Geometrical Frustration

Statistical physics is one of the most active and exciting current areas of research in the physical sciences. Published in collaboration with Centre d'Etudes de Saclay, one of the leading European centers of research in this area, this carefully selected collection includes topical books in statistical physics in its broadest sense, including condensed matter physics, hydrodynamics, dynamical systems, and chaos. Titles published in this series will be at graduate and research level. Aléa is a French word meaning an unpredictable event, and is derived from the Latin word 'alea' meaning 'dice'. This 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 geometric frustration in periodic structures with large cells and quasi-periodic 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.