Electron microscopy diffraction contrast in quasicrystals: some rules

Maurice Kléman; Wolfgang Staiger; Dapeng Yu

doi:doi:10.1051/jp1:1992165

Numéro		J. Phys. I France Volume 2, Numéro 5, May 1992


Page(s)		537 - 543
DOI		https://doi.org/10.1051/jp1:1992165

DOI: 10.1051/jp1:1992165
J. Phys. I France 2 (1992) 537-543

Electron microscopy diffraction contrast in quasicrystals: some rules

Maurice Kléman, Wolfgang Staiger and Dapeng Yu

Université de Paris-Sud, Centre d'Orsay, Laboratoire de Physique des Solides, Bâtiment 510, 91405 Orsay Cedex, France

(Received 10 October 1991, revised 27 January 1992, accepted 19 February 1992)

Abstract
A number of authors have observed dislocations in icosahedral quasicrystals and advanced some rules to the effect of measuring their Burgers vectors, on the basis of the two-beam method in the kinematical approximation. We first shortly review their results, which state that the determination of the direction of the Burgers vector ${\rm b}={\rm b}_{\parallel} +{\rm b}_{\perp}$ , ( ${\rm b}_{\parallel}$ in I $\!$ P $_{\parallel}$ , ${\rm b}_{\perp}$ in I $\!$ P $_{\perp}$ ), which has six components, can be suitably simplified if the five necessary extinctions fall into two classes, viz. four so-called `strong extinction conditions' (SEC) ${\rm G}_{\parallel}^{\alpha} \cdot {\rm b}_{\parallel} = {\rm G}_{\perp}^{\alpha} \cdot {\rm b}_{\perp}=0$ , and one so-called `weak extinction condition' (WEC) ${\rm G}_{\parallel}^i\cdot {\rm b}_{\parallel}+ {\rm G}_{\perp}^i\cdot {\rm b}_{\perp}=0.$ We then state the relationships between the ${\rm b}_{\parallel}$ and the ${\rm b}_{\perp}$ components which result from these conditions. We show that the modulus and sign can be determined without ambiguity by examining two incommensurate non-extinguishing diffractions ( ${\rm G}^{\alpha} \cdot {\rm b} = n\neq 0$ , n integer). Any `perfect' dislocation obeys at least approximately the rules which follow from this analysis. Dislocations which fail to obey them can be `imperfect' dislocations (we define them), whose existence should not be discarded.