module defects in crystals

• Published in: Acta crystallographica. Section A, Foundations and advances Foundations and advances, 2017-11, Vol.73 (6), p.427-437
• Main Authors: Sirindil, Abdullah, Quiquandon, Marianne, Gratias, Denis
• Format: Article
• Language: English
• Subjects: defects; dislocations; intermetallic alloys; modules; Research Papers; twins
• ISSN: 2053-2733; 2053-2733
• DOI: 10.1107/S2053273317013882

An analysis is presented of the new types of defects that can appear in crystalline structures where the positions of the atoms and the unit cell belong to the same ‐module, i.e. are irrational projections of an N > 3‐dimensional (N‐D) lattice Λ as in the case of quasicrystals. Beyond coherent irrationally oriented twins already discussed in a previous paper [Quiquandon et al. (2016). Acta Cryst. A72, 55–61], new two‐dimensional translational defects are expected, the translation vectors of which, being projections of nodes of Λ, have irrational coordinates with respect to the unit‐cell reference frame. Partial dislocations, called here module dislocations, are the linear defects bounding these translation faults. A specific case arises when the Burgers vector B is the projection of a non‐zero vector of Λ that is perpendicular to the physical space. This new kind of dislocation is called a scalar dislocation since, because its Burgers vector in physical space is zero, it generates no displacement field and has no interaction with external stress fields and other dislocations. New kinds of defects can appear in crystals where the atoms and unit cell sit on the nodes of ‐modules, i.e. on three‐dimensional projections of N‐dimensional lattices. These defects are the result of the symmetry breaking due to the projection of the structure from N to three dimensions. Examples are given that illustrate the processes. A new kind of dislocation, here called a `scalar dislocation', is expected; it generates no deformation and has no interaction with stress fields.