# Difference between revisions of "Incommensurate composite crystal"

### From Online Dictionary of Crystallography

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− | + | <font color="blue">Cristal composite incommensurable</font> (''Fr''). <font color="red">Inkommensurabler Kompositkristall</font> (''Ge''). <font color="black">Cristallo composito incommensurabile</font> (''It''). <font color="purple">非整合複合結晶</font> (''Ja''). <font color="green">Estructura inconmensurable compuesta crystal</font> (''Sp''). | |

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An ''incommensurate composite crystal'' is a compound with two or more (''N'') subsystems that are | 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. | themselves modulated structures, with basis structures that are mutually incommensurate. | ||

− | Each subsystem (numbered by ν) has a reciprocal lattice for its | + | 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 | <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 | 3''N'' basis vectors <math>A_j^*</math> such that | ||

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''n'' is the rank of the vector module. | ''n'' is the rank of the vector module. | ||

− | + | == Applications == | |

Examples are intergrowth crystals and adsorbed monolayers. To the former belongs | Examples are intergrowth crystals and adsorbed monolayers. To the former belongs | ||

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by AsF<sub>6</sub> octahedra. Another example is nonadecane in the channels of a urea | by AsF<sub>6</sub> octahedra. Another example is nonadecane in the channels of a urea | ||

host crystal. | host crystal. | ||

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+ | [[Category:Fundamental crystallography]] |

## Latest revision as of 17:15, 14 November 2017

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.