Local atomic structures of amorphous Pd80Si20 alloys and their configuration heredity in the rapid solidification

The local atomic structures of amorphous Pd₈₀Si₂₀ alloys and their configuration heredity in the rapid solidification are investigated by a molecular dynamics simulation with the help of cluster-type index method based on Honeycutt–Anderson bond-type index and an inversely tracking technique of atomic trajectories. Their short-range orders are found to be various Kasper clusters as well as their distorted configurations, and among which (10 2/1441 8/1551) bi-capped square Archimedean anti-prism (BSAP) clusters are dominated, e.g. Si-centred Pd₁₀Si₁ clusters. These Kasper clusters mainly exist in the form of isolated basic clusters. Few medium-range orders can be detected, especially for Si-centred Kasper clusters. Similarly to icosahedrons of Cu–Zr amorphous alloys, their sustainable configuration heredity also occurs firstly in the super-cooled liquid region, and BSAP clusters have higher onset temperature T_onset and bigger descendible fraction F than other Kasper clusters in the rapid solidification of Pd₈₀Si₂₀ alloys.     

Stability of Disclinations in Nematic Liquid Crystals

In the light of φ-mapping method and topological current theory, the stability of disclinations around a spherical particle in nematic liquid crystals is studied. We consider two different defect structures around a spherical particle: disclination ring and point defect at the north or south pole of the particle. We calculate the free energy of these different defects in the elastic theory. It is pointed out that the total Frank free energy density can be divided into two parts. One is the distorted energy density of director field around the disclinations. The other is the free energy density of disclinations themselves, which is shown to be concentrated at the defect and to be topologically quantized in the unit of (k-k₂₄)π/2. It is shown that in the presence of saddle-splay elasticity a dipole (radial and hyperbolic hedgehog) configuration that accompanies a particle with strong homeotropic anchoring takes the structure of a small disclination ring, not a point defect.     

Effect of Saddle-Splay Elasticity on Stability of Disclination Rings in Nematic Liquid Crystals

In this paper, the stability of disclination ring in nematic liquid crystals is studied. In the presence of saddle-splay elasticity (characterized by k₂₄) the disclination ring has a universal equilibrium radius. Depending on the values of the saddle-splay constant k₂₄, the universal equilibrium radius is altered. When k₂₄>0.92k (m=1/2) and k₂₄>0.88k (m=-1/2), the disclination will be a point rather than a ring, where $k$ is the Frank elastic constant in the one-constant approximation.     

Defects in smectic C* liquid crystals

We consider the structure and properties of various topological defects that can occur in smectic C* liquid crystals. The polarization field associated with disclinations, the effect of incommensuration on the structure of dispirations, some interesting situations in the interaction between dispiration and disclination and between dispirations themselves have been discussed in detail. The properties of cholesteric type disclinations and a possible model for the core structure of a wedge disclination have also been dealt with. The author felicitates Prof. D S Kothari on his eightieth birthday and dedicates this paper to him on this occasion.     

Fields of stress and electric displacement produced by dislocations and disclinations in three-dimensional,anisotropic, elastic,and piezoelectric media. II. Infinite straight dislocation and Frank disclination

The fields of stress and electric displacement caused by infinitely extended straight dislocations and Frank disclinations are deduced from the author's statements for the fields caused by a continuous distribution of dislocations and disclinations (S. Minagawa, Phil. Mag. 84 2229 (2004)). The multiple integrals in the original statements are converted into functions of space coordinates. Cauchy's theorem plays an important part. The improper integral that appears in computations of the fields around a Frank disclination is interpreted as its finite part by Hadamard. Examples are the fields around an infinite straight defect in caesium copper chloride, as well as those in gallium arsenide. The contours and zero lines are plotted to illustrate the fields caused by a dislocation and a disclination dipole.     

Effect of Disclination Lines on Free Energy of Nematic Liquid Crystals

In the light of φ-mapping method-and topological current theory, the effect of disclination lines on the free energy density of nematic liquid crystals is studied. It is pointed out that the total Frank free energy density can be divided into two parts. One is the distorted energy density of director field around the disclination lines. The other is the saddle-splay energy density, which is shown to be centralized at the disclination lines and to he topologically quantized in the unit of kπ/2 when the Jacobian determinant of the director field does not vanish at the singularities of the director field. The topological quantum numbers are determined by the Hopf indices and Brouwer degrees of the director field at the disclination lines, i.e., the disclination strengthes. When the Jacobian determinant vanishes, the generation, annihilation, intersection, splitting and merging processes of the saddle-splay energy density are detailed in the neighborhoods of the limit points and bifurcation points, respectively. It is shown that the disclination line with high topological quantum number is unstable and will evolve to the low topological quantum number states through the splitting process.     

Atomic quantum diffusion,tunnelling states and some related phenomena in condensed systems

This article presents a review of some basic problems and results in the theory of atomic quantum diffusion, atomic tunnelling states and some related phenomena in condensed systems: crystals and amorphous materials.General concepts, including the defecton concept, are reviewed in the introduction. The first part of this paper considers the principal ideas, results and problems in the quantum diffusion theory for both underbarrier and overbarrier transitions of atomic particles in solids. Much attention is given to the fundamental role of the interactions between a weakly tunnelling particle and its environment, i.e. defects, other tunnelling particles and thermal fluctuations of atomic configurations.The second part of this review deals with the theory of atomic tunnelling states, their peculiar origin and low-temperature effects and, particularly, the origin and effects of the intrinsic atomic low-energy excitations in amorphous materials. The third part of this article discusses some related low-temperature phenomena. Some experimental data associated with the phenomena under consideration are presented. Finally, some actual problems of the theory are discussed in the Concluding Remarks.The review contains a discussion of results mainly coming to our attention by the summer of 1982.     

Atomic resolution imaging of the (001) surface of UHV cleaved MgO by dynamic scanning force microscopy

The (001) surface of UHV cleaved single MgO crystals was imaged with dynamic mode scanning force microscopy. Large-scale images show various defects, like steps of mostly one atomic height, rectangular holes of nanometer size, and some complex adstructures. First time images with atomic resolution show one square ionic sublattice in its bulklike dimension with a corrugation of up to 40 pm along the <001> direction. Most images exhibit atomic point defects which appear as depressions including a few ionic lattice sites proving that point defects are stable on flat terraces.     

Molecular dynamics simulation of polyhedron analysis of Cu–Ag alloy under rapid quenching conditions

In this study, the formation mechanism of polyhedron clusters in Cu₅₀Ag₅₀ binary alloy system consisting of 50 000 atoms has been investigated by using molecular dynamics simulations based on embedded atom method (EAM) during the rapid cooling processes. The cluster-type index method (CTIM) has been used to describe the evaluation properties of clusters and the structural development has been investigated by using radial distribution function (RDF). The simulation results show that the amorphous phase is formed by the main bonded pairs of 1551, 1541 and 1431 in the system, and ideal icosahedral (icos) cluster (12 0 12 0) and other basic polyhedron clusters, such as defective icos, Frank–Kasper, Bernal polyhedron, play a critical role under the rapid cooling conditions. The results of our simulations that have been disclosed show that high cooling rate favors the icos and defective icos clusters for model alloy system.     

Disordered solids: Universal behavior of structure, dynamics, and transport phenomena

Disordered materials (glasses and amorphous substances, melts, polymers, biological media, etc.) are an important class of objects. Despite the chaos usually associated with their structure, glasses and amorphous substances of various kinds (semiconducting, dielectric, metallic) possess a universal spatial scale length ∼1 nm, an order parameter, which can be as important theoretically as the unit cell for crystals. The disorder in disordered substances is not absolute; the periodicity positions of atomic inherent in crystals is maintained within a few coordination spheres and is then somehow destroyed. The way in which the order breaks down makes it possible to distinguish the glasses from amorphous materials in terms of the form of the structural correlation function. The inhomogeneities in question are not exotic, unique formations or analogs of defects in crystals, but are the fragments out of which amorphous substances and glasses are entirely constructed. The spatial inhomogeneity of disordered substances having a characteristic scale length of ∼1 nm leads to some universal characteristics in their vibrational properties, changes the relaxation mechanism for electronic excitation, and determines the specific features of charge transport. Fiz. Tverd. Tela (St. Petersburg) 41, 805–808 (May 1999)     

Models of the cores of dislocations in metals and disclinations in liquid crystals

The development of dislocation core models in metals with non-close-packed crystalline structure is reviewed. The paper starts with the Peierls-Nabarro model generalized to the case of non-planar cores to describe dislocation splitting in bcc metals. Atomistic studies of dislocations cores in bcc metals and intermetallic compounds with L1₂ and B2 structures are then discussed and the principal features of non-planar cores emphasized. Finally, an analogy between dislocations in solid and disclination in liquid crystals is presented and similarities and differences in the treatment of core structures of these defects in solid and liquid crystals discussed.Dedicated to Dr. Frantiek Kroupa in honour of his 70^th birthday.This work was supported by the U.S.-Czech S & T Program under contract No. 94048, by the National Science Foundation-International Programs, INT-93-07418 and by the Grant Agency of the Czech Republic under contract No 106/93/0513.     

Fast and slow dynamics in a discotic liquid crystal with regions of columnar order and disorder

Aromatic disk-shaped molecules tend to self-organize into a herringbone packing where the disks are inclined at angles ±θ with respect to the axis of the column. In discotic liquid crystals this can introduce defects between stacks of limited length. In a C(3)-symmetric hexa-peri-hexabenzocoronene, solid-state NMR, x-ray scattering, and rheology identifies such a packing with θ=43° and stacks of about seven disks. Disordered regions containing defects fill the space in between the ordered stacks. Biaxial intra- and intercolumnar dynamics differing by eight decades are identified.     

Electronic structure of carbon nanoparticles

The electronic structure of graphitic nanoparticles is investigated within a gauge field-theory model. The local and total densities of states (DOS) near the pentagonal defects (disclinations) are calculated for three geometries: sphere, cone, and hyperboloid. It is found that the low-energy electron states have a rather specific dependence on both the energy and the distance from a disclination line. In particular, the low-energy total DOS has a cusp that drops to zero at the Fermi energy for disclinations with the Frank index v<1/2, while a region of a nonzero DOS across the Fermi level is formed for v=1/2. The true zero-mode fermion state is found for the graphitic hyperboloid. The appearance of an enhanced charge density near the Fermi level for nanocones with a 60° opening angle (180° disclination) is predicted.     

Structure of blue phase III of cholesteric liquid crystals

We report large scale simulations of the blue phases of cholesteric liquid crystals. Our results suggest a structure for blue phase III, the blue fog, which has been the subject of a long debate in liquid crystal physics. We propose that blue phase III is an amorphous network of disclination lines, which is thermodynamically and kinetically stabilized over crystalline blue phases at intermediate chiralities. This amorphous network becomes ordered under an applied electric field, as seen in experiments.     

Fe基体中包含Cu团簇的Fe-Cu二元体系在升温过程中结构变化的原子尺度计算

采用基于嵌入原子方法的分子动力学方法模拟了具有体心立方晶格结构的Fe基体中包含小尺寸Cu纳米粒子的Fe-Cu二元体系在升温过程中的原子堆积结构变化.进行了Cu原子均方位移、Cu原子对分布函数和原子的径向密度分布函数的计算,并对纯Cu原子区、Fe-Cu界面区和纯Fe基体区的分区域原子堆积结构进行了分析.结果表明,Fe基体内Cu团簇的尺寸及其在Fe基体内所能占据区域的大小,对不同温度下的Cu团簇内原子堆积结构及Fe基体的原子堆积结构具有影响.升温过程中不同尺寸受基体约束Cu团簇对Fe基体结构改变的影响表现出很大差异.对于Fe_(bulk)-Cu_(135)体系,基体的应变临近Fe-Cu界面区,同时在团簇中间的基体区域出现大量空位缺陷和应变集中区;对于Fe_(bulk)-Cu_(141)体系,随温度升高,基体中出现的应变区域表现为小尺寸、数量多向大尺寸、小数量的变化.     

Elastic properties of nematoid arrangements formed by amoeboid cells

In culture migrating and interacting amoeboid cells can form nematoid arrangements in analogy to a nematic liquid crystal phase. A nematoid arrangement is formed if the interaction has an apolar symmetry. Different cell types like human melanocytes (= pigment cells of the skin), human fibroblasts (= connective tissue cells), human osteoblasts (= bone cells), human adipocytes (= fat cells) etc., form a nematoid structure. Our hypothesis is that elastic properties of these nematoid structures can be described in analogy to that of classical nematic liquid crystals. The orientational elastic energy is derived and the orientational defects (disclination) of nematoid arrangements are investigated. The existence of half-numbered disclinations shows that the nematoid structure has an apolar symmetry. The density- and order parameter dependence of the orientational elastic constants and their absolute values are estimated. From the defect structure, one finds that the splay elastic constant is smaller than the bend elastic constant (melanocytes). The core of a disclination is either a cell free space or occupied by non oriented cells (isotropic state), by a cell with a different symmetry, or by another cell type. Received 3 May 1999 and Received in final form 29 September 1999     

Disclinations in the nematic phase of a magnet with spin 1

Two-dimensional topological defects, spin disclinations, exist for a magnet with spin 1 and strong biquadratic interaction, in which the spin nematic state is realized. The spin disclinations have a nonsingular macroscopic core with a saturated magnetic moment and destroyed nematic order. These singular lines have common features with disclinations in nematic liquid crystals, singular disclinations in antiferromagnets, and magnetic vortices. However, significant differences of their properties from the above-mentioned topological defects also exist. The dynamic properties of a disclination in the spin nematic are characterized by the “freezing in the condensate” and by the gyroscopic force.     

不同衬底条件下石墨烯结构形核过程的晶体相场法研究

利用可描述气-固转变的三模晶体相场模型,在原子尺度上研究了不同衬底条件下石墨烯结构的形核过程.结果表明:无论衬底存在与否,气态原子均是先聚集为无定形过渡态团簇,随着气态原子的不断堆积和固相团簇中原子位置的不断调整,过渡态团簇逐渐转变为有序的石墨烯晶核,在此过程中,五元环结构具有重要的过渡作用;石墨烯在结构匹配较好的衬底(如面心立方(face-centered cubic,FCC)结构(111)和(110))上生长时,可形成几乎没有结构缺陷单晶石墨烯岛;在无衬底或结构匹配性较差的衬底(如FCC结构(100)面)上生长时,形成的石墨烯岛结构缺陷和晶界较多,不利于高质量石墨烯的制备.     

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.