Analytic theory of hexagonal monolayer interacting with hexagonal substrate

2007

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We present a procedure for the generation of all rigid commensurate monolayer-surface structures of a given symmetry, up to a certain number of adsorbate particles, N ads , in the unit cell. It is shown that the minimum energy structures in each unit cell are related to a well-defined sequence of Fourier terms of the single-particlesurface potential. This fact allows the prediction of stable commensurate monolayer-surface structures with the only knowledge of Fourier coefficients of the atom-surface potential. The impact of the presented theory for theoretical and experimental determination of atomic and molecular monolayer ground states, as well as its extension to higher dimensions ͑i.e., for intercalated crystals͒, is discussed.

Section: Application Of the Theory To Real Systemssupporting

confidence: 74%

“…[11][12][13][14] For further discussion about the validity of rigid hexagonal approximation for real systems, see, e.g., Ref. 15.…”

Section: Introductionmentioning

confidence: 99%

Commensurate monolayers on surfaces: Geometry and ground states

2007

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“…As shown in Ref. 20, the second Fourier term is fully conserved for a perfect hexagonal arrangement with three atoms per unit cell ͓e.g., the ͑ ͱ 7 ϫ ͱ 7͒R19.1°structure͔. Therefore, it is expected that its inclusion will drive the monolayer to recover the hexagonal structure with higher symmetry.…”

Section: Discussionmentioning

confidence: 84%

“…For detailed analysis of this case, see Ref. 20. One conclusion of that study was that the first Fourier term ͑presumably the most important one͒ vanishes in the neighborhood of rigid hexagonal commensurate structures with more than one atom per unit cell.…”

Section: V͑r͒mentioning

confidence: 97%

Role of high-order Fourier terms for stability of monolayer-surface structures: Numerical simulations

2006

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The role of high-order atom-surface Fourier terms is analyzed for the monolayer with coverage = 3 7 on ͑111͒ surface in cells with variable number of adsorbate atoms, allowed to relax to obtain the global minimum in each of the unit cells. A Fourier expansion with one or two shells of reciprocal cell vectors is used and three different models for the lateral interactions in the monolayer are tested, from purely repulsive to a real HFD-B2 potential. It is found that the simple commensurate ͑ ͱ 7 ϫ ͱ 7͒R19.1°three-atom structure is the most stable only when the contribution of the second Fourier term is included. In contrast to the conventional view, higher corrugation of the single-term Fourier model favors incommensurability. Evidence is collected that the highorder Fourier terms are mandatory for the stabilization of commensurate structures of an infinite monolayer.

“…When either the surface corrugation or the ͑repulsive͒ lateral interaction is strong, hexagonal ͑in͒commensurate monolayer-surface structures emerge. 23,24 Therefore, it is reasonable to assume that the lowest-energy structures for a given coverage are located in cells where the formation of perfect hexagonal monolayers is possible.…”

Section: The Model and Systemsmentioning

confidence: 99%

Comprehensive study of the potential energy surface minima of a monolayer on (111) surface

2007

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The potential energy landscape of a monolayer adsorbed on well-ordered ͑111͒ surface is analyzed for periodic cells with a variable number of adsorbate ͑N ads ͒ and substrate ͑N sub ͒ particles. The atom-surface potential is described by the first Fourier series term with variable corrugation, while the lateral interaction in the monolayer is modeled by a repulsive exponential term. Special attention is devoted to the determination of the total number of minima for given N ads and N sub and the probability of relaxation to the global minimum in each of the unit cells, as well as the construction of the lowest energy versus coverage curve as a function of the atom-surface potential corrugation. We find that the global appearance of the energy landscape in the majority of the unit cells is particularly simple, characterized by the global minimum positioned in a very wide basin and the high-energy minima forming a tail structure. However, this rule is broken for several unit cells when the corrugation of the atom-surface potential becomes large, making the location of the global minimum a rather difficult task. Despite the simplicity of our model, phase transitions from commensurate to striped incommensurate to hexagonal incommensurate rotated structures are observed.