We discuss about the basic structural properties of quasilattices and the principles of various methods of constructing them. Our discussion focuses on the mathematical aspects of the subjects. We present them by exemplifying several dodecagonal quasiperiodic tilings in two dimensions.
Modulated structures in the new high- Tc superconducting oxides found in a Bi-Sr-Ca-Cu-O system are examined by high resolution transmission electron microscopy. Strong lattice distortions are induced in the [Bi2O2] layers to form “Bi- concentrated”and “Bi-deficient” bands in both 80K phase Bi2Sr2CaCu2Oy and 110K one Bi2Sr2Ca2Cu3 Oy . These distortion bands are arranged to form body- centered orthorhombic lattices with bs = 2.6nm which is about 4.8 times of the b parameter of the tetragonal sub-structure. Twinning with twin boundary at the center of Bi2O2 layer is also observed in the 80 K phase. The modulated structure in the 20 K phase Bi2Sr2CuOy is, on the other hand, described by the monoclinic structure. Structural relations of various modulated structures are discussed.
It is shown that zeolites are one of the potential candidates for dielectric container to make low- dimensional materials, and that the characterization of the defects in zeolites, which affect the physical and chemical properties seriously, is an important subject in zeolite science. The high capability of high resolution electron microscopy for tackling these problems is confirmed by showing two examples, i, e., direct observations of Se atoms incorporated in the channels of mordenite, and sodalite and offretite intergrowths in erionite.