# Difference between revisions of "Incommensurate composite crystal"

### From Online Dictionary of Crystallography

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3''N'' basis vectors '''A'''<sub>j</sub><sup>*</sup> such that | 3''N'' basis vectors '''A'''<sub>j</sub><sup>*</sup> such that | ||

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

where Z<sub>ij</sub><sup>ν</sup> are integer coefficients. | where Z<sub>ij</sub><sup>ν</sup> are integer coefficients. |

## Revision as of 18:20, 18 May 2009

Incommensurate Composite Crystal

Cristal composite (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 ν) has a reciprocal lattice for its basic structure with three basis vectors
**a**_{i}^{*ν}. There is a basis of the module of diffraction spots that has at most
3*N* basis vectors **A**_{j}^{*} such that

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

where Z_{ij}^{ν} 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_{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.