Arrays of Charged (±2π)-Twist Disclinations in Ferroelectric Liquid Crystals

The notion of an electrostatic charge of (±2)-twist disclinations is used to approximate the evaluation of the electrostatic interaction energy among disclinations forming arrays in finite samples of ferroelectric chiral smectic C liquid crystals. Screening effects of free charges in a material surrounding the disclination are taken into account by introducing a phenomenological depolarisation factor.The electrostatic interaction energy is important in chiral smectic C materials with high values of the spontaneous polarisation when screening effects of free charges are small. Then the electrostatic interaction leads to elimination of disclinations from the sample. When there is a high concentration of free charges in the sample (smaller value of depolarisation factor), the electrostatic interaction energy is of the order of the elastic interaction energy of disclinations what influences the equilibrium of disclination arrays in the sample. Two disclination configurations are considered. In the Brunet-Williams configuration the disclinations of opposite topological charge have also the opposite electrostatic charge so their attraction is augmented. This attraction can be balanced by the helical structure in the central part of the sample when the sample thickness is rather high.On the contrary, in the Glogarová-Pavel configuration the disclinations of opposite topological charge have the electrostatic charge of the same sign. The equilibrium in this configuration is either a balance of elastic attraction and electrostatic repulsion if elastic and Coulomb forces are of the same order or it is governed by the value of the anchoring energy when electrostatic interaction prevails over the elastic one.     

Lattice Boltzmann Simulation of 3D Nematic Liquid Crystal near Phase Transition

Phase transition between nematic and isotropic liquid crystal is a very weak first order phase transition.We avoid to use the normal Landau-de Gennes‘s free energy that reduces a strong first order transition,and set up a data base of free energy calculated by means of Tao-Sheng-Lin‘s extended molecular field theory that can explain the experiments of the equilibrium properties of nematic liquid crystal very well.Then we use the free energy method of lattice Boltzmann developed by Oxford group to study the phase decomposition,pattern formation in the flow of the liquid crystal near transition temperature.     

Electron-beam-initiated crystallization of iron-carbon films

A structure formed in nanocrystalline iron-carbon films exposed to an electron beam was studied. Explosive crystallization (EC) with the formation of dendrite and cellular-dendritic instabilities at a rate of up to 1 cm/s was observed. It was shown that the dependence between the growth rate of dendrite branches (or cells) during EC and the rounding radius of dendrite branch tips can be approximately described by equations used to calculate the crystal growth in supercooled melts. To explain the EC mechanism, a model of a liquid zone formed at the crystallization front was used. It was shown that the liquid zone arises due to energy accumulated in the film in the nanocrystalline state. It was assumed that this energy was accumulated due to the energy of elastic stresses.     

Density functional theory for chiral nematic liquid crystals

ABSTRACT

In this note, the density functional theory for chiral nematic liquid crystals is expressed in terms of rotational invariant expansion coefficients of the pair-excluded area at fixed separation. This modification from the standard approach, without making any additional assumptions, yields a more efficient procedure for minimising the free energy, as well as providing insight into the origins of the effect away from the long-pitch limit.     

拓扑荷在圆盘状向列相液晶薄膜中的尺寸效应

拓扑现象对于病毒颗粒的空间分布、高分子聚合物纳米囊泡的成型以及玻色-爱因斯坦凝聚物等方面都发挥着重要作用.本文利用Landau-de Gennes理论,构建模型来模拟液晶中拓扑荷分布及其他现象.通过对数值模型序参量场的演化,以及模拟液晶薄膜中所生成的拓扑荷之间的相互作用来分析液晶(Lqc)薄膜的尺寸对拓扑荷的影响.研究结果表明,随着液晶盘半径增大,拓扑荷间最优距离与半径之比渐增并趋于稳定.此研究结论对利用拓扑荷凝聚颗粒物效应设计分离容器有指导意义,有助于进一步理解拓扑胶体和液晶以及液晶共聚物等软物质中的拓扑现象.     

Electroexplosive Carburizing of Iron: Surface Relief,Phase Composition and Defect Substructure

Surface relief, phase composition and defect substructure of the surface layer of iron specimens are investigated using scanning and transmission electron microscopy after high-energy electroexplosive carburizing treatment. The structure formed is shown to exhibit a conspicuous gradient character resulting from variations in carbon content with the layer depth. It is found out that a liquid melt of the sublayer of nanocrystalline structure is formed at the boundary of the melt pool. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 36–41, September, 2005.     

The evolution of coordination structure in liquid GaSn alloy

The dynamic viscosity and the liquid structure of Ga₉₈Sn₂ alloy melt at different temperatures were measured by a torsional oscillation viscometer and an x-ray diffraction. The viscosity of the liquid Ga₉₈Sn₂ alloy increases with decreasing temperature and an obvious turning point is observed on the Arrhenius curve. The breakpoint in Arrhenius plot emerges when the structure of Ga₉₈Sn₂ alloy melt is transformed from the high coordinated polyhedron clusters to the low coordinated polyhedron clusters. It is found that the change of the viscosity is a characteristic of microstructure transformation in the alloy melt.     

液晶在电场和剪切耦合作用下的流变学行为

本文通过理论和实验对液晶 5CB在剪切和电场耦合作用下流变行为进行了研究. 采用液晶连续理论, 建立了包括界面锚定能, 弹性自由能, 介电自由能和流动能在内的系统 Gibbs自由能公式, 通过最小化系统自由能的方法求解液晶在剪切和电场耦合作用下的取向分布及其黏度变化, 从分子基础模型上揭示了液晶在耦合作用下的流变行为、微观机理及其影响规律, 并通过流变测试对此进行验证. 对比分析了理论和试验结果的误差和原因, 发现界面锚定效应对于液晶分子的取向和黏度具有重要影响. 理论和试验结果均表明, 液晶在电场作用下具有明显的电黏效应, 表现出非牛顿流变行为, 其黏度值由剪切和电场的竞争和耦合作用共同决定. 在外电场作用下液晶的黏度可以增加到初始值的 4倍左右, 液晶这种其自身黏度可随着外场 (例如运动速度) 改变的特性在一定的条件下可以自适应地满足不同工况对黏度的要求, 这对实现智能摩擦润滑具有重要的意义. 关键词： 液晶 流变行为 电黏效应 耦合作用     

Acoustic identification of nanocrystalline media

Two-dimensional (2D) models of nanocrystalline media with close proximity (a hexagonal lattice) and with non-dense packing (a square lattice) are considered in this paper. It is supposed that particles have a round shape and possess two translational and one rotational degrees of freedom. The differential equations describing the propagation of acoustic and rotational waves in such media have been derived. Analytical relationships between the macroelasticity constants of the medium and microstructure parameters have been found. These relationships appear to be different for nanocrystalline media with hexagonal and square lattices. It has been shown that identification of macroparameters of a nanocrystalline medium can be obtained by measurement of wave velocities and the form of dispersion dependences of acoustic and rotational waves.     

Anisotropic growth of multigrain in equiaxial solidification simulated with the phase field method

The phase field method has been mainly used to simulate the growth of a single crystal in the past. But polycrystalline materials predominate in engineering. In this work, a phase field model for multigrain solidification is developed, which takes into account the random crystallographic orientations of crystallites and preserves the rotational invariance of the free energy. The morphological evolution of equiaxial multigrain solidification is predicted and the effect of composition on transformation kinetics is studied. The numerical results indicate that due to the soft impingement of grains the Avrami exponent varies with the initial melt composition and the solidification fraction.     

Formation and structure of nanocrystals in an Al86Ni11Yb3 alloy

The formation and structure of the nanocrystalline phase in the Al₈₆Ni₁₁Yb₃ alloy are investigated using differential scanning calorimetry (DSC), transmission electron and high-resolution electron microscopy, and x-ray diffraction. The nanocrystalline phase is formed upon controlled crystallization of the amorphous alloy prepared by quenching of the melt on a rapidly moving substrate. It is revealed that the nanocrystalline alloy consists of aluminum nanocrystals (5–12 nm in size) randomly distributed in the amorphous matrix. The maximum fraction of the nanocrystalline phase does not exceed 25%. The nanocrystal size substantially increases at the initial stage of isothermal treatment (at 473 K) and then changes insignificantly. It is found that nanocrystals are usually free of defects. However, some nanocrystals have a more complex microstructure with twins and dislocations. The size distributions of nanocrystals are determined at several durations of isothermal treatment. It is demonstrated that the nucleation of nanocrystals predominantly occurs through the heterogeneous mechanism. The experimental distributions are compared with those obtained from a computer simulation. The activation energy of crystallization, the time-lag, and the coefficient of ytterbium diffusion in the alloy are estimated     

Melting of embedded anisotropic particles: PbIn inclusions in Al

Small particles embedded in the solid state can assume facetted shapes that indicate the anisotropy in interfacial free energy between the particle and the embedding phase. Previous in situ transmission electron microscopy (TEM) of Al–In has shown that such facetted nanoparticles with cubic symmetry embedded in a solid can produce a series of complex melt configurations. To determine the dependence of melt configuration on solid–solid facet energies, this work numerically calculates the equilibrium melt trajectory for a family of cuboctahedral particles parameterized by the ratio of matrix–particle interfacial free energies for orientations taken with respect to the crystal axes of the matrix, ??=?γ₁₀₀/γ₁₁₁. The calculations assume that equilibrium occurs with the minimization of the total interfacial free energy to determine the stable internal melt configuration for a fixed volume of melt confined within a member of the cuboctahedral family. At particular melt volume fractions, abrupt transitions in shape occur when a stable configuration reaches a touching or necking instability. In situ TEM of a dilute Al alloy containing embedded nanosized PbIn inclusions that gradually melt as the temperature is increased from 230 to 260°C is consistent with the results calculated for ??=?1.245.     

On the control of microstructure in rapidly solidified Nd–Fe–B alloys through melt treatment

Rapidly solidified (RS) Nd₂Fe₁₄B alloys were prepared by melt-spinning under different melt treatment conditions i.e., the melt temperature was varied prior to ejection onto the quenching wheel. X-ray diffraction, transmission electron microscopy, thermal analysis and magnetic measurement were conducted on the as-quenched alloys to investigate their structural and magnetic characteristics. RS Nd₂Fe₁₄B alloys may display a variety of microstructures depending upon the thermal history of the melt before ejection: it was possible to synthesize an entirely amorphous structure, a partially amorphous structure containing nuclei and/or nanophases and a nanocrystalline structure. The relationship between the formation of crystalline nuclei or nanophases and the thermal history of the melt was studied. A lower melt ejection temperature produced a nanocrystalline microstructure, while higher melt ejection temperatures (T>1723 K) largely eliminated the presence of nuclei and associated nanophases and produced an amorphous product. The experimental results indicated that optimization of the melt treatment conditions will produce rapidly solidified Nd–Fe–B alloys with a more uniform microstructure.     

毛细作用的变分法理论

以圆柱形毛细管内壁、毛细管内的液体和气体为研究对象.设毛细管液体的表面为旋转面,写出了系统的自由能(表面能及重力势能)的泛函.使自由能泛函取极值的欧拉方程就是关于附加压强的拉普拉斯公式.泛函取极值时在可动边界(毛细管内壁)上的边界条件就可导出关于接触角的杨氏方程.此二方程是自由能取极值的密不可分的两个必要条件.     

Effective interactions between concentration fluctuations and charge transfer in chemically ordering liquid alloys

Summary The correlations between long-wavelength fluctuations of concentration in a liquid binary alloy are determined by a balance between an elastic-strain free energy and an Ornstein-Zernike effective interaction. The latter is extracted from thermodynamic data in the case of the Li−Pb system, which is well known to chemically order with stoichiometric composition corresponding to Li₄Pb. Strong attractive interactions between concentration fluctuations near the composition of chemical ordering originate from electronic charge transfer, which is estimated from the electron-ion partial structure factors as functions of composition in the liquid alloy. In honour of Prof. Fausto Fumi on the occasion of his retirement from teaching.     

磷化铟单晶生长中的传热和流动分析

用有限元法对轴向磁场存在下3英寸磷化铟单晶液封提拉法生长中的传热和流动进行了求解．结果表明:液封改变了晶体表面被封部分的换热,进而影响生长界面的形状．增加磁场强度能有效减弱熔体和封层内的流动,并使生长界面形状发生变化。增加提拉速度,生长界面形状由凸变凹．随晶体转速的增加,多涡胞流动出现．     

向列型液晶中短程序的计算

向列型液晶中的短程序有重要的物理效应。本文在格胞理论的基础上,用新的数值方法计算这些效应。不用任何函数展开,通过平衡态方程送代求解,得到精确的取向分布函数。从而计算各种物理量,给出了相变点序参数、熵变等量的精确数值。     

Contribution of Disclination Lines to Free Energy of Liquid Crystals in Single-Elastic Constant Approximation

In the light of C-mapping method and topological current theory, the contribution of disclination lines to free energy density of liquid crystals is studied in the single-elastic constant approximation. It is pointed out that the total free energy density can be divided into two parts. One is the usual distorted energy density of director field around the disclination lines. The other is the free energy density of disclination lines themselves, which is shown to be centralized at the disclination lines and to be topologically quantized in the unit of kn/2. The topological quantum numbers are determined by the Hopf indices and Brouwer degrees of the director l~eld at the disclination lines, i.e. the disclination strengths. From the Lagrange‘s method of multipliers, the equilibrium equation and the molecular field ofliquid crystals are also obtained. The physical meaning of the Lagrangian multiplier is just the distorted energy density.     

On the crystallization of two-dimensional electron system in strong magnetic field

The possibility of the two-dimensional electron crystallization in the strong magnetic field is discussed by comparison between electron free energies in liquid and crystal states. The electron free energy in the liquid state is determined in Hartree-Fock approximation, while the correlation phenomena are proved to be negligible. The electron free energy in the crystal state is calculated in the harmonic approximation. The magnetic field is shown to “nonmonotonously” affect the crystal formation. From one hand, an electron crystal may exist in an interval of the strong magnetic field H at rather high density, where that is impossible at H=0. From the other hand, at any density the sufficiently strong field forces electron lattice to melt at finite temperature.     

Growth kinetics of polymer crystals in bulk

Temperature-dependent measurements of spherulite growth rates carried out for i-polystyrene, poly(ε -caprolactone) and linear polyethylene show that the controlling activation barrier diverges at a temperature which is 14K, 22K and 12K, respectively, below the equilibrium melting points. We discuss the existence of such a “zero growth temperature” T _zg in the framework of a recently introduced thermodynamic multiphase scheme and identify T _zg with the temperature of a (hidden) transition between the melt and a mesomorphic phase which mediates the crystal growth. The rate-determining step in our model of crystal growth is the attachment of chain sequences from the melt onto the lateral face of a mesomorphic layer at the growth front. The necessary straightening of the sequence prior to an attachment is the cause of the activation barrier. A theory based on this view describes correctly the observations. With a knowledge of T _zg it is possible to fully establish the nanophase diagram describing the stability ranges of crystalline and mesomorphic layers in a melt. An evaluation of data from small-angle X-ray scattering, calorimetry and optical growth rate measurements yields heats of transition and surface free energies of crystals and mesophase layers, as well as the activation barrier per monomer associated with the chain stretching. According to the theory, the temperature dependence of the crystallization rate is determined by both the activation energy per monomer and the surface free energy of the preceding mesomorphic layer. Data indicate that the easiness of crystallization in polyethylene is first of all due to a particularly low surface free energy of the mesomorphic layer.