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Incommensurate composite crystal

An incommensurate composite crystal is a compound with two or more (Nsubsystems that are themselves modulated structures, with basis structures that are mutually incommensurate. Each subsystem (numbered by ν) has a reciprocal lattice for its basic structure with three basis vectors a_i^{*\nu}. There is a basis of the vector module of diffraction spots that has at most 3N basis vectors A_j^* such that

 a_i^{*\nu}~=~\sum_{j=1}^n Z_{ij}^{\nu}  A_j^* ~~~(i=1,2,3), where Z_{ij}^{\nu} are integer coefficients. If n is larger than the dimension of space (three), the composite crystal is an aperiodic crystal. n is the rank of the vector module.


Examples are intergrowth crystals and adsorbed monolayers. To the former belongs Hg3-δAsF6 with two systems of Hg chains inside the host lattice formed by AsF6 octahedra. Another example is nonadecane in the channels of a  urea  host crystal.