Liquid Rb Research Articles

Collective modes in simple liquids: A semiempirical model.

A semiempirical model for the dynamical structure factor, S(Q,\ensuremath{\omega}), in a simple liquid is presented. This is a modification of the Lorentzian form predicted by linear hydrodynamics that enable it to be extended into the viscoelastic region while still retaining finite moments. The model leads directly to a criterion for the existence of a sound mode which includes the possibility of soft modes and dispersion gaps. By a suitable choice of parameters the experimental results for liquid Ar and molten Rb may be explained.

Effective Interatomic Pair-Potentials in Liquid Alkali Metals via the RPA and MC Simulation Methods

Abstract A useful method which is based on the RPA and Monte Carlo computer simulation is presented for calculating an effective interatomic pair-potential from an observed structure factor. The method is applied to liquid Na, K, Rb and Cs and gives reliable pair-potentials compatible with the predictions of the pseudopotential theory. The lack of elaborate scattering experiments, however, seriously limits the use of the present method in extracting a reliable effective pair-potential.

Temperature dependence of the quadrupolar relaxation rate in liquid metals

A calculation of the quadrupolar relaxation rate, R Q, in a liquid Rb model is reported and shown to be consistent with experimental estimates. When the electric field gradient function in a metal is short-ranged the theory predicts that the variation of R Q( T) along an isochore is somewhat slower than T −1 2 .

Magnetic Susceptibility and Optical Absorption Studies of Rb – Au Alloys

AbstractThe magnetic susceptibility of liquid Rb – Au alloys and the optical absorption of the solid and liquid equimolar alloy RbAu have been measured up to temperatures of 1000°C. The optical gap of solid RbAu shows Urbach type behaviour with E0 = 2.75 ± 0.1 eV. On melting it is reduced by about 1 eV: Eg(510°C) = 1.35 ± 0.1 eV. The magnetic susceptibility exhibits a strong diamagnetic minimum near the equiatomic composition yielding further evidence that liquid RbAu is semiconducting and predominantly ionic in bonding. The observed deviation from the expected susceptibility value for purely ionic RbAu and the high optical absorption in the near infrared suggest that localized paramagnetic electron states exist in the ionic liquid, possibly in equilibrium with free carriers. Like Cs – Au the alkali metal‐gold system Rb – Au thus closely resembles the alkali metal‐halogen systems the major differences arising from the reduced charge transfer and chemical ordering in these alloys.

Thermodynamically Consistent Theory of Classical Liquid Structure and Inverse Problem of Extracting Pair Potential

Abstract The direct correlation function c(r) is divided into two parts, following the work of Kumar et al. One part, c(r) potential [tbnd] c p(r), contributes the entire compressibility and decays at large r as-φ(r)/KBT, with φ(r) the density independent pair potential. The definition of c p(r) as–φ(r)/KBT{(1/6ρr 2)∂2/∂ρ∂r[ρ2 r 3 g(r)]{ is motivated by the condition of thermodynamic consistency, and for a hard core liquid leads to c p(r) small inside an atomic diameter. The second part c(r) cooperative [tbnd] cc(r) is not expressible simply in terms of φ(r) and the pair function g(r), and is expected to differ in range between condensed rare gases and liquid metals say. Also, for a given liquid like argon, cc(r) can be shorter or longer range than c p(r) depending whether one is near the triple point, or near critical conditions. At the critical point, or alternatively in the presence of a collective mode as in liquid Rb, the long-range behaviour of cc(r) can be dominated by cooperative effects. To illus...

Experimental results for liquid alkali-group IV alloys

Neutron diffraction experiments and measurements of the Knight shift and the electrical resistivity are presented for the liquid systems LiSn, NaPb, NaSn, LiGe, KPb and RbPb. They provide strong evidence for compound formation. There are indications for the existence of anion-clusters in all of these systems, except in LiSn.

On the accuracy of the liquid theory approximate methods for the description of liquid metal thermodynamics

The accuracy of the various liquid theory methods for calculating the thermodynamic properties of liquid metals is investigated. The calculations have been made for liquid Na, Rb, Mg and Al over wide ranges of temperature T and density n using (i) the variational method and hard-sphere reference system (the HSV method), (ii) the Barker-Henderson (BH) method, (iii) the Weeks-Chandler-Andersen (WCA) method and (iv) the expressions for energy and pressure in terms of the radial distribution function found in the Percus-Yevick approximation (the PYEP method). The results of the calculations are compared with each other and with experiment. The pseudopotential model is used which describes all the atomic properties of the alkali metals to a high precision, those of Mg rather well, and of Al fairly well. It has been shown that the simple HSV approximation suitable for a semi-quantitative description of the liquid metal properties is insufficient for quantitative calculations of differential characteristics, such as melting temperatures, entropies of fusion, entropies of liquid alloy mixing, etc. The PYEP and BH methods allow the authors to calculate some thermodynamic potentials rather precisely but the computational difficulties prevent them from being used for calculating other thermodynamic properties. The WCA method has been found to combine high accuracy with sufficient simplicity of calculations and seems, therefore, to be the most promising one for quantitative calculations of liquid metal thermodynamics. They also discuss the problems of applicability of the methods considered at various T and n (particularly in the vicinity of the critical point), of the dependence of their accuracy on the metal valency and the sensitivity of the results to the type of pseudopotential model used.

Magnetic susceptibilities of liquid binary alloys

A description of the concentration dependence of the magnetic susceptibilities of a number of liquid binary alloys of simple metals is effected in three stages. First, a previous pseudopotential formalism is extended to enable the calculation of the conduction electron diamagnetic susceptibilities in the pure liquid metals, Li, Na, K, Rb, Cs, In and Pb. These results are then combined with much earlier calculated values of the diamagnetic susceptibilities of the core electrons and with observed values, existing in the literature, of the total magnetic susceptibilities to infer the conduction electron paramagnetic susceptibilities of the above pure liquid metals. Second, the expressions for the two diamagnetic contributions are modified permitting the determination of their concentration dependence in a number of nearly-free-electron (NFE) like liquid binary alloys. The Landau theory of a Fermi liquid is used to infer the concentration dependence of the paramagnetic contribution. Third, Li-Pb, which is not NFE like over the entire concentration range is treated separately as a special but closely related case. The observed results for the concentration dependence of the total magnetic susceptibility are favourably reproduced, both for those alloy systems exhibiting smooth variations and for those with large variations.

Structure analysis of liquid Rb and Cs

The observed correlation functions $g(r)$ on liquid Rb and Cs have been compared with theoretical correlation functions which were calculated by means of three-dimensional convolution polynoms. These are given in terms of paracrystalline distorted body-centered tetragonal lattices with $\frac{c}{a}=1.23$. The lattice types of fcc and bcc can be excluded. The present method provides detailed statistical information about the short-range atomic arrangement in the liquid state. From the macroscopic density of the liquids and the nearest-neighbor average distance it can be concluded that about 4-7% of the atoms lie on interstices.

Anomalously Small Knight Shift and Relaxation Rate in the Nonalloying System: Isolated Yttrium Ions in Liquid Rubidium

Time-differential and stroboscopic measurements of the perturbed angular $\ensuremath{\gamma}$-ray distribution for isolated $^{88}\mathrm{Y}$ ions in liquid Sr and Rb are reported. A drastic drop in the Knight shift and the nuclear relaxation rate is observed as the Sr matrix is replaced by Rb. This implies an almost vanishing density of $5s$ states on the Y ion in Rb at the Fermi level. A volume expansion of the Y Wigner-Seitz cell is suggested as the mechanism causing this anomalous behavior in $\mathrm{Rb}$ Y.

Measurement of the transport properties of liquid Rb using automated equipment

Equipment to perform low-level thermocouple thermometry using a computer, a digital voltmeter, and very low thermal offset switching has been used to measure the thermal conductivity, electrical resistivity, and thermoelectric power of Rb from its melting point, near 313 K, to 650 K. The data obtained, which are accurate to the percent level, may be explained by combining the effect of the elastic scattering of electrons by ionic density fluctuations, and the effect of electron–electron scattering.

Sound Velocities and Entropies of Non-Simple Liquid Metals Based on the Percus-Yevick Phonon Description

Abstract Recently, Yokoyama, Ohkoshi and Young1 (hereafter I) reported calculations of ‘phonon dispersion curves’ and sound velocities of liquid Na, K, Rb and Pb by invoking a perturbation theory based on a zeroth order system of independent density fluctuations having wave indices between 0 and k 0 = 31/3 kD . They suggested that sound velocities of liquid metals can be well predicted by the phonon perturbation approach, the details of the temperature dependence of the structure factor at constant volume being important for this. With the increased availability of structure-factor data within the phonon region in k space,2 it has now become possible to extend the calculations of I to a variety of non-simple liquid metals for evaluation of sound velocities. The aim of this short communication is to present such results which suggest the efficacy of the phonon method in this respect. The overall success of the calculations lend further credibility to the form of {∂ ln a(k/k 0)/∂ ln T}Ω proposed in I. This ...

Small Angle Scattering from Liquids: Van der Waals Forces in Argon and Collective Mode in Na

Abstract Because of discrepancies between recent estimates of van der Waals forces in liquid metals, we have examined available experimental data on the small angle scattering of X-rays from liquid Na, and have compared it with neutron scattering data on liquid argon. In the latter case, it follows from first principles that the liquid structure factor S(k) has the small k expansion Therefore we have plotted (S(k)–S(0))/k 2 from available data for both Na and Ar, and they are immediately found to be qualitatively different. For a given state of argon, a 2 and a 3 can be extracted and are quite consistent with theoretical estimates. For Na, the small angle scattering does not have the form (i) and it is demonstrated that there is a term proportional to k at small k. This means that one of the leading terms determining the approach of the radial distribution function g(r) to its asymptotic value of unity at large r is proportional to r −4. It is shown that this behaviour arises from the dispersion of a collective mode, in which the density fluctuations oscillate independently with a well defined dispersion relation ω(k). This relation has the form, with vs the velocity of sound, We have estimated the dispersion for Na, K and Rb from an approximate theory and have compared it with the experimentally observed collective mode for liquid Rb. Finally, after extracting the k term discussed above, the magnitude of the k 3 term is estimated from experimental data on Na. It is quite consistent with the data to take the coefficient of k 3 as zero and possible reasons for this are discussed.

X-ray analysis of the structure of liquid Rb and Cs

X-ray-transmission measurements have been performed and the diffraction patterns using Ag $K\ensuremath{\alpha}$ and Mo $K\ensuremath{\alpha}$ radiation have been determined for liquid rubidium at 40 and 90\ifmmode^\circ\else\textdegree\fi{}C and for liquid cesium at 65 and 100\ifmmode^\circ\else\textdegree\fi{}C, respectively. A new sample holder has been used. The structure factors $a(q)$ do not agree very well with measurements of neutron diffraction, but there is good agreement with the x-ray pattern of Huijben et al. in the case of Cs.

Effective-field approach to transverse correlations in simple liquids

The transverse counterparts of the effective-field theories for the longitudinal mode are constructed on the basis of the kinetic theory of simple liquids. The connection between the effective-field representation and generalised hydrodynamics is shown. By means of a Gaussian ansatz for the frequency-dependent collision damping function, calculations have been performed for liquid Ar and Rb. The relaxation time in the ansatz is determined by the use of sum rules up to the fourth moment.

On the memory functions in simple classical liquids

The relation between the two memory function formalisms for correlation functions in classical liquids is discussed. It is found that the kinetic equation formalism of Duderstadt and Akcasu with a simple exponential memory function can account for the double Gaussian form of the memory function in the generalized-hydrodynamics approach. The former therefore gives reasonably good results for the coherent scattering function S(k, ω), as is shown for the case of liquid Rb at 315 K in the range 1.25 ⩽k ⩽ 5.5 A−.

Triplet correlations in model liquids

Some features of a simple mathematical model for disorder structures, previously proposed, are investigated by computing the triplet correlation functiong(3) (r, s, t) for liquid Ar and Rb. The results, when compared with molecular dynamics and Monte, Carlo computations, appear rather encouraging.

Positron annihilation in the liquid alkali metals

Positron annihilation in the liquid alkali metals at just above their melting points is theoretically studied. A perturbation approach based on NFE model is used. The positron and electron momentum distributions including only the ionic density correlation have been selfconsistently calculated within a complex energy approximation. The positron resolution functions including both the ionic correlation and coulombic interactions have also been calculated by taking the simplest self energy diagram in the combined perturbation expansion into consideration. The angular correlation curves for liquid Na agrees well with the corresponding experimental curve over the full range of momentum within the error limits but there are still some appreciable deviations between them for liquid Rb.

The resistivity versus temperature at constant volume of liquid Na, K and Rb

Abstract The temperature dependence of the electrical resistivity at constant volume was studied to provide more accurate data for comparing Ziman's theory with experiment. Our results were obtained with greater precision over a larger temperature interval than Endo reported. No anomaly in the ρ(T) curves were found for sodium, potassium, or rubidium as was reported for lithium. The definite linear nature of the temperature dependence should make x-ray measurements of I(K) useful in testing the Born approximation.

Wavenumber-dependent elastic moduli in liquid metals

The wavenumber-dependence of the instantaneous elastic moduli of liquid Na, K, Rb and Mg has been calculated, using an interatomic potential determined from the measured phonon dispersion curves or the elastic constants of the corresponding solid.