{{Short description|Collective excitation in aperiodic materials}} {{Technical|date=May 2019}}
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. The phason can also be seen as a degree of freedom unique to quasicrystals. 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". In the language of the superspace picture commonly employed in the description of aperiodic crystals in which the aperiodic function is obtained via projection from a higher dimensional periodic function, the 'phason' displacement can be seen as displacement of the (higher-dimensional) lattice points in the perpendicular space.<ref name=":0">{{Cite book |last1=Fujiwara |first1=T |title=Quasicrystals |last2=Ishii |first2=Y |publisher=Elsevier |year=2008 |isbn=978--0444-51418-9 |pages=}}</ref>
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.<ref>{{Cite web |last=Laboratory |first=Oak Ridge National |title=Neutrons reveal key to extraordinary heat transport |url=https://phys.org/news/2023-02-neutrons-reveal-key-extraordinary.html |access-date=2023-02-24 |website=phys.org |language=en}}</ref> Different phasonic modes can change the material properties of a quasicrystal.<ref>{{cite web |last1=Zyga |first1=Lisa |title=What do phasons look like? |url=https://phys.org/news/2012-06-phasons.html |website=phys.org |language=en}}</ref>
In the superspace representation, aperiodic crystals can be obtained from a periodic crystal of higher dimension by projection to a lower dimensional space– this is commonly referred to as the cut-and-project method. 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, direct, or external) space, whereas phasons are excitations of the perpendicular (also called internal or virtual) space.<ref>{{cite journal | vauthors = de Boissieu M | title = Ted Janssen and aperiodic crystals | journal = Acta Crystallographica Section A | volume = 75 | issue = Pt 2 | pages = 273–280 | date = March 2019 | pmid = 30821260 | pmc = 6396404 | doi = 10.1107/S2053273318016765 }}</ref>
Phasons may be described in terms of hydrodynamic theory: when going from a homogenous fluid to a quasicrystal, hydrodynamic theory predicts six new modes arising from the translational symmetry breaking in the parallel and perpendicular spaces. Three of these modes (corresponding to the parallel space) are acoustic phonon modes, while the remaining three are diffusive phason modes. In incommensurately-modulated crystals, phasons may be constructed from a coherent superposition of phonons of the unmodulated parent structure, though this is not possible for quasicrystals.<ref name=":0" /> 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.<ref name="pmid9936890">{{cite journal | vauthors = Lubensky TC, Ramaswamy S, Toner J | title = Hydrodynamics of icosahedral quasicrystals | journal = Physical Review B | volume = 32 | issue = 11 | pages = 7444–7452 | date = December 1985 | pmid = 9936890 | doi = 10.1103/physrevb.32.7444 | bibcode = 1985PhRvB..32.7444L }}</ref> Therefore, metastable quasicrystals grown by rapid quenching from the melt exhibit built-in phason strain<ref>{{cite journal | vauthors = Tsai AP | title = Icosahedral clusters, icosaheral order and stability of quasicrystals—a view of metallurgy. | journal = Science and Technology of Advanced Materials | date = April 2008 | volume = 9 | issue = 1 | article-number = 013008 | doi = 10.1088/1468-6996/9/1/013008 | pmid = 27877926 | pmc = 5099795 | bibcode = 2008STAdM...9a3008T }}</ref> associated with shifts and anisotropic broadenings of X-ray and electron diffraction peaks.<ref name="pmid10033450">{{cite journal | vauthors = Lubensky TC, Socolar JE, Steinhardt PJ, Bancel PA, Heiney AP | title = Distortion and peak broadening in quasicrystal diffraction patterns | journal = Physical Review Letters | volume = 57 | issue = 12 | pages = 1440–1443 | date = September 1986 | pmid = 10033450 | doi = 10.1103/PhysRevLett.57.1440 | bibcode = 1986PhRvL..57.1440L }}</ref><ref>{{cite journal | vauthors = Yamada T, Takakura H, Euchner H, Pay Gómez C, Bosak A, Fertey P, de Boissieu M | title = Atomic structure and phason modes of the Sc-Zn icosahedral quasicrystal | journal = IUCrJ | volume = 3 | issue = Pt 4 | pages = 247–58 | date = July 2016 | pmid = 27437112 | pmc = 4937780 | doi = 10.1107/S2052252516007041 | doi-access = free}}</ref>
== See also == *Quasicrystal *Quasiparticle
== References == {{reflist}} 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== {{refbegin}} * {{cite book | vauthors = Steinhardt PJ, Ostlund S | title = The Physics of Quasicrystals | location = Singapore | publisher = World Scientific | date = 1987 | isbn = 978-9971-5-0226-3 }} * {{cite book | veditors = Jaric MV | title = Introduction to Quasicrystals | series = Aperiodicity and Order | volume = 1 | isbn = 978-0-12-040601-2 | publisher = Academic Press | date = 1988 }} * {{cite book | veditors = Jaric MV | title = Introduction to the Mathematics of Quasicrystals | series = Aperiodicity and Order | volume = 2 | isbn = 978-0-12-040601-2 | publisher = Academic Press | date = 1989 }} * {{cite book | veditors = DiVincenzo DP, Steinhardt PJ | title = Quasicrystals: The State of the Art | series = Directions in Condensed Matter Physics | volume = 11 | publisher = World Scientific | location = Singapore | isbn = 978-981-02-0522-5 | date = 1991 }} * {{cite book | vauthors = Senechal M | author-link1 = Marjorie Senechal | title = Quasicrystals and Geometry | title-link = Quasicrystals and Geometry | publisher = Cambridge University Press | date = 1995 | isbn = 978-0-521-57541-6 }} * {{cite book | vauthors = Patera J | title = Quasicrystals and Discrete Geometry | publisher = American Mathematical Society | date = 1998 | isbn = 978-0-8218-0682-1 }} * {{cite book | veditors = Belin-Ferre E, Berger C, Quiquandon M, Sadoc A | title = Quasicrystals | date = 2000 | publisher = World Scientific Publishing Company | isbn = 978-981-02-4281-7 }} * {{cite book | veditors = Trebin HR | title = Quasicrystals: Structure and Physical Properties | publisher = Wiley-VCH | date = 2003 | isbn = 978-3-527-40399-8 }} * {{cite book | vauthors = Janssen T, Chapuis G, Boissieu | title = Aperiodic structures: from modulated structures to quasicrystals | publisher = Oxford Science Publications | date = 2018 | isbn = 978-0-19-882444-2 }} * {{cite book | vauthors = Fujiwara T, Ishii Y | title = Quasicrystals | location = Singapore | publisher = Elsevier | date = 2008 | isbn = 978-0-444-51418-9 }}
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Category:Quasiparticles Category:Crystallography
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