Liquid Alkali Metals Research Articles

Building blocks for electron density in free molecules and in condensed matter phases

AbstractWith the density functional theory as the underlying framework, the modeling of the ground‐state density p(r), using fragments or bonds as appropriate, is considered in both free molecules and in some condensed phases. Emphasis is placed on bringing the models into contact with both first‐principles quantum mechanics and available diffraction experiments. Clusters of alkali metals are specifically referred to, since cluster science affords a bridge between the quantum chemistry of small molecules and condensed phases. Finally, amorphous silicon and both solid and liquid alkali metals are considered. © 1994 John Wiley & Sons, Inc.

The structure and electronic density distribution in the liquid alkali metals

We present ab initio calculations for the electronic density distribution, and electron-ion and ion-ion correlation functions for the liquid alkali metals at conditions near the melting point. Our calculations are based on the use of the neutral pseudoatom method to derive the interionic pair potential and on the variational modified hypernetted chain integral equation theory of liquids. The resulting theory is free of adjustable parameters, using the atomic numbers as the only input data. The interionic pair potentials obtained follow the expected trends, whereas the theoretical structural functions show a good agreement with experiment.

Three-particle correlation function and structural theories of dense metallic liquids

The first member of the Born-Green-Yvon hierarchy relates the pair correlation function g(r) and the three-particle correlation function g 3 via an (assumed) pair potential φ(r). With the further assumption that the pair potential φ(r) and the potential of mean force separately possess their own Fourier transforms, one can derive the result that S(k)∼φ(k)/k B T = -⩳(k), where S(k) is the liquid structure factor, ∼φ(k) the Fourier transform of φ(r), while ⩳(k) can be written in terms of the Fourier components of g 3 and φ(r). It is then shown that the precise form of ⩳(k) can be calculated for the one-component plasma in two dimensions with a ln r interaction for one particular coupling strength using the analytical pair function of Jancovici. This exact result is compared with results from two approximate dense liquid structural theories. Finally, some results are also presented for the liquid alkali metals Na and K near their freezing points, invoking electron theory for their pair potentials and X-ray m...

Equation of State for Soft Reference System

Abstract We present an analytical equation of state for soft reference system such as liquid alkali metals. Thermodynamic properties—Excess entropy and diffusion coefficient have been calculated for liquid alkali metals using this equation of state. The calculated values of the self diffusion constant are compared with those corresponding to a hard-sphere fluid which shows that the softness plays a significant role in reducing diffusion.

Liquid alkali metals: microscopic dynamics and transport coefficients

The dynamical and transport properties of liquid Na, K, Rb and Cs near the melting point are investigated in a series of molecular dynamics simulations encompassing both single-particle and collective aspects. By a proper scaling procedure, all the results can be cast in a ‘universal’ from valid for all the considered elements. Further, the simulation data are found to support the predictions of the microscopic theories of liquid-state dynamics based on a combined kinetic and mode-coupling framework.

Dynamic properties of liquid metals

The static and dynamic properties of three liquid alkali metals were studied using molecular dynamics: lithium (at 470 K), rubidium (over a temperature range from 350 to 1873 K) and cesium (just above the melting point, at 308 K). The interatomic potential is based for Li on an OPW pseudopotential and for Rb and Cs on an empty-core pseudopotential. From the raw computer data, both single-particle and collective dynamic correlation functions were extracted. Interpretation of these correlation functions in terms of hydrodynamic, memory-function and (simple) mode-coupling models allows one to derive both thermodynamic and elastic properties. The dynamic structure factors have been compared for all three metals with recent neutron-scattering data. It is found that — except for the higher temperature states of Rb (i.e., at the onset of the metal-non-metal transition) — agreement between theory and experiment is good. Concerning elastic and thermodynamic properties, differences of 10–15% with respect to the experimental data are encountered.

Critical phenomena in metallic one-component liquids.

Proofs are given that the cohesive energy of liquid alkali metals tends to zero at the critical point. This leads to the conclusion that, in a case of alkali metals, the Coulomb energy of interaction at the critical density is very close in magnitude to the ionization potential of the isolated atoms.

The electronic structure of liquid heavy alkali metals from electron spectroscopy

The first investigation of the liquid alkali metals K, Rb and Cs by photoelectron spectroscopy has been performed, complementing previous studies of liquid Li and Na. The shallow bands of these metals enable in some cases their entire investigation by rather unconventional satellite lines of a noble gas discharge lamp. The trend found for the light alkali metals is continued, i.e., a systematic narrowing of the valence bandwidth with increasing atomic mass. The photoemission bandwidths appear to be significantly reduced compared with both the free electron model (FEM) and calculated photoelectron spectra based on ab initio calculations of the electronic structure. The triangular shape of the valence band spectra is reasonably reproduced by the calculated spectra indicating a distinct binding energy dependence of the partial photoelectric yields.

Density profile of liquid metal surface within the square-gradient approximation: density-functional approach

The density profile of a liquid metal surface is calculated from density-functional theory within the square-gradient approximation. The asymptotic solutions of the Euler-Lagrange equations, which determine ion and electron surface density profiles, are obtained analytically in the bulk liquid phase. Using these solutions as the trial functions for the variational calculation, the ion and electron density profiles of liquid alkali metals are determined simultaneously. Both ion and electron density profiles show oscillations similar to those predicted from reflectivity measurements and computer simulations.

Structure and dynamics of expanded liquid alkali metals

The main objective of the study of expanded liquid alkali metals like Rb and Cs is to find out how the structure, dynamics and effective interaction potential change during the expansion of the liquid metals from the melting point towards their liquid-vapour critical point. Near their critical point, the change from a liquid metal to a non-metal takes place, which implies that the interatomic forces must exhibit drastic changes when the critical point is approached. The static structure factor of expanded liquid alkali metals from the melting point up to their critical point have been measured and characteristic changes of the microscopic structure have been observed. In order to obtain additional information about dynamical properties, such as the self-diffusion coefficient, single particle and collective excitations, measurements of the dynamic structure factor of expanded liquid rubidium have been performed. In particular, these measurements provide information about the existence of collective phonon-like excitations in the expanded liquid metal and about the transition region from collective to more localized dynamical behaviour as the metal—non-metal transition is approached.

Structure Factor of Liquid Alkali Metals by the Integral Equation Theory

AbstractThe pair correlation function g(r) and the structure factor S(q) of liquid alkali metals are calculated using an integral equation developed by Madden and Rice, which is based on the soft core mean spherical approximation. It is found that this closure relation is particularly well adapted to the treatment of the Friedel oscillations of the pair potential, which are seen to be most influential in determining the peculiarities of S(q). A good agreement is obtained with experimental data for Na and Li.

Liquid alkali metals at the melting point: Structural and dynamical properties.

In this paper we report the results of a comprehensive simulation study of the structural and dynamical properties of liquid Na, K, Rb, and Cs near the melting point. An important consequence of this investigation is that both the equilibrium and the time-dependent correlations can be cast in a properly scaled form, which is to a very good approximation the same for all the alkali metals. In particular, for liquid Cs the simulation findings for the dynamic structure factor are found to be in excellent agreement with the inelastic-neutron-scattering data recently reported. Finally, the analysis is extended to the two main transport properties, the diffusion and the shear-viscosity coefficients. The simulation results compare satisfactorily with the actual experimental findings and confirm the validity of the simplified mode-coupling approaches recently proposed for these two quantities.

Processing, Properties and Applications of High-Temperature Niobium Alloys

AbstractNiobium alloys are used in a variety of high-temperature applications ranging from light bulbs to rocket engines and nuclear reactors. The unique physical and chemical properties of these alloys have often dictated that only niobium alloys could fulfill certain application requirements. Compared to other refractory metals, niobium alloys have low density and are very ductile even at cryogenic temperatures. Most niobium alloys are also very resistant to corrosion by acids and liquid alkali metals; however, oxidation resistance at high temperatures is usually catastrophic unless protective coatings are used.An overview of the commercial high-temperature alloys is presented. Some of the unique properties of these alloys, which require unusual processing methods and equipment, are highlighted. Important physical properties of these alloys are discussed with reference to specific applications. The needs and design restraints of these applications provide valuable insights for those developing other high-temperature materials.

Development of High-Strength-Fabricable Tantalum-Base Alloys

AbstractIn the 1950s, Ta-7.5%W and the Ta-2.5%W were the only tantalum alloys of commercial significance. An intensive alloy development effort occurred between 1958 and 1968 in response to Air Force and Navy aerospace needs for high-temperature, oxidation-resistant alloys for rocket and air-breathing engines and airframe applications. Compatibility with oxidation-resistant coatings, high-temperature short-time strength, fabricability and weldability were of prime importance. These programs led to the development of Ta-10w%W, Ta-30w%Nb-7.5w%V, T-111(Ta-8w%W-2w%Hf), and T-222(Ta-10w%W-2.5w%Hf-O.Olw%C). T-111, with its demonstrated compatibility with liquid alkali metals, and combination of strength, fabricability and weldability, was selected by NASA as the baseline reference alloy for space nuclear power systems studies. Significant quantities of T- 111 and T-222 were produced in the 1960s. Today, however, production is limited to unalloyed tantalum and the tantalum-tungsten binaries because of the demand of the chemical industry for materials with outstanding acid corrosion resistance. To again produce T-11 and T-222 on a commercial basis will require relearning by the refractory metal alloy producers. The current lack of experience in the refractory metal industry with these high temperature alloys will necessitate recovery of the expertise needed for the United States to effectively compete in this technology arena.

Unified Pair Potential for the Structure Factor of Liquid Alkali Metals

Abstract An analytical expression for the direct correlation function (dcf) is presented based on a unified pair potential to calculate the structure factor of soft liquid metals in the random phase approximation. A similar expression for the dcf as proposed by Colot et al. 7 can be derived as a particular case of our proposed expression. The results show good agreement between the structure factors of liquid alkali metals and experiment.

Microscopic dynamics in liquid alkali metals.

The structural and dynamical properties of liquid alkali metals near melting are investigated by realistic computer simulations, which support the idea that several important features follow from suitable scaling criteria. The data are found to be in excellent agreement with the recent theories of single-particle dynamics in simple liquids.

Thermodynamics and structure of liquid metals: a critical assessment of the charged-hard-sphere reference system

The authors calculate the Helmholtz free energies of the liquid alkali metals at various temperatures and those of several polyvalent metals (Mg, Cd, Al, In, Tl and Pb) near freezing, using the variational approach based on the Gibbs-Bogoliubov inequality in conjunction with the charged-hard-sphere reference fluid and with ab initio non-local pseudopotentials for the electron-ion interactions. The reference fluid introduces two variational parameters, i.e. the plasma coupling strength Gamma and the packing fraction eta , and is treated by a thermodynamically self-consistent approach which reduces to a highly accurate description of the one-component classical plasma for eta =0 and of the neutral-hard-sphere fluid for Gamma =0.

Evidence of an oscillatory density profile in liquid metal surfaces: an asymptotic solution

The asymptotic solution for the Euler-Lagrange equation which describes the surface density profile of liquid metals is derived. The liquid metal is modelled as consisting of a Fermi electron gas and classical one-component-plasma ions. These latter systems are coupled via a first-order electron-ion pseudopotential which is considered to be appropriate for characterizing liquid alkali metals. It is demonstrated here that the density profile can be classified as either a monotonic or an oscillatory type, but the numerical data show that all liquid alkali metals fall into the latter category.

Single-Particle and Collective Effects in Liquid Metals Near Freezing and in their Hot Solids

Abstract A 'jump' model of single-particle motion in a liquid is first used to calculate the frequency spectrum g(ω) of a liquid metal near freezing. In this treatment g(ω) is characterized by shear (η) and bulk viscosities, plus a time τ breaking the coherence of normal mode oscillations within a ‘cell’ or subvolume. The connection with earlier treatments of the relation between self-diffusion coefficient D and η at the melting temperature Tm of liquid metals is pointed out. The self motion, characterized by g(ω), is considered then in relation to the dynamical structure factor S(q ω) of a liquid metal such as Rb. In particular, theories of the dispersion relation ω q of the collective mode in liquid alkali metals and in their hot solids are re-examined, with -kBTc(q) used as an effective q space form of a pseudo-pair potential, c being the direct correlation function. This leads to a new proposal for the dispersion relation ω q , which in turn is related to the static structure factor S(q). The close re...

Molecular dynamics study of the structure of expanded liquid rubidium and caesium

The temperature/density dependences of the structure of expanded liquid metals rubidium and caesium have been calculated along the liquid-vapour coexistence curve using the molecular dynamics technique. In contrast to previous simulation studies, we adopt a full density dependent pairwise potential constructed from a highly reliable and accurate non-local model pseudopotential. For both liquid alkali metals, we find that our Fourier-transformed liquid structure factors generally agree quite well with the neutron diffraction data for the wave number ∼0.6 Å −1 and above, whereas for thermodynamic states near the critical point and for wave numbers smaller than ∼0.6 Å −1 we observe large discrepancies which we are unable to account for adequately in the present work. Nevertheless, by examining and comparing the variation of our calculated pair potential as well as the liquid structure factor with temperature/density, our present results provide further information on the validity of nearly-free-electron theory notably for thermodynamic states approaching the critical regime. Specifically, we conjecture break-down temperatures possibly occurring at T ≈ 1700 K and T ≈ 1600 K for liquid rubidium and caesium metals, respectively.