Symmetry of diffraction patterns of two-dimensional crystal structures
Küçük Resim Yok
Tarih
2021
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Elsevier
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
Conventionally, 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.
Açıklama
Anahtar Kelimeler
Graphene, Bilayer graphene, Transition metal dichalcogenide (TMD), Transmission electron microscopy, TEM, Electron diffraction, Weak phase approximation
Kaynak
Ultramicroscopy
WoS Q Değeri
Q1
Scopus Q Değeri
Q1
Cilt
228
