Extending the cluster scaling technique to ruthenium clusters with hcp structures

Soini, Thomas M.; Ma, Xingxiao; Aktürk, Olcay Üzengi; Suthirakun, Suwit; Genest, Alexander; Rösch, Notker

doi:10.1016/j.susc.2015.06.020

Cited by 9 publications

(13 citation statements)

References 47 publications

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“…Figure b shows the mean Pt–Pt distance ⟨ d Pt–Pt ⟩ as a function of particle size compared to the bulk distance (2.77 Å). We find that ⟨ d Pt–Pt ⟩ scales linearly when plotted against the number of Pt atoms to the power of −1/3, N Pt –1/3 , as has been shown previously for Pt and other transition metals. − The scaling is best for particles exhibiting the cuboctahedral shape (black dots) with the exception of the smallest Pt 13 cluster, which we attribute to quantum size effects. The chemical potential, which we approximate as the average energy per atom, , is shown as a function of N Pt –1/3 in Figure c, and we observe a linear trend for all three particle shapes investigated here.…”

Section: Resultssupporting

confidence: 77%

“…As already mentioned, the trends described in Figure are not unique to Pt but have also been observed for other transition metals, for example, Pd, , Ru, and Au, but also main group metals like Al or alkaline earth metals like Mg. , With this in mind we investigated transition metals of groups 8, 9, 10, and 11 as well as Mg and Al. All metals were investigated in the fcc structure, although we note that Ru, Os, Co, and Mg crystallize in the hcp structure.…”

Section: Resultsmentioning

confidence: 52%

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Modeling the Size Dependency of the Stability of Metal Nanoparticles

Dietze¹,

Pleßow²,

Studt

2019

J. Phys. Chem. C

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In this work, we use density functional theory (DFT) to study cuboctahedral, octahedral and cubic nanoparticles of the late transition metals as well as Al and Mg in order to identify their stability as a function of size. We developed a simple model that not only includes the surface energies as in the commonly used Wulff construction but additionally accounts for energies related to edges and corners. Importantly, this model only requires the bulk cohesive energy and the surface energies of the fcc(111) and fcc(100) surfaces, which are used to extrapolate to lower coordination numbers. We find that our model estimates the stability of nanoparticles with a mean absolute error of only 0.09 eV.

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Section: Resultssupporting

confidence: 77%

Section: Resultsmentioning

confidence: 52%

Modeling the Size Dependency of the Stability of Metal Nanoparticles

Dietze¹,

Pleßow²,

Studt

2019

J. Phys. Chem. C

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“…For Cu, the effect of geometry optimization is studied explicitly. For free standing metal Cu clusters ranging from 13 to 923 atoms, a linear relation between the mean Cu-Cu distance, the chemical potential which is approximated by the average energy per atom, and the number of atoms to the power of -1/3 (see Figure S3) is observed, similarly to what has been found for other metals [13,34,[38][39][40][41][42][43][44][45]. Figure 1 shows the adsorption energy of an oxygen atom on the Cu clusters with increasing size.…”

supporting

confidence: 69%

Theoretical Investigation of the Size Effect on the Oxygen Adsorption Energy of Coinage Metal Nanoparticles

Hakimioun¹,

Dietze

Vandegehuchte

et al. 2021

Catal Lett

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This study evaluates the finite size effect on the oxygen adsorption energy of coinage metal (Cu, Ag and Au) cuboctahedral nanoparticles in the size range of 13 to 1415 atoms (0.7–3.5 nm in diameter). Trends in particle size effects are well described with single point calculations, in which the metal atoms are frozen in their bulk position and the oxygen atom is added in a location determined from periodic surface calculations. This is shown explicitly for Cu nanoparticles, for which full geometry optimization only leads to a constant offset between relaxed and unrelaxed adsorption energies that is independent of particle size. With increasing cluster size, the adsorption energy converges systematically to the limit of the (211) extended surface. The 55-atomic cluster is an outlier for all of the coinage metals and all three materials show similar behavior with respect to particle size. Graphic Abstract

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“…The calculated results of Ru clusters up to 64 atoms indicate that the simple cubic is the most stable structure for clusters up to 40 atoms, 36 while the icosahedral structure is the most stable for more than 40 atoms. The scaling behaviors for hcp and fcc Ru-NPs between 55 and 323 atomic systems were also established by Soini et al 37 The cohesive energies of hcp Ru-NPs were always higher than those of fcc Ru-NPs. In this analysis, only two samples were treated as the icosahedral structure.…”

Section: ■ Introductionsupporting

confidence: 61%

“…The specified truncation length results in lower cohesive energy. In ref , hcp Ru-NPs consisting of 57 and 153 atoms (Figures S9(a) and (b)) were considered. The cohesive energies of the hcp Ru 57 and Ru 153 were lower than the regression line obtained from the cohesive energies of the icosahedral fcc Ru-NPs (Figure S9(c)).…”

Section: Resultsmentioning

confidence: 99%

Structural Stability of Ruthenium Nanoparticles: A Density Functional Theory Study

2017

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We have analyzed the crucial factors that stabilize face-centered cubic (fcc) ruthenium nanoparticles (Ru-NPs) using the density functional theory method. We calculated the cohesive energy of the decahedral fcc, icosahedral fcc, truncated octahedral fcc, and hexagonal close-packed (hcp) Ru-NPs with between 55 and 1557 atoms. The cohesive energy of the icosahedral fcc Ru-NPs became closer to that of the hcp Ru-NPs with decreasing number of atoms, i.e., particle size. This characteristic is mainly caused by the high coordination number of the icosahedral fcc Ru-NP and the negative twin boundary energy for fcc {111}. On the other hand, the d-band center of Ru atoms in the surface layer of icosahedral fcc Ru-NPs is less negative than those of the other structures. This characteristic is caused by the longer interatomic distance between Ru atoms in the surface layer of the icosahedral fcc Ru-NP. Together with the structural stability, the icosahedral fcc structure shows a unique electronic structure compared with the other structures. Our results are expected to be helpful for controlling and designing the properties, such as stability and catalytic activity, of Ru-NPs from the shape of the NP.

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Extending the cluster scaling technique to ruthenium clusters with hcp structures

Cited by 9 publications

References 47 publications

Modeling the Size Dependency of the Stability of Metal Nanoparticles

Modeling the Size Dependency of the Stability of Metal Nanoparticles

Theoretical Investigation of the Size Effect on the Oxygen Adsorption Energy of Coinage Metal Nanoparticles

Structural Stability of Ruthenium Nanoparticles: A Density Functional Theory Study

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