Self-assembly of monatomic complex crystals and quasicrystals with a double-well interaction potential

For the study of crystal formation and dynamics, we introduce a simple two-dimensional monatomic model system with a parametrized interaction potential. We find in molecular dynamics simulations that a surprising variety of crystals, a decagonal, and a dodecagonal quasicrystal are self-assembled. In the case of the quasicrystals, the particles reorder by phason flips at elevated temperatures. During annealing, the entropically stabilized decagonal quasicrystal undergoes a reversible phase transition at 65% of the melting temperature into an approximant, which is monitored by the rotation of the de Bruijn surface in hyperspace.     

Elasticity and dislocations in quasicrystals with 18-fold symmetry

Elasticity problems of quasicrystals with 18-fold rotational symmetry are studied. Constitutive equations and governing equations are obtained. For static elasticity problems, the displacement vectors in two phason fields are expressed in terms of two pairs of associated harmonic functions or two analytic functions. For dynamic problems, the displacement vectors can be represented in terms of an auxiliary function satisfying a fourth-order partial differential equation. A general solution of phasons is given by the solution of two diffusion equations. Phason elastic fields induced by a dislocation in a quasicrystal with 18-fold symmetry are determined and exhibit an inverse singularity.     

Energy characteristics of edge dislocations in quasicrystals

A model is developed for describing phason defects in quasicrystals in the form of dilation filaments. This model is used to calculate the energy of edge dislocations in quasicrystals including the interaction of this type of dislocation with its “intrinsic” phason defects and with the equilibrium phason defects present in a quasicrystal. It is shown that the contribution of “intrinsic” phason defects to the total energy of an edge dislocation in a quasicrystal is substantial. Fiz. Tverd. Tela (St. Petersburg) 39, 2003–2007 (November 1997)     

Isotropic and anisotropic physical properties of quasicrystals

Since quasicrystals have positional and orientational long-range order, they are essentially anisotropic. However, the researches show that some physical properties of quasicrystals are isotropic. On the other hand, quasicrystals have additional phason degrees of freedom which can influence on their physical behaviours. To reveal the quasicrystal anisotropy, we investigate the quasicrystal elasticity and other physical properties, such as thermal expansion, piezoelectric and piezoresistance, for which one must consider the contributions of the phason field. The results indicate that: for the elastic properties, within linear phonon domain all quasicrystals are isotropic, and within nonlinear phonon domain the planar quasicrystals are still isotropic but the icosahedral quasicrystals are anisotropic. Moreover, the nonlinear elastic properties due to the coupling between phonons and phasons may reveal the anisotropic structure of QCs. For the other physical properties all quasicrystals behave like isotropic media except for piezoresistance properties of icosahedral quasicrystals due to the phason field.     

Growth of entropy stabilized quasicrystals

A simplified version of the model by Elser and Joseph for the process of growth of an entropically stabilized, two-dimensional quasicrystal with no dynamics in the bulk, is proposed. The phason fluctuations are modeled by a scalar field on a periodic lattice. The choice of the master equation for the growth is restricted by the requirement that its detailed balance solution describes the equilibrium fluctuations of the field with a quadratic Hamiltonian. The model is parametrized by the chemical potential bias and the microscopic surface tension coefficient . The phase diagram of the system on the plane (, ) shows several distinct regimes of growth, separated by relatively narrow transition zones. Within the regions corresponding to these regimes, the phason fluctuations do not depend on and . Analytic expressions for the spectra of phason fluctuations are obtained and confirmed by numerical simulation. Received 30 June 2000     

Thermodynamics of rotating self-gravitating systems

We investigate the statistical equilibrium properties of a system of classical particles interacting via Newtonian gravity, enclosed in a three-dimensional spherical volume. Within a mean-field approximation, we derive an equation for the density profiles maximizing the microcanonical entropy and solve it numerically. At low angular momenta, i.e. for a slowly rotating system, the well-known gravitational collapse “transition” is recovered. At higher angular momenta, instead, rotational symmetry can spontaneously break down giving rise to more complex equilibrium configurations, such as double-clusters (“double stars”). We analyze the thermodynamics of the system and the stability of the different equilibrium configurations against rotational symmetry breaking, and provide the global phase diagram. Received 8 July 2002 Published online 15 October 2002 RID="a" ID="a"e-mail: demartino@hmi.de     

Comparing light-induced colloidal quasicrystals with different rotational symmetries

Quasicrystals are aperiodic structures with long-range orientational order. Unlike crystals, quasicrystals can, in principle, possess any non-crystallographic rotational symmetry. However, only a few of these rotational symmetries have been observed. By using Monte Carlo simulations of colloidal particles in laser interference patterns with quasicrystalline symmetry, we compare the onset of quasicrystalline order for different rotational symmetries in two dimensions. We find that quasicrystals with 5-, 8-, 10-, and 12-fold rotational axes can be induced with lower laser intensities than quasicrystals with other non-crystallographic rotational symmetries. We relate this finding to the number of local symmetry centers in the respective interference patterns.     

Analytical solutions for some defect problems in 1D hexagonal and 2D octagonal quasicrystals

We study some typical defect problems in one-dimensional (1D) hexagonal and two-dimensional (2D) octagonal quasicrystals. The first part of this investigation addresses in detail a uniformly moving screw dislocation in a 1D hexagonal piezoelectric quasicrystal with point group 6mm. A general solution is derived in terms of two functions φ ₁, φ ₂, which satisfy wave equations, and another harmonic function φ ₃. Elementary expressions for the phonon and phason displacements, strains, stresses, electric potential, electric fields and electric displacements induced by the moving screw dislocation are then arrived at by employing the obtained general solution. The derived solution is verified by comparison with existing solutions. Also obtained in this part of the investigation is the total energy of the moving screw dislocation. The second part of this investigation is devoted to the study of the interaction of a straight dislocation with a semi-infinite crack in an octagonal quasicrystal. Here the crack penetrates through the solid along the period direction and the dislocation line is parallel to the period direction. We first derive a general solution in terms of four analytic functions for plane strain problem in octagonal quasicrystals by means of differential operator theory and the complex variable method. All the phonon and phason displacements and stresses can be expressed in terms of the four analytic functions. Then we derive the exact solution for a straight dislocation near a semi-infinite crack in an octagonal quasicrystal, and also present the phonon and phason stress intensity factors induced by the straight dislocation and remote loads.      

Random Tilings of High Symmetry: II. Boundary Conditions and Numerical Studies

We perform numerical studies including Monte Carlo simulations of high rotational symmetry random tilings. For computational convenience, our tilings obey fixed boundary conditions in regular polygons. Such tilings are put in correspondence with algorithms for sorting lists in computer science. We obtain statistics on path counting and vertex coordination which compare well with predictions of mean-field theory and allow estimation of the configurational entropy, which tends to the value 0.568 per vertex in the limit of continuous symmetry. Tilings with phason strain appear to share the same entropy as unstrained tilings, as predicted by mean-field theory. We consider the thermodynamic limit and argue that the limiting fixed boundary entropy equals the limiting free boundary entropy, although these differ for finite rotational symmetry.     

寻找囚禁在光腔中的玻色-爱因斯坦凝聚体的八重准晶

准晶是一种拥有长程序但不具有周期性结构的一种物质.实验上通过将玻色-爱因斯坦凝聚体(BEC)放置在一个由四个光学腔组成的系统中,通过四个腔中激光照射在凝聚体上从而得到具有八重旋转对称性的准晶.本文结合虚时演化方法和分步傅里叶法从理论上得到了八重准晶体.我们通过这种方法可以实现更为复杂的晶体结构,从而为将来探索新物质提供了可能.     

Random Tilings of High Symmetry: I. Mean-Field Theory

We study random tiling models in the limit of high rotational symmetry. In this limit a mean-field theory yields reasonable predictions for the configurational entropy of free boundary rhombus tilings in two dimensions. We base our mean-field theory on an iterative tiling construction inspired by the work of de Bruijn. In addition to the entropy, we consider correlation functions, phason elasticity and the thermodynamic limit. Tilings of dimension other than two are considered briefly.     

N重旋转对称的二维准晶电子态与声子态的简并性

通过相似变化矩阵,对具有N重旋转对称的二维准晶系统的哈密顿量和动力学矩阵进行对角约化。当N为偶数时,电子态与声子态中有(N-2)/(N+2)是双重简并,而4/(N+2)是非简并;当N为奇数时,电子态与声子态中有(N-1)/(N+1)是双重简并,而2/(N+1)是非简并。利用群论方法得到相同的结论。 关键词：     

Lithium Storage Property of Graphite/AlCuFe Quasicrystal Composites

Quasicrystals have long-range quasi-periodic translational ordering and non-crystallographic rotational symmetry.Al-Cu-Fe quasicrystals have great potential for lithium storage because of their high Al content and a large number of defects in the structure.In our previous study(J.Alloys Compd.805(2019)942)we showed that Al-Cu-Fe quasicrystals have good initial capacity whereas its cycle stability is poor.In the present study,graphite/AlCuFe is prepared by the mechanical alloying method.The results show that graphite/AlCuFe quasicrystal composites are successfully synthesized by planetary ball milling at 550 rpm for 80 h.The quasicrystal particle size decreases and the amorphous graphite forms onion-like carbon(OLC)when the two phases mix evenly.OLC forms on the surface of the Al-Cu-Fe quasicrystalline powder.Charge and discharge tests show that graphite/AlCuFe quasicrystal composites have high-stability capacity of 480 mAh/g after 20 cycles,which is larger than the sum of capacities of graphite and Al-Cu-Fe quasicrystals.     

Correlation functions and the dynamical structure factor of quasicrystals

The icosahedral or decagonal symmetry of quasicrystals is well described by a periodic structure in higher dimensions. One consequence is the existence of dynamic phason modes in addition to the phonon modes. In an atomistic model phasons show up as correlated atomic jumps. We detect the phasons by the calculation of correlation functions and the dynamical structure factor in molecular dynamics simulations similar to the procedure used for phonons. In the simulations it is also possible to observe atomic jump processes directly. The models studied here represent icosahedral AlCuLi and decagonal AlCuCo quasicrystals. Ring processes are observed in the icosahedral case, and flips in the decagonal model. Received 17 March 2000 and Received in final form 8 June 2000     

Quasicrystals in a monodisperse system

We investigate the formation of a two-dimensional quasicrystal in a monodisperse system, using molecular dynamics simulations of hard-sphere particles interacting via a two-dimensional square-well potential. We find that more than one stable crystalline phase can form for certain values of the square-well parameters. Quenching the liquid phase at a very low temperature, we obtain an amorphous phase. By heating this amorphous phase, we obtain a quasicrystalline structure with fivefold symmetry. From estimations of the Helmholtz potentials of the stable crystalline phases and of the quasicrystal, we conclude that the observed quasicrystal phase can be the stable phase in a specific range of temperatures.     

Numerical entropy and phason elastic constants of plane random tilings with any 2D-fold symmetry

We perform Transition matrix Monte Carlo simulations to evaluate the entropy of rhombus tilings with fixed polygonal boundaries and 2D-fold rotational symmetry. We estimate the large-size limit of this entropy for D=4 to 10. We confirm analytic predictions of [N. Destainville et al., J. Stat. Phys. 120, 799 (2005) and M. Widom et al., J. Stat. Phys. 120, 837 (2005)], in particular that the large size and large D limits commute, and that entropy becomes insensible to size, phason strain and boundary conditions at large D. We are able to infer finite D and finite size scalings of entropy. We also show that phason elastic constants can be estimated for any D by measuring the relevant perpendicular space fluctuations.     

Green's functions for infinite bi-material planes of cubic quasicrystals with imperfect interface

The problem of an infinite plane which is composed of two half-planes with different cubic quasicrystal materials subjected to line phonon and phason forces is investigated. By virtue of the general solution of cubic quasicrystals, a series of displacement functions is adopted to obtain Green's functions in the closed form. For the bonding along the bi-material interface three different models account for different coupling conditions.     

Elastic theory of icosahedral quasicrystals - application to straight dislocations

In quasicrystals, there are not only conventional, but also phason displacement fields and associated Burgers vectors. We have calculated approximate solutions for the elastic fields induced by two-, three- and fivefold straight screw- and edge-dislocations in infinite icosahedral quasicrystals by means of a generalized perturbation method. Starting from the solution for elastic isotropy in phonon and phason spaces, corrections of higher order reflect the two-, three- and fivefold symmetry of the elastic fields surrounding screw dislocations. The fields of special edge dislocations display characteristic symmetries also, which can be seen from the contributions of all orders. Received 21 February 2001 and Received in final form 27 June 2001     

The Fulde-Ferrell-Larkin-Ovchinnikov states in s and d-wave superconductor with spin-dependent bandwidth imbalance on square lattice

We study numerically the phase diagram for s and d-wave fermionic superfluidity/superconductivity with spin-dependent bandwidth imbalance on a two-dimensional square-lattice. We also investigate the spontaneous space symmetry breaking states at low temperatures by solving the Bogoliubov-de Gennes equations. It is found that, the spatial configuration of the order parameter,both the uni-directional Fulde-Ferrell-Larkin-Ovchinnikov(FFLO) states and the two-dimensional FFLO state may show up in the presence of finite spin-dependent bandwidth imbalance. Moreover, we calculate the spectra of local density of states, and the experimental proposals of observing such FFLO states are therefore suggested.     

Group-theoretical method for physical property tensors of quasicrystals

In addition to the phonon variable there is the phason variable in hydrodynamics for quasicrystals. These two kinds of hydrodynamic variables have different transformation properties. The phonon variable transforms under the vector representation, whereas the phason variable transforms under another related representation. Thus, a basis (or a set of basis functions) in the representation space should include such two kinds of variables. This makes it more difficult to determine the physical property tensors of quasicrystals. In this paper the group-theoretical method is given to determine the physical property tensors of quasicrystals. As an illustration of this method we calculate the third-order elasticity tensors of quasicrystals with five-fold symmetry by means of basis functions. It follows that the linear phonon elasticity is isotropic, but the nonlinear phonon elasticity is anisotropic for pentagonal quasicrystals. Meanwhile, the basis functions are constructed for all noncrystallographic point groups of quasicrystals.