Phase diagram of a random tiling quasicrystal

We study the phase diagram of a two-dimensional random tiling model for quasicrystals. At proper concentrations the model has 8-fold rotational symmetry. Landau theory correctly gives most of the qualitative features of the phase diagram, which is in turn studied in detail numerically using a transfer matrix approach. We find that the system can enter the quasicrystal phase from many other crystalline and incommensurate phases through first-order or continuous transitions. Exact solutions are given in all phases except for the quasicrystal phase, and for the phase boundaries between them. We calculate numerically the phason elastic constants and entropy density, and confirm that the entropy density reaches its maximum at the point where phason strains are zero and the system possesses 8-fold rotational symmetry. In addition to the obvious application to quasicrystals, this study generalizes certain surface roughening models to two-dimensional surfaces in four dimensions.     

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.     

On the electrical resistivity of the quasicrystalline decagonal Al–Mn system

A simple effective-medium approach is used to study anisotropy properties of the electrical resistivity in the quasicrystalline decagonal Al–Mn system.     

Disorder diffuse scattering from quasicrystals

Very sharp Bragg reflections accompanied by diffuse scattering phenomena are typical for most stable quasicrystals. The correlation length of the quasiperiodic average structure can reach several micrometers as proved by high-resolution X-ray diffraction experiments. This corresponds to a structural perfection of some quasicrystals similar to that of silicon. Nevertheless, the omnipresent diffuse scattering indicates significant deviations from a strictly ordered quasiperiodic structure especially in the case of decagonal phases. These structural deviations may be caused by phason fluctuations, by disorder in the packing of the basic atomic clusters, by the formation of nanodomains, by chemical disorder, or by superstructure formation on a short-range scale. Characteristic examples of different types of structural disorder present in icosahedral and decagonal quasicrystals are reported. The diffuse scattering phenomena in decagonal Al-Co-Ni as a function of composition and temperature are discussed in more detail.     

Phasons, sliding modes and friction

Aperiodic crystals may have additional low frequency modes related to the possibility to describe them in a higher-dimensional space. Dynamics associated with these degrees of freedom is called phasonic, but there are very different phenomena of this type. A discussion is given of the use of the term. The relation between phason modes, the crystal structure, and the modulation and sliding modes is discussed. Finally a relation with frictionless motion is studied. Received 4 April 2002 / Received in final form 22 July 2002 Published online 17 September 2002     

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.     

Quasicrystal surfaces: structure and growth of atomic overlayers

We review recent developments in surface studies of single-grain quasicrystals under ultra high-vacuum conditions, focusing on two different topics: surface structure and growth of atomic overlayers on surfaces. Quasicrystalline phases are currently used for investigation of the first topic are icosahedral (i) Al-Pd-Mn, i-Al-Cu-Fe, i-Al-Cu-Ru, i-Ag-In-Yb and decagonal (d) Al-Ni-Co, and d-Al-Cu-Co. We report the progress made with all of these phases. The second topic covers the study of single-element overlayer growth by vapor deposition.     

The partition function and state equation of the point group 12mm two-dimensional dodecagonal quasicrystal

This study extends the analysis of the vibrational spectrum of the one-dimensional hexagonal quasicrystal to the two-dimensional quasicrystal with the 12mm point group. Several thermodynamic functions and the state equation of the material are shown. Received 18 July 2002 Published online 27 January 2003 RID="a" ID="a"e-mail: litongtzb@263.net