Metal surface energy

Although fused oxides and halides have been less extensively studied than liquid metals, surface energies have been determined for a number of such compounds. In the absence of models for estimating the surface energy of oxide or halide mixtures, this quantity must be determined experimentally. 

This result is a definitive counter-example to the short wavelength hypothesis. However, note that these values for a are not very much different numerically, suggesting that the short wavelength hypothesis may not be too bad in practice. (We have also found that, for the metal surface energy contribution in the semiclassical infinite barrier model, o = 0 both exactly and in the LSD.)... 

FlQ. 35. Potential energy of electron at a clean metal surface. Energy levels appropriate for high index plane of tungsten. xt—position of Schottky saddle EF—Fermi energy. 

Related articles are Contact angles and interfacial tension. Surface characterization by contact angles - polymers. Surface characterization by contact angles - metals. Surface energy and Wetting kinetics. 

Schreifels, J.A., et al.. Adsorption of a metal deactivator addditive onto metal surfaces. Energy Fuels, 5(2), 263-268(1991). 

An interesting concept to achieve the latter regime i.e. to obtain increased radiative rates, has been suggested by Enderlein. As depicted in figure 15, a dye molecule is fixed in the center of a metallic sphere. As it is away from the metal surface, energy transfer is less important, while the increase in field strength increases the molecular... 

N. Martensson, H.B. Saalfeld, H. Kuhlenbeck, M. Neumann, Stnictural dependence of the 5d-metal surface energies as deduced from surface COTe-level shift measurements. Phys. 

The best results have been obtained by embedded-atom-type methods, applied first with good success to many metallurgical properties of pure metals surface energy, point-defect properties (see for example Foiles et al., 1986 Chapter 4 by Voter in this volume). In these methods, the energy of each atom is computed from the energy F,(p,) needed to embed it in the local-electron density pi provided by the other atoms of the alloy (approximated by the superposition of atomic-electron densities Pj=Hj, /Pj(Ry)), plus an additional electrostatic short-range core-core repulsion y Rij) = Zj(Rf)Zj(Rjj)/Rjj. The total energy is then written as... 

The calculation of the surface energy of metals has been along two rather different lines. The first has been that of Skapski, outlined in Section III-IB. In its simplest form, the procedure involves simply prorating the surface energy to the energy of vaporization on the basis of the ratio of the number of nearest neighbors for a surface atom to that for an interior atom. The effect is to bypass the theoretical question of the exact calculation of the cohesional forces of a metal and, of course, to ignore the matter of surface distortion. 

The second model is a quantum mechanical one where free electrons are contained in a box whose sides correspond to the surfaces of the metal. The wave functions for the standing waves inside the box yield permissible states essentially independent of the lattice type. The kinetic energy corresponding to the rejected states leads to the surface energy in fair agreement with experimental estimates [86, 87],... 

Metals A and B form an alloy or solid solution. To take a hypothetical case, suppose that the structure is simple cubic, so that each interior atom has six nearest neighbors and each surface atom has five. A particular alloy has a bulk mole fraction XA = 0.50, the side of the unit cell is 4.0 A, and the energies of vaporization Ea and Eb are 30 and 35 kcal/mol for the respective pure metals. The A—A bond energy is aa and the B—B bond energy is bb assume that ab = j( aa + bb)- Calculate the surface energy as a function of surface composition. What should the surface composition be at 0 K In what direction should it change on heaf)pg, and why ... 

If a surface, typically a metal surface, is irradiated with a probe beam of photons, electrons, or ions (usually positive ions), one generally finds that photons, electrons, and ions are produced in various combinations. A particular method consists of using a particular type of probe beam and detecting a particular type of produced species. The method becomes a spectroscopic one if the intensity or efficiency of the phenomenon is studied as a function of the energy of the produced species at constant probe beam energy, or vice versa. Quite a few combinations are possible, as is evident from the listing in Table VIII-1, and only a few are considered here. 

For example, energy transfer in molecule-surface collisions is best studied in nom-eactive systems, such as the scattering and trapping of rare-gas atoms or simple molecules at metal surfaces. We follow a similar approach below, discussing the dynamics of the different elementary processes separately. The surface must also be simplified compared to technologically relevant systems. To develop a detailed understanding, we must know exactly what the surface looks like and of what it is composed. This requires the use of surface science tools (section B 1.19-26) to prepare very well-characterized, atomically clean and ordered substrates on which reactions can be studied under ultrahigh vacuum conditions. The most accurate and specific experiments also employ molecular beam teclmiques, discussed in section B2.3. 

Figure Bl.6.10 Energy-loss spectrum of 3.5 eV electrons specularly reflected from benzene absorbed on the rheniiun(l 11) surface [H]. Excitation of C-H vibrational modes appears at 100, 140 and 372 meV. Only modes with a changing electric dipole perpendicular to the surface are allowed for excitation in specular reflection. The great intensity of the out-of-plane C-H bending mode at 100 meV confimis that the plane of the molecule is parallel to the metal surface. Transitions at 43, 68 and 176 meV are associated with Rli-C and C-C vibrations.

Smith D P 1967 Scattering of low-energy noble gas ions from metal surfaces J. Appl. Phys. 38 340-7... 

Suurmijer E P Th M and Boers A L 1973 Low-energy ion reflection from metal surfaces Surf. Sc/. 43 309-52... 

Figure Bl.26.21. Potential energy curves for an electron near a metal surface. Image potential curve no applied field. Total potential curve applied external field = -E. ...

Our intention is to give a brief survey of advanced theoretical methods used to detennine the electronic and geometric stmcture of solids and surfaces. The electronic stmcture encompasses the energies and wavefunctions (and other properties derived from them) of the electronic states in solids, while the geometric stmcture refers to the equilibrium atomic positions. Quantities that can be derived from the electronic stmcture calculations include the electronic (electron energies, charge densities), vibrational (phonon spectra), stmctiiral (lattice constants, equilibrium stmctiires), mechanical (bulk moduli, elastic constants) and optical (absorption, transmission) properties of crystals. We will also report on teclmiques used to study solid surfaces, with particular examples drawn from chemisorption on transition metal surfaces. 

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