Liquid Alkali Metals Research Articles

A review of experimental data and heat transfer correlations for parallel flow of alkali liquid metals and lead-bismuth eutectic in bundles

A comprehensive review is performed of the reported experimental data on convection heat transfer for parallel flows of the alkali liquid metals of sodium, NaK-44, NaK-56, and NaK-78 alloys, and liquid lead-bismuth eutectic (LBE) in bundles of uniformly heated bare tubes in a triangular lattice at Pe=4–3074. The performed experiments by various investigators have employed either a heat exchanger or hexagonal and cylindrical bundles of 7–37 heated tubes with P/D=1.06–1.95. The compiled experimental database of 746 Nusselt number values for Na and various NaK alloys is used to develop the following continuous correlation:Nu=[10.7(P/D)-7.1]+0.024[1-e-10.4((P/D)-1)]Pe0.85For the entire ranges of P/D and Pe values in the experiments, this correlation is in good agreement, within ±15%, with the compiled Nu data. The compiled Nu database for LBE flows in bundles of bare heated tubes with grid spacers, has 205 values for P/D=1.33–1.80 and Pe=211–3049. The present Nu correlation for alkali liquid metals agrees with the LBE data to within ±20%. This agreement suggests that the proposed Nu correlation for alkali liquid metals in bundles of bare tubes may also be used to calculate Nu for LBE.

9-3-2 液体アンモニアとアルカリ金属水素化物を用いた化学的高圧水素製造(Session 9-3 水素製造・貯蔵・利用III)

9-3-2 液体アンモニアとアルカリ金属水素化物を用いた化学的高圧水素製造(Session 9-3 水素製造・貯蔵・利用III)

Experimental evidence for two different dynamical regimes in liquid rubidium

We present evidence for changes in the dynamics of liquid rubidium with rising temperature. The thermal expansion of this liquid alkali metal shows a changing derivative with temperature in a temperature range of about 400-500 K. With neutron scattering the amplitude at the structure factor maximum demonstrates a changing slope with increasing temperature. A derived averaged structural relaxation time can be understood that an additional relaxation process sets in upon cooling. The deduced generalized viscosity and high frequency shear modulus indicate a change in dynamics in the same temperature range. All these findings point to a change in dynamics of the equilibrium liquid metal state with a dynamical crossover from a viscous to a fluid-like liquid metal well above the melting point.

Examination of Solubility Models for the Determination of Transition Metals within Liquid Alkali Metals

The experimental solubility of transition metals in liquid alkali metal was compared to the modeled solubility calculated using various equations for solubility. These equations were modeled using the enthalpy calculations of the semi-empirical Miedema model and various entropy calculations. The accuracy of the predicted solubility compared to the experimental data is more dependent on which liquid alkali metal is being examined rather than the transition metal solute examined. For liquid lithium the calculated solubility by the model was generally larger than experimental values, while for liquid cesium the modeling solubility was significantly smaller than the experimental values. For liquid sodium, potassium, and rubidium the experimental solubilities were within the range calculated by this study. Few data approached the predicted temperature dependence of solubility and instead most data exhibited a less pronounced temperature dependence.

The SW-MSA Calculation of Self-Diffusion Coefficients in Liquid Lithium and Rubidium

Successfully used recently for liquid Na and K the approach combined the linear trajectory approximation with the square-well model in the semi-analytical representation of the mean spherical approximation to calculate the self-diffusion coefficients is applied here to liquid Li and Rb. As well as earlier for Na and K, the results obtained are found to be in reasonable agreement with the available experimental data and confirm previous conclusion that the square-well model within the mean spherical approximation is quite useful for description of diffusion properties in liquid alkali metals.

Studying structural properties of rubidium and cesium liquid metals using an effective hard-core Yukawa potential

In this work, we investigate the applicability of a modification of the random phase approximation (RPA) theory with an effective hard-core Yukawa potential to the static structure factor for the rubidium and cesium liquid metals. Based upon the perturbation theory, we assume that the core contribution of the direct correlation function is related to the geometric effects via a linear form for a hard-sphere fluid, in which the molecular diameter is obtained at any temperature and, its tail contribution is related to the long-range intermolecular interactions of the system via a linear form. We use the long-range Yukawa potential in the modeling of liquid alkali metals (LAMs) with the decay parameter λ = 1.8 and a well depth potential that is state-dependent. The linear isotherm regularity (LIR) equation of state (EOS) is applied to obtain the long-range interactions. The results obtained show that the proposed approach for LAMs can predict the behavior of the structure factor, S(k), at a wide range of k values with a good accuracy, as compared to the experimental data, over the whole liquid states. The interaction model used is also successful in the presentation of the Ornstein–Zernike (OZ) behavior of S(k) at the low-k region including the S(0) values.

Pressure-induced emergence of unusually high-frequency transverse excitations in a liquid alkali metal: Evidence of two types of collective excitations contributing to the transverse dynamics at high pressures.

Unlike phonons in crystals, the collective excitations in liquids cannot be treated as propagation of harmonic displacements of atoms around stable local energy minima. The viscoelasticity of liquids, reflected in transition from the adiabatic to elastic high-frequency speed of sound and in absence of the long-wavelength transverse excitations, results in dispersions of longitudinal (L) and transverse (T) collective excitations essentially different from the typical phonon ones. Practically, nothing is known about the effect of high pressure on the dispersion of collective excitations in liquids, which causes strong changes in liquid structure. Here dispersions of L and T collective excitations in liquid Li in the range of pressures up to 186 GPa were studied by ab initio simulations. Two methodologies for dispersion calculations were used: direct estimation from the peak positions of the L/T current spectral functions and simulation-based calculations of wavenumber-dependent collective eigenmodes. It is found that at ambient pressure, the longitudinal and transverse dynamics are well separated, while at high pressures, the transverse current spectral functions, density of vibrational states, and dispersions of collective excitations yield evidence of two types of propagating modes that contribute strongly to transverse dynamics. Emergence of the unusually high-frequency transverse modes gives evidence of the breakdown of a regular viscoelastic theory of transverse dynamics, which is based on coupling of a single transverse propagating mode with shear relaxation. The explanation of the observed high-frequency shift above the viscoelastic value is given by the presence of another branch of collective excitations. With the pressure increasing, coupling between the two types of collective excitations is rationalized within a proposed extended viscoelastic model of transverse dynamics.

ChemInform Abstract: Facile and Efficient Exfoliation of Inorganic Layered Materials Using Liquid Alkali Metal Alloys.

AbstractSingle‐ and few‐layer MoS2, WS2, and BN nanosheets are prepared through intercalation and exfoliation using liquid NaK or NaLi alkali metal alloys in DME at room temperature for 24—48 h.

Thermochemical ablation therapy of VX2 tumor using a permeable oil-packed liquid alkali metal.

ObjectiveAlkali metal appears to be a promising tool in thermochemical ablation, but, it requires additional data on safety is required. The objective of this study was to explore the effectiveness of permeable oil-packed liquid alkali metal in the thermochemical ablation of tumors.MethodsPermeable oil-packed sodium–potassium (NaK) was prepared using ultrasonic mixing of different ratios of metal to oil. The thermal effect of the mixture during ablation of muscle tissue ex vivo was evaluated using the Fluke Ti400 Thermal Imager. The thermochemical effect of the NaK-oil mixture on VX2 tumors was evaluated by performing perfusion CT scans both before and after treatment in 10 VX2 rabbit model tumors. VX2 tumors were harvested from two rabbits immediately after treatment to assess their viability using trypan blue and hematoxylin and eosin (H.E.) staining.ResultsThe injection of the NaK–oil mixture resulted in significantly higher heat in the ablation areas. The permeable oil controlled the rate of heat released during the NaK reaction with water in the living tissue. Perfusion computed tomography and its parameter map confirmed that the NaK–oil mixture had curative effects on VX2 tumors. Both trypan blue and H.E. staining showed partial necrosis of the VX2 tumors.ConclusionsThe NaK–oil mixture may be used successfully to ablate tumor tissue in vivo. With reference to the controlled thermal and chemical lethal injury to tumors, using a liquid alkali in ablation is potentially an effective and safe method to treat malignant tumors.

Solubility and the periodic table of elements

Abstract Interesting general tendencies of changes of solubilities of elements and groups of compounds may be observed when the corresponding solubility data are arrayed according to the increasing atomic number of the elements. Such trends are exemplified with the data of various systems (metallic and salt-water type) evaluated in several volumes of the IUPAC-NIST Solubility Data Series. The solubilities of elements in mercury as well as in liquid alkali metals, when ordered according their atomic numbers, change roughly in a corresponding way as the temperatures and energies of melting or boiling points of the elements. However, majority of transition metals dissolved in alkali metals are subject to some side reactions with nonmetallic impurities that may drastically elevate their concentration levels. The solubilities of intermetallic compounds in mercury depend primarily on the energies of formation of these intermetallics in the binary alloys and then on the dissolution energies of the component metals in mercury. It has been observed that the experimental solubilities of metal halates in water show quite well defined periodical changes. The arrayed solubility data of rare earth metal fluorides and chlorides in water display quite smooth changes with the increasing atomic numbers if the solutes are isomorphic. Some exceptions from the smooth changes for rare earth metal bromides and iodides are explained. These general observations are useful in evaluating and predicting solubilities in experimentally unknown systems.

Simulation of properties of liquid alkali metals at high temperatures and pressures by ab initio molecular dynamics method

The properties of liquid alkali metals Na and Cs over the entire temperature range of the existence of liquid state are investigated for the first time by the ab initio molecular dynamics (AIMD) method. The simulation was performed using the SIESTA software package. A pseudopotential is selected, and a model of liquid metal is constructed for a supercell with the number of atoms being 54, 250, and 1024. The total energy, heat capacity, diffusion coefficient, radial distribution function of atoms, and density of electron states are calculated. The temperature dependence of the heat capacity upon approaching the critical point manifests a feature correlating with the experimentally observed one, while the density of electron states has substantial deviations from the model of almost free electrons. It is shown that the AIMD method selected makes it possible to evaluate the melting point.

Facile and efficient exfoliation of inorganic layered materials using liquid alkali metal alloys.

A facile and efficient exfoliation process has been reported to produce single- and few-layer nanosheets of MoS2, WS2 and BN using liquid alloys of alkali metals at room temperature. The colloidal dispersions of MoS2 and WS2 layers were highly stable over several months, which allowed us to easily prepare films of MoS2 and WS2 by vacuum filtration or spraying.

Planar High Temperature Heat Pipes for SOFC/SOEC Stack Applications

AbstractTargeting transient operation of high temperature solid oxide cell (SOC) systems this paper proposes an enhanced heat management mechanism using planar high temperature heat pipes that can be integrated into the SOC‐stack structure. Flat heat pipes with thicknesses down to 4 mm filled with liquid alkali metals for almost isothermal 2D heat spreading, even for intense heat transfer rates, are demonstrated. A new pathway towards a temperature gradient shrinking in SOC‐stacks without using large amounts of additional air‐cooling is shown. The paper will present latest development results on design concepts, size reduced fabrication and filling procedure. An experimental study demonstrates the heat spreading capabilities and power limitations of planar heat spreaders for high temperature applications as in SOEC/SOFC stacks.

Equation of state and artificial neural network to predict the thermodynamic properties of pure and mixture of liquid alkali metals

A statistical mechanical equation of state is developed to predict the volumetric properties of pure and mixture liquid alkali metals at different temperatures, pressures and compositions. The temperature dependent parameters of the equation of state have been calculated using corresponding states correlation based on the normal boiling point parameters as scaling constants. It is shown that the knowledge of just normal boiling point and its liquid density are sufficient to estimate the thermodynamic properties of pure and mixture liquid alkali metals in different conditions. Besides, the performance of artificial neural network (ANN) based on back propagation training with 10 neurons in hidden layer for prediction of behavior of presented systems was investigated. A collection of 512 data points for above systems in different temperatures and pressures was used. The Tao–Mason equation of state (TM EOS) and ANN model results have good agreement with the experimental data with absolute average deviations of 0.74% and 0.299%, respectively.

Vapor-liquid (insulator-metal) phase transition in alkali metal vapors

A simple physical model is proposed that describes a vapor-liquid phase transition in alkali metal vapors. The model is based on an assumption made on the character of binding between atoms in the gas phase near the critical point. This is the collective quantum cohesive energy, well-known in the theory of liquid alkali metals, which arises due to the appearance of conduction electrons and is extended to the gas region near the critical point. The parameters of the critical points of the transition and of the binodal are determined on the basis of the model calculation of the binding energy for all alkali metals. Combined, these parameters well agree with experimental results and the predictions made by other authors. The minimum metallic conductivity is evaluated. Its behavior allows one to conclude that vapor-liquid and insulator-metal transitions in alkali metal vapors coincide. This fact sheds light on the Zel’dovich-Landau problem as applied to alkali metal vapors.

An analysis of incipient boiling superheat in alkali liquid metals

Studies on the incipient boiling superheat (IBS) in alkali liquid metals have revealed that many factors can have effects on IBS. However, existing results about the effects of most variables are inconsistent and even conflicting. It is possible that effects of many variables are only apparent and the complex results can be explained with several simple factors. Three basic variables, i.e. the effects of inert gas diffusion, oxide layer and dynamic process were involved in our model to show their effects on IBS. Analysis showed that the inert gas diffusion should be carefully considered because it may result in large variation of IBS in a short time. Existence of oxide layer could help reducing IBS by keeping large cavities un-wetted and enhancing nucleation contact angle. The effect of dynamic process on IBS which may cause apparent velocity and heat flux effects may be explained with the variation of apparent nucleation contact angle caused by interface speed, and a correlation with some empirical coefficients was proposed to describe its effect. To verify the model several sets of experimental data were carefully selected. Predictions considering these effects were compared with these experimental data and good agreements were gained.

Plasmon Line Width in Liquid Metals

With the recent development of synchrotron radiation sources and the instrumentations, inelastic X-ray scattering (IXS) has become an important tool for observing plasmons in materials. One of the significant advantages of IXS is that it can be applied to liquid samples, which is considerably difficult for electron energy loss spectroscopy. Thus far, the IXS study of plasmons in liquid samples has been performed for several systems such as liquid lithium, liquid aluminum, or lithium ammonia solutions. However, the properties of plasmons in the liquid phase are less clearly understood than those in the crystalline phase. One of such properties is the plasmon line width. For the solid state, the finite line width observed in experiments can be evaluated using the formulations derived in previous theoretical studies, in which the effect of interband transitions, phonon-assisted intraband (or interband) transitions, and the excitations of two electron–hole (e–h) pairs are considered. These effects should also play an important role in liquid, because a finite line width is also observed in liquid samples. The effects of phonon and two e–h pairs are readily extended to liquid systems, since these effects can be calculated without using information on the ionic structure. On the other hand, the effect of interband transitions is difficult to extend to the liquid state, because it strongly depends on the ionic structure. In this work, we show the derivation of a formula for evaluating the plasmon line width at the zero momentum transfer, q 1⁄4 0, in metallic liquid. The formula describes how the ionic structure influences the plasmon line width for metallic liquid. The application of the formula to liquid alkali metals is also shown. The plasmon line width at q 1⁄4 0, E1=2ð0Þ, is written as E1=2ð0Þ 1⁄4 h !p Im ð!pÞ; ð1Þ

Temperature Dependent Surface Properties of Liquid Alkali Metals

Temperature dependent surface properties like surface tension (γ) and surface entropy (SV) of liquid alkali metals are studied in the present paper. Our newly constructed parameter free model potential is used to describe the electron-ion interaction. To see the influence of local field correction function on surface properties of liquid alkali metal, we have used Sarkar et al local field correction function. The present results are found in good agreement with available experimental data as well as other theoretical data. Lastly we conclude that our model potential is capable to explain surface properties of liquid alkali metals.

The Temperature Dependent Elastic Moduli of Liquid Potassium

Near the melting point liquid alkali metals show positive dispersion, which can be described within generalized hydrodynamics as a visco-elastic reaction of the simple liquid. To understand an upward bending of the dispersion relation at small momentum transfer, treatment of pseudopotential theory on liquid potassium is performed at different temperatures in entire liquid regime. In the present study, we used the modified empty core potential due to Hasegawa et al. along with a local field correction due to Ichimaru-Utsumi (IU) to explain an electron-ion interaction. The potential used is composed of a full electron-ion interaction and a repulsive delta function to incorporate the orthogonalisation effect due to the s-core states. The temperature dependence of pair potential is calculated by using the damping term, exp(-πkBTr/2kF). While the expression for phonon dispersions are derived within the memory function formalism. Results for longitudinal phonon frequencies, and thus derived sound velocities and elastic modulii are compared with recent inelastic X-ray scattering experiment. It is found sufficient to carried temperature effect into the description only via the damping factor, keeping the volume of normal melting.

Density prediction of liquid alkali metals and their mixtures using an artificial neural network method over the whole liquid range

In this study, the application of artificial neural network (ANN) method in predicting the density of alkali metals and their mixtures is investigated. A total number of 595 different data points of these compounds were used to train, validate and test the model. A typical three-layer feedforward backpropagation neural network has been trained by the Levenberg Marquardt algorithm. The tansig-tansig transfer functions with 15 neurons in the hidden layer makes the least error, so a network with (8-15-1) structure was used to design the ANN model. The average relative deviations for train, validation, and test sets are 0.1029, 0.1396, and 0.1002, respectively. A comparison between our results and those obtained from some previous works shows that this work, as an excellent alternative, can provide a simple procedure to predict the density of these compounds in a better accord with experimental data up to high temperature, high pressure (HTHP) conditions.