Phasons

A pecuhar sohd phase, which has been discovered not too long ago [172], is the quasi-crystalline phase. Quasi-crystals are characterized by a fivefold or icosahedral symmetry which is not of crystallographic type and therefore was assumed to be forbidden. In addition to dislocations which also exist in normal crystals, quasi-crystals show new types of defects called phasons. Computer simulations of the growth of quasicrystals [173] are still somewhat scarce, but an increasing number of quasi-crystalline details are studied by simulations, including dislocations and phasons, anomalous self-diffusion, and crack propagation [174,175]. 

Ferroelectric liquid crystals where a continuous symmetry group is broken at Tc and the doubly degenerate relaxational soft mode of the high-temperature phase splits below Tc into an amphtudon -type soft mode and a symmetry restoring Goldstone (i.e., phason ) mode [e.g., p-decyloxybenzylidene p -amino-2-methylbutylcinnamate (DOBAMBC)]. 

The phasons of the incommensurate situation now have a gap. They have become the finite-energy harmonic-phase oscillations in one of the r pinning minima. They will couple to external electric fields and can explain why the intramolecular symmetric phonons can show up in optical reflectivity measurements as in TEA-TCNQ2 [52]. The tunneling at low temperature is the manifestation of solitonic excitations [53]. The solitons... 

The 13C-NMR line-shape analysis at T < TN in (TMTTF)2Br has proved that the periodicity of the magnetic modulation is commensurate with the underlying lattice [52]. The spin lattice relaxation is activated in the SDW ground state since there exists a finite energy gap in the phason modes of this commensurate SDW phase (Fig. 8). 

Bmssaard, L.A. Fasolino, A. Janssen, T. Phason mode in M-alkane/urea composites. Physica, B 2002, 316. 174. 

FIGURE 21.20. Scheme of the collective and molecular dynamics in FLC The Goldstone-mode corresponds to fluctuations of the phase (phason) and the soft-mode of the amplitude d (amplitudon) of the helical superstructure. The high frequency p-relaxation is assigned to librations of the mesogen around Its long molecular axis. 

Fig. 9 Calculated variation in the potential energy surface as a function of different defect types for a tip-induced transition from the c(4 x 2) structure shown in (i) to the two-phason state shown in (iii), via the three-in-a-row configuration shown in (ii). From Ref 44.

Related phases and phase transitions in terms of phason planes... 

Phason lines and phason planes can assume a dual function in s-type phases. On the one hand, they are structural defects, for instance in the phases Sg-Al-Pd-Mn and -Al-Pd-Mn. On the other hand, phason lines and phason planes can arrange regularly, forming a related e-type phase with larger c-lattice constant, and hence become elements of a new ideal structure. Phason lines and phason planes are pivotally connected to metadislocation formation and movement, as well as in phase transitions and formation of e-phases. 

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