Phason Explained

In physics, a phason is a form of collective excitation found in aperiodic crystal structures. Phasons are a type of quasiparticle: an emergent phenomenon of many-particle systems. Similar to phonons, phasons are quasiparticles associated with atomic motion. However, whereas phonons are related to the translation of atoms, phasons are associated with atomic rearrangement. As a result of this rearrangement, or modulation, the waves that describe the position of atoms in the crystal change phase -- hence the term "phason".

Phasons can travel faster than the speed of sound within quasicrystalline materials, giving these materials a higher thermal conductivity than materials in which the transfer of heat is carried out only by phonons.^[1] Different phasonic modes can change the material properties of a quasicrystal.^[2]

Within superspace representation, aperiodic crystals can be obtained by taking a section of a periodic crystal of higher dimension (up to 6D) and cutting at an irrational angle. While phonons change the position of atoms relative to the crystal structure in space, phasons change the position of atoms relative to the quasicrystal structure and the cut-through superspace that defines it. Therefore, phonon modes are excitations of the "in-plane" real (also called parallel or external) space, whereas phasons are excitations of the perpendicular (also called internal) space.^[3]

Models of describing phasons include hydrodynamic theory (which describes phasons as a continuous pattern of motion), and 'phasonic flips', where atoms collectively 'jump' to new sites. Hydrodynamic analysis of quasicrystals predicts that, while the strain relaxation of phonons is relatively rapid, relaxation of phason strain is diffusive and is much slower.^[4] Therefore, metastable quasicrystals grown by rapid quenching from the melt exhibit built-in phason strain^[5] associated with shifts and anisotropic broadenings of X-ray and electron diffraction peaks.^{[6] [7]}

See also

• Quasicrystal
• Quasiparticle

References

Freedman, B., Lifshitz, R., Fleischer, J. et al. Phason dynamics in nonlinear photonic quasicrystals. Nature Mater 6, 776–781 (2007). https://doi.org/10.1038/nmat1981

Books

• Book: Steinhardt PJ, Ostlund S . The Physics of Quasicrystals . Singapore . World Scientific . 1987 . 978-9971-5-0226-3 .
• Book: Jaric MV . Introduction to Quasicrystals . Aperiodicity and Order . 1 . 978-0-12-040601-2 . Academic Press . 1988 .
• Book: Jaric MV . Introduction to the Mathematics of Quasicrystals . Aperiodicity and Order . 2 . 978-0-12-040601-2 . Academic Press . 1989 .
• Book: DiVincenzo DP, Steinhardt PJ . Quasicrystals: The State of the Art . Directions in Condensed Matter Physics . 11 . World Scientific . Singapore . 978-981-02-0522-5 . 1991 .
• Book: Senechal M . Marjorie Senechal . Quasicrystals and Geometry . Quasicrystals and Geometry . Cambridge University Press . 1995 . 978-0-521-57541-6 .
• Book: Patera J . Quasicrystals and Discrete Geometry . American Mathematical Society . 1998 . 978-0-8218-0682-1 .
• Book: Belin-Ferre E, Berger C, Quiquandon M, Sadoc A . Quasicrystals . 2000 . World Scientific Publishing Company . 978-981-02-4281-7 .
• Book: Trebin HR . Quasicrystals: Structure and Physical Properties . Wiley-VCH . 2003 . 978-3-527-40399-8 .
• Book: Janssen T, Chapuis G, Boissieu . Aperiodic structures: from modulated structures to quasicrystals . Oxford Science Publications . 2018 . 978-0-19-882444-2 .

Notes and References

1. Web site: Laboratory . Oak Ridge National . Neutrons reveal key to extraordinary heat transport . 2023-02-24 . phys.org . en.
2. Web site: Zyga . Lisa . What do phasons look like? . phys.org . en.
3. de Boissieu M . Ted Janssen and aperiodic crystals . Acta Crystallographica Section A . 75 . Pt 2 . 273–280 . March 2019 . 30821260 . 6396404 . 10.1107/S2053273318016765 .
4. Lubensky TC, Ramaswamy S, Toner J . Hydrodynamics of icosahedral quasicrystals . Physical Review B . 32 . 11 . 7444–7452 . December 1985 . 9936890 . 10.1103/physrevb.32.7444 . 1985PhRvB..32.7444L .
5. Tsai AP . Icosahedral clusters, icosaheral order and stability of quasicrystals—a view of metallurgy. . Science and Technology of Advanced Materials . April 2008 . 9 . 1 . 013008 . 10.1088/1468-6996/9/1/013008 . 27877926 . 5099795 .
6. Lubensky TC, Socolar JE, Steinhardt PJ, Bancel PA, Heiney AP . Distortion and peak broadening in quasicrystal diffraction patterns . Physical Review Letters . 57 . 12 . 1440–1443 . September 1986 . 10033450 . 10.1103/PhysRevLett.57.1440 . 1986PhRvL..57.1440L .
7. Yamada T, Takakura H, Euchner H, Pay Gómez C, Bosak A, Fertey P, de Boissieu M . Atomic structure and phason modes of the Sc-Zn icosahedral quasicrystal . IUCrJ . 3 . Pt 4 . 247–58 . July 2016 . 27437112 . 4937780 . 10.1107/S2052252516007041 .