt surfaces are no longer present on PtCu3. Instead, the particles have an oxidized copper surface. This is in line with the titration experiment, where a full monolayer of oxygen was observed by Kim et al,50 and the oxygen coverages in the simulations are >0.95 ML (Figure S5). We note that these shape changes may not occur in practice if the nanoparticles become kinetically trapped by the formation of the surface oxide.

Conclusions. We have generated cluster expansions to predict Pt-Cu nanoparticle structures in both vacuum and oxidizing conditions. Our results demonstrate that explicitly 16


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including potential adsorbates in cluster expansions can significantly improve the quality of the predicted structures of alloy nanoparticles at experimentally relevant sizes. The success of this method is promising as it can also be used to predict adsorbate binding energies, which are often important descriptors of catalytic activity, on different sites of nanoparticles with different structures. Thus we expect this approach will provide valuable insights into the structures and properties of nanocatalysts in different chemical environments and facilitate rational nanomaterials design.

Supporting Information The Supporting Information is available free of charge on the ACS Publications website. Details of building cluster expansions, predictions of lattice parameter, layer-by-layer composition; Density functional theory calculations; Details of EDX, HAADF-STEM, and N2O-H2 titration measurements are provided. (PDF) Corresponding Author *E-mail: [email protected]; [email protected] Author Contributions †C.L. and D.R. contributed equally. The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes. The authors declare no competing financial interests. Acknowledgements. This work was supported by the National Science Foundation through award CHE-1437396. T. Mueller, C. Li and L. Cao acknowledge the computational resources provided by the Center for Functional Nanomaterials at Brookhaven National Laboratory under grant 35838 and by XSEDE through award DMR-140068. Atomic-scale structural images were 17



generated using VESTA.67 The STEM imaging and element mapping analysis were performed at the Center for Nanophase Materials Sciences (CNMS), Oak Ridge National Laboratory, which is a user facility supported by the U.S. Department of Energy, Office of Science.

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Improved Prediction of Nanoalloy Structures by the ... - ACS Publications

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