Two solid state structures, which are characterized by lack of crystalline symmetries, yet having, to some extent, the orderness, are discussed in a unified manner. They are the modulated strutures on one dand, which are ordered ones having not necessarily translational periodicities; and the amorphous structures on the other hand retaining only short- and medium-range orders. Energetically they are both frustrated. The topology of those structures are readily represented by introducing the 4th dimension in direct as well as reciprocal spaces, i. e., by extending the space group considerations to the 4-dimensional flat or curved spaces. The argument by De Wolf [Acta Cryst. A30, 777 (1974) ] and that of Sadoc [J. Non-Cryst. Solid. 44, 1 (1981) ] are adopted for discussing modulated and amorphous structures respectively. In this context similarities existing in those strucutres are suggested, which lead, in particular, to a reinterpretation of the dense random packing model for amorphous solids in relation to the micro-crystalline model. [J. Cryst. Soc. Jpn. 27, 239 (1985) ] .
Various structure changes of potassium monolayers on Cu (001) have been observed under deposition of potassium at 330 K by low-energy electron diffraction (LEED) . The LEED pattern clearly has shown that the potassium overlayer underwent sequential transitions with increasing coverage : disorder to short-range order, short-range order to long-range order (uniaxial commensurate), commensurate to commensurate through uniaxially incommensurate phases, and commensurate to incommensurate. Rotational epitaxy was found in the incommensurate phase. Halo patterns observed in the short-range-ordered phase and the commensurate-incommensurate transition were analyzed.
The microstructure of strontium titanate internal boundary layer capacitors at various stages in their processing was characterized in detail using high resolution transmission electron microscopy. Freezed equilibrium phase at high temperature in rapidly quenched samples and the structural changes during cooling process were revealed.