Calculation of Sound Velocities of Liquid Metals at their Melting Point via the Percus-Yevick Theory of Melting

Abstract

In this brief note, we utilize the 3N collective coordinate theory of liquids of Percus and Yevick¹ as applied to the phenomenon of melting by Omini² to calculate the sound Velocities in various simple liquid metals at their melting temperatures. We perform this calculation by taking derivatives of Omini's² calculated Percus-Yevick dispersion relations for their “liquid phonon” collective coordinate elementary excitations of the liquid. We compare these calculated sound velocities with experimental data, where possible, to ascertain the validity of the liquid phonon dispersion relation as a source of sound velocities.     

Virtual Crystal Model of Melting and the Structure Factor of Liquid Alloys

Abstract

In this paper, we extend the theory of melting entropy of metals, of Omini, based on the Percus-Yevick collective coordinate theory of liquids, to binary liquid alloys. We reformalate Omini's use of the Percus-Yevick theory to include binary liquid alloys and calculate the long wavelength limit of the binary liquid alloy structure factor as a function of solute concentration for the systems: Li-Na, K-Rb. Rb-Cs, Al-Zn, Zn-Ca and AI-Ga which are the most nearly equi-valent and equi-volumeatom pairs Omini worked with.     

Bulk Viscosity and the Relation between Transport Coefficients

Abstract

The longitudinal and bulk viscosity of the fluid Argon is calculated using its relation with self diffusion coefficient. This relation was derived by developing the relation between coherent and incoherent scattering functions. The results obtained are compared with recent simulation data of bulk viscosity. A good agreement is achieved for a wide range of temperatures at the triple point density. Our results successfully explain the increase in bulk viscosity with decrease in temperature near the triple point. The validity of the relation between diffusion and longitudinal viscosity is also tested for liquid metals. The results obtained for liquid metals of the longitudinal viscosity, at their melting points, are not found to be in agreement with experimental results. A relation between thermal conductivity and self-diffusion coefficient is proposed.     

Pair Function and Structure Factor of an Interacting Electron Liquid

Abstract

Recent work on small angle scattering from liquid metals has caused renewed interest in the electron pair function in the uniform interacting electron liquid, jellium. Therefore we have re-examined this problem, starting from an analysis of the exchange hole, in which the only correlations are due to the Pauli Principle and solely therefore between parallel spin electrons. The pair function g(r) of noninteracting Fermions is expressed in terms of the density of the p-component in the free electron density matrix. This motivates the treatment of the Coulomb repulsion via a potential energy V(r) To close the theory, one must either invoke self-consistency to determine V(r), or relate it to the (direct) correlation function c(r) as in classical liquids. Both methods are briefly considered; the second has the advantage that here the collective plasma oscillations can be introduced through their zero-point energy.     

Statistical mechanical theory of liquid entropy

The multiparticle correlation expansion for the entropy of a classical monatomic liquid is presented. This entropy expresses the physical picture in which there is no free particle motion, but, rather, each atom moves within a cage formed by its neighbors. The liquid expansion, including only pair correlations, gives an excellent account of the experimental entropy of most liquid metals, of liquid argon, and of the hard-sphere liquid. The pair correlation entropy is well approximated by a universal function of temperature. Higher-order correlation entropy, due to n-particle irreducible correlations for n ≥ 3, is significant in only a few liquid metals, and its occurrence suggests the presence of n-body forces. When the liquid theory is applied to the study of melting, we discover the important classification of normal and anomalous melting, according to whether there is not or is a significant change in the electronic structure upon melting, and we discover the universal disordering entropy for melting of a monatomic crystal. Interesting directions for future research are extension to include orientational correlations of molecules, theoretical calculation of the entropy of water, application to the entropy of the amorphous state, and correlational entropy of compressed argon. We clarify the relation among different entropy expansions in the recent literature. © 1994 John Wiley & Sons, Inc.     

Properties of glass-forming metallic liquids: when is there a hard-sphere-like behaviour?

Chathoth and coworkers (Phys. Rev. Lett. 101, 037801 (2008)) have reported examples of multicomponent glass-forming metallic liquids in which the packing fraction appears to be a dominant parameter. Here, we first summarise, for 15 pure liquid metals, properties of the Ornstein–Zernike direct correlation function c(r) which provide a necessary, though not sufficient, condition for hard-sphere-like (HS) liquid behaviour. Returning to multicomponent melts, NiNb and NiNbSn systems have been studied by Chathoth and coworkers. Pure Ni, according to c(r) data near melting, satisfies the necessary condition for HS behaviour, while Sn certainly does not. But the Sn concentration is low in the metallic glass-forming liquid NiNbSn investigated by Chathoth and coworkers. Suitable experimental diffraction data to obtain c(r) in pure liquid Nb seems not to be available presently. Finally, a brief discussion is given of atomic transport in supercooled multicomponent metallic liquids, the status of the Stokes–Einstein relation being one focus.     

Optimized Random Phase Approximation for the Structure of Liquid Alkali Metals as Electron-Ion Plasmas

Abstract

In a previous publication¹ we have shown that the model of the one-component classical plasma on an inert background (OCP) provides a basis for calculating the liquid structure factor of the alkali metals. This was achieved by allowing the conduction electrons to screen the structure of the OCP through the formalism of linear screening theory, but an empirical cut-off of the screening correction at the first node of the electron-ion pseudpotential in wavenumber space was found to be necessary. The purpose of this letter is to stress that the above results point the way towards an unconventional optimized-random-phase-approximation (ORPA) approach² to the structure of these liquid metals, and in fact provide already a good first-order solution for such an approach.     

Investigation of terminal olefine in the isothiocyanatotolane liquid crystals with alkoxy end group

Three series of liquid crystals based on isothiocyanatotolane core with terminal alkenoxy groups (4A-1?4C-2) have been synthesised via multi-step reactions. Their thermotropic mesophases and physical properties are evaluated by comparison with the alkoxyl analogues (4a-1?4c-2). The results show that the isothiocyanatotolane LCs with alkenoxyl terminals deliver higher birefringence (0.410~0.436), lower melting points, lower melting enthalpies and viscosity. The effects of the alkenoxy terminal groups and the lateral fluoro substituents on the mesomorphic behaviour and physical properties are discussed. The formulation of the mixture containing isothiocyanatotolane liquid crystals with alkenoxyl terminals provides evidence of an useful candidate for liquid crystal photonics.     

A molecular-dynamics study of thermal and physical properties of platinum nanoclusters

Metallic nanoclusters are interesting because of their utility in catalysis and sensors. The thermal and physical characteristics of metallic Pt nanoclusters with different sizes were investigated via molecular-dynamics simulations using Quantum Sutton-Chen (QSC) potential. This force field accurately predicts solid and liquid states properties as well as melting of the bulk platinum. Molecular dynamic simulations of Pt nanoclusters with 256, 456, 500, 864, 1372, 2048, 2916, 4000, 5324, 6912, 8788 atoms have been carried out at various temperatures. The Pt-Pt radial distribution function, internal energy, heat capacity, enthalpy, entropy of the nanoclusters were calculated at some temperatures. These properties are used to characterize the physical phase and also to determine the melting transition of each nanocluster. The melting point predicted by the various properties is consistent with each other and shows that the melting temperature increases with the particle size, approaching to the bulk limit for the largest one. The size dependence of the melting point has been reported, both experimentally and theoretically for the atomic nanoclusters. We have found that the melting of the platinum nanoclusters commences at the surface and the relation T_m,N=T_m,bulk−αN^−1/3 between the melting point of nanocluster (T_m,N) and that of the bulk (T_m,bulk) holds. The extrapolation of T_m,N versus N^−1/3 gives T_m,bulk = 2058.1 K which is in a good agreement with the experimental value of 2041 K.     

基于季戊四醇的三代硅碳烷液晶树状物研究

用发散法合成了季戊四醇-四烯丙基醚为核、周边含硝基偶氮苯介晶基元(M-NO₂)端基的新型三代硅碳烷液晶树状物PCSi-3G-NO₂, 并利用元素分析、红外光谱(IR)、核磁共振(NMR)、偏光显微镜(POM)、差示扫描量热法(DSC)和X射线衍射(XRD)进行表征. PCSi-3G-NO₂显示胆甾相和近晶S_E相, 其液晶相行为是K57S_E115I100Ch80S_E53K. 而对应的介晶基元M-NO₂显示向列相, 二者在熔点、清亮点和液晶态温区等方面差别较大.     

Free Energies in the Landau and Molecular Field Approaches

Abstract

An expression for the entropy as a power series in the order parameter is derived in the context of molecular field theory. The expression is valid both at and away from equilibrium. It is a unique generalization of molecular field theory to non-equilibrium situations. Discrepancies with certain expressions which have appeared in the literature are resolved. Analysis of the radius of convergence of the power series indicates that in certain cases, including the Maier-Saupe model of liquid crystals, molecular field theory and Landau theory cannot be made to agree over the entire range of possible values of the order parameter.     

All‐electron relativistic computations on the low‐lying electronic states,bond length,and vibrational frequency of CeF diatomic molecule with spin–orbit coupling effects

Ab initio all‐electron computations have been carried out for Ce⁺ and CeF, including the electron correlation, scalar relativistic, and spin–orbit coupling effects in a quantitative manner. First, the n‐electron valence state second‐order multireference perturbation theory (NEVPT2) and spin–orbit configuration interaction (SOCI) based on the state‐averaged restricted active space multiconfigurational self‐consistent field (SA‐RASSCF) and state‐averaged complete active space multiconfigurational self‐consistent field (SA‐CASSCF) wavefunctions have been applied to evaluations of the low‐lying energy levels of Ce⁺ with [Xe]4f¹5d¹6s¹ and [Xe]4f¹5d² configurations, to test the accuracy of several all‐electron relativistic basis sets. It is shown that the mixing of quartet and doublet states is essential to reproduce the excitation energies. Then, SA‐RASSCF(CASSCF)/NEVPT2 + SOCI computations with the Sapporo(‐DKH3)‐2012‐QZP basis set were carried out to determine the energy levels of the low‐lying electronic states of CeF. The calculated excitation energies, bond length, and vibrational frequency are shown to be in good agreement with the available experimental data. © 2018 Wiley Periodicals, Inc.     

Relationships between the internal pressure,the cohesive energy,and the surface tension of liquids

The relationship between the internal pressure P_int on the one hand and the cohesive energy density ced on the other and the ratio of the surface tension to the cube root of the molar volume σ/V^1/3 (also called the Gordon parameter) was examined for a large number of liquids. These consisted of four classes: molecular liquids, liquid metals, room temperature ionic liquids (RTILs), and molten salts. Linear dependences, rather than proportionalities suggested by theory, were obtained in all cases, their slopes being independent of the type of the liquid (the exceptions being noted), but differ for P_int and ced.     

Temperature and density dependence of the structure of liquid lithium from an improved pseudopotential theory

Leribaux, H.R., and Lemarchand, J.L., 1978. Temperature and density dependence of the structure of liquid lithium from an improved pseudopotential theory. Fluid Phase Equilibria, 2: 79–90.The structure of liquid lithium and alloys has recently been measured more accurately near their melting point. We present for liquid lithium a modification of a previous pseudopotential for liquid metals, obtained by including explicitly the Xα exchange energy in the electron pseudopotential. The structure factor S(q), obtained from this model potential via the effective pair potential, and calculated by our solution of the Percus—Yevick equation, is found to have the right oscillations compared with the experimental structure factor, the first peak also having the right magnitude. A Percus—Yevick hard-sphere structure factor is also obtained via thermodynamic perturbation and is found to be surprisingly good even for lithium, except for the high-q oscillations. We present computed structures and radial distributions for several higher temperatures involved typically in the liquid lithium alloys, up to the highest temperatures at which saturated density is measured. Our model potential predicts also the correct cohesive energy for liquid lithium and liquid lithium—magnesium.     

AN EXCELLENT APPROACH TOWARDS THE DESIGNING OF A SCHIFF-BASE TYPE OLIGOCALIX[4]ARENE,SELECTIVE for THE TOXIC METAL IONS

ABSTRACT

A new Schiff-base type oligocalix[4]arene containing two nitrile ligating sites at narrow rim was synthesized via a simple condensation reaction through a wide rim of the calixarene moiety. The extraction ability of the oligomer with selected alkali and transition metals is compared with its monomeric analogous. It has been observed that the oligomer 6 is not selective as compared to its analogae 2 and 3, but shows a remarkable high affinity towards toxic metal cations such as Cu²⁺, Hg²⁺ and Pb²⁺.     

Extraction of Palladium(II) and Platinum(IV) from Hydrochloric Acid Solutions with Trioctylammonium Nitrate Ionic Liquid without Dilution

The fundamental properties and extraction capability of an ionic liquid (IL), trioctylammonium nitrate ([HTOA][NO₃]), for Pd^II and Pt^IV, are investigated. At room temperature, [HTOA][NO₃] is a solid (melting point: 30.7 °C), but it becomes a liquid (melting point: 16.7 °C) when saturated with water. Water-saturated [HTOA][NO₃] exhibits a viscosity of 267.1 mPa·s and an aqueous solubility of 2.821?×?10^?4 mol·dm^?3 at 25 °C, and can be used as an extraction solvent without dilution. [HTOA][NO₃] exhibits an extremely high extraction capability for Pd^II and Pt^IV in dilute hydrochloric acid (0.1–2 mol·dm^?3 HCl); the distribution ratio reaches 3 × 10⁴ for both the metals. From electrospray ionization mass spectrometry analysis, the species extracted in the IL phase are [PdCl₃]^? and [PdCl₂(NO₃)]^? for Pd^II and [PtCl₆]^2? and [PtCl₅]^? for Pt^IV. A majority of the other transition metals are considerably less or marginally extracted into [HTOA][NO₃] from a 0.1 mol·dm^?3 hydrochloric acid solution. The extraction capacity of [HTOA][NO₃] is greater than that of other hydrophobic ILs such as [HTOA]Cl and bis(trifluoromethanesulfonyl)imide-based ILs. The metals extracted into the IL phase are quantitatively back-extracted using an aqueous solution containing thiourea and nitric acid. By controlling the thiourea concentration and shaking time, Pd^II and Pt^IV are mutually separated to some extent in the back extraction process. The IL phase used for the back extraction can be reused for the forward extraction of these metals after scrubbing it with an aqueous nitric acid solution.     

Surface tension of pure liquid lanthanide and early actinide metals

A systematic theoretical study of the surface tension of liquid rare earth metals and early actinides is performed. An equation, based on the theoretical considerations suggested by Eyring, enables one to calculate the surface tension of elementary substances in a wide temperature range from melting to boiling points. The results of temperature-dependent surface tension calculations of a pure liquid terbium (1629–1880?K) are fitted as γ?=?845?0.1 (T???T _m) (mJ?m²), where the surface tension decreases linearly with temperature. The surface tension was also calculated, at melting points, for all the liquid rare earth metals from La to Lu and for the first six metals of the actinide series from Ac to Pu. It is observed that the lanthanides may be divided into three groups in accordance with their electronic structure. Mostly, the calculated results agree well with available experimental data.