Mechanistic Understanding and the Rational Design of Sinter

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Mechanistic Understanding and the Rational Design of Sinter-Resistant Heterogeneous Catalysts Emmett D. Goodman, Jay A. Schwalbe, and Matteo Cargnello ACS Catal., Just Accepted Manuscript • DOI: 10.1021/acscatal.7b01975 • Publication Date (Web): 11 Sep 2017 Downloaded from http://pubs.acs.org on September 11, 2017

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Mechanistic Understanding and the Rational Design of Sinter-Resistant Heterogeneous Catalysts Emmett D. Goodman, Jay A. Schwalbe, Matteo Cargnello* Department of Chemical Engineering and SUNCAT Center for Interface Science and Catalysis, Stanford University, Stanford, CA 94305, USA *

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ABSTRACT

The activity and selectivity of heterogeneous catalysts are strong functions of the morphology of a catalytic active phase, which governs both the density and type of active sites. To realize materials with desired reactivity, cutting-edge catalysts are often the product of novel synthetic strategies and advanced computational studies. Combining these approaches allows for the prediction and fabrication of active motifs in a directed manner. However, catalyst active phases are ordinarily in the nanometer or atomic regime, and small morphological changes can result in large differences in catalytic properties. Given painstaking efforts to design and fabricate active materials at the nanoscale, it is essential that these engineered structures and superior catalytic properties are preserved during working conditions. The stability of a highly active catalyst morphology is crucial for long-term, sustained activity, especially for industrial applications. Unfortunately, catalyst sintering, or processes in which active surface area is lost due to irreversible agglomeration of atomic species or particles, inevitably leads to reduced active surface area and decreased catalytic activity. This problem has led to the development of many schemes, applied with varying degrees of success, which attempt to counteract these aging processes. Undoubtedly, for the directed development of stable, sinter-resistant, heterogeneous catalysts, a fundamental understanding of the species and mechanisms contributing to sintering processes is required. To highlight the importance of fundamental mechanistic understanding of sintering processes, the first portion of this perspective highlights recent approaches to characterize sintering dynamics in heterogeneous catalysts. Next, we showcase recent examples illustrating intentional measures taken to protect against particular sintering mechanisms. We believe that by reviewing


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examples with mechanistic understanding of these aging phenomena, we can select approaches with the highest probability of successful application to new catalytic systems. These approaches are divided into two main categories: chemical approaches, which are based on modification of the chemistry of the catalytic materials, and physical approaches, based on increased physical barriers to sintering. Our goal is to stimulate more work both on the fundamental understanding of sintering mechanisms, and on the production of stable catalysts by directly targeting and suppressing specific sintering processes.

KEYWORDS: Heterogeneous catalysis, structure-stability relationships, sintering


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1. Why is Preventing Sintering Important? Activity and selectivity are crucial parameters to consider when designing an effective catalyst. Unfortunately, if the catalyst does not maintain these properties for a reasonable amount of time (from a few seconds to few years, depending on the application1), it is unlikely that it will be translated into industrial practice. Stability is of utmost importance for industrial applications, as catalyst replacement and regeneration are very expensive tasks due to a loss of productivity during reactor downtime. Stability is especially critical when rare or expensive noble metals are used as catalyst active phases. Notable examples include fuel cells, where the cost of Pt can approach half the overall stack cost,2 and catalytic converters which each harbor up to 15 grams of rare platinum-group metals.3 Nevertheless, sooner or later any catalyst unavoidably expires; to best delay this event, the study of catalyst deactivation phenomena is crucial. Finding universal strategies to avoid deactivation and maintain catalytic activity and selectivity is a broadly important challenge - general solutions will have widespread appeal and impact for several catalytic applications. Different phenomena can lead to catalyst deactivation according to chemical, mechanical and thermal mechanisms.4,5 Among the several causes of catalyst loss of activity, sintering occupies a central position. Sintering is the process by which large catalyst nanoparticles grow at the expense of smaller nanoparticles, leading to an overall loss of active surface area. Such processes are especially common under demanding conditions where atom and particle mobility is increased. Often, sintering is couched in terms of catalysts that operate at high temperatures for extended periods of time during which the thermal energy is sufficient to change the morphology of the catalyst. However, sintering is not only a concern for traditional, large scale thermal catalysis. Sintering is also observed in low temperature systems, like proton exchange membrane


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fuel cells (PEMFCs).6–8 Although sintering processes are clearly a concern in terms of long-term catalytic operation, start-up/shut-down operations and temperature/voltage excursions can also be particularly challenging on a material because they abruptly expose the catalyst to very different environments (temperature, reaction atmosphere, potential). A classic example is that of automotive catalytic converters, for which ceria-zirconia has been discovered as a crucial additive to promote textural and catalytic stability by acting as oxygen buffer to reduce the variability in feed that the catalyst is exposed to.9 These start-up/shut-down operations will become more important in the future due to coupling of intermittent, renewable sources of energy with traditional methods of energy conversion, which would require catalysts that can operate for shorts period of time at high activity, and in a resting state for some other periods of time.10 Successfully designing catalytic systems that can couple to intermittent resources will also require developing tools and materials to fundamentally understand and tolerate such demanding conditions. Reflecting morphological changes at the nanoscale, sintering will usually manifest itself in decreased catalytic activity or selectivity. Sintering is particularly detrimental for nanostructured catalysts because: i) available active surface area decreases, thus reducing the overall active site density, which is crucial especially when utilizing expensive materials (e.g. noble metals, engineered nanostructures); ii) small particles may contain large fractions of specific active sites, such as undercoordinated atoms at edges, corners and vertices,11 that are lost if particles change morphology and/or size;


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iii) electronic properties may change, as those of small particles are different from larger ones, which could provide very different adsorption energies of reactants on the catalytic active phase12 and thus very different reactivity. Gold, in this respect, is an exemplary case.13–15 The need for improved stability in catalytic systems has increased especially since tools to synthesize and prepare highly functional materials with atomic accuracy are now more readily available. Synthesis procedures to obtain non-equilibrium materials with high-energy structures,16,17 nanocrystals of specific shapes that expose particular crystallographic facets,18 single-atom catalysts19 and atomically precise clusters (clusters with a specific number of atoms, according to the stability of filled shells, also known as magic-size clusters),20,21 or materials with specifically designed interfacial active sites22 have recently emerged as powerful tools to explore the reactivity of tailored nanostructures in catalytic processes. The drawback is that the special properties of these materials are lost if morphology and structure are not stable under reaction conditions, questioning the efforts in obtaining these structures in first place. Luckily, advanced synthetic techniques can be used not only to generate highly active and selective catalysts, but also to preserve them. The development of more active catalysts therefore must be coupled with strategies that can maintain the structure (hence, the activity) of these materials under demanding reaction conditions. In this perspective, we highlight promising methods and strategies that can be used to prevent sintering in heterogeneous catalysts. In doing that, we ask the following fundamental questions: How does sintering occur? How can we study these processes? What strategies can we use to prepare sinter-resistant catalysts? These questions are strongly connected to each other: if we understand how sintering processes occur, we can better craft strategies to avoid sintering. To tackle these questions, we highlight examples spanning thermal and electrocatalytic systems to


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underline similarities in hopes of inspiring connections in designs and strategies from one area of research to another. We aim to highlight successful schemes that show fundamental understanding of the underlying sintering processes, because we think these examples will be most translatable to new systems. It is in the spirit of this perspective to provide a critical report of these areas of catalysis research through published examples and general strategies that both characterize sintering processes, and aim to prevent them.

2. How does sintering occur? How can we study these processes? Fundamental understanding of the sintering processes that lead to catalyst deactivation is crucial in designing materials that can withstand these processes. Although loss of catalyst surface area and activity may occur in many ways, in this perspective we limit our focus to studying sintering mechanisms of the catalyst active phase in supported systems, avoiding cases where support morphology or irreversible material loss from the system contribute to catalyst deactivation. In the following, we highlight recent and promising approaches used to unravel these underlying sintering processes. Many illuminating strategies involve either carefully designed materials, and/or detailed spectroscopic observation. We hope these studies elucidating fundamental behavior of sintering mechanisms will both motivate future mechanistic studies on sintering and translate into new synthetic methods to protect against them.

2.1 Do sintering processes occur? Recognizing that sintering has occurred in a catalyst is the first step towards understanding this mechanism of catalyst deactivation. While a decrease in mass activity may be indicative of sintering, it is not definitive proof of a loss of active surface area. One needs to consider how


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changes in reaction conditions, oxidation state, or restructuring might be affecting the overall catalytic activity. Ultimately, an in-depth analysis of the active phase dispersion is required in order to demonstrate that sintering is the major cause of loss of activity. Many ex-situ methods have been developed that give static pictures describing the state of catalytic dispersion. In thermal and electrocatalysis, it is possible to identify changes in dispersion of a supported phase through several techniques that provide direct or indirect measurements of particle size distributions. Chemisorption and electrochemical surface area measurements are indirect methods based on the use of probe molecules that bind to surface atoms of the active phase. Electron microscopy (EM) and scanning tunneling microscopy (STM) are often used to provide atomic detail of catalyst morphology.23 Extended x-ray absorption fine structure (EXAFS), x-ray diffraction (XRD) and small-angle x-ray scattering (SAXS) techniques are indirect methods used to extract average particle size and particle size distributions from metal coordination number, coherence length of ordered crystallographic structures and scattering form factor, respectively. Diffuse reflectance infrared spectroscopy (DRIFTS) also provides indirect information on particle morphology by indicating the relative populations of specific facets, edges, and other geometric features. In electrocatalytic systems, impedance spectroscopy produces data typically fitted to an equivalent circuit model which is used to estimate surface area or extract interfacial charge transfer properties. Each of these methods have pros and cons, and complete analysis requires agreement between multiple techniques. Of all these techniques, EM is the only one that provides local, single-particle information on realistic powder catalysts; all other techniques provide average results based on an ensemble of many particles. Unfortunately, small variations are harder to be evidenced using bulk techniques. However, in EM, the analysis may not be statistically representative of the entire sample, which


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is instead true for bulk techniques such as EXAFS, XRD and SAXS. Thus, direct and indirect characterization are required complementary tools to describe overall catalyst morphology. A detailed analysis of the catalyst in the fresh state and after exposure to reaction conditions is the first step towards understanding what changes have occurred to the sample as a consequence of the catalytic reaction. Unfortunately, at a molecular level, snapshots of a sintered catalyst before and after reaction often provide limited information on exactly how the sintering process occurred. In some cases, this information may even be misleading as some processes may be reversible and therefore very challenging to probe with pre- and post-reaction analysis, such as in the case of processes that involve metal redispersion,24 which may accompany sintering in some cases.25 (While beyond the scope of this sintering perspective, metallic dispersion via ex-solution is a promising technique for the development of durable catalysts; in these systems, active phases can be atomically dispersed within a solid solution, and precipitated on the surface of the material under reducing conditions.26–28) Depending on the sintering mechanism, particularly in atomic ripening, stopping a sintering process at certain stages may lead to increased dispersion. Fundamental knowledge of how sintering occurs can be translated toward the development of sinter-resistant materials.29–31 To effectively combat sintering processes and design sinter-resistant catalysts, research must turn towards obtaining a fundamental mechanistic understanding of the underlying sintering processes at an atomic level, via in-situ observation or by using uniform model materials.

2.2 How do sintering processes occur? Identifying how deactivation occurs is crucial for designing better materials for an appropriate application. As a notable example, ceria-based supports were initially thought to deactivate


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through loss of their oxygen storage ability, such as during the water-gas shift-reaction,32 which would preclude their utilization under reducing conditions. However, detailed studies clearly showed a dependence of catalytic rates on exposed metal surface area and a decrease in overall metal surface area after reaction, thus demonstrating that sintering was instead the main cause of catalyst deactivation.33 This knowledge inspired the development of strategies based on geometrical approaches to encapsulate Pd particles within ceria-based supports in catalysts that showed stable activity for this reaction.34,35 Most sintering processes can be broadly classified into two categories: particle migration and coalescence (PMC) and atomic ripening (AR) (Figure 1). PMC involves the coordinated motion of multiple metal atoms, or nanoparticles, and it is related to temperature-induced increased mobility and to the lower melting point of small particles.36 AR involves the movement of species containing one metallic atom (in most cases bonded to other atoms to form oxides or complexes, such as in the case of volatile carbonyl species) from smaller to larger nanoparticles, either on the surface of the support, or in the vapor or electrolyte phases.37 We decided here to use the term AR over the widely used Ostwald ripening as a more general term to indicate any process involving the migration of atomic species. The thermodynamic driving force in both PMC and AR is minimization of surface energy, which is relatively high in nanoparticles of small sizes which contain a large fraction of surface atoms.


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Figure 1. Schematic of potential sintering mechanisms of catalyst active phase. (a) Particle migration and coalescence (PMC); (b) vapor- or electrolyte-facilitated atomic ripening (AR) via detachment and redeposition; (c) surface-mediated atomic ripening (AR). (d) Final sintered state showing a larger aggregate.

Kinetic models often provide a useful framework towards understanding the atomic motions associated with sintering. For PMC sintering mechanisms, rates of particle diffusion and rates of particle coalescence stands as important physical parameters governing the aging process. For AR mechanisms, one must consider whether the system is operating in an “interface control” regime or a “diffusion control” regime; either regime will be described by a unique governing equation.38 Assumptions on particle geometry, wetting, free energy, surface features, etc. also help provide a valuable mindset on sintering dynamics.39 Although it may be difficult to directly measure the physical parameters for these models, researchers have had success.40 Certainly, distinguishing between the modes of sintering is not straightforward, and controversy exists over these mechanisms, which are highly dependent on the material system


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(type of metal and support) and on the reaction conditions and temperature. In the last decade, carefully designed model systems, operando/in-situ spectroscopic tools, computation, and theory have aided in differentiating between these mechanisms, allowing us to start targeting approaches that mitigate sintering processes. Ideal techniques and approaches for characterizing sintering processes achieve (1) minimal perturbation/interference of the observed system; (2) monitoring of nanoparticles on realistic catalysts, under realistic conditions; (3) atomic resolution; (4) frequent system sampling; and (5) high throughput analysis. Often successful characterization of a phenomenon will rely on corroboration between multiple experimental techniques (bulk and non-bulk), as well as computation and theory.

2.3 How to distinguish between different sintering mechanisms 2.3.1 Electron Microscopy Electron microscopy (EM) is perhaps the most powerful way of understanding morphological changes in a catalyst. In order to investigate sintering processes, EM studies were originally performed by comparing particle size and shape distributions before and after a catalyst treatment performed ex-situ. Although in principle particle size distributions may help in distinguishing between the two main sintering mechanisms, information gained from such studies is often limited due to non-uniform materials and difficulty in relocating a unique sample region between treatments; so while such characterization is indeed broadly useful for identifying sintering, it is generally accepted that these analyses often provide little mechanistic insight.41 Recent approaches have involved careful control over uniform catalyst starting materials, such that any particular micrograph is more representative of the overall composition. More importantly, modern electron microscopy techniques have been developed towards filming


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‘atomic movies’ of the evolution of powder catalysts under realistic working conditions using environmental TEM, special sample holders, and nanofabricated cells, to allow in-situ and operando characterization of catalysts while treating them with gases at atmospheric pressure.42– 44

A major risk in EM characterization of catalysts is the potential role of the highly reducing

electron beam in modifying the morphology and evolution of nanostructured materials, and appropriate measures have to be taken in order to clearly demonstrate which changes are due to reaction environment and which to beam effects.45 Uniform nanoparticles offer a well-defined starting state for a system, thus making it simpler to characterize evolution of a nanoparticle ensemble. Hu et al. investigated sizedependent sintering mechanisms on atomically selected Au nanoparticles containing a precise number of atoms (magic sizes) on a TEM grid using particles that were synthesized via magnetron sputtering gas condensation.46 The researchers observed a size-dependent shift in ripening mechanism for Au nanoclusters during the CO oxidation reaction via ex-situ analysis of Au nanoparticles size distributions. The use of size-selected nanoparticles with a well-defined geometry allows the authors to gain insight from a post-aging particle size distribution. Specifically, when starting with small clusters, the particle size distribution broadens, with the formation of nanoparticles even smaller than the original particle size. This could only arise from atomic ripening. On the other hand, when starting with larger nanoparticles, sintering produces only aggregates that are equal to or larger than any of the particles in the original sample. Remarkably, when the integrated HAADF signal is used to indicate particle size, discrete particle sizes corresponding to dimers, trimers, and higher combinations of the original particles are observed, a strong indication of PMC. Thus atomically uniform nanocrystals demonstrate a size-


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dependent shift from atomic ripening at smaller nanocrystal sizes, to PMC at larger nanocrystal sizes. For samples where nanoparticle catalysts must be dispersed on flat, conductive substrates, such as in the case of electrochemical studies, scanning electron microscopy (SEM) offers a way to capture the nanoscale detail of the electrode and follow sintering processes.47 Importantly for electrochemistry, SEM, unlike transmission techniques, does not require thin samples. This advantage enables SEM to easily characterize actual electrodes both before and after use. While frequently used as a means to confirm that minimal structural changes have occurred in an electrode rather than to study them directly, work done by Manthiram et al. leverages SEM to identify particle migration and coalescence in a model system composed of gold nanoparticles deposited on a carbon support (Figure 2).48 Perhaps surprisingly, rich dynamics are observed in a system operating at room temperature and -1.2 V. Under the relatively mild reductive potentials of the hydrogen evolution (or CO2 reduction) conditions, the gold particles move randomly around the electrode until they collide, at which point they either stick to each other, or detach and continue in their random motion. This sticking leads to dendritic structures, which can be clearly seen with SEM and quantitatively reproduced via computational modeling. Because the electrode can be visualized as-removed from the electrochemical cell, with no elaborate or damaging sample preparation, there is little doubt that the electrochemistry led to the observed sintered morphology. A shortcoming of this study is that it does not probe the chemical nature of the particle-particle and particle-surface interactions. This, for example, means that we cannot understand the origin of the particle movement. Especially for low temperature systems, where thermal energy is not as large as it is for high


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temperature catalysis, it is important to understand why particles move and if other factors, like gas evolution or electric fields, may play a role.

Figure 2. SEM time series data of gold NPs sintering on an electrode after 0, 10, and 100 minutes of polarization at -1.2 V in 0.1M NaHCO3 buffer. Reproduced with permission from ref 48. Copyright 2014 American Chemical Society. In-situ electron microscopy is one of the most powerful techniques to distinguish between particle migration and atomic ripening sintering mechanisms.49 However, this technique comes with a unique set of challenges. Care must be taken to prevent the entire column from being exposed to atmosphere, necessitating differential pumping or specialized cells. The electron beam can also interact with the gas layer, exacerbating beam effects. In a powerful example of this technique, Helveg and co-workers first revealed a ripening-mediated sintering of Pt NP on an idealized planar support in 10 mbar oxygen atmosphere.50,51 Although the work reports a clear demonstration of atomic ripening, it is not yet a realistic catalyst because of the planar nature.


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Further work tended towards modeling sintering processes under conditions closer to catalytic applications, with more realistic powder catalysts. In 2011, under 3.6 mbar of H2O/H2, Datye and co-workers clearly identified ripening as the mechanism of sintering in Ni/MgAl2O4 systems.52 By performing microscopy on a single location, the authors were able to show that small nanoparticles shrank, but did not move under these conditions. While the change in particle size of large particles was not detectable, the kinetics of metal evaporation would be too slow to account for the loss, since changes occurred in the space of few minutes. The data was fit to a kinetic model that assumed fast surface diffusion, where the rate limiting step was moving an atom from the particle to the surface. The powerful combination of advanced materials and in-situ electron microscopy is an emerging class of approaches which is invaluable for the identification of mechanisms and driving forces behind sintering. An example of advanced materials for these types of studies are size-controlled clusters and nanocrystals. Synthetically, the advantage of size-controlled materials is not only in the uniformity of the materials, but also in the fact that these building blocks can be dispersed onto arbitrary supports with tunable concentration. In a direct exploitation of this advantageous feature, it is possible to program particle size distributions by using particles of different sizes, such that atomic ripening mechanisms on and off.40 By creating an artificial bimodal distribution with Pt particles of either ~2.2 or ~4.4 nm onto an alumina support, and using an atmospheric gas cell TEM holder with temperature control, it has been shown that when there is a size difference between the particles, the mechanism of deactivation is predominantly atomic ripening (Figure 3). However, when a sample with a single uniform particle size is used, this driving force is removed, and migration and coalescence is mainly responsible for any sintering. In this monomodal case, it is observed that smaller nanoparticles


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have a much higher mobility compared to larger ones, thus leading to increased sintering via particle migration and coalescence in smaller nanoparticle catalysts. Due to a lower mobility, monomodal catalysts with larger nanoparticles are observed to be much more resistant to sintering. Rather than relying exclusively on nanoparticle size distributions, direct observation of nanoparticle growth events are used to substantiate these mechanistic claims.

Figure 3. (a) Representative HAADF-STEM images of Pt/Al2O3 catalyst coimpregnated with mixed preformed nanocrystals of two distinct sizes, ~2.2 and ~4.4 nm. (b) - (e) Time evolution of same bimodal catalyst, showing the gradual disappearance of a smaller Pt nanocrystal via atomic ripening (red arrow). Observations taken via in-situ TEM under 5% H2/Ar at 800 oC, with careful experimental control to minimize beam effects. Elapsed time in seconds indicated at the top of each image. Reprinted from ref 40. Copyright 2016 with permission from Elsevier.

2.3.2 Scanning Tunneling Microscopy


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Scanning Tunneling Microscopy (STM), similarly to TEM, is a powerful technique for atomic resolution of mobile nanoscopic species. While both techniques achieve atomic spatial resolution, the unique advantage of STM lies in distinguishing electronic signatures of a sintering process. For example, while the effect of organic species cannot be observed in TEM, in STM one may notice the distorted electronic state of a metal coordinated to organic species. Using this technique, coordinating moieties such as H,53 OH,54 and CO55 have been shown to play strong roles in the diffusion or anchoring of atomic surface species. Unfortunately, STM can only be used on very simplified systems, such as single crystal surfaces, and often under significantly reduced pressures. The presence of large features (i.e. sintered aggregates) can make STM difficult to operate. For these reasons, the applicability of STM is often limited to conditions that are far removed from realistic catalytic applications. In 2013, Parkinson and co-workers performed an in-depth study, from single-atoms to larger clusters, of the sintering dynamics of a model Pd-Fe2O3 catalyst using STM.55 Interestingly, authors show that sintering initiates via a CO-induced coalescence of atomic Pd-CO species (Figure 4). After the formation of sintered nanoclusters, further coarsening occurs via cluster diffusion and coalescence. Hydroxyl groups have the opposite effect: these groups act to anchor Pd atoms. The effects of these CO and OH moieties were deduced from electronic states of the scanned material, over multiple hours of scanning at reduced pressures (~10-10 mbar). This study shows how adsorbed species can influence sintering dynamics, and how STM can be used to deduce the effects of these coordinating species.


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Figure 4. Atomic sintering dynamics of Pd atoms on an Fe3O4(001) surface. Selected STM images of Pd adatom mobility, recorded at the same location. Time progresses a-d. Dark blue areas represent Fe3O4 substrate, green/yellow atoms represent Pd atoms, and the bright fuzzy feature in each image is an excited Pd-CO complex. Arrows show migration pathway over the surface. Images taken at room temperature (RT) and background pressure of 6×10-11 mbar. Reprinted by permission from Macmillan Publishers Ltd: Nature Materials, reference 55, copyright 2013.

In a similar study, Yang et al. used in-situ STM to directly probe the sintering dynamics of Au NPs under CO oxidation conditions.56 At temperatures up to 137 °C and relatively high pressures (0.1 Torr) of reactant gases, the authors observe an atomic ripening mechanism, at which large particles grow at the expense of nearby smaller ones (Figure 5). This process is evidenced by the disappearance of small particles, while larger particles grow without noticeable translational motion. Surprisingly, this mechanism is only facilitated in the presence of both


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reactive gases (CO, O2). The authors postulate a reaction-induced mechanism, seen in other systems,57 where the energy generated from CO oxidation might be transferred to the nanoparticle, and facilitate the formation of migrating atomic species.

Figure 5. In-situ STM images of Au/TiO2(110) surfaces in the presence of 0.1 Torr mixture of CO and O2 at 27 °C. STM images are acquired at the same region of the sample. Bold circles indicate particle growth, while dashed circles indicate particle decay. Images taken at (a) 0 min, (b) 42 min, (c) 120 min, (d) 280 min. Reproduced with permission from ref 56. Copyright 2009 American Chemical Society.

2.3.3 In-situ/Operando XAS Electron and scanning tunneling microscopy techniques are powerful tools to observe individual nanoparticles and atoms, in small ensembles. However, they are limited to collecting information about only a small fraction of the sample. Such techniques can be complemented by bulk spectroscopies, which provide information about the entire sample. X-ray spectroscopies, due to


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their small wavelength, can easily probe the length scales (

Mechanistic Understanding and the Rational Design of Sinter

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