Separation of 5d and 4f contributions to the electric field gradient in heavy rare-earths

We calculate the conduction electron contribution to the electric field gradient in heavy rare earth metals assuming 5d virtual bound state character present. The results are in better agreement with experiment than found previously and predict antishielding parameters for Er and Tm in good agreement with those calculated directly.     

Systematics of the rare-gas core contributions to the positron annihilation spectra of some simple and transition metals

Taking into account the core electron enhancement factor the rare-gas core contribution to the angular correlation positron annihilation spectra and to the total annihilation rate in some simple and transition metals are calculated. It is shown that the valence high-momentum part of the Gaussian fraction is not negligible in simple metals. In 3d and 4d metals, the rare-gas core part of the total annihilation rate amounts from 9 to 37%. The results are expected to help in the correct interpretation of the positron annihilation data.     

Specific heat of electron gas of arbitrary dimensionality

The exchange contribution to the specific heat of an electron gas in d dimensions is calculated and is shown to lead to a logarithmic temperature dependence at low temperatures in all dimensions (d > 1).     

Non-spherical contributions to the vacancy formation energy

A linear response formalism is presented which allows the calculation of the non-spherically symmetric (angular momentum index, l ≠ 0) response to a random external charge perturbation when the spherically symmetric response is available. This procedure is applied to the problem of the energy of vacancy formation so that the electron charge depletion in the vicinity of vacancy is taken into account. The non-spherical contribution to the energy formation for the alkali metals is estimated and found to be non-negligible.     

Anisotropic k-ƒ interactions from spin-orbit coupled 5d intermediate states

The anisotropy of the conduction electron-4? local moment interaction ($\text{k-?}$) gives rise to anisotropic transport effects. The contribution from the orbital character of the 4? moment has been well documented by magnetotransport studies on noble metals containing non-S state rare-earth ions. To determine whether there is an additional contribution to the anisotropy from the spin-orbit coupled 5d electron states we have studied the magnetoresistivity of Ag: Gd alloys. We have not found any significant anisotropy of the magnetoresistivity. By comparing this result and previous Hall effect and magnetoresistivity data on noble metal-rare earth alloys with our model calculation, we come to the conclusion that the spin-orbit splitting of the 5d virtual bound state is relatively small. We discuss the details of the resulting anisotropy of the $\text{k-?}$ interaction.     

Amorphous metals and their superconductivity

Quite a number of metals and alloys can be forced into the amorphous state by quenching. In particular, condensation onto a substrate cooled to He-temperature is very effective. The superconductivity and related properties of these metals are considered in this article. The influence of the amorphous structure on the electron and the phonon system is discussed. In simple metals the electrons show a free electron behaviour. The transverse phonons are softened but maintainn the ω³-density of states at low frequencies. The electron-phonon interaction does not conserve momentum due to the loss of translational invariance in the amorphous metal and yields a large contribution to α²F(ω) at low frequencies. Therefore the amorphous superconductors are strong coupling. The strong coupling character alters the temperature dependence of several superconducting parameters such as critical fields etc. The characteristic superconducting properties and superconducting fluctuations are discussed.     

Coulomb forces in the three-body problem with application to direct nuclear reactions

Faddeev equations are considered in the case of three charged particles interacting with both separable nuclear two-body interactions and also including Coulomb forces. Modified Faddeev equations with Coulomb Green's functions are introduced. The three-body amplitudes are given into pure Coulomb and distorted-Coulomb amplitudes. Introducing a decomposition in the angular momentum states, a set of three-body integral equations is obtained. The effect of pure coulomb amplitudes is studied in direct nuclear reactions and found to give a large contribution to the cross sections. The three-body integral equations obtained are applied for direct nuclear reactions. The angular distributions for¹²C(⁶Li,d)¹⁶O,¹⁶O(⁶Li,d)²⁰Ne, and¹²C(⁶Li,α)¹⁴N transfer reactions are calculated as well as for the⁶Li elastic scattering on¹²C. From the good agreement between the theoretically calculated and experimental data, better spectroscopic factors are extracted. The effect of including Coulomb forces in the three-body problem is found to improve the results by about 16.26%.     

Nuclear spin relaxation in disordered conductors

The relaxation timesT ₁ andT ₂ for nuclear spins interacting with the conduction electrons of disordered metals are calculated. An explicite expression for Warren's relaxation enhancement in terms of electron spectra is obtained, showing in particular that the proportionality ofT ₁ and the conductivity is a universal feature of high resistivity conductors. A formula for an inhomogeneous line width contribution due to disorder induced static Knight shift fluctuations is found. Two dimensional electron spin diffusion is shown to imply various logarithmic line width corrections.     

Orbital angular momentum of 3d impurities in metals

It is shown that 3d impurities often have a significant orbital moment due to the high symmetry of the crystalline electric field in typical metallic hosts. The EPR behavior which has been observed for such impurities is clarified and further predictions are made. The configurations of 3d impurities in noble metals are established: for example, Fe has 6 3d electrons andS=2. A spin-orbit splitting of about 0.02 eV is expected for Fe impurities, which may be observable by inelastic neutron scattering. The influence of orbital angular momentum on the Kondo effect is briefly discussed.     

探测二茂铁外价轨道(e,2e)反应中的扭曲波效应

利用第三代高效率电子动量谱仪,分别在600和1500 eV两种不同入射电子能量下获得了二茂铁(ferrocene)分子外价轨道的电离能谱和电子动量谱的相关实验结果.并利用非相对论与标量相对论密度泛函方法计算出了二茂铁的重叠型和交错型两种不同构象的理论动量谱.两种构象的外价轨道一一对应,理论电子动量谱基本一样.对二茂铁的外价轨道,在低动量区观测到了强烈的扭曲波效应,这与这些轨道主要由铁原子的3d轨道构成有关.通过相对论和非相对论计算结果的比较,表明相对论效应对于二茂铁的外轨道动量分布几乎没有影响. 关键词： 二茂铁分子 电子动量谱 相对论效应 扭曲波效应     

Revised model for 5d electrons in the heavy rare earth metals

A revised version of a recently published model for 5d electrons in the ferromagnetic state of the heavy rare earth metals is described. The model involves the broadening of local 5d states into overlapping bands with individual widthsW. In the new approach it is assumed that the local 5d wave functions lie at some point between those for atomic 4f _n 5d 6s ² configurations and those calculated for such configurations subject to the restriction that the 4f shell is kept with its moment rigidly fixed in some given direction. The admixture of non-aligned 4f states as in the atom lowers the local energy, but it also lowers the 5d bandwidth due to misfit of the 4f states which occur with and without the presence of a 5d electron. This second effect raises the energy of the low lying states in the band. The best local states are determined by minimising the total electronic energy of the system, using approximations which are most suitable for 4f shells with large excitation energies. Bandwidths are found by fitting the observed saturation magnetic moments in Gd and Tm, and satisfyW?1 eV.     

Contribution electronique au gradient de champ electrique sur une impurete de transition dans un environnement metallique anisotrope

The experimental data related to the electric field gradient at transition impurities either in hexagonal metals, or in cubic metals where the isotropy is perturbed by a next impurity, can be explained neither by the lattice contribution nor by the electronic contribution from the conduction band. A model is proposed here to investigate the electronic contribution arising from virtual bound 3d states on the impurity, by studying the local crystal field influence in a Friedel-Anderson model. It appears that at the 0°K limit, the localized electronic contribution to the EFG can be linearly related to the density n_d(?_F) of 3d states at the Fermi level. As a first approximation, this law is valid even at temperature different from 0°K so establishing a linear correlation between the EFG, the impurity resistivity and the amplitude of the charge perturbation around the impurity.     

Improved description of the Van der Waals interaction in physisorption

The attractive interaction between an atom and a metal surface is calculated, taking into account the d-electron contribution to the metal response, together with an atomic polarizability going beyond the dipole approximation. A numerical calculation is presented for helium on noble metals, giving a slightly deeper physiosorption well compared to the “standard” treatment.     

Surface energies of metals in both liquid and solid states

Although during the last years one has seen a number of systematic studies of the surface energies of metals, the aim and the scientific meaning of this research is to establish a simple and a straightforward theoretical model to calculate accurately the mechanical and the thermodynamic properties of metal surfaces due to their important application in materials processes and in the understanding of a wide range of surface phenomena. Through extensive theoretical calculations of the surface tension of most of the liquid metals, we found that the fraction of broken bonds in liquid metals (f) is constant which is equal to 0.287. Using our estimated f value, the surface tension (γ_m), surface energy (γ_SV), surface excess entropy (−dγ/dT), surface excess enthalpy (H_s), coefficient of thermal expansion (α_m and α_b), sound velocity (c_m) and its temperature coefficient (−dc/dT) have been calculated for more than sixty metals. The results of the calculated quantities agree well with available experimental data.     

Kinks and d-waves from phonons: The intermediate coupling story

I present results from an approach that extends the Eliashberg theory by systematic expansion in the vertex function; an essential extension at large phonon frequencies, even for weak coupling. In order to deal with computationally expensive double sums over momenta, a dynamical cluster approximation (DCA) approach is used to incorporate momentum dependence into the Eliashberg equations. First, I consider the effects of introducing partial momentum dependence on the standard Eliashberg theory using a quasi-local approximation; which I use to demonstrate that it is essential to include corrections beyond the standard theory when investigating d-wave states. Using the extended theory with vertex corrections, I compute electron and phonon spectral functions. A kink in the electronic dispersion is found in the normal state along the major symmetry directions, similar to that found in photo-emission from cuprates. The phonon spectral function shows that for weak coupling Wλ<ω₀, the dispersion for phonons has weak momentum dependence, with consequences for the theory of optical phonon mediated d-wave superconductivity, which is shown to be 2nd order in λ. In particular, examination of the order parameter vs. filling shows that vertex corrections lead to d-wave superconductivity mediated via simple optical phonons. I map out the order parameters in detail, showing that there is significant induced anisotropy in the superconducting pairing in quasi-2D systems.     

A simple model for calculating the height of Schottky barriers at contacts of transition metals with silicon carbide polytypes

The heights of Schottky barriers at contacts of Ag, Au, Pd, Pt, Ti, Ru, Ni, Cr, Al, Mg, and Mn metals with different polytypes of silicon carbide SiC are self-consistently calculated in the framework of a simple model proposed earlier. The results of calculations performed for contacts of transition metals with silicon carbide polytypes are in quite reasonable agreement with experimental data under the assumption that silicon vacancies with an energy E_d=E_V+2.1 eV make a dominant contribution to the Schottky barrier height.     

Anisotropy in the compton profile of copper

Directional Compton profiles of high statistical accuracy are measured by means of a 412 keV gamma-ray Compton spectrometer. The experimental anisotropies are in very satisfactory agreement with earlier measurements and there is good qualitative agreement between the experimental data and a recent band structure calculation. Quantitatively, however, the experimental anisotropy is significantly smaller than predicted by theory.A simple model calculation based on the Seitz approximation, in which higher order Fermi surface volumes all of spherical shape are taken into account in obtaining the momentum density, demonstrates that the major contribution to the Compton profile anisotropy in copper is due to the hybridization which has mixedd-electrons and nearly-free electrons in the top band. Any fine structure in the theoretical anisotropy due to the detailed shape of the Fermi surface cannot be resolved in the present experiment.The potential of analysing the electronic structure of transition metals in terms ofB(r), the Fourier transform of the momentum density, is discussed in detail. The major contribution to the anisotropy arises from localised peaks inB(r) centered on the sites of the translational lattice. Within the Seitz approximation it could be shown that these secondary maxima are caused by the presence of localisedd-electrons in the highest partly occupied band. In conclusion we anticipate that a proper treatment of electron correlation would produce a marked quantitative improvement in the agreement between the present experimental data and the Compton profiles obtained from current band structure calculations.     

Optical constants of copper in s-d model

A non-interacting s-d band model is used to evaluate ?₂(ω) in copper. The free electron approximation is used for electrons in s-band, while a simplified tight-binding scheme is used for the d-electrons. It is found that only d-bands with m = 0 contribute to optical transitions. The transition matrix elements are explicitly calculated. The calculated ?₂(ω) gives reasonable agreement with measured optical conductivity.     

Density functional calculation of Compton profiles of metals using phase-space approach

Spherically averaged electron momentum densities (EMD) in Al, V and Cu metals have been calculated by using density functional theory in the phase-space approach. Compton profiles, J(q) and expectation values 〈pⁿ〉 have been computed. These theoretical results show satisfactory agreement with the experimental data for Al, V and Cu.     

Angular momentum decomposition of k = 0 Bloch functions in group IV and zincblende crystals

The angular momentum contents of $\text{k}\text{= 0}$ Bloch functions for a number of group IV and zincblende crystals are examined using a pseudopotential approach. The large amplitudes for d and f character functions found even for valence electron wave functions are related to the overlap of p and s symmetry states on different atoms. In zincblende crystals the strength of the d and f components increases around cations and decreases around anions for the valence bands. The f-like component is appreciable for the Γ₁ conduction band particularly around a cation.