Resistivity and thermoelectric power of molten aluminium: experiment and theory

The electrical resistivity?ρ?of metallic liquid aluminium is measured as a function of temperature. The measurement needs an experimental design able to get the resistivity of a very reactive liquid metal. Liquid aluminium seems to be a simple metal. We first interpret the experimental results by using an ab initio calculation of the electrical resistivity ρ(E) as function of the electron energy, taking into account recent exchange and correlation contributions in the framework of the generalized gradient approximation (GGA). But surprisingly the classical theoretical interpretation leads to an apparent inconsistency. Thus we discuss the sensitivity of the calculation on the inputs and propose improvements of the theoretical approach. They allow a better physical understanding of pure liquid aluminium which is absolutely necessary before undertaking the study of liquid aluminium alloys.     

Stability criteria, atomization and non-thermal processes in liquids

Analyzing the first equation in the BBGKY chain of equations for an equilibrium liquid–gas system, we derived the analytical expression for the atom work function from liquid into gas. The coupling between the atom work function from liquid into vacuum and the stability criterion of liquid in limiting points of the first type was shown (using I.Z. Fisher classification). As it turned out, Fisher’s criterion corresponds to the condition of atomization. We have expressed the state equation in terms of the atom work function from liquid into vacuum and performed calculations of the limiting line of stability composed of limiting points of the first type for argon. Our model discovers an interesting effect of the negative atom work function: at a constant volume of liquid, on a temperature rise (also at a fixed temperature and decreasing specific volume of liquid) the atom work function drops and takes a negative value with a modulus that is significantly larger than the atomic thermal energy. We propose a new two-stage mechanism of sonoluminescence based on non-thermal processes in liquid in a state with a negative atom work function. The first stage includes the emission of atoms from the interior of the bubble into gas at hyper-thermal velocities. At the second stage, a collision of emitted flow takes place between the gas atoms along with the implosion of the central part of the bubble. As a result of the impact excitation, ionization and the subsequent recombination, a flash of electromagnetic radiation develops that can be seen in sonoluminescence experiments.     

Bosonization of coupled electron-phonon systems

We calculate the single-particle Green’s function of electrons that are coupled to acoustic phonons by means of higher dimensional bosonization. This non-perturbative method is not based on the assumption that the electronic system is a Fermi liquid. For isotropic threedimensional phonons we find that the long-range part of the Coulomb interaction cannot destabilize the Fermi liquid state, although for strong electron-phonon coupling the quasi-particle residue is small. We also show that Luttinger liquid behavior in three dimensions can be due to quasi-one-dimensional anisotropy in the electronic band structure or in the phonon frequencies.     

Structure of liquid Al and Al67Mg33 alloy: comparison between experiment and simulation

We report data on the structure of liquid Al and an Al₆₇Mg₃₃ alloy obtained from state-of-the-art X-ray diffraction experiments and ab initio molecular dynamics (AIMD) simulations. To facilitate a direct comparison between these data, we develop a method to elongate the AIMD pair correlation function in order to obtain reliable AIMD structure factors. The comparison reveals an appreciable level of discrepancy between experimental and AIMD liquid structures, with the latter being consistently more ordered than the former at the same temperature. The discrepancy noted in this study is estimated to have significant implications for simulation-based calculations of liquid transport properties and solid–liquid interface kinetic properties.     

A biaxial nematic liquid crystal composed of matchbox-symmetric molecules

By means of Monte Carlo simulations in the isothermal-isobaric ensemble, we investigate the structure and phase behaviour of a thermotropic liquid crystal composed of matchbox-symmetric (or board-like) molecules. Besides the isotropic phase the liquid crystal exhibits also uniaxial and biaxial nematic phases. The interaction potential is derived through an expansion in terms of Stone's rotational invariants [A. J. Stone, Mol. Phys. 78, 241–256 (1978).] that can be reexpressed in terms of Cartesian tensors. This latter formulation is particularly well suited for computer simulations. We analyse the orientation distribution function which allows us to distinguish between intrinsic and extrinsic biaxiality. In addition, we study the orientation-dependent correlation functions. In the limit of large intermolecular separations, the value of the orientation correlation function corresponds to the uniaxial and biaxial order parameters which are coupled in a complex fashion.     

Electron bound states on liquid helium

Using an exactly soluble model of image potential which has the form -Ze²/ (z+β), we have calculated the energy levels of electrons trapped on the surface of liquid helium as a function of the parameter β. Our results show that the experimental values of Grimes et al can be fit very well by locating the effective liquid helium-vacuum interface at β = 1.01 Å.     

The equation of state of a system of hard spherocylinders

Using the Monte Carlo method, we have computed the equation of state of a system of hard spherocylinders (cylinders with a hemisphere at each end), of length-to-breadth ratio equal to 3, in the isotropic liquid phase. We obtain a pressure slightly smaller than that predicted by the scaled-particle theory (SPT). The SPT predicts a liquid to nematic transition when the density is increased; we have observed that the isotropic liquid phase is stable up to densities significantly higher than the SPT transition density. Using the free-volume theory, we have also determined the behaviour of the pressure at very high densities, for any value of the length-to-breadth ratio γ. Moreover, we have shown that the packing fraction (number density times the volume of one spherocylinder) corresponding to the beginning of the fusion of the solid is an increasing function of γ.     

共振价键波函数在高压液氢量子蒙卡模拟中的适用性研究

在共振价键理论基础上, 选取高压液氢电子主要占据轨道的线性组合作为基组, 构建由Jastrow项和反对称孪生函数乘积项 (AGP) 组成的波函数. 考虑电子关联作用的共振价键 (RVB) 波函数得出的能量值低于LDA能量值; 当满足r_s<1.75或T >15000 K时引入backflow项以改善波函数结点面, 改善后的能量值下降约1 mHa/atom, 能量方差值变小. 将构建的RVB波函数与电子-离子耦合的蒙特卡罗法 (CEIMC) 相结合, 计算结果与实验及其他ab-initio结果相符合, 获得的液氘单次冲击Hugoniot曲线基本通过所有加载类型实验误差棒, 液氘在50.3 GPa处具有最大压缩率4.48, 在100–120 GPa内未发现压缩率有急剧增大的现象. 构建的RVB 波函数能够适用于较宽密度与温度范围内(1.0< r_s<2.2, 2800 K< T<60000 K)液氢的模拟, 与CEIMC法相结合可提高液氢冲击特性的模拟精度. 关键词： 共振价键理论 波函数 量子蒙卡法 液氢     

Spin-spin correlation effect on the thermodynamic properties of the polarized liquid 3He at finite temperature

We have used the lowest order constrained variational (LOCV) method to calculate some thermodynamic properties of the polarized liquid ³He at finite temperature with the spin-dependent correlation function. For each value of the temperature and density we have shown that the main contribution to the potential energy comes from the spin-triplet state. For the polarized liquid ³He, we have seen that the differences between the thermodynamic properties of the spin-dependent and the spin-independent cases decrease by increasing both polarization and temperature. For all relevant temperatures and densities, our results do not show any ferromagnetic phase transition.     

Molecular Dynamics Simulations of Liquid Phosphorus at High Temperature and Pressure

By performing ab initio molecular dynamics simulations, we have investigated the microstructure, dynamical and electronic properties of liquid phosphorus （P） under high temperature and pressure. In our simulations, the calculated coordination number （CN） changes discontinuously with density, and seems to increase rapidly after liquid P is compressed to 2.5 g/cm3. Under compression, liquid P shows the first-order liquid-liquid phase transition from the molecular liquid composed of the tetrahedral P4 molecules to complex polymeric form with three-dimensional network structure, accompanied by the nonmetal to metal transition of the electronic structure. The order parameters Q6 and Q4 are sensitive to the microstructural change of liquid P. By calculating diffusion coefficients, we show the dynamical anomaly of liquid P by compression. At lower temperatures, a maximum exists at the diffusion coefficients as a function of density; at higher temperatures, the anomalous behavior is weakened. The excess entropy shows the same phenomena as the diffusion coefficients. By analysis of the angle distribution functions and angular limited triplet correlation functions, we can clearly find that the Peierls distortion in polymeric form of liquid P is reduced by further compression.     

Stabilization of electron-hole liquid in uniaxially strained germanium in a strong magnetic field

Luminescence spectra of uniaxially and uniformly strained high-purity germanium crystals at liquid-helium temperatures in a magnetic field of up to 14 T have been investigated. In strongly strained Ge crystals, a new line has been detected on the low-energy side of the excitonline in magnetic fields higher than 4 T. Studies of this line’s characteristics as functions of pressure, temperature, and magnetic field have led us to conclude that its presence is due to recombination of electron-hole pairs in an electron-hole liquid. The experimental data suggest that the metallic electron-hole liquid is stabilized in a strong magnetic field. By approximating the shape of the newly detected line using the model of metallic electron-hole liquid, we have obtained the electron-hole liquid density n _EHL(B) and Fermi energies E _Fe,h of electrons and holes. The liquid binding energy ø as a function of magnetic field has been estimated.     

Stability of the Landau–Fermi Liquid Theory

The stability of the Landau–Fermi liquid theory is investigated. It has been shown that if the interaction function of the Fermi system is a finite function of the angle between the momenta of two particles at the Fermi surface, then the liquid can be stable. We have shown that the absolute value of the expansion coefficients of the interaction functions in Legendre polynomials are decreasing function of the coefficients indices. We solve the stability condition for one photon exchange (OPE) in an electron gas. The results show that we must use the massive boson propagator (higher order corrections to the photon propagator). Similar to previous works (Abrikosov et al. in Method of Quantum Field Theory in Statistical Physics, Pergamon, Elmsford, 1965), our result is proportional to g ². The density and temperature dependence of results is occulted in the effective mass of the system.     

State-dependent diffusion coefficients and free energies for nucleation processes from Bayesian trajectory analysis

ABSTRACT

The rate of nucleation processes such as the freezing of a supercooled liquid or the condensation of supersaturated vapour is mainly determined by the height of the nucleation barrier and the diffusion coefficient for the motion across it. Here, we use a Bayesian inference algorithm for Markovian dynamics to extract simultaneously the free energy profile and the diffusion coefficient in the nucleation barrier region from short molecular dynamics trajectories. The specific example we study is the nucleation of vapour bubbles in liquid water under strongly negative pressures, for which we use the volume of the largest bubble as a reaction coordinate. Particular attention is paid to the effects of discretisation, the implementation of appropriate boundary conditions and the optimal selection of parameters. We find that the diffusivity is a linear function of the bubble volume over wide ranges of volumes and pressures, and is mainly determined by the viscosity of the liquid, as expected from the Rayleigh–Plesset theory for macroscopic bubble dynamics. The method is generally applicable to nucleation processes and yields important quantities for the estimation of nucleation rates in classical nucleation theory.     

Freedericksz transition in polymer-stabilized nematic liquid crystals

We have constructed polymer-stabilized nematic liquid crystals by photopolymerizing diacrylate monomers in the nematic phase. The orientation of the liquid crystal was controlled by the polymer network. We studied the Freedericksz transition in these systems. Experimentally we studied the transition by measuring the capacitance of the liquid crystal cells as a function of applied voltage. The transition was affected profoundly by the dispersed polymer network. The threshold was higher with shorter interpolymer network distance. Theoretically we studied the systems using a two-dimensional model in which the polymer networks were represented by parallel cylinders with random location. The interaction between the liquid crystal and the polymer network was described by the boundary condition imposed by the polymer network. By fitting the experimental data, we found that the polymer cylinders had diameters of a few submicrons, and a substantial amount of liquid crystal was trapped inside the cylinders.     

Electrohydrostatic wetting of poorly-conducting liquids

The wetting behavior of poorly conducting fluids between two parallel conducting plates is studied, both, theoretically and experimentally. In the absence of an applied potential, the interface shape and height are determined by gravity and parameterized using the Bond number. In the presence of an electric field at sufficiently high values on the order of (1 kV/mm), there is modification of the interfacial stresses and liquid level. Here we measure the liquid level height as a function of the hydrostatic and electric Bond numbers.     

Fermi liquid theory: a renormalization group approach

We show how Fermi liquid theory results can be systematically recovered using a renormalization group (RG) approach. Considering a two-dimensional system with a circular Fermi surface, we derive RG equations at one-loop order for the two-particle vertex function in the limit of small momentum () and energy () transfer and obtain the equation which determines the collective modes of a Fermi liquid. The density-density response function is also calculated. The Landau function (or, equivalently, the Landau parameters F _l ^s and F _l ^a ) is determined by the fixed point value of the -limit of the two-particle vertex function (). We show how the results obtained at one-loop order can be extended to all orders in a loop expansion. Calculating the quasi-particle life-time and renormalization factor at two-loop order, we reproduce the results obtained from two-dimensional bosonization or Ward Identities. We discuss the zero-temperature limit of the RG equations and the difference between the Field Theory and the Kadanoff-Wilson formulations of the RG. We point out the importance of n-body () interactions in the latter. Received: 27 June 1997 / Received in final form: 17 December 1997 / Accepted: 26 January 1998     

The mean field model with P2θ2 coupling for the smectic A-smectic C* phase transition in liquid crystals

Using mean field theory with a P²θ² coupling term in the free energy expansion, we calculate the polarization as a function of temperature for the smectic A-smectic C* phase transition in a liquid crystalline material. Our calculated polarization values are in good agreement with the experimental data.     

Analysis of roughness of Cs surfaces via evaluation of the autocorrelation function

At low temperature prepared quench-condensed Cs surfaces are analysed on a nanometer scale via scanning tunneling microscopy. The analysis of surface roughness is presented with the help of the evaluation of their autocorrelation function. In order to extract the correct autocorrelation function we present the requirement regarding the scan resolution of scanning probe microscopy (SPM) images in general. This is supported by a ‘numerical experiment’. Furthermore, we present some methods of deducing higher orders of autocorrelation lengths, which are needed to evaluate SPM images with non-random distribution of roughness amplitudes. These characteristic values of the autocorrelation function could play the key role in further statistical calculations, e.g., on how surface roughness alters the wetting behaviour of liquid helium adsorbed on the cesium surfaces.     

Theoretical and computer simulation study of density fluctuations in liquid binary alloys

The dynamical properties of liquid alloys are investigated by means of memory function equations and molecular-dynamics simulation. A simple model for the second-order memory function in a binary liquid, based on Mori's memory function formalism, is proposed and applied in numerical calculations of the time correlation functions and dynamic structure factor of liquid K_0.7Cs_0.3 and K_0.3Cs_0.7 alloys. Obtained results are discussed in comparison with the results of computer simulations. Received: 27 February 1998 / Revised: 24 July 1998 / Accepted: 27 July 1998