Quasicrystals at grain boundaries

Grain Boundaries as Projections from Higher-Dimensional Lattices

“…A. P. Sutton (1988) observed that the simplest irrational tilt boundaries may be described as a quasiperiodic sequence of appropriate fundamental structural units. This result was supported by the suggestion (Rivier & Lawrence, 1988) that a quasicrystalline grain boundary has the minimal Gibbs free energy under specific boundary conditions. Finally, it was found useful to consider a six-dimensional lattice to study the symmetries of general grain boundaries in three dimensions (Gratias & Thalal, 1988).…”

Phyllotactic patterning of gerbera flower heads

“…The subsequent reduction of parastichy numbers according to the reversed Fibonacci sequence is explained by the stacking model of van Iterson ( 19 ) and its more recent refinements, e.g., refs. 7 , 21 , and 51 , as well as by the analyses of Rivier and Lawrence ( 52 , 53 ), who characterized the patterns of primordia in transitional zones in terms of quasicrystals. Our experimental and modeling results highlight, however, that an assumption underlying these models—the radial symmetry of the meristem and the pattern front—is not necessary, and some departures from it do not substantially alter the resulting patterns ( Fig.…”

High-resolution electron microscopy of interfaces in fcc materials

“…Thus a CSL bicrystal conceptually will always generate a periodic boundary as long _s the GB lies on a rational plane. However tilt GBs on irrational planes can be considered one dimensional quasicrystals [9,10]. Ultimately the physically relevant structural units of an interface are determined by the atomic relaxations.…”

“…Theoretically it has been shown that suci rrational GBs can be considered quasiperiodic, in analogy with the structures of quasicrystalline materials [9,10,78].…”