Applications of the coherent state representation in the theory of magnetism: II. Helical spin configurations

In a previous paper, the coherent state representation of spin wave states was used to derive the low temperature expansion for the free energy of the Heisenberg model of a ferromagnet. In this paper, the same formalism is applied to anisotropic systems which are usually described semiclassically. The coherent state parameters are shown to be ideally suited for describing certain of the resulting helical spin configurations. The coherent state approach emphasizes the analogy of these states to superfluid boson systems. A model spin Hamiltonian appropriate to Erbium is chosen and discussed in this light. In particular, the transition in a transverse magnetic field from the ground state cone configuration to a fan configuration, the stability and possible metastability of these states and the fluctuations about them are investigated. Numerical estimates show at least qualitative agreement with experiment.     

Structural phase transition in a large cluster

The effect of a phase transition between structures in a large cluster with a pair interatomic interaction on the thermodynamic parameters of the cluster is analyzed. The statistical parameters of a cluster consisting of 923 atoms are determined for an icosahedron and a face-centered cubic (fcc) structure. The specific heat and entropy of this cluster are calculated in the case when the transition between the icosahedron and fcc structures has the greatest effect on these parameters, so that at zero temperature this cluster has the structure of an icosahedron, and as the temperature increases to the melting point it assumes an fcc structure. Even with this, the contribution of the excitations of the atomic configurations to the thermodynamic parameters of a cluster is small compared with the excitation of vibrations in the cluster. The contribution of a configurational excitation in the thermodynamic parameters of a cluster becomes substantial for the liquid state of clusters.     

Configurational phase transition in AuxCu1−x nano-alloy: first principle and Monte-Carlo calculations

We report on the calculation of phase transition in the configurational state (i.e. atomic arrangement) of Au_xCu_1?x nanoparticle (or nano-alloy). The cluster expansion, represented by the formation energies of several atomic configurations, has been determined from full potential, linearized augmented-plane-wave first-principle calculation. The cluster expansion was then used as a Hamiltonian for the Monte-Carlo calculation of the phase transition between the configurational ground states (gs). Clear observation of plateau structures, associated with the calculated ‘gs’, in the plane of the composition (x) versus the chemical potential, have been observed at low temperatures <100?K. The plateaus smeared out at higher temperatures, giving rise to the order–disorder transition as the temperature rises. The critical temperature for this transition was estimated at 100?K, agreeing with the reported trend of the transition temperature with the nano-alloy size. Our results are thus relevant to applications concerning deposition of dispersed (i.e. well separated) nano-alloys.     

A New Proof of Ruelle's Superstability Bounds

For a slightly stronger assumptions on the interaction we give a very transparent proof of Ruelle's result in the language of Poisson integral measure representation for the correlation functions on the configuration space using some kind of cluster expansion in the densities of configurations.     

Molecular Dynamics Simulation of Icosahedral Transformations in Solid Cu-Co Clusters

We study the icosahedral transformations of solid Cu Co clusters with different initial configurations by using molecular dynamics with the embedded atom method. It is found that the formation of symmetric icosahedral cluster is strongly related to the atomic number and initial configuration. The transformation originates from the surface into the interior of the cluster and is a structural change which is rapid and diffusionless. The icosahedral clusters with any composition and configuration, such as core-shell or three-shell duster, can be prepared by the means of solid-solid phase transition in bimetallic clusters.     

Searching for alloy configurations with target physical properties: impurity design via a genetic algorithm inverse band structure approach

The ability to artificially grow different configurations of semiconductor alloys--random structures, spontaneously ordered and layered superlattices--raises the issue of how different alloy configurations may lead to new and different alloy physical properties. We address this question in the context of nitrogen impurities in GaP, which form deep levels in the gap whose energy and optical absorption sensitively depend on configuration. We use the "inverse band structure" approach in which we first specify a desired target physical property (such as the deepest nitrogen level, or lowest strain configuration), and then we search, via genetic algorithm, for the alloy atomic configurations that have this property. We discover the essential structural motifs leading to such target properties. This strategy opens the way to efficient alloy design.     

Numerical study of shock wave interaction in steady flows of a viscous heat-conducting gas with a low ratio of specific heats

Specific features of shock wave interaction in a viscous heat-conducting gas with a low ratio of specific heats are numerically studied. The case of the Mach reflection of shock waves with a negative angle of the reflected wave with respect to the free-stream velocity vector is considered, and the influence of viscosity on the flow structure is analyzed. Various issues of nonuniqueness of the shock wave configuration for different Reynolds numbers are discussed. Depending on the initial conditions and Reynolds numbers, two different shock wave configurations may exist: regular configuration interacting with an expansion fan and Mach configuration. In the dual solution domain, a possibility of the transition from regular to the Mach reflection of shock waves is considered.     

Vacuum heating of large atomic clusters by a superintense femtosecond laser pulse

The analytic approach of vacuum (Brunel) heating mechanism is generalized to the case of large atomic clusters irradiated by a superintense femtosecond laser pulse. The hydrodynamic cluster expansion is taken into account in this approach. Simple universal expressions are obtained for the absorbed laser energy by a cluster and for the radius of an expanding cluster. The absorption of laser energy and the cluster expansion are determined by only one dimensionless field parameter.     

Characteristic features of the melting of two-dimensional mesoscopic Wigner clusters

Two-dimensional Wigner microclusters in a semiconductor dot are studied. Their melting is investigated in detail and it is shown that, for typical mesoscopic clusters possessing a shell structure, melting occurs in two stages: orientational melting (rotation of the shells relative to one another) and total melting, where the shells start to overlap with one another and exchange particles. An example of a “magic” microstructure which has a triangular structure and melts in a single stage is presented. For this, the temperature dependences of various quantities characterizing cluster structure are investigated. The change in the distribution of cluster configurations over local minima of the potential energy with increasing temperature is investigated. At temperatures below the temperature of total melting, a cluster is always located near the configuration of a global minimum and, at temperatures above the temperature of complete melting, a cluster can be located with finite probability near configurations corresponding to various local minima of the potential energy. Fiz. Tverd. Tela (St. Petersburg) 41, 1499–1504 (August 1999)     

Electronic correlation effects on the properties of an half-filled octahedron cluster in a magnetic field

The present study focuses on electronic correlation effects on magnetic energy, the spin-spin correlation function of an octahedron cluster in the (3↑, 3 ↓) electronic configuration threaded by a magnetic field. Some other spin configurations are also discussed and various field directions are considered. An accurate diagonalisation technique has been used to solve the Hubbard Hamiltonian. A result is analysed on a linear energy stabilisation at low magnetic flux. Moreover, two types of antiferromagnetic transition versus the flux occurring for a correlation term larger than a critical one have been observed, i.e. the likelihood of a charge excitation before the antiferromagnetic transition. Finally, a comparison between the results obtained from the exact diagonalisation and the Gutzwiller method has been carried out, leading to a suggested modification of the Gutzwiller approach in order to improve it. Received 23 June 1999 and Received in final form 28 July 2000     

Chaotic cluster itinerancy and hierarchical cluster trees in electrochemical experiments

Experiments on an array of 64 globally coupled chaotic electrochemical oscillators were carried out. The array is heterogeneous due to small variations in the properties of the electrodes and there is also a small amount of noise. Over some ranges of the coupling parameter, dynamical clustering was observed. The precision-dependent cluster configuration is analyzed using hierarchical cluster trees. The cluster configurations varied with time: spontaneous changes of number of clusters and their configurations were detected. Simple transitions occurred with the switch of a single element or groups of elements. During more complicated transitions subclusters were exchanged among clusters but original cluster configurations were revisited. At weaker coupling the system itinerated among lower-dimensional quasistationary chaotic two-cluster states and higher-dimensional states with many clusters. In this region the transitions showed characteristics of on-off intermittency.     

Vertex configuration rules to grow an octagonal Ammann–Beenker tiling

Based on vertex configurations in the Ammann–Beenker tiling, we propose an algorithm for aggregation of square and rhombus tiles to generate an octagonal quasilattice, which mimics the growth process of a two-dimensional quasicrystal. Local matching rules with configuration selection are used to guide the way that tiles are joined to a cluster and form Ammann lines according to a generalized Fibonacci sequence. Our results reveal that vertex configuration selection can improve the performance of the algorithm, which provides an approach for growing a perfect octagonal quasiperiodic structure.     

Thermal expansion of amorphous Zr Al Cu Ni in the vicinity of the glass transition

The thermal expansion of non-crystalline Zr₆₅Al_7.5Cu_17.5 Ni₁₀ has been studied in the range of the glass transition and in the undercooled liquid using a dilatometric device. The measuring technique used permits reliable experimental results up to 40 K above the glass transition temperature. The linear thermal expansion coefficient obtained is almost constant in the glassy state with a value of . It discontinuously increases at the glass transition temperature yielding a value of in the undercooled liquid. The results are compared with specific heat measurements of the amorphous material in this temperature range and are interpreted in the framework of a cluster model. Received 5 March 1999 and received in final form 11 June 1999     

Coexistence of different cluster configurations in light neutron-rich nuclei

On the basis of the algebraic version of the resonating-group method (RGM) and within the framework of the discrete representation in the Fock-Bargmann space, a microscopic theory of nuclear reactions with due regard for a coexistence of different cluster configurations in a compound nucleus is realized. Fundamental tenets of the algebraic version of the RGM are stated both for a single binary cluster configuration and for a compound system, where several cluster configurations coexist. Several examples of norm kernels, their eigenvalues, phase shifts, and effective cross sections are given for a number of binary cluster systems. The text was submitted by the authors in English.     

Independent variables in foam clusters

We find, by counting the degrees of freedom of two-dimensional bubble clusters (finite or periodic) of given topology and bubble areas, that the Plateau laws determine a unique configuration of a finite free cluster, but allow an infinite number of configurations of a periodic cluster. Each of these configurations is associated with a particular strain (stress) state of the cluster; there is in general one unstrained configuration, which corresponds to the minimum of the (surface) energy. Configurations of given topology that satisfy Plateau's laws may only exist in certain ranges of bubble area ratios and/or strains. Received 31 May 2001 and Received in final form 12 September 2001     

Statistical description of the sol-gel transition in systems with thermoreversible chemical bonds

A general statistical model is proposed for describing network-forming systems. The model is based on the representation of the partition function for all possible configurations of a thermoreversible network in the form of a functional integral over a scalar field. According to this model, two types of first-order phase transitions can occur in the systems under consideration: macroscopic phase separation with the structural phase transition due to the change in the configuration of the spatial network and the sol-gel transition due to the formation of a thermoreversible percolation cluster consisting of bound structural units. A detailed analysis is performed of the thermodynamic and structural properties of a solution of monomers that have f functional groups and can form thermoreversible chemical bonds. The influence of specific features of the chemical and volume interactions on the phase diagram of the system is investigated. The mutual position of the sol-gel transition line and the phase diagram is determined for different model parameters. It is revealed that two substantially different regimes of the behavior of the sol-gel transition line in the “temperature-volume fraction of structural units” plane are observed with a change in the rigidity of chemical bonds.     

A first-order phase transition in a three-dimensional vertex model

For a specific three-dimensional vertex model, it is proven that it will show a first-order phase transition. The critical temperature is given in terms of the energy of some local vertex configurations. The approach used is similar to the Nagle approach. Some classes of compounds are considered which may be related to this model.     

基于原子晶体构型的高压固氩中的多体相互作用

X射线衍射实验显示固氩是面心立方(fcc)晶格结构,目前对晶体氩的研究只限于两体,三体以及四体相互作用势.本文利用多体展开方法和超分子单、双(三)重激发耦合簇理论(CCSD(T))对固氩fcc晶格结构的三体和四体的几何构型、几何参数、不同体积下所有三体和四体构型的势能以及各构型所占比例等几个方面进行了准确的量子化学计算.结果表明:所有三体构型中对总的三体势能贡献最大的是构型1、构型6、构型12和构型23;三体势及其交换部分和色散部分的计算结果与现有解析经验势在长程部分符合得非常好,但在短程部分有较小差异.所有的四体构形中对总的四体势能贡献最大的是构型1,构型2,构型4,构型5,构型7和构型8;四体势及其交换势部分和色散部分的计算结果尚无解析经验势可比较.利用这些特殊构型的相关数据并结合其它构型,可拟合出更准确的三体经验势函数及其参数,也为拟合四体经验势函数及其参数提供了重要的参考价值.     

Correlation effects in the first-row transition metal atoms and ions: Choosing the configurations

A detailed study of core-valence and core-correlation effects using the configuration interaction approach soon becomes unwieldly due to the large number of configuration needed in the expansion. We examine the possibility of reducing the number of vector-coupled configurational functions in the configuration interaction expansion, formed from different coupling schemes, by coupling the orbital functions in a different order.