Density Functional Theory Study of Nucleation and Growth of Pt

Jan 14, 2015 - Trends in the Adsorption and Growth Morphology of Metals on the MoS2(001) ... Theoretical and Experimental Chemistry 2015 51, 141-162 ...
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Density Functional Theory Study of Nucleation and Growth of Pt Nanoparticles on MoS2(001) Surface Wissam A. Saidi* Department of Mechanical Engineering and Materials Science, University of Pittsburgh, Pittsburgh, Pennsylvania 15261, United States S Supporting Information *

ABSTRACT: The dispersion of Pt metallic nanoparticles on different supports is of high relevance for designing more efficient and less expensive catalysts. In order to understand the nucleation and epitaxial growth of Pt nanoparticles and thin films on MoS2 monolayers, we have systematically analyzed, by first-principles density functional calculations, the evolution of morphology and atomic structure of supported (Pt)n nanoparticles (NPs) on MoS2(001) for n ≤ 12. We find that n = 5 is the cluster size where the growth of the NPs transforms from two- to three-dimensional (2D to 3D). Owing to the topography of MoS2(001), the 2D NPs mostly attach to the support via direct bonding with Mo atoms that sit in the troughs of the surface, while the 3D NPs are bonded to the sulfur atoms that are more extended in the vacuum region. Furthermore, we find that Pt is sufficiently mobile on the surface where the number of hopping events per second is ≈103 s−1 along [101̅] and ≈10 s−1 along [11̅0] at room temperature. The somewhat large mobility suggests that monomer diffusion is not likely to be the rate-limiting step for Oswald ripening and that Pt sputtering on MoS2(001) will result in relatively large particles rather than a fine dispersion. The existence of a fast diffusion channel along [101]̅ suggests that the morphology of the NPs is anisotropic.

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INTRODUCTION Metallic nanoparticles (NPs) have many applications, especially as model catalysts to provide important insights into the behavior of real heterogeneous catalysts.1−3 To obtain the highest possible surface area of the NPs and reduce sintering, two-dimensional (2D) materials are generally sought as a support where metal−substrate interactions can influence the heterostructure properties in two main aspects.4−7 First, the high degree of dispersion of the NPs makes their supportassisted catalytic activities, determined, for example, by the NP’s oxidation/reduction state induced by the substrate, dependent on the interactions and metal−support interface. Second, the metal−substrate interactions are pivotal to morphology and nucleation of the NPs, where a weak anchoring force between the NPs and the substrate will generally lead to particle agglomeration and the growth of three-dimensional (3D) metal islands; that is resulting in shrinkage of catalyst surface area and decrease of catalytic efficiency. Thermodynamically, the growth of supported NPs in the high-coverage limit can follow three major types: (1) Frank−van der Merwe mode, which consists of layer-by-layer growth of the adlayers; (2) Volmer−Weber growth, describing 3D clustering of adatoms on a bare substrate; and (3) Stranski−Krastanov growth, involving 3D clustering after one or a few complete adlayers are formed first.8 Therefore, a fundamental question in catalytic research is how to exploit metal−substrate interactions to optimize the NP morphology © XXXX American Chemical Society

to achieve a good balance between catalytic activity, selectivity, and sintering suppression.3 The transition metal dichalcogenides (TMDs), and in particular MoS2, are an emerging class of materials that are currently heavily researched due to their potential use in different fields including sensing, catalysis, and electronics.9−12 Their 2D nature makes them especially attractive as a support for metallic NPs. Recently, it was demonstrated by a wetchemical synthetic approach that MoS2 nanosheets can be used to direct the epitaxial growth of Pd, Pt, and Ag nanostructures under ambient conditions.13 On the modeling side, there have not been many studies investigating the interfaces between MoS2 and metallic contacts,14−16 but more is yet to come, judging from the many investigations of different metal/ graphene contacts. Furthermore, little is known about the energetics and mechanisms for nucleation of metallic NPs and eventually epitaxial growth, which depend on MoS2 specific chemistry, stiffness, and surface topography. Clearly, a full understanding of these topics is of prime importance to optimize NP catalytic activity and their dispersion on MoS2 during catalyst preparation and use. In this paper, we systematically study the growth of (Pt)n islands with n ≤ 12 on a monolayer MoS2(001) substrate via a Received: September 5, 2014 Revised: December 16, 2014

A

DOI: 10.1021/cg5013395 Cryst. Growth Des. XXXX, XXX, XXX−XXX

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Crystal Growth & Design

perpendicular to the slab and in conjunction with the dipole correction.46 All of the atomic coordinates in (Pt)n/MoS2 are relaxed by use of a convergence threshold of 0.005 eV/Å on the atomic forces. We deposit atoms on only one side of the monolayer to better mimic experimental situations where MoS2 monolayer is typically grown on another substrate such as SiO2 or mica. The stability of the Pt optimized clusters is checked by computing the harmonic vibrational frequencies in the frozen lattice approximation, where the Hessian matrix is computed by a finite difference approach with a step size of 0.01 Å for displacement of the Pt atoms along each Cartesian coordinate. We find that the supported Pt NPs on MoS2 are nonmagnetic although they are generally magnetic in isolation. Thus, our DFT calculations are spin-averaged for supported NPs and spin-polarized for isolated NPs. Previously, it was found that Pt NPs on rutile TiO2 are also nonmagnetic,24 while on α-Al2O3(0001) they were magnetic but with a reduced magnetization compared to the isolated clusters.19 Analysis of the electronic properties including density-of-states, electron density plots, etc., is based on Kohn−Sham wave functions obtained from a plane wave cutoff of 450 eV and a tight convergence of 10−8 eV on the energies in the self-consistent step. The electronic density is partitioned by a Hirshfeld scheme47 with Hartree−Fock allelectron reference atomic densities48,49 to obtain atomic charges. Charge decomposition analysis can give more understanding of the enhanced catalytic activities of the supported metallic NPs.5,50 It should be noted that there are several methods for atomic charge decomposition of the electron density, such as Bader, Löwdin, and Mulliken. Generally, all of these schemes can result in somewhat different values of the atomic charges but often yield consistent trends that can help to better understand the electronic nature of the system. Computationally, it is very challenging to find the global minima or even enumerate a large number of the local minima for isolated or supported metallic NPs. This is because metallic nanoclusters have a fluxional character where they can exhibit several structurally different configurations that lie within a narrow energy window. In this study, as well as in previous studies,19−24,26,28 putative global minima structures of supported (Pt)n clusters are attained by relaxing many different initial configurations and choosing the lowest-energy structure. We find that, for n < 5, the optimum cluster configurations can be predicted reliably by using the smaller metallic clusters as motifs, especially those obtained at the monomer level. For larger NPs with n ≥ 5, we find that ab initio molecular dynamics (AIMD) is an effective tool to generate the initial structures as was employed before, for example, in ref 51. In this approach, we first heat the system up to 1000−1500 K for 1−2 ps with velocity rescaling and then let the system relax for 2−3 ps without any constraints. The structures corresponding to low-energy configurations along the MD trajectory are then singled out and used as initial structures for a refined T = 0 K relaxation. For computational efficiency, we used a relatively large time-step value of 8 fs in integrating the molecular dynamic equations, which is nevertheless a good approximation because we are primarily interested in sampling a large configurational space to obtain a wide range of different initial structures. The binding energy per Pt for (Pt)n on MoS2(001) substrate is computed by use of eq 1:

density functional theory approach. Pt is a very important catalyst component employed in many reactions such as oxidation of CO and other hydrocarbons used in automobile exhaust gas purification17 and oxygen reduction in fuel cells.18 This explains why several studies were devoted to understanding the growth of Pt nanoclusters on supports such as αAl2O3(0001),19 anatase TiO2(101),20−22 rutile TiO2(110),23,24 graphene,25−28 ceria CeO2 (111),29 and BN.30 The relatively large cohesive energy of Pt makes it highly probable that atomic layer deposition (ALD) will produce a dispersion of Pt NPs and formation of 3D islands rather than thin films, as was found previously on several substrates.19,21−24,29 However, the smallest cluster size of NPs above which the growth transforms from 2D to 3D is generally the result of a delicate interplay between metal−metal and metal−substrate interactions. The rest of the paper is organized as follows. The next section gives a description of computational setup and the approach used to find the optimum structures. The main findings of this study are then presented under Results and Discussion: (i) determination of the optimum structures of the supported NPs with n ≤ 12 atoms and the critical island size, defined as the minimum cluster that can only grow or remain constant;3 (ii) change of growth mode of supported NPs from 2D to 3D for n ≥ 5; (iii) possible kinetic limitations of the 2D NP structures; (iv) nature of the adhesion of NP to the support, as 2D NPs mostly attach to Mo sites whereas 3D NPs or Pt monolayers16 bond to sulfur; (v) Pt mobility map on the surface, with relatively fast diffusion channel along [101̅] and slow diffusion along [110̅ ], where the ratio between the two rates is ≈100 at room temperature. These anisotropic diffusion rates suggest that the deposited Pt atoms on MoS2(001) will agglomerate into relatively large anisotropic islands rather than forming a fine dispersion, at least at high temperatures.

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COMPUTATIONAL DETAILS

Density functional theory (DFT) calculations are carried out with the Vienna Ab Initio Simulation Package (VASP).31−33 Electron−nuclei interactions are described by use of the projector-augmented waves of Blöchl34 in the implementation of Kresse and Joubert.35 The Kohn− Sham wave functions are expanded in plane waves up to a cutoff of 350 eV, and the convergence of the energies in the self-consistent step is achieved by use of a 10−6 eV threshold. Orbitals are occupied according to a Fermi−Dirac distribution with kBT = 0.05 eV to aid in the convergence of the electronic self-consistent step. For the slab and isolated system calculations, the integration over the Brillouin zone is limited to the Γ point only, while as for bulk metal calculations we used a 12 × 12 × 12 Monkhorst−Pack k-grid. In our calculations we employed the generalized-gradient approximation by Perdew, Burke, and Ernzerhof36 (PBE). van der Waals interactions are relatively weak compared to the calculated PBE binding energies of Pt to MoS2 (vide infra) and thus are not included, although these forces alter significantly the binding energies for extended systems due to their accumulative nature.16,37−45 The MoS2 substrate is modeled by use of (3 × 3) and (5 × 5) lateral supercells to accommodate various sizes of the clusters, with a MoS2 lattice constant of 3.18 Å.16 For computational efficiency, the supported NPs are initially relaxed with the small supercell and then transformed to the large supercell for a more refined optimization. The differences in energy of the supported clusters with (3 × 3) and (5 × 5) supercells are smaller than 0.1 eV for all investigated clusters. For consistency, all of our results are reported for the larger (5 × 5) supercell, which describes the metallic NPs in isolation, that is, without the fictitious interactions between the periodic images of the clusters. In the supercell approach for modeling the MoS2(001) monolayer, the interactions between slabs along the nonperiodic direction are mitigated by use of more than 10 Å of vacuum in the direction

E BE =

1⎡ ⎤ ⎣E MoS2 + (Pt)n − E MoS2 − nE Pt ⎦ n

(1)

where EMoS2+(Pt)n is the energy of the (Pt)n/MoS2 heterostructure in the optimum geometry, EMoS2 is the energy of the pristine MoS2 monolayer, and EPt is the energy of an isolated Pt atom with two unpaired electrons according to Hund’s rules. In this convention of the binding energy, negative values of EBE indicate stable adsorption configurations. To gain further insight into the metal−metal vs metal-slab stabilizing interactions, we partition the binding energy as follows: E BE = ΔE MoS2 + ΔE(Pt)n + ΔEMS B

(2) DOI: 10.1021/cg5013395 Cryst. Growth Des. XXXX, XXX, XXX−XXX

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Crystal Growth & Design Table 1. Total Binding Energies ΔEBE for (Pt)n Clustersa l ̅ (Å)

energy (eV) configuration

ΔEBE

ΔEMoS2

ΔE(Pt)n

ΔEMS

Pt−Mo

Pt−S

−3.19 −2.40 −2.30

2.76

2.29 2.35 2.08

−2.26 −2.01 −1.78

2.87 2.79 2.80

2.33 2.28 2.28

2.85 2.74 2.65

−1.44 −1.63 −1.83

2.89 2.99 2.90

2.34 2.37 2.32

2.52 2.81 2.93

−1.74 −1.56

2.89 2.91

2.34 2.35

2.58 2.61

−1.16 −1.45 −1.62

2.86 2.91 2.92

2.34 2.34 2.36

2.65 2.62 2.69

2.94

2.40 2.20 2.44

2.62 2.62 2.66

2.22 2.33

2.65 2.60

Pt−Pt

(Pt)1 t-Mo h-S t-S

−2.83 −2.25 −2.20

0.26 0.06 0.01

0.10 0.10 0.10

t-(Mo)2 t-Moh t-MoS

−2.96 −2.86 −2.85

0.30 0.32 0.23

−1.00 −1.17 −1.29

(Pt)3-Λ t-(Mo)3-S t-(Mo)3-h

−3.20 −3.12 −3.06

0.29 0.39 0.42

−2.05 −1.88 −1.65

t-(Mo)4-h t-(Mo)4-S

−3.47 −3.43

0.41 0.44

−2.14 −2.30

3D-(Pt)5 2D-(Pt)5 t-(Mo)4-h

−3.45 −3.44 −3.43

0.35 0.46 0.48

−2.64 −2.44 −2.30

3D-(Pt)6-1 3D-(Pt)6-2 2D-(Pt)6

−3.57 −3.56 −3.55

0.48 0.04 0.33

−2.72 −2.83 −2.57

(Pt)2

(Pt)3

(Pt)4

(Pt)5

(Pt)6 −1.33 −0.77 −1.31 (Pt)12 3D-(Pt)12-1 3D-(Pt)12-2

−4.09 −4.08

0.14 0.41

−3.50 −3.45

−0.73 −1.03

Decomposition of ΔEBE into ΔEMoS2, ΔE(Pt)n, and ΔEMS as defined in eq 2 is also listed. All energies are normalized by the number of Pt atoms except ΔEMoS2 (see text). Average bond lengths l ̅ are computed with a threshold of 3 Å.

a

Figure 1. Monomer adsorption configurations. (a, b) Side views for t-Mo and t-S; (c) side and top views for h-S configuration. S, Mo, and Pt atoms are shown as yellow, pink and blue spheres, respectively. Here, the first term ΔEMoS2 (positive) is the MoS2 deformation energy, defined as the energy penalty to deform MoS2 into the structure adopted in the bonding configuration. The second term ΔE(Pt)n (negative) measures the energy gain due to the metal−metal bonds and is defined as

ΔE(Pt)n =

1⎡ ⎤ ⎣E(Pt)n − nE Pt ⎦ n

calculations, E(Pt)n is also computed with spin-averaged calculation while the monomer reference energy EPt is computed with spin polarization. This explains the small value of ΔE(Pt)1 = 0.01 eV for the monomer even though there is no metal−metal interaction (see Table 1). Equations 1, 2, and 3 serve to define the metal−substrate energy EMS (negative) that measures the interaction between the metal and the substrate. A similar scheme for dissecting the binding energies was previously employed to understand the interactions between COOH groups and carbon nanotubes.52 All energy terms in eq 2 are normalized with respect to the number of Pt atoms in the cluster except ΔEMoS2, which is chosen to be independent of the metal cluster

(3)

where E(Pt)n is the energy of the metallic nanocluster in the frozen geometry they adopt on the MoS2 slab. For consistency with EMoS2+(Pt)n C

DOI: 10.1021/cg5013395 Cryst. Growth Des. XXXX, XXX, XXX−XXX

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Crystal Growth & Design size. As shown in Table 1, ΔEMoS2 is relatively small and thus this choice has a small effect on the results. We employ transition-state theory (TST) to compute the diffusion or reaction rate: ⎛ ΔE ⎞ k = ν0exp⎜− ⎟ ⎝ kBT ⎠

comparable to that of h-S, because of the relatively short Pt− S bond length of 2.08 Å and the weak perturbation of the substrate evidenced by the small ΔEMoS2 = 0.01 eV value (see Table 1). In addition to Pt adsorption on the surface of MoS2(001), we also investigated Pt replacements of Mo or S within the support. As expected, these substitutional defects are energetically very costly and thus unlikely to be observed experimentally. Also, we examined the incorporation of Pt within MoS2. There are two potential interstitial sites: both are located at the center of a triangle formed from three Mo atoms, but they differ in whether the site is coordinated or not with two S atoms. After full relaxation, Pt is expelled from within the layer system to the surface. In fact, by constraining the Pt atoms to the interstitial site, it is found that these configurations cost more than 5 eV. The high energy of Pt as a substitutional defect as well as when incorporated within the monolayer is due to the rigidity of the MoS2 that is held by strong Mo−S covalent bonds12 (Pauling electronegativities of Mo and S are 2.16 and 2.58, respectively). (Pt)2. For Pt dimer, we investigated different combinations obtained from positioning the two Pt atoms at the highsymmetry sites of MoS2(001). We find several stable configurations with binding energies that range between −2.3 and −2.96 eV/atom (see Figure S1 in Supporting Information). t-Mo is the preferred adsorption configuration at the monomer level, and thus it is expected that t-(Mo)2, where two Pt atoms occupy neighboring t-Mo sites, will be favorable for a dimer. This is indeed the case with a binding energy of −2.96 eV/ atom. In this configuration, the two Pt atoms decrease their initial separation from 3.18 Å, given by the distance between two Mo sites, to a distance Pt−Pt = 2.85 Å in the optimum configuration. The shift of Pt from the atop Mo site weakens the Pt−Mo bond, increasing its value from 2.76 Å in the monomer to 2.87 Å in the dimer case. The weakening can also be seen by examining the metal−substrate term ΔEMS in Table 1, which increases from −3.19 eV in t-Mo to −2.26 eV in t(Mo)2. Overall t-(Mo)2 is a compromise for the dimer between forming a strong bond with the surface via bonding to Mo or forming Pt−Pt metallic bonds. It should be noted that the formed bond in t-(Mo)2 with Pt−Pt = 2.85 Å is still larger than the bond length of isolated Pt dimer (2.45 Å) or in facecentered cubic (fcc) crystal (2.79 Å). Because of the ordering of adsorption sites at the monomer level, it is expected that (Pt)2 configurations higher in energy than t-(Mo)2 will involve binding of at least one Pt atom at t-S or h-S sites. This is the case as shown in Figure 2b,c for the two lowest-energy structures t-MoS and t-Moh, which are nearly equal in energy with the second one lower by 15 meV/atom. In t-MoS, the Pt dimer is positioned nearly atop a bonded Mo−S pair with a P−Pt bond length of 2.65 Å, Pt−Mo is 2.80 Å, and ∠Pt−S−Pt = 73°. In t-Moh, the Pt dimer is nearly atop the Mo−S pair where S belongs to the second-nearest neighbors of Mo with Pt−Pt = 2.74 Å, Pt−Mo = 2.80 Å, and ∠Pt−Pt−S = 94°. t-MoS and t-Moh are higher than the most stable t-(Mo)2 configuration by only ≈0.1 eV/atom, and thus these structures are likely to exist on the surface, at least in a transient phase. To quantify this, we find that the transition barrier between t(Mo)2 and t-MoS is 0.26 eV in the forward direction and 0.08 eV in the reverse direction, with estimated rates of 108 s−1 and 1011 s−1 at room temperature, respectively. That is, the

(4)

−1

where ν0 = 10 s is the rate prefactor, assumed to be a constant independent of the reaction or the hopping event; kB is the Boltzmann constant; and T is the temperature. ΔE is the energy barrier computed from the minimum energy pathway between two configurations employing the climbing-image nudged elastic band (NEB) method.53 13

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RESULTS We first present and discuss briefly the most stable (Pt)n structures. In particular, we determine the cluster size where the growth mode transitions from 2D to 3D. As discussed before, for each case we chose several initial configurations to find the putative global minima (energies for most of the structures are shown in Figure S1 in Supporting Information). Table 1 summarizes the relevant structural parameters and adsorption energies for the lowest-energy configurations that are most relevant to the nucleation process. In passing, we note that the binding energies reported in Table 1 can be used in conjunction with an ab initio thermodynamic approach to map the region of stability of the supported NPs versus environmental variables, following a similar approach as in ref 54. This can be done by first defining the Pt reservoir, for example, based on atomic Pt in vapor deposition or Pt salt in electroreduction. (Pt)1. The adsorption of Pt monomer is first investigated at the high-symmetry sites of the MoS2 surface. The preferential adsorption configuration is the atop-Mo site (t-Mo) with a binding energy of 2.83 eV, followed by the S-hollow site (h-S), 2.25 eV, and atop-S site (t-S), 2.20 eV (see Figure 1). All of these structures are verified to be stable due to the absence of imaginary vibrational modes, as well as by examining the potential energy surface (PES) map (vide infra). The bridge configuration where Pt sits between two bonded S atoms was not stable. The large adsorption energy indicates that the rate of evaporation, proportional to exp[−EBE/(kBT)], is negligible, and monomer diffusion with the smaller diffusion barrier ≈0.6−0.7 eV (vide infra) is the more prevalent atomistic process for Pt after landing on the substrate. It should be noted that the interaction of Pt with MoS2 is as strong as that of Pt on anatase TiO2(101).21,22 This suggest that MoS2 can be used as a support for metal dispersion because reducible oxides such as TiO2 are among the most popular materials used as a mat to disperse metals due to their strong metal−support interactions. Binding energies of the monomers and ordering of the different adsorption sites can be rationalized by examining the optimum structures. In the t-Mo configuration shown in Figure 1a, Pt is bonded to Mo with a bond length of 2.76 Å, as well as to three S atoms with a bond length of 2.29 Å. The high coordination of the t-Mo site explains the strong adsorption energy. This binding configuration turns out to be an important motif that drives the growth of larger clusters in the 2D limit (vide infra). Similarly, in the h-S configuration, Pt is also adsorbed at a high-coordinated site, forming bonds with three S atoms with equal bond lengths of 2.35 Å. This configuration is weaker than t-Mo due to the absence of bonding to Mo and the longer bond length to sulfur. The t-S configuration is the least coordinated site but nevertheless has a binding energy D

DOI: 10.1021/cg5013395 Cryst. Growth Des. XXXX, XXX, XXX−XXX

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Crystal Growth & Design

Figure 2. Top and side views for lowest-energy (Pt)2 configurations.

conversion of t-MoS to t-(Mo)2 is likely to take place in ≈10 ps, while the reverse process requires ≈10 ns. We also investigated the possibility of stabilizing Pt at an interstitial site due to adsorption of another Pt atom at the surface. Similar to the monomer case, this configuration was not stable, which is somewhat anticipated because Pt adsorption does not significantly perturb the MoS2 layer, as can be seen from the relatively small deformation energy ΔEMoS2 reported in Table 1. Therefore, it is unlikely that interstitial sites will play any role in the nucleation process and they will not be investigated further. For a multilayer MoS2 slab, interstitial sites are not expected to play any role as well. However, the wide spacing of 6.49 Å between the MoS2 layers that are held by van der Waals forces55 allows for intercalation of the metal atoms, and thus this complexity compared to the monolayer case should be investigated, especially if the barriers for Pt intercalation are not too high. (Pt)3. For Pt trimer, we find several stable configurations all within ≈0.2 eV/atom (see Figure S1 in Supporting Information). The lowest-energy structure corresponds to the case where two Pt atoms are located at t-Mo sites and the third one is between the two Pt atoms such that the (Pt)3 plane is perpendicular to the MoS2(001) surface as shown in Figure 3a. Because of the similarity to the Greek letter Λ, this structure is referred to as (Pt)3-Λ. In this configuration, the two Pt atoms atop Mo have a bond length of 3.04 Å, and both form equal bond lengths of 2.51 Å with the third Pt atom in the second layer. In contrast to the dimer t-(Mo)2, this configuration takes advantage of the bonding interaction with the substrate, where the two Pt atoms with Pt−Pt = 3.04 Å are nearly atop Mo sites (Mo−Mo distance is 3.18 Å), whereas in the dimer Pt−Pt = 2.81 Å. However, this seems to contradict the ΔEMS value of −1.44 eV/atom which is larger than the dimer t-(Mo)2 value of −2.26 eV/atom (see Table 1). This can be explained because the trimer ΔEMS is normalized by the number of Pt atoms (three) although only two Pt atoms are interacting with the substrate.

Figure 3. (a−c) Top and side views for lowest-energy (Pt) 3 configurations. (d) Potential energy surface for the transformation between them. (Inset) Energy barriers for forward and reverse processes ( in eV).

t-Mo and t-(Mo)2 are the most preferable configurations for monomer and dimer, and thus t-(Mo)3 with three occupied atop Mo sites is likely to be a low-energy structure. Depending on whether the three neighboring Mo atoms are bonded to the same S or not, there are two possible t-(Mo)3 configurations, shown in Figure 3, that we refer to as t-(Mo)3-S and t-(Mo)3-h, respectively. Energetically, it is found that these two structures are ≈0.1 eV/atom higher in energy than (Pt)3-Λ, whereas t(Mo)3-S is 60 meV/atom lower in energy than t-(Mo)3-h. As seen from the figure, t-(Mo)3-S is more compact than t-(Mo)3h because of the extra binding to the S atom. In t-(Mo)3-S, the Pt atoms have shorter average Pt−Pt bond length l ̅ by ≈0.1 Å than t-(Mo)3-h. It is noted that the t-(Mo)3 configuration where three linear Mo sites are occupied is higher in energy than the triangular islands due to the decrease in number of metal−metal bonds. (Pt)4. For the Pt tetramer, the most stable structure corresponds to a triangular pyramid with the flat (Pt)3 structure found before, as shown in Figure 4a,b. Depending on whether the base is t-(Mo)3-h or t-(Mo)3-S, there are two possible configurations that we refer to as t-(Mo)4-h and t-(Mo)4-S, respectively. We find that t-(Mo)4-h is lower in energy than t(Mo)4-S by 45 meV/atom. Here, interestingly, the energy ordering of the optimum tetramer structures is opposite to the trimer case. Thermodynamically, the two tetramer configurations are likely to coexist given the small energy difference between them. Additionally, both can equally nucleate starting from the trimer configurations during Pt deposition. To check for possible kinetic hindrances, we examined two low-energy paths E

DOI: 10.1021/cg5013395 Cryst. Growth Des. XXXX, XXX, XXX−XXX

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Crystal Growth & Design

Figure 4. (a, b) Top views for lowest-energy (Pt)4 configurations. (c) Potential energy surface for transformation between t-(Mo)4-h and t(Mo)4-S following monomer-diffusion mechanism.

based on monomer and dimer diffusion. Starting from t-(Mo)4h or t-(Mo)4-S, the monomer-diffusion mechanism is a twostep process where the Pt atom located at the apex of the pyramid diffuses first to the unoccupied t-Mo site, transforming the structure into a flat t-(Mo)4 tetramer as shown in the inset of Figure 4c. In the second step, the Pt atom occupying the site opposite the first Pt atom diffuses to the top of the triangle formed from the (Pt)3 cluster. On the other hand, in the dimerdiffusion process, starting from either structure, the interconversion proceeds if the dimer formed from the center Pt atom and another Pt atom follows a concerted move to an empty neighboring t-Mo site. Our calculations show that the monomer- and dimer-diffusion mechanisms have similar energy barriers. The potential energy curve (PEC) for the monomer case in Figure 4c shows that either tetramer has to overcome a large barrier of 1.2 eV for interconversion, despite the small energy difference of 45 meV/atom between them, and suggests that both islands are likely to be observed during Pt deposition. (Pt)5. The growth of a pentamer Pt island marked a deviation from the previous cases, where the preferable lowestenergy structure is 3D in nature as shown in Figure 5a. In contrast to previous (Pt)n/MoS2(001) heterostructures with n < 5 where one Pt is found in the second layer, here this configuration is characterized by two layers, where the lower layer has three Pt atoms and the top one has two Pt atoms. For comparison, the growth of (Pt)8 on rutile TiO2(110) showed a 3D nature with more than one atom residing in the second layer.24 The 3D-(Pt)5 is characterized by one short Pt−S bond with S ≈ 2 Å and three longer Pt−S bonds with S ̅ ≈ 2.5 Å. Here the loss of direct bonding with the Mo sites is counterbalanced by eight Pt−Pt bonds with S ̅ ≈ 2.65 Å. Figure 5b shows a pyramidlike structure denoted as 2D-(Pt)5 that is only 14 meV/atom higher in energy than 3D-(Pt)5. Despite the small energy difference, the two configurations are markedly different, which is not very surprising because of that the fluxional nature of metallic NPs. 2D−(Pt)5 can be seen as a combination between the tetramer t-(Mo)4-h and monomer tMo structures, at which four Pt atoms form nearly a flat base with three Pt atoms at t-Mo sites and the fourth close to atop Mo site. Here there are only five Pt−Pt bonds with S ̅ ≈ 2.62 Å. However, the decrease of number of Pt−Pt bonds in 2D-(Pt)5

Figure 5. Top and side views of lowest-energy (Pt)5 configurations.

compared to 3D-(Pt)5 is balanced by an increase in bonding to Mo, as noted before. The fact that close-in-energy 3D-(Pt)5 and 2D-(Pt)5 structures exist, where one is driven by strong metal− metal bonding while the second is driven by strong metal− substrate interactions, is indicative that the pentamer is the smallest cluster size where the nature of the growth mode changes from 2D to 3D. (Pt)6. Similarly to the (Pt)5 cluster, the hexamer has 2D and 3D optimum structures that are close in energy. Figure 6a,b shows two 3D structures, 3D-(Pt)6-1 and 3D-(Pt)6-2, both of which adapt a two-layer configuration with three atoms/layer. The three Pt atoms of the lower base are attached to MoS2, through nearly three S−S bridge sites for 3D-(Pt)6-1 and through three atop S sites in 3D-(Pt)6-2. Energetically, 3D(Pt)6-2 is less stable than 3D-(Pt)6-1 by 20 meV/atom, but it is a more compact structure with only three short Pt−S bonds S ̅ ≈ 2.20 Å, whereas 3D-(Pt)6-1 has nine Pt−S bonds with S ̅ ≈ 2.40 Å. Both configurations have no Pt−Mo bonds but form instead a large number of Pt−Pt bonds, ≈10, with S ̅ ≈ 2.62 Å. 2D-(Pt)6, shown in Figure 6, is only 0.1 eV/atom higher in energy than 3D-(Pt)6-1 but is characterized by a large contact area with the surface, as evidenced by three Pt−Mo bonds with S ̅ ≈ 2.94 Å, 13 Pt−S bonds with S ̅ ≈ 2.44 Å, and only six Pt−Pt bonds with S ̅ ≈ 2.66 Å. (Pt)12. The two lowest-energy structures for (Pt)12 are shown in Figure 7. The binding energy is ≈ −4.1 eV/atom as summarized in Table 1, which is lower than the (Pt)6 energy by 0.5 eV/atom. For comparison, the binding energy of Pt monolayer on MoS2(001) is −4.43 eV/atom.16 As seen from Figure 7, these configurations adapt a 3D morphology characterized by either a two-layer configuration, as in 3D(Pt)12-1, or a hollow-cage type, as in 3D-(Pt)12-2. In the twolayered 3D-(Pt)12-1 structure, there are six atoms in each layer, and the atoms adapt a hexagonal atom arrangement with fcc (111) symmetry. In the hollow-cage 3D-(Pt)12-2 structure, F

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these changes are localized in the S and Mo atoms that directly interact with the metallic NP. For example, in the most stable tMo configuration, the Mo atom directly bonded to Pt is only displaced vertically by 0.05 Å from its optimal position in freestanding MoS2. Also, this can be judged from the relatively small deformation energy ΔEMoS2 in Table 1, where for the monomer case, ΔEMoS2 = 0.26, 0.06, and 0.01 eV for t-Mo, h-S, and t-S, respectively. For larger NPs, ΔEMoS2 becomes negligible compared to the metal−metal and metal−substrate interactions (values reported in Table 1 are not normalized with respect to the number of Pt atoms in the metal island). Furthermore, we can see from Table 1 that the interaction between metal NPs and the substrate, ΔEMS, generally decreases as the cluster size increases. For example, at the monomer level ΔEMS ≈ −3 eV, which increases to ≈ −1 eV for (Pt)12. However, despite this increase, the overall binding energy to the substrate decreases, which can be explained due to the decrease in metal−metal interactions ΔE(Pt)n. The enhanced ΔE(Pt)n can also be seen from the decrease in Pt−Pt bond length where l ̅ decreases from 2.85 Å in (Pt)2 to 2.65 Å for (Pt)12 (see Table 1). This is consistent with previous investigations19,22,24 and can be rationalized because (Pt)n/ MoS2 lowers its total energy by taking more advantage of the strong metal−metal bond at the expense of metal−substrate bonding. This behavior is expected for metals with large cohesive energy such as Pt, which makes it challenging for deposition techniques such as ALD to wet the surface and explains the eventual transformation of the supported Pt growth mode from 2D to 3D, as observed in this study with MoS2(001) substrate as well as other substrates.19,21−24,29 The NP morphology transitions from 2D to 3D with increasing NP size due to the competition between metal− surface and metal−metal interactions. For small numbers of metal particles, the first term dominates and hence the cluster adopts a 2D nature that interacts more strongly with the surface. For large clusters, metal−metal interactions dominate and the cluster adopts a 3D morphology. Furthermore, the nature of adhesion of metal NPs to the support changes as the growth mode evolves from 2D to 3D. In the 2D growth regime, the optimum structures of the supported NPs are characterized by direct bonds between the metals and Mo atoms that sit in the troughs of the MoS2(001) surface. On the other hand, in the 3D structures, the clusters attach to the substrate through S atoms that are more extended in the vacuum region. This was also observed in the epitaxial growth of Pt monolayers on MoS2(001).16 For 3D islands where metal−metal interactions dominate, the metal atoms cannot take advantage of the strong Mo adsorption centers due the topography of the MoS2(001) substrate with a relatively large distance of 3.18 Å between neighboring Mo atoms. Because MoS2 has the smallest distance between the metal atoms,12,55 this is also expected to be the case with other TMD members. These results suggest that S rather than Mo substitutions might be a more effective means for the NPs to adhere more strongly to MoS2 substrate. Furthermore, the effects of Mo substitutions are not expected to be direct but rather mediated by the Mo−S covalent bond of the MoS2 surface. Examining the charge decomposition, we find that Pt NPs can donate or accept charge from MoS2 depending on the bonding configuration. For example, for the monomer case, Pt donates charge in t-Mo and h-S configurations but accepts

Figure 6. Top and side views of lowest-energy (Pt)6 configurations.

Figure 7. Top and side views of lowest-energy (Pt)12 configurations.

which is less compact than 3D-(Pt)12-1, there are eight atoms in contact with the surface and four atoms arranged on a plane inclined 27° with respect to the top sulfur plane of MoS2(001), thus forming a hollow-cage type. This configuration has no analogue in gas-phase structures but resembles hollow structures predicted previously for supported gold clusters on MgO(001) in the size range between 23 and 42 Au atoms.56 Also, as seen in the figure, 3D-(Pt)12-1 and 3D-(Pt)12-2 attach to MoS2 through six and nine direct Pt−S bonds with a bond length S ̅ ≈ 2.2 Å, and both have a relatively large number of Pt−Pt bonds, 24 and 22, with an average distance S ̅ ≈ 2.6 Å.

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DISCUSSION The interactions of Pt with the MoS2 substrate induce small changes in the optimal MoS2 atomic positions, where most of G

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The PES of Figure 8a shows that, for on-surface diffusion between two t-Mo sites, there exist two low-energy pathways,

charge in the t-S configuration. Similarly, the Pt dimers donate charge in t-(Mo)2 configuration but accept charge in t-MoS and t-Moh configurations. Charge analysis based on real-space charge-density differences is also consistent with the results based on Hirshfeld partitioning, as shown in Figures S2 and S3 in Supporting Information. To a very large extent, only MoS2 atoms that are directly bonded to Pt are involved in the charge rearrangement, which is consistent with the previous results that showed small/negligible changes of atomic positions in MoS2. For instance, in the t-Mo configuration, Pt and the bonded Mo donate respectively 59 and 12 millielectrons to the closest three sulfur atoms. In the TS configuration, 61 millielectrons are donated to Pt, mostly from the bonded S atom. As the NPs grow, there is more charge transfer from MoS2 to the metallic NP. For example, for the largest cluster investigated, (Pt)12, there is a charge transfer of ≈200 millielectrons. This charge-rearrangement picture agrees with the real-space charge-density map shown in Figure S4 in Supporting Information. The direction of charge transfer can be understood by noting that large clusters attach to the surface through Pt−S type bonding, which is characterized by charge donation from MoS2 to the surface as seen in the monomer case. Also, charge transfer from MoS2 to large Pt clusters agrees with what was observed recently in heterostructures formed between Pd and Pt monolayers with (111) orientation grown pseudomorphically on MoS2(001).16 Step-by-Step Nucleation of (Pt) n Clusters on MoS2(001). On the basis of the stable adsorption configurations, we now discuss the growth of Pt NPs by subsequent attachment of a Pt monomer to an island during the sputtering. Adsorption of Pt atom from gas phase on MoS2(001) is the first step, after which atoms migrate on the surface and either form a stable nucleus, by attaching to an island that has atoms greater than critical size, or evaporates back into the gas phase instead. The nucleation of new sites continues upon increasing the metal upload on the surface, until the distance between two neighboring islands is less than the diffusion length of Pt on MoS2(001), at which the density of nuclei reaches saturation. After that, all arriving adatoms are attached to existing islands either directly or after diffusion along the substrate surface (see, for example, ref 3). The mobility of Pt on clean MoS2(001) terraces due to activated thermal hopping is the most important kinetic process in film growth, at least in the early stages of deposition with low Pt coverage. To gain a detailed understanding of the low-energy diffusion paths on MoS2, we construct the PES by relaxing the height z of a Pt atom above the MoS2(001) as well as MoS2 layer for different positions of Pt above the surface. In practice, the Pt coordinates are drawn from a fine triangular mesh that is generated only in the primitive surface unit cell and then extended to the large supercell by use of crystal symmetries. The local minima on the PES constitute the stable binding sites, while the saddle points are the transition states for adatom diffusion. The diffusion barrier is obtained from the difference in energy between local minima and saddle points. It should be noted that the constructed PES accounts only for surface diffusion, which is nevertheless not a limitation for Pt/MoS2 because substitutional defects as well as interstitial sites are not stable (vide supra). Furthermore, the fact that substitutional defects are energetically very costly means that Pt diffusion on the MoS2(001) surface through an exchange mechanism is highly improbable.

Figure 8. (a) Potential energy surface (PES) of a Pt atom on MoS2(001), showing the anisotropic nature of the surface diffusion process. The primitive unit cell is shown in solid black lines, and the circles mark the projections of t-Mo, t-S, and h-S sites. (b) Cuts through the PES for diffusion of Pt between two neighboring atop Mo sites, along [101̅] via h-S site, with a diffusion barrier of 0.6 eV, and along [110̅ ] via t-S sit,e with a barrier of 0.7 eV.

one where the adatom passes through the h-S site and another one via the t-S site. Cuts through the PES corresponding to these two paths are shown in Figure 8b. The first path along [101]̅ has a diffusion barrier of 0.6 eV, while the second one along [11̅0] has a barrier of 0.7 eV. Here it should be noted that the t-S and h-S sites are both local minima on the PES, as verified before from the vibrational analysis, and this is also seen from the PEC of Figure 8b. This is why the diffusion barrier is not given as the energy difference between the corresponding adsorption energies at high-symmetry sites. As seen from Figure 8b, the actual barriers are larger and show more the anisotropy of Pt diffusion on the surface. Using the computed energy barriers and employing the TST of eq 4, we estimate the number of hopping events per second between two Mo sites as ≈103 s−1 along [101̅] and ≈10 s−1 along [11̅0] at room temperature. This shows that Pt monomers are moderately mobile on MoS2, whereas the fast diffusion channel along [101̅] is a factor of 100 larger than the slow diffusion channel. At a typical ALD temperature of 600 K, the hopping rates for the two directions increase to 108 and 107 s−1, respectively. For comparison, the hopping rates at room temperature are a few orders of magnitude larger than on anatase TiO2(101), previously estimated to be ≈10−2 s−1.22 H

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The tetramer (Pt)4 case is also a direct extension of the trimer (Pt)3-Λ after the adsorption of a Pt monomer at t-Mo and diffusion to the trimer island. Here, there are two possible t-Mo sites located on opposite sides perpendicular to the (Pt)3 plane, which can be seen as the precursors for t-(Mo)4-h or t(Mo)4-S. Furthermore, the two tetramer configurations t(Mo)4-h and t-(Mo)4-S can also be nucleated from the corresponding trimer configurations t-(Mo)3-h or t-(Mo)4-S after an adsorption/diffusion event to a neighboring t-Mo site. Starting from the transition state shown in Figure 4c, it is seen that t-(Mo)4-h and t-(Mo)4-S are accessible after surmounting barriers of 0.2 and 0.4 eV, respectively. However, despite the small barriers, this path is not likely to be dominant in the formation of tetramers at finite temperatures because t-(Mo)3-h and t-(Mo)4-S are only transient states that transform to (Pt)3Λ (vide supra) . Formation of 2D structures with n ≥ 5 is also seen as a simple extension from the smaller clusters in conjunction with monomers occupying t-Mo sites. For example, the pyramidlike 2D-(Pt)5 cluster can be easily accessed form the tetramer configurations t-(Mo)4-h and t-(Mo)4-S shown in Figure 4a,b after deposition/diffusion event of Pt atom to a neighboring tMo site. We refer to these two structures respectively as t(Mo)5-h and t-(Mo)5-S, which are found to be stable and have energies nearly 10 meV/atom higher than 2D-(Pt)5. t-(Mo)5-h is shown in Figure 5c. We find that the transformation of t(Mo)5-h to 2D-(Pt)5 is almost barrierless with a value less than 0.1 eV. Similarly, 2D-(Pt)6 is a simple extension from 2D-(Pt)5 after the attachment of a monomer to the island or as a combination between tetramer t-(Mo)4-h and t-Moh configurations. The path for formation of 3D Pt clusters with n ≥ 5 atoms is generally harder to quantify than the 2D structures. However, it is likely that these structures are not significantly kinetically limited, mostly because they are obtained upon relaxation from configurations that are extracted from an AIMD trajectory sampled at ≈1000 K.

Therefore, Pt is sufficiently mobile to allow for coarsening and growth of large islands rather than a fine dispersion during the deposition and is not likely to be the rate-limiting step for Oswald ripening. Additionally, the existence of fast and slow diffusion tracks suggests that these islands are likely to be anisotropic. The t-(Mo)2 dimer binding energy per atom is lower by 0.1 eV/atom than the monomer t-Mo energy, which shows that the deposited Pt atom prefers to bind to an adsorbed Pt atom rather than to a site that is far away. For comparison, the clustering energy for Pt on anatase TiO2(101) is 0.3 eV.21 We also find that the clustering effect is somewhat short-ranged, where Pt atoms adsorbed on two Mo sites belonging to secondnearest neighbors (5.51 Å separation) have a binding energy the same as that of the monomer. The clustering effect increases the attachment rates for a newly deposited atom to bond to an existing occupied site after possible diffusion events. To show this explicitly, we see from Figure 9 that the barrier for

Figure 9. Energy barriers for monomer attachment−detachment process.

detachment of a monomer from a t-(Mo)2 dimer to the noninteracting monomer limit is 0.91 eV, while the barrier for attachment of a monomer to an existing t-Mo monomer to form t-(Mo)2 is 0.67 eV. At room temperature this translates into rates of 10−3 and 101 s−1; that is, the monomer attachment is more probable than detachment by a factor of 104. This shows that the critical size of nucleation of Pt on MoS2(001) is 1. The two flat trimers t-(Mo)3-S and t-(Mo)3-h shown in Figure 3b,c are easily accessible during metal deposition, as this involve only low-energy monomer diffusion events to reach a dimer island. However, it is not clear whether (Pt)3-Λ of Figure 3a, which is the lowest in energy, can be observed during the time scale of the nucleation process. By mapping the PEC curve connecting the two flat trimers shown in Figure 3d, we find that (Pt)3-Λ is located on this low-energy path, although this configuration is a local minimum rather than a transition state as verified from vibrational frequencies. As seen from the figure, the barriers for transforming the flat configurations t-(Mo)3-h and t-(Mo)3-S to (Pt)3-Λ are 0.2 and 0.1 eV, while as the reverse processes have barriers of 0.6 and 0.5 eV, respectively. At room temperature, the rates for conversion to the (Pt)3-Λ configuration are 109 and 1011 s−1, indicating that this will take place on the order of 1 ns and 0.2 ps for t-(Mo)3-h and t(Mo)3-S, respectively. This shows that (Pt)3-Λ is not kinetically limited and should be the prevalent trimer island morphology during Pt sputtering due to thermodynamic as well as kinetic factors.

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CONCLUSION Using density functional theory calculations, we examined the low-energy (Pt)n clusters with n ≤ 12 that are likely to form on MoS2(001) during the deposition of Pt. We showed that for n < 5, the optimum structures adapt a 2D morphology, where Pt atoms mostly bond to the Mo sites that are located in the troughs of MoS2(001) surface. For n ≥ 5, the (Pt)n clusters adopt a 3D nature where the cluster attaches to the surface by bonding to the sulfur atoms that are more extended into the vacuum region. We also find that Pt atoms attract each other on the surface with a 0.1 eV clustering energy for the dimer. Additionally, we find that monomer−monomer attractions make the probability for a monomer to attach to an existing island (monomer size) 104 higher than the detachment probability from an existing dimer at room temperature. This suggest that the monomer is the critical island size, defined as the minimum cluster than can only grow or remain constant. The potential energy surface shows anisotropic mobility of Pt on the surface, at which the number of hopping events per second between two Mo sites is ≈103 s−1 along [101̅] and ≈10 s−1 along [11̅0] at room temperature. Overall, the high mobility of Pt atoms suggests that Pt sputtering on MoS2 will result in relatively large islands rather than a fine dispersion. Additionally, the existence of a fast track for diffusion suggests that these islands are likely to be anisotropic. I

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ASSOCIATED CONTENT

S Supporting Information *

Additional text describing real-space charge analysis and four figures showing adhesion energies for most of the investigated structures in this study and plane-integrated charge rearrangements for the monomer, dimer, and 3D-(Pt)12-1 configurations shown in Figure 1. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation Grant OCI-1053575.

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DOI: 10.1021/cg5013395 Cryst. Growth Des. XXXX, XXX, XXX−XXX

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DOI: 10.1021/cg5013395 Cryst. Growth Des. XXXX, XXX, XXX−XXX