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.     

Temperature dependent atomic transport properties of liquid Sn

A simple analytical model for atomic motion of Tankeshwar et al. [J. Phys.: Condens. Matter 3, 3173 (1991)] is used to obtain velocity autocorrelation function (VACF) with the inter-atomic potential and the pair correlation function as required inputs for liquid Sn. For the electron-ion interaction the modified empty-core potential is used, which represents the orthogonalisation effect due to s-core states in such sp-bonded metals. Temperature dependence of structure factor is considered through temperature dependent potential parameter in the pair potential. The coherent behaviour of liquid Sn in terms of the dynamic structure factor employing viscoelastic theory has also been studied. Intrinsic temperature effect has been studied through damping term\hbox{${\exp}( {-\frac{{\pi k}_{{B}} {T}}{{2k}_{{F}} }{r}} )$} exp (?πkBT2kFr)in the pair potential. The predicted results for VACF, cosine power spectrum, mean square displacement, diffusion and viscosity coefficients have been compared with recent available data, and a good agreement has been achieved.     

Effects of electron correlations,dynamical screening and plasmon excitations on muon diffusion in metals

An investigation is made of the effects of electron-electron interaction on muon diffusion in metals. It is shown that electron-electron correlation plays an important role in the motion of muons. The equation-of-motion method is used to calculate the correlation function. It is shown that electron correlations effectively reduce the muon hopping rate at low temperatures. It is also shown that the effect of dynamic screening increases the hopping rate. We found that due to plasmon excitation, the hopping rate is reduced by a factor which can be as larger as one to two orders of magnitude.     

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.     

Structure of molten silicon and germanium by X-ray diffraction

X-ray diffraction patterns have been obtained from molten silicon and germanium near the melting point. In both cases the structure factor was a low first peak maximum with a small hump on its high angle side in contrast with those of simple molten metals such as sodium and aluminum. It was also found that the pair correlation functions for these molten elements are characterized by a low peak maximum which follows the usual first peak maximum corresponding to the nearest neighbour distance. The electrical resistivity and thermoelectric power have been calculated on the Ziman theory using thet-matrix of muffin-tin potential based on the structural data observed in this work. Good agreement was found in most cases.     

Ergodic to nonergodic transition in liquids with a local order: the case of m-toluidine

The dynamic structure factor of m-toluidine has been measured by inelastic x-ray scattering in the mesoscopic Q range between 1 and 10 nm(-1), where a prepeak is revealed in the static structure factor resulting from the existence of hydrogen bonded, nanometer size clusters. Evidence is given of (i) a square-root cusp in the nonergodicity factor and of (ii) critical nonergodicity parameters which oscillate in phase with the static structure factor. These results demonstrate that local order in a liquid can coexist with the signatures of the ergodic to nonergodic transition predicted by the mode coupling theory for simple, dense liquids.     

Effect of the gaseous medium in the process of rolling on the microhardness of aluminum and iron

The load dependence of the microhardness of polycrystalline aluminum and iron specimens produced by rolling in a nitrogen, helium, or air medium has been investigated. It has been found that nitrogen and helium have different effects on the microhardness of these metals in the low-load range. This difference is associated with the specific features in the intensity of dynamic penetration of nitrogen and helium into the surface layer of aluminum and iron, which depends on the initial defect crystal structure of the metals, as well as on the type of bonding of helium atoms and nitrogen molecules with metal atoms. It has been shown that the effect of the gaseous medium of the rolling on the microhardness manifests itself only in a very thin surface layer of metal specimens, where the microhardness exhibits a size effect, and an increase in the microhardness indentation depth remains unchanged with an increase in the load and does not depend on the gaseous medium of the prerolling of the specimens.     

Calculation of the contribution of conduction electrons to the atomic factors of simple metals

An expression for the Fourier transform of the screening electron density of simple metals has been derived using smooth nonlocal model potentials of simple metals. The expression describes the contribution of conduction electrons to the atomic factors of X-ray scattering in simple metals. Aluminum was used as an example for numerical checking. Comparison with the results of similar calculations for the form factor of the Krasko-Gurskii model potential shows the importance of taking the nonlocality of the model potential into account.     

New pair potentials from an improved born-green integral equation: Application to liquid metals

With an improvement of the superposition approximation in the Born-Green integral equation recently proposed an attempt is made to extract new effective pair potentials from structure factors of simple liquids. The improvement is obtained by taking the first three terms of a hard-core density expansion of the triplet correlation function. The method of calculation is based on the solution of the integral equation in k-space. It is shown that the resulting potential of the improved Born-Green equation from a hard-core structure factor actually is hard-core like contrary to the Born-Green result. From measured structure factors of some simple liquid metals (Na-100°C, Al-670°C and Ni-1600°C) pair potentials are determined. With this application a significant improvement over the Born-Green theory can be achieved. In comparison to the old discrepancy between the Born-Green equation and theoretical models the results agree very well with theoretical calculations in the repulsive range of the potential.     

The use of positive muons in metal physics

The present status of work in metal physics by the new method of “muon spin rotation” is reviewed. This spectroscopy is based on the spin interactions of positive or negative muons and resembles NMR as far as the interpretation of interactions in metals is concerned. The positive muon behaves in several respects as a light isotope of hydrogen in metals. Local properties like site symmetry, local magnetic field, dynamic effects from surrounding spins as well as effects from the diffusion of the particle itself can be measured with high sensitivity.A brief review of the technical aspects is given. The problems of diffusion of light positive particles in metals are discussed, with regard to specific mechanisms at low temperatures, trapping of muons by impurities, etc. The local electronic structure around this kind of impurity in normal metals as well as ferromagnets has been subject to a large nnumber of studies. Other applications include the interaction of muons with other kinds of defects, the study of metal hydrides and measurements on the dynamics of spin glasses.     

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.     

Anharmonic Excitations,Time Correlations and Electric Conductivity

We study the influence of anharmonic mechanical excitations of a classical ionic lattice on its electric properties. First, to illustrate salient features, we investigate a simple model, an one‐dimensional (1D) system consisting of ten semiclassical electrons embedded in a lattice or a ring with ten ions interacting with exponentially repulsive interactions. The lattice is embedded in a thermal bath. The behavior of the velocity autocorrelation function and the dynamic structure factor of the system are analyzed. We show that in this model the nonlinear excitations lead to long lasting time correlations and, correspondingly, to an increase of the conductivity in a narrow temperature region, where the excitations are supersonic soliton‐like. In the second part we consider the quantum statistics of general ion‐electron systems with arbitrary dimension and express ‐ following linear response transport theory ‐ the quantum‐mechanical conductivity by means of equilibrium time correlation functions. Within the relaxation time approach an expression for the effective collision frequency is derived in Born approximation, which takes into account quantum effects and dynamic effects of the ion motion through the dynamic structure factor of the lattice and the quantum dynamics of the electrons. An evaluation of the influenec of solitons predicts for 1D‐lattices a conductivity increase in the temperature region where most thermal solitons are excited, similar as shown in the classical Drude‐Lorentz‐Kubo framework. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the use of the one-component-plasma model for the structure factors of liquid metals

It is demonstrated that the perturbative correction, appearing in the structure factor of the simple liquid metals in the one-component-plasma model, is important and may have to be calculated more rigorously than by the usual semi-non-local or local pseudopotential theory.     

Effect of correlated disorder on the temperature of unconventional cooper pairing: 3He in aerogel

It has been shown by the example of ³He in aerogel that the correlation in the position of impurities may have a considerable effect on the transition temperature T _c of a Fermi fluid to an unconventional superfluid or superconducting state if the correlation radius of the system of impurities exceeds the correlation length ξ₀ of the emerging superfluid phase. A decrease in T _c of ³He in aerogel has been expressed in terms of the structure factor of aerogel. Taking into account the fractal structure of aerogel provides a simple formula that satisfactorily describes the observed decrease in T _c.     

Structure and effective interionic potential of liquid palladium,platinum and zirconium

The structure of palladium, platinum and zirconium in the liquid state has been studied by X-ray diffraction near the melting point. In all the cases the structure factor looks similar to those of liquid metals such as copper and silver in contrast to mercury, tin and bismuth which show the small hump or the large asymmetry of the first peak maximum in the structure factor. The atomic radial distribution function was evaluated from the structure factor and the interatomic distance and coordination number of each liquid metal were also obtained. The effective interionic potential was derived from the structural data obtained in this work using the Born-Green equation and applied to the estimation of self-diffusion coefficient and viscosity coefficient in these liquid metals by the kinetic theory of fluids.     

Theory of collective excitations in simple liquids

We present a parameter-free theory of the collective excitations in simple liquids such as liquid metals or rare gases. The theory is based on the mode-coupling theory (MCT), which has been previously applied successfully for explaining the liquid-to glass transition. The only input is the liquid structure factor. We achieve good agreement both for the liquid dispersion (maximum of the longitudinal current spectrum) and width (damping) with experimental findings. The time-dependent memory function predicted by MCT has a two-step exponential decay as previously found in computer simulations. Furthermore MCT predicts a scaling of the liquid dispersion with the effective hard-sphere diameter of the materials. This scaling is obeyed by the available experimental data.