# Incommensurate composite crystal

### From Online Dictionary of Crystallography

Cristal composite incommensurable (*Fr*). Inkommensurabler Kompositkristall (*Ge*). Cristallo composito incommensurabile (*It*). 非整合複合結晶 (*Ja*). Estructura inconmensurable compuesta crystal (*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
3*N* 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-δ}AsF_{6} with two systems of Hg chains inside the host lattice formed
by AsF_{6} octahedra. Another example is nonadecane in the channels of a urea
host crystal.