Symmetry of diffraction patterns of two-dimensional crystal structures

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dc.authoridMorozov, Sergey/0000-0003-3075-7787
dc.authoridLatychevskaia, Tatiana/0000-0001-6693-8681
dc.authoridZAN, RECEP/0000-0001-6739-4348
dc.contributor.authorLatychevskaia, Tatiana
dc.contributor.authorZan, Recep
dc.contributor.authorMorozov, Sergey
dc.contributor.authorNovoselov, Kostya S.
dc.date.accessioned2024-11-07T13:35:20Z
dc.date.available2024-11-07T13:35:20Z
dc.date.issued2021
dc.departmentNiğde Ömer Halisdemir Üniversitesi
dc.description.abstractConventionally, theoretical considerations in electron microscopy employ the weak phase approximation (WPA), which is only valid for weak scattering atomic elements (C, B, N) but not for transition metal dichalcogenide (TMD) materials. This leads to many exciting phenomena being overlooked. The present theoretical study goes beyond the weak phase approximation and thus the obtained results can be applied for two-dimensional (2D) crystals made of weakly as well of strongly scattering atoms, including the TMD materials. We show that the symmetry of an electron diffraction pattern, characterized by the Friedel's pairs, is governed by the symmetry of the exit wave distribution. For an infinite periodic crystal, the exit wave is an infinite and periodic 2D distribution which can be assigned an exit wave unit cell. The latter is determined by both the chemical composition of the crystallographic unit cell and the distance between the atomic layers. For 2D crystals of identical atoms, such as graphene, the exit wave unit cell is symmetrical and, thus, a symmetrical diffraction pattern is expected. For TMD materials, the exit wave unit cell is not symmetrical and a non-symmetrical diffraction pattern is expected for both monolayer and bilayer. Conventionally asymmetry in diffraction patterns has been explained by presence of dynamical (multiple) scattering effects. Our study shows that the asymmetry of a diffraction pattern can be explained solely by the asymmetry of the exit wave unit cell. The exit wave unit cell can be asymmetrical even in kinematic (single) scattering model. Therefore, conclusions about dynamical (multiple) scattering effects in 2D materials cannot be made based solely on asymmetry of a diffraction pattern. We also show that for hexagonally arranged atoms the second-order diffraction peaks show perfectly symmetrical intensities independently on the symmetry of the exit wave unit cell distribution.
dc.description.sponsorshipEU Flagship Program (Graphene) [CNECTICT-604391]; European Research Council Synergy Grant Hetero2D [319277]; Royal Society; EPSRC grant [EP/N010345/1, EP/P026850/1, EP/S030719/1]; Russian Science Foundation [17-12-01393]; EU Flagship Program (2D-SIPC Quantum Technology); Academy of Finland (AKA) [319277] Funding Source: Academy of Finland (AKA); European Research Council (ERC) [319277] Funding Source: European Research Council (ERC); EPSRC [EP/S030719/1] Funding Source: UKRI
dc.description.sponsorshipThis work was supported by EU Flagship Programs (Graphene CNECTICT-604391 and 2D-SIPC Quantum Technology), European Research Council Synergy Grant Hetero2D (319277), the Royal Society, EPSRC grants EP/N010345/1, EP/P026850/1, EP/S030719/1. S. V. M. acknowledges the support from the Russian Science Foundation (17-12-01393).
dc.identifier.doi10.1016/j.ultramic.2021.113336
dc.identifier.issn0304-3991
dc.identifier.issn1879-2723
dc.identifier.pmid34174662
dc.identifier.scopus2-s2.0-85108445086
dc.identifier.scopusqualityQ1
dc.identifier.urihttps://doi.org/10.1016/j.ultramic.2021.113336
dc.identifier.urihttps://hdl.handle.net/11480/16456
dc.identifier.volume228
dc.identifier.wosWOS:000677638900005
dc.identifier.wosqualityQ1
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.indekslendigikaynakPubMed
dc.language.isoen
dc.publisherElsevier
dc.relation.ispartofUltramicroscopy
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzKA_20241106
dc.subjectGraphene
dc.subjectBilayer graphene
dc.subjectTransition metal dichalcogenide (TMD)
dc.subjectTransmission electron microscopy
dc.subjectTEM
dc.subjectElectron diffraction
dc.subjectWeak phase approximation
dc.titleSymmetry of diffraction patterns of two-dimensional crystal structures
dc.typeArticle

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