On the relationship between cubic crystalline coincidence site lattices and quasiperiodic superlattices

Quasiperiodic superlattice (QPSL) can be understood as a structure consisting of quasiperiodic arrangements of tiles of rational dimension and can be viewed as a quasiperiodic atomic decoration of a disordered lattice. Varieties of QPSLs have been generated by varying the orientation of the projection plane in the projection formalism. The coincidence site lattice (CSL) has been found to be related to the interfaces of these QPSLs. The structural relationship between the CSLs and the QPSLs related to the octagonal quasilattice has been pointed out for the first time. The physical significance of CSLs have been discussed in the context of the projection formalism.