Simplified SCF calculations on the diatomic alkali metal molecules

An account is given of a new formalism for calculating energy levels in molecules using techniques that derive from the band theory of metals. After showing how the molecular potential may be transformed into a cellular potential we define the basis set of muffin-tin orbitals and discuss some of their properties. The relationship between the scattered wave formulation of Johnson, which is restricted to muffin-tin potentials, and our more general approach based on the use of a linear combination of muffin-tin orbitals (L.C.M.T.O.) is explicitly indicated. We then show how the properties of the muffin-tin orbitals, together with the technique of cellular integration, give rise to a hamiltonian matrix. This matrix is as general as, but simpler than that obtained by the use of atomic orbitals, and it is linear in energy and therefore computationally faster than the secular matrix of the scattered wave method.     

Shear deformation potentials in metals

The differential approach, based on the Green's function method and the muffin-tin approximation for the crystal potential, which was proposed recently as a convenient method of obtaining accurate deformation potentials in metals is discussed briefly here with particular emphasis on the relation of the method to stress-modulation experiments. Specific results are presented for the deformation potentials under tetragonal and trigonal shears of some of the states of Cu, Ag, and Au at symmetry points in the Brillouin zone, and comparison is made with available experimental data.     

液态金属和玻璃的若干研究进展

概述了液态金属和玻璃的的结构和性质研究的一些近期发展，如液态金属的原子间相互作用势和结构的普适性描述，二元液态合金的物理性质的计算和金属－－非金属转变的解释，以及玻璃的结构、熔化和弛豫的微观描述。     

Structure of liquid metals

A brief review is given of the structure of liquid metals. The structure is examined from the viewpoints of how the pair potential in metals gives rise to various structural properties and how the structure of liquid metals effects other properties. Use is made of the Paskin and Rahman molecular dynamic calculations on liquid sodium to illustrate the insensitive nature of the structure to details in the pair potential. Diffraction data are used to demonstrate that a law of corresponding states exists, at the melting point, for simple liquids, metals and insulators. The molecular dynamic calculations of sodium are also used to demonstrate that some time dependent correlation functions may be more sensitive to the form of the pair potential than the structure factor is to the potential. Some analysis is also made of the role of structure in the electrical resistivity. It is noted that more accurate structure data are needed to answer some of the questions raised in recent attempts to use the structure to extract pair potentials and in detailed correlations of resistivity and structure data.     

Influence of interatomic repulsion on the structure of liquids at melting

Radial distribution functions and liquid structure factors for fluids of particles interacting through 1/rⁿ repulsive potentials are computed ‘exactly’ and systematically compared at crystallization for several values of n ranging between the two extremes of hard spheres (n = ∞) and Coulomb forces (n = 1). Striking similarities are pointed out in the large r behaviour (beyond the first peak) of the various radial distribution functions, and in the small k behaviour (including the first peak) of the various structure factors. Some information about the steepness of the repulsive potential in liquid rare gases and in liquid alkalis is gained from a comparison of the damping of successive peaks of the structure factors with experimental data.     

Many-particle-effects in the theory of the extended X-ray absorption fine structure

The Lee-Beni-procedure for the calculation of the extended X-ray absorption fine structure (EXAFS) is extended so as to include the effects of the electronic charge density outside the localized muffin-tin potentials. In our scheme EXAFS is caused by back-scattering of an elementary excitation of a homogeneous electron gas by localized energy dependent many-particle muffin-tin potentials. The difference between the two schemes is negligible at large k's, as expected from physical grounds. However, at small and intermediate k-values the difference is quite large. The effect of the outer electrons as compared to the Lee-Beni-model is twofold. First, they renormalize the scattered electron in the usual way. Second, they are missing within the scattering muffin-tins. Hence, we avoid to count some of the electrons twice. Results are presented for Cu as an example.     

Electrical resistivity of alkali metals: Inflation–deflation effect of Fermi surface

The electrical resistivity of liquid alkali metals was calculated using the extended Ziman formula. The possible role of Fermi surface (FS) inflation–deflation (ID) was examined. The calculations reveal that replacing the sharp free electron FS by the expanded (respectively, contracted) one substantially improves the results. This was achieved directly by considering a FS correction factor of the Fermi radius and indirectly by a shift in the muffin-tin zero (MTZ) of the potential from its initial values. Consequently, a correlation between the shift of the MTZ of the potential and the FS factor parameter is revealed. The role of this correlation might contribute to a better understanding of the electron transport properties of other liquid metals and their alloys.     

Analysis of semi-empirical interatomic potentials appropriate for simulation of crystalline and liquid Al and Cu

We investigate the application of embedded atom method (EAM) interatomic potentials in the study of crystallization kinetics from deeply undercooled melts, focusing on the fcc metals Al and Cu. For this application, it is important that the EAM potential accurately reproduces melting properties and liquid structure, in addition to the crystalline properties most commonly fit in its development. To test the accuracy of previously published EAM potentials and to guide the development of new potential in this work, first-principles calculations have been performed and new experimental measurements of the Al and Cu liquid structure factors have been undertaken by X-ray diffraction. We demonstrate that the previously published EAM potentials predict a liquid structure that is too strongly ordered relative to measured diffraction data. We develop new EAM potentials for Al and Cu to improve the agreement with the first-principles and measured liquid diffraction data. Furthermore, we calculate liquid-phase diffusivities and find that this quantity correlates well with the liquid structure. Finally, we perform molecular dynamics simulations of crystal nucleation from the melt during quenching at constant cooling rate. We find that EAM potentials, which predict the same zero-temperature crystal properties but different liquid structures, can lead to quite different crystallization kinetics. More interestingly, we find that two potentials predicting very similar equilibrium solid and liquid properties can still produce very different crystallization kinetics under far-from-equilibrium conditions characteristic of the rapid quenching simulations employed here.     

Temperature dependence of transport coefficients in liquid and amorphous metals

We apply the muffin-tin effective medium approximation to calculate the temperature dependence of the resistivity and thermopower of amorphous and liquid metals. The results show unambiguously that a large resistivity is accompanied by a negative temperature coefficient, in agreement with the experimental situation. This behavior is shown to result from a pseudo-gap which opens in the one-particle spectrum due to strong scattering at the quasi zone boundary and which tends to close under an increase in temperature. In turn the thermopower is found to have non-trivial density and temperature dependences.     

Self-consistent calculations for the electronic structure of a vacancy in copper. A solution of the embedding problem

The charge density and the local density of states for a vacancy in Cu and for the first shell of Cu neighbours are calculated by the KKR-Green's function technique. The muffin-tin potentials for the vacancy and the neighbour shell atoms are determined self-consistently in the local density approximation of density functional theory. By the use of the proper host Green's function the embedding of this cluster of 13 perturbed muffin-tins into the infinite array of bulk Cu muffin-tin potentials is described rigorously, thus representing a solution of the embedding problem. The calculations demonstrate a rather large charge transfer of 1.1 electrons from the first neighbour shell to the vacancy.     

Temperature-dependence of phonons,solid state properties and liquid structure of noble metals: A comparison of pair-potentials

Two groups of effective pair-potentials are studied from the viewpoint of their suitability in being able to describe solid state properties and liquid state structure of noble metals Cu, Ag and Au over a wide temperature range. Since the effective pair-potentials are usually empirical in nature, with parameters obtained by fitting to some reference state properties, the objective of the present study is to determine whether a particular parametrization scheme has any definite advantage over another. We consider Morse potentials with parameters determined by equilibrium lattice parameter, cohesive/sublimation energies as well as bulk modulus values of the solid at low/room temperatures. The other group of potentials considered is Erkoç potentials, where the parameters were determined first by studying dimers and further modified using bulk stability condition and bulk cohesive energy values. The potentials were then used to study the energetics of microclusters containing 3–7 atoms. Quasiharmonic results for the solid obtained at different temperatures and Monte Carlo simulation for the liquid state show that phonon spectra, thermal expansion, temperature-dependence of specific heats and liquid structure are much better described by the latter group. The first group of potentials may have an advantage in reproducing the temperature-dependence of elastic constants and bulk moduli, since they are based on room temperature values of these properties, which show only weak temperature-dependence in general for all metals. It is argued that potentials based on parameters fitted to the properties at a single volume are less versatile in capturing the temperature-dependence of various thermodynamic properties over a wide range. Potentials capable of reproducing the energetics of clusters of different co-ordination numbers and volumes per atom may fare better in this regard.     

Universality in the effective pair interaction ofd-shell metals — Compressibility and vacancy formation energy of 3d-liquid metals

Like liquid alkali metalsd-shell liquid metals show scaling behaviour in structure and interaction potentials. A realistic interaction potential model, properly parametrized can reasonably describe the universality in the isothermal compressibility and vacancy formation energy of 3d-liquid metals in electron ion plasma model.     

Polarization effects in liquid metals and charge stabilized colloidal dispersions

The induced polarization contributions to the effective interionic potentials are derived for liquid metals, liquid alloys and charge stabilized colloidal dispersions. These contributions have been obtained within a perturbative scheme that includes up to three-body terms. The formalism is illustrated by calculating the static structure factor S(k) of liquid Ga near melting. It is found that the main effects due to the induced polarization in S(k) are first lowering the height of the principal diffraction peak, and second sharpening the subsidiary peak present in liquid Ga.     

The influence of pair potentials on the structure of polyvalent liquid metals

The structure factors of some polyvalent liquid metals show a shoulder on their first peak. We explain these shoulders on the basis of ionic pair potentials : a shoulder is expected near the wave vector 2k_F, the wave length of the oscillations in the metallic pair potentials. To show this quantitatively, we used the “optimized random phase approximation” of Andersen et al.     

Ionization potentials and bond lengths for CO,N2, and F2 using the SCF-Xα-SW method: A study of the effect of overlapping spheres

Using a simple, arbitrary, but fixed procedure for the choice of sphere sizes in the overlapping sphere version of the SCF-Xα-SW method, results for the ionization potentials of CO, N₂, F₂, and H₂O are in considerably better agreement with experiment than those of the muffin-tin version. The agreement is as good as those of the SCF-Hartree-Fock, Discrete Variational-Xα, and LCAO-Xα methods. For the first time the overlapping sphere modification has been used to calculate binding curves and results in equilibrium bond lengths for CO, N₂, and F₂ all within 0·3 a ₀ (0·16 Å) of the experimental values, a dramatic improvement over the muffin-tin results. The variation of the calculated ionization potentials under a moderate change in the amount of sphere overlap is found to be rather small, being of the order of the differences between the DV-Xα and LCAO-Xα methods, both of which completely avoid the muffin-tin approximation.     

Unified study and transport properties of simple metals

The resistivity, thermoelectric power at the melting points and temperature variation of resistivity of the liquid alkali metals are studied with local Heine-Abarenkov and the modified Ashcroft pseudopotentials. The parameters of the model potentials are obtained from a unified study of the static and dynamic properties of the metals. The effect of different dielectric function and structure factor on the transport properties is discussed. It is shown that the simple modified Ashcroft pseudopotential reproduces the result fairly well except for Li and Cs.     

Electronic states in early-late transition metal glasses: Application to Cu0.60Zr0.40

The electronic properties of amorphous Cu_0.60Zr_0.40 are studied within the two component muffin-tin EMA framework. We argue that an understanding of the photoemission spectrum of this system requires that short range order effects be incorporated in both the construction of the atomic potentials and the calculation of the average spectrum. However, we show that the essential features of the density of states can be understood on the basis of simpler calculations in which the glass is modeled as either a substitutional alloy or a liquid with just a single pair distribution function.     

Wetting properties of rare gases on weak substrates

Since the original prediction that liquid He does not wet Cs at low temperatures and the soon after experimental observation of a wetting transition on this system, noble gases on alkalis have become model systems for the study of wetting transitions and of their accompanying line of prewetting transitions off coexistence. Here we review very briefly the theory of wetting and prewetting and discuss some results on the properties of rare gases adsorbed on alkali surfaces obtained with the use of the density functional theory and of accurate adsorbate-substrate potentials.