Symmetry Analysis of Interface Triple Junctions

Abstract

The symmetry properties of triple junctions formed by crystal interfaces are presented using colour crystallography. Triple junctions are treated as composites of three crystals and are studied using the principle of superposition of symmetries. The conclusions are used for the understanding of the equivalences and invariances within one tricrystal composite and for studying such composites from the point of view of interfacial connectivity. A dissymmetrization procedure is established through which tricrystals equivalent by symmetry and their ways of coexistence can be found. Also, the relations between the symmetry properties of the tricrystal and those of the three bicrystals participating in the junction are given. Emphasis is placed on a particular class of composities that are termed variant constituted tricystals. In these, two out of three bicrystals belong to orientation variants of the same dichromatic pattern. Such composites are usual in polycrystals and can exhibit interesting symmetry properties. The ordinary symmetry and antisymmetry in the third bicrystal can be predicted using a given algorithm. Appropriate examples are given to illustrate the application of the analysis.

Coincidence site lattice theory of multicrystalline ensembles

“…The triple junctions in this microstructure correspond to the case considered in Fig. 5 of Dimitrakopulos & Karakostas (1996). It is easy to see that this polycrystal has AE multi 9 ( AE GB 9).…”

“…The triple junctions in this microstructure correspond to the case considered in Fig. 8 of Dimitrakopulos & Karakostas (1996). It is certainly possible to generate AE27a grain boundaries in this network by simple topological transformations.…”

The defect character of interface junction lines

“…It would also be possible to include shape changes due to phase transformations and the generation of additional grain and interfacial defects through deformation processes. The discussion has been limited to topological aspects, and needs to include thermodynamic [30] and further symmetry considerations [23] to be comprehensive. We have described a crystallographic framework using the notion of circuit mapping to characterise junction lines.…”

“…In this case, a polychromatic complex [23] must be defined, and a circuit initially constructed around the junction line must subsequently be mapped into this space. Any closure failure of the mapped circuit can then be identified and hence the defect character of the junction line established.…”

“…3. Let the three grains be designated white ()Q, black (#) and red (g) [23]; the interfaces separating these grains are labelled )qz, Ize, …”