Phason

Phason is a collective excitation in quasicrystals representing rearrangements of the quasiperiodic order that change the phase of the structure without creating defects in the local environment. Phasons are distinct from phonons, the usual elastic vibrations of atoms about their equilibrium positions.

In the superspace (higher-dimensional) formulation, a quasicrystal is obtained by projecting a periodic lattice from extra dimensions; phason coordinates correspond to displacements in the perpendicular, or phason, directions. In tiling models such as the Fibonacci chain or Penrose tiling, phason degrees of freedom can be described by local tile flips that alter the long-range order while preserving local tile frequencies.

Phason fluctuations carry an elastic energy, described by a phason elastic constant; in random tiling or disordered quasicrystals, this leads to phason strain terms in the free energy. Phason dynamics can be diffusive, with fluctuations relaxing over time, or, in some approximations and at low temperatures, exhibit propagating character as additional soft modes; the behavior depends on material and disorder.

Experimentally, phason effects appear as diffuse scattering around Bragg peaks in X-ray and neutron diffraction and as time-dependent relaxation in scattering and spectroscopy experiments. Phason disorder is an important factor in the physical properties of some quasicrystals, influencing stability, diffusion, and thermal response.