Electronic structure of liquid metals

A review is given of the electronic structure of liquid metals. The theoretical formalism is developed in terms of the density matrices of the system, and the conditions under which these can be obtained are described, and the limitations found at present. The experimental material is then reviewed and it is shown how experimental results are interpreted in terms of values and averages over the density matrices.     

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.     

Electronic structure of transition metals under pressure

Conclusions In this short review we have tried to demonstrate the advances made in the intensive study of the behavior of the electronic structure of metals under pressure in recent years. The alloys of transition metals, including intermetallic ordered compounds, have for the time being proved to lie outside the scope of this review, mainly because of the lack, in practice, of theoretical calculations in this area. Clearly, progress in this field is also being held up by the lack of detailed experimental investigations devoted to the behavior of alloys under pressure. This is due to the complexities involved in carrying out many traditional experimental procedures under high pressures. We should like to emphasize, however, that at the present time theoretical calculations have taken on a predictive power and this gives reason to hope that progress in calculations will in turn stimulate progress in experimentation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 50–62, December, 1982.     

Electronic surface resonances and crystal surface structure

A new method of determination of the lateral structure of crystal surfaces is presented. The method is based on earlier work showing the existence of resonances in the elastic scattering of low-energy electrons at crystal surfaces. The method consists of: (a) Measurement of the surface resonance band structure Ek_∥E, k_∥ respectively denote the electron energy and surface-parallel momentum for which resonances occur) and (b) Interpretation of E(k_∥) to determine the lateral variation of the effective potential acting on electrons at the surface.The surface resonance band structure is measured by a net-current electron reflection method. The measurement method is basically the same as used previously but here its precision is greatly enhanced by the use of digital methods of data handling including a digital filter to remove background due to inelastic and non-resonance elastic scattering. The surface resonance band structure is interpreted by a two-dimensional nearly-free electron scheme. In this scheme the interaction elements are Fourier coefficients of an effective potential which is an average of a pseudopotential with respect to the depth distribution of electron density in a surface resonance — the surface-weighted pseudopotential. Experimental surface resonance band structure for Ni(001), Ni(001) p(2 × 2)O and two different Ni(001) c(2 × 2)O surfaces (one of them with an oxygen-saturated Ni substrate) are presented for E = 1–30 eV and k_∥ running halfway from $\text{}\text{?}$gG towards H? in the surface Brillouin zone for Ni(001). The experimental results are fitted, using the nearly-free electron scheme, to determine the Fourier coefficients of the surface-weighted pseudopotential. Surface potential variations synthesized from the above data are discussed in comparison with the atomic arrangements known from LEED. It is demonstrated that the new method can give a correct picture of the lateral structure of surfaces. It is emphasized that these results are obtained without costly equipment or computations called for by other methods.     

Electronic structure of hydrogen-like impurities in nearly-free-electron metals

Recent developments in our understanding of the electronic structure of hydrogen and its isotopes in simple metals is reviewed. The role of nonlinear electron density distribution in the interpretation of the electronic properties of hydrogen-like impurities is emphasized. Calculated Knight shifts and hyperfine fields at + site and electric field gradients at cubic host nuclear sites due to interstitial + are compared with recent experimental data. The feasibility of using positive muon as a probe of defect structure is discussed. Future experiments and theoretical investigations aimed at a deeper understanding of the electronic properties of + are suggested.Work supported by the National Science Foundation and the U. S. Department of Energy.     

Electronic structure of the self-trapped exciton in rare gas solids

The Rydberg-like series of the self-trapped exciton R₂¹ in rare gas solids (Ar, Kr and Xe) are obtained by solving the effective mass equation which incorporates different corrections, including the central cell correction. The results are in good agreement with the recent transient optical absorption data in which the electron is excited into higher excited states. The origin of the luminescence bands is interpreted by analogy with a similar structure of the self-trapped excitons in alkali halides.     

Electronic structure of the SiAu surface

The electronic density of states of the SiAu surface is calculated using a continued fraction technique. The geometric structure of the surface alloy Au₄Si is generated by molecular dynamics. The local density of states on Si atoms in a metallic environment differs qualitatively from the sp spectrum of a typical semiconductor. The calculated densities of p states of Si are in good agreement with recent X-ray spectra of Si in a metallic environment.     

LaNi5晶体表面态的计算研究

用"团簇埋入自洽计算法"对LaNi5晶体表面进行了全电子、全势场、自旋极化的从头计算.在原子纵向坐标充分弛豫的条件下,得到处于最低基态总能量下LaNi5晶体的非平整表面空间结构及其电子结构.LaNi5晶体最表面La原子向外凸出,Ni原子向里收缩,凹凸不平的表面层增加了表面原子与氢原子的接触面积;而表面层的有效体积增大了约9%,有利于氢原子的进入.LaNi5晶体表面态的费米能量大大高于体材料的费米能量.在费密面上主要是Ni的3d电子,价带未填满,显示金属性.LaNi5晶体表面第一、第二层有1.15个电子从La原子向Ni原子转移,这两层有反向的微小自旋磁矩,从而使表面显示顺磁性.得到了LaNi5晶体表面的价带电子态密度.用过渡态方法计算了LaNi5晶体表面的电离能和电子亲和势.所有计算结果显示:LaNi5晶体表面的性质与体性质显著不同,而与氢化物LaNi5H7的性质非常相近.这说明LaNi5晶体的表面结构有利于氢原子的吸收.     

Electronic structure of regular bacterial surface layers

We report photoemission and near-edge x-ray absorption fine structure measurements of the occupied and unoccupied valence electronic states of the regular surface layer of Bacillus sphaericus, which is widely used as the protein template for the fabrication of metallic nanostructures. The two-dimensional protein crystal shows a semiconductorlike behavior with a gap value of approximately 3.0 eV and the Fermi energy close to the bottom of the lowest unoccupied molecular orbital. We anticipate that these results will open up new possibilities for the electric addressability of biotemplated low-dimensional hybrid structures.     

Electronic structure of the Cu(111) surface

Self-consistent electronic structure calculations are reported on bulk Cu, and 3- and 5-layer Cu films. These yield a size insensitive work function, φ = 5.0±.1 eV, and a surface energy of 0.75 eV, in agreement with experiment. Good size convergence of the film potential permits the construction of a self-consistent potential for an 11-layer Cu(111) film, whose spectral properties we studied. A prominent p-like surface band was found within 0.1 eV of experiment, serving as a check on the surface potential.     

Electronic fluctuation,the nature of interactions and the structure of liquid metals

Summary Interactions controlling ionic motion and structure in liquid metals can be systematically developed beginning with the ultimate view of such systems as neutral assemblies of nuclei and electrons, and proceeding to standard reduced Hamiltonians reflecting assemblies ofions and electrons. The assumption of electronically rigid ion leads via response methods and pseudopotentials to statically screened ion-ion potentials and beyond. Fluctuations are introduced into this otherwise common viewpoint by relaxing the assumption of electronically rigid ion cores and also by treating electronic response beyond linear order. It is argued that both effects can lead to more attractive pair interactions and possibly to effects much larger than, for example, Friedel oscillations. These contributions are state (i.e. density) dependent and their presence might be expected on the basis of clustering behavior seen for some systems in theirvapour phases. This leads to two limiting viewpoints on the liquid-state structure of such systems, the first as an entirely monoatomic phase but with a pair interaction that is unusual, the second as a system supporting transient clusters whose presence reflects the complexities argued on the basis of a more extended treatment of the electron problem. Paper presented at the workshop ?Highlights on Simple Liquids?, held in Turin at ISI on 1– May, 1989.     

Electronic structure of transition metal monoantimonides: Analogy to the transition metals

A simple metallic band model is proposed for the transition metal monoantimonides, by analogy to the transition metals. It is assumed that the metal 3d electrons are itinerant in narrow bands which energetically overlap broader antimony 5p-derived bands, and the Fermi level lies in the overlap region. Consistency of the model with available data is assessed and found to be quite good.     

Band structure and the fermi surface of rare earth metal europium

In order to understand consistently the origin of the helical spin ordering of the bcc Eu observed below T_N = 91 K, we have calculated the band structure and investigated the detailed shape of the Fermi surface, by the KKR method. The present results are compared with those of the previous calculations.