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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
<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<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.