Sadoc J.-F., Mosseri R. Geometrical Frustration

Cambridge University Press, UK, 2006. – 319 p. – ISBN: 0 521 44198 6This book shows how the concept of geometrical frustration can be used to elucidate the structure
and properties of non-periodic materials such as metallic glasses, quasicrystals, amorphous semiconductors and complex liquid crystals.
Geometrical frustration is introduced through examples and idealized models, leading to a consideration of how the concept can be used to identify ordered and defective regions in real materials. Then it is shown how these principles can also be used to model physical properties of materials, in particular specific volume, melting, the structure factor and the glass transition.
Final chapters consider geometrical frustration in periodic structures with large cells and quasiperiodic order. Appendixes give all necessary background on geometry, symmetry and tilings. The text considers geometrical frustration at different scales in many types of materials and structures, including metals, amorphous solids, liquid crystals, amphiphiles, cholesteric systems, polymers, phospholipid membranes, atomic clusters and quasicrystals.
This book will be of interest to researchers in condensed matter physics, materials science and structural chemistry, as well as mathematics and structural biology.Introduction to geometrical frustration
Ideal models
Finite structures
Decurving and disclinations
Hierarchical polytopes
Some physical properties
Periodic structures with large cells
Quasiperiodic order and frustration
Appendixes
Spaces with constant curvature
Quaternions and related groups
Hopffibration
Polytopes and honeycombs
Polytope {3,3,5}
Frank and Kasper coordination polyhedra
Quasiperiodic tilings: cut and projection
Differential geometry and parallel transport
Icosahedral quasicrystals and the ES lattice