Adatom and nanoparticle dynamics on single-atom catalyst substrates

Single-atom catalysts represent an essential and ever-growing family of heterogeneous catalysts. Recent studies indicate that besides the valuable catalytic properties provided by single-atom active sites, the presence of single-atom sites on the catalyst substrates may significantly influence the population of supported metal nanoparticles coexisting with metal single atoms. Treatment of ceria-based single-atom catalysts in oxidizing or reducing atmospheres was proven to provide precise experimental control of the size of the supported Pt nanoparticles, and, correspondingly, control of catalyst activity and stability. Based on dedicated surface science experiments, ab-initio calculations and kinetic Monte-Carlo simulations we demonstrate that the morphology of Pt nanoparticle population on ceria surface is a result of a competition for Pt atoms between Pt single-atom sites and Pt nanoparticles. In oxidizing atmosphere, Pt single-atom sites provide strong bonding to single Pt atoms and Pt nanoparticles shrink. In reducing atmosphere, Pt single atom sites are depopulated and Pt nanoparticles grow. We formulate a generic model of Pt redispersion and coarsening on ceria substrates. Our model provides a unified atomic-level explanation for a variety of metal nanoparticle dynamic processes observed in single-atom catalysts under stationary or alternating oxidizing/reducing atmospheres, and allows to classify the conditions when nanoparticle ensembles on single-atom catalysts substrates can be stabilized against Ostwald ripening.


Introduction
Activity, selectivity and stability of most heterogeneous catalysts depend sensitively on the size of supported metal nanoparticles [1], [2]. Experimental techniques and practical approaches have been developed targeting the nanoparticle size during catalyst activation [3], [4], operation [5], [6] and regeneration [7], [8] with the aim to optimize the catalyst utilization and to improve understanding of nanoparticle dynamic changes throughout the catalyst lifetime. With realization of single-atom catalysts [9], [10] the range of controlled metal nanoparticle sizes has reached a limit of one supported metal atom. Single supported metal atoms do not represent a thermodynamically stable entity on their own. To prevent nucleation of metal atoms to metal nanoparticles, single-atom catalyst substrates must be available, providing sites with strong enough chemical bonding to single metal atoms to overcome metal cohesion [11], [12]. Still, the stabilization of single metal atoms on the catalyst substrate does not guarantee a single-atom catalyst operation. Often, the strong bonding of single atoms to the substrate compromises their catalytic activity [13]- [15], or single atoms are destabilized by interaction with reactants during catalyst operation and metal nanoparticles become the active phase instead [16], [17].
Highly dynamic behavior of metal load on single-atom catalyst substrate has been documented for platinum (Pt) on ceria (CeO2). Ceria can provide strong bonding to metal nanoparticles resulting in high metal dispersion and small nanoparticle size [18]. Recently it was proven that Pt nanoparticles on ceria/alumina substrates are destabilized in oxidizing conditions and at high temperatures and decompose to Pt single atoms bonded to O atoms at surface defects on ceria, particularly at monoatomic surface steps [19]. Such Pt single atoms show small activity towards CO oxidation [20], [21]. Activation of Pt single atoms on ceria for low-temperature CO oxidation can be achieved via treatment of the single-atom catalyst under reducing conditions when in turn, Pt single atom traps are destabilized and threedimensional Pt nanoparticles of optimal size nucleate [22], [23]. When Pt nanoparticles further grow in size by Ostwald ripening and low-temperature CO oxidation activity is suppressed, catalyst treatment under oxidizing atmosphere can reset the Pt single atom dispersion and make the catalyst ready for new activation [22]. These results indicate exciting possibilities for activation, regeneration and long-time operation of metal nanoparticle catalysts supported on single-atom catalyst substrates [24]- [27] and call for elucidating the mechanisms of Pt redispersion and coarsening on ceria in oxidizing and reducing atmospheres.
We address the issues of Pt redispersion and coarsening in a model system of Pt nanoparticles on CeO2(111) single crystalline substrate [28]. Flat CeO2(111) surfaces can be investigated by microscopic and spectroscopic techniques of surface science obtaining direct quantitative information unavailable for real Pt-ceria catalysts: density of surface defects or single atom sites [29], charge state of the surface [30], and occupation of single-atom sites by single Pt atoms [31]. Previously, such quantitative information, combined with ab-initio calculations, allowed identifying Pt single atom dispersion on CeO2(111) at monoatomic steps acting as single atom traps, configuration of the stable single Pt atom as Pt 2+ ion bonded to 4 neighboring surface O atoms in a square-planar configuration, and capacity of monoatomic steps on CeO2(111) to accommodate up to one Pt 2+ single ion per one step Ce site [31].
Binding energy of Pt in the single-atom sites was investigated as a function of the concentration of Pt and O atoms at CeO2(111) step edges [32]. Under oxidizing conditions, and in the presence of excess O atoms at step edges, Pt atoms are accommodated at step edges as single Pt 2+ ions with binding energy E1 ox larger than Pt cohesive energy Ec. Under reducing conditions, and in the absence of excess or lattice O atoms at step edges, single Pt atoms are accommodated at step edges as partially charged Pt δ+ species with binding energy E1 re smaller than Pt cohesive energy Ec.
In the present work, we perform dedicated surface science experiments revealing the dynamic character of Pt load on CeO2(111), particularly the thermally activated nature of redispersion of deposited Pt to single Pt 2+ ions [19], [31]- [33], and Pt coarsening and redispersion in alternating reducing and oxidizing conditions [22], [23], [34]. With further support from abinitio calculations we formulate a generic model of Pt redispersion and coarsening comprising Pt adatom diffusion on CeO2(111) terraces, Pt adatom interaction with single-atom traps at CeO2(111) step edges, and Pt adatom interaction with Pt nanoparticles on CeO2(111) surface.
We show that thermal activation during Pt redispersion and coarsening is required for breaking Pt-Pt bonds in Pt nanoparticles on the way towards minimization of the total energy of Pt/CeO2(111) system. In oxidizing conditions, capture of Pt adatoms in single atom traps is preferred (E1 ox > Ec) and Pt nanoparticles shrink. In reducing conditions, single-atom traps are depopulated (E1 re < Ec) and Pt nanoparticles grow by Ostwald ripening. Kinetic Monte Carlo simulations within the proposed model allow us to identify general conditions under which metal nanoparticle catalysts on single-atom catalyst substrates can be optimized and operated in a stable, sinter-resistant manner.

Results
Thermally activated nature of Pt redispersion on CeO2(111). To obtain efficient redispersion of Pt deposit to supported Pt single atoms on model and real CeO2 substrates, thermal activation is required [19], [31]- [33]. We investigate this process in detail in a series of surface science ultra-high vacuum (UHV) experiments in which Pt is deposited at 300 K on CeO2(111) samples prepared with well-defined concentrations of surface monoatomic steps providing single-atom Pt adsorption sites [19], [27], [31], [32]. Upon Pt deposition, the samples are subjected to repeated flash annealing to increasingly higher temperatures and characterized with synchrotron radiation photoelectron spectroscopy (SRPES). In the SRPES of Pt 4f, the Pt 2+ signal corresponds to the amount of occupied Pt single-atom sites, whereas the Pt 0 signal represents partially charged Pt δ+ atoms and Pt nucleated as metal nanoparticles Figure S1 a, e, i). The fraction of Pt 2+ signal in the total Pt 4f signal thus allows us to determine the fraction of Pt deposit dispersed as single atoms. No Pt 4+ signal is observed by SRPES in the present experiments.
We repeat these experiments on four CeO2(111) samples prepared with step densities 6, 11, 15, and 16% monolayer (ML), always depositing 7% ML Pt. 1 ML represents the density of Ce atoms on the CeO2(111) surface (7.9×10 14 cm -2 or 7.9 nm -2 ). The results are summarized in Figure 1. For each sample, a progressive redispersion of Pt is observed with increasing temperature. Three other effects can be identified. At 300 K, the fraction of Pt deposit dispersed as single atoms is increasing with increasing step concentration. Upon final annealing at 700 K, the fraction of Pt deposit dispersed as single atoms adopts two values. For samples where the step density is higher than the amount of deposited Pt, majority of Pt is dispersed as single atoms. For the sample where the step density is lower than the amount of   [19], [22], [35]. Here we perform analogous experiments on model CeO2(111) surfaces by means of SRPES and Scanning Tunneling Microscopy (STM). On the CeO2(111) surface with 15% ML of monoatomic steps we deposit Pt at 300 K, and anneal at 700 K in UHV to obtain Pt redispersion. Afterwards, we perform alternating cycles of sample reduction (in 1×10 -5 Pa CH3OH) and sample oxidation (in 1×10 -5 Pa O2, see Experimental and Computational Details). In between the cycles, we characterize the chemical state of the sample by SRPES. We select CH3OH as a reducing agent because, in contrast to CO or H2, it strongly interacts with clean CeO2(111) surfaces and provides a reliable reduction of CeO2(111) surface under UHV conditions of surface science experiments [36]. Reduction with CH3OH does not change the density of monoatomic steps on CeO2 (111) surfaces [32].
On all samples, we observe coarsening of the Pt deposit (decrease of the Pt 2+ signal, increase of Pt 0 signal) upon reduction treatments ("red1"-"red5"), and redispersion (increase of the Pt 2+ signal, decrease of Pt 0 signal) upon oxidation treatments ("ox1"-"ox5"). Coarsening and redispersion also influence the total Pt 4f signal due to partial screening of Pt 0 signal from metallic Pt nanoparticles. Screening is becoming more efficient for larger nanoparticles; the total Pt 4f signal can thus serve as a qualitative indication of the Pt nanoparticle size. For Pt amounts smaller than the step density (2 and 6% ML Pt) redispersion on the as-prepared samples ("Pt as prep") is almost complete, and subsequent coarsening and redispersion of Pt in the five observed reduction/oxidation cycles is very reversible. For Pt amounts larger than the step density (16 and 26% ML Pt) redispersion on the as-prepared samples is incomplete.  [37]. A complete coarsening (suppression of the Pt 2+ signal) in the reduction cycles was accomplished by reducing the samples to values of RER > 1.0 [32].
Upon oxidizing cycles, RER decreases to < 0.1 corresponding to almost fully stoichiometric CeO2(111) [32]. Reduced CeO2-x(111) surface is highly reactive towards water and alcohols resulting in strong OH adsorption at the surface ( Figure S1 g, h). The use of organic reductant (CH3OH) in the reduction cycles results in the presence of carbonaceous adsorbates at the surface upon both reducing and oxidizing cycles ( Figure S1 d, h, l). This indicates that the redispersion provided to Pt by ceria-based single-atom catalyst supports is robust with respect to organic and carbonaceous contaminants. conditions. Pt was deposited at 300 K and annealed at 700 K in UHV ("Pt as prep") followed by annealing at 600 K in alternating reducing (CH3OH, "red") and oxidizing (O2, "ox") conditions. Experiments were performed for Pt amounts between 2 and 26% ML deposited on

Activation barriers for filling Pt single atom traps on CeO2(111).
Understanding the thermally activated nature of the Pt redispersion on CeO2 in oxidizing conditions requires considering Pt transport processes on CeO2(111) surface at the atomic scale. Pt nanoparticle diffusion can be excluded, because single atom traps at CeO2(111) step edges must be populated by diffusing species containing single Pt atoms. In some studies, Pt mass transport through gas phase via volatile PtO2 is invoked [27], [38], [39]. On geometrically flat model CeO2(111) substrates, however, formation and desorption of PtO2 would lead to a fast removal of Pt deposit which is not observed. Ab-initio calculations predict that due to small binding energy of a PtO2 molecule on CeO2(111), surface diffusion of PtO2 does not take place [27]. The presence of carbonaceous species on our samples ( Figure S1 d, h, l) may invoke consideration of Pt transport via Pt carbonyls [40]. This mechanism however cannot account for all observed phenomena, e.g. for the Pt redispersion after deposition ( Figure 1, Figure S1 d). Moreover, monodispersed Pt 2+ ions at ceria step edges do not interact with CO [31]. It seems reasonable to assume mass transport of Pt on CeO2(111) surfaces via diffusion of Pt single atomsadatoms. Theoretical studies predict the binding energy of Pt adatom on CeO2(111) surface 3.3 eV [31], and the activation energy for Pt adatom hopping on clean CeO2(111) surface 0.5 eV, rendering surface diffusion of Pt adatoms a fast and efficient process [41].
Single-atom traps for Pt adatoms are localized at the step edges of CeO2(111) [19], [27], [31], [32] and must be occupied by surface diffusion of Pt adatoms from upper or lower CeO2 (111) terraces adjacent to the step edges. This process may account for the experimentally observed thermal activation of Pt redispersion provided that energy barriers preventing adatom attachment at the step edge from the upper or the lower terrace are present [42], [43]. Here we estimate such step-edge barriers for Pt adatom capture at CeO2(111) monoatomic step edges based on density functional theory (DFT) calculations [44].
Following our previous works on Pt incorporation and reactivity at CeO2(111) step-edges [31], [32], [45], we select two different low-energy step geometries, which we label as Type I and Type II [46]. For each step geometry, we consider both stoichiometric step edges as well as step edges in the presence of excess oxygen atoms decorating the steps ( Figure S4). We have previously demonstrated that excess O atoms bind preferentially at step edges leading to the formation of stable peroxide species. Peroxide species in turn determine the preferential binding of Pt adatoms to the oxidized step edges, and increase the Pt binding energy by 1.6 eV with respect to stoichiometric step edges. This large increase in Pt binding energy correlates with the formation of characteristic square-planar PtO4 units [31]. The adsorption energy of Pt on all the considered model steps is summarized in Table S1.
In order to quantify the step-edge barrier for the Pt incorporation at CeO2(111) step edges via surface diffusion, we have calculated the minimum energy path corresponding to the diffusion of a Pt adatom from a CeO2(111) terrace to a step edge. This process has been calculated considering diffusion paths from both sides of the step edge (i.e. from the upper and lower terraces), for both model step edges (Type I and Type II), and for different degrees of stepedge oxidation (stoichiometric and with excess oxygen). The minimum energy paths have been computed using the climbing image nudged elastic band (CI-NEB) method, which provided the activation energy for Pt diffusion at the ceria step edge. Schematic illustration of the calculation for Step Type II with excess oxygen is in Figure 3, all calculated configurations are summarized in Figure S5.

From lower terrace From upper terrace
Step Type I Stoichiometric 0.47 eV 0.75 eV Step Type II Stoichiometric 0.59 eV 0.42 eV Step Type I Excess Oxygen 0.60 eV 0.60 eV Step Type II Excess Oxygen 0.16 eV 0.40 eV

Generic model of metal redispersion and coarsening on single-atom catalyst substrates.
The absence of the step-edge barrier for Pt adatom capture in single-atom traps on CeO2 (111) step edges resulting from our DFT calculations ( Figure 3, Table 1) indicates that Pt adatom capture is a diffusion-limited process and the thermal activation in the present (Figures 1, 2) and previous experimental observations [19], [24], [31]- [33] is rather required to increase the  (Figure S6 a) and reduced step edge E1 re (Figure S6 b). All Pt adatom hops in the model are assigned the same activation energy Ed, and no additional energy barrier is associated with Pt attachment or detachment to and from the step edges and Pt nanoparticles. Energy parameters of the model are selected in the way that they obey the relationship E1 ox > Ec > E1 re determined previously based on ab-initio calculations [31], [32]. In order to achieve manageable computational times, E1 ox , Ec, and E1 re are set approximately 1 eV lower than predicted by abinitio calculations resulting in an effective downshift of the simulation temperatures by 100-150 K relative to the temperatures in the experiment. Parameters of the KMC simulation are summarized in Table 2 while the relation of binding energies in the KMC simulation to the results of ab-initio calculations is illustrated in Figure S8.   Figure 1, we perform KMC simulation depositing 5% ML Pt at 300 K on substrates containing 6%, 10% or 17% monoatomic steps. Ceria substrates before Pt deposition are considered partly oxidized with oxidized and reduced steps each representing 50% of the step-edge sites (Figure S6 c). Upon Pt deposition, we simulate 30 s annealing cycles at temperatures 350 K, 400 K … 700 K and evaluate the Pt dispersion on the samples at the end of each annealing cycle. In analogy to previous experimental and theoretical studies [31]- [33], the intensity of the simulated Pt 2+ SRPES signal is considered proportional to the amount of isolated Pt adatoms at oxidized steps. All other Pt atoms in the simulation contribute to the intensity of the simulated Pt 0 SRPES signal ( Figure S7). For the evaluation of the simulated Pt 0 SRPES signal, the exponential attenuation of the signal from subsurface Pt atoms is taken into account ( Figure S7). KMC simulations clearly illustrate that the thermal activation required for redispersion of Pt load on CeO2(111) is due to kinetic limitations preventing the Pt adatoms from reaching oxidized step edges rather than due to the microscopic nature of the interactions between Pt adatoms and steps (cf. Table 1). Assuming sufficient thermal activation, we now attempt at simulating Pt coarsening and redispersion in reducing and oxidizing conditions ( Figure 2). On CeO2(111), changes in the oxygen content at monolayer step edges result in the changes of binding energy of Pt single-atomsfrom low E1 re at oxygen deficiency to high E1 ox at oxygen surplus and vice versa (Table S1, Table 2, [31], [32]).

At stationary reducing conditions, only an unstable solution is available. 3D clusters undergo
Ostwald ripening which is, in the absence of additional constraints on characteristic system sizes [56], [57], a nonstationary process [58].
In alternating oxidizing/reducing conditions, the stability of the nanoparticle populations requires, in addition to sufficient ox, a suitable timing. We perform KMC simulations of the nanoparticle population for Pt = 10% ML, and ox =17% ML (Pt < ox), and at simulation temperature 650 K when the redispersion and coarsening times are reduced to an order of single seconds, comparable to, e.g. alternating oxidizing/reducing conditions in three-way automotive catalytic converters [59], [60].   The presented view of Pt redispersion and coarsening on ceria as a competition for Pt adatoms between single-atom traps at ceria step edges and Pt nanoparticles can be, in many cases, applied to real ceria catalysts. Monoatomic step edges are ubiquitous on well-annealed nanoparticulate and nanoporous ceria supports [19], [27], [61], [62]. Excess O atoms at ceria step edges required for strong bonding of single Pt 2+ ions are present already in the conditions of model UHV experiments [31], [32]. Excess O in the form of peroxo and superoxo species is readily observed and available for Pt 2+ stabilization also on real ceria catalysts in air or in lean, oxygen-containing reaction mixtures [63]- [65]. As is the case of model experiments, monoatomic step edges on real Pt/ceria catalysts exhibit limited capacity to accommodate single Pt 2+ species during high-temperature treatment in air. Full Pt dispersion to Pt 2+ species was observed for ρox>ρPt. For ρox<ρPt saturation of step edges was observed, resulting in coexistence of isolated Pt 2+ species and Pt nanoparticles ( [27] , cf. Figure 5). In real Pt/ceria catalysts, mass transport of Pt on the ceria surface via Pt adatom diffusion can be efficient at lower temperatures, and within the surface of individual ceria nanoparticles as observed e.g. by TEM in [22]. At higher temperatures, or for Pt transport among the ceria nanoparticles sublimation of PtO2 species and Pt mass transport through gas phase may be invoked [27], [38]. The efficacy of mass transport via PtO2 in real catalysts may however need verification by further experiments, e.g. to determine its substrate dependence when Pt load seems unstable on alumina [66] and stable on ceria [57], [59].
The change from oxidizing conditions to reducing conditions in the presented model is considered instantaneous ( Figure S6). In real catalysts, a chemical reaction in oxygen deficient rich reducing reaction mixture must proceed removing O atoms (excess O or lattice O) from Pt 2+ complexes at step edges. This reaction is expected to proceed fastest at the Pt 2+ complexes, and at superoxo, peroxo, and lattice O sites at ceria step edges since the binding energies of O at these sites are smaller than on the facets of ceria nanoparticles [31], [67]. The amount of removed oxygen atoms required to deactivate all Pt 2+ traps at ceria step edges and initiate nucleation and growth of Pt nanoparticles is on the order of monoatomic step density, i.e. 10 % of surface Ce atoms [32]. With bulk sensitive experimental methods employed for characterization of Pt/ceria catalysts under reaction conditions such amount of removed O or reduced Ce 3+ may be difficult to detect and the deactivation of Pt 2+ traps in reducing conditions can happen before the reduction of ceria bulk is observed [23].
Apart from single Pt atoms in Pt 2+ chemical state and metallic Pt nanoparticles some studies on real Pt/ceria catalysts report one dimensional (1D) and two-dimensional (2D) Pt objects of oxidized or mixed oxidized/metallic chemical state and a specific catalytic activity different from single Pt 2+ ions or metallic Pt nanoparticles [26]. Our model suggests that such objects may be related to ceria step edges densely populated with Pt 2+ ions or to 2D Pt objects at step edges ( Figure 6b). 2D decoration of ceria step edges with Pt in a mixed oxidized/metallic chemical state has been proposed earlier based on ab-initio calculations [32]. were performed at UHV apparatuses using procedures described in detail in our previous publications [31], [32]. Particularly, CeO2(111) thin films were prepared by evaporation of Ce metal (Goodfellow, 99.95%) from Mo or Ta crucible on Cu(111) surfaces (MaTecK) in 5×10 -5 Pa O2 (Linde, SIAD, 4.7). Density of monoatomic steps was controlled via deposition temperature, reduction/oxidation procedures or postdeposition annealing as summarized in Table S2. Density of monoatomic steps was determined from STM images via superimposing a manual outline of step edges on a properly scaled and oriented mesh of surface Ce atoms on CeO2(111), and counting the number of Ce atoms at step edges [31], [32]. Pt (Safina, Goodfellow, 99.95%) was deposited at 300 K, the amount of deposited Pt was controlled via a combination of quartz crystal microbalance (QCM) and XPS measurements of the attenuation of Ce 3d or Cu 2p3/2 signals [31], [32].
Upon Pt deposition, redispersion to Pt 2+ was performed by annealing in UHV at 700 K or lower as described in the text (Figure 1). Reduction treatments of the samples were performed via 1 min annealing the samples in 1×10 -5 Pa CH3OH at 600 K. Reduction treatments were repeated, eventually, until the ceria reduction indicated by RER (Figure S1 b, f, j) increased above 1.0. Oxidation treatments of the samples were performed via 10 min exposure to 1×10 -5 Pa O2 at 300 K followed by flash annealing at 600 K in the same O2 background. Oxidation treatments were repeated, eventually, until RER decreased below 0.1. After the oxidation the samples were flash annealed at 700 K in UHV.
In between the redispersion/reduction/oxidation steps oxidation state of Pt deposit and ceria support were characterized at 300 K by XPS, SRPES, and RPES. Overview of the evaluated data and the corresponding fitting and background subtraction is presented in Figures S1 and   S2. STM experiments were performed at 300 K using a mechanically cut Pt-Ir STM tip.
Complementary images of occupied states and empty states were obtained (Figure 2 b and Figure S3).

DFT Calculations
All calculations were based on the DFT employing ultrasoft pseudopotentials and the Perdew, Burke and Ernzerhof (PBE) generalised gradient-corrected approximation for the exchange and correlation functional [72], [73]. The electronic wave function and density were described with a plane-wave basis set employing energy cutoffs of 40 and 320 Ry, correspondingly.
Following the established practice we use the PBE+U approach to describe the electronic structure of ceria-based materials, employing the implementation of Cococcioni and de Gironcoli [74] which includes an additional Hubbard-U term to the Kohn-Sham functional that disfavors fractional occupancies of the Ce 4f states. The value of the parameter U was set to 4.5 eV [75]. All calculations have been performed using the Quantum-ESPRESSO computer package [76]. The minimum energy paths at 0 K have been computed using the CI-NEB algorithm using a Broyden scheme as implemented in the Quantum-ESPRESSO package. The reaction path was sampled with 8-12 intermediate images.
The adsorption of Pt atoms at ceria step edges was modelled with periodic supercells describing vicinal surfaces. Two of the lowest energy model steps proposed in Ref. [46] have been selected. Following this work, we label our two model step surfaces as Step Type I and Step Type II. In both models, the step edge exposes 3 independent O atoms. The step edge is

KMC simulation
We adapt a solid-on-solid (no vacancies, no overhangs) KMC model on a cubic lattice with a periodic boundary condition [51]. The model is implemented within the Bortz-Kalos-Lebowitz algorithm [77] allowing to set the simulation temperature and evaluate the simulation time. We consider mobile adatoms of the deposit (Pt) on substrates with fixed stepped geometry (ceria). Lattice parameters of the substrate and deposit are the same, i.e. no strain is considered. Pt-Pt interactions are approximated by a bond-counting scheme [50]. To account for 3D character of Pt nucleation, both lateral and vertical Pt-Pt bonds are considered. Geometry and bonding properties of monoatomic steps on the substrates in the simulation ( Figure S6) are defined in a way that the interaction of Pt adatoms with adatom traps at lower step edges corresponds to the experimentally and theoretically determined interaction of Pt adatoms with monoatomic steps on CeO2(111) [31], [32]. Activation and binding energies in the model are summarized in Table 2. Binding energies in the model are scaled with respect to binding energies predicted by ab-initio calculations ( Figure S8). This results in an effective shifting of the temperature scale of the simulation to lower values compared to experiment. Rescaling the activation energies in KMC allowed to obtain manageable computing times in the range of weeks for a 3600 s simulation (Figures 6, 7) on a single core.
Activation energy of Pt adatom hopping in the model is defined for 4 different situations: Ea Pt➔Pt , Ea Pt➔Ce , Ea Ce➔Ce , and Ea Ce➔Pt , depending on the type of the underlying atom to the Pt adatom before and after the hop. The 3D character of Pt growth is obtained by assigning the Ea Pt➔Ce hops one more broken bondthe vertical one. Activation energies for Pt hopping in the model are determined as follows: Ea Pt➔Pt = Ed + n En, Ea Pt➔Ce = Ed + (n+1) En, Ea Ce➔Ce = Ea Ce➔Pt = Ed + n En + i1 E1 ox + i2 E1 re , where Ed is the activation energy for Pt adatom diffusion both on ceria and on Pt, En is the energy associated with breaking a Pt-Pt nearestneighbor bond, n is the number of lateral Pt-Pt nearest neighbors before the hop (n = 0…4), and i is the type of the step edge underlying the Pt adatom before the hop (i = 0, 1, 2 for none, oxidized and reduced step, respectively). Hopping frequencies are evaluated in a standard way, νx = ν0 exp(-Ea x /kBT) where ν0 = 10 13 s -1 , kB is the Boltzmann constant and Ea x is the activation energy of an x-th process.
The charge state of Pt in the simulation, and the simulated Pt 2+ and Pt 0 SRPES signals are determined based on the local geometry of Pt atoms in the simulation according to previous experimental and theoretical findings [31], [32] as described in Figure S7. Experimental cycles of annealing in UHV, in reducing, and in oxidizing conditions are simulated by instantaneous switching of the binding energy of the step-edge traps in the model from deep to shallow or vice versa (cf. Figure S6). Evaluation of KMC configurations are performed at the end of particular simulation cycles without simulating the cooldown to 300 K and a subsequent heating up for the next cycle. Initial KMC configurations for the presented calculations are obtained in analogy to the experimental treatments by simulated deposition and annealing cycles. Parameters of the presented KMC simulations are summarized in Table   S3.