Editing Chirality (physics) (section)

== Chirality in materials science ==
{{see also|Materials science}}
Chirality in other branches of physics is often used for classifying and studying the properties of [[Physical body|bodies]] and materials under external influences. Classification by chirality, as a special case of [[Symmetry (physics)|symmetry]] classification, allows for a better understanding of [[Ab initio|first-principles]] construction of [[molecule]]s, [[crystal]]s, [[quasicrystal]]s, and more. An example is the [[homochirality]] of [[amino acid]]s in all known forms of [[life]],<ref>
{{cite book
 |url=https://shop.elsevier.com/books/origins-of-life/zubay/978-0-12-781910-5
 |title=Origins of Life
 |date=2000-01-04
 |language=en-US
 |isbn=978-0-12-781910-5
}}</ref> which can be reproduced in physical experiments under external influence.<ref>{{cite news |title=On the origins of life's homochirality: Inducing enantiomeric excess with spin-polarized electrons |last1=Ozturk |first1=S. Furkan |last2=Sasselov |first2=Dimitar D. |date=2022-07-12 |language=en |journal=Proceedings of the National Academy of Sciences |volume=119 |doi=10.1073/pnas.2204765119 |pmc=9282223 |pmid=35787048 |issue=28 |doi-access=free }}</ref> [[Optical activity]] (including [[circular dichroism]]<ref name=":0">{{cite web |url=https://ukrayinska.libretexts.org/Хімія/Аналітична_хімія/Фізичні_методи_в_хімії_та_нанонауці_(Barron)/07:_Молекулярна_та_твердотільна_структура/7.07:_Спектроскопія_кругового_дихроизму_та_її_застосування_для_визначення_вторинної_структури_оптично_активних_видів |title=7.7: Circular dichroism spectroscopy and its application in determining the secondary structure of optically active species |date=2022-10-25 |website=LibreTexts - Ukrayinska |language=en |access-date=2024-11-07 }}</ref> and [[magnetic circular dichroism]]<ref name=":0" />) of [[material]]s is determined by their chirality.

Chiral [[Physical system|physical systems]] are characterized by the absence of [[Invariant_(physics)|invariance]] under the [[Parity (physics)|parity operator]]. An ambiguity arises<ref name=":1">{{cite journal |url=https://pubs.acs.org/doi/abs/10.1021/ja00278a029 |title=True and false chirality and absolute asymmetric synthesis |last=Barron |first=L. D. |date=1986 |pages=5539–5542 |language=en |journal=Journal of the American Chemical Society |volume=108 |doi=10.1021/ja00278a029 |issue=18 |access-date=2024-11-07 |url-access=subscription }}</ref> in defining chirality in physics depending on whether one compares directions of motion using the [[Reflection (physics)|reflection]] or [[Euclidean space|spatial]] [[Point reflection|inversion]] operation. Accordingly, one distinguishes<ref name=":1" /><ref name=":2">{{cite journal |url=https://www.sciencedirect.com/science/article/abs/pii/S2451910322001934 |title=Enantiomer discrimination in absorption spectroscopy and in voltammetry: highlighting fascinating similarities and connections |last1=Mussini |first1=Patrizia Romana |last2=Arnaboldi |first2=Serena |last3=Magni |first3=Mirko |last4=Grecchi |first4=Sara |last5=Longhi |first5=Giovanna |last6=Benincori |first6=Tiziana |date=2023-02-01 |pages=101128 |journal=Current Opinion in Electrochemistry |volume=37 |doi=10.1016/j.coelec.2022.101128 |access-date=2024-11-07 |hdl=11379/574245 |hdl-access=free }}</ref> between "true" chirality (which is [[Invariance|invariant]] under the [[T-symmetry|time-reversal]] operation) and "false" chirality (non-invariant under time reversal).

Many [[Physical quantity|physical quantities]] change sign under the [[T-symmetry|time-reversal operation]] (e.g., [[velocity]], [[Power (physics)|power]], [[electric current]], [[magnetization]]). Accordingly, "false" chirality is so typical in physics that the term can be misleading, and it is clearer to speak of [[T-symmetry|T]]-invariant and [[T-symmetry|T]]-non-invariant chirality.<ref name=":2" /> Effects related to chirality are described using [[pseudoscalar]] or [[axial vector]] physical quantities in general, and particularly, in magnetically ordered media, are described<ref>{{cite news |url=https://link.aps.org/doi/10.1103/PhysRevLett.113.165502 |title=Eight Types of Symmetrically Distinct Vectorlike Physical Quantities |last=Hlinka |first=J. |date=2014-10-15 |language=en |journal=Physical Review Letters |volume=113 |doi=10.1103/PhysRevLett.113.165502 |issue=16 |access-date=2024-11-08 }}</ref><ref name=":3">{{cite journal |url=https://www.sciencedirect.com/science/article/abs/pii/S0921452611005606 |title=Magnetic symmetry based definition of the chirality in the magnetically ordered media |last=Tanygin |first=B. M. |date=2011-09-15 |pages=3423–3424 |journal=Physica B: Condensed Matter |volume=406 |doi=10.1016/j.physb.2011.06.012 |issue=18 |access-date=2024-11-08 |url-access=subscription }}</ref> using time-direction-dependent chirality. This approach is formalized using [[Dichromatic symmetry|dichromatic]] symmetry groups. [[Time reversal|T]]-invariant chirality corresponds to the absence in the symmetry group of any symmetry operations that include [[Euclidean space|spatial]] inversion <math>\bar{1}</math> or [[Reflection (physics)|reflection]] m, according to [[Hermann–Mauguin notation|international notation]]. The criterion for [[T-symmetry|T]]-non-invariant chirality is the presence of these symmetry operations, but only when combined with [[T-symmetry|time reversal]] <math>1'</math>,<ref name=":3" /> such as operations m′ or <math>\bar{1}'</math>.

At the level of atomic structure of materials, one distinguishes<ref>{{cite journal |url=https://www.nature.com/articles/s41535-022-00447-5 |title=Magnetic chirality |last1=Cheong |first1=Sang-Wook |last2=Xu |first2=Xianghan |date=2022-04-08 |pages=1–6 |language=en |journal=npj Quantum Materials |volume=7 |doi=10.1038/s41535-022-00447-5 |issue=1 |access-date=2024-11-08 |doi-access=free }}</ref> vector, scalar, and other types of chirality depending on the direction/sign of [[Triple product|triple]] and [[Cross product|vector]] products of [[Spin_(physics)|spin]]s.