Na-Cs Alloys Research Articles

Excess entropy of mixing for binary square-well fluid in the mean spherical approximation: Application to liquid alkali-metal alloys

The expression for the entropy of binary square-well (SW) mixture is derived in the framework of the semi-analytical approach [J. Non-Cryst. Solids 353 (2007) 1798] for the mean spherical approximation. This expression is applied to calculate the concentration dependencies of the excess entropy of mixing for liquid Na-K and Na-Cs alloys at T=373K. It is shown that the SW model allows to achieve a better agreement with experiment than the hard-sphere model with the same values of hard-core parameters.

Analysis of van der waal equation near the critical point

We report detailed thermodynamic properties of Na in molten Na-Cs alloys obtained by using the simple theoretical model of Heterocordination. This model has been utilized to determine the free energy of mixing, concentration fluctuations in the long wavelength limit Scc (0), the Warren Crowley short-range order parameter, heat of mixing, entropy of mixing and diffusion coefficient. From these thermodynamic quantities we find that Na-Cs exhibits strong deviation from ideality at all the composition, therefore, it is truly a demixing liquid alloy. This conclusion was justified by the plot of Scc (0), which showed that its values are far greater than the ideal values. Qualitative agreement between the calculated and the experimental quantities for most of the thermodynamics properties was also obtained for the liquid alloys. These liquid alloys further exhibit a high asymmetry in their thermodynamics properties such as the Gibbs free energy and its diffusion.

The Role of Size Effects on Surface Properties

Abstract A theoretical model based on the grand partition function has been developed to investigate the role of size effects on surface tension and surface segregation of liquid binary alloys. The necessary relation, which connects the surface composition with surface tension through order potential, surface coordination and volume ratio, is obtained. This has been applied to liquid Na-Cs alloys. Likewise bulk properties, surface segregation and surface tension of Na-Cs liquid alloys are also affected appreciably by the size difference and are anomalous around C Na = 0.8.

The chemical dynamics of Na-in liquid 12-crown-4 solutions deduced from23Na nuclear spin relaxation rates

Solutions containing the sodium anion (Na-) were prepared by dissolving either NaK, NaRb or NaCs alloys in liquid 12-crown-4, 12C4. The 23Na nuclear spin-lattice (T 1n ) and spin-spin (T 2n ) relaxation times of the N.M.R. signal originating from Na- have been measured as a function of temperature, concentration and counter-cation K+, Rb+ or Cs+. The details of the inequality between T 1n and T 2n shown that the lifetime of Na- is limited by a two-step process. In the first step a strong complex of an alkali cation and 12C4 molecules dissociates to yield an uncomplexed cation to which one 3s electron from Na- is transferred in the second step. The 23Na nuclear spin relaxation data are combined with the results of previous EPR and pulse radiolysis experiments to deduce both the reactions generating Na- as well as further equilibria involving both complexed and uncomplexed cations, solvated electrons and a variety of paramagnetic species containing an electron and a cation.

Description ofScc(0) in Liquid NaCs Alloys using The Bhatia-Young Model of Mixtures

Abstract The Bhatia-Young expression for the free energy of mixing of a binary fluid has been used to study the concentration fluctuation in liquid NaCs alloys. This system has a strong tendency to homocoordination at sodium concentration near 0.8. In spite of this fact, good overall agreement with the experimental Scc (0) data is provided by assuming an ordering potential which is independent of concentration.

Inelastic neutron scattering studies of molten NaCs alloys

The authors have measured inelastic neutron scattering spectra of molten Na0.5Cs0.5 and Na0.85Cs0.15 alloys using the time-of-flight spectrometer IN6 at the Institut Laue-Langevin. The composition Na0.85Cs0.15 corresponds to the maximum value of Scc(Q to 0) indicating a tendency to phase separation. The width of the total dynamical structure factor ST(Q, omega ) at low Q is significantly larger for Na0.85Cs0.15 than for Na0.5Cs0.5. Quasi-dispersion curves derived from peak positions of the total longitudinal current power spectra show a single (overdamped) 'Na-like' mode for Na0.85Cs0.15 and both 'Na-like' and 'Cs-like' modes for Na0.5Cs0.5. Appropriate dynamical variables in this Q range for these alloys are therefore atom type. No evidence of propagating acoustic modes is found in the (Q, omega ) range studied.

Comment on the structures of the liquid–vapor interfaces of Na and Na–Cs alloys

We report the results of Monte Carlo simulations of the liquid–vapor interfaces of Na and of two Na–Cs alloys. The calculations are intended to test, on larger samples and using different geometries, the previously reported stratification of the liquid– vapor interface of a metal. Our results show that stratification of the liquid–vapor transition zone of a metal is independent of sample size and geometry. We also demonstrate how the segregation of one component of an alloy at the surface influences the structure of the liquid–vapor interface, and how the pair correlation function in the liquid–vapor interface of a free cluster depends on the radius of curvature of the cluster.

Concentration Fluctuations in Liquid Sodium-Caesium Alloys

The non-random two-liquid (NRTL) theory developed by Renon and Prausnitz has been used to calculate the concentration fluctuations in liquid Na-Cs alloys. The agreement with experiment is better than with other theories used previously.

Variational calculation of Helmholtz free energies with applications to simple liquid metals and alloys

The authors first demonstrate how their recently suggested calculation of the Helmholtz free energy, F, including the usual high-order pseudopotential perturbation corrections, can be applied to improve the theoretical F significantly so that the mean atomic volume can be determined theoretically with good accuracy, once T is given, for the NFE-like liquid metals and their binary alloys. They then proceed to calculate (i) the bulk modulus and the thermal expansion coefficient for the alkali, Mg and Al metals and the alkali binary alloys in their liquid states in a self-consistent manner and (ii) the free energy and heat of mixing for the Na-K and Na-Cs alloys for which the existing theoretical results are still not satisfactory. Reasonable success is achieved even for the Na-Cs alloys, in which the effects of the valence-electron charge transfer appear to be very important for the mixing properties.

Variational thermodynamic calculation for simple liquid metals and alkali alloys

The authors first propose an approach for treating a correction from the higher-order perturbative terms to the usual low-order pseudopotential perturbation calculation for the one-valence-electron states in a disordered metal. Then, the previously used energy-independent non-local model pseudopotential (EINMP) with this correction is applied along with the original EINMP to the variational thermodynamic calculation in the framework of a hard-sphere reference system for the alkalis in the liquid phase and for the K-Rb, Na-K and Na-Cs liquid alloys. The results obtained for (i) the hard-sphere diameter, sigma , (ii) the isothermal compressibility, chi T, and (iii) the excess entropy, Sexc, are carefully examined and discussed. It appears that in going from the pure alkalis to their binary alloys, (i) the change in sigma follows closely the concept of valence-electron charge transfer, introduced previously to interpret the corresponding concentration dependence of the electrical resistivities and (ii) the deviations of chi T and Sexc from ideality for the Na-K and Na-Cs alloys are largely due to the valence-electron charge transfer, which affects sigma in Sexc and also affects the contribution from the volume dependence of the screening to chi T.

The structure of the liquid-vapour interface of sodium-caesium alloys

The structure of the liquid-vapour interface of Na-Cs alloys has been determined from Monte-Carlo simulations.

Cs5pAbsorption Edge in Na-Cs Alloys

New results for Cs excitation spectra from Na-Cs alloys are presented and the effect of environment on the Cs 5p edge is discussed.Received 1 June 1982DOI:https://doi.org/10.1103/PhysRevLett.49.815©1982 American Physical Society

Chemical potentials and related thermodynamic properties of molten Na-Cs and Na-Bi alloys

Reports detailed data on the chemical potential of Na in molten Na-Bi and Na-Cs alloys. The measurements employed an electrochemical cell with beta alumina as the electrolyte. The concentration range was from 0 to 50 at.% Na in Bi and from 20 to 30 at.% Na in Cs. The temperature range was from the liquidus to 600 degrees C in the Bi system and from the liquidus to 150 degrees C in the Cs alloy. The latter measurements were extended very close to the eutectic at -29 degrees C. The Na-Bi system exhibits strong deviations from ideality at all but the most dilute Na concentrations while the Na-Cs system is very close to ideal throughout the range studied.

Heat of mixing of equiatomic alkali-alkali alloys

The Gibbs-Bogoliubov variational technique is used to study the internal energy and entropy of liquid alkali metals as well as heat of mixing and excess entropy of mixing for equiatomic NaK, KRb and NaCs alloys. A Heine-Abarenkov-type model potential has been considered with Hartree, Hubbard-Sham and Vashishta-Singwi exchange and correlation functions. It is found that alloying properties are sensitive to the form of the potential used, the dielectric screening function and the volume of mixing.

A self-consistent pseudopotential applied to transport coefficients of liquid binary alloys of alkali metals

The energy-independent model pseudopotential theory, developed and used previously for simple metals, is extended to the binary alloys of these simple metals and a self-consistent pseudopotential, which contains a detailed concentration dependence, is derived for the calculation of various properties of these alloys. This pseudopotential is applied within a low-order perturbation theory to calculate the form factors and transport coefficients for the K-Rb, Na-K and Na-Cs alloys in the liquid state. The calculated results show that a very significant fraction of the valence electrons is localised on the electronegative component in the liquid Na-Cs alloy, as compared with the other alloys considered, and, as a result, the electrical resistivity is very much greater for the liquid Na-Cs alloy than for the liquid Na-K and K-Rb alloys, as demonstrated in experiment. Finally, the applicability of the pseudopotential perturbation theory to the liquid alloys of simple metals is discussed.

Investigations on the structure of liquid Na-Cs alloys

The structure of liquid sodium-caesium alloys has been investigated for a large number of compositions covering the whole concentration range. X-ray as well as neutron diffraction techniques were employed. Special attention has been paid to the small-angle region of the diffraction pattern. The long-wavelength limit of the structure factor has been interpreted by applying a model proposed by Bhatia and March. Appreciable concentration fluctuations, indicating a tendency to phase separation, occur in the liquid. The size of the clusters was estimated using Guinier's model. For a few concentrations, molecular dynamics computer simulations have been carried out. Different models for evaluating the three partial structure factors have been considered.

Resistivity calculations for liquid Na-Cs and K-Cs alloy systems

The resistivities of liquid Na-Cs alloys are calculated as a function of the composition. A version of the Heine-Abarenkov model potential is used with special attention to three corrections: first, concentration-dependent core shifts are introduced, secondly, effective masses are taken into account and thirdly, many-electron effects are included by taking the Toigo and Woodruff dielectric function. For the partial structure factors of the alloys the solutions of the Percus-Yevick equations for a binary mixture of hard spheres are applied. The discrepancy between theoretical and experimental values is of the order of twenty percent.

Chemical potentials and fluctuations in liquid sodium-cesium alloys

Measurements of the chemical potential of Na in Na-Cs alloys are used to calculate the mean square composition fluctuations. Large fluctuations are found in the range 0.7<xNa<1.0 and suggest that a phase separation occurs there.