Defects in quasicrystals, revisited II- perfect and imperfect dislocations

Abstract

In this paper, the second part of a survey of the geometric properties of defects in quasicrystals studied from the Volterra viewpoint (see ref. [1]), we show that: 1$-$ a {\sf disvection line} L${}_{||}\subset {\mathrm{E}}_{||}$ of Burgers vector $\text{b}={\text{b}}_{||}+{\text{b}}_{\perp }$ splits naturally along L${}_{||}$ into a {\sf perfect dislocation} of Burgers vector ${\text{b}}_{||}$ and an {\sf imperfect dislocation} of Burgers vector related to ${\text{b}}_{\perp }$, akin to a stacking fault, (a 'phason' defect), 2$-$ the 'phason' defects are classified according to the relative position of ${\Sigma }_{\perp }$ with respect to a partition of the acceptance window AW which depends on the direction of ${\text{b}}_{\perp }$. The perpendicular cut surface ${\Sigma }_{\perp }\subset \mathrm{AW}$ here introduced is a mapping of the usual cut surface ${\Sigma }_{||}\subset {\mathrm{E}}_{||}$. Imperfect dislocations in QCs are somewhat similar to Kronberg's synchroshear dislocations. It is also shown that climb must generically be easier than glide.

arXiv comment18 pages, 10 figures The part relative to the mapping of the physical cut surface on the perpendicular space has been expanded