Liquid Rb Research Articles

A Novel Method for Rubidium Bulb Bonding and Key Characterization for Future Space Clocks.

RF-discharge lamp is a key component in space- and ground-based compact and portable atomic clocks, such as rubidium atomic frequency standards (RAFSs). Precise thermal, structural design, and control of a rubidium (Rb) bulb is of crucial importance for long-term reliable operation of the onboard clocks. An important aspect is the potting material that is used to mount the Rb bulb. Potting material directly determines the thermal contact between liquid Rb pool inside glass bulb enclosure and the heating element, which is the only path to control the Rb bulb's temperature. Failure or degradation of thermal contact of the Rb bulb with its metallic base will lead to Rb clock degradation or failure. Considering this, we have successfully designed, simulated, implemented, characterized, and tested the use of indium metal as a replacement to epoxy for the Rb bulb bonding that can be implemented in future space Rb atomic clocks. Its thermal advantage over other routine space-qualified epoxies and flexibility for multiple bonding and unbonding mechanisms make it ideal for such applications. The usefulness of key properties of indium for various other space and ground applications is discussed.

Computation of thermophysical properties of liquid metals and alloys on the basis of generalized version of hole theory

• Modification of Frenkel’s hole theory has been applied to liquid metals and alloys. • Liquid metals Na, K, Rb, Cs, Sn and Pb and four alloys K-Rb, Na-Cs, Sn-Pb and Na-K. • Various expressions for r h ,V h , α, β T , P int , E h , ∆E V , ced, α vdw and u were derived. • Interaction study of alkali metal alloys with the help of hole theory. • The calculated and experimental values show excellent. A generalized version of hole theory, recently developed as a modification of Frenkel’s hole theory has been applied successfully, for the first time, to six pure liquid metals (K, Rb, Na, Cs, Pb and Sn) and four liquid metal alloys (K-Rb, Na-Cs, Sn-Pb and Na-K) at different temperatures. Various expressions for r h ,V h , α, β T , P int , E h , ΔE V , ced, α vdw and u were derived for the pure liquid metals and alloys. The calculated and experimental values show excellent agreement demonstrating the success of the theory to the pure liquid metals and alloys.

Structural and electronic transition in liquid rubidium

Rubidium, like the other alkali metals, exhibits multiple structural transformations in its solid phase upon application of pressure. Recent experiments and calculations suggest it also goes through a phase transformation in its liquid state, along the 573 K isotherm, slightly above its melting curve. We employ ab initio molecular dynamic simulations to study the structural and electronic characteristics of this liquid-liquid transition. Applying the quasicrystalline model, we find that the short-range order of liquid Rb changes abruptly from bcc-like to $\ensuremath{\beta}$-Sn-like at a pressure significantly lower than the bcc to $\ensuremath{\beta}$-Sn transition in the solid phase at lower temperatures. In contrast to previous claims, the transition in the liquid cannot be related to the Peierls transition, as the liquid does not exhibit formation of a pseudogap at the Fermi level, nor to the transfer of charge from the $s$ state to the $d$ state, which is found to progress monotonically with pressure. Instead, a qualitative change in the shape of the electronic $d$ band is shown to occur at the same pressure range as the structural phase transition, which leads to the conclusion that the $\mathit{sd}$ hybridization must be accompanied by a significant change in the electronic band structure, observed in the solid phase, in order to produce a phase transition.

Antifungal Properties of Fucus vesiculosus L. Supercritical Fluid Extract Against Fusarium culmorum and Fusarium oxysporum.

In this study, potential antifungal properties of a brown alga Fucus vesiculosus were evaluated. The algal extract was obtained with the use of supercritical fluid extraction (scCO2) at a temperature of 50 °C under a pressure of 300 bar. The aqueous solution of the extract at the concentration of 0.05%, 0.2%, 0.5% and 1.0% was studied against pathogenic fungi on a liquid RB medium. This study is the first report on antifungal properties of the brown algae F. vesiculosus scCO2 extract against Fusarium culmorum and Fusarium oxysporum phytopathogens. The concentrations of the studied extract (0.5% and 1.0%) were demonstrated to have an ability to inhibit 100% growth of macroconidia within 144 h, as well as an ability to cause their total degradation. As a result of the study, the antifungal effect of fucosterol against F. culmorum was also indicated. The total macroconidia growth was inhibited by 1.0% fucosterol. Moreover, at lower concentrations (0.05–0.2%) of fucosterol, macroconidia were characterized by shorter length and structural degradation was observed. The mycelial growth of Fusarium oxysporum (Fo38) by 1% scCO2 F. vesiculosus extract was analyzed at the level of 48% after 168 h of incubation, whereas 100% extract was found to be effective in F. culmorum (CBS122) and F. oxysporum (Fo38) growth inhibition by 72% and 75%, respectively after 168 h of incubation.

Plasmons in Liquid Rb at Elevated Temperatures Studied by Inelastic X-ray Scattering

Inelastic X-ray scattering measurements have been carried out to investigate the energy and line width of plasmons in liquid Rb at elevated temperatures (300 and 500 °C). The plasmon energy decreas...

Simple-to-Complex Transformation in Liquid Rubidium.

We investigated the atomic structure of liquid Rb along an isothermal path at 573 K, up to 23 GPa, by X-ray diffraction measurements. By raising the pressure, we observed a liquid-liquid transformation from a simple metallic liquid to a complex one. The transition occurs at 7.5 ± 1 GPa which is slightly above the first maximum of the T-P melting line. This transformation is traced back to the density-induced hybridization of highest electronic orbitals leading to the accumulation of valence electrons between Rb atoms and to the formation of interstitial atomic shells, a behavior that Rb shares with Cs and is likely to be common to all alkali metals.

Determination of structure factor and effective intermolecular parameters of liquid alkali metals using mean spherical approximation theory

The structural properties of liquid cesium (Cs) were investigated in the temperature range of 400–2000 K by application of the effective hard-core attractive Yukawa (H-Y) potential function to the mean spherical approximation (MSA) theory. An analytical equation of state was applied to calculate the molecular parameters of a potential function at any thermodynamic state. The proposed approach was used to predict the behavior of the structure factor, S(k), at a wide range of wave vectors (k). The results obtained were compared with the available experimental measurements, which revealed a good agreement over the whole liquid range for Cs. The structure factor at a long wavelength limit, S(0), was also calculated and compared with the experimental data, which showed the accuracy of the Ornstein-Zernike (OZ) behavior of S(k) at the thermodynamic states below the boiling temperature (Tb). For the case of Cs, the presented intermolecular potential model was very much responsive to the thermodynamic states and led to the indication of the two distinct isotherm ranges T <Tb and T >Tb. Two analytical expressions were obtained for the temperature dependency of the potential well-depth (Keff) over the temperature ranges of T <Tb and T >Tb. Furthermore, the proposed approach showed several metal-nonmetal transitions for Cs at about 500, 1100, 1350, and 1650 K. Using the Keff relations for the other liquid alkali metals Na, K, and Rb provided the S(k) results that were more accurate in comparison with the experimental data.

De Gennes Narrowing and Hard-Sphere Approach

The energy width Δω of the quasielastic coherent dynamic structure factor S(Q, ω) for a simple liquid exhibits the oscillating dependence on wavenumber Q with the sharp minimum at Qmax corresponding to the maximum of the structure factor S(Q). The only known expression for Δω(Q) was derived for a dense hard-sphere (HS) fluid (Cohen et al., Phys. Rev. Lett. 1987, 59, 2872). Though this expression has been frequently used for the analysis of the experimental data obtained for liquid metals, until now, it has never been tested against a true HS fluid. A test performed by means of HS molecular dynamic simulations reveals a considerable discrepancy between the simulations results and the examined model. The main output of the analysis is the finding that the ΔωHS(Q) behavior is defined in terms of the average cage size, ⟨Lc⟩, rather than of the HS diameter, σHS. The simulated ΔωHS(Q) has been compared with the results for the soft-spherical potential. The microscopic dynamics of the soft-sphere fluid shows significant difference in comparison to the HS system. Nevertheless, the diffusive mobility of soft spheres can be characterized within the HS approximation using an effective diameter, σeff, and this parameter can be found from Δω(Q) at Q ≈ Qmax. A similar result has been obtained for the neutron scattering data measured for liquid Rb.

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.

Microfabricated alkali vapor cell with anti-relaxation wall coating

We present a microfabricated alkali vapor cell equipped with an anti-relaxation wall coating. The anti-relaxation coating used is octadecyltrichlorosilane and the cell was sealed by thin-film indium-bonding at a low temperature of 140 °C. The cell body is made of silicon and Pyrex and features a double-chamber design. Depolarizing properties due to liquid Rb droplets are avoided by confining the Rb droplets to one chamber only. Optical and microwave spectroscopy performed on this wall-coated cell are used to evaluate the cell's relaxation properties and a potential gas contamination. Double-resonance signals obtained from the cell show an intrinsic linewidth that is significantly lower than the linewidth that would be expected in case the cell had no wall coating but only contained a buffer-gas contamination on the level measured by optical spectroscopy. Combined with further experimental evidence this proves the presence of a working anti-relaxation wall coating in the cell. Such cells are of interest for applications in miniature atomic clocks, magnetometers, and other quantum sensors.

Temperature dependent atomic transport properties of liquid Rb

A simple analytical model for atomic motion is used to obtain velocity autocorrelation function (VACF) for liquid Rb. The modified empty-core potential due to Hasegawa et al., which represents the orthogonalisation effect due to s-core states in such sp-bonded metals, is used for electron–ion interaction. The potential parameter rc is determined at different temperatures from the knowledge of structure factor. We find quantitative explanation for the density and temperature dependence of VACF and self-diffusion coefficients. The coherent behaviour of liquid Rb in terms of the dynamic structure factor employing viscoelastic theory has also been studied. Intrinsic temperature effects have been studied through damping term 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 molecular dynamics (MD) data and a good agreement has been achieved.

Inelastic x-ray scattering study of plasmon dispersions in solid and liquid Rb

The plasmon dispersion relations in solid and liquid Rb were determined by inelastic x-ray scattering techniques. In liquid Rb, the plasmon energy increases with the momentum transfer $q$, whereas in solid Rb, the dispersion curve exhibits a cusplike shape. We also found that the plasmon linewidth in liquid Rb is narrower than that in solid Rb near $q=0$. These features suggest that the conduction electrons in liquid Rb are more suitably described by the electron gas model than in solid Rb, since the electron gas model predicts a smooth increase in the plasmon energy with $q$ and the infinite lifetime at $q=0$. The origins of the observed variations in the plasmon energy and the linewidth upon melting are investigated with the aid of theoretical calculations.

Dynamical Crossover at the Liquid-Liquid Transformation of a Compressed Molten Alkali Metal

Density-driven phase transformations are a known phenomenon in liquids. Pressure-driven transitions from an open low-density to a higher-density close-packed structure were observed for a number of systems. Here, we show a less intuitive, inverse behavior. We investigated the electronic, atomic, and dynamic structures of liquid Rb along an isothermal line at 573 K, at 1.2-27.4 GPa, by means of ab initio molecular dynamics simulations and inelastic x-ray scattering experiments. The excellent agreement of the simulations with experimental data performed up to 6.6 GPa validates the overall approach. Above 12.5 GPa, the breakdown of the nearly-free-electron model drives a transition of the pure liquid metal towards a less metallic, denser liquid, whose first coordination shell is less compact. Our study unveils the interplay between electronic, structural, and dynamic degrees of freedom along this liquid-liquid phase transition. In view of its electronic nature, we believe that this behavior is general for the first group elements, thus shedding new light into the high-pressure properties of alkali metals.

Thermodynamics of liquid alkali metals using pseudopotential Perturbation scheme

Recently proposed model potential of Baria and Jani is used with the exchange and correlation effect of Sarkar et al. to calculate internal energy (Enthalpy), Entropy and Helmholtz free energy of liquid Na, K, Rb and Cs at various temperatures with the variational approach. The parameter of the potential is determined with the standard zero pressure condition. The structure factor derived by Percus-Yevick solution for hard sphere fluids which is characterized by hard sphere diameter \sigma is used. A good agreement between theoretical investigations and experimental findings has confirmed the ability of the model potential to the liquid alkali metals.

Dispensing and hermetic sealing Rb in a miniature reference cell for integrated atomic clocks

An innovative method for fabricating the reference cell for a Rubidium (Rb) integrated atomic clock is presented. This method uses low-temperature solder sealing technique for producing mini-cells of the size of 14mm×10mm×3mm, suitable for Rb miniature atomic clocks. Top and bottom of the cell consists of two glass slides. An LTCC (low-temperature cofired ceramic) module of 2mm thickness, equipped with a small reservoir for confining the Rb is placed in between the two walls, acting as a spacer, increasing the total volume of the cell. A solder ring joins together the LTCC and the top of the cell. This paper also presents a new technique for handling the Rb, which allows its safe handling and long storage. The alkali metal is stored inside a pool of dodecane, which protects it from oxidation. Pure liquid Rb is then dispensed inside the adjacent reservoir using a glass micropipette; finally, the cell is heated in vacuum, in order to carry out the sealing. The achieved sealing hermeticity was tested, without Rb, by sealing N2O gas and monitoring its pressure through absorbance measurements using FTIR spectroscopy. Hermeticity was also tested with Rb by integrating a pressure sensor in the LTCC module.

Electron transport in liquid Na, K and Rb: t-matrix formalism revisited

We have performed ab initio calculations based on t-matrix formalism in the framework of the nearly free electron [NFE] theory to determine the electrical resistivity ρ and the thermoelectric power S of three liquid alkali metals, namely, Na, K and Rb. The present approach is primarily based on the Dreirach model that considers a shift E B between the bottom of the free electrons density-of-states (DOS) and the muffin tin zero ( V MTZ ). Concurrently the second model initiated by Esposito et al. that takes into account the nearly free electrons (NFE) without any gap between NFE-DOS and V MTZ has also been tested. The results ρ and S obtained from the Esposito et al. model are not consistent with experimental counterparts. A substantial improvement of ρ and S values is obtained from Dreirach model provided the temperature dependence of ρ versus energy is considered in order to reproduce the correct sign for S. This observation is presumably related to the fact that in the range between 0 and E F on the energy scale, the DOS for these metals fairly resemble those of free electrons yielding their effective valence N c to be very close to the valence number Z but with a shift of the bottom of the band which cannot be neglected.

The calculation of Cs and Rb conductivities in the region of liquid–plasma transition

The conductivity and thermal conductivity of Cs and Rb are calculated in the liquid phase and in the region between the plasma (gas) and the liquid states. The last area is located at the temperatures higher than the critical one, near the critical point. The Ziman formalism originated from the liquid metal theory was used for the calculations. The results of present calculations were compared with available experiments and calculations of other researchers. It was found that the liquid state formalism can be applied to expanded liquid Cs and Rb at densities higher than the critical one, but another type of models is necessary at lower densities.

Dispensing and hermetic sealing Rb in a miniature reference cell for integrated atomic clocks

An innovative method for filling and sealing the reference cell for a Rubidium (Rb) integrated atomic clock is presented. We used a simple, low-temperature solder sealing technique for producing mini-cells of the size of 12×10×2 mm, suitable for Rb miniature atomic clocks. The cell is made by two glass slides acting as the top and bottom walls, joined by a solder ring acting as the sidewall. In the frame of this research, we also developed a safe and convenient method for easily handling Rb: the alkali metal is stored inside a ‘pool’ of dodecane, which protects it from oxidation. Pure liquid Rb is then dispensed inside the cell using a glass micropipette; finally, the cell is heated in vacuum, in order to realize the sealing. The hermeticity achieved by the cell was tested by sealing N2O gas and monitoring its pressure through absorbance measurements using FTIR spectroscopy. The presented method allows easy handling and long-term storage of Rb, and finally led to the production of functional hermetic mini-cells.

First-Principles Understanding of the Anomalous Structural Change in an Expanded Liquid Alkali Metal

Based on a model derived from the first-principles Hamiltonian by treating the electron–ion pseudopotential as perturbation, we have studied the local ionic structure of an expanded liquid alkali metal to find that the distance between adjacent ions decreases despite the increase of the mean interionic distance with volume expansion. This anomalous feature of the interionic contraction, which is in quantitatively good accord with experiment for liquid Rb, is attributed to an enhanced attraction working between valence electrons in the low-density electron gas, combined with the existence of the ionic core region from which valence electrons are excluded.

Neutron and X-ray diffraction from liquid Rb

Motivated by the recent X-ray diffraction experiments by Matsuda, Tamura, and Inui (Phys. Rev. Letters 98, 096401 (2007)). on liquid Rb, it is stressed that important information about electron–ion and electron–electron correlations is embodied in a comparison of their X-ray data with the neutron observations of Franz, Freyland, Glaser, Hensel, and Schneider (J. Phys. (Paris) Colloq. 8, 194 (1980)). Electron diffraction experiments on liquid Rb would also be important, if feasible.