Frustration and defects in non-periodic solids

Geometrical frustration arises whenever a local preferred configuration (lower energy for atomic systems, or best packing for hard spheres) cannot be propagated throughout space without defects. A general approach, using unfrustrated templates defined in curved space, have been previously applied to analyse a large number of cases like complex crystals, amorphous materials, liquid crystals, foams, and even biological organizations, with scales ranging from the atomic level up to macroscopic scales. In this paper, we discuss the close sphere packing problem, which has some relevance to the structural problem in amorphous metals, quasicrystals and some periodic complex metallic structures. The role of sets of disclination line defects is addressed, in particular with comparison with the major skeleton occurring in complex large-cell metals (Frank–Kasper phases). An interesting example of 12-fold symmetric quasiperiodic Frank–Kasper phase, and its disclination network, is also described.