Moments developments II. Application to the crystalline structures and the stacking fault energies of transition metals

Ducastelle, F.; Cryot-Lackmann, F.

doi:10.1016/0038-1098(70)90187-0

Cited by 6 publications

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“…The oscillatory trends in structural stability can be directly related to the topology of the molecule by the moments theorem first introduced by Ducastelle and Cyrot-Lackmann in 1971. 51 One important feature observed in Figure 5 is that the number of nodes in the energy difference curve (including those at N = 0 and 8) is 3, which is equal to the order of the first disparate moment between the two. 53 Owing to second moment scaling, both have the common moment at least up to the second order.…”

Section: Theoretical Backgroundmentioning

confidence: 95%

“…By applying eq to the eigenvalue spectrum shown in Figure b, it is possible to plot the energy difference between the structures represented by graphs G 1 and G 2 as a function of the number of electrons (see Figure ). The oscillatory trends in structural stability can be directly related to the topology of the molecule by the moments theorem first introduced by Ducastelle and Cyrot-Lackmann in 1971 …”

Section: Theoretical Backgroundmentioning

confidence: 99%

“…What is the point of revisiting the subject that has already undergone a thorough examination by Hoffmann and co-workers? − In the present study, we actually calculate the orbitals for the adsorbed structures, but we will mainly focus on something different from the orbital, linking geometry, and energy: the method of moments originally proposed by Cyrot-Lackmann and co-workers. , We will detail the topological aspects of adsorption, grounded in orbital interactions at the interface between the surface and adsorbate.…”

Section: Introductionmentioning

confidence: 99%

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Adsorption Site Preference Determined by Triangular Topology: Application of the Method of Moments to Transition Metal Surfaces

Tsuji

Yoshizawa

2022

J. Phys. Chem. C

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The adsorption sites of the top and hollow on the close-packed surfaces of transition metals are well known. In this paper, which site is more preferred for the adsorption of atoms and molecular fragments on the metal surfaces is discussed based on the topology of the adsorption geometry. For this purpose, the method of moments for the electronic density of states is applied to the surface. Adsorption at the hollow site generates a triangular topology, leading to a more negative value of the third moment (μ 3 ) than that at the top site, which generates no triangular topology. When the difference in energy between the two adsorption sites is plotted against the band filling of the metal surface, a characteristic node at around the intermediate band filling can be found. This is a signature that the energy difference curve is controlled by μ 3 . Roughly speaking, the hollow-site adsorption, which has a more negative μ 3 value, takes precedence at low band fillings, while the top site adsorption, which has a less negative μ 3 value, takes precedence at high band fillings. One can conclude that an adsorption structure with more three-membered rings on a surface is more stable at low electron counts whereas that with less three-membered rings is more stable at high electron counts. However, if the strength of the metal−adsorbate bond is significantly greater than that of the metal−metal bond, the effect of the second moment (μ 2 ) on the energy difference curve cannot be neglected. The hollow-site adsorption leads to a larger value of μ 2 due to the topological feature of a larger coordination number around the adsorbate atom. As a result, the hollow-site adsorption is preferred over the top site at any band filling.

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Section: Theoretical Backgroundmentioning

confidence: 95%

Section: Theoretical Backgroundmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Adsorption Site Preference Determined by Triangular Topology: Application of the Method of Moments to Transition Metal Surfaces

Tsuji

Yoshizawa

2022

J. Phys. Chem. C

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“…Knowledge of the moments allows for the construction of the electronic DOS that yields the bond energy by integration to the Fermi level as described in the framework of BOPs in various previous works [41][42][43][44]. This leads to close relations between the moments and the trends of structural stability with band filling, see e.g., [27][28][29]40,42,47,48].…”

Section: Moments Of the Density-of-statesmentioning

confidence: 97%

Crystal-Structure Analysis with Moments of the Density-of-States: Application to Intermetallic Topologically Close-Packed Phases

Hammerschmidt¹,

Ladines²,

Koßmann³

et al. 2016

Crystals

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Abstract:The moments of the electronic density-of-states provide a robust and transparent means for the characterization of crystal structures. Using d-valent canonical tight-binding, we compute the moments of the crystal structures of topologically close-packed (TCP) phases as obtained from density-functional theory (DFT) calculations. We apply the moments to establish a measure for the difference between two crystal structures and to characterize volume changes and internal relaxations. The second moment provides access to volume variations of the unit cell and of the atomic coordination polyhedra. Higher moments reveal changes in the longer-ranged coordination shells due to internal relaxations. Normalization of the higher moments leads to constant (A15,C15) or very similar (χ, C14, C36, µ, and σ) higher moments of the DFT-relaxed TCP phases across the 4d and 5d transition-metal series. The identification and analysis of internal relaxations is demonstrated for atomic-size differences in the V-Ta system and for different magnetic orderings in the C14-Fe 2 Nb Laves phase.

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“…One of the most powerful applications of moments was published by two members of the Friedel school of tight binding in 1971 (Ducastelle & Cyrot-Lackmann 1971). François Ducastelle and Françoise Cyrot-Lackmann presented a theorem involving moments of the densities of states.…”

Section: The Friedel School Of Tight Binding and The Theory Of The Trmentioning

confidence: 99%

Jacques Friedel. 11 February 1921 — 27 August 2014

Duparc

2015

Biogr. Mems Fell. R. Soc.

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Jacques Friedel was the father of condensed matter and materials physics in France. He was an educator, researcher and leader who transformed physics in France after World War II. He was one of the most respected and influential scientists in Europe, a co-founder of the Laboratory of Solid State Physics at Orsay, President of the European Physical Society, and President of the Academy of Sciences in France.

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Moments developments II. Application to the crystalline structures and the stacking fault energies of transition metals

Cited by 6 publications

References 0 publications

Adsorption Site Preference Determined by Triangular Topology: Application of the Method of Moments to Transition Metal Surfaces

Adsorption Site Preference Determined by Triangular Topology: Application of the Method of Moments to Transition Metal Surfaces

Crystal-Structure Analysis with Moments of the Density-of-States: Application to Intermetallic Topologically Close-Packed Phases

Jacques Friedel. 11 February 1921 — 27 August 2014

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