Incommensurate composite crystal

Cristal composite incommensurable (Fr). Inkommensurabler Kompositkristall (Ge). Cristallo composito incommensurabile (It). 非整合複合結晶 (Ja). Estructura inconmensurable compuesta (Sp).

An incommensurate composite crystal is a compound with two or more (N) subsystems 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 [math]a_i^{*\nu}[/math]. There is a basis of the vector module of diffraction spots that has at most 3N basis vectors [math]A_j^*[/math] such that

[math] a_i^{*\nu}~=~\sum_{j=1}^n Z_{ij}^{\nu} A_j^* ~~~(i=1,2,3),[/math]

where [math]Z_{ij}^{\nu}[/math] 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.

Applications

Examples are intergrowth crystals and adsorbed monolayers. To the former belongs Hg_3-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.