Calculated surface energies of the 4d transition metals: A study of bond-cutting models

The surface energies of the low-index surfaces of the 4d transition metals were calculated using density-functional theory and the full-potential linear muffin-tin orbital method. The results are discussed in the context of bound-cutting models. It is found that the usual approach, which ignores the decrease of the bond strength with increasing coordination number, is incompatible with the calculated results. The coordination number — bond strength relation was calculated explicitly for several metals, showing that the bond strength decreases roughly as the reciprocal of the square-root of the coordination number. A modified model which takes this into account correctly describes the magnitude and the surface depencence of the calculated surface energies. In addition, we discuss the previously ignored role of the free-atom orbital structure in bond-cutting models.     

Face dependent surface energies of simple metals

Using a simple ansatz for the $\text{inhomogeneous}$ screened linear electron gas susceptibility, we obtain the face dependent surfaces energies, σ, of the simple metals, through second order. In contrast to results of the first-order Lang-Kohn method and the $\text{one-dimensional}$ variational values of Monnier and Perdew, we obtain $\text{weakly}$ face dependent σ values consistent with experiment. Our results hinge on two previously neglected considerations: (i) ion induced inhomogeneity of the bulk electron density prior to cleavage and (ii) ion induced electron density inhomogeneity in the surface region after cleavage.     

Analytical properties of theS-matrix applied to the resonance model of transition metals

Summary A method to construct ionic potentials for transition metals from the knowledge of the resonantd-band phase shiftη ₂=tg^-21/2W/(E-E_d) is developed. This is based on an inversescattering approach using the analytic properties of theS-matrix and Jost functions to reconstruct the interparticle potential in the spirit of the Marchenko and Gel'fand-Levitan formalisms. A specific form of the solution of the resulting integral equation is discussed and possible applications to a host of transition metal properties are outlined.

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Riassunto Si mette a punto un metodo per costruire potenziali ionici per metalli di transieione partendo dalla conoscenza dello sfasamento risonante della bandad,η ₂=tg^-21/2W/(E-E_d). Questo è basato su un approccio allo scattering inverso che tiene conto delle proprietà analitiche della matriceS e delle funzioni di Jost per ricostruire il potenziale tra particelle nell'ambito dei formalismi di Marchenko e Gel'fand. Si discute una forma specifica dell'equazione integrale risultante e si sottolineano le possibili applicazioni ad una grande quantità di proprietà dei metalli di transizione.

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Резюме Развивается метод для конструирования ионных потенциалов для переходных металлов, исходя из знания резонансного фазового сдвигаd-зоны,η ₂=tg^-21/2W/(E-E_d). Этот метод основан на обратной задаче рассеяния с использованием аналитических свойствS-матрицы и функций Йоста для конструирования междучастичного потенциала в духе формализма Марченко и Гельфанда-Левитана. Обсуждается специальная форма решения полученного интегрального уравнения. Указываются возможные применения для описания свойств переходных металлов.

     

Compressive surface stress in magnetic transition metals

Because of the increased electron density within the surface layer, metal surfaces are generally expected to have tensile surface stress. Here, using first-principles density functional calculations, we demonstrate that in magnetic 3d metals surface magnetism can alter this commonly accepted picture. We find that the thermodynamically stable surfaces of chromium and manganese possess compressive surface stress. The revealed negative surface stress is shown to be ascribed to the enhanced magnetic moments within the surface layer relative to the bulk values.     

Electronic surface states in cleaved transition metals

The local densities of states (LDS) on clean low-index surfaces of fcc Ni and bcc Fe are presented. They are calculated within the tight-binding approximation using a moment method and a continued fraction analysis. The d band degeneracy and the charge rearrangement occurring near the surface when cleaving the crystal are fully taken into account by computing exactly a large number of moments (22–26). The surface LDS are found to be strongly dependent on the cleavage plane. Indeed, whereas the LDS on dense planes are rather bulk like, sharp peaks arising from states localized near the surface are obtained near the atomic level of the metal on non-dense planes of cleavage. In addition, the bandwidth is broadened by surface states for Ni. On the contrary, for bcc Fe the surface potential is not strong enough to modify the bandwidth. A comparison is made with spectroscopic observations.The method lends itself to other interesting applications in the surface physics field and, as an example, we present the results of calculations of the spatial distribution of the electronic charge near the surface and its deviation from spherical symmetry. The charge asphericity is slightly increased when going from a bulk to a surface site as the difference between the occupations of two surface orbitals can reach 0.34 ē instead of 0.15 ?c for a bulk site. Diagrams are shown for (100) and (110) cleaved Ni to illustrate the results. The consequences upon preferred adsorption sites according to the electronic affinity and size of the adsorbate are discussed.     

Phase transformations and vacancy formation energies of transition metals by positron annihilation

The technique of the coincidence count rate at the peak of the angular correlation curve (CCR) in positron annihilation has been applied to the investigation of vacancy formation energies in thermal equilibrium in nickel, cobalt, and iron. The monovacancy formation energyE ^1v/F has been determined to (1.55±0.05) eV and (1.34±0.07) eV for nickel and cobalt, and (1.60±0.10) eV for α-iron, and (1.40±0.15) eV for γ-iron, respectively. The structural phase transformations in cobalt (693 K) and iron (1183 K, 1663 K) are exhibited by discontinuities of the CCR. In the case of cobalt the CCR follows exactly the change of the thermal expansion at the transition temperature. The temperature dependence of the CCR in the prevacancy region is found to be proportional to the thermal expansion for all metals investigated.     

On thed-electron surface density of states of transition metals

Using the moment method and the continued fraction expansion for the one-particle Green's function we have studied thed-electron surface density of states for a transition metal. Besides the reduction of nearest neighbours for a surface atom compared to a bulk atom we have also taken into account the effect that the atomic environment of a surface atom is quite different from that of a bulk atom. This leads to important modifications in the surface density of states which can effect e.g. magnetic surface properties.Work supported in part by the ESIS program (Universities of Liege and Antwerpen)     

On thed-electron surface density of states of transition metals

It is shown that thed-electron surface density of states of a transition metal is strongly influenced not only by “off-diagonal” surface effects (e.g. reduction of nearest neighbors at the surface) but also by “diagonal” surface effects. Latter result from differences in the effective atomic potential for differentd-orbitals. They lead generally to large resonant contributions to the surface density of states. It is demonstrated that the “diagonal” effects must be included in any realistic calculation of the surface density of states.     

Surface relaxation and surface stress of 4d transition metals

Using the density functional theory formulated within the framework of the exact muffin-tin orbitals method, we present a systematic study of the top layer relaxation and surface stress of 4d transition metals. Our calculations predict layer contractions for most surfaces. We also find that the relaxations of the close packed surfaces decrease with increasing atomic number through the 4d series. We propose that the relaxation is mainly due to the reduction of the number of sp electrons in the surface layer relative to bulk. The surface stress is found to be very sensitive to the relaxation and, therefore, an accurate determination of the layer relaxation is necessary for obtaining reliable values for the surface stress. Comparing the top layer relaxations for the close packed surfaces, we see essential deviations between data derived in different ab initio calculations. At the same time, the overall trend for the present surface stress of 4d metals is in reasonable agreement with recent full-potential data.     

Ab initio calculations of generalized-stacking-fault energy surfaces and surface energies for FCC metals

The ab initio calculations have been used to study the generalized-stacking-fault energy (GSFE) surfaces and surface energies for the closed-packed (1 1 1) plane in FCC metals Cu, Ag, Au, Ni, Al, Rh, Ir, Pd, Pt, and Pb. The GSFE curves along (1 1 1) direction and (1 1 1) direction, and surface energies have been calculated from first principles. Based on the translational symmetry of the GSFE surfaces, the fitted expressions have been obtained from the Fourier series. Our results of the GSFEs and surface energies agree better with experimental results. The metals Al, Pd, and Pt have low γ_us/γ_I value, so full dislocation will be observed easily; while Cu, Ag, Au, and Ni have large γ_us/γ_I value, so it is preferred to create partial dislocation. From the calculations of surface energies, it is confirmed that the VIII column elements Ni, Rh, Ir, Pd, and Pt have higher surface energies than other metals.     

Surface free energies of solid metals: Estimation from liquid surface tension measurements

An equation is derived on semi-theoretical grounds which expresses the solid-vapour surface free energy as a function of the liquid surface tension and the solid-liquid interfacial free energy. A means of calculating reliable values for the solid-liquid energy is presented, which then allows an accurate estimate of solid surface energy at the melting temperature, T_m, to be made for the large number of elements for which dependable liquid surface tension data exist. A method of estimating surface entropy is presented, and has been used to calculate the energies typical of “average”, high-index surfaces at temperatures ranging from 0 K to T_m. It is felt that this paper describes the most accurate method presently available for the calculation of the surface energy of solids in the absence of direct experimental measurement.     

Magnetic surface anisotropy and surface states of a semiinfinite crystal of ferromagnetic transition metals

The main aim of the present paper is to estimate the magnitude of the magnetic surface anisotropy of a semiinfinite intinerant ferromagnet by calculating the contribution of surface states to the surface energy. Surface states are investigated without and with the consideration of the spin-orbit interaction (which causes the dependence of the sample energy on the magnetization direction). Different more or less realistic estimates of the surface parameters are used. Only threeT _2g 3d-bands described in the tight-binding approximation are used to represent a 3d transition metal. Numerical calculation was performed for the (100) Ni surface. For this case the presence of the axial magnetic surface anisotropy was confirmed. The surface anisotropy constant corresponding to the surface-state contribution is estimated to be ?0·2 to ?0·3 erg/cm².     

Investigation of surface properties of liquid transition metals: Surface tension and surface entropy

In the present study, surface properties namely surface tension and surface entropy of liquid transition metals have been reported. The surface entropy of liquid Fe, Co and Ni metals has been investigated using the expression derived by Gosh et al. [R.C. Gosh, A.Z. Ziauddin Ahmed, G.M. Bhuiyan, Eur. Phys. J. B 56 (2007) 177]. To describe interionic interaction the pseudopotential approach has been used and radial distribution functions have been determined from the solution of Ornstein-Zernike integral equation. The calculated values of surface tension and surface entropy agree well with experiment. The present study shows that the expression derived by Gosh et al. leads to a good estimation for the surface entropy.     

Interactions of surface states of copper with transition metals and cesium

The pseudopotential augmented-plane-wave method was used to study the surface structure of thin copper films with monolayers of Co, Ni, and Cs. Local densities of electron states, distributions of charge densities in the layers, and electron energy spectra are analyzed. The effect of adsorbates on the electronic properties of the Cu(001) surface and work function are discussed. Satisfactory agreement with available experimental data has been obtained.