Work function calculation of solid solution alloys using the image force model

Rothschild, Jonathan A.; Eizenberg, M.

doi:10.1103/physrevb.81.224201

Cited by 44 publications

(32 citation statements)

References 35 publications

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“…In fact, we proposed before that both the surface and islands larger than 7 nm 2 consist of a Cu/Ag alloy [17]. The small shift in energy is consistent with the vanishing shift of the work function for dilute alloys and the nonlinear dependence of the work function on alloy ratio for metal alloys [34]. The energy decreases slightly for island sizes ranging from 15 to 5 nm 2 .…”

Section: -3supporting

confidence: 76%

“…The energy decreases slightly for island sizes ranging from 15 to 5 nm 2 . This energy decrease might reflect the dealloying of the islands leading eventually to the formation of pure copper islands at island sizes below 5 nm 2 [34]. The exact processes during alloying and reasons for it demands a large scale calculation and further high resolution imaging during dealloying.…”

Section: -3mentioning

confidence: 99%

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Quantitative determination of a nano-object's atom density without atomic resolution

et al. 2014

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We outline a possibility to determine the adatom density of individual nano-objects via measurement of their electronic structure. For this aim, the nonlinear shift of image potential states measured on individual Cu nanoclusters on Ag(100) by low-temperature scanning tunneling spectroscopy is carefully analyzed. The quantitative analysis is confirmed by density-functional theory calculations. A peak width analysis furthermore reveals whether the clusters are purely metallic or alloyed. For nanotechnology a structural control on the nanoscale is essential, because the physical as well as chemical properties of nanoscale objects depend on the exact arrangement of their atoms [1]. As a first step, it is of vital importance for scientists and engineers to resolve the internal structure of the nanosystems to understand and, in a subsequent step, tune the resulting macroscopic properties. The atomic structure of nanoparticles can be determined directly by scanning transmission microscopy (STEM) with high resolution down to 50 pm [2], which shows a two-dimensional projection of the crystal in some high-index direction of particles. With STEM, nanoparticles were imaged three dimensionally [3]. Even single defects within nanoparticles were identified recently [4]. Due to the width of the electron beam, the extraction of the data demands sophisticated procedures.For two-dimensional nanoparticles on surfaces, scanning tunneling microscopy (STM) turned out to be a simple and versatile tool for high resolution imaging. However, atomic resolution is often impossible for discrete entities consisting of only a few atoms, in particular for nanoclusters. These objects have the tendency to be moved or restructured at the tunneling parameters necessary for atomic resolution. On the other hand, structural information of a metal surface is clearly reflected in the energetic positions of its image potential states [5,6]. A Rydberg-like series of these states emerges, when an outside charge polarizes a metal surface and is attracted to the induced polarization charge. As the energy levels of these states are pinned to the vacuum level, they are closely related to the work function, which in turn varies with both the chemical composition of the surface and the surface orientation, and thus with atom density. Surface averaged values of energy, dispersion (and lifetime) of image potential states were extensively probed, first by inverse photoemission (IPES) [7] and later by two-photon photoemission spectroscopy (2PPE) [8]. High spatial resolution of an image potential state was achieved by scanning tunneling spectroscopy (STS) [9,10] . The shifts are consistent with a lateral confinement of the electrons as described by textbook (two-dimensional) particle-in-a-box models [14]. Such an assignment assumes atomically flat islands with perfect coordination, though a relation to potential relaxation or reconstruction of the latter has not been made so far [16]. In this article, we present a method for the analysis of metallic nanostructures ...

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Section: -3supporting

confidence: 76%

Section: -3mentioning

confidence: 99%

Quantitative determination of a nano-object's atom density without atomic resolution

et al. 2014

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“…Computational methods and theoretical correlations based on image force, dipole layer, surface mixture, and dual phase mixture approaches have been proposed. 37 In the case of contact electrification, the situation is much simpler than with alloys, because only one surface layer is affected, whereas in alloys the components can be completely mixed. Alloying changes the Fermi level in two ways: by contact electrification, as described above, and by changing the lattice structure of the metal, directly affecting the chemical potential of electrons in the alloy.…”

Section: ■ Electrostatics Of Conductors With Different Work Functionsmentioning

confidence: 99%

Contact Potentials, Fermi Level Equilibration, and Surface Charging

2016

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This article focuses on contact electrification from thermodynamic equilibration of the electrochemical potential of the electrons of two conductors upon contact. The contact potential difference generated in bimetallic macroand nanosystems, the Fermi level after the contact, and the amount and location of the charge transferred from one metal to the other are discussed. The three geometries considered are spheres in contact, Janus particles, and core−shell particles. In addition, the force between the two spheres in contact with each other is calculated and is found to be attractive. A simple electrostatic model for calculating charge distribution and potential profiles in both vacuum and an aqueous electrolyte solution is described. Immersion of these bimetallic systems into an electrolyte solution leads to the formation of an electric double layer at the metal−electrolyte interface. This Fermi level equilibration and the associated charge transfer can at least partly explain experimentally observed different electrocatalytic, catalytic, and optical properties of multimetallic nanosystems in comparison to systems composed of pure metals. For example, the shifts in the surface plasmon resonance peaks in bimetallic core−shell particles seem to result at least partly from contact charging.

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“…Using Brodie's concept as the starting point, Halas and Durakiewicz (H-D) have combined the polarization length of metal-lattice plasma (MLP) with the Fermi energy to calculate the polycrystalline WF of sixty elements [12]. Their new model [13], using the free-electron gas and classical electrodynamics approach, leads to a good agreement with WF experimental data concerning metals, rare earth elements as well as alloys and yields the most reliable data despite its phenomenological character [9].…”

Section: Introductionmentioning

confidence: 65%

“…There are also phenomenological approaches to the electron work function (WF) which is one of the most important characteristics of materials. In order to ensure a wide area of applicability to metals and alloys, such * E-mail: jacek.brona@ifd.uni.wroc.pl approaches use the classical electrostatic image or the unscreened Coulomb potential [9][10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Two-extremum electrostatic potential of metal-lattice plasma and the work function of an electron

Surma

Brona

Ciszewski

2015

Materials Science-Poland

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Metal-lattice plasma is treated as a neutral two-component two-phase system of 2D surface and 3D bulk. Free electron density and bulk chemical potential are used as intensive parameters of the system with the phase boundary position determined in the crystalline lattice. A semiempirical expression for the electron screened electrostatic potential is constructed using the lattice-plasma polarization concept. It comprises an image term and three repulsion/attraction terms of second and fourth orders. The novel curve has two extremes and agrees with certain theoretical forms of potential. A practical formula for the electron work function of metals and a simplified schema of electronic structure at the metal/vacuum interface are proposed. This yields 10.44 eV for the Fermi energy of free electron gas; −5.817 eV for the Fermi energy level; 4.509 eV for the average work function of bcc tungsten. Selected data are also given for fcc Cu and hcp Re. For harmonic frequencies ∼ 10E16 per s of the self-excited metal-lattice plasma, energy gaps of 14.54 and 8.02 eV are found, which correspond to the bulk and surface plasmons, respectively. Further extension of this thermodynamics and metal-lattice theory based approach may contribute to a better understanding of theoretical models which are employed in chemical physics, catalysis and materials science of nanostructures.

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Work function calculation of solid solution alloys using the image force model

Cited by 44 publications

References 35 publications

Quantitative determination of a nano-object's atom density without atomic resolution

Quantitative determination of a nano-object's atom density without atomic resolution

Contact Potentials, Fermi Level Equilibration, and Surface Charging

Two-extremum electrostatic potential of metal-lattice plasma and the work function of an electron

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