Geometry and Thermodynamics: Common Problems of Quasi-Crystals, Liquid Crystals, and Incommensurate Systems

ISBN-13: 9781461367024 / Angielski / Miękka / 2012 / 466 str.

J. C. Toledano

Opis

Distinct scientific communities are usually involved in the three fields of quasi-crystals, of liquid crystals, and of systems having modulated crystalline structures. However, in recent years, there has been a growing feeling that a number of common problems were encountered in the three fields. These comprise the need to recur to "exotic" spaces for describing the type of order of the atomic or molecular configurations of these systems (Euclidian "superspaces" of dimensions greater than 3, or 4-dimensional curved spaces); the recognition that one has to deal with geometrically frustrated systems, and also the occurence of specific excitations (static or dynamic) resulting from the continuous degeneracies of the stable structures considered. In the view of discussing these problems, aNA TO-Advance Research Workshop has assembled in Preveza (Greece), in september 1989,50 experts of the three considered fields (with an equal proportion of theorists and experimentalists). 35 hours of conferences and discussions have led to a more detailed evaluation of the similarities and of the differences in the approaches implemented in the studies of the three types of systems. The papers contained in this NATO-series book provide the substance of this workshop. The reader will find three types of papers. Some very short papers giving the main ideas stated on a subject. Papers comprising 8-10 pages which stick closely to the contents of the talks presented. Longer papers providing more extensively the background and results relative to a given topic. It is worth summarizing the principal outputs of the workshop.

Spis treści

Structure and Geometry.- Hierarchic structure.- The structure of quasicrystals: from diffraction patterns to atom positions.- Determination of quasi-crystal structures by higher dimensional analysis.- Six-dimensional atoms for a decorated three-dimensional Penrose tiling.- Metrical aspects of quasicrystal embedding in superspace.- Landau theory and direct methods for crystal structures analysis.- Geometry of films of amphiphile molecules: a curved space approach.- Geometrical approach of blue phases.- Electron microscopy and quasicrystals.- On the dark field imaging behaviour of icosahedral phases in rapidly cooled aluminium alloys.- Electron microscopy of modulated structures.- Models for Stability and Growth.- Physical models of perfect quasicrystal growth.- Generation and dynamics of defects in two-dimensional quasicrystals.- Intrinsic stability of quasicrystals and behavior under a load of Frenkel defects.- Reconstructive phase transition to the icosahedral phase.- Structure and growth of twoand three-dimensional hexatic liquid crystals.- The tiling structure of simple liquids: squares and triangles in two dimensions.- Does cholesteric blue phase III have an icosahedral structure ?.- Intrinsic frustration and space curvature in smectic A liquid crystals.- Critical behavior of polymorphic smectic-A liquid crystals.- Universal behavior in phospholipid multimembrane systems.- Pattern formation during the ordering processes in nematic liquid crystals.- Spatially modulated structures in models with competing interactions some new results.- Weakly periodic structures with a singular continuous spectrum.- The Anderson metal-insulator transition: incommensurate versus disordered systems.- Theory of phase transition between two incommensurate phases in NbTe4.- The origin of polytypes in SiC and ZnS.- Structural modulations in the high-temperature superconductor YBa2Cu3O7.? and semi conducting WO3-x, aspects of non-equilibrium behaviour.- Incommensurate modulations in bismuth-based high-Tc superconductors.- Incommensurate commensurate phase transition of Cu2-xTe. (x < 0.05).- Review of the commensurate and incommensurate transitions in BCCD.- Amorphous and quasicrystalline Al-Cr and Al-Cr-Si phases produced by solid state diffusion of alternating thin layers.- Dynamics and Phasons.- Phasons and amplitudons in modulated structures.- Phonons in quasicrystals and related structures.- Phasons in ferroelectric liquid crystals.- Atomic Debye-Waller factors and phasons in modulated incommensurate structures.- The Landau free energy and acoustic anomalies in incommensurate insulators.- NMR and NQR in incommensurate systems.- Do we understand optical activity in the incommensurate phase of the A2BX4 family.- The coupling between phason and soft modes near the smectic-C* to smectic-A phase transition.- Optical measurements of diffusivities in incommensurate barium sodium niobate.