Incommensurate composite crystal

From Online Dictionary of Crystallography

Revision as of 17:13, 14 November 2017 by BrianMcMahon (talk | contribs) (Tidied translations and added German and Spanish (U. Mueller))

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.


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.