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[[Incommensurate Composite Crystal]]



<Font color="blue">Cristal composite</font> (Fr.)

 '''Definition'''

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 &nu;) has a reciprocal lattice for its  basic structure with three basis vectors
'''a'''<sub>i</sub><sup>*&nu;</sup>. There is a basis of the module of diffraction spots that has at most
3''N'' basis vectors  '''A'''<sub>j</sub><sup>*</sup> such that

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

where Z<sub>ij</sub><sup>&nu;</sup> are integer coefficients.
If ''n'' is larger than the dimension of space (three), the composite crystal is an aperiodic crystal.

 '''Applications'''

Examples are intergrowth crystals and adsorbed monolayers. To the former belongs
Hg<sub>3-&delta;</sub>AsF<sub>6</sub> with two systems of Hg chains inside the host lattice formed
by AsF<sub>6</sub> octahedra. Another example is nonadecane in the channels of a urea
host crystal.